ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 This would then explain the fast decline of N-rav ciuission of knots along the jet., This would then explain the fast decline of X-ray emission of knots along the jet.3 The final hot spot iu our io0del would represent a termination shock of the relativistic flow when the jet runs out of CITE neutral-beam decay products that sustain the forward progress of the relativistic, The final hot spot in our model would represent a termination shock of the relativistic flow when the jet runs out of UHE neutral-beam decay products that sustain the forward progress of the relativistic4 S0.1 (7).. 2)). 2)). ?)). 2)). Letter ?)). of (2???.hereafterPOS)..," $\lesssim 0.1$ \citep{sarazin86}. \citealt{pf06}) \citealt{bt95}) \citealt{nm01}) \citealt{kim05}) \citealt{quat08}) \citep[][hereafter5PQS]{pq08,bog09,pqs09}."6 (7 in clusters. iucliding major mergers. the motion of ealaxies throueh the ICM. (galaxy wakes). aud ACN jets and bubbles.," \citealt{sharma09} in clusters, including major mergers, the motion of galaxies through the ICM (galaxy wakes), and AGN jets and bubbles."7 Cosmological bydrodvuamiuic simulations of ye‘luster formation find that turbulence can contribute ~ of the total pressure even in relaxed clusters. with --je turbulent pressure declining at small τας towards --ιο cluster core (?2)..," Cosmological hydrodynamic simulations of cluster formation find that turbulence can contribute $\sim 1$ of the total pressure even in relaxed clusters, with the turbulent pressure declining at small radii towards the cluster core \citep{lkn09}."8" Iu thisLetter, we consider a sitaple imodel for the interplay between turbulence. anisotropic thermal conduction. and radiative cooling in galaxy cluster cores: we externally vsti” the ICAL in our previous global cluster core sinmuatious (οσοι, PQS) in order to mimic the effects of the various sources of turbulence noted above."," In this, we consider a simple model for the interplay between turbulence, anisotropic thermal conduction, and radiative cooling in galaxy cluster cores: we externally “stir” the ICM in our previous global cluster core simulations (e.g., PQS) in order to mimic the effects of the various sources of turbulence noted above."9 The ΠταΊος of this approach are discussed in 8?7.., The limitations of this approach are discussed in \ref{sec:disc}.10 Near the completion of this work. ? presented results simular to those found here using indepeudent uuucrical techniques and cluster models.," Near the completion of this work, \citet{rus10} presented results similar to those found here using independent numerical techniques and cluster models."11 We solve the equations of MIID using theAthena MIID code (?7).. with the addition of anisotropic thermal conduction (2?) and optically thin cooling (see eqs [5]12) of PQS).," We solve the equations of MHD using the MHD code \citep{gs08,sg08}, with the addition of anisotropic thermal conduction \citep{ps05,sh07} and optically thin cooling (see eqs [8]--[12] of PQS)."12 Iu particular. the couductive heat flix is eiven by Q=habbονΤ where Ba is the Spitzer hermal conductivitv aud b is a unit vector along the uaenetic feld.," In particular, the conductive heat flux is given by $\boldsymbol{Q} = -13\kappa_{\textrm{Sp}}\boldsymbol{\hat{b}\hat{b}}\cdot\boldsymbol{\nabla}T$ , where $\kappa_{\textrm{Sp}}$ is the Spitzer thermal conductivity and $\boldsymbol{\hat{b}}$ is a unit vector along the magnetic field."14 We use the ? cooling curve and a eniperature floor of T.—0.05 keV. below which UV lines ecole maiportant.," We use the \citet{tn01} cooling curve and a temperature floor of $T=0.05\,\textrm{keV}$ , below which UV lines become important."15 Our initial condition is a cluster inspired to resciuble hat of Abell 2199 as observed iu 2.., Our initial condition is a cluster inspired to resemble that of Abell 2199 as observed in \citet{johnstone02}.16" We use a static NEW eravitational potential with a scale radius of c,—390kpc and a mass of Mj=3.8osLOMAS..."," We use a static NFW gravitational potential with a scale radius of $r_s =17390\,\textrm{kpc}$ and a mass of $M_0 = 3.8 \times 10^{14} M_{\odot}$."18 The siuulations are carried out on a Cartesian grid iu a computational domain thatexteudsfromthecenteroftheclusterout to 210 kpe., The simulations are carried out on a Cartesian grid in a computational domain thatextendsfromthecenteroftheclusterout to 240 kpc.19 Thesimmlationsare (128°). corresponding," Thesimulationsare $128^3$ ), corresponding"20Fiver et al (1998): (3)the phase transition from neutron star to strange star (Cheng Dai 1996): C1) the transition of normal nuclear matter to matter with pion coudensation in neutron star (e.g. Πασικο et al 1990. Muto et al 1993): (5) rapidly rotating neutron star with extremely laree magnetic feld (Usov 1992. Duncan Thompson 1992): (6) a failed supernova type Ib (Woosley 1993). or nücroquasar (Paczvisski 1998) ete.,"Fryer et al (1998); (3)the phase transition from neutron star to strange star (Cheng Dai 1996); (4) the transition of normal nuclear matter to matter with pion condensation in neutron star (e.g. Haensel et al 1990, Muto et al 1993); (5) rapidly rotating neutron star with extremely large magnetic field (Usov 1992, Duncan Thompson 1992); (6) a failed supernova type Ib (Woosley 1993), or microquasar (Paczyńsski 1998) etc."21 Therefore. if we want to find the hosts of GRB sources. it is logical to loo- for cosinological sources with a lot of compact objects.," Therefore, if we want to find the hosts of GRB sources, it is logical to look for cosmological sources with a lot of compact objects."22 From the stellar evolution point of view. the progenitors of compact objects. c.g. neutron stars; are massive stars (approxinatelv 5~2OAL.).," From the stellar evolution point of view, the progenitors of compact objects, e.g. neutron stars, are massive stars (approximately $5\sim 20 M_{\odot}$ )."23 7From the observations of afterelows of GRBs it has been deduced by Paczyüssl (1995) that CRB nav associate with the star formation reeion., >From the observations of afterglows of GRBs it has been deduced by Paczyńsski (1998) that GRB may associate with the star formation region.24 We note that most of the masses of the massive stars. consisting of a lot of heavy clemeuts. will be ejected diving the supernova explosion aud a ietalrich region will be formed.," We note that most of the masses of the massive stars, consisting of a lot of heavy elements, will be ejected during the supernova explosion and a metal-rich region will be formed."25 Naturally. galaxies with high abundance of compact object should be metal-rich.," Naturally, galaxies with high abundance of compact object should be metal-rich."26 Therefore it is logical to look for cosmological sources with lieh metal abundance., Therefore it is logical to look for cosmological sources with high metal abundance.27 In order to observe the sources located at cosmological distauce. these sources must be hDuuuimnous.," In order to observe the sources located at cosmological distance, these sources must be luminous."28 It should be noted that most ACCNS/OQSOx ire metal-rich CArtviuowicz. Liu Waouupler 1993. IEunaun et al 1997).," It should be noted that most AGNs/QSOs are metal-rich (Artymowicz, Lin Wampler 1993, Hamann et al 1997)."29" This may be the real reason why GRBs may be related to ACNs aud QSOs as reported by Schartel. Auderuach (απο (1996). aud Burenin ct al (1998) who cli there are xossible association of +-rav burst with radio quiet quasar. and with active galactic uuclei. respectively,"," This may be the real reason why GRBs may be related to AGNs and QSOs as reported by Schartel, Andernach Greiner (1996), and Burenin et al (1998) who claim there are possible association of $\gamma$ -ray burst with radio quiet quasar, and with active galactic nuclei, respectively."30 However the physical scenario of this association remains open if it is rue. at least. some of GBD are related with ACNs/QSOs.," However the physical scenario of this association remains open if it is true, at least, some of GRB are related with AGNs/QSOs."31 It has been sugeested that CRB may be produced in a star ornmation region which leads to expectation of the burst rate of GRD proportional to the formation rate of star oei the cosmiological galaxies (Paczyviüsski 1998)., It has been suggested that GRB may be produced in a star formation region which leads to expectation of the burst rate of GRB proportional to the formation rate of star in the cosmological galaxies (Paczyńsski 1998).32 Because ie Lifetime of AGCN/OSO is rather short (generallv. less van 107 vr). the possible host objects of CRB are iiostly ones related with galaxies.," Because the lifetime of AGN/QSO is rather short (generally less than $10^8$ yr), the possible host objects of GRB are mostly ones related with galaxies."33 Alternatively here we suggest iat the interaction between accretion disk and stars iu deuse cluster may lead to the formation of a large number compact objects in the central cugine of active galactic inclei., Alternatively here we suggest that the interaction between accretion disk and stars in dense cluster may lead to the formation of a large number compact objects in the central engine of active galactic nuclei.34 The formation aud interactions amoue the compact objects in the nuclei might associate with GRD., The formation and interactions among the compact objects in the nuclei might associate with GRB.35 Therefore active ealactic nuclei are one kind of its host objects if GRBs are indeed associated with compact objects., Therefore active galactic nuclei are one kind of its host objects if GRBs are indeed associated with compact objects.36 The imechanigu for the enhancement of moetalbrich elemieuts has been suggested bv a wav of evolution of 1uain sequence stars. which are captured by the accretion disk surrounding the supermassive black hole iu the center of quasar (for a review cf.," The mechanism for the enhancement of metal-rich elements has been suggested by a way of evolution of main sequence stars, which are captured by the accretion disk surrounding the supermassive black hole in the center of quasar (for a review cf."37 Lin Papaloizou 1996)., Lin Papaloizou 1996).38 The captured stars would accrete material from the disk aud Increase their masses up to 50 solar masses in less than 104 vears., The captured stars would accrete material from the disk and increase their masses up to 50 solar masses in less than $10^4$ years.39 These massive stars evolve rapidly toward tlic supernova stage and the ejecta of the supernovae provide enough heavy clement to produce the features sugeestec by observations., These massive stars evolve rapidly toward the supernova stage and the ejecta of the supernovae provide enough heavy element to produce the features suggested by observations.40 The metal abundance expressed im terms 6 the ratio between NV aud CTW is related to the total uunuber of captured main sequence stars Nyy curing the active phase of quasar as follows (Artvimowicz. Lin Wampler 1993: Zurek et al 1991) Ἠοπονο this mechanisia results im other implications. such as formation of neutron stars/black holes iu the vicinity of the accretion disk.," The metal abundance expressed in terms of the ratio between NV and CIV is related to the total number of captured main sequence stars $N_{\rm MS}$ during the active phase of quasar as follows (Artymowicz, Lin Wampler 1993; Zurek et al 1994) However this mechanism results in other implications, such as formation of neutron stars/black holes in the vicinity of the accretion disk."41 As we will argue in the subsequent section. it exists an effücient wav to form conipact object - compact object (i.e. NS/BIT. NS/DBID binaries via the formation of compact object - red eiaut star (NS/BIT. RC) binaries.," As we will argue in the subsequent section, it exists an efficient way to form compact object - compact object (i.e. NS/BH, NS/BH) binaries via the formation of compact object - red giant star (NS/BH, RG) binaries."42 The CNS/BII. NS/DBII) binary will be formed after the explosion of the red eiaut. star.," The (NS/BH, NS/BH) binary will be formed after the explosion of the red giant star."43 Iu such a scheme the merger rate of (NS/BIT. NS/BIT) binary approximately equals to the capture rate of main sequence star. therefore it is proportional to the metal abundance.," In such a scheme the merger rate of (NS/BH, NS/BH) binary approximately equals to the capture rate of main sequence star, therefore it is proportional to the metal abundance."44 If the mereer of (NS/BIL NS/BIT) binary or Teli core of RO and black hole is oue of the possible mechanisius of GRBs. then active galactic nuclei and quasars should associate with CRBs.," If the merger of (NS/BH, NS/BH) binary or Helium core of RG and black hole is one of the possible mechanisms of GRBs, then active galactic nuclei and quasars should associate with GRBs."45 Iu fact the coalescence of two compact objects also produces itese transicut eravitational waves which should be detected by LIGO/VIRGO iu LCpe radius., In fact the coalescence of two compact objects also produces intense transient gravitational waves which should be detected by LIGO/VIRGO in 1Gpc radius.46 We asstuue that the nucleus of the quasar consists of a massive black hole surrounded by au accretion disk. which are cuclosed by a star cluster.," We assume that the nucleus of the quasar consists of a massive black hole surrounded by an accretion disk, which are enclosed by a star cluster."47" The structure of disk is described by the standard model im which the local height and the surface deusitv of the accretion disk are given by (o.c. Frank. et al 1992) aud respectively. aud the inward drift velocity due to the outward transportation of the angular ποιοται in disk reacls or the time scale of inward drift is where ip is dimensionless accretion rate scaled with the Eddington lait. o is the viscosity cocfiicicut. rq = aa is the radius of disk normalized by Scluvartzchild radius Re=Uu, aud A denotes the mass of central black hole (Mp) ia units of 1057..."," The structure of disk is described by the standard model in which the local height and the surface density of the accretion disk are given by (e.g. Frank, et al 1992) and respectively, and the inward drift velocity due to the outward transportation of the angular momentum in disk reads or the time scale of inward drift is where $\dot{m}$ is dimensionless accretion rate scaled with the Eddington limit, $\alpha$ is the viscosity coefficient, $r_{\rm d}$ = $\frac{R}{R_s}$ is the radius of disk normalized by Schwartzchild radius $R_s=\frac{GM_{\rm BH}}{c^2}$, and $M_8$ denotes the mass of central black hole $M_{\rm BH}$ ) in units of $10^8M_{\odot}$."48 The main sequence stars in the star cluster will be captured by the disk aud the τανο of the captured main sequence stars iu the annular RoR|dR is estimated as (Artvinowicez. Lin Wampler 1993).," The main sequence stars in the star cluster will be captured by the disk and the number of the captured main sequence stars in the annular $R-R+dR$ is estimated as (Artymowicz, Lin Wampler 1993),"49"Figure 2 shows evolution tracks in the (logTem,logpx) plane for solar-composition stars of between 0.85 and 1.0Mo.","Figure \ref{fig:evolution} shows evolution tracks in the $(\log\teff,\log\rho_\star)$ plane for solar-composition stars of between $0.85$ and $1.0\,\rm M_\odot$."50" For about 100MMa, the stars contract and heat up from a low-temperature, low-density initial state, the so-called pre-main-sequence phase (PMS)."," For about $100$ Ma, the stars contract and heat up from a low-temperature, low-density initial state, the so-called pre-main-sequence phase (PMS)."51 They then reach a maximum in their density and very gradually expand while on the main-sequence (MS)., They then reach a maximum in their density and very gradually expand while on the main-sequence (MS).52" In the case of CoRoT-2, the observational constraints on Τεῃ and p, are met either on the PMS, for ages ~ 30MMa, or at much older ages in the MS phase."," In the case of CoRoT-2, the observational constraints on $\teff$ and $\rho_\star$ are met either on the PMS, for ages $\sim 30$ Ma, or at much older ages in the MS phase."53 Only stars with masses between roughly 0.84 and 1.04Mo intercept the box of constraints at some point in their evolution.," Only stars with masses between roughly $0.84$ and $1.04\,\rm M_\odot$ intercept the box of constraints at some point in their evolution."54 Figure 2 also shows that the presence of spots yields solutions at smaller masses than when spots are not taken into account., Figure \ref{fig:evolution} also shows that the presence of spots yields solutions at smaller masses than when spots are not taken into account.55" The agreement between CESAM and BCAH98 models isgenerally very good, with differences in Teg of generally ~1% or less, and differences in p, that can reach ~10% but in only a limited region of the PMS evolution phase."," The agreement between CESAM and BCAH98 models isgenerally very good, with differences in $\teff$ of generally $\sim 1\%$ or less, and differences in $\rho_\star$ that can reach $\sim 10\%$ but in only a limited region of the PMS evolution phase."56" In Fig. 3,,"," In Fig. \ref{fig:evolution_A},"57" we explore the effect of a ""reasonable"" (215906) modification of the mixing length parameter a on the evolution tracks.", we explore the effect of a “reasonable” $\pm 15\%$ ) modification of the mixing length parameter $\alpha$ on the evolution tracks.58 The effect is not negligible in terms of its impact on both the effective temperature and the stellar density., The effect is not negligible in terms of its impact on both the effective temperature and the stellar density.59 A higher value of @ implies a more efficient energy transport and therefore higher effective temperatures and generally a faster evolution., A higher value of $\alpha$ implies a more efficient energy transport and therefore higher effective temperatures and generally a faster evolution.60" Less intuitively perhaps, it leads to a higher maximal stellar density at the early stages of the MS phase."," Less intuitively perhaps, it leads to a higher maximal stellar density at the early stages of the MS phase."61" However, we emphasize that these models with modified mixing lengths have not been calibrated and do not properly reproduce the present Sun."," However, we emphasize that these models with modified mixing lengths have not been calibrated and do not properly reproduce the present Sun."62 The consequences of metallicity variations are shown in Fig. 4.., The consequences of metallicity variations are shown in Fig. \ref{fig:evolution_Z}.63" An increase in the [Fe/H] value by a factor 1/3 leads to a global decrease in the effective temperature by about2%,, larger than the lo error in the measurements, but slightly smaller than the uncertainty in Τε obtained when including spots."," An increase in the [Fe/H] value by a factor 1/3 leads to a global decrease in the effective temperature by about, larger than the $1\sigma$ error in the measurements, but slightly smaller than the uncertainty in $\teff$ obtained when including spots."64 This effect is thus significant and shoud be included in the search for solutions matching the observational constraints., This effect is thus significant and shoud be included in the search for solutions matching the observational constraints.65 We present in Fig., We present in Fig.66" 5 the ensemble of solutions in the (R,,age) space obtained with various assumptions."," \ref{fig:rstar_age} the ensemble of solutions in the $(R_\star ,{\rm age})$ space obtained with various assumptions."67 The top panels correspond to our preferred solutions using our calibrated CESAM evolution model and including all metallicities., The top panels correspond to our preferred solutions using our calibrated CESAM evolution model and including all metallicities.68" At 3c, a wide range of solutions is found that extends from ages between 30 MMa and more than 10 GGa."," At $3\sigma$ , a wide range of solutions is found that extends from ages between $30$ Ma and more than $10$ Ga."69calibration corresponds to the phase difference between the right-cireularly polarized aud left-circularly polarized signals at (he relerence antenna. and has been shown to be constant to within a few degrees over as long as several vears. if no adjustments are made to the receiver affecting (his instrumental parameter (?2)..,"calibration corresponds to the phase difference between the right-circularly polarized and left-circularly polarized signals at the reference antenna, and has been shown to be constant to within a few degrees over as long as several years, if no adjustments are made to the receiver affecting this instrumental parameter \citep{ReynoldsCawthorneGabuzda01}."70 Our observations were only a few months alter those of ?: moreover. the EVPA calibration lor 5 Gllz VLBI observations obtained in June 2000. based on simultaneous VLA polarization measurements and also reduced using Los Alamos as the reference antenna. indicates that this calibration had remained the same to within a lew degrees (Gabuzda. O'Sullivan Gurvils. private communication). thus justifving the application of the 5 GIIz EVPÀ calibration for the March.April 1998 VLBA observations to our 5 GIIz data.," Our observations were only a few months after those of \citet{Charlot06}; moreover, the EVPA calibration for 5 GHz VLBI observations obtained in June 2000, based on simultaneous VLA polarization measurements and also reduced using Los Alamos as the reference antenna, indicates that this calibration had remained the same to within a few degrees (Gabuzda, O'Sullivan Gurvits, private communication), thus justifying the application of the 5 GHz EVPA calibration for the March–April 1998 VLBA observations to our 5 GHz data."71described in Petrovich&Reisenegger(2010).,described in \citet{petro10}.72. The latter is the framework we use throughout this paper., The latter is the framework we use throughout this paper.73 Therefore. we just point out the fundamental equations for completeness and to clarify the notation of the present paper.," Therefore, we just point out the fundamental equations for completeness and to clarify the notation of the present paper."74 We consider the simplest model of a neutron star core. composed of neutrons. protons. electrons. andmuons (peg matter). rgnoring the potential presence of exotic particles.," We consider the simplest model of a neutron star core, composed of neutrons, protons, electrons, andmuons $npe\mu$ matter), ignoring the potential presence of exotic particles."75 The internal temperature. redshifted to a distant observer. To. is taken to be uniform inside the star because we are modeling the thermal evolution. over timescales much longer than the diffusion time (Reisenegger.1995).," The internal temperature, redshifted to a distant observer, $T_\infty$, is taken to be uniform inside the star because we are modeling the thermal evolution over timescales much longer than the diffusion time \citep{reis95}."76. Thus. the evolution of the internal temperature for an isothermal interior is given by the thermal balance equation (Thorne.1977) where C is the total heat capacity of the star. Li) is the total power released by the heating mechanism. L7 the total power emitted as neutrinos due to Urca reactions. and L7 the power released as thermal photons.," Thus, the evolution of the internal temperature for an isothermal interior is given by the thermal balance equation \citep{thorne77} where $C$ is the total heat capacity of the star, $L_H^{\infty}$ is the total power released by the heating mechanism, $L_\nu^\infty$ the total power emitted as neutrinos due to Urca reactions, and $L_\gamma^\infty$ the power released as thermal photons."77 The amount of energy released by each Urca-type reaction IS Hop=Hn—HpHi CT= eq. where qr; is the chemical potential of the particle species i.," The amount of energy released by each Urca-type reaction is $\eta_{npl}=\mu_n-\mu_p- \mu_l$ ( $l=e,\mu$ ), where $\mu_{i}$ is the chemical potential of the particle species $i$."78" Thus. we write the total energy dissipation rate as where AL,,;=yop)—Vy; is the net reaction rate of the Urea reaction integrated over the core involving the lepton /."," Thus, we write the total energy dissipation rate as where $\Delta\tilde{\Gamma}_{npl}=\tilde{\Gamma}_{n\rightarrow pl}-\tilde{\Gamma}_{pl\rightarrow n}$ is the net reaction rate of the Urca reaction integrated over the core involving the lepton $l$."79" The photon lummosity is calculated by assuming black-body radiation LY=απσκς,Ti. where Ry, and T, are the radius and the surface temperature of the star measured by an observer at infinity. respectively."," The photon luminosity is calculated by assuming black-body radiation $L_\gamma^\infty=4\pi\sigma R_\infty^2 T_{s,\infty}^4$, where $R_\infty$ and $T_{s,\infty}$ are the radius and the surface temperature of the star measured by an observer at infinity, respectively."80 To relate the internal and the surface temperatures. the fully accreted envelope model of Potekhinetal.(1997) is used.," To relate the internal and the surface temperatures, the fully accreted envelope model of \citet{potetal97} is used."81" The evolution of the redshifted chemical imbalances. also uniform throughout the core. is given by where the terms Zn). Zip. Zap. Wap. and W,,, are constants that depend on the stellar structure and are kept unchanged with respect to their latest definition in Reiseneggeretal. (2006).. and QO is the product of the angular velocity and its time derivative (proportional to the spin-down power)."," The evolution of the redshifted chemical imbalances, also uniform throughout the core, is given by where the terms $Z_{np}$, $Z_{npe}$ , $Z_{np\mu}$ , $W_{npe}$, and $W_{np\mu}$ are constants that depend on the stellar structure and are kept unchanged with respect to their latest definition in \citet{reis06}, and $\Omega \dot{\Omega}$ is the product of the angular velocity and its time derivative (proportional to the spin-down power)."82 As Petrovich&Reisenegger(2010) showed. the results of the evolution with rotochemical heating when computing LY and Maine in the presence of superfluid nucleons are substantially different from. their superfluid counterparts calculated by Fernández&Reisenegger(2005).. since superfluidity strongly inhibits. these reactions.," As \citet{petro10} showed, the results of the evolution with rotochemical heating when computing $L_\nu^\infty$ and $\Delta\tilde{\Gamma}_{npe}$ in the presence of superfluid nucleons are substantially different from their superfluid counterparts calculated by \citet{FR05}, since superfluidity strongly inhibits these reactions."83 Thus. the chemical imbalances become larger during the quasi-steady state. lengthening the timescale to arrive at this state compared with the non-superfluid case. and predicting highertemperatures in old NSs.," Thus, the chemical imbalances become larger during the quasi-steady state, lengthening the timescale to arrive at this state compared with the non-superfluid case, and predicting highertemperatures in old NSs."84 In this paper. we include the powerful direct Urca reactions to our previous study.," In this paper, we include the powerful direct Urca reactions to our previous study."85 In the core. neutrons are believed to form Cooper pairs because of their interaction in the triplet P» states via the anisotropic channels η=0 (type B) or η=2 (type C). while protons form isotropic. singlet ‘Sq pairs (type A) (Yakovlevetal..2001).," In the core, neutrons are believed to form Cooper pairs because of their interaction in the triplet $^3P_2$ states via the anisotropic channels $|m_J|=0$ (type B) or $|m_J|=2$ (type C), while protons form isotropic, singlet $^1S_0$ pairs (type A) \citep{yak01}."86. Additionally. in the outermost core and inner crust. neutrons are believed tc form singlet-state !So pairs.," Additionally, in the outermost core and inner crust, neutrons are believed to form singlet-state $^1S_0$ pairs."87 The ?P« (type B and C) state description is rather uncertain in the sense that the energetically most probable state of ni- pars (η=0.1.2) is not known. being extremely sensitive to the still unknown 7;ui-1nteraction (see. e.g. AmundsenOstgaard1985)).," The $^3P_2$ (type B and C) state description is rather uncertain in the sense that the energetically most probable state of $nn$ -pairs $|m_J|=0,1,2$ ) is not known, being extremely sensitive to the still unknown $nn$ -interaction (see, e.g. \citealt{amundsen}) )."88 Taking this classification into account. Villain&Haensel(2005). solve numerically the suppression due to each type of superfluidity of the net reaction rate for direct Urea and modified Urca reactions out of beta equilibrium. finding that the suppression due to type A superfluidity is of strength between the suppression due to anisotropic channels type B and type C superfluidity. respectively.," Taking this classification into account, \citet{villain} solve numerically the suppression due to each type of superfluidity of the net reaction rate for direct Urca and modified Urca reactions out of beta equilibrium, finding that the suppression due to type A superfluidity is of strength between the suppression due to anisotropic channels type B and type C superfluidity, respectively."89" For simplicity. we consider the energy gaps for the neutrons A, and the protons A, at zero temperature. redshifted to a distant observer. as parameters that are isotropic So pairs) and uniform throughout the core of the NS."," For simplicity, we consider the energy gaps for the neutrons $\Delta_n$ and the protons $\Delta_p$ at zero temperature, redshifted to a distant observer, as parameters that are isotropic $^1S_0$ pairs) and uniform throughout the core of the NS."90 The phase transition for a nucleon species into a superfluid state takes place when its temperature falls below a critical value 7..., The phase transition for a nucleon species into a superfluid state takes place when its temperature falls below a critical value $T_c$ .91 This temperature is related to the energy gap atzero temperature A(T=0): for the isotropic pairing channel !$0. A(T=0)1.76447).," This temperature is related to the energy gap atzero temperature $\Delta(T=0)$; for the isotropic pairing channel $^1S_0$, $\Delta(T=0)=1.764 k T_c$."92 Additionally. when the transition occurs. the amplitude of the energy gap dependson the temperature by means of the BCS equation (Yakovlevetal..2001).. which can be fitted by the practical formula of (1994) for the isotropic gap where 6 is the variable used in the phase-space integrals in Sect. 2.3..," Additionally, when the transition occurs, the amplitude of the energy gap dependson the temperature by means of the BCS equation \citep{yak01}, which can be fitted by the practical formula of \citet{levyak94} for the isotropic gap where $\delta$ is the variable used in the phase-space integrals in Sect. \ref{sec:theory_emiss}."93 It is straightforward to check that the limiting cases are reproduced by Eq. (5))," It is straightforward to check that the limiting cases are reproduced by Eq. \ref{eq:delta}) ),"94".Le. 0=O when7=T, and ACT=OKT when TZ«T,.. Levent",i.e. $\delta=0$ when$T=T_c$ and $\delta=\Delta(T=0)/kT$ when $T\ll T_c.$.95"ish&Yakovlev(1994) claim that intermediate values of 7/7, are also reproduced by this formula with a maximum error less than 5%. which ts accurate enough for the purposes of this work."," \citet{levyak94} claim that intermediate values of $T/T_c$ are also reproduced by this formula with a maximum error less than $5\%$ , which is accurate enough for the purposes of this work."96 Having defined the energy gap of the nucleon A; with p. itis possible to express the momentum dependence of the nucleon energy ejp;) near the Fermilevel. ie. |p;-—py]« pr... as follows (Yakovlevetal..2001) where pj. Py. vp. and pe; are the momentum. the Fermi momentum. the Fermi velocity. and the chemical potential of species /=7. p. respectively.," Having defined the energy gap of the nucleon $\Delta_i$ with$i=n,p$ , it is possible to express the momentum dependence of the nucleon energy $\epsilon_i(p_i)$ near the Fermilevel, i.e. $|p_i-p_{F_i}|\ll p_{F_i}$ , as follows \citep{yak01}97 where $p_{i}$ $p_{F_i}$ , $v_{F_i}$ , and $\mu_i$ are the momentum, the Fermi momentum, the Fermi velocity, and the chemical potential of species $i=n,p$ , respectively."98The fastest reactions in NS cores are the direct Urea processes,The fastest reactions in NS cores are the direct Urca processes99Submillimetre Galaxies (SAIGS Snuul. Ivison Blain 1997) contribute significantly to the rapid buildup of stellar mass in the Universe at 2~ 2.,"Submillimetre Galaxies (SMGs – Smail, Ivison Blain 1997) contribute significantly to the rapid buildup of stellar mass in the Universe at $z\,\sim\,$ 2."100 SMCGs have a typical redshift of z~2.2 (Chapman et 22005: Wardlow et 22010). are massive svstenis (441:1077thay. Swinbank et 22004: Greve et 22005: Tuacconi ct 22006) ancl are diverse in the extent and dvnaniues of their molecular eas reservoirs (e.g... Facconi et 22008: Bothwell ct 22010: lvison et 22010a.2010b).," SMGs have a typical redshift of $z\sim2.2$ (Chapman et 2005; Wardlow et 2010), are massive systems $M_* \sim 10^{10-11} M_\odot$, Swinbank et 2004; Greve et 2005; Tacconi et 2006) and are diverse in the extent and dynamics of their molecular gas reservoirs (e.g., Tacconi et 2008; Bothwell et 2010; Ivison et 2010a,2010b)."101 Interferomoetric observations of SACS. CO molecular gas suggest that the most. luminous SMGs (δα) c 5 mJy are merging svtems (IEngel et 22010) with high star formation elliciencies. compared to typical galaxies of similar mass (Dadcdi ct 22008)., Interferometric observations of SMGs' CO molecular gas suggest that the most luminous SMGs $\mu$ m) $>$ 5 mJy are merging sytems (Engel et 2010) with high star formation efficiencies compared to typical galaxies of similar mass (Daddi et 2008).102 Llowever. their selection at iis inherently biased towards colcler-cdlust UWLIRGs. particularly at zz1 (Ealesetal.2000:Blain2004)..," However, their selection at is inherently biased towards colder-dust ULIRGs, particularly at $>$ 1 \citep{eales00,Blain04a}."103 In particular. since subnim observations probe the blackbody emission. of dust in the Ravleigh-Jeans regime. thev are anti-correlated with dust temperature (κου«X fora eiven infrared luminosity. and galaxies with warmer Taledust can fall below the detection limit of current subi instruments.," In particular, since submm observations probe the blackbody emission of dust in the Rayleigh-Jeans regime, they are anti-correlated with dust temperature $_{850} \propto $ $_{\rm dust}^{-4.5}$ for a given infrared luminosity, and galaxies with warmer dust can fall below the detection limit of current submm instruments."104 Recent work (c.g.Chapmanetal.2004a:Caseyct2009) has demonstrated. that S5Osm--faint. high-redshift ULIRGs exist. and may contribute significantly to. the cosmic star formation rate density at dts. peak.," Recent work \citep[e.g.][]{C04a,casey09a} has demonstrated that -faint, high-redshift ULIRGs exist and may contribute significantly to the cosmic star formation rate density at its peak."105" These Optically Faint-Itadio Galaxies (OFIts) are defined as radio sources having inferred ULIBG luminosities. with starburst (SB) or. hybrid. SB-AGN spectral features. in the UV. and having 2.5-o limits on their subnim fluxes which are consistent with them being fainter than mindy at SSOyan. They have a comoving volume cdensitv (i.e. ~10""AIpe Pat domκA. Chapman et 22001. 2004). stellar masses ancl radio sizes comparable to SMCs. and some have a dust temperature of ~52 Ix. (Casey. ct 22009. 2010a. 2010b)."," These Optically Faint-Radio Galaxies (OFRGs) are defined as radio sources having inferred ULIRG luminosities, with starburst (SB) or hybrid SB-AGN spectral features in the UV, and having $\sigma$ limits on their submm fluxes which are consistent with them being fainter than mJy at $\mu$ m. They have a comoving volume density (i.e., $\sim10^{-5} Mpc^{-3}$ at $1 < z < 3$, Chapman et 2001, 2004), stellar masses and radio sizes comparable to SMGs, and some have a dust temperature of $\sim$ 52 K (Casey et 2009, 2010a, 2010b)."106 Studies of other infrared-DIuminous galaxy populations bothpre-ZZersehiet (sceDevetal.2008:Youngeretal.2009:Bussmann2009) and.Llerschel (seeOliveretal.2010:MagisctRoseboometal.2010:Chanial2010) present even more evidence for diverse populations of luminous. dusty starbursts at 11.," Studies of other infrared-luminous galaxy populations both \citep[see][]{dey08,younger09,bussmann09} and \citep[see][]{Oliver10,Magdis10,Roseboom10,Chanial10}107 present even more evidence for diverse populations of luminous, dusty starbursts at 1."108 Llowever. sparse infrared. data. particularly in the wwaveleneth range have limited the interpretation of the SALGs and OFRGs.," However, sparse infrared data, particularly in the wavelength range have limited the interpretation of the SMGs and OFRGs."109 Many of their fundamental properties still rely on indirect. measurements., Many of their fundamental properties still rely on indirect measurements.110 Direct. determinations of SALG and OFT. dust. temperatures are limited and have only been cone using either a single rest-[arll, Direct determinations of SMG and OFRG dust temperatures are limited and have only been done using either a single rest-farIR111 Direct. determinations of SALG and OFT. dust. temperatures are limited and have only been cone using either a single rest-[arlli, Direct determinations of SMG and OFRG dust temperatures are limited and have only been done using either a single rest-farIR112Now all derivatives up to fourth order can be calculated aH PY inserting the current case.,			Now all derivatives up to fourth order can be calculated just by simply inserting the current case.113 For example OX)insertingοEXPHW can be read off from (38)) by i=/k=!ΜΗ]l.abxande-d-x As we can see from (38)). all antisymmetric parts cancel out during the differentiation.," For example $\partial_{1}^{2}(\fe{x})\partial_{1}^{2}(\fe{x}')|_{\fe{J}=0}\exp\source$ can be read off from \ref{al:dif}) ) by inserting $i=j=k=l=1, \fe{a}=\fe{b}=\fe{x}\ \text{and} \ \fe{c}=\fe{d}=\fe{x}'$: 			As we can see from \ref{al:dif}) ), all antisymmetric parts cancel out during the differentiation."114 Thus although M. was not explicitly restricted to be symmetric. only the symmetric elements of the magnetic correlation tensor remain in the end.," Thus although $\fe{M}$ was not explicitly restricted to be symmetric, only the symmetric elements of the magnetic correlation tensor 			remain in the end."115 However. it is important to understanc that these symmetric elements actually preserve the intrinsic antisymmetric parts that constitute the magnetic correlation tensor.," However, it is important to understand that these symmetric elements actually preserve the intrinsic antisymmetric parts that constitute the magnetic correlation tensor."116 As mentioned above. this is because we take into accountthe inversion of the vector r when transposing the tensor elements.," As mentioned above, this is because we take into accountthe inversion of the vector $\fe{r}$ when transposing the tensor elements."117" A look at (7)) reveals. that the minus sigt of the Levi-Civita-tensor €;;, we encounter under interchanged indices is exactly cancelled by the minus sign occuring due to inversion of the vector r: This means that although the tensor (41)) is symmetric in the general way defined in (30)). it is not index-symmetric due to its individual antisymmetric constituents."," A look at \ref{al:MO}) ) reveals, that the minus sign of the Levi-Civita-tensor $\epsilon_{ijm}$ we encounter under interchanged indices is exactly cancelled by the minus sign occuring due to inversion of the vector $\fe{r}$: 			This means that although the tensor \ref{again}) ) is symmetric in the general way defined in \ref{al:sym}) ), it is not index-symmetric due to its individual antisymmetric constituents."118 The consequence is that rf we carry out the derivatives using the Wick theorem we not only have to take care of the right combination. of indices but also of the corresponding vectors r or —r and. in the end only the symmetric parts of M. as defined in (30) appear.," The consequence is that if we carry out the derivatives using the Wick theorem we not only have to take care of the right combination of indices but also of the corresponding vectors $\fe{r}$ or $-\fe{r}$ and, in the end only the symmetric parts of $\fe{M}$, as defined in \ref{al:sym}) ), appear."119 And further. this does mean that if we encounter index-symmetric expressions such as Μα=(Mij(ry+Mjir9/2. the intrinsic antisymmetric part related to the helical power spectrum in (41)) ts lost during the differentiation.," And further, this does mean that if we encounter index-symmetric expressions such as $M_{ij}(\fe{r})=\big(M_{ij}(\fe{r})+M_{ji}(\fe{r})\big)/2$, the intrinsic antisymmetric part related to the helical power spectrum in \ref{again}) ) is lost during the differentiation."120 A careful look at (38)) reveals that with the right combination for i.κ. and a.b.c.d and a sum of terms as in (38)). it is possible to get such combinations.," A careful look at \ref{al:dif}) ) reveals that with the right combination for $i,j,k,l$ and $\fe{a},\fe{b},\fe{c}, \fe{d}$ and a sum of terms as in \ref{al:dif}) ), it is possible to get such combinations."121 For example In this section the polarisation 2-point function (PUK_)P*(k pis calculated to serve us as an example for the general calculation to obtain the other correlation functions of our observables., For example 	In this section the polarisation 2-point function $\langle P(\textbf{k}_{\perp}) \cdot P^*(\textbf{k}_{\perp}') \rangle_{B}$ is calculated to serve us as an example for the general calculation to obtain the other correlation functions of our observables.122 Since the steps are similar for all correlation functions and differ only in complexity. we intend to present them in detail only for a single case here and just list the other calculations in the Appendix AppendixΑ:..," Since the steps are similar for all correlation functions and differ only in complexity, we intend to present them in detail only for a single case here and just list the other calculations in the Appendix \ref{ap:cal}."123 As (OXK0-P'(K'ὃν is of fourth order in the magnetic field and. in addition. P has a rather complex dependence on B. it is convenient to introduce a compact notation for P(x_)=[dzBx)+Bx. in order to clarify the calculation as far as possible.," 	 	As $\langle P(\textbf{k}_{\perp}) \cdot P^* (\textbf{k}_{\perp}') \rangle_{B}$ is of fourth order in the magnetic field and, in addition, $P$ has a rather complex dependence on $\bf{B}$, it is convenient to introduce a compact notation for $P(\textbf{x}_{\perp})=\int_{0}^{L} dz (B_{1}(\textbf{x})+iB_{2}(\textbf{x}))^{2}$ in order to clarify the calculation as far as possible."124 Defining B.=LI+(Bs) allows the expression P(x_)=ndz2B2(x) and Px)czndz2B(x, Defining $B_{\pm}=\frac{1}{\sqrt{2}}(B_{1} \pm iB_{2})$ allows the expression $P(\fe{x}_{\perp})=\int_{0}^{L} dz \ 2B_{+}^{2}(\fe{x})$ and $P^*(\fe{x}_{\perp})=\int_{0}^{L} dz \ 2B_{-}^{2}(\fe{x})$.125 Thus. a change of basis of B is introduced. mapping B=(B.B..Bi)—B=(B..B_.Bx).," Thus, a change of basis of $\textbf{B}$ is introduced, mapping $\textbf{B}=(B_{1},B_{2},B_{3}) \longrightarrow \tilde{\textbf{B}}=(B_{+},B_{-},B_{3})$ ."126" We can then work effectively with 2B7(x)-2B2(x"")instead of (By(x)+iBstxthis(By(x)—iBXx0).", We can then work effectively with $2B_{+}^{2}(\textbf{x}) \cdot 2B_{-}^{2}(\textbf{x}')$ instead of $(B_{1}(\textbf{x})+iB_{2}(\textbf{x}))^{2} \cdot (B_{1}(\textbf{x}')-iB_{2}(\textbf{x}'))^{2}$ .127 With regard to the correlation function. results in: Regarding the differentiation with respect to J. we need to establish a relation between ον. and J..," With regard to the correlation function, this results in: 	Regarding the differentiation with respect to $J_{\pm}$ we need to establish a relation between $J_{1/2}$ and $J_{\pm}$."128" The basis transformation should preserve all sealar products, therefore. we have J)B_+J_B_+J,By=-4BiJy+J, Bs."," The basis transformation should preserve all scalar products, therefore, we have $J_{+}^{\dagger}B_{+}+J_{-}^{\dagger}B_{-}+J_{3}^{\dagger}B_{3}=J_{1}^{\dagger}B_{1}+J_{2}^{\dagger}B_{2}+J_{3}^{\dagger}B_{3}$ ."129" Using this we establish the required relations: Thus. the transformation matrices J=OJ and J=ο, are: We now need to express the argument J'MJ of the exponential in (43)) in terms of the transformed quantities: Some elements of M that will soon become important are:"," Using this we establish the required relations: 	Thus, the transformation matrices $\textbf{J}=\textbf{O}\tilde{\textbf{J}}$ and $\tilde{\textbf{J}}=\textbf{O}^{\dagger}\textbf{J}$ are: 	We now need to express the argument $\textbf{J}^{\dagger}\textbf{M}\textbf{J}$ of the exponential in \ref{al:pol}) ) in terms of the transformed quantities: 	Some elements of $\tilde{\textbf{M}}$ that will soon become important are:"130Jailin Steinmatz 2005: Oguri ct al.,Bailin Steinmatz 2005; Oguri et al.131 2005: Allgood ct al., 2005; Allgood et al.132 2006: Ixnecbe Wicbner 2006:ί Ixublen. Dicmand Macau 2007).," 2006; Knebe ner 2006; Kuhlen, Diemand Madau 2007)."133 These studies include measuring the distribution of halo triaxalities. studying the ellects of barvons (which tend to reduce the triaxiality compared. to dark matter only models). and. investigating the relationships between halo shapes ancl angular momentum.," These studies include measuring the distribution of halo triaxalities, studying the effects of baryons (which tend to reduce the triaxiality compared to dark matter only models), and investigating the relationships between halo shapes and angular momentum."134 The purely triaxial treatment of dark matter halocs overlooks another well-established result from CDM simulations: incivicual haloes do not have a smooth density profile they contain sub-structure (Lacey Cole 1993: Moore et al., The purely triaxial treatment of dark matter haloes overlooks another well-established result from CDM simulations: individual haloes do not have a smooth density profile – they contain sub-structure (Lacey Cole 1993; Moore et al.135 1999: Ghigna et al., 1999; Ghigna et al.136 2000)., 2000).137 While the triaxial nature of dark matter haloes can be expressed. empirically (c.g. Jing Suto 2002). quantifving the sub-structure remains a challenge.," While the triaxial nature of dark matter haloes can be expressed empirically (e.g. Jing Suto 2002), quantifying the sub-structure remains a challenge."138 A shapelet-space representation of dark matter haloes provides a potential solution., A shapelet-space representation of dark matter haloes provides a potential solution.139 To demonstrate our approach. we use a sample of 200 candidate dark matter haloes selected. [rom a cosmological N-bocy simulation performed: with GADCIET-2 (Springel 2005).," To demonstrate our approach, we use a sample of 200 candidate dark matter haloes selected from a cosmological $N$ -body simulation performed with GADGET-2 (Springel 2005)."140 The cosmological parameters were Qu= 0.27. Au= 0.73. hb=0.71 and ax=0.9. and candidate haloes were identified using the Subkined grouplinder (Springel et al.," The cosmological parameters were $\Omega_0 = 0.27$ , $\Lambda_0 = 0.73$ , $h = 0.71$ and $\sigma_8 = 0.9$, and candidate haloes were identified using the SubFind groupfinder (Springel et al."141 2001)., 2001).142 Using particle number. Αν. as à proxy for mass. we pay particular attention to the twelve most massive haloes. haloes AL. and the twelve least massive. haloes M-X. from the sample.," Using particle number, $N_p$, as a proxy for mass, we pay particular attention to the twelve most massive haloes, haloes A–L, and the twelve least massive, haloes M-X, from the sample."143 We consider these two-subsets as being representative of tvpical halo shapes and. presence of sub-structure. along with limiting any mass-clepencdent biases that may occur.," We consider these two-subsets as being representative of typical halo shapes and presence of sub-structure, along with limiting any mass-dependent biases that may occur."144 For each halo. the triaxality. Z7. is caleulatect using the approach described in Appendix B.. and tabulated in ‘Table 1..," For each halo, the triaxality, $T$, is calculated using the approach described in Appendix \ref{app:triax}, and tabulated in Table \ref{tbl:shapfits}."145 Further quantities presented. in this table are described below., Further quantities presented in this table are described below.146" Of the twelve ""heavy haloes. two are oblate (Ex 1/3). eight are prolate (£7.2:2/3) and two are triaxial (1/3 2/3)."," Of the twelve `heavy' haloes, two are oblate $T \leq 1/3$ ), eight are prolate $T \geq 2/3)$ and two are triaxial $1/3 < T < 2/3$ )."147 Both the oblate haloes CX and L) have clear centra cores. while the triaxial haloes (D and J) do πο possess such a core.," Both the oblate haloes (A and L) have clear central cores, while the triaxial haloes (D and J) do not possess such a core."148 None of the ‘light’ haloes are oblate. ten were prolate. and two were triaxial (this time. haloes with centra COLCS).," None of the `light' haloes are oblate, ten were prolate, and two were triaxial (this time, haloes with central cores)."149 We perform a three-dimensional shapele decomposition on cach halo. with the following input parameters fixed: Ny5]. nua==—24 ane ο ," We perform a three-dimensional shapelet decomposition on each halo, with the following input parameters fixed: $N_g = 51$, $n_{\rm max} = 24$ and $\beta = \beta_{\rm scale} x_{\rm max}/\sqrt{2 N_g}$."150To select an appropriate ous Dor classification of halo shapes. we define a fitness estimator in terms ofthe peak signal-to-noise ratio: where Max(fiii) is the maximum value in the volume. and the mean-square error is:," To select an appropriate $\beta_{\rm scale}$ for classification of halo shapes, we define a fitness estimator in terms ofthe peak signal-to-noise ratio: where $\mbox{Max}(f_{ijk})$ is the maximum value in the volume, and the mean-square error is:"151"well known and studied: star-forming regions. d) varied morphologics. iii) submillimetre bright. (Jenness.Scott&Pacman 1995): and iv) observable from the JCMIT in Llawail (ie. 40°<0| TO"").","well known and studied star-forming regions, ii) varied morphologies, iii) submillimetre bright \citep{timscott}; and iv) observable from the JCMT in Hawaii (i.e. $-40^{\circ}152\leq \delta \leq +70^{\circ}$ )."153 The observations took place over several nights between 1998 Alay 16 anc 2000 October 10 at the James Clerk Alaxwell Telescope CCND) in. Hawaii., The observations took place over several nights between 1998 May 16 and 2000 October 10 at the James Clerk Maxwell Telescope (JCMT) in Hawaii.154 Phe Submillimetre Common User Bolometer Array (SCUBA) (Llollandοἱal.19009) was used in conjunction with the polarimeter consisting of a rotating quartz hall-wave retarder ahead of a lixed wire-grid analyser: Greavesetal.(2003) which was mounted on the entrance window to SCUBA., The Submillimetre Common User Bolometer Array (SCUBA) \citep{holland} was used in conjunction with the polarimeter – consisting of a rotating quartz half-wave retarder ahead of a fixed wire-grid analyser; \citet{jane} – which was mounted on the entrance window to SCUBA.155 The Jigele-mapping mode of observation was used. involving ‘jiggling’ the secondary mirror to fully sample the beam.," The Jiggle-mapping mode of observation was used, involving `jiggling' the secondary mirror to fully sample the beam."156 Sixteen dillerent positions (1 second exposures at each) are required to fully sample the map — these positions have a separation of for the Long-Waveleneth (850//m). array., Sixteen different positions (1 second exposures at each) are required to fully sample the map – these positions have a separation of for the Long-Wavelength $\mu$ m) array.157 “Phe secondary mirror performed the usual chop during the jigele pattern to provide atmospheric cancellation., The secondary mirror performed the usual chop during the jiggle pattern to provide atmospheric cancellation.158 Phe nod was carried out over periods of around 10-20 seconds to eliminate slowly varving sky eracdients., The nod was carried out over periods of around 10-20 seconds to eliminate slowly varying sky gradients.159 The polarimeter complicates the normal observing oocedure such that. complete 16-point jiggle maps are required at specific positions of the half-wave retarder. each separated by22.," The polarimeter complicates the normal observing procedure such that complete 16-point jiggle maps are required at specific positions of the half-wave retarder, each separated by."16057.. Pherefore 16 jigele maps are observed o complete one evele of the retarder., Therefore 16 jiggle maps are observed to complete one cycle of the retarder.161 The direction of the chop-throw was decided: based on the morphology of the arect., The direction of the chop-throw was decided based on the morphology of the target.162 The cata reduction was carried out using the routines rom the SCUBA User Recluction Facility (SURE) (Jenness&Liehtfoot1998) to reduce the SCUBA images and routines from POLPACI (Berry&Ισ2001) were used to reduce the polarimetry., The data reduction was carried out using the routines from the SCUBA User Reduction Facility (SURF) \citep{jennesslight} to reduce the SCUBA images and routines from POLPACK \citep{berry} were used to reduce the polarimetry.163 The nod and chop of the telescope were corrected. for and the Uat-ficld applied: to the observations in the standard manner., The nod and chop of the telescope were corrected for and the flat-field applied to the observations in the standard manner.164 The atmospheric extinction was calculated based on the start and end times of cach observation: throughout the night. the Caltech Submillimetre Observatory (CSO) phase monitor measures he Tescas (or Teso). and a polynonual was fitted to the measured points.," The atmospheric extinction was calculated based on the start and end times of each observation: throughout the night the Caltech Submillimetre Observatory (CSO) phase monitor measures the $\tau_{225 GHz}$ (or $\tau_{CSO}$ ), and a polynomial was fitted to the measured points."165" Εμις polynomial was then applied to the start and end times of the observation to calculate the reso or the observation and converted into 7«50,,5 using: or the data taken before October 2000. and: or the data taken during. and alter October 2000."," This polynomial was then applied to the start and end times of the observation to calculate the $\tau_{CSO}$ for the observation and converted into $\tau_{850 \mu m}$ using: for the data taken before October 2000, and: for the data taken during and after October 2000."166 The extinction is assumed. to vary linearly throughout he observation., The extinction is assumed to vary linearly throughout the observation.167 The airmass at which cach bolometer measurement was mace is caleulated then multiplied by the zenith sky extinction., The airmass at which each bolometer measurement was made is calculated then multiplied by the zenith sky extinction.168 Each data point was then multiplied w the exponential of the optical depth to give the value that would have been measured in the absence of the atmosphere., Each data point was then multiplied by the exponential of the optical depth to give the value that would have been measured in the absence of the atmosphere.169 Bolometers which were cleemec excessively noisy were switched: olf at this point in the data reduction., Bolometers which were deemed excessively noisy were switched off at this point in the data reduction.170 The sky noise was removed using bolometers that had no significant lux from the source., The sky noise was removed using bolometers that had no significant flux from the source.171 The average (mean) flux from these »xoLomieters was assumed to come from sky emission. and was subtracted from all of the bolometers in order to remove the sky signal.," The average (mean) flux from these bolometers was assumed to come from sky emission, and was subtracted from all of the bolometers in order to remove the sky signal."172 Phe instrumental polarisation was removed in the usual manner., The instrumental polarisation was removed in the usual manner.173 The data were re-ericded using a Gaussian weighting function. with the scale set to (ball the beamsize).," The data were re-gridded using a Gaussian weighting function, with the scale set to (half the beamsize)."174 The pixel size was set to matching the jigele pattern. in order to calculate the polarimetry vectors accurately.," The pixel size was set to, matching the jiggle pattern, in order to calculate the polarimetry vectors accurately."175" POLPACHK packages are then used to calculate the Stokes parameters by fitting the following curve Axon1999) to the data: where Z7 is the expected intensity in image J£ is the wire- analyser transmission factor. e is the analyser polarising ellicieney. factor ancl o, is the elfective retarder position angle alter correction for the parallactic angle for image A."," POLPACK packages are then used to calculate the Stokes parameters by fitting the following curve \citep{axon} to the data: where $I'_{k}$ is the expected intensity in image $k$, $t$ is the wire-grid analyser transmission factor, $\epsilon$ is the analyser polarising efficiency factor and $\phi_{k}$ is the effective retarder position angle after correction for the parallactic angle for image $k$."176 The polarisation percentage ancl position angles of the vectors are then caleulatecd from the Stokes parameters. without any binning.," The polarisation percentage and position angles of the vectors are then calculated from the Stokes parameters, without any binning."177 The catalogue was clipped such that noisy polarisation vectors were not included., The catalogue was clipped such that noisy polarisation vectors were not included.178 The clipping used: was {0 and dP«0.75., The clipping used was $I>0$ and $dP<0.75$.179 For polarisation. this represents a maximum. position angle error of7.," For polarisation, this represents a maximum position angle error of."18015°.. It was chosen to clip the vectors on polarisation errors instead. of signal-to-noise. as clipping on the latter would. result. in disposing of points where the polarisation is low or zero. both of which are perfectly valid measurements.," It was chosen to clip the vectors on polarisation errors instead of signal-to-noise, as clipping on the latter would result in disposing of points where the polarisation is low or zero, both of which are perfectly valid measurements."181 Finally. lux calibration (Jennessetal.2002) was carried out. using observations of Uranus. Saturn. and CILL26858.," Finally, flux calibration \citep{tim02} was carried out using observations of Uranus, Saturn and CRL2688."182 The flux calibration factors (FCs) are listecl in table 1.., The flux calibration factors (FCFs) are listed in table \ref{tab:fcf}.183 These. ΕςΕν were applied to the data. with any objects observed over more than one night having the data for each night. reduced separately. then the flux. calibrated images co-adcded to create the final image.," These FCFs were applied to the data, with any objects observed over more than one night having the data for each night reduced separately, then the flux calibrated images co-added to create the final image."184 Since the introduction of SCUBA on the JCAL. it has become “standard” to reduce. SSOpmi data with a pixe spacing of.," Since the introduction of SCUBA on the JCMT, it has become “standard” to reduce $\mu$ m data with a pixel spacing of."185". This is mainly due to a 3.09"" jigele-step being require: to fully sample the beam at 45054n. This allowed for easier comparisons between 45050 and Sb0í/m data.", This is mainly due to a 3.09” jiggle-step being required to fully sample the beam at $\mu$ m. This allowed for easier comparisons between $\mu$ m and $\mu$ m data.186 The methoc of data reduction naturally continued when the polarimeter was introciuced., The method of data reduction naturally continued when the polarimeter was introduced.187" Careful. inspection of data. reduced. by. this. metho (pixel size set to 3.00""7and. with 2.2 binning of vectors) . . . ⋜⋯∠⇂↓⋅∢⊾∠⇂⊔⊓⋅∠⇂⊔⊳∖↓⊔⋏∙≟⋜↧↓≻∟∖⋖⊾↓⊳∖↓∠⋖⊾∪⊔≻⊳↓↖∖∖∖⋎∐↓↥⊔∪∣⋡↓⊔⊔↓⊔⋏∙≟⊳ ⋅⋅∕∕⋠ ⋠⋠ ↓⋅∢⊾∖⇁⋖⋅⋜↧↓⋖⋅∠⇂⊳∖⊀↓⋏∙≟⊔⊲↓∐≼⇍⋜⋯⇂∠⇂↕↓↥⋅∢⊾↓⋅∢⊾↓↕≼∼∢⊾≻⊲↓⊔⇂↓↕⋖⊾⊔⊔⊔↓∣⋈⋅↓⋅"," Careful inspection of data reduced by this method (pixel size set to and with $\times$ 2 binning of vectors) and reduced using a pixel size of with no binning, revealed significant differences in the number of vectors."188∪⇂∎∖⇁⋖⋅≼∙↿∪↓⋅≱∖⋡↾∐⊔⋅ polarisation errors in the latter reduction were higher than, The polarisation errors in the latter reduction were higher than189the total number of pcores stabilises.,the total number of p–cores stabilises.190 Phe final number of sink particles in Figure 1H. is very similar to the final number of pcores. and the tailoll in the rate of sinkformation appears to be due simply to the fact that there are only a finite number of cores available from which to form sink particles.," The final number of sink particles in Figure \ref{fig:sink_rate} is very similar to the final number of p–cores, and the tailoff in the rate of sink–formation appears to be due simply to the fact that there are only a finite number of cores available from which to form sink particles."191 The topheavy form of the mass function is then a consequence of the carly pulse of sinkparticle formation coupled with the fact that all sink particles share a common environment and thus accrete at comparable rates., The top–heavy form of the mass function is then a consequence of the early pulse of sink–particle formation coupled with the fact that all sink particles share a common environment and thus accrete at comparable rates.192 We refer to this process as oligarchic accretion. since it is the sink particles that form first that acerete most of the shell’s The purpose of this paper was to simulate the fragmentation of an expanding shell. following the evolution well into he nonlinear regime to see if the predictions of the hinshell and. PAGL models (nominally only valid in the incar regime) can be extrapolated to accurately. determine he mass function of fragments formed.," We refer to this process as oligarchic accretion, since it is the sink particles that form first that accrete most of the shell's The purpose of this paper was to simulate the fragmentation of an expanding shell, following the evolution well into the non–linear regime to see if the predictions of the thin–shell and PAGI models (nominally only valid in the linear regime) can be extrapolated to accurately determine the mass function of fragments formed."193 We find that the mass function of objects located by our. clump.finding code agrees reasonably well with the predictions of the hinshell model in the early stages of fragmentation rclore significant. numbers of fragments become bound., We find that the mass function of objects located by our clump–finding code agrees reasonably well with the predictions of the thin–shell model in the early stages of fragmentation before significant numbers of fragments become bound.194 We also find that the assumption implicit in the mocdel tha ragments do not interact. appears to be sound., We also find that the assumption implicit in the model that fragments do not interact appears to be sound.195 Llowever. once pcores start to become bound. the numbers of »cores. detected: levels. olf at à. number consistent with he most unstable wavenumber at. this epoch.," However, once p–cores start to become bound, the numbers of p–cores detected levels off at a number consistent with the most unstable wavenumber at this epoch."196 Once the irst cores become bound. they suppress the formation of new fragments.," Once the first cores become bound, they suppress the formation of new fragments."197 Once sink particles begin to from from the »cores. the rate of sink formation is initially high. bu alls olf as the available cores are consumed.," Once sink particles begin to from from the p–cores, the rate of sink formation is initially high, but tails off as the available cores are consumed."198 Sink particles continue to accrete at roughly constant rates. since they al inhabit a similar environment. so that the initial pulse of sinkparticle formation translates into a topheavy miass function in which the mass corresponding to the mos unstable wavelength at the time of the pcores becoming bound. is overrepresented. with respect. to other modes.," Sink particles continue to accrete at roughly constant rates, since they all inhabit a similar environment, so that the initial pulse of sink–particle formation translates into a top–heavy mass function in which the mass corresponding to the most unstable wavelength at the time of the p–cores becoming bound is over–represented with respect to other modes."199 Vhe analvsis o£ ?.. in which the first unstable wavenumber is taken as representative of the mass function. describes fragmentation better than the analysis of ? in which all modes contribute to the mass We refer to this process as oligarchic accretion. since re objects that [orm first win simply by virtue of being first.," The analysis of \cite{1994MNRAS.268..291W}, in which the first unstable wavenumber is taken as representative of the mass function, describes fragmentation better than the analysis of \cite{2001A&A...374..746W} in which all modes contribute to the mass We refer to this process as oligarchic accretion, since the objects that form first win simply by virtue of being first."200 This mechanism is very. different from the competitive vecretion described by 2.. since. in that model it is the erent environments of the few. stars in the dense gas wu a cluster centre that enable them to accrete more than wir siblings.," This mechanism is very different from the competitive accretion described by \cite{2001MNRAS.323..785B}, since in that model it is the different environments of the few stars in the dense gas at a cluster centre that enable them to accrete more than their siblings."201 Ln the simulations presented here. most of Ίο sink particles form in gas of the same density. around re time when the shell expansion stalls.," In the simulations presented here, most of the sink particles form in gas of the same density, around the time when the shell expansion stalls."202 Ht is instead the time of formation and the nonuniform rate of formation of sink particles which is important in determining the final mass of a given object., It is instead the time of formation and the non–uniform rate of formation of sink particles which is important in determining the final mass of a given object.203 Those objects forming first are able to acerete more mass., Those objects forming first are able to accrete more mass.204 The mass function becomes skeweel because the rate of sink particle formation declines as the supply of pcores formed. during the linear. phase of the shells evolution is consumed., The mass function becomes skewed because the rate of sink particle formation declines as the supply of p–cores formed during the linear phase of the shells evolution is consumed.205 2? observe a similar process in the evolution of a turbulent protocluster. where the mass function. becomes skeweel towards higher masses as the star formation clliciency becomes large and the gas reservoirs required to form new cores are depleted.," \cite{2000ApJS..128..287K} observe a similar process in the evolution of a turbulent protocluster, where the mass function becomes skewed towards higher masses as the star formation efficiency becomes large and the gas reservoirs required to form new cores are depleted."206 The accretion process may also be aided by the fact that. at a time of 2:20. Myr. the shell begins to contract.," The accretion process may also be aided by the fact that, at a time of $\approx$ 20 Myr, the shell begins to contract."207 However. the contraction is slow compared. to the rate of sink particle formation and accretion. and the fragment mass function is already strongly topheavy at this epoch. so contraction of the shell cannot be the primary driver of oligarchic Lt is possible that. in the case of a shell sweeping up mass as it expands. so that reserves of fresh gas in the shell are. constantly. replenished. p.cores would be able o form at all times. resulting in a mass function. more closely resembling a power law.," However, the contraction is slow compared to the rate of sink particle formation and accretion, and the fragment mass function is already strongly top–heavy at this epoch, so contraction of the shell cannot be the primary driver of oligarchic It is possible that, in the case of a shell sweeping up mass as it expands, so that reserves of fresh gas in the shell are constantly replenished, p–cores would be able to form at all times, resulting in a mass function more closely resembling a power law."208 However. such a shell would experience the Vishniac instability (2).. probably. altering he mass spectrum of fragments in the nonlinear portion of the shells evolution.," However, such a shell would experience the Vishniac instability \citep{1983ApJ...274..152V}, probably altering the mass spectrum of fragments in the non–linear portion of the shell's evolution."209 This is important. since our results sugeest that the most unstable mode at the time when xind objects begin to form is overrepresented in the mass unction.," This is important, since our results suggest that the most unstable mode at the time when bound objects begin to form is over–represented in the mass function."210 To unequivocally demonstrate that aceretion of pesh material would allow unabated pcore formation and »oduce a powerlaw mass function would require that the shells gas reservoir be replenished in some way during sink ormation., To unequivocally demonstrate that accretion of fresh material would allow unabated p–core formation and produce a power–law mass function would require that the shell's gas reservoir be replenished in some way during sink formation.211 This is difficult in the case presented here. since most of the sinks form when the shell is almost stationary.," This is difficult in the case presented here, since most of the sinks form when the shell is almost stationary."212 The only way to replenish the gas would then be to actively eed matter into the shell. perhaps allowing it to infall rom a reservoir just outside the shells maximum radius. a üghlv artificial construction.," The only way to replenish the gas would then be to actively feed matter into the shell, perhaps allowing it to infall from a reservoir just outside the shell's maximum radius, a highly artificial construction."213 We therefore defer answering his question to a later paper in which we analyse the effect of the Vishniac instability on a momentumcriven. shell sweeping up an external The mass functions produced. by our simulations bear little resemblance to any known stellar or cluster mass function., We therefore defer answering this question to a later paper in which we analyse the effect of the Vishniac instability on a momentum–driven shell sweeping up an external The mass functions produced by our simulations bear little resemblance to any known stellar or cluster mass function.214 As explained in Section 3. the mass resolution of our sink particles is goock enough. to resolve lowmass," As explained in Section 3, the mass resolution of our sink particles is good enough to resolve low–mass"215 the trends are similar.,"for the higher case), but the trends are similar."216⋅⋅ The↴ same treud is. appareut when oosNoe.iu.for.thehighercase).but unavailable. a-chain network.. is used. instead of:," The same trend is apparent when }, unavailable in the $\alpha$ -chain network, is used instead of }."217" ""Ne. is in ∙∙fact :stronger with 72NeDAH :becauseflowtheDUARThetreud: of additionaleil paths that become available.", The trend is in fact stronger with } because of additional flow paths that become available.218 While the above has demonstrated the active role neon plays in the ignition process. its effect is much stnaller than that of carbon. which is the primary source of fuel iu this burning process.," While the above has demonstrated the active role neon plays in the ignition process, its effect is much smaller than that of carbon, which is the primary source of fuel in this burning process."219 As a result. in the more realistic case when au increase iu neon comes at the expense of both carbon aud oxveen. this effect is reduced. (for nall neon fractious) or completely reversed (for moderate noon fractious).," As a result, in the more realistic case when an increase in neon comes at the expense of both carbon and oxygen, this effect is reduced (for small neon fractions) or completely reversed (for moderate neon fractions)."220 This is slow. for lustance. in Fie. 7..," This is shown, for instance, in Fig. \ref{fig:nediff2}."221 In this case. increased inctallicity of the progenitor svstemi has the opposite effect: it makes the ignition time significantly longer for hotspots in the resulting white dw.," In this case, increased metallicity of the progenitor system has the opposite effect; it makes the ignition time significantly longer for hotspots in the resulting white dwarf."222 Detonation waves are a supersonie mode of propagating combustion., Detonation waves are a supersonic mode of propagating combustion.223" A shock wave heats up material. which thenignites. releasing enerey which further powers the shock. (See.foriustance.textbookssuchasο},"," A shock wave heats up material, which thenignites, releasing energy which further powers the shock. \citep[See, for instance, textbooks such224as][]{glassman96,williams}."225" There are. broadly. four states in a detonation: the uushocked material: the shocked material muuediatelv belind the shock: an induction zone. where the heated material slowly begins burning aud then the reaction zone, Where the bulk of the exothermic burning takes place."," There are, broadly, four states in a detonation: the unshocked material; the shocked material immediately behind the shock; an induction zone, where the heated material slowly begins burning and then the reaction zone, where the bulk of the exothermic burning takes place."226 Unsupported. sclfsustaimine detouations can be of the Chapiman-Jouget (CJ) type. where at the end of the reaction zoue the flow becomes sonic. or of the pathological type. where the sonic point occurs witlin reaction zone. decoupling the ow downstream of the sonic poiut from the shock.," Unsupported, self-sustaining detonations can be of the Chapman-Jouget (CJ) type, where at the end of the reaction zone the flow becomes sonic, or of the pathological type, where the sonic point occurs within reaction zone, decoupling the flow downstream of the sonic point from the shock."227 Pathological detonatious cau occur in material where there are eudothermie reactions or other dissipative or cooling effects. and mav have speeds slightly higher (typically by a few percent) than the CJ speed.," Pathological detonations can occur in material where there are endothermic reactions or other dissipative or cooling effects, and may have speeds slightly higher (typically by a few percent) than the CJ speed."228 Detonations within highly degencrate white-chwarf material (px> 0.2) are of the pathological type (2).. largely because some regions of the flow," Detonations within highly degenerate white-dwarf material $\rho_8 > 0.2$ ) are of the pathological type \citep{khokhlov89}, , largely because some regions of the flow"229 When [£j—6|€£3<ἐν+& is satisfied. A!(£4.6.£3) is the area of a triangle with side lengths £4.£» and (3.," When $|\ell_1-\ell_2| < \ell_3 < \ell_1 + \ell_2$ is satisfied, $\Lambda^{-1} \br{\ell_1,\ell_2,\ell_3}$ is the area of a triangle with side lengths $\ell_1,\ell_2$ and $\ell_3$."230 We use the transfer function to evaluate the linear three-dimensional matter power spectrum. and the fitting function for the nonlinear power spectrum.," We use the transfer function to evaluate the linear three-dimensional matter power spectrum, and the fitting function for the nonlinear power spectrum."231 ote that there is no intrinsic. ellipticity noise in the observed bispectrum. since the galaxy intrinsic. ellipticity distributior is assumed to be skewless.," Note that there is no intrinsic ellipticity noise in the observed bispectrum, since the galaxy intrinsic ellipticity distribution is assumed to be skewless."232 Under the assumptions of a compact survey geometry and scales much smaller than the extent of the survey area. (24) provides à bispectrum covariance that naturally incorporates the scaling with survey size. is not restricted to integer angular frequencies. and allows for any appropriate binning.," Under the assumptions of a compact survey geometry and scales much smaller than the extent of the survey area, ) provides a bispectrum covariance that naturally incorporates the scaling with survey size, is not restricted to integer angular frequencies, and allows for any appropriate binning."233 In terms of Fisher information. the result given by this approach and the Hu00 one agree to high accuracy2009).," In terms of Fisher information, the result given by this approach and the Hu00 one agree to high accuracy."234 In this section we present a toy model for generating GGI systematics., In this section we present a toy model for generating GGI systematics.235 Since the physical generation of intrinsic-shear alignments concerns nonlinear growth of structure and complex astrophysical processes which are not easy to quantify. a realistic model is not yet available.," Since the physical generation of intrinsic-shear alignments concerns nonlinear growth of structure and complex astrophysical processes which are not easy to quantify, a realistic model is not yet available."236 Current simulations involving baryonic matter also have some way to go before they can simulate the generation of the GGI systematics reliably., Current simulations involving baryonic matter also have some way to go before they can simulate the generation of the GGI systematics reliably.237 Up to now there has not been any attempt to measure GGI and GIL in galaxy surveys., Up to now there has not been any attempt to measure GGI and GII in galaxy surveys.238 studied these systematics using ray-tracing simulations., studied these systematics using ray-tracing simulations.239 They provided fits in real space to projected GIL and GGI signals. but the results are still too crude to lead to sufficient constraints on an intrilsic-shear alignment model.," They provided fits in real space to projected GII and GGI signals, but the results are still too crude to lead to sufficient constraints on an intrinsic-shear alignment model."240 This situation emphasizes the importance of a method intended to control intrinsic-shear. alignment to be model-independent. especially at the three-point level.," This situation emphasizes the importance of a method intended to control intrinsic-shear alignment to be model-independent, especially at the three-point level."241 Since this 1s the case for the nulling technique. for this work we only require a simple model for Bi which satisfies the characteristic redshift dependence and leads to a reasonable bias.," Since this is the case for the nulling technique, for this work we only require a simple model for $B_{\textrm {GGI}}^{(ijk)}$ which satisfies the characteristic redshift dependence and leads to a reasonable bias."242 Based on the observation that the lensing bispectrum expression (23) comes directly from (12) andthe definition of the tomography bispectrum (14). we link n also to a dimensional bispectrum B; via Similar to Bs(ky.Ks.ks) which is given by Bs; is defined via where 0)(4) 1s the three-dimensional density field which is responsible for the intrinsic alignment. and it satisfies oni. The definition of both x? and Oo) originates from the deterministic part of galaxy intrinsic ellipticity eh.," Based on the observation that the lensing bispectrum expression ) comes directly from ) andthe definition of the tomography bispectrum ), we link $B_{\textrm {GGI}}^{(ijk)}$ also to a three-dimensional bispectrum $B_{\delta_I\delta\delta}$ via Similar to $B_{\delta}(k_1,k_2,k_3)$ which is given by $B_{\delta_I\delta\delta}$ is defined via where $\tilde{\delta}_{\rm I}(\vek{k})$ is the three-dimensional density field which is responsible for the intrinsic alignment, and it satisfies 243chi , } The definition of both $\tilde{\kappa}^{(i)}_{\rm I}$ and $\tilde{\delta}_{\rm I}$ originates from the deterministic part of galaxy intrinsic ellipticity $\epsilon_{\rm I}^{\rm det}$."244 We have assume the existence of these underlying smooth fields., We have assume the existence of these underlying smooth fields.245 Similar quantities have been defined in(2009). see also and(2010).," Similar quantities have been defined in, see also and."246 We would like to point out again that. although we introduce these quantities for the clarity of our model. we do not need them for the main purpose of this paper.," We would like to point out again that, although we introduce these quantities for the clarity of our model, we do not need them for the main purpose of this paper."247 What we need to model ts the projected GGI bispectrum Bu., What we need to model is the projected GGI bispectrum $B_{\textrm {GGI}}^{(ijk)}$.248" ote that in (27). the weight for the lowest redshift bin 7 isthe source distribution funetion py’ which is zero outside redshift bin 7. rather than the lensing weight W'"" which is a much broader function."," Note that in ), the weight for the lowest redshift bin $i$ isthe source distribution function $p_{\rm s}^{(i)}$ which is zero outside redshift bin $i$, rather than the lensing weight $W^{(i)}$ which is a much broader function."249" Since RU depends only on physical processes at redshift bin / and is inferred from ellipticity measurements in this bin. and &< is linked to the three-dimensional matter density through the lensing weight Ἠο, this assignment of weight functions will ensure the correct redshift dependence of Bu."," Since $\tilde{\kappa}_{\rm I}^{(i)}$ depends only on physical processes at redshift bin $i$ and is inferred from ellipticity measurements in this bin, and $\tilde{\kappa}_{\rm G}^{(j)}$ is linked to the three-dimensional matter density through the lensing weight $W^{(j)}$, this assignment of weight functions will ensure the correct redshift dependence of $B_{\textrm {GGI}}^{(ijk)}$."250 When the redshift bins are not disjunct. however. the intrinsic alignment signal can no longer be associated with bin i.," When the redshift bins are not disjunct, however, the intrinsic alignment signal can no longer be associated with bin $i$."251 There will be two permutations in both the left-hand side of (16) and the right-hand side of (27). similar to the two-point case. e.g. Eq.," There will be two permutations in both the left-hand side of ) and the right-hand side of ), similar to the two-point case, e.g. Eq."25211 in(2004)., 11 in.253 The modeling of B; is then a pure matter of choice., The modeling of $B_{\delta_I\delta\delta}$ is then a pure matter of choice.254 We build a simple three-dimensional GGI bispectrum with power-law dependence on both redshift z and spatial frequency &: where eu Is the median redshift of the whole survey. and SL. Ku. r. s are free parameters.," We build a simple three-dimensional GGI bispectrum with power-law dependence on both redshift $z$ and spatial frequency $k$: where $z_{\textrm {med}}$ is the median redshift of the whole survey, and ${\cal A}$, $k_{\textrm {ref}}$, $r$, $s$ are free parameters."255 Among them the parameter Kj is designed to be a characteristic wave number. whose value we set to be a weakly nonlinear scale of 10ΛΜΡΟ! here.," Among them the parameter $k_{\textrm {ref}}$ is designed to be a characteristic wave number, whose value we set to be a weakly nonlinear scale of $10\;h{\rm Mpc}^{-1}$ here."256 The minus sign ensures that the contamination of GGI systematics leads to an underestimation ofthe GGG signal. as found by (2008).," The minus sign ensures that the contamination of GGI systematics leads to an underestimation ofthe GGG signal, as found by ."257 Little is known about the redshift and angular. scale dependence of δν., Little is known about the redshift and angular scale dependence of $B_{\delta_I\delta\delta}$ .258 However one can roughly estimate how it compares to the B4; signal., However one can roughly estimate how it compares to the $B_{\delta\delta\delta}$ signal.259 A linear alignment model suggests OfXOlinος(1+z)D(D (see 2004). in which pz) is the mean density of the universe. D(9) Is," A linear alignment model suggests $\delta_I \propto \delta_{\rm lin}\,\bar{\rho}(z)/((1+z)\,D_{+}(z))$ <cit.>[see , in which $\bar{\rho}(z)$ is the mean density of the universe, ${D_{+}}(z)$ is"2602011).. where both types are suberoups of C- asteroids.,", where both types are subgroups of C-type asteroids."261 Interestingly. these spectral classifications mean that. unlike Scheila. they are more plysically simular to nearby main-belt asteroids than to classical coniets (Licaudroefa£2011).. even though we believe the active episodes for these objects were actually sublianatiou-diiven in nature. while Scheila’s was not.," Interestingly, these spectral classifications mean that, unlike Scheila, they are more physically similar to nearby main-belt asteroids than to classical comets \citep{lic11b}, even though we believe the active episodes for these objects were actually sublimation-driven in nature, while Scheila's was not."262" The unclei of MBCs 238P(Read. P/Cirradd. and P/2010 R2 (La Saera). as well as that of P/2010 A2. have vet to be characterized spectroscopically due to the πια sizes of 238P and P/2010 À2 (Ilsehcfαἱ2011b:Jewittc£al,2010). and significant cometary activity at the time of all currently published observations of P/Carradd aud P/La Sagra (Jewittctαἱ.2009:Morenoefαἱ,2011a)."," The nuclei of MBCs 238P/Read, P/Garradd, and P/2010 R2 (La Sagra), as well as that of P/2010 A2, have yet to be characterized spectroscopically due to the small sizes of 238P and P/2010 A2 \citep{hsi11b,jew10} and significant cometary activity at the time of all currently published observations of P/Garradd and P/La Sagra \citep{jew09,mor11a}."263. As discussed above (Section 1)). direct spectroscopic detections of gas cussion in AIBCs have been elusive (ey...2011).," As discussed above (Section \ref{intro}) ), direct spectroscopic detections of gas emission in MBCs have been elusive \citep[{\it e.g.},."264 Successtul nionubiguous cletections of ice have been likewise difficult to obtain., Successful unambiguous detections of ice have been likewise difficult to obtain.265 No spectroscopic evidence of exposed water ice has been found on any of the MDCs (e.g...2011).," No spectroscopic evidence of exposed water ice has been found on any of the MBCs \citep[{\it e.g.},."266 Tlowever. Usich&Jewitt(2006). hvpothesize that cometary activity for these objects is beimg driven by small areas of exposed subsurface ice (hundredsofsquare 2009)..," However, \citet{hsi06} hypothesize that cometary activity for these objects is being driven by small areas of exposed subsurface ice \citep[hundreds of square meters on km-sized bodies; cf.][]{hsi04,hsi09b}."267 Tf that approximate ratio of active to inactive surface material is correct. we would actually expect uuresolved cisk-intcerated reflectance spectroscopy to be of linüted use without sensitivity levels to one part in ~LO! ον better.," If that approximate ratio of active to inactive surface material is correct, we would actually expect unresolved disk-integrated reflectance spectroscopy to be of limited use without sensitivity levels to one part in $\sim10^4$ or better."268 While this sensitivity level is bevoud the reach of current Earth-bouud facilities for the knmescale (and stnaller) AMIBCs at the distance of the asteroid bolt. Rivlin&Emery(2010) ancl Couupiusctal(2010) have reported water ice detections (correspouding to much larger surface coverage than predicted for the MDBCs) for the 100-kii-scale asteroid (21) Themis. which belougs to the same Themis asteroid family that also coutains 133P and 176P (sich&Jewitt2006).," While this sensitivity level is beyond the reach of current Earth-bound facilities for the km-scale (and smaller) MBCs at the distance of the asteroid belt, \citet{riv10} and \citet{cam10} have reported water ice detections (corresponding to much larger surface coverage than predicted for the MBCs) for the 100-km-scale asteroid (24) Themis, which belongs to the same Themis asteroid family that also contains 133P and 176P \citep{hsi06}."269. A similar absorption feature has also been detected on outer belt asteroid (65) Cybele (Licaudroetaf2011).., A similar absorption feature has also been detected on outer belt asteroid (65) Cybele \citep{lic11a}.270. The attribution of the absorption feature observed by these groups to water ice has been challenged by Beckctal.(2011) hough. who suggest that the absorption feature can © equally well explained by the non-volatile mineral eoecthite.," The attribution of the absorption feature observed by these groups to water ice has been challenged by \citet{bec11} though, who suggest that the absorption feature can be equally well explained by the non-volatile mineral goethite."271 Rivkin&Emery(2010) aud Campinsetal.(2010). acknowledge the thermal instability of water ice hat they claim to detect aud propose various scenarios row such surface ice could be maintaimed., \citet{riv10} and \citet{cam10} acknowledge the thermal instability of water ice that they claim to detect and propose various scenarios how such surface ice could be maintained.272 However. noue of these scenarios has vet been confirmed to actually dlausibly account for a widespread. long-lived surface aver of water ice as implied by their observations.," However, none of these scenarios has yet been confirmed to actually plausibly account for a widespread, long-lived surface layer of water ice as implied by their observations."273 We rther note that no outeassing or dust enission has ever en observed for (21) Themis (alsonotedbyRivkin&Emery 2010). aud as such. the connection between ice on mnainu-belt asteroids aud the activity of AIBCs remains Tuisubstautiated.," We further note that no outgassing or dust emission has ever been observed for (24) Themis \citep[also noted by][]{riv10}, and as such, the connection between ice on main-belt asteroids and the activity of MBCs remains unsubstantiated."274" Iun smnnauuw. while the hypothesis that activity iu MBCs is subliuatiou-driven is supported bv indirect evidence such as αποΊσα modeling results and observations showing recurrent activity (6.4...2011b). it remains unsubstantiated by the unambiguous detection of either ice or sublimation products,"," In summary, while the hypothesis that activity in MBCs is sublimation-driven is supported by indirect evidence such as numerical modeling results and observations showing recurrent activity \citep[{\it e.g.}, it remains unsubstantiated by the unambiguous detection of either ice or sublimation products."275 As such. if the nou-detectious of ice or gas Cluission via spectroscopy currently do not preclude the designation of an object as an MDC. the same detections of ice and σας cluission for Scheila (Section3.2: necessarily must also be considered inadequate criteria for concluding that the object is a disrupted asteroid. at least ou their own.," As such, if the non-detections of ice or gas emission via spectroscopy currently do not preclude the designation of an object as an MBC, the same non-detections of ice and gas emission for Scheila \citep[Section \ref{specresults}; necessarily must also be considered inadequate criteria for concluding that the object is a disrupted asteroid, at least on their own."276 We must also consider other evidence., We must also consider other evidence.277 The most obvious aspect of Sclicila’s dust cloud that should bear clues as to its origi is its unusual morphology., The most obvious aspect of Scheila's dust cloud that should bear clues as to its origin is its unusual morphology.278 Uulike mauv other comets which typically exhibit a single tail. often pointed in the autisolar direction. and a coma. Scheila exhibits two distinct curved dust plumes extending to the North aud the South (Figure 63).," Unlike many other comets which typically exhibit a single tail, often pointed in the antisolar direction, and a coma, Scheila exhibits two distinct curved dust plumes extending to the North and the South (Figure \ref{scheila_image}) )."279" Deeper and higher resolution imagery also shows a faint westward-pointing dust ""spike (Jewitt", Deeper and higher resolution imagery also shows a faint westward-pointing dust “spike” \citep{jew11}.280 The two iain dust plumes are nof easily explained by the standard cometary dust ejection piuradieimi where eraius are cjecteck isotropically ancl subsequently follow well-defiued svudvue aud svuchroue curves (cf. 1968). ," The two main dust plumes are not easily explained by the standard cometary dust ejection paradigm where grains are ejected isotropically and subsequently follow well-defined syndyne and synchrone curves \citep[{\it cf}. ,"281aud therefore Sugeest the action of amore unusual ejection mechaisin., and therefore suggest the action of a more unusual ejection mechanism.282 Ishiguroc£al(2011b) present numerical modeling results that show that the clouds morphology cau ο accounted for bv a hollow cone of dust (asex-oected.οanimpact:e.y.. ejected Sunsard aud thew turned back by radiation xessure.," \citet{ish11b} present numerical modeling results that show that the cloud's morphology can be accounted for by a hollow cone of dust \citep[as expected from an impact; {\it e.g.}, ejected Sunward and then turned back by radiation pressure."283 The hollowness of the cone is suggested by the dust clouds apparent lub brightening(GCG.c.. Scheilas rorthern and southeru plumes) consistent with the ereater optical depth expected of such a structure along its edges.," The hollowness of the cone is suggested by the dust cloud's apparent limb brightening, Scheila's northern and southern plumes), consistent with the greater optical depth expected of such a structure along its edges."284 A solid cone of ejected dust fas expected roni a sublimation-driven jet} similarly pushed back would instead exhibit ceutral brightening due to ereater optical depth in the jets core. aud not appear to exhibit -iultiple plumes.," A solid cone of ejected dust (as expected from a sublimation-driven jet) similarly pushed back would instead exhibit central brightening due to greater optical depth in the jet's core, and not appear to exhibit multiple plumes."285 The disparate strenetls of the northern and southern phunes may indicate an oblique angle of incidence for the impact. with more dust expected downrange of the iubound mapactor 2011b).," The disparate strengths of the northern and southern plumes may indicate an oblique angle of incidence for the impact, with more dust expected downrange of the inbound impactor \citep[cf.][]{ish11b}."286. While the scenario modeled by Ishiewroefaf(20115) dlausibly accounts for the appearance of multiple dust phunes with a single impact. if Scheila’s dust cloud is produced by a sublimation-driven process. aly scenario that similarly accounts for multiple observed dust plumes likely requires inultiple active sites.," While the scenario modeled by \citet{ish11b} plausibly accounts for the appearance of multiple dust plumes with a single impact, if Scheila's dust cloud is produced by a sublimation-driven process, any scenario that similarly accounts for multiple observed dust plumes likely requires multiple active sites."287 If these active sites are collisionally excavated. multiple impacts would have to have occurred on timescales shorter than their depletion timescales.," If these active sites are collisionally excavated, multiple impacts would have to have occurred on timescales shorter than their depletion timescales."288" This scenario is wulikely. however. eiven the typically low rate of inipacts on auy single body in the asteroid belt (οιο,,Fariuneclla&Davis1992) aud the expected short depletion timescales for surface volatiles onu inain-hbelt asteroids (sich2009).."," This scenario is unlikely, however, given the typically low rate of impacts on any single body in the asteroid belt \citep[e.g.,][]{far92} and the expected short depletion timescales for surface volatiles on main-belt asteroids \citep{hsi09b}."289. Multiple active sites could be possible if ucar-surface ice is abundant. trigecring sublimation at uniltiple points via thermal stresses.," Multiple active sites could be possible if near-surface ice is abundant, triggering sublimation at multiple points via thermal stresses."290 This scenario is contradicted though by Scheila's listorv of observed inactivity until 2010. aud the fact that it first exhibited a comoet-lHike dust cloud at »—2107. well before perihelion. when the surface was receiving only ~60:4 of the solar flux that it would at perihelion.," This scenario is contradicted though by Scheila's history of observed inactivity until 2010, and the fact that it first exhibited a comet-like dust cloud at $\nu\sim240\degr$, well before perihelion, when the surface was receiving only $\sim60$ of the solar flux that it would at perihelion."291 Itf Scheila were particularly icy. we would expect to lave observed past activity and at times of maxim solar heating.," If Scheila were particularly icy, we would expect to have observed past activity and at times of maximum solar heating."292 We thereforefind auy scenario invoking multiple, We thereforefind any scenario invoking multiple293In Fiewe 2. wo present the spectrum of NTE Jli1s8|480 obtained by averaging the individual spectra observed ou wieght March 31.,"In Figure \ref{fig2}, we present the spectrum of XTE J1118+480 obtained by averaging the individual spectra observed on night March 31."294 The spectra slows clearly the presence of broad double-peaked cussion lines of ALGSG6 and the Balmer series (up to Πο)., The spectrum shows clearly the presence of broad double-peaked emission lines of $\lambda$ 4686 and the Balmer series (up to $\delta$ ).295 Weaker A5112 aud emission lines from at AALITI. 1921. 5815. and 6678 are recognizable.," Weaker $\lambda5412$ and emission lines from at $\lambda\lambda$ 4471, 4921, 5875, and 6678 are recognizable."296 Except for Πα. the enüssion cores in the Balmer lines aud ALIT1 are contained within broad absorption features.," Except for $\alpha$, the emission cores in the Balmer lines and $\lambda4471$ are contained within broad absorption features."297 The Bowen blend AA16101650 is uot present durius this might (but see below)., The Bowen blend $\lambda\lambda 4640-4650$ is not present during this night (but see below).298 The broad bump at 1200 is probally an instrumental artifact., The broad bump at 4200 is probably an instrumental artifact.299 The main interstellar feature is the faint bleud due to the Na D doublet at 5890. aud 58096À., The main interstellar feature is the faint blend due to the Na D doublet at 5890 and 5896.300. We measure the equivalent width of this feature to be ~0.02 (close to the noise level) indicating very low iuterstellar absorption., We measure the equivalent width of this feature to be $\sim0.02$ (close to the noise level) indicating very low interstellar absorption.301 However. we caunot exclude a contribution from the A5875 emissiou line and consequently the measured equivalent width is au upper limit.," However, we cannot exclude a contribution from the $\lambda$ 5875 emission line and consequently the measured equivalent width is an upper limit."302 Loneward of — 6800 Α.. the spectra are contanunated by telluric features.," Longward of $\sim$ 6800 , the spectra are contaminated by telluric features."303 As reported by Carciaetal.(2000)... two παρα] absorption features at 6179 and 6516 were preseut ou the blueward side of the Πα profile in all our observations (see Figures 3. and ly).," As reported by \citet{gar00}, two unusual absorption features at 6479 and 6516 were present on the blueward side of the $\alpha$ profile in all our observations (see Figures \ref{fig3} and \ref{fig4}) )."304 They ust be associated with the accretion disk because in outburst the disk spectrum strongly dominates over the spectrum of the faint (W=18.8) secondary star., They must be associated with the accretion disk because in outburst the disk spectrum strongly dominates over the spectrum of the faint (V=18.8) secondary star.305 We suggest that both features are due to the superposition of a single broad absorption trough aud an enmiüssiou conipouent due to a blend of lines., We suggest that both features are due to the superposition of a single broad absorption trough and an emission component due to a blend of lines.306" This metallic bleud is observed iu absorption at A6195 in late CAIs stars (Ilorne.Wade&Szkody 1986).. which implies that it originates in reeious of the disk with T.,;,;~ 1200-6000 Is. It is also possible that A6516 contributes to the absorption features at this waveleneth."," This metallic blend is observed in absorption at $\lambda6495$ in late G-K stars \citep{hor86}, which implies that it originates in regions of the disk with $_{eff}\sim$ 4200-6000 K. It is also possible that $\lambda6516$ contributes to the absorption features at this wavelength."307 The spectra acquired during the same night or coutigous welts (Gwheu the nuuber of spectra was Dlnited) were averaged., The spectra acquired during the same night or contigous nights (when the number of spectra was limited) were averaged.308 The resulting mean spectra were de-reddeucd using E(BWV)0021 aud A-/E(BVW)= 3.1., The resulting mean spectra were de-reddened using $E(B-V)=0.024$ and $A{_V}/E(B-V)=3.1$ .309 The colour excess was estimated by using the hydrogen colin in the liue of sight (Nj=1.311079 7: Dickey&Lock-man 19903) aud the relation between Ny aud £(BV) of Bohlin.Savage&Drake(1978)., The colour excess was estimated by using the hydrogen column in the line of sight ${_H}=1.34\times10^{20}$ $^{-2}$; \citealt{dic90}) ) and the relation between $_H$ and $E(B-V)$ of \citet{boh78}.310". Next we fitted the de-reddened spectra with a power law of the form FyxXA"" after masking the major cussion lines.", Next we fitted the de-reddened spectra with a power law of the form ${F_\lambda}\propto{\lambda^\alpha}$ after masking the major emission lines.311 We measure a mean power law iudex of a=2.540.1 in agreement with the values reported by Dubusetal.(2001)., We measure a mean power law index of $\alpha=-2.5\pm0.1$ in agreement with the values reported by \citet{dub01}.312. We studied the more intense euissiou lines as follows: for cach spectrum we fitted a low order spline to the adjaceut contimmun of every profile after masking the lines. aud the spectrum was divided by the fitted function.," We studied the more intense emission lines as follows: for each spectrum we fitted a low order spline to the adjacent continuum of every profile after masking the lines, and the spectrum was divided by the fitted function."313 Next. for those nights caving which we obtained more than two spectra. we averaged the spectra.," Next, for those nights during which we obtained more than two spectra, we averaged the spectra."314 The Πα aud ÀAl656 line profiles were fitted with a 2-eaussian function and the I> profile with a 3-eaussian function (with one used to account for the absorption component) usine the Marquardt algorithm (Deviugton1969)., The $\alpha$ and $\lambda$ 4686 line profiles were fitted with a 2-gaussian function and the $\beta$ profile with a 3-gaussian function (with one used to account for the absorption component) using the Marquardt algorithm \citep{bev69}.315. Tables 2. aud 3 dist the values of the main fitted line parameters for the nichts with good orbital coverage., Tables \ref{haheii} and \ref{hb} list the values of the main fitted line parameters for the nights with good orbital coverage.316 In Table | we eive the measured full width zero intensity (FWZI) aud equivalent widths (EWs) for Ta. IT. and Af686.," In Table \ref{fwzi} we give the measured full width zero intensity (FWZI) and equivalent widths (EWs) for $\alpha$, $\beta$, and $\lambda$ 4686."317 The EW>s for additional lines are presented iu Table 5.., The EWs for additional lines are presented in Table \ref{ew}.318 The uncertainties m the EWs aud FWZls were estimated by looking at the scatter in the values when selecting differeut wavelength intervals to set the local coutimauiun level., The uncertainties in the EWs and FWZIs were estimated by looking at the scatter in the values when selecting different wavelength intervals to set the local continuum level.319 The mean peak-to-peak velocity separation for the Πα aud IL} lines is comparable (~ 1200 kin 1) with little change between different epochs., The mean peak-to-peak velocity separation for the $\alpha$ and $\beta$ lines is comparable $\sim$ 1200 km $^{-1}$ ) with little change between different epochs.320 Tle peal-to-peals velocity separation of the A 1686 line ranges from 1600 to 2000 kins ., The peak-to-peak velocity separation of the $\lambda$ 4686 line ranges from 1600 to 2000 km $^{-1}$.321 This result sugeests that the emission at IIo aud ILJ arises at a simular distauce from the compact object aud the Al68G line is enütted from regions closer to the compact object., This result suggests that the emission at $\alpha$ and $\beta$ arises at a similar distance from the compact object and the $\lambda$ 4686 line is emitted from regions closer to the compact object.322 The velocity separatio- of the double-peaks iu the Ilo liue is consistent with he values reported for other black hole NRNe during quiescence aud outburst (sec e.g. Table Lin Suüth.Filip-ko&Leonard19001)., The velocity separation of the double-peaks in the $\alpha$ line is consistent with the values reported for other black hole XRNe during quiescence and outburst (see e.g. Table 1 in \citealt{smi99}) ).323 The FWZI of the IL?) absorption conrponeut miplies a projected velocity of  2900 lan or the inner part of the optically-thick accretion dis- cluitting at this wavelength., The FWZI of the $\beta$ absorption component implies a projected velocity of $\sim$ 2900 km $^{-1}$ for the inner part of the optically-thick accretion disk emitting at this wavelength.324" The iuost remarkable feature im the evolution of he cussion lines is the change iu the double-pearos, intensity. from almost svinnietric peaks to euhlauce redshifted or blueshifted. peaks (soe Figure 3))."," The most remarkable feature in the evolution of the emission lines is the change in the double-peak intensity, from almost symmetric peaks to enhanced redshifted or blueshifted peaks (see Figure \ref{fig3}) )."325 Eve hough this behavior in the poorly sampled nights might © attributable to an S-wave. a different explauation is required for the svnuuetric/asvunuetiic averaged profiles on March 31. April 12. 29. and May 25. where uniforii orbital phase coverage should eusiue the cancellation of any S-wave effect in the averaged profiles.," Even though this behavior in the poorly sampled nights might be attributable to an S-wave, a different explanation is required for the symmetric/asymmetric averaged profiles on March 31, April 12, 29, and May 25, where uniform orbital phase coverage should ensure the cancellation of any S-wave effect in the averaged profiles."326 Finally. the Bowen blend appears niarginallvy ou April 3. probably blended with A1686 ou April 12 and clearly ehhanced on April 29.," Finally, the Bowen blend appears marginally on April 3, probably blended with $\lambda$ 4686 on April 12 and clearly enhanced on April 29."327 A elauce at the RNTE/ASM lieht curve (1.3-12.2 keV) of NTE J1118|£80 (sec Figure 13) shows that the enhancement iu mteusifv occurs uear the 1iaxinmuu iu X-ray flux., A glance at the RXTE/ASM light curve (1.3-12.2 keV) of XTE J1118+480 (see Figure \ref{fig1}) ) shows that the enhancement in intensity occurs near the maximum in X-ray flux.328 Ou Mav 25. during the slow decay of the N-vav outburst. both the Bowen Blend aud Al686 have decreased i intensity.," On May 25, during the slow decay of the X-ray outburst, both the Bowen Blend and $\lambda$ 4686 have decreased in intensity."329 Although the oenüssiou lines show variations in the double-peak structure due to απ S-wave enuüssiou conrponeut. our attempts to find a periodic radial velocity 1iodulatiou failed due maiuly to our low spectral resolution and the complexity of the line profiles.," Although the emission lines show variations in the double-peak structure due to an S-wave emission component, our attempts to find a periodic radial velocity modulation failed due mainly to our low spectral resolution and the complexity of the line profiles."330 Fortunately. we can obtain valuable iuformation by using the Doppler Tomoegrapliy technique (Marsh&Ποιο1988). on those data sets with good orbital phase coverage.," Fortunately, we can obtain valuable information by using the Doppler Tomography technique \citep{mar88} on those data sets with good orbital phase coverage."331 This technique reconstructs the brightuess distribution of the binary system in velocity space. allowing us to localize the Cluission structures which are not casily recognizable iu the individualspectra.," This technique reconstructs the brightness distribution of the binary system in velocity space, allowing us to localize the emission structures which are not easily recognizable in the individualspectra."332 We use the imaxiuun-eutropy method (MEM). of building the tomograns. which eradually buills the chussion structure froma default uniform nuage by reducing the 4? between the data and the model fit.," We use the maximum-entropy method (MEM) of building the tomograms, which gradually builds the emission structure froma default uniform image by reducing the $\chi^2$ between the data and the model fit."333 The optimal solution isselected amouginfinite possibilities by maxiuiziug the eutropy of the miage., The optimal solution isselected amonginfinite possibilities by maximizing the entropy of the image.334" To obtain the tomogram. the orbitalphases were deterumued using au orbital period D,,4,—0.16995740.000007 d aud a time"," To obtain the tomograms, the orbitalphases were determined using an orbital period ${_{orb}}=0.169937\pm0.000007$ d and a time"335sample.,sample.336 Then the bootstrap estimate of A is given bv the average of the resampled marks: just like A is given by the average of (he actual marks., Then the bootstrap estimate of $K$ is given by the average of the resampled marks: just like $\hat{K}$ is given by the average of the actual marks.337 Note (hat in an actual implementation of the procedure. all (hat is required is keeping (rack of how many times each point is resaaipled.," Note that in an actual implementation of the procedure, all that is required is keeping track of how many times each point is resampled."338 The step-by-step procedure for estimating aud resampling the «quantity (2)) is as follows: A [ew remarks about the procedure are in order., The step-by-step procedure for estimating and resampling the quantity \ref{eqn:estimator}) ) is as follows: A few remarks about the procedure are in order.339 Instead of randomly placing blocks. the observation region can be divided into a number of subregions. and (he regions selected randomly with replacement.," Instead of randomly placing blocks, the observation region can be divided into a number of subregions, and the regions selected randomly with replacement."340 This latter method is sometimes referred. (o as using fixed blocks as opposed to moving blocks., This latter method is sometimes referred to as using fixed blocks as opposed to moving blocks.341 It is eenerallv considered that the moving blocks bootstrap works better in terms of convergence rales in asvniptolic arguments., It is generally considered that the moving blocks bootstrap works better in terms of convergence rates in asymptotic arguments.342 The number of blocks used is so that the total area/volume of the blocks is equal to the original area/volume of the observation region., The number of blocks used is so that the total area/volume of the blocks is equal to the original area/volume of the observation region.343 Note that in this case N* would usually not be equal to N. though they will be of the same order of magnitude.," Note that in this case $N^*$ would usually not be equal to $N$, though they will be of the same order of magnitude."344 However. (his does not pose problems since (he statistic A is a mean of the marks.," However, this does not pose problems since the statistic $\hat{K}$ is a mean of the marks."345 There is no real consenus on (he size of the resampling blocks to use., There is no real consenus on the size of the resampling blocks to use.346 did some work on determining the optimal block size from data., \citet{buhlmann99} did some work on determining the optimal block size from data.347 Intuitivelv. (he procedure needs large blocks so that the correlation structure is less distorted. ancl a large enough number of blocks so that there is enough variability between bootstrap samples.," Intuitively, the procedure needs large blocks so that the correlation structure is less distorted, and a large enough number of blocks so that there is enough variability between bootstrap samples."348 If, If349Distance determination to open aud elobular clusters is key to placing them iu the proper Galactic evolutiouary coutext aud an iudispeusable component in evaluating stellar evolution as a function of mass. chemical composition. aud age.,"Distance determination to open and globular clusters is key to placing them in the proper Galactic evolutionary context and an indispensable component in evaluating stellar evolution as a function of mass, chemical composition, and age."350 For nearby. clusters like the Hyacles. Praesepe. the Pleiades aud Coma. Hipparcos parallaxes (EuropeanSpaceAgency 1997).. coupled with," For nearby clusters like the Hyades, Praesepe, the Pleiades and Coma, $Hipparcos$ parallaxes \citep{esa}, coupled with"351"means that across the MMHz bandwidth of this dataset, the TOA precision does not benefit from conducting sub-band template matching.","means that across the MHz bandwidth of this dataset, the TOA precision does not benefit from conducting sub-band template matching."352 The effect could become significant when the observing bandwidth is comparable to or larger than the scintillation frequency scale., The effect could become significant when the observing bandwidth is comparable to or larger than the scintillation frequency scale.353" Still, as the effect can be dealt with through the application of frequency-dependent template matching, we conclude that it will not be a limiting factor to TOA precision with either current or future telescopes."," Still, as the effect can be dealt with through the application of frequency-dependent template matching, we conclude that it will not be a limiting factor to TOA precision with either current or future telescopes."354 Shape distortion induced by instrumental effects obscures the true pulse shape and can therefore be expected to decrease the precision of timing., Shape distortion induced by instrumental effects obscures the true pulse shape and can therefore be expected to decrease the precision of timing.355 Two main digitisation effects are pertinent to a low-bit observing system., Two main digitisation effects are pertinent to a low-bit observing system.356 The first effect is caused by the underestimation of the undigitised power in a system with low dynamic range (e.g. only 2 bits per sample)., The first effect is caused by the underestimation of the undigitised power in a system with low dynamic range (e.g. only 2 bits per sample).357" As discussed in ? (hereafter JA98) the earlier arrival of pulsar emission at the high end of the observing bandwidth causes an increase in undigitised power, and therefore a decrease of the digitised-to-undigitised power ratio at all frequencies if the output power level is kept constant."," As discussed in \cite{ja98} (hereafter JA98) the earlier arrival of pulsar emission at the high end of the observing bandwidth causes an increase in undigitised power, and therefore a decrease of the digitised-to-undigitised power ratio at all frequencies if the output power level is kept constant."358" As a result, the off-pulse power will be decreased in the rest of the band."," As a result, the off-pulse power will be decreased in the rest of the band."359" This effect can be avoided through dynamically setting the output power levels, which provides the required dynamic output range and therefore does not result in negative off-pulse dips on either side of the pulse profile."," This effect can be avoided through dynamically setting the output power levels, which provides the required dynamic output range and therefore does not result in negative off-pulse dips on either side of the pulse profile."360" 'The second artefact is caused by quantisation errors as a second-order distortion, and manifests itself as an increase in white noise uniformly redistributed across all frequency channels, which is induced by the increase in pulsed power in one part of the band (JA98)."," The second artefact is caused by quantisation errors as a second-order distortion, and manifests itself as an increase in white noise uniformly redistributed across all frequency channels, which is induced by the increase in pulsed power in one part of the band (JA98)."361" This scattered power broadens the profile and causes additional pulse shape variations as a function of observing frequency, which decreases the achievable TOA precision."," This scattered power broadens the profile and causes additional pulse shape variations as a function of observing frequency, which decreases the achievable TOA precision."362" In this paper, all CPSR2 data presented were corrected for the low dynamic range artefact during on-line processing, by the dynamic output level setting algorithm implemented in (?).."," In this paper, all CPSR2 data presented were corrected for the low dynamic range artefact during on-line processing, by the dynamic output level setting algorithm implemented in \citep{vb10}."363 The scattered power was mitigated during offline processing through application of the correction algorithm implemented in (?).., The scattered power was mitigated during off-line processing through application of the correction algorithm implemented in \citep{hvm04}.364" Given the uncorrected, mean digitized power ó? in each pulse phase bin, this algorithm inverts Eq. ("," Given the uncorrected, mean digitized power $\hat\sigma^2$ in each pulse phase bin, this algorithm inverts Eq. ("365A5) of JA98 to estimate the mean undigitised power o? and the mean scattered power A via Eqs. (,A5) of JA98 to estimate the mean undigitised power $\sigma^2$ and the mean scattered power $A$ via Eqs. (366"45) and (43) of JA98, respectively.","45) and (43) of JA98, respectively."367" The effect, of correction is demonstrated in Fig. 4,,"," The effect of correction is demonstrated in Fig. \ref{profresispc},"368" which shows the pulse profile formed from the 2005-07-24 dataset with and without application of the algorithm, as well as the difference between the two."," which shows the pulse profile formed from the 2005-07-24 dataset with and without application of the algorithm, as well as the difference between the two."369 The decreased pulse width of the corrected profile allows higher timing precision., The decreased pulse width of the corrected profile allows higher timing precision.370 Note that the distortion would not change significantly once the back-end settings are stable., Note that the distortion would not change significantly once the back-end settings are stable.371 This means that the TOA precision would still scale with effective collecting area as described by the radiometer equation., This means that the TOA precision would still scale with effective collecting area as described by the radiometer equation.372" We therefore conclude that this effect does not limit the current TOA precision, and will not limit it for future telescopes either, which are likely to employ digitisers with a higher number of digitisation levels."," We therefore conclude that this effect does not limit the current TOA precision, and will not limit it for future telescopes either, which are likely to employ digitisers with a higher number of digitisation levels."373" When a fixed-linear-feed, alt-azimuth radio telescope tracks a polarised source across the sky, the feed will rotate with respect to the plane of polarisation by the parallactic angle (q), which is defined as the angle between the object-zenith great circle and the hour circle."," When a fixed-linear-feed, alt-azimuth radio telescope tracks a polarised source across the sky, the feed will rotate with respect to the plane of polarisation by the parallactic angle $q$ ), which is defined as the angle between the object-zenith great circle and the hour circle."374" The change of q combined with the instrumental response, will result in a variation of the observed Stokes parameters with time."," The change of $q$ combined with the instrumental response, will result in a variation of the observed Stokes parameters with time."375" Polarisation calibration, the aim of which is to reveal the intrinsic profile, will correct this time-dependent variation, but the correction will only be partial if any non-orthogonality of the receptors is not fully modelled."," Polarisation calibration, the aim of which is to reveal the intrinsic profile, will correct this time-dependent variation, but the correction will only be partial if any non-orthogonality of the receptors is not fully modelled."376" In this case, a difference between profiles at different q will be seen even after calibration."," In this case, a difference between profiles at different $q$ will be seen even after calibration."377" In practice, a “single axis"" model considering only the differentials in gain and phase for the two linear polarisation probes is usually applied (e.g.?).."," In practice, a “single axis” model considering only the differentials in gain and phase for the two linear polarisation probes is usually applied \citep[e.g.][]{scr+84}."378" The most recent (here mentioned as “full reception"") model, described by ?,, solves the matrix description of the polarisation measurement equations, accounting for differential gains and phases, as well as for coupling and leakage effects between the receiverfeeds."," The most recent (here mentioned as “full reception”) model, described by \cite{van04a}, solves the matrix description of the polarisation measurement equations, accounting for differential gains and phases, as well as for coupling and leakage effects between the receiverfeeds."379" For comparison, here we used both the “single axis"" and the ""full reception"" model (constructed from the 2005-07-24"," For comparison, here we used both the “single axis” and the “full reception” model (constructed from the 2005-07-24"380by Basu οἱ al. (,by Basu et al. (3812004) that the adiabatic index. Dy of active regions is considerably different from that of quiet regions and the amount of change increases will increasing strength of the active region.,"2004) that the adiabatic index, $\Gamma_1$ of active regions is considerably different from that of quiet regions and the amount of change increases with increasing strength of the active region."382 Figure 1. shows the acliabatic index for (wo of the active regions studied bv Basu et al. (, Figure \ref{fig:f1} shows the adiabatic index for two of the active regions studied by Basu et al. (3832004). and one can see that the magnitude of the depression in Py at the second helium ionization zone decreases with increasing strength of the active region.,"2004), and one can see that the magnitude of the depression in $\Gamma_1$ at the second helium ionization zone decreases with increasing strength of the active region."384 This leads us to question whether similar changes occur globally in the Sun as solar aclivily increases — of course one would expect the changes to be much smaller than (hose seen in active regions because global activity levels are much smaller than in active regions., This leads us to question whether similar changes occur globally in the Sun as solar activity increases — of course one would expect the changes to be much smaller than those seen in active regions because global activity levels are much smaller than in active regions.385 Although the He II ionization zone is too shallow for studying temporal changes directly by inverting the currently available data sets. there are indirect wavs by which we can study {his region.," Although the He II ionization zone is too shallow for studying temporal changes directly by inverting the currently available data sets, there are indirect ways by which we can study this region."386 Anv spherically svimmetric localized. sharp feature or discontinuity in the Sun's internal structure leaves a definite signature on (he solar p-mode frequencies.," Any spherically symmetric localized, sharp feature or discontinuity in the Sun's internal structure leaves a definite signature on the solar p-mode frequencies."387" Gough (1990) showed that abrupt changes of this tvpe contribute a characteristic oscillatory component to the frequencies 7,, of those modes which penetrate below the localized perturbation."," Gough (1990) showed that abrupt changes of this type contribute a characteristic oscillatory component to the frequencies $\nu_{n,\ell}$ of those modes which penetrate below the localized perturbation."388 The amplitude ol the oscillations increases with increasing “severity” of the cliscontinuity. and the wavelength of (he oscillation is essentially (he acoustic depth of the sharp-leature.," The amplitude of the oscillations increases with increasing “severity” of the discontinuity, and the wavelength of the oscillation is essentially the acoustic depth of the sharp-feature."389 Solar modes encounter two such features. the base of the convection zone (hencelorth CZ) and the He II ionization zone.," Solar modes encounter two such features, the base of the convection zone (henceforth CZ) and the He II ionization zone."390 The (ransition of the temperature gradient [rom the adiabatic to radiative values al the CZ base gives rise to the oscillatory signal in lrequencies of all modes which penetrate below the CZ base: the depression in the adiabatie index [Py in the He II ionization zone causes the second signal., The transition of the temperature gradient from the adiabatic to radiative values at the CZ base gives rise to the oscillatory signal in frequencies of all modes which penetrate below the CZ base; the depression in the adiabatic index $\Gamma_1$ in the He II ionization zone causes the second signal.391 The two oscillatory signals have very different wavelengths and hence can be decoupled., The two oscillatory signals have very different wavelengths and hence can be decoupled.392 Not all modes see both features. only low degree modes (6S25) see the CZ base. higher degree modes only see the ionization zone. and the very high degree modes see neither.," Not all modes see both features, only low degree modes $\ell \la 25$ ) see the CZ base, higher degree modes only see the ionization zone, and the very high degree modes see neither."393 This signal has been used previously (o study the CZ base (Monteiro. Christensen-Dalseaard Thompson 1994; Basu. Antia Narasimha 1994). ancl also study changes in that region (Monteiro et al.," This signal has been used previously to study the CZ base (Monteiro, Christensen-Dalsgaard Thompson 1994; Basu, Antia Narasimha 1994), and also study changes in that region (Monteiro et al."394 2000)., 2000).395 In (his work we use the oscillatory signal from the depression in Py to study whether or not there are changes in Py in that region that are correlated with solar activity., In this work we use the oscillatory signal from the depression in $\Gamma_1$ to study whether or not there are changes in $\Gamma_1$ in that region that are correlated with solar activity.396 The amplitude of the signals from the CZ base as well as [rom (he Ie II ionization zone are small. hence we first amplify them by taking the fourth differences of the frequencies:," The amplitude of the signals from the CZ base as well as from the He II ionization zone are small, hence we first amplify them by taking the fourth differences of the frequencies:"397pep~poconst.,$p_B\sim p_l\sim {\rm const}$.398" Setting ay=1/3 and ap—0. one has Since f,ox. the svuchrotron losses are always donnant over the ICS losses."," Setting $\alpha_V=1/3$ and $\alpha_B=0$, one has Since $t_b\to\infty$, the synchrotron losses are always dominant over the ICS losses."399 The svuchrotron losses dominate over the adiabatic losses at f>f4., The synchrotron losses dominate over the adiabatic losses at $t>t_a$.400" Eq (313) implies the characteristic size One may express the total power as a power-law of the size. P,~D?."," Eq \ref{eq:ta3}) ) implies the characteristic size One may express the total power as a power-law of the size, $P_\nu\sim D^{-\delta}$."401" For D<D,. one has 6=3."," For $D<D_a$, one has $\delta=-3$."402" Since the particle spectra im the svuchrotron regine with fofg|Tay has the same slope as in the adiabatic case. one has 6=3 for D>D, as well."," Since the particle spectrum in the synchrotron regime with $t\ll t_0+\tau_{s0}/\gamma_*$ has the same slope as in the adiabatic case, one has $\delta=-3$ for $D>D_a$ as well."403 The particle spectruii due to the svuchrotron losses iu constant maenetic fields has the same form as (21)) with Tros replaced byzy., The particle spectrum due to the synchrotron losses in constant magnetic fields has the same form as \ref{eq:NSC}) ) with $\tau_{ICS}$ replaced by$\tau_{s0}$.404 The power grows with increasing size., The power grows with increasing size.405 However. when f~ty|ru corresponding to the size Doll|(Craoffo)(C9rpuο3µ?. the spectrum of the emitting particles steepeus from p to p|1 aud becomes indepeudeut of time.," However, when $t\sim t_0+\tau_{s0}/\gamma_*$, corresponding to the size $\sim D_0[1+(\tau_{s0}/t_0)(3\nu_{B0}/4\nu)^{1/2}]^{1/2}$, the spectrum of the emitting particles steepens from $p$ to $p+1$ and becomes independent of time."406 As a result. the power remains constant with à=0.," As a result, the power remains constant with $\delta=0$."407 The model would precict a steep spectrum with a=p/21 for p=2., The model would predict a steep spectrum with $\alpha=p/2=1$ for $p=2$.408" Although there is no direct measurements of the radio spectral iudex distrbution in the sample of 2dFCRS galaxies used to derive the P, D diagram in Figure 3.. there is strong evidence from the lower frequency data that low-hunuinositv radio ealalxies on average lave flatter radio spectra (Alauchetal.2003:Blundell.Rawlings&Willott 1999)."," Although there is no direct measurements of the radio spectral index distrbution in the sample of 2dFGRS galaxies used to derive the $P_\nu$ $D$ diagram in Figure \ref{fig:LRG}, there is strong evidence from the lower frequency data that low-luminosity radio galalxies on average have flatter radio spectra \citep{metal03,betal99}."409. A possible interpretation for this spectral trend is that for low-Iuninositv radio galaxies. the core component becomes important (Sleeetal.1991).. 1.6. one may obtain fat spectra by appealing to solf-absorption.," A possible interpretation for this spectral trend is that for low-luminosity radio galaxies, the core component becomes important \citep{setal94}, i.e. one may obtain flat spectra by appealing to self-absorption."410 However. the steep spectral feature predicted by the constant-pressure model would extend to the majority of loxw-Iuninositv sources. which is not consistent with observations.," However, the steep spectral feature predicted by the constant-pressure model would extend to the majority of low-luminosity sources, which is not consistent with observations."411" Figure |. shows plots of P, as à function of D for ow-Iuninosityv sources (FR Is). obtained iu the coustaut-xessure model with :=0 aud ο=0."," Figure \ref{fig:PD2} shows plots of $P_\nu$ as a function of $D$ for low-luminosity sources (FR Is), obtained in the constant-pressure model with $z=0$ and $\beta=0$."412 The model xuwanmieters and their typical values are listed in Table 2.., The model parameters and their typical values are listed in Table \ref{tab:parameters}.413 Tf oue considers the external iiecdiunmi as an ideal gas. he three parameters. ο. Ty and p. are not indepedeut.," If one considers the external medium as an ideal gas, the three parameters, $\rho_c$, $T_0$ and $p_c$ are not indepedent."414" Ilere we treat the external pressure as an indepeudeut xuanieter and ds assuned to be po,=pe3x10H Pa."," Here we treat the external pressure as an independent parameter and is assumed to be $p_{ex}=p_c=3\times10^{-11}\,\rm Pa$ ."415 As we assuue that the maguctic cucrey is In equipartition. with kinetic energv of particles. the nagnetic feld pressure is not an indepeudent parameter.," As we assume that the magnetic energy is in equipartition with kinetic energy of particles, the magnetic field pressure is not an independent parameter."416 The justifications for the choice of the particle spectrum are the sune as that for high-luninosity sourcesparticles are accelerated by diffusive shocks (cf., The justifications for the choice of the particle spectrum are the same as that for high-luminosity sources–particles are accelerated by diffusive shocks (cf.417 Sec., Sec.418 1)., 4).419 The typical value of the adiabatic iudex. - 1/23. is applicable for relativistic plasmas. (," The typical value of the adiabatic index, $\Gamma=4/3$ , is applicable for relativistic plasmas. ("420For a cold plasiia. one has EP2 5/3.),"For a cold plasma, one has $\Gamma=5/3$ .)"421 The dividing liue between high- aud low-huninosity sources iu terius of the input power from, The dividing line between high- and low-luminosity sources in terms of the input power from422"the IRAC and/or the MIPS photometry, and an impressive consistency is evident between the two data sets, which were taken several months apart (see Tables 2 and 3)).","the IRAC and/or the MIPS photometry, and an impressive consistency is evident between the two data sets, which were taken several months apart (see Tables \ref{spitzerphot} and \ref{spitzerspec}) )."423" Variability is detected in the source 3C 390.3, however, not of the strength typical of blazars."," Variability is detected in the source 3C 390.3, however, not of the strength typical of blazars."424 T'he flux increase is a factor of «2 over period of four years., The flux increase is a factor of $<2$ over a period of four years.425" Given athat the infrared emission in our sources is thermal and that the hot dust emission seems to be emitted isotropically (see Section 4.1.1)), we can now carry out a consistency check for the calculated viewing angles."," Given that the infrared emission in our sources is thermal and that the hot dust emission seems to be emitted isotropically (see Section \ref{blackbody}) ), we can now carry out a consistency check for the calculated viewing angles."426" Along the lines of argument presented by ?,, we plot in Fig."," Along the lines of argument presented by \citet{Wills95}, , we plot in Fig."427" 7 the ratio between the integrated core radio luminosity (calculated from the data listed in Table 1)) and the peak luminosity of the hot blackbody component (calculated from the fluxes listed in Table 6,, column (7)) versus the jet viewing angle."," \ref{vatest} the ratio between the integrated core radio luminosity (calculated from the data listed in Table \ref{general}) ) and the peak luminosity of the hot blackbody component (calculated from the fluxes listed in Table \ref{dust}, column (7)) versus the jet viewing angle."428" In such a diagram, we expect that the stronger a source is relativistically beamed, the higher its ratio between beamed and isotropic emission."," In such a diagram, we expect that the stronger a source is relativistically beamed, the higher its ratio between beamed and isotropic emission."429 Fig., Fig.430" 7 shows that the resulting trend in viewing angle for our sample is qualitatively correct; the smaller the viewing angle, the higher the ratio between (beamed) core radio power and (isotropic) dust luminosity."," \ref{vatest} shows that the resulting trend in viewing angle for our sample is qualitatively correct; the smaller the viewing angle, the higher the ratio between (beamed) core radio power and (isotropic) dust luminosity."431" The only pronounced exception is the source S5 0615+820, for which the viewing angle appears to be highly overestimated."," The only pronounced exception is the source S5 $+$ 820, for which the viewing angle appears to be highly overestimated."432" Due to the shortcomings in AGN torus models invoking continuous dust distributions, new models based on clumpy media have recently been put forward (e.g.,??????7).."," Due to the shortcomings in AGN torus models invoking continuous dust distributions, new models based on clumpy media have recently been put forward \citep[e.g.,][]{Schart05, Schart08, Hoenig06, Hoenig10b,433 Nen02, Nen08a, Nen08b}."434" The most detailed of these models are those of Nenkova and collaborators (named CLUMPY), and they can be accessedon-line?."," The most detailed of these models are those of Nenkova and collaborators (named CLUMPY), and they can be accessed."435". In short, these authors solved the radiative transfer problem in clumpy media by assuming that the medium is composed of clouds that are individually optically thick (Tv 21), that each cloud can be considered a point sourceof"," In short, these authors solved the radiative transfer problem in clumpy media by assuming that the medium is composed of clouds that are individually optically thick $\tau_{\rm V}$$\gg$ 1), that each cloud can be considered a point sourceof"436outward lavers of the star falls outo tjio black hole.,outward layers of the star falls onto the black hole.437 In fgure 2 we plot the critical accretion rates for disks accreting 0.1 and LO Mslo , In figure 2 we plot the critical accretion rates for disks accreting $0.1$ and $10$ $M_\odot s^{-1}$.438Note that the accretion rate through the disk iced. uot be related to (and at late times. is 1uuci higher than) the accretion along he rotation axis.," Note that the accretion rate through the disk need not be related to (and at late times, is much higher than) the accretion along the rotation axis."439 For colmparison. we plot the accretion ratess Of stars with masses range from ML... (Raascher et al.," For comparison, we plot the accretion rates of stars with masses ranging from $M_\odot$ (Rauscher et al."440 2002) versus mass coorinate of the accreting liass laver., 2002) versus mass coordinate of the accreting mass layer.441 When the accretion rate of stellar| qnaterial ‘all gaoue the polar axis crops beow the critical aceretio rrate for a given disk. the jeutrinos froni he csk will dive an explosion and. very lisely. cdigupt he cutive star.," When the accretion rate of stellar material falling along the polar axis drops below the critical accretion rate for a given disk, the neutrinos from the disk will drive an explosion and, very likely, disrupt the entire star."442 For a given disk structure. hen. this crossing point gives a rot ehestimate of he remmant mass (e.g. from Fig.," For a given disk structure, then, this crossing point gives a rough estimate of the remnant mass (e.g. from Fig."443" 2 we seo that ‘OL a dis caceretion rate of (LAL.1 outo a black role rotating near breakup: a=0.95. the remlant lack ho Cinass for a 20A, star is roughly LOAL...)"," 2 we see that for a disk accretion rate of $0.1 M_\odot s^{-1}$ onto a black hole rotating near breakup: a=0.95, the remnant black hole mass for a $30M_\odot$ star is roughly $10M_\odot$ .)"444 Noe also. tiat if the neutriuo emission was as uch as hat eiven by he disks accreting at LWAL.s+ TOu Popham ct al. (," Note also, that if the neutrino emission was as high as that given by the disks accreting at $10M_\odot s^{-1}$ from Popham et al. ("4451999). then the explosion would occur nmjiediatelv.,"1999), then the explosion would occur immediately."446 However. Di Matteo. Pexaa. Narava1 (2002) ive found hat these cisss actuaIv produce a nich lower 101trino flux.," However, Di Matteo, Perna, Narayan (2002) have found that these disks actually produce a much lower neutrino flux."447 Eveπα if πιch ligh neutrino lhuuinosiies could be constructed. hey wot14 disrupt their star ininediately.," Even if such high neutrino luminosities could be constructed, they would disrupt their star immediately."448 We note that these results aro 0ilv rough approxiniafions. since a inniber of caveats πιά! he quantitative accuracy of these caculations.," We note that these results are only rough approximations, since a number of caveats limit the quantitative accuracy of these calculations."449 Besides asstuning a fairly simple model for he 110)meitum deposition. relativistic effects ou he j0utiiιο. cherey ancl 1101uentunu. the effects of rotation on the 1falling matter aud he evolution of the black hole mass and spin were all iceleced.," Besides assuming a fairly simple model for the momentum deposition, relativistic effects on the neutrino energy and momentum, the effects of rotation on the infalling matter and the evolution of the black hole mass and spin were all neglected."450 If maenetic feds drive the explosion. he explosion can occur at nmuuch earjer fines. alcL sinularly. the disk wiids seen by MacFadye- Woosley (2000). also would eject tjo star af ecarlicr times.," If magnetic fields drive the explosion, the explosion can occur at much earlier times, and similarly, the disk winds seen by MacFadyen Woosley (2000) also would eject the star at earlier times."451" Most oftrese effects wotd lead te hieher critical deusities aid lower remjut black hol Classes,", Most of these effects would lead to higher critical densities and lower remnant black hole masses.452 Ilowever. if woe restrict ourselves to neutrine-driven explosions ouly. i6 dmnajor uucertaintv is the strucure of the ]xogenitor star.," However, if we restrict ourselves to neutrino-driven explosions only, the major uncertainty is the structure of the progenitor star."453 Figure 3 slrows tli| dmnufall accretion rates for rotating and non-rotatiug stars of O and GU M. (Ileger 2002)., Figure 3 shows the infall accretion rates for rotating and non-rotating stars of 40 and 60 $M_\odot$ (Heger 2002).454 Note hat the renulant lass differs dramatically depeudius upon the amount of rotation., Note that the remnant mass differs dramatically depending upon the amount of rotation.455 Couparing the nou-otatiug 60 AL. case of Fie.3 witli that of Fie.2 shows the variations arising from stars produced with different versions of the same sCllar code: Rauscher et al. (, Comparing the non-rotating 60 $M_\odot$ case of Fig.3 with that of Fig.2 shows the variations arising from stars produced with different versions of the same stellar code: Rauscher et al. (4562002) and Ileger (2002) use different versions of the IE&epler code (Weaver. Zimerman. Woosley 1975).,"2002) and Heger (2002) use different versions of the Kepler code (Weaver, Zimmerman, Woosley 1978)."457 Iu addition to 1ucertaimties in single star evolution. it is likely that collapsar GRBs arise from binary syvstenis. ancl binary progenitors of GRBs have not vet been constructed.," In addition to uncertainties in single star evolution, it is likely that collapsar GRBs arise from binary systems, and binary progenitors of GRBs have not yet been constructed."458" For most values of the disk accretion rates (wilin roughly 0.051M.s+) the critical deusitv lies iu a fairly narrow range between 10!156cin""s"," For most values of the disk accretion rates (within roughly $0.05-1459M_\odot s^{-1}$ ) the critical density lies in a fairly narrow range between $10^4-10^8 {\rm g \, cm^{-3}}$."460" These deusities agree well witi the results frou, MlacFadven Woosley (1999).", These densities agree well with the results from MacFadyen Woosley (1999).461" For lower disk accretion rates. the energy deposition fiΌλα neufrmo annihilation decreases dramatically aud the critical deusitv for explosions drops below 10οcm""s"," For lower disk accretion rates, the energy deposition from neutrino annihilation decreases dramatically and the critical density for explosions drops below $10 {\rm g \, cm^{-3}}$."462 The maerial along the voles does not reach his density until nearly all of he star has :vcereted outo the black hole. aud this will not produce a GRD.," The material along the poles does not reach this density until nearly all of the star has accreted onto the black hole, and this will not produce a GRB."463 Similarly. lugher neutrine unmumnosities would disrupt the star inunediatelv and probally* never form du nature.," Similarly, higher neutrino luminosities would disrupt the star immediately and probably never form in nature."464 With such a ALLOW LANE» of explosion conditions at the black role source. one would expect some similarities in the CRB outbursts produced by meutiimos.," With such a narrow range of explosion conditions at the black hole source, one would expect some similarities in the GRB outbursts produced by neutrinos."465 However. bear in 1üind that the propogation of the jet through the star (which cau differ iu cüffereut roecnitors) can significantly alter the observable outburst.," However, bear in mind that the propogation of the jet through the star (which can differ in different progenitors) can significantly alter the observable outburst."466 Wha does differ dramaically is the time after he collapse at which the explosion occurs., What does differ dramatically is the time after the collapse at which the explosion occurs.467 From Heures 2 and 3. we know the mass zone of the star hat is ¢riven to explosion x the neutrinos.," From figures 2 and 3, we know the mass zone of the star that is driven to explosion by the neutrinos."468" Using he 10.607, of Heger and asstuning that. along tie rotation axis. 1C critical mass zone collapses at free-fall. we find tat disks accreting at OMus! dive explosious at much differeut times."," Using the $40,60 M_\odot$ of Heger and assuming that, along the rotation axis, the critical mass zone collapses at free-fall, we find that disks accreting at $0.1M_\odot469s^{-1}$ drive explosions at much different times."470 For the LOAL.. star. iufalliug material along the pole is turned around at 50.60 or 104 after the initial οςapse for black hole spin rates of asO.95.0.75 and 0. respecively.," For the $M_\odot$ star, infalling material along the pole is turned around at 50,60 or $10^4$ s after the initial collapse for black hole spin rates of a=0.95,0.75 and 0, respectively."471" For the GOAL. star. the corresponding exXosion fines are: 3h, S00. 1x LO%s. Ilence. we should expect a"," For the $M_\odot$ star, the corresponding explosion times are: 35, 300, $3.1\times10^6$ s. Hence, we should expect a"472reprocessed with the “chandra_rrepro” script using the subpixel event repositioning algorithm of Lietal.(2004).,reprocessed with the repro” script using the subpixel event repositioning algorithm of \cite{LI04.4}.473". Intervals of strong background flaring were searched for, but none were found."," Intervals of strong background flaring were searched for, but none were found."474" We made a sky image of the field of at a resolution of 000492 per pixel with events in the 0.3-8.0 keV energy range, and we fit two-dimensional models to that image."," We made a sky image of the field of at a resolution of 0492 per pixel with events in the 0.3–8.0 keV energy range, and we fit two-dimensional models to that image."475 All fits were performed in Sherpa (Freemanetal.2001) using modified Cash statistics in Sherpa) and the Nelder(1979)&Mead(1965) optimization(“cstat” method (“simplex” in Sherpa)., All fits were performed in Sherpa \citep{FR01.2} using modified \citet{CA79.1} statistics (“cstat” in Sherpa) and the \citet{NE65.1} optimization method (“simplex” in Sherpa).476" A family of fits was performed, using a grid of parameter starting points to ensure a proper sampling of the multidimensional fit space."," A family of fits was performed, using a grid of parameter starting points to ensure a proper sampling of the multidimensional fit space."477 We fit a two-component source model with a fixed background (based on a source-free region near JJ171544.05+600835.7)., We fit a two-component source model with a fixed background (based on a source-free region near J171544.05+600835.7).478" Thesource model was a B profile, which is a two-dimensional Lorentzian with a varying power law of the form I(r)=A(1+(r/ro)?)-? and is a good match to the PPSF."," Thesource model was a $\beta$ profile, which is a two-dimensional Lorentzian with a varying power law of the form $I(r) = A(1+(r/r_0)^2)^{-\alpha}$ and is a good match to the PSF."479" Based on other work (Pooleyetal. the power law index o was tied to the rp parameter, and 2009),,both components were required to have the same ro."," Based on other work \citep{PO09.1}, the power law index $\alpha$ was tied to the $r_0$ parameter, and both components were required to have the same $r_0$."480 Their positions and amplitudes were unconstrained., Their positions and amplitudes were unconstrained.481" The best fit amplitudes are and counts pixel""! for the northern and southern sources, respectively, and where the southern source is detected at 3.76."," The best fit amplitudes are and counts $^{-1}$ for the northern and southern sources, respectively, and where the southern source is detected at $\sigma$."482" The two X-ray components are separated by 1.85+0.22 hz kpc, or 068+0/08, at a position angle of 147?X9? east of north, where both the separation and the position angle are consistent with those measured for the two emission components in the Lick/Kast longslit spectra 2.2))."," The two X-ray components are separated by $1.85 \pm 0.22$ $h^{-1}_{70}$ kpc, or $0\farcs68\pm0\farcs08$, at a position angle of $147^\circ \pm 9^\circ$ east of north, where both the separation and the position angle are consistent with those measured for the two emission components in the Lick/Kast longslit spectra \ref{lick}) )."483 The best fit model is shown in Figure 2.., The best fit model is shown in Figure \ref{fig:xrayimage}.484" To estimate the fluxes of the two components, we cannot reliably extract spectra of and make response files for the two separately."," To estimate the fluxes of the two components, we cannot reliably extract spectra of and make response files for the two separately."485 We therefore extracted a spectrum of both sources together and use the results of our two-dimensional image fits to assign appropriate fractions of the total flux to each component., We therefore extracted a spectrum of both sources together and use the results of our two-dimensional image fits to assign appropriate fractions of the total flux to each component.486 We fit the unbinned spectrum in Sherpa using cstat statistics and the simplex method., We fit the unbinned spectrum in Sherpa using cstat statistics and the simplex method.487 The spectral model was a simple absorbed power law with the column density constrained to be at least the Galactic value of ng=2.6x102°cm-? (Dickey&Lockman1990)., The spectral model was a simple absorbed power law with the column density constrained to be at least the Galactic value of $n_H=\ee{2.6}{20}~\pcmsq$ \citep{DI90.1}.488" No additional absorption was preferred in the fit, and the best fit power law index was 1.9+0.2."," No additional absorption was preferred in the fit, and the best fit power law index was $1.9\pm0.2$."489 The total unabsorbed 0.5-8 keV flux is er, The total unabsorbed 0.5–8 keV flux is } .490"gcm~?uncertainty1.53:0.4x10714 s-!.. The was calculated using the “sample_eenergy_fflux” tool in Sherpa, which takes into account uncertainties in all model parameters."," The uncertainty was calculated using the flux” tool in Sherpa, which takes into account uncertainties in all model parameters."491" Using the results of our two-dimensional image fit, the northern component has a best-fit flux of Fossa=L1x10-!4ergcm?5”, and the southern component has Fo5-3;10715ergcem? s7!."," Using the results of our two-dimensional image fit, the northern component has a best-fit flux of $F_{0.5-8}=\ee{1.1}{-14}~\ergcms$, and the southern component has $F_{0.5-8}=\ee{4.4}{-15}~\ergcms$ ."492" The 2-10 keV fluxes are P5.10=64+3.1x10715ergοιs! for the northern component and Foo=2.741.5x10715ergcms! for the southern component, which we compare? to the 2-10 keV fluxes predicted from the fluxes using the scaling relation for Type 2 AGN in Heckmanetal. (2005).."," The 2–10 keV fluxes are $F_{2-10}=6.4 \pm 3.1 \times 10^{-15}~\ergcms$ for the northern component and $F_{2-10}=2.7 \pm 1.5 \times 10^{-15}~\ergcms$ for the southern component, which we compare to the 2--10 keV fluxes predicted from the fluxes using the scaling relation for Type 2 AGN in \cite{HE05.1}."493" The predicted 2-10 keV fluxes are 3.3+7.9x10:14ergcm?s! and 2.1+5.1x10714ergcm~?s-! for the redshifted and blueshifted components ofA5007,, respectively."," The predicted 2–10 keV fluxes are $3.3 \pm 7.9 \times 10^{-14}~\ergcms$ and $2.1 \pm 5.1 \times 10^{-14}~\ergcms$ for the redshifted and blueshifted components of, respectively."494 The measured 2-10 keV fluxes [Oare III]hence factor of several lower than but within the broad uncertaintiesa of the predictions from Heckmanetal., The measured 2–10 keV fluxes are hence a factor of several lower than but within the broad uncertainties of the predictions from \cite{HE05.1}.495" Although we cannot fit (2005)..separate spectra for the two components, we can extract the counts in small regions centered on them and form hardness ratios, defined as HR=(H—S)/(H4- where H is the number of counts in the 2-8 keV rangeS) and S is the number of counts in the 0.5-2 keV range."," Although we cannot fit separate spectra for the two components, we can extract the counts in small regions centered on them and form hardness ratios, defined as $\mathrm{HR}=(H-S)/(H+S)$ where $H$ is the number of counts in the 2–8 keV range and $S$ is the number of counts in the 0.5–2 keV range."496" Counts were extracted from 0/225 radius regions centered on each source, yielding 20 counts from the northern source with HR=—0.57*$ and 10 counts from the southern source with HR15= —0.37*935."," Counts were extracted from 25 radius regions centered on each source, yielding 20 counts from the northern source with $\mathrm{HR}=-0.57\err{0.15}{0.19}$ and 10 counts from the southern source with $\mathrm{HR}=-0.37\err{0.24}{0.30}$ ."497 Uncertainties on the hardness ratios were calculated using the Bayesian Estimation of Hardness Ratios package (Parketal., Uncertainties on the hardness ratios were calculated using the Bayesian Estimation of Hardness Ratios package \citep{PA06.1}.498" Judging from the measured hardness ratios, neither 2006)..source is as hard as would be expected for moderately absorbed (but not Compton-thick) AGN, although the signal-to-noise ratio is very modest."," Judging from the measured hardness ratios, neither source is as hard as would be expected for moderately absorbed (but not Compton-thick) AGN, although the signal-to-noise ratio is very modest."499is explained in the following proof.,is explained in the following proof.500" For thermal emission mocified by an emissivity function that scales as 7. the total energy. emitted in a single wave band (ων). should scale as where The total integrated thermal emission Lior, will scale according to The ratio of vl, to Li will be approximately constant (e.g. independent. of grain. temperature) when it is close to à maximum. which occurs when Since e""7 lI. then Assuming that 97 equals 2 (Li&Draine2001).. this condition is met at. 160 jn when the dust temperature is 15 Ix. Because the peak of the spectral energy distribution is actually at à shorter wavelength than 160 yam. the ratio of 160 jin emission to total infrared emission should decrease slightly as the illuminating raciation field increases."," For thermal emission modified by an emissivity function that scales as $\nu^\beta$, the total energy emitted in a single wave band $\nu501L_\nu$ ) should scale as where The total integrated thermal emission $L_{total}$ will scale according to The ratio of $\nu L_\nu$ to $L_{total}$ will be approximately constant (e.g. independent of grain temperature) when it is close to a maximum, which occurs when Since $e^x >> 1$ , then Assuming that $\beta$ equals 2 \citep{ld01}, this condition is met at 160 $\mu$ m when the dust temperature is $\sim15$ K. Because the peak of the spectral energy distribution is actually at a shorter wavelength than 160 $\mu$ m, the ratio of 160 $\mu$ m emission to total infrared emission should decrease slightly as the illuminating radiation field increases."502 We use the 3.6. 8.0. 24. 70. ancl 160 jam data taken withSpitzer as part of SINGS.," We use the 3.6, 8.0, 24, 70, and 160 $\mu$ m data taken with as part of SINGS."503 The 3.6 ancl 8.0 jim observations were performed with LAC., The 3.6 and 8.0 $\mu$ m observations were performed with IRAC.504 The observations for cach object consisted of a series of 5 arenin 5 aremin individual frames taken in either a mosaic or a single field αππου pattern., The observations for each object consisted of a series of 5 arcmin $\times$ 5 arcmin individual frames taken in either a mosaic or a single field dither pattern.505 The 24. 70. ancl 160. pam observations performed with AILPS are composed of two scan maps for each target.," The 24, 70, and 160 $\mu$ m observations performed with MIPS are composed of two scan maps for each target."506 Each object was observed twice in cach wave band to identify ancl remove transient phenomena. particularly asteroids.," Each object was observed twice in each wave band to identify and remove transient phenomena, particularly asteroids."507 The full-width ballmasxima (EWIIM) of the point spread functions. (PSEs). as stated. in the. Spitzer Observer's Manual (SpitzerScienceCenter2006) are l.y.note 2.0. 6. pzand BS aresec at 3.6. 8.0. 24. and. 160. sam. respectively.," The full-width half-maxima (FWHM) of the point spread functions (PSFs), as stated in the Spitzer Observer's Manual \citep{sscmanual06}, are 1.7, 2.0, 6, and 38 arcsec at 3.6, 8.0, 24, and 160 $\mu$ m, respectively."508" Details on the observations can be found in the documentation for the SINGS fourth cata delivery (SINGSuniformly.""oam2006) ", Details on the observations can be found in the documentation for the SINGS fourth data delivery \citep{sings06} .509The 7]RAC data were processed using the SINGS LRAC pipeline. which combines multiple frames of cata using a drizzle technique.," The IRAC data were processed using the SINGS IRAC pipeline, which combines multiple frames of data using a drizzle technique."510 A deseription of the technique is presented in Reeanetal.(2006)., A description of the technique is presented in \citet{retal06}.511. The final images may contain residual background. emission. from. the telescope or sky that is subtracted during the analysis., The final images may contain residual background emission from the telescope or sky that is subtracted during the analysis.512 The MIPS. data were processed using the MIPS Data Analysis Tools version 3.06 (Gordonetal.2005)., The MIPS data were processed using the MIPS Data Analysis Tools version 3.06 \citep{getal05}.513. Additional software was used to remove zocliacal light emission and improve the fatfielding in the 24 jim data and to remove short-term variations in the background signal (commonly referred to as drift) in the 70 ancl 160 pm data., Additional software was used to remove zodiacal light emission and improve the flatfielding in the 24 $\mu$ m data and to remove short-term variations in the background signal (commonly referred to as drift) in the 70 and 160 $\mu$ m data.514 Any additional background olfset left in the final images was measured in regions outside the optical discs and. subtracted., Any additional background offset left in the final images was measured in regions outside the optical discs and subtracted.515 Additional details are presented. in endoοἱal.(2006)..., Additional details are presented in \citet{betal06}.516 Full details on the data processing are also available in the SINGS documentation for the fourth data delivery (SINGSTeam2006)., Full details on the data processing are also available in the SINGS documentation for the fourth data delivery \citep{sings06}.517. 'To perform this analysis. we need to resolve substructures in the 160 jaa images. which have PSEs with FWIIM of 38 arcsec.," To perform this analysis, we need to resolve substructures in the 160 $\mu$ m images, which have PSFs with FWHM of 38 arcsec."518 We therefore limit the sample to spiral galaxies in SINGS where the major axes of the Dos isophote specifiec by deVaucouleursetal.(1991). are larger than 5 arcmin., We therefore limit the sample to spiral galaxies in SINGS where the major axes of the $_{25}$ isophote specified by \citet{ddcbpf91} are larger than 5 arcmin.519 Since we want to be able to distinguish between radial colour variations and colour variations related to the presence of substructures ancl since such substructures are dillieult. to study in eclee-on galaxies. we only use galaxies that are inclined less than 60deg.," Since we want to be able to distinguish between radial colour variations and colour variations related to the presence of substructures and since such substructures are difficult to study in edge-on galaxies, we only use galaxies that are inclined less than $\sim60\deg$."520 Phe inclinations are calculate using The value q is the observed (projected) minor-to-major axis ratio., The inclinations are calculated using The value $q$ is the observed (projected) minor-to-major axis ratio.521 Phe value qi is the intrinsic optical axial ratio (the ratio of the unprojected optical axis perpendicular the plane of the galaxy to the cliameter of the disc). which is equivalent to 0.20 for most cise galaxies. (Lully1998).," The value $q_o$ is the intrinsic optical axial ratio (the ratio of the unprojected optical axis perpendicular the plane of the galaxy to the diameter of the disc), which is equivalent to 0.20 for most disc galaxies \citep{t88}."522. Jocause the optical disc of NGC 5194 may be distorted by its interaction with NGC 5195. its inclination is not calculated using this equation.," Because the optical disc of NGC 5194 may be distorted by its interaction with NGC 5195, its inclination is not calculated using this equation."523 Instead. the inclination as well as the position angle given by Giarcta-Gómoezetal.(2002). are used for the analysis.," Instead, the inclination as well as the position angle given by \citet{gab02} are used for the analysis."524 Six of the SINGS galaxies. that meet. the above criteria are unsuitable for the analysis., Six of the SINGS galaxies that meet the above criteria are unsuitable for the analysis.525 NGC 1512. and NGC 4826 are not used. because only the central regions were detected. at the 5o. levels in all of the convolved maps (described in the next. section))., NGC 1512 and NGC 4826 are not used because only the central regions were detected at the $5\sigma$ levels in all of the convolved maps (described in the next section).526 The 8.0 jin images of NGC LOOT. NGC 1566. and NGC 4736 are. heavily wlected by muxbleed artelacts (artificially bright. cobumns of pixels associated with high-surlace brightness sources) that cross over significant fractions of the optical disces. so those data are not usable for this analysis.," The 8.0 $\mu$ m images of NGC 1097, NGC 1566, and NGC 4736 are heavily affected by muxbleed artefacts (artificially bright columns of pixels associated with high-surface brightness sources) that cross over significant fractions of the optical discs, so those data are not usable for this analysis."527 “Pwo very bright foreground. stars in the 3.6 and 8.0 jim images. of NGC 3621 cause problems in the analysis. so NGC 3621 needs to be excluded. from the sample as well.," Two very bright foreground stars in the 3.6 and 8.0 $\mu$ m images of NGC 3621 cause problems in the analysis, so NGC 3621 needs to be excluded from the sample as well."528 Phe other 15 galaxies that meet the above criteria. which are roughly distributed. between Hubble types Sab ancl Sd. are listed in Fable 1 along with information on the galaxies ντ ΡΜ axes. distances. nuclear spectral types. and nebular oxvgen abundances (12|log(O/I11). which is treated as representative of the global metallicities of the ealaxies)," The other 15 galaxies that meet the above criteria, which are roughly uniformly distributed between Hubble types Sab and Sd, are listed in Table \ref{t_sample} along with information on the galaxies' morphologies, optical axes, distances, nuclear spectral types, and nebular oxygen abundances (12+log(O/H), which is treated as representative of the global metallicities of the galaxies)."529 Alany studies of infrared. colour variations within individual galaxies have relied. on [lux densities measured within discrete subregions that are chosen either by eve or by source identification software., Many studies of infrared colour variations within individual galaxies have relied on flux densities measured within discrete subregions that are chosen either by eye or by source identification software.530 However. thisselection process may be biased.," However, thisselection process may be biased."531 Some subregions within the galaxy, Some subregions within the galaxy532detail in the Appoeudix below.,detail in the Appendix below.533 At face value. LEs that lic above the lower dashed curve overproduce the ionizing vackeround: those above the upper dashed curve by a actor of 220.," At face value, LFs that lie above the lower dashed curve over–produce the ionizing background; those above the upper dashed curve by a factor of $>20$."534 Tlowever. iu practice this result has aree uncertainties," However, in practice this result has large uncertainties."535 First. although the adopted quasar LF vields the total ionizing ciissivity. the prediction of he ioniziung backerounc involves the mean free path of ioniziug photous. which is highly uucertain at the redshifts of interest here.," First, although the adopted quasar LF yields the total ionizing emissivity, the prediction of the ionizing background involves the mean free path of ionizing photons, which is highly uncertain at the redshifts of interest here."536 A small mean free path would reduce the vackeround., A small mean free path would reduce the background.537 Secoud. a smaller fraction of ionizing photous wieht escape from the deuse surroundings of highτου» quasars than from their lowerredshift counterparts.," Second, a smaller fraction of ionizing photons might escape from the dense surroundings of high–redshift quasars than from their lower–redshift counterparts."538 Tun this paper. we computed the expected lensing probabilities of 26 quasars by intervening galaxies.," In this paper, we computed the expected lensing probabilities of $z\sim6$ quasars by intervening galaxies."539 The a posteriori probability that az~6 quasar is stronely leused (bv a factor po>10 in flux cnhancciment). but without producing two images detectable im the Sloan Survey. can be very large. depending on the shape of the LF.," The a posteriori probability that a $z \sim 6$ quasar is strongly lensed (by a factor $\mu>10$ in flux enhancement), but without producing two images detectable in the Sloan Survey, can be very large, depending on the shape of the LF."540 The LFs we use are consistent with other available observational coustraiuts. vet these coustraimts still allow for a wide range of possibilities.," The LFs we use are consistent with other available observational constraints, yet these constraints still allow for a wide range of possibilities."541" Though au observed bright-cud slope of 3),=1.3 could be ruled out at the 99 percent confidence level (Fan et ((20013). lensing alters the slope so that the appareut LF willhave a slope close to ~23.0 if inagnificatiou bias is important."," Though an bright-end slope of $\beta_h=4.3$ could be ruled out at the 99 percent confidence level (Fan et (2001)), lensing alters the slope so that the apparent LF willhave a slope close to $\sim 3.0$ if magnification bias is important."542 As illustrated in Fig. L.," As illustrated in Fig. \ref{fig:lfobs},"543 even the steepest intrinsic LF we consider. with a bright eud slope of £5. is consistent with the SDSS Init ou slope.," even the steepest intrinsic LF we consider, with a bright end slope of $4.5$, is consistent with the SDSS limit on slope."544 This will be true for arbitrarily steep slopes. provided that the characteristic DIuniuositv is uot mereased.," This will be true for arbitrarily steep slopes, provided that the characteristic luminosity is not increased."545 Iu a similar probability calculation. Writhe Loch (2002) concluded. that the observed probability reaches 30% that a single 2~6 quasar is lensed and maenified by a factor of LO or more.," In a similar probability calculation, Wyithe Loeb (2002) concluded that the observed probability reaches $30 \%$ that a single $z \sim 6$ quasar is lensed and magnified by a factor of 10 or more."546 If we restrict our analysis to the choices of LFs cousidered in their paper. we aeree with this result.," If we restrict our analysis to the choices of LFs considered in their paper, we agree with this result."547 However. we here use a wider range of quasar LFs aud conclude that the lensing probability can reach essentiallyL00%.," However, we here use a wider range of quasar LFs and conclude that the lensing probability can reach essentially."548. As a result. the current observations are consistent with all four 26 SDSS quasars being stronely leused.," As a result, the current observations are consistent with all four $z \sim 6$ SDSS quasars being strongly lensed."549 If the probability that all four quasars are lensed were laugh. then this would alleviate the problematic tine constraints on assembliug supermassive black holes at the earliest stages in the evolution of the universe.," If the probability that all four quasars are lensed were high, then this would alleviate the problematic time constraints on assembling supermassive black holes at the earliest stages in the evolution of the universe."550 However. iu a separate analysis. based on the apparcutly laree size of the ionized region around the SDSS quasar at +=6.28. Taian Cen (2002) place a stroug constraint on the eusing magnification of this source. and find qi«5.," However, in a separate analysis, based on the apparently large size of the ionized region around the SDSS quasar at $z=6.28$, Haiman Cen (2002) place a strong constraint on the lensing magnification of this source, and find $\mu<5$."551 This result depeuds primarily on the assumption that the source is clubedded iu a neutral (rather than ionized) intergalactic ueciuin., This result depends primarily on the assumption that the source is embedded in a neutral (rather than ionized) intergalactic medium.552 We have also considered the probabilities for lensing events that would have been detectable by SDSS., We have also considered the probabilities for lensing events that would have been detectable by SDSS.553 The ack of such detections can be used to place constraints on the quasar LF., The lack of such detections can be used to place constraints on the quasar LF.554 Although constraints from the curreut our quasars are mild. the situation is likely to improve.," Although constraints from the current four quasars are mild, the situation is likely to improve."555 As illustrated in Fig. 6..," As illustrated in Fig. \ref{fig:contour0},"556 increasing the SDSS sample from £ to 20 objects. something that is likely to happen over the next ew vears. would allow one to rule out interesting quasar LF inodels.," increasing the SDSS sample from 4 to 20 objects, something that is likely to happen over the next few years, would allow one to rule out interesting quasar LF models."557 The expected probability of detecting multiple nuages is also sensitive to the angular resolution of the observations., The expected probability of detecting multiple images is also sensitive to the angular resolution of the observations.558" In terms of the counstraiuts ou the shape of the intrinsic LE. observing four quasars at a resolution of 0.1"" is roughly equivalent to observing 20 objects at the resolution of the SDSS (1)."," In terms of the constraints on the shape of the intrinsic LF, observing four quasars at a resolution of $0.1 ''$ is roughly equivalent to observing 20 objects at the resolution of the SDSS $1 ''$ )."559 Hence. upcoming observations. in particular with theTelescope.. should reveal whether a siguificaut fraction of the +~6 quasars is lensed. and will allow us to place strong constraints on their intrinsic LE.," Hence, upcoming observations, in particular with the, should reveal whether a significant fraction of the $z\sim 6$ quasars is lensed, and will allow us to place strong constraints on their intrinsic LF."560 We thank Michael Strauss aud Niaolwi Faun for many useful ciscussions., We thank Michael Strauss and Xiaohui Fan for many useful discussions.561 The work preseuted here is based ou the senior thesis of JC at Princeton Uhiversity., The work presented here is based on the senior thesis of JC at Princeton University.562 She thanks Neta Dahcall for her cucouragement and advice., She thanks Neta Bahcall for her encouragement and advice.563 This work was supported by NASA through the Iubble Fellowship graut HE-01119.01-09À. awarded to ZII bx the Space Telescope Scieuce. Tustitute. which is operated by the Association of Universities for Research in Απώμώμιν. Iuc.. for NASA under coutract NAS 5-26555.," This work was supported by NASA through the Hubble Fellowship grant HF-01119.01-99A, awarded to ZH by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA under contract NAS 5-26555."564 JS acknowledges support from the W. M. Weck foundation., JS acknowledges support from the W. M. Keck foundation.565 Tere we discuss constraiuts ou the lighredshift quasar LF from their integrated ionizing radiation., Here we discuss constraints on the high–redshift quasar LF from their integrated ionizing radiation.566 Given au LF. we compute the total comoving enuüssivitv as [ESL ME: ," Given an LF, we compute the total comoving emissivity as $\nu \epsilon_\nu=\int L \Phi(L) dL$ ."567"This gives ve, at restfameAA: however. with a spectral slope of ἐνx7+ this is independent of wavelength. aud has the same value atAA."," This gives $\nu568\epsilon_\nu$ at rest–frame; however, with a spectral slope of $\epsilon_\nu\propto \nu^{-1}$ this is independent of wavelength, and has the same value at."569". The background ionization rate per hydrogenatom TP is then given by where we have assumed e;Xvt. ay=6.3610em7 is the lydrogen ionization cross section at the Lyman limit (and we asstuucd ty(v7)xv? above the threshold). Pp is the Planck constant. my=3.29« ΤΠ, is the frequency of a Lyiuan Bit photon. aud Aye, is the mean free path of ionizing photons."," The background ionization rate per hydrogenatom $\Gamma$ is then given by where we have assumed $\epsilon_\nu\propto\nu^{-1}$, $\sigma_H=6.3\times57010^{-18}~{\rm cm^{-2}}$ is the hydrogen ionization cross section at the Lyman limit (and we assumed $\sigma_H(\nu)\propto \nu^{-3}$ above the threshold), $h_{\rm P}$ is the Planck constant, $\nu_{\rm H}=3.29\times 10^{15}$ Hz is the frequency of a Lyman limit photon, and $\lambda_{\rm mfp}$ is the mean free path of ionizing photons."571" We also define Tow=T/loPs1,"," We also define $\Gamma_{-12}=\Gamma/10^{-12}~{\rm572s^{-1}}$."573" We assume that the effective mean free path corresponds to a redshift interval of Az=0.17 at 2=3 (see Taardt Madan 1996 and Steidel. Ῥω Adelberger 2001). and scales with redshift as Awe,7M(L127)PS towards higher redshift (Con MeDonald 2002)."," We assume that the effective mean free path corresponds to a redshift interval of $\Delta z=0.17$ at $z=3$ (see Haardt Madau 1996 and Steidel, Pettini Adelberger 2001), and scales with redshift as $\lambda_{\rm574mfp}\propto (1+z)^{-6}$ towards higher redshift (Cen McDonald 2002)."575 Based on recent measurements (ee. Cen McDonald. 2002. sce also Becker et al.," Based on recent measurements (e.g. Cen McDonald 2002, see also Becker et al."576 2001:McDonald Miralda-Exscudé 2001 and Fan et al., 2001;McDonald Miralda-Escudé 2001 and Fan et al.577 2002). we require TowxQdos+ at z=6.," 2002), we require $\Gamma_{-12}<0.1~{\rm s^{-1}}$ at z=6."578 We find that iu some of our models. at 2=6. this bound is violated by up to a factor of 13: D.ο=1.3 (Pei LF): ED.i5=039 (AVL LF with a brightcud slope of jj= 15): P.4»=0.08 (Pei LF with 6 times higher L.).," We find that in some of our models, at $z=6$, this bound is violated by up to a factor of 13: $\Gamma_{-12}=1.3$ (Pei LF); $\Gamma_{-12}=0.39$ (WL LF with a bright–end slope of $\beta_h=4.5$ ); $\Gamma_{-12}=0.08$ (Pei LF with 6 times higher $L_\ast$ )."579 More geucrallv. contours of coustaut Poy=O. and DPyo=2 are shown in Figure 6..," More generally, contours of constant $\Gamma_{-12}=0.1$ and $\Gamma_{-12}=2$ are shown in Figure \ref{fig:contour0}."580 The appareutly laree ioniziug cuissivitics aplv that in ow LF withthe lowest L.. the backeround is overproduced. although this result is subject to several uncertainties: (1) the escape fraction of ionizing photous iav be only —1054 at := 6: (2) the mean free path evolves more steeply than (1|:) 0. (3) the faintcud slope is considerably shallower than Jj= 1.61. or (1) there can be significant svstematic errors on the observational," The apparently large ionizing emissivities imply that in our LF withthe lowest $L_\ast$, the background is over--produced, although this result is subject to several uncertainties: (1) the escape fraction of ionizing photons may be only $\sim 10\%$ at $z=6$ ; (2) the mean free path evolves more steeply than $(1+z)^{-6}$ (3) the faint–end slope is considerably shallower than $\beta_l=1.64$ , or (4) there can be significant systematic errors on the observational"581is now believed (hat soft eumma repeaters (SGIUs) - a small class (4 confirmed ancl one candidate) of high energy. (rausient discovered through their emission of bright N-rav/5-rav bursts. which repeat on (üimescales of seconds {ο vears - ave magnetars.,"is now believed that soft gamma repeaters (SGR's) - a small class (4 confirmed and one candidate) of high energy transient discovered through their emission of bright $%582\gamma -ray bursts, which repeat on timescales of seconds to years - are magnetars."583 There is evidence (hat the giant SGR flares involve the cooling of a confined e--photon plasma in an ulüirastrong magnetic field2002)., There is evidence that the giant SGR flares involve the cooling of a confined $e^{\pm }$ -photon plasma in an ultrastrong magnetic field.584. Some authors have suggested thal SGIVs are strange stars. motivated in part by the Iuminosities of their eiant flares.," Some authors have suggested that SGR's are strange stars, motivated in part by the super-Eddington luminosities of their giant flares."585" The magnetars differ Irom the canonical pulsars (with low magnetic fields of the order Dzz10H—10"" Gauss) in the sense that they spin down much more rapidly.", The magnetars differ from the canonical pulsars (with low magnetic fields of the order $B\approx 10^{11}-10^{13}$ Gauss) in the sense that they spin down much more rapidly.586 If we assume that the spin-down of the magnetar is completely determined by the torque of its relativistic wind emission. generated via (he magnetic dipole radiation. then the time variation of the angular velocity O of the star is given by where J is the moment of inertia of the star and pp=R'B is the magnetic dipole moment.," If we assume that the spin-down of the magnetar is completely determined by the torque of its relativistic wind emission, generated via the magnetic dipole radiation, then the time variation of the angular velocity $\Omega $ of the star is given by where $I$ is the moment of inertia of the star and $\mu =R^{3}B$ is the magnetic dipole moment."587 When the star is born will a spin period much shorter that the observed one. the age ol the star is the spin-down age ty=P/P. where P and P? are the present spin period and ils time derivative.," When the star is born with a spin period much shorter that the observed one, the age of the star is the spin-down age $%588\tau _{sd}=P/\dot{P, where $P$ and $\dot{P}$ are the present spin period and its time derivative."589" If (he spin-down is entirely due to the magnetic dipole radiation we obtain By adopting5 for the moment of inertia ancl the radius of the magnetar5 the tvpical values I=10"" ean? and R—10° em. and by assuming5S that the star was born with a magneticος field of the order of Bx10 Gauss and with an angular velocity of Qy=6000 !. the spin down age is given by τι21125 s. From Eq. (52))"," If the spin-down is entirely due to the magnetic dipole radiation we obtain By adopting for the moment of inertia and the radius of the magnetar the typical values $I=10^{45}$ $^{2}$ and $R=10^{6}$ cm, and by assuming that the star was born with a magnetic field of the order of $B\approx 10^{15}$ Gauss and with an angular velocity of $\Omega _{0}=6000$ $^{-1}$, the spin down age is given by $\tau _{sd}\approx 1125$ s. From Eq. \ref{dec}) )"590" it follows that the decay law of the angular velocity O of the star is οἱ the form where €, is the initial angular velocity of the star."," it follows that the decay law of the angular velocity $%591\Omega of the star is of the form where $\Omega _{0}$ is the initial angular velocity of the star."592 Hence. in a time interval of around /zz10° s and for a magnetic field B=10’ G the angular velocity of the star decreases from Q)=6000 toQ142rads = +.," Hence, in a time interval of around $t\approx 10^{6}$ s and for a magnetic field $B=10^{15}$ G the angular velocity of the star decreases from $\Omega _{0}=6000$ }$ to $\Omega =142$ $^{-1}$."593 For an initial angular velocity of the order of O=8000 + and for a magnetic field of the order of DBzz101 G. ry225 s. In a time interval of around /zz600 s the angular velocity of the star decreases to O22579 1," For an initial angular velocity of the order of $\Omega =8000$ $^{-1}$ and for a magnetic field of the order of $B\approx 10^{16} $ G, $\tau594_{sd}\approx 5$ s. In a time interval of around $t\approx 600$ s the angular velocity of the star decreases to $\Omega \approx 579$ $^{-1}$ ."595"is the bulk Loreutz factor of region 3 measured iu the rest fraane of region L. and as, is the fomvelocity of region 3 measured iu the rest frame of the TS.","is the bulk Lorentz factor of region 3 measured in the rest frame of region 4, and $u_{3t}$ is the four-velocity of region 3 measured in the rest frame of the TS."596 When Ps)δν1. which is easilv satisfied in this model (Yu Dai 2007). Eqs. (," When $\Gamma_{34}\gg1$, which is easily satisfied in this model (Yu Dai 2007), Eqs. ("597"9) aud (10) can be simplified as and vs, can be solved analytically from δίσ|Dad,(867|WeLek,0?=0 (Zhang Kobayashi 200",9) and (10) can be simplified as and $u_{3t}$ can be solved analytically from $8(\sigma+1)u_{3t}^4-(8\sigma^2+10\sigma+1)u_{3t}^2+\sigma^2=0$ (Zhang Kobayashi 2004).598 Following Eq. C, Following Eq. (599I). the total kinetic energy of region 2 be can calculatedas Ey»—(Po.Lig|Hhole?Tate leue. where Hang AUC Hae are the rest masses of the GRD ejecta iux swept-up mediuu. respectively.,"4), the total kinetic energy of region 2 can be calculated as $E_{k,2}=(\Gamma_2-1)(m_{\rm ej}+m_{\rm600sw})c^2+\Gamma_2(\Gamma_2-1)m_{\rm sw}c^2$ , where $m_{\rm ej}$ and $m_{\rm sw}$ are the rest masses of the GRB ejecta and swept-up medium, respectively."601" Energy conservatiou requires that auv increase in ££,» should be equal to the work done bv region 2. 1.6.. where the thermal and magnetic compoucuts ofthe pressure of region 3 can be respectively calculated by Pho,=404αιΗμffy aud Pha=BJαπ]SESstr?inerageJDe accordingH to the shock jump. conditions."," Energy conservation requires that any increase in $E_{k,2}$ should be equal to the work done by region 3, i.e., where the thermal and magnetic components ofthe pressure of region 3 can be respectively calculated by $P'_{\rm602th,3}={1\over3}e'_3=\frac{4}{3}\Gamma_{34}^2n'_4m_ec^2f_af_b $ and $P'_{B,3}={{B'}_3^2}/({8\pi})=8\Gamma_{34}^2n'_4m_ec^2\sigma f_b^2$ according to the shock jump conditions."603eye Substituting the expression of £j.» iuto Eq. (," Substituting the expression of $E_{k,2}$ into Eq. ("604"13). we can obtain Meauwlhile. the relationships between the properties of the two sides of the contact discontinuity surface show (Blaudford [οίνος 1976) where the similarity variable cau be solved to be For a closing dynamic equation set. we also imtroduce another two equations in order to calculate the increasing lnasses of regions 2 and 3 as and (Dii Lu 2002) Finally, we woul like to poiuted out that. in Dai (2001) aud Yu Dai (2007). the authors onlv took the existence of the TS before T,, mto account since the shallow decay aftevelosw phase during ~105? s was mainly coucerned there.","13), we can obtain Meanwhile, the relationships between the properties of the two sides of the contact discontinuity surface show (Blandford McKee 1976) where the similarity variable can be solved to be For a closing dynamic equation set, we also introduce another two equations in order to calculate the increasing masses of regions 2 and 3 as and (Dai Lu 2002) Finally, we would like to pointed out that, in Dai (2004) and Yu Dai (2007), the authors only took the existence of the TS before $T_m$ into account since the shallow decay afterglow phase during $\sim10^{3-5}$ s was mainly concerned there."605 Iu contrast. here such an artificial cutoff of the TS has heen abaucoucd for a more general investigation.," In contrast, here such an artificial cutoff of the TS has been abandoned for a more general investigation."606 Combining the above dynamic equatious with the relationships of df=(1Adἐςο) for region 3 and dt=(1MURCoe) for region 2. we can nuuericallv caleulate the temporal evolution of the shock dyuauics.," Combining the above dynamic equations with the relationships of $dt=(1-\beta_3)dR/(\beta_3c)$ for region 3 and $dt=(1-\beta_2)dR/(\beta_2c)$ for region 2, we can numerically calculate the temporal evolution of the shock dynamics."607 As inentioned iu Sect., As mentioned in Sect.608 2. since f£=0 is set at the transition iue from the prompt phase to the afterglow phasc. the initial couditious for our calculation is taken as R;=101 em. Do;=150. and Eye=107 ore. which correspond o the deceleration timescale of the GRB ejecta.," 2, since $t=0$ is set at the transition time from the prompt phase to the afterglow phase, the initial conditions for our calculation is taken as $R_{i}=10^{16}$ cm, $\Gamma_{2, i}=150$, and $E_{k,2,i}=10^{51}$ erg, which correspond to the deceleration timescale of the GRB ejecta."609 Figure l shows the evolution of the bulk Lorentz factors of the wi TS aud the CRD ES with different values of σ., Figure 1 shows the evolution of the bulk Lorentz factors of the wind TS and the GRB ES with different values of $\sigma$.610 The jearlv. overlapping of he curves with σ varying from 0 to 3 indicates that the dvuamic evolutions of both the shocks are insensitive to the degree of magnetization of the wincl., The nearly overlapping of the curves with $\sigma$ varying from 0 to 3 indicates that the dynamic evolutions of both the shocks are insensitive to the degree of magnetization of the wind.611 It is not surprising to obtain such a result. which actually has been know for a loug time for ordinary pulsar wind uchbulae (e... Enunering Chevalier 1987: Bucciantini et al.," It is not surprising to obtain such a result, which actually has been know for a long time for ordinary pulsar wind nebulae (e.g., Emmering Chevalier 1987; Bucciantini et al."612 2003: Del Zauua ot al., 2003; Del Zanna et al.613 2001)., 2004).614 With the propagation of the shocks. the bulk kinetic energv of the GRD cjecta and the maguetar wiud would be eracdually couverted into internal cucreyv of he shocked aaterials.," With the propagation of the shocks, the bulk kinetic energy of the GRB ejecta and the magnetar wind would be gradually converted into internal energy of the shocked materials."615" As usual. we assume that the internal energv of the shocked mediun is shared by uaenetie fields. electrons. and protons with fractious ER. EeVER (Aledvedey 20060) and 1€, €p. respectively."," As usual, we assume that the internal energy of the shocked medium is shared by magnetic fields, electrons, and protons with fractions $\epsilon_{B}$, $\epsilon_{e}\sim\sqrt{\epsilon_{B}}$ (Medvedev 2006) and $1-\epsilon_{e}-\epsilon_{B}$ , respectively."616 For the shocked wind. the ΟΠΟΙΟΥ: ryactions of the leptous and maguctic fields cal e determined bv the shock jump condition with a certain a.," For the shocked wind, the energy fractions of the leptons and magnetic fields can be determined by the shock jump condition with a certain $\sigma$."617" Considering the shock acceleration of charge particles. he electrons iu shocked regions are assumed to distribute AS Hes;/rpi with a mini electron Loreutz factor: ↷/mnsενin(Ee1) for ↽⊳⋅⊲⋠region 2 aud at55,4_= p ⋅⋅⋅ ⊀ 1)."," Considering the shock acceleration of charge particles, the electrons in shocked regions are assumed to distribute as $n_{{\gamma'},i}^{'} \propto {\gamma'}_i^{-p}$ with a minimum electron Lorentz factor: ${\gamma'}_{m,2}618=\epsilon_{e}g_p(m_p/m_e)(\Gamma_2-1)$ for region 2 and ${\gamma'}_{m,3}=g_p{e'_3}/({n'_3m_ec^2})$ for region 3 with $g_p\equiv(p-2)/(p-1)$ ."619" Oving to the svuchrotrou cooling of the clectrous. a cooling Lorentz factor: >"",ὄπιηρο⋅(σιBGT2it) should also be defined by equaliug the cooling time to the dynanüic time. where 6,, is Thomson cross section."," Owing to the synchrotron cooling of the electrons, a cooling Lorentz factor ${\gamma'}_{c,i} =6\pi620m_ec/(\sigma_{_{T}}{B'}^2_i\Gamma_it)$ should also be defined by equaling the cooling time to the dynamic time, where $\sigma_{_{T}}$ is Thomson cross section."621" Characterized bv /ue 55, and p (the subscript / is omitted hereafter). a quasi-static distribution of the electrous cau be written as (ane et al."," Characterized by ${\gamma'}_{m}$, ${\gamma'}_{c}$ and $p$ (the subscript $i$ is omitted hereafter), a quasi-static distribution of the electrons can be written as (Huang et al."622" 2000) where sf,=amax(4.51)h 5j=amndnG.5)2 aud so—2 forXs, aud s—p for ον> "," 2000) where $\gamma'_{H}=\max(\gamma'_{m},\gamma'_{c})$, $\gamma'_L=\min(\gamma'_m,\gamma'_{c})$, and $x=2$ for ${\gamma'}_{c}\leq{\gamma'}_{m}$ and $x=p$ for ${\gamma'}_{c}>{\gamma'}_{m}$ ."623"5, σα!~4BRιο). is the maxima electron. Lorentz factor with gq. the electron charee.", $\gamma'_M\sim q_eB'R/(m_ec^2)$ is the maximum electron Lorentz factor with $q_e$ the electron charge.624 For the N-rax band of interest in this paper.we ouly cousider the svuchrotron radiation of the electrous iu both regions 2 and 3.," For the X-ray band of interest in this paper,we only consider the synchrotron radiation of the electrons in both regions 2 and 3."625 The svuchrotron cussion coctfficieut at, The synchrotron emission coefficient at626 WA>1,if $\lambda>1$.627" UA «1. the right hand side of equation (3-19)) is always positive and no instability OCelLs,"," If $\lambda628< 1$, the right hand side of equation \ref{dispersion}) ) is always positive and no instability occurs."629 Although eq. (3-19)), Although eq. \ref{dispersion}) )630" is valid in genaral for a thin disk with any radial distribution of (he mass-to-IIux ratio A. it has the same form as (he dispersion relation obtained by Shu Li (1997) for the special case ofa disk with spatially uniform A (an ""isopedic disk)."," is valid in genaral for a thin disk with any radial distribution of the mass-to-flux ratio $\lambda$, it has the same form as the dispersion relation obtained by Shu Li (1997) for the special case ofa disk with spatially uniform $\lambda$ (an “isopedic” disk)."631 In parücular. (he marginal stabilitv of isopedic disks with A=1 was demonstrated explicitly bv Zweibel Lovelace (1997).," In particular, the marginal stability of isopedic disks with $\lambda=1$ was demonstrated explicitly by Zweibel Lovelace (1997)."632 The magnetically modified Toomre Qi; parameter. which provides the boundary of stability for axisvnunetric Gr=0) perturbations. is (hus eiven by Qu =(," The magnetically modified Toomre $Q_M$ parameter, which provides the boundary of stability for axisymmetric $m=0$ ) perturbations, is thus given by Q_M =."633321) Note that the definition of © in equation (2-20)) differs slightly from that of Shu Li (1997)., Note that the definition of $\Theta$ in equation \ref{Theta_eps}) ) differs slightly from that of Shu Li (1997).634" For Qa,<1. perturbations with wavenunber between fe=F4VvA| are unstable. will A4,=(e/O)/,; being (he wavenumber of maximum growth. and where hy=xnGMg/a is the Jeans wavenumber."," For $Q_M<1$, perturbations with wavenumber between $k_\pm=k_{\rm max}(1\pm635\sqrt{1-Q_M^2})$ are unstable, with $k_{\rm max}=(\epsilon/\Theta)636k_J$ being the wavenumber of maximum growth, and where $k_J=\pi G637\Sigma_0/a^2$ is the Jeans wavenumber."638 Since e/O«1. the effect of the magnetic field is {ο increase the length scale of the gravitational instability with respect to the Jeans length scale.," Since $\epsilon/\Theta <1$, the effect of the magnetic field is to increase the length scale of the gravitational instability with respect to the Jeans length scale."639 Another important [factor that determines Q3; in eq. (3-21)), Another important factor that determines $Q_M$ in eq. \ref{qmagnetic}) )640 is the epievelie [reeuueney., is the epicyclic frequency.641 Disks around voung stars that have dragged in magnetic fields [rom the interstellar medium by gravitational collapse do not rotate at keplerian speeds because magnetic tension mocifies the force balance equation (see. e.g.. eq. (," Disks around young stars that have dragged in magnetic fields from the interstellar medium by gravitational collapse do not rotate at keplerian speeds because magnetic tension modifies the force balance equation (see, e.g., eq. ("64218) of SOT when magnetic tension dominates over magnetic and gas pressure).,18) of S07 when magnetic tension dominates over magnetic and gas pressure).643 SOT showed that in magnetized disks (hat are viscously accreting bv the MIRE. the rotation curve is subkeplerian by a constant fraction f.," S07 showed that in magnetized disks that are viscously accreting by the MRI, the rotation curve is subkeplerian by a constant fraction $f$."644 In their models. the subkeplerian parameter f is determined by their equation (73) (hat states that the magnetic flux brought in bv star formation is conserved andis left behind in the disk.," In their models, the subkeplerian parameter $f$ is determined by their equation (73) that states that the magnetic flux brought in by star formation is conserved andis left behind in the disk."645" Thus. for a given mass-to-[Iux ratio A. the factor f depends on (he stellar mass. M, (necessary (o recover the flux brought in by star formation). the mass accretion rate. Mj. and the system age. Lage"," Thus, for a given mass-to-flux ratio $\lambda $, the factor $f$ depends on the stellar mass, $M_\star$ (necessary to recover the flux brought in by star formation), the mass accretion rate, $\dot M_d$, and the system age, $t_{\rm age}$."646 For A~4. SO7 obtained values of f/ in the range 0.39 0.95 for disks around. low-mass and INassive voung stars (see their Table 2).," For $\lambda \sim 4$, S07 obtained values of $f$ in the range $0.39$ $0.95$ for disks around low-mass and massive young stars (see their Table 2)."647 For subkeplerian disks. the epicvclic frequency. is given bv w= qo icai l= ," For subkeplerian disks, the epicyclic frequency is given by = f _K = f ( G ^3 ."648Therefore. the inclusion of magnetic fields produces competing effects on the instability parameter Qu: The strong fiekls enforce subkeplerian flow. which reduces (Qi; aud leads to," Therefore, the inclusion of magnetic fields produces competing effects on the instability parameter $Q_M$ : The strong fields enforce subkeplerian flow, which reduces $Q_M$ and leads to"649"ud ΠοΠz107 the abundance of molecular hydrogen increases by au order of maguitude. with a correspouding increase in the IL,He CIA opacity bv the same factor.","and $\rm He/H\wig>10^{3}$ the abundance of molecular hydrogen increases by an order of magnitude, with a corresponding increase in the $\rm H_2-He$ CIA opacity by the same factor."650 This improvement is a new. siguificaut effect that must be included in realistic modeling of very cool white dwarf atinosplhieres.," This improvement is a new, significant effect that must be included in realistic modeling of very cool white dwarf atmospheres."651 We have shown that the non-ideal effects affect tow.rouely the abundances of even trace species -oi the atmosphere., We have shown that the non-ideal effects affect strongly the abundances of even trace species in the atmosphere.652 This strongly sueecst the necessity of revising the abuudances of other trace species with siguificaut opacity for similar effects, This strongly suggest the necessity of revising the abundances of other trace species with significant opacity for similar effects.653 We expect that the study of thei abunudances and absorption processes in fluid heli will sienificautly: improve our unuderstaudius of the atmospheric plysics. composition. and evolution of the oldest aud coolest white dwarts.," We expect that the study of their abundances and absorption processes in fluid helium will significantly improve our understanding of the atmospheric physics, composition, and evolution of the oldest and coolest white dwarfs."654 I thank D. Saumon for useful discussions aud the referee. P. Dergerou. for suggestions that nuproved the clarity. of the manuscript.," I thank D. Saumon for useful discussions and the referee, P. Bergeron, for suggestions that improved the clarity of the manuscript."655 This research was supported by the United States Departinent of Enerey under contract W-7105-, This research was supported by the United States Department of Energy under contract W-7405-ENG-36.656 , 657je eravitationiad potential. is reduced accordingly.,"the gravitational potential, is reduced accordingly."658 Protostars located in the densest portion of the clump ancl/or those that by chance have je lowest relative velocity with respect to the gas tend to grow in mass most rapidly., Protostars located in the densest portion of the clump and/or those that by chance have the lowest relative velocity with respect to the gas tend to grow in mass most rapidly.659 In is shuulation. accreted eas lowers the orbital angular momentum of the stars about the ]ump center since the clump is assumed to be non rotating.," In this simulation, accreted gas lowers the orbital angular momentum of the stars about the clump center since the clump is assumed to be non rotating."660 Thus. as (μον grow in mass. ely orbits decay aud (he most massive objects migrate to the clump center.," Thus, as they grow in mass, their orbits decay and the most massive objects migrate to the clump center."661 The most rapidly growing protostars form a non-hierarchical svstem near the center., The most rapidly growing protostars form a non-hierarchical system near the center.662 As they come to dominate (he mass in this region. mutual gravitational interactions reconfigure the svstem into a hierarchy consisting of one or more lightly bound compact binaries plus ejected stars.," As they come to dominate the mass in this region, mutual gravitational interactions reconfigure the system into a hierarchy consisting of one or more tightly bound compact binaries plus ejected high-velocity stars."663 Multiple ruus of the simulation with different randomly chosen initial locations and velocities almost always produce mass-seggregated. non-hierarchical svstems of massive stars al (heir centers.," Multiple runs of the simulation with different randomly chosen initial locations and velocities almost always produce mass-seggregated, non-hierarchical systems of massive stars at their centers."664 This model illustrates one plausible scenario Lor the formation of a svstem of massive stars and their subsequent ejection., This model illustrates one plausible scenario for the formation of a non-hierarchical system of massive stars and their subsequent ejection.665 Three essential features are missing from this simplified model: the dynamic ejection of gas from the central region by the orbital motion of the massive stars. the presence of accretion disks. and the stveamers that transport mass from the inner-boundarv of the envelope onto these disks.," Three essential features are missing from this simplified model; the dynamic ejection of gas from the central region by the orbital motion of the massive stars, the presence of accretion disks, and the streamers that transport mass from the inner-boundary of the envelope onto these disks."666 Previous simulations of binary star formation have shown these features to be present (e.g. Lubow Artvmowiez 1996)., Previous simulations of binary star formation have shown these features to be present (e.g. Lubow Artymowicz 1996).667 In a multiple star system. matter (hat enters (he region where (he stars orbit each other tends to be expelled by gravitational torques.," In a multiple star system, matter that enters the region where the stars orbit each other tends to be expelled by gravitational torques."668 As a result. gas bound to (the svstem is likely to be organized into (wo components: an extended outer envelope having an inner boundary with a radius somewhat larger than the semi-major axis of the largest stellar orbit. and inner disks surrounding the stars with outer radii several (mes smaller than the periastron separations (Artvmowicz Lubow 1994; Günnther Ixlev 2002).," As a result, gas bound to the system is likely to be organized into two components; an extended outer envelope having an inner boundary with a radius somewhat larger than the semi-major axis of the largest stellar orbit, and inner disks surrounding the stars with outer radii several times smaller than the periastron separations (Artymowicz Lubow 1994; Günnther Kley 2002)."669 For pre-cecay interstellar separations of 100 AU. matter located within ~ 300 AU of the cluster would either be accreted onto disks with outer radii less than about. 30 AU or be expelled to bevond 300 AU.," For pre-decay interstellar separations of 100 AU, matter located within $\sim$ 300 AU of the cluster would either be accreted onto disks with outer radii less than about 30 AU or be expelled to beyond 300 AU."670 Gas in an envelope bound to a 40 AL. cluster of stars with an inner radius of 300 AU would have Kepler speeds less than 11 kms +., Gas in an envelope bound to a 40 $_{\odot}$ cluster of stars with an inner radius of 300 AU would have Kepler speeds less than 11 km $^{-1}$.671 The outer boundary where the cluster has significant influence on the envelope can be defined by (he radius where the gravitational influence of the cluster falls below the velocity dispersion. about 2 to 3 km ! for OMCH.," The outer boundary where the cluster has significant influence on the envelope can be defined by the radius where the gravitational influence of the cluster falls below the velocity dispersion, about 2 to 3 km $^{-1}$ for OMC1."672 Disks with 30 AU outer radii orbiting 10 AL. stars would have Kepler speeds greater than 17 km |., Disks with 30 AU outer radii orbiting 10 $_{\odot}$ stars would have Kepler speeds greater than 17 km $^{-1}$.673 Since non-hierarchical multiples likely have chaotic orbits. disks may be truncated al smaller radii.," Since non-hierarchical multiples likely have chaotic orbits, disks may be truncated at smaller radii."674 Gas falling from the outer envelope onto individual cireumstellar disks max form transient streams in the region of avoidance., Gas falling from the outer envelope onto individual circumstellar disks may form transient streams in the region of avoidance.675 Fieurese 5 illustrates a possible scenario for the evolution of the ONIC cloud core., Figures 5 illustrates a possible scenario for the evolution of the OMC1 cloud core.676 Figuree 5a shows the lormation of several protostellar seeds destined to become massive stus as (hev, Figure 5a shows the formation of several protostellar seeds destined to become massive stars as they677we can deduce how the results are likely to scale to other galaxies for which we currently lack direct observations.,we can deduce how the results are likely to scale to other galaxies for which we currently lack direct observations.678 For a sell-eravitating disc. the circular velocity is roughly. VioncMaaPaus πο . namely M," For a self-gravitating disc, the circular velocity is roughly $V_{d,200}^2 \simeq M_{d,11}/R_{d,10}$, so $\epsfftwo \propto \dot{M}_{d*} V_{d}^{-3}$ , namely ."679"uR, A constant cr,5 (~ 1) is consistent with the SER being5 a constant fraction of the barvon accretion rate. because the latter is roughly proportional to halo mass (?7):Mog."," A constant $\epsfftwo$ $\sim 1$ ) is consistent with the SFR being a constant fraction of the baryon accretion rate, because the latter is roughly proportional to halo mass \citep{neistein06a,birnboim07a}:."680 The fact that the SER follows the accretion rate is a natural result of the fact that the SER is proportional to the mass of the available gas (22).. ancl is consistent with the finding from simulations when compared to observed SEI (?)..," The fact that the SFR follows the accretion rate is a natural result of the fact that the SFR is proportional to the mass of the available gas \citep{bouche09a,dutton09b}, and is consistent with the finding from simulations when compared to observed SFR \citep{dekel09b}."681 We learn that e is only weakly dependent on Al., We learn that $e$ is only weakly dependent on $M$ .682" The redshift dependence at a given halo mass. using VxALGO|2)?? and Mx (112).isαπshes,"," The redshift dependence at a given halo mass, using $V^3 \propto \Mv (1+z)^{3/2}$ and $\dot{M} \propto (1+z)^2$, is."683" The system can adjust the SER to mateh the rate of gas supply by aceretion with eg,2o Lat all times by slight variations in the contraction factor s.", The system can adjust the SFR to match the rate of gas supply by accretion with $\epsfftwo\sim 1$ at all times by slight variations in the contraction factor $s$.684 At higher redshift. the clumps should contract a bit further and form stars at a somewhat higher surface density.," At higher redshift, the clumps should contract a bit further and form stars at a somewhat higher surface density."685 Our discussion. of clump survival in the preceding sections is based on the assumption that giant clumps represent single star-forming molecular clouds. although we of course expect them to possess significant substructure. as do local molecular clouels.," Our discussion of clump survival in the preceding sections is based on the assumption that giant clumps represent single star-forming molecular clouds, although we of course expect them to possess significant substructure, as do local molecular clouds."686 ‘These substructures are unresolved. by current observations and by simulations., These substructures are unresolved by current observations and by simulations.687 Here we discuss how their presence allects our conclusions., Here we discuss how their presence affects our conclusions.688 First note that. for this purpose. we do not care whether any sub-clumps within the giant clumps themselves survive star formation feedback. and. form bound stellar clusters.," First note that, for this purpose, we do not care whether any sub-clumps within the giant clumps themselves survive star formation feedback and form bound stellar clusters."689 To see why. consider an extreme case in which all the sub-clumps within the giant chump expel most of their gas. and. thus do not leave behind bound remnants.," To see why, consider an extreme case in which all the sub-clumps within the giant clump expel most of their gas, and thus do not leave behind bound remnants."690 Εις is what we might expect to happen if all the sub-clumps had. surface. densities similar to that of their parent giant clump. but. had masses well low the ~LO?105 41. minima survival mass that we computed in 2..," This is what we might expect to happen if all the sub-clumps had surface densities similar to that of their parent giant clump, but had masses well below the $\sim 10^5-10^6$ $\msun$ minimum survival mass that we computed in \ref{sec:survival}."691 In this case the sub-clumps would. all formi stars. expel their gas. and. disperse. but. both the stars and the expelled: gas would. still remain trapped. within the much larger eravitational potential well of the giant clump.," In this case the sub-clumps would all form stars, expel their gas, and disperse, but both the stars and the expelled gas would still remain trapped within the much larger gravitational potential well of the giant clump."692 They could. escape from this potential well onlv if the giant clump as a whole were disrupted by eas expulsion. which we have already shown in 2 will happen only if (p is much larger than the expected: value.," They could escape from this potential well only if the giant clump as a whole were disrupted by gas expulsion, which we have already shown in \ref{sec:survival} will happen only if $\epsff$ is much larger than the expected value."693 Thus the end result of this scenario would be a bound giant star cluster without anv bound sub-clusters inside it., Thus the end result of this scenario would be a bound giant star cluster without any bound sub-clusters inside it.694 At the opposite extreme. suppose that all the sub-Chimps were to remain bound and undergo nevligible eas expulsion.," At the opposite extreme, suppose that all the sub-clumps were to remain bound and undergo negligible gas expulsion."695 We might expect this scenario if the sub-clumps all had surface densities much higher than that of their parent giant clump., We might expect this scenario if the sub-clumps all had surface densities much higher than that of their parent giant clump.696 In this case the sub-clumps would. convert most of their mass to stars. forming bound. clusters.," In this case the sub-clumps would convert most of their mass to stars, forming bound clusters."697 All the bound. clusters would irradiate the remaining mass in the giant clump. -imparting momentum toit.," All the bound clusters would irradiate the remaining mass in the giant clump, imparting momentum to it."698 If the stars imparted enough momentum. this gas would be expelled.," If the stars imparted enough momentum, this gas would be expelled."699 Assuming most of the mass were in the inter-clump medium. as is the case for local molecular clouds. this. expulsion would. unbind the giant clump. producing many small individually bound clusters that are not bound to one another.," Assuming most of the mass were in the inter-clump medium, as is the case for local molecular clouds, this expulsion would unbind the giant clump, producing many small individually bound clusters that are not bound to one another."700 Conversely. if the imparted. momentum were not sullicient to unbind the giant clump. as we expect. the result. would be a giant star cluster consisting of many smaller bound. clusters. all gravitationally bound to one another.," Conversely, if the imparted momentum were not sufficient to unbind the giant clump, as we expect, the result would be a giant star cluster consisting of many smaller bound clusters, all gravitationally bound to one another."701 In either extreme scenario. whether or not. sub-clumpsx survive does not make any dillerence to whether a giant clump as a whole survives.," In either extreme scenario, whether or not sub-clumps survive does not make any difference to whether a giant clump as a whole survives."702 This is dictated solely by the expulsion fraction from the giant clum, This is dictated solely by the expulsion fraction from the giant clump.703 Llowever. sub-clumping still could make a cillerence for giant clump survival by raising the value of ejr.," However, sub-clumping still could make a difference for giant clump survival by raising the value of $\epsff$."704" In this case the sub-clumps would still have ej27I. but the giant clump would have eg,2l because it would have the same star formation rate but a much lower mean density. and thus a longer free-fall timo."," In this case the sub-clumps would still have $\epsfftwo\sim 1$, but the giant clump would have $\epsfftwo\gg 1$ because it would have the same star formation rate but a much lower mean density, and thus a longer free-fall time."705 ‘To see whether this is likely to happen. we note that the turbulent motions within a giant clump are likely to break it up into smaller sub-clumps. much a local molecular clouds are broken up into clump. filamentary structures by turbulence.," To see whether this is likely to happen, we note that the turbulent motions within a giant clump are likely to break it up into smaller sub-clumps, much a local molecular clouds are broken up into clump, filamentary structures by turbulence."706 In. such a configuration. a majority. of the mass is at a density higher than the volumetric mean density p that we have computed. and would therefore have a shorter free-fall time and a higher star formation rate.," In such a configuration, a majority of the mass is at a density higher than the volumetric mean density $\bar{\rho}$ that we have computed, and would therefore have a shorter free-fall time and a higher star formation rate."707" Quantitativelv. we have computed the star formation rate as AM,=(rMharé). where Al is the total mass of the giant clumip. p ds its volume-averaged density. and fyp is the free-fall time computed ab that density."," Quantitatively, we have computed the star formation rate as $\dot{M}_* = \epsff M/t_{\rm ff}(\bar{\rho})$, where $M$ is the total mass of the giant clump, $\bar{\rho}$ is its volume-averaged density, and $t_{\rm ff}$ is the free-fall time computed at that density."708 However. if most of the mass is at a density pzp. the appropriate mass might be the mass Λοp) above that higher density. and the appropriate timescale might be fir) computed. for that density.," However, if most of the mass is at a density $\rho > \overline{\rho}$, the appropriate mass might be the mass $M(>\rho)$ above that higher density, and the appropriate timescale might be $t_{\rm ff}(\rho)$ computed for that density."709 While one might worry that this could be a significant ellect. ? point out that itis in reality.quite small.," While one might worry that this could be a significant effect, \citet{krumholz07g} point out that itis in realityquite small."710 ‘Turbulent systems generally have lognormal density distributions., Turbulent systems generally have lognormal density distributions.711 For such a distribution. the fraction of the cloud mass with density greater than p is given by where 5 p/p. p is the volumetric mean density.," For such a distribution, the fraction of the cloud mass with density greater than $\rho$ is given by where $x = \rho/\bar{\rho}$ , $\bar{\rho}$ is the volumetric mean density,"712"If we have incident radiations at the upper and. lower boundaries as { and qp. respectively, the. boundary conditions are and where zb=mATο).","If we have incident radiations at the upper and lower boundaries as $I_0^{\rm in}$ and $I_{\rm L}^{\rm in}$, respectively, the boundary conditions are and where $\tau_{\rm e}^{\rm L}=\tau_{\rm L}\sqrt{3(1-\omega)}$."713 Phe solution. of⋅ equation. (Bs) with the boundary V3xtlconcitions (B9) and (DIO) is where y=V1ως, The solution of equation (B8) with the boundary conditions (B9) and (B10) is where $\chi=\sqrt{1-\omega}$.714" In the case without incident radiation (i.e. 45=fp"" 0). this solution is exactly. same as equation (28) of Mivake&Nakagawa(1993)."," In the case without incident radiation (i.e. $I_0^{\rm in}=I_{\rm L}^{\rm in}=0$ ), this solution is exactly same as equation (28) of \cite{miy93}."715. Then. let us consider the outbound. intensity at.the surface of the medium.," Then, let us consider the outbound intensity atthe surface of the medium."716" At 7= 0. the outbound intensity can be where αν b. and c can be called as ""thermal. ""pellection. ancl “transmission” coellicients.. respectively."," At $\tau=0$ , the outbound intensity can be where $a$, $b$, and $c$ can be called as “thermal”, “reflection”, and “transmission” coefficients, respectively."717" Since J(0)=(1/2)| 49""). weobtain from. equation (D11)"," Since $J(0)=(1/2)(I_0^{\rm in}+I_0^{\rm out})$ , weobtain from equation (B11)"718Bower 1999).Kaullmannetal. (,"Bower 1999).\cite{kauffmann04}, ,"7192004).. DeProprisοἱal.(2004) and Crotonοἱal.(2005) show that most of the galaxies forming stars al the present epoch have relatively low luminosities ancl consist mostly of dwarl spirals and iregulhus. while giants are mostly quiescent and tend 1o reside in the denser environments (Yangοἱal.2005a).," \cite{depropris04} and \cite{croton05} show that most of the galaxies forming stars at the present epoch have relatively low luminosities and consist mostly of dwarf spirals and irregulars, while giants are mostly quiescent and tend to reside in the denser environments \citep{yang05a}."720. This suggests Chat a study of the behavior of dwarf (ancl intermediate luminosity) galaxies in (he group environment. together wilh a comparison of stu-Iormineg ancl quiescent galaxies may provide useful insight into the mechanisms that transform field galaxies into tvpical cluster members.," This suggests that a study of the behavior of dwarf (and intermediate luminosity) galaxies in the group environment, together with a comparison of star-forming and quiescent galaxies may provide useful insight into the mechanisms that transform field galaxies into typical cluster members."721 One of the most versatile (1E simplistic) tools for studies of galaxy. population variations is (he galaxy luminosity function (LE)., One of the most versatile (if simplistic) tools for studies of galaxy population variations is the galaxy luminosity function (LF).722 The characteristic magnitude M provides a measure of the variation of eiant galaxy huninosity or mass. while the [aint end slope a can be related to the properties of the dwar! population.," The characteristic magnitude $M^*$ provides a measure of the variation of giant galaxy luminosity or mass, while the faint end slope $\alpha$ can be related to the properties of the dwarf population."723 LEs in different wavebands. or selected according to appropriate color cuts. may be used (to understand the stellar populations and star formation histories of the galaxy. population under study.," LFs in different wavebands, or selected according to appropriate color cuts, may be used to understand the stellar populations and star formation histories of the galaxy population under study."724 In this paper we consicler the variation of the galaxy LF in a sample of nearby groups spanning a wide range of masses., In this paper we consider the variation of the galaxy LF in a sample of nearby groups spanning a wide range of masses.725 This topic was previously investigated by Christlein(2000).. using Las Campanas hedshift Survey data (though this survey is now known to suller from significant. surface brightness selection effects). and by Ekeetal.(2004a).. who looked at three. dynamically determined. mass bins.," This topic was previously investigated by \cite{christlein00}, using Las Campanas Redshift Survey data (though this survey is now known to suffer from significant surface brightness selection effects), and by \cite{eke04a}, who looked at three, dynamically determined, mass bins."726 Here. we consider the entire population. split (his into several group Iunminosity. bins ancl consider quiescent (red) aud star-forming (blue) ealaxies separately. in order (o explore the possible roles of mergers and star formation suppression.," Here, we consider the entire population, split this into several group luminosity bins and consider quiescent (red) and star-forming (blue) galaxies separately, in order to explore the possible roles of mergers and star formation suppression."727 We mainiv concentrate on the behavior of lower Iuninosity galaxies. i.e. on the faint end of the LE. as a function of group properties. as this is where we expect lo see the strongest signature of evolutionary effects.," We mainly concentrate on the behavior of lower luminosity galaxies, i.e. on the faint end of the LF, as a function of group properties, as this is where we expect to see the strongest signature of evolutionary effects."728 Dwarls are believed to be fragile svstems. whose properties are easily affected by dense environments (e.g. Mooreetal. 1996)).," Dwarfs are believed to be fragile systems, whose properties are easily affected by dense environments (e.g. \citealt{moore96}) )."729 We start by describing the selection of groups and the derivation of the LF parameters in section 2. and in Section 3 we discuss the observed trends and present possible interpretations of our [indings.," We start by describing the selection of groups and the derivation of the LF parameters in Section 2, and in Section 3 we discuss the observed trends and present possible interpretations of our findings."730" We adopt a cosmology with O4,=0.3 and O4\=0.7 (though this has minimal impact on our results) and normalize distances to Ly=100 km + ! (ie. all quoted magnitudes should be read as M—5logh. where fh=14/100( km ! !)."," We adopt a cosmology with $\Omega_M=0.3$ and $\Omega_{ \Lambda}= 0.7$ (though this has minimal impact on our results) and normalize distances to $_0=100$ km $^{-1}$ $^{-1}$ (i.e. all quoted magnitudes should be read as $M - 5 \log h$, where $h = H_0/100$ km $^{-1}$ $^{-1}$ )."731 The largest publicly available group sample is the 2dF Percolation-lnferred Galaxy Groups (2PIGG) catalog (Ekeetal. 2004a).. selectedfrom the 2dF Galaxy Redshift Survey," The largest publicly available group sample is the 2dF Percolation-Inferred Galaxy Groups (2PIGG) catalog \citep{eke04a}, , selectedfrom the 2dF Galaxy Redshift Survey"732that P29 responds more quickly to changes in the global mass accretion rate than the meaΕν svslem.,that P29 responds more quickly to changes in the global mass accretion rate than the mean system.733" One possible explanation is that the long cooling time of the white dwarl keeps thT mean svstem luminosity well above its quiescent value: indeed in December WZ See was sti— much brighter in (he UV than when in quiescence,", One possible explanation is that the long cooling time of the white dwarf keeps the mean system luminosity well above its quiescent value; indeed in December WZ Sge was still much brighter in the UV than when in quiescence.734 The 27.87 s periodicity was not detected. nor was the ~15 s quasiperioclicily seen bv Kknigge et al. (," The 27.87 s periodicity was not detected, nor was the $\sim$ 15 s quasi–periodicity seen by Knigge et al. ("7352002) inHST UV observations earlier in the outburst.,2002) in UV observations earlier in the outburst.736 However. a broad feature near 18 s is present in the September observations which we idenlily as a oscillation (QDO).," However, a broad feature near 18 s is present in the September observations which we identify as a quasi--periodic oscillation (QPO)."737 In Fig., In Fig.738 3 we show the September observations in more detail., 3 we show the September observations in more detail.739 The power spectrum was recomputed using only a linear detrending. thus (he rapid rise in power at low-Irequencies due to flickering remains present.," The power spectrum was recomputed using only a linear detrending, thus the rapid rise in power at low-frequencies due to flickering remains present."740 Fig., Fig.741 3 also shows (he mean light curve and (he amplitude (from the square root of the power) of the P29 and QPO perioclicities., 3 also shows the mean light curve and the amplitude (from the square root of the power) of the P29 and QPO periodicities.742 The P29 and QPO amplitudes were computed [rom short segments of the light curve. each 118 s in duration.," The P29 and QPO amplitudes were computed from short segments of the light curve, each 118 s in duration."743 Fifty such segments were used: they are not independent. having overlap between them.," Fifty such segments were used; they are not independent, having overlap between them."744 The frequency resolution of such short light curves is very poor so the power spectrum was oversampled by a [factor of 4., The frequency resolution of such short light curves is very poor so the power spectrum was oversampled by a factor of 4.745 After removing the white noise background. the power was summed over (he intervals 27.833.7 s for the P29 signal and 16.919.7 s for the QPO signal.," After removing the white noise background, the power was summed over the intervals 27.8–33.7 s for the P29 signal and 16.9–19.7 s for the QPO signal."746 The Ilickering red noise background remains present in (hese banclpasses. so these amplitudes are still somewhat biased hieh: (he uncertainties in (he amplitudes are roughly half the values of aaiplitudes themselves.," The flickering red noise background remains present in these bandpasses, so these amplitudes are still somewhat biased high; the uncertainties in the amplitudes are roughly half the values of amplitudes themselves."747 The most noticeable features of the amplitudes are (heir rapid variations and lack of correlation with (he mean light curve or each other., The most noticeable features of the amplitudes are their rapid variations and lack of correlation with the mean light curve or each other.748 No periodicity in P29 or QPO amplitude is apparent., No periodicity in P29 or QPO amplitude is apparent.749 It is interesting to note (hat despite the P29 signal being present at 4 epochs spanning 3 months. the signal can vary from being «quite strong to undetectable in a span of less than a few hundred seconds.," It is interesting to note that despite the P29 signal being present at 4 epochs spanning 3 months, the signal can vary from being quite strong to undetectable in a span of less than a few hundred seconds."750 Longterm stability is present while short.term stability is not., Long–term stability is present while short–term stability is not.751 Although hard to quantify. the amplitude of the QDPO is roughly 0.31 mJv or of the mean system brightness.," Although hard to quantify, the amplitude of the QPO is roughly 0.31 mJy or of the mean system brightness."752 If only a single sinusoid is lit to the broad QPO signal. an amplitude of 0.27 mJy (1.38%)) at a period of 17.95 s is measured.," If only a single sinusoid is fit to the broad QPO signal, an amplitude of 0.27 mJy ) at a period of 17.95 s is measured."753 The relationship. if anv. between this weak QPO and the much stronger 15 s and 26.5 8 QPOs seen 20 days earlier in (he outburst (INnigge at al.," The relationship, if any, between this weak QPO and the much stronger $\sim$ 15 s and $\sim$ 6.5 s QPOs seen 20 days earlier in the outburst (Knigge at al."754 2002) is unclear., 2002) is unclear.755 Based on the sameLST UV spectra as used in (his work. Sion et al. (," Based on the same UV spectra as used in this work, Sion et al. ("7562003) measured the white dwarl’s temperature decline from 29.000 IX in 2001 September to 18.000 Ik in December.,"2003) measured the white dwarf's temperature decline from 29,000 K in 2001 September to 18,000 K in December."757last-decaving X-ray afterglow. which is generally found to be consistent with the observations.,"fast-decaying X-ray afterglow, which is generally found to be consistent with the observations."758 If as argued above. the prompt optical emission ofGRB 990123 and the fast-cecay phase of Swift X-ray afterelows have the same origin. then the former could also be identified with the large-angle emission. produced. during the burst.," If, as argued above, the prompt optical emission of GRB 990123 and the fast-decay phase of Swift X-ray afterglows have the same origin, then the former could also be identified with the large-angle emission produced during the burst."759 This conjecture can explain why the optical emission ofGIU 990123 appears uncorrelated with that at 5-ravs., This conjecture can explain why the optical emission of GRB 990123 appears uncorrelated with that at $\gamma$ -rays.760 As shown in Figure 1.. the optical emission of GRB 990123 is weaker during the first. pulse. exhibits à maximum curing the tail of the second pulse Gvhich. peaks at 38 s). and then decays monotonically throughout the third GRB pulse and after the burst end.," As shown in Figure \ref{lc}, the optical emission of GRB 990123 is weaker during the first pulse, exhibits a maximum during the tail of the second pulse (which peaks at 38 s), and then decays monotonically throughout the third GRB pulse and after the burst end."761 Ehe decoupling of the optical and *-ray emissions of GRB 990123 can be explained if the optical counterpart is identified with the larec-anegle emission released during the second IUS pulse (vhen the optical counterpart peaks) and if the optical emission of other pulses is weaker than that of the second. GRB pulse., The decoupling of the optical and $\gamma$ -ray emissions of GRB 990123 can be explained if the optical counterpart is identified with the large-angle emission released during the second GRB pulse (when the optical counterpart peaks) and if the optical emission of other pulses is weaker than that of the second GRB pulse.762 Given the simple structure of GRB 990123 light-curve ancl the sparse sampling of the optical counterpart. the lack of an optical-5-rav temporal correlation could also be the result. of Ductuations in the optical-to-5-ray output ratio from pulse to pulse.," Given the simple structure of GRB 990123 light-curve and the sparse sampling of the optical counterpart, the lack of an $\gamma$ -ray temporal correlation could also be the result of fluctuations in the $\gamma$ -ray output ratio from pulse to pulse."763 Thus. the large-angle emission is not a unique explanation for the uncorrelated optical and burst emissions of CRB 990123: it just represents a possible reason and a working assumption for the calculations below.," Thus, the large-angle emission is not a unique explanation for the uncorrelated optical and burst emissions of GRB 990123; it just represents a possible reason and a working assumption for the calculations below."764 Jased on the above arguments. in this work we attribute the optical prompt emission of CRB 990123 to the larec-angle svnchrotron emission. produced during the second GRB pulse and identify the prompt 5-rav emission with up-scatterings of the svnchrotron photons.," Based on the above arguments, in this work we attribute the optical prompt emission of GRB 990123 to the large-angle synchrotron emission produced during the second GRB pulse and identify the prompt $\gamma$ -ray emission with up-scatterings of the synchrotron photons."765 The observational constraints imposed on this scenario are presented in refobs ancl used in refmodel— to. determine the outflow parameters which accommocdate them., The observational constraints imposed on this scenario are presented in \\ref{obs} and used in \\ref{model} to determine the outflow parameters which accommodate them.766 Inrefextra.. we discuss some implications of the [arge-angle emission scenario for the optical counterpart and a possible shortcoming of the svnchrotron self-Compton model. which can be circumvented if the magnetic field ἄοσανς and. does not fill the entire CIUS outflow.," In, we discuss some implications of the large-angle emission scenario for the optical counterpart and a possible shortcoming of the synchrotron self-Compton model, which can be circumvented if the magnetic field decays and does not fill the entire GRB outflow."767 We emphasize two aspects of the Following treatment of 1e unification of the *-ray and prompt optical emissions of ο.RB 000123., We emphasize two aspects of the following treatment of the unification of the $\gamma$ -ray and prompt optical emissions of GRB 990123.768 First. we do not assume a certain mechanism for 10 dissipation of the relativistic outllow οποιον.," First, we do not assume a certain mechanism for the dissipation of the relativistic outflow energy."769 This mechanism could be (7) internal shocks in an unsteady wind. as proposed by Mésszárros Rees (1999). or (7) we external reverse-shock. as proposed. by Sari DPiran (1999) (fe.," This mechanism could be $(i)$ internal shocks in an unsteady wind, as proposed by Mésszárros Rees (1999), or $(ii)$ the external reverse-shock, as proposed by Sari Piran (1999) (fig."770 1 of Panaitescu Alésszarros 1998 also shows wt a lO16th magnitude optical emission could arise [rom 10 reverse-shock). and further investigated by Kobavashi Sari (2000). Soderberg lItunirez-ltuiz (2002). Fan (2002). Panaitescu Ixumar (2004). Nakar Piran (2005). ancl MeMahon. Ixumar Piran (2006).," 1 of Panaitescu Mésszárros 1998 also shows that a 10–16th magnitude optical emission could arise from the reverse-shock), and further investigated by Kobayashi Sari (2000), Soderberg Ramirez-Ruiz (2002), Fan (2002), Panaitescu Kumar (2004), Nakar Piran (2005), and McMahon, Kumar Piran (2006)."771 Thus. the scenario proposed here does not represent a new theoretica ramework for the GRB emission.," Thus, the scenario proposed here does not represent a new theoretical framework for the GRB emission."772 second. the calculations below address. primarily the implications of the proposed unifying scenario and represen a dest of that scenario only to the extent that the resulting physical parameters are plausible.," Second, the calculations below address primarily the implications of the proposed unifying scenario and represent a test of that scenario only to the extent that the resulting physical parameters are plausible."773 Otherwise. the »xoposed scenario for the optical counterpart of GARB 991023 is motivated bv. (7) the similarity between its temporal properties and those of the A-ray emission following Swift rusts. and (77) the identification of the latter with the large-angle burst emission.," Otherwise, the proposed scenario for the optical counterpart of GRB 991023 is motivated by $(i)$ the similarity between its temporal properties and those of the X-ray emission following Swift bursts, and $(ii)$ the identification of the latter with the large-angle burst emission."774 The only observational test. lor the »oposed scenario is the consistency between the decay. of he optical emission of CRB 990123 ancl the expectation rom the large-angle emission for the measured low-encrey slope of the burst spectrum refobs))., The only observational test for the proposed scenario is the consistency between the decay of the optical emission of GRB 990123 and the expectation from the large-angle emission for the measured low-energy slope of the burst spectrum \\ref{obs}) ).775 The optical measurements of GRB 990123. shown in figure l. are too sparse to pinpoint when the lux peaked. but sullicient to show that a substantial fraction of the. post-peak optical ux arose during the second. CRB pulse.," The optical measurements of GRB 990123, shown in figure \ref{lc}, are too sparse to pinpoint when the flux peaked, but sufficient to show that a substantial fraction of the post-peak optical flux arose during the second GRB pulse."776 As burst emission. episodes may be dynamically: independent. the decay of the ROTSIS optical emission should be timed from the onset of the second. GRB pulse. which occurred abo30 s after the GRB trigger. as shown in Figure 2..," As burst emission episodes may be dynamically independent, the decay of the ROTSE optical emission should be timed from the onset of the second GRB pulse, which occurred at $\sim 30$ s after the GRB trigger, as shown in Figure \ref{t30}."777 The optical counterpart emission decays as à power in time FO)xt7. with index àx1.5.," The optical counterpart emission decays as a power in time $F(t) \propto t^{-\alpha}$, with index $\alpha 778\simeq 1.5$."779 The available optical coverage of Swift. afterglows indicates that. quite often. the optical emission decays as a power-law from the first observations. at only LOO200 s after trigger (see figure 1 o£ Panaitescu 2006).," The available optical coverage of Swift afterglows indicates that, quite often, the optical emission decays as a power-law from the first observations, at only 100–200 s after trigger (see figure 1 of Panaitescu 2006)."780 This sugeests that the forward-shock contributes to the optical emission just at the end of the burst ancl motivates us to back-extrapolate the 0.12 day optical emission of GRB, This suggests that the forward-shock contributes to the optical emission just at the end of the burst and motivates us to back-extrapolate the 0.1–2 day optical emission of GRB7811e common CMB normalization of the linear amplitude in all ye models.,the common CMB normalization of the linear amplitude in all the models.782 The increase in the halo number density. displayed in the bottom plot of each panel as the ratio of the halo mass 'unction of each model over the ACDM case. shows a clear mass dependence. being more significant at large masses and suggesting a possible further extrapolation of these results to more massive avalos than the ones found in the catalogs.," The increase in the halo number density, displayed in the bottom plot of each panel as the ratio of the halo mass function of each model over the $\Lambda $ CDM case, shows a clear mass dependence, being more significant at large masses and suggesting a possible further extrapolation of these results to more massive halos than the ones found in the catalogs."783 In particular. ye EXPOO3 model shows an increase of almost a factor of 20 at Al~LO5107 M./h while at this redshift the EXPOO02 and SUGRAO03 models determine a comparable increase of a factor 4 S5autthe same mass.," In particular, the EXP003 model shows an increase of almost a factor of $20$ at $M\sim 1.0\times 10^{14}$ $_{\odot}/h$ while at this redshift the EXP002 and SUGRA003 models determine a comparable increase of a factor $\sim 4-5$ at the same mass."784 An accurate fit of the mass function. that we defer to an upcoming publication (23... will clearly be required in order to determine a reliable extrapolation of these numerical results to larger masses and to investigate in detail to which extent the deviation in the number counts is degenerate with the evolution of the linear growth factor.," An accurate fit of the mass function, that we defer to an upcoming publication \citep{Cui_etal_2011}, will clearly be required in order to determine a reliable extrapolation of these numerical results to larger masses and to investigate in detail to which extent the deviation in the number counts is degenerate with the evolution of the linear growth factor."785 Nevertheless. a rough estimate suggests that both the EXPOO? and the SUGRAO03 cosmologies might reach üt >=2.5 an enhancement factor of ~10 with respect to the ACDM halo mass function at Alz3.6«104 M.fh.," Nevertheless, a rough estimate suggests that both the EXP002 and the SUGRA003 cosmologies might reach at $z=2.5$ an enhancement factor of $\sim 10$ with respect to the $\Lambda $ CDM halo mass function at $M\approx 3-6\times 10^{14}$ $_{\odot}/h$."786 At later times. as one can see from the central panel referring to z=1.6. the situation is already significantly different.," At later times, as one can see from the central panel referring to $z=1.6$, the situation is already significantly different."787 While the EXPOO03 model still provides the strongest effect. reaching a factor of ~LO in the increase of the halo mass function at Alx210! M./h. the EXPQO2 and SUGRAGQO3 models now show a significantly different amplitude of the number counts enhancement: the former reaches an increase of a factor ~6 at Al~2.5.10! M.fh. while a factor of ~3 is attained by the latter at the same halo mass.," While the EXP003 model still provides the strongest effect, reaching a factor of $\sim 10$ in the increase of the halo mass function at $M\approx 2\times 10^{14}$ $_{\odot}/h$, the EXP002 and SUGRA003 models now show a significantly different amplitude of the number counts enhancement: the former reaches an increase of a factor $\sim 6$ at $M\approx 2.5\times 10^{14}$ $_{\odot}/h$, while a factor of $\sim 3$ is attained by the latter at the same halo mass."788 Also in this case. the enhancement shows a clear mass trend in all the models. and a larger effect can be expected for halo masses beyond the range covered by the catalogs.," Also in this case, the enhancement shows a clear mass trend in all the models, and a larger effect can be expected for halo masses beyond the range covered by the catalogs."789 The central result of the present work is shown by the direc comparison of the top and central panels of Fig., The central result of the present work is shown by the direct comparison of the top and central panels of Fig.790 6 just discussed with the bottom panel. that displays the halo mass functions of the different models at >=0.," \ref{fig:massfunction} just discussed with the bottom panel, that displays the halo mass functions of the different models at $z=0$."791 While both the standard exponentia cDE models EXPOO2. and EXPOO3 still show at the present time a similar enhancement of the halo number density as found a higher redshifts. with an increase at AJz3.0.1077 M./h of a factor of ~4 and ~15. respectively. the bouncing cDE mode SUGRAOQ03 does not show any excess in the halo number density over the whole mass range of the sample. and is therefore found to be perfectly consistent with the ACDM predictions on the cluster abundance at >=0.," While both the standard exponential cDE models EXP002 and EXP003 still show at the present time a similar enhancement of the halo number density as found at higher redshifts, with an increase at $M\approx 3.0\times 10^{15} $ $_{\odot}/h$ of a factor of $\sim 4$ and $\sim15$, respectively, the bouncing cDE model SUGRA003 does not show any excess in the halo number density over the whole mass range of the sample, and is therefore found to be perfectly consistent with the $\Lambda $ CDM predictions on the cluster abundance at $z=0$."792 This is a very remarkable result. since i shows how the dynamic degree of freedom associated with a cDE scalar field © can provide. for suitable self-interaction potentials. a natural mechanism to explain an excess of massive clusters a high redshift as compared to the ACDM expectations. withou affecting the very tightly constrained cluster mass function at the present time.," This is a very remarkable result, since it shows how the dynamic degree of freedom associated with a cDE scalar field $\phi $ can provide, for suitable self-interaction potentials, a natural mechanism to explain an excess of massive clusters at high redshift as compared to the $\Lambda $ CDM expectations without affecting the very tightly constrained cluster mass function at the present time."793 Such behavior could not easily arise in the context of standard gravity theories or non-Gaussian cosmological scenarios. and would therefore represent a clear indication of a dynamica nature of DE.," Such behavior could not easily arise in the context of standard gravity theories or non-Gaussian cosmological scenarios, and would therefore represent a clear indication of a dynamical nature of DE."794 Further detections of anomalously massive clusters at high redshift could therefore be considered as a “smoking gun” for the existence of a dynamic degree of freedom in the dark sector.," Further detections of anomalously massive clusters at high redshift could therefore be considered as a “smoking gun"" for the existence of a dynamic degree of freedom in the dark sector."795 In the present paper we have proposed a new model of interacting dark energy based on a SUGRA self-interaction potential and on a constant coupling between dark energy and CDM particles., In the present paper we have proposed a new model of interacting dark energy based on a SUGRA self-interaction potential and on a constant coupling between dark energy and CDM particles.796 The most relevant feature of the SUGRA self-interaction potential for the analysis carried. out in this work. is the presence of a global minimum that allows the dark energy scalar field to oscillate. thereby changing its direction of motion during the expansion history of the universe.," The most relevant feature of the SUGRA self-interaction potential for the analysis carried out in this work, is the presence of a global minimum that allows the dark energy scalar field to oscillate, thereby changing its direction of motion during the expansion history of the universe."797 Such feature makes our SUGRA coupled dark energy scenario significantly different from previously proposed models of dark energy interactions. us i allows an inversion of the energy flow between the two interacting components at relatively recent cosmological epochs.," Such feature makes our SUGRA coupled dark energy scenario significantly different from previously proposed models of dark energy interactions, as it allows an inversion of the energy flow between the two interacting components at relatively recent cosmological epochs."798 We have therefore compared the cosmological evolution of standard coupled dark energy models based on an exponentia self-interaction potential to our proposed SUGRA cDE scenario. both concerning the background dynamics and the evolution of linear and nonlinear perturbations.," We have therefore compared the cosmological evolution of standard coupled dark energy models based on an exponential self-interaction potential to our proposed SUGRA cDE scenario, both concerning the background dynamics and the evolution of linear and nonlinear perturbations."799" For the latter task. we have also made use of large N-body simulations results through the publicly available halo catalogs that include the specific models of dark energy interaction under investigation,"," For the latter task, we have also made use of large N-body simulations results through the publicly available halo catalogs that include the specific models of dark energy interaction under investigation."800 Already at the background level. the SUGRA ¢DE scenario shows a series of interesting features.," Already at the background level, the SUGRA cDE scenario shows a series of interesting features."801 First of all. the inversion of the direction of motion of the dark energy scalar field happens in our specific model at tiny6.8 which is a redshift already relevant for astrophysical processes and for the early stages of nonlinear structure. formation.," First of all, the inversion of the direction of motion of the dark energy scalar field happens in our specific model at $z_{\rm inv}\sim 6.8$ which is a redshift already relevant for astrophysical processes and for the early stages of nonlinear structure formation."802" This inversion of motion corresponds to a ""bounce"" of the dark energy equation of state parameter uw, on the cosmological constant barrier a,=—1. and imprints a specific pattern in the low-redshift evolution of the Hubble function tha might provide a way to directly constrain the model."," This inversion of motion corresponds to a “bounce"" of the dark energy equation of state parameter $w_{\phi }$ on the cosmological constant barrier $w_{\phi }=-1$, and imprints a specific pattern in the low-redshift evolution of the Hubble function that might provide a way to directly constrain the model."803 Furthermore. the inversion of the energy flow between dark energy and CDM particle during cosmic evolution implies. for the specitic mode presented here. that the CDM particles mass has very similar values at the redshift of the CMB and at the present time. thereby avoiding any mismatch of the cosmological parameters between scarp anc Ld.," Furthermore, the inversion of the energy flow between dark energy and CDM particle during cosmic evolution implies, for the specific model presented here, that the CDM particles mass has very similar values at the redshift of the CMB and at the present time, thereby avoiding any mismatch of the cosmological parameters between $z_{\rm CMB}$ and $z=0$."804 The most significant result of the present work. however. concerns the evolution of perturbations and the formation of linear and nonlinear structures in the context of the SUGRA cDE scenario. as this is shown to provide appealing features to accoun for possible anomalous detections of massive clusters at. high redshifts.," The most significant result of the present work, however, concerns the evolution of perturbations and the formation of linear and nonlinear structures in the context of the SUGRA cDE scenario, as this is shown to provide appealing features to account for possible anomalous detections of massive clusters at high redshifts."805 At the linear level. we have demonstrated for the first time by numerically solving the linear perturbations. equations. that a bouncing coupled dark energy model. and in particular the SUGRA cDE scenario presented here. can determine the same amplitude of linear perturbations as a corresponding .\CDM cosmology both at CMB and at the present time. while featuring a significant deviation from ACDM at intermediate redshifts.," At the linear level, we have demonstrated for the first time by numerically solving the linear perturbations equations that a bouncing coupled dark energy model, and in particular the SUGRA cDE scenario presented here, can determine the same amplitude of linear perturbations as a corresponding $\Lambda$ CDM cosmology both at CMB and at the present time, while featuring a significant deviation from $\Lambda $ CDM at intermediate redshifts."806" In xrtieular. both the amplitude of scalar perturbations at CMB and he value of σς at z=0 are the same between the standard ACDM model and our proposed SUGRA cDE scenario. while the latter eatures a significantly larger amplitude of density perturbations at intermediate redshifts. with a peak in correspondence of the dark energy ""bounce"" at z;,,."," In particular, both the amplitude of scalar perturbations at CMB and the value of $\sigma _{8}$ at $z=0$ are the same between the standard $\Lambda $ CDM model and our proposed SUGRA cDE scenario, while the latter features a significantly larger amplitude of density perturbations at intermediate redshifts, with a peak in correspondence of the dark energy “bounce"" at $z_{\rm inv}$."807 Therefore. the SUGRA cDE model can be simultaneously consistent with CMB and local constraints on he perturbations amplitude. while allowing for significant freedom at intermediate epochs.," Therefore, the SUGRA cDE model can be simultaneously consistent with CMB and local constraints on the perturbations amplitude, while allowing for significant freedom at intermediate epochs."808 We have then studied the evolution of the halo mass function as predicted by large N-body simulations that include all the characteristic features of the different interacting dark energy, We have then studied the evolution of the halo mass function as predicted by large N-body simulations that include all the characteristic features of the different interacting dark energy809"radius to star radius IURI: impact parameter 5; RV semi-amplitude /; Lagrangianelements €cosc and €sinc, where w is the longitude of periastron; and the systematic offset velocity .","radius to star radius $R_{\rm P}^{2}$ $_{*}^{2}$; impact parameter $b$ ; RV semi-amplitude $K$ ; Lagrangianelements $e\cos \omega$ and $e \sin \omega$, where $\omega$ is the longitude of periastron; and the systematic offset velocity $\gamma$."810" In this particular case, (wo systematic velocities were fit to allow for instrumental offsets between the SOPHIEand FIES datasets."," In this particular case, two systematic velocities were fit to allow for instrumental offsets between the SOPHIEand FIES datasets."811" Thesewere found to be: uopiiuis = -20.3834 + 0.0027 land ""μις = 20.4290 + 0.00171.", Thesewere found to be: $\gamma_{\rm SOPHIE}$ = -20.3834 $\pm$ 0.0027 and $\gamma_{\rm FIES}$ = -20.4290 $\pm$ 0.0017.812" The chain length was 10,000 points and the resulting best-fit parameters and uncertainties are shown in Table 3.."," The chain length was 10,000 points and the resulting best-fit parameters and uncertainties are shown in Table \ref{pparams}."813" The photometric error bars were re-scaled to take into account any underesümation in the uncertainties so that V ""n V""/dof = 1 (dof = number of points - number of fitted parameters).", The photometric error bars were re-scaled to take into account any underestimation in the uncertainties so that $\chi^{2}_{red}$ = $\chi^{2}$ /dof = 1 (dof = number of points - number of fitted parameters).814 We used the ?? non-linear limb darkening coefficients for the appropriate stellar temperature and photometric passband appropriate for each light curve.," We used the \citet{claret00, claret04} non-linear limb darkening coefficients for the appropriate stellar temperature and photometric passband appropriate for each light curve."815" In order to estimate the stellar mass and properties derived [rom it, we used the ? empirical calibrations from eclipsing binaries."," In order to estimate the stellar mass and properties derived from it, we used the \citet{Torres10star} empirical calibrations from eclipsing binaries."816" This method, adapted by ?.. computes the stellar mass as a function ofTag. logpy and |M/H| and has the advantage of being independent of stellar models."," This method, adapted by \citet{Enoch10}, computes the stellar mass as a function of, $\log \rho_{*}$ and [M/H] and has the advantage of being independent of stellar models."817" We find 17,2 1.30 + 0.03., similar to the stellar mass derived from the isochrone analysis undertaken here (47,2 1.36 + 0.04., Padova models) and in T10 (A7,2 1.39 + 0.05M.... YY models)."," We find = 1.30 $\pm$ 0.03, similar to the stellar mass derived from the isochrone analysis undertaken here = 1.36 $\pm$ 0.04, Padova models) and in T10 = 1.39 $\pm$ 0.05, YY models)."818 We performed the MCMC fit and derived the following planetary parameters: == 2.25 + 0.06Μα. ==1.19+0.05 aand == 1.33 + 0.16p).," We performed the MCMC fit and derived the following planetary parameters: = 2.25 $\pm$ 0.06, = 1.19 $\pm$ 0.05 and = 1.33 $\pm$ 0.16."819". In addition, we analysed the data solely from T10 and found that the fitted parameters were completely consistent with their results."," In addition, we analysed the data solely from T10 and found that the fitted parameters were completely consistent with their results."820" Finally, we analysed all the datasets simultaneously in order to optimise the best-fit solution using all the information available."," Finally, we analysed all the datasets simultaneously in order to optimise the best-fit solution using all the information available."821 The results are shown in Table 3 and are in good agreement., The results are shown in Table \ref{pparams} and are in good agreement.822" In an initial fit to the SOPHIE and FIES RVs, the eccentricity was allowed to float. yielding e = 0.054 + 0.017."," In an initial fit to the SOPHIE and FIES RVs, the eccentricity was allowed to float, yielding $e$ = 0.054 $\pm$ 0.017."823 We analysed the datasets independently and found that a jitter term of 15 ms.1 was required to be added in quadrature to the FIES RV uncertainties in order to obtain V 47 V., We analysed the datasets independently and found that a jitter term of 15 m $^{-1}$ was required to be added in quadrature to the FIES RV uncertainties in order to obtain $\chi^{2}_{red}$ = 1.824" This may due to astrophysical noise, as also noted by T10, and/or instrumental systematic noise which has not been accounted for."," This may due to astrophysical noise, as also noted by T10, and/or instrumental systematic noise which has not been accounted for."825" The FIES RVs do not significantly detect an eccentric orbit, yielding e = 0.04 + 0.03, but equally do not rule one oul."," The FIES RVs do not significantly detect an eccentric orbit, yielding e = 0.04 $\pm$ 0.03, but equally do not rule one out."826" In contrast, the SOPHIE RVs do not require any jiller term (ο reconcile the rms scatter with the measureduncertainties."," In contrast, the SOPHIE RVs do not require any jitter term to reconcile the rms scatter with the measureduncertainties."827" Fitüng the SOPHIE RVs alone, a more significant detection of eccentricily was found, e = 0.081 + 0.022 with \? = 2.0 for 9 RV points and 4 fittedparameters (Av, € cosa, € sina, ΙΟ ΡΙΙΙΙ)."," Fitting the SOPHIE RVs alone, a more significant detection of eccentricity was found, $e$ = 0.081 $\pm$ 0.022 with $\chi^{2}$ = 2.0 for 9 RV points and 4 fittedparameters $K$, $e \cos \omega$ , $e \sin \omega$ , $\gamma_{\rm SOPHIE}$ )."828" Fitüng a purely circular orbit to the same data, we found - — 22.6."," Fitting a purely circular orbit to the same data, we found $\chi^{2}_{\rm circ}$ = 22.6."829" Applying the Lucy-Sweeney test (2)., the eccentricity is detected at the 3o level."," Applying the Lucy-Sweeney test \citep*{Lucy71}, , the eccentricity is detected at the $\sigma$ level."830hints that these svstems are likely to have larec TTVs.,hints that these systems are likely to have large TTVs.831 However. the timescale for laree TTVs in resonant svstenis can be quite loug.," However, the timescale for large TTVs in resonant systems can be quite long."832 For a svsteum of Neptune-iass plaucts libratiug about a 2:1 MMR. we would not expec to detect TTTVs based on the QU and QL data preseuted.," For a system of Neptune-mass planets librating about a 2:1 MMR, we would not expect to detect TTVs based on the Q0 and Q1 data presented."833 Moreover. for libratiug systenas with sinaller masses or that are very close to exact resonance. the time needed to distinguish a TTV signal from a coustaut period lengthens. also requiring additional data.," Moreover, for librating systems with smaller masses or that are very close to exact resonance, the time needed to distinguish a TTV signal from a constant period lengthens, also requiring additional data."834 οπιο the relative frequency of planets with various orbital spacings will require a population analysis that corrects for the ecometric transit xobabilities., Inferring the relative frequency of planets with various orbital spacings will require a population analysis that corrects for the geometric transit probabilities.835 Of course. there may be additional 1on-transiting planets. or sinall transiting planets. οίνου WOT 191.02 and 191.01 or in any of the candidate svsteiis presented.," Of course, there may be additional non-transiting planets, or small transiting planets, between KOI 191.02 and 191.01 or in any of the candidate systems presented."836 In some cases; TTVs or radial velocity follow-up could ideutifv such anets.," In some cases, TTVs or radial velocity follow-up could identify such planets."837 Iu other cases. the nou-transiting plauets will remain undetected. further complicating i population analysis.," In other cases, the non-transiting planets will remain undetected, further complicating a population analysis."838 The sample of multiple anet candidate systems presented here is too sunallaud not necessarily unbiased=for such an analysis., The sample of multiple planet candidate systems presented here is too small—and not necessarily unbiased—for such an analysis.839 For two of the transit candidates preseuted. ο] one transit has been observed.," For two of the transit candidates presented, only one transit has been observed."840 There is a sanall chance that a second transit occured durius a data gap., There is a small chance that a second transit occured during a data gap.841 However. this is unlikely aud the extended transit durations also support large orbital periods.," However, this is unlikely and the extended transit durations also support large orbital periods."842 The periods listed in Table L1 are lower limits based upon the uon-observatiou of a second transit iu he data., The periods listed in Table \ref{tabPeriods} are lower limits based upon the non-observation of a second transit in the data.843 Also included. 10WOVOL. are estimates based upon the transit duration assundue a circular orbit aud a ceutral transit of the planet.," Also included, however, are estimates based upon the transit duration assuming a circular orbit and a central transit of the planet."844 With these latter estimates. it is clupting to identity the IKOI 209 svstem as line rear a XE MAIR and the KOT 152 system as being rear a L:2:1 MAIR.," With these latter estimates, it is tempting to identify the KOI 209 system as lying near a 3:1 MMR and the KOI 152 system as being near a 4:2:1 MMR."845" Hosvever. we caution rat the uncertaintv in the orbital period estimated from a single transit is far too large to have confidence hat these systems are near ΑΡΑ,"," However, we caution that the uncertainty in the orbital period estimated from a single transit is far too large to have confidence that these systems are near MMR."846 Nonetheless. YeeaudCoudi(2008) show that orbital period estimates based upon single trausit durations need rot be as conservative as the estimates that we state.," Nonetheless, \citet{yee2008} show that orbital period estimates based upon single transit durations need not be as conservative as the estimates that we state."847" For cach neigliboriug pair of planet caudidates. we measure the ratio£=GD;,/Dour)PoelPin>he. where Dis the transit duration aud P is the orbital period."," For each neighboring pair of planet candidates, we measure the ratio $\xi \equiv (D_{in}/D_{out})(P_{out}/P_{in})^{1/3}$, where $D$ is the transit duration and $P$ is the orbital period."848 In cach case the ratio is near unity (see Table 3)). as expected for a pair of objects on circular and coplanar orbits around a conuuon star.," In each case the ratio is near unity (see Table \ref{orbittable}) ), as expected for a pair of objects on circular and coplanar orbits around a common star."849 We compare these ratios to the results of Monte Carlo simulations of the distribution of © (denoted ἕνιο). for pairs of planets on circular and coplanar orbits with orbital periods similar o those observed., We compare these ratios to the results of Monte Carlo simulations of the distribution of $\xi$ (denoted $\xi_{\text{MC}}$ ) for pairs of planets on circular and coplanar orbits with orbital periods similar to those observed.850 We assume random viewiug angles. subject to the constraint that both planets rausit.," We assume random viewing angles, subject to the constraint that both planets transit."851 The 16th. 50th. aud Sith percentile of hese distributions are included in Table 3..," The 16th, 50th, and 84th percentile of these distributions are included in Table \ref{orbittable}."852 Iu uo case do we find evidence for a large eccentricity or for a blend of multiple stars cach with one rausiting object., In no case do we find evidence for a large eccentricity or for a blend of multiple stars each with one transiting object.853 The largest deviation from unitv is that for KOT 191. but in this case the observed and expected values are very close. duc to the arge ratio of senuniajor axes.," The largest deviation from unity is that for KOI 191, but in this case the observed and expected values are very close, due to the large ratio of semimajor axes."854 In the cases of 209 and 896. the ratio is slightly less than expected for coplanar. circular orbits.," In the cases of 209 and 896, the ratio is slightly less than expected for coplanar, circular orbits."855 However. this could be casily reconciled if one planet iu cach svsteni were to have a modest eccentricity (~0.05 for IXOI 209. 0.1 for NOT 896).," However, this could be easily reconciled if one planet in each system were to have a modest eccentricity $\sim 0.05$ for KOI 209, $\sim 0.1$ for KOI 896)."856 One important question suroundius these uulti-candidate svstems is the ecometric probability hat would see both planets transiting., One important question surrounding these multi-candidate systems is the geometric probability that would see both planets transiting.857 Following RagozzineaudΠοια(2010).. and used on the method of BoruckiandSuu-πας (1981). we calculate this probabilitv bv considering the area of the region on thecelestial sphere. centered ou the star. that is aligned o see both planets transit (seealsoBeattyandSeager2010:Callonetal. 2010).," Following \citet{rago2010}, and based on the method of \citet{boru1984}, we calculate this probability by considering the area of the region on thecelestial sphere, centered on the star, that is aligned to see both planets transit \citep[see also][]{beat2010,gill2010}."858. We also rote here the analytical approximation eiven by RagozzineaudTolman(2010). for the probability of observing both plancts transit as a fuuction of he true uutual iuclination between the planets. o.," We also note here the analytical approximation given by \citet{rago2010} for the probability of observing both planets transit as a function of the true mutual inclination between the planets, $\phi$."859 The result is different in low a1 lugh nmutua inclination regimes. with the critical angle betweeu he regiues as GeirccRoafay where A is the radius of the star aud ay is the orbital distance of he innermost. transiting plauct.," The result is different in low and high mutual inclination regimes, with the critical angle between the regimes as $\phi_{\rm crit} \simeq R_*/a_1$ where $R_*$ is the radius of the star and $a_1$ is the orbital distance of the innermost, transiting planet."860 In the low iiutua inclination regine. the probability of seciug both danets transit is Ray Where 09 is the orbita distance ofthe outer planet.," In the low mutual inclination regime, the probability of seeing both planets transit is $R_*/a_2$ where $a_2$ is the orbital distance of the outer planet."861 Thus. the probability of secing both plauets transit is equal to the xobabilitv that the more distant planet transits.," Thus, the probability of seeing both planets transit is equal to the probability that the more distant planet transits."862 Iu the hig[um uutual inclination regime. this is no ouger true. aud only observations along the line of nodes ofthe orbital planes will see both planets ransit (Isoch1995:TolanaudMurray 2005)..," In the high mutual inclination regime, this is no longer true, and only observations along the line of nodes of the orbital planes will see both planets transit \citep{koch1995,holm2005}. ."863 Tn, In864We explicitly develop techniques for two general situations: quasi-periodic perturbers and transient perturbers.,We explicitly develop techniques for two general situations: quasi-periodic perturbers and transient perturbers.865 The former case is motivated bv halo of super-massive black holes (c.g. Lacey Ostriker 1985)., The former case is motivated by halo of super-massive black holes (e.g. Lacey Ostriker 1985).866 The latter case includes almost evervthing else: for example. unbound dwarf encounters (Iv-by). orbiting substructure decaving due to dynamical friction. cisrupting dwarfs. and mixing tidal debris.," The latter case includes almost everything else; for example, unbound dwarf encounters (fly-by), orbiting substructure decaying due to dynamical friction, disrupting dwarfs, and mixing tidal debris."867 There is no practical constraint on deriving the Fokker-Planck coellicients for transient. noise but that the process can be represented. as an expansion in some biorthogonal basis., There is no practical constraint on deriving the Fokker-Planck coefficients for transient noise but that the process can be represented as an expansion in some biorthogonal basis.868 For dwarfs on decaving or unbound orbits. this is particularly easy and can be done by quadrature.," For dwarfs on decaying or unbound orbits, this is particularly easy and can be done by quadrature."869 Alternatively. one may construct an n-body simulation using the expansion method and let the simulation produce the time series of coellicients directly.," Alternatively, one may construct an n-body simulation using the expansion method and let the simulation produce the time series of coefficients directly."870 The companion paper (Paper 2) applies the apparatus described here to investigate the evolution of haloes during the noisy epoch of galaxy formation., The companion paper (Paper 2) applies the apparatus described here to investigate the evolution of haloes during the noisy epoch of galaxy formation.871 We find that both unbound encounters and decaving substructure drives the halo profile to a sell-similar form similar to those found recently in cosmological simulations., We find that both unbound encounters and decaying substructure drives the halo profile to a self-similar form similar to those found recently in cosmological simulations.872 Phere are a number of interesting applications., There are a number of interesting applications.873 For example. the distribution of binary semi-major axes e in the field star populations is proportional to e+ over several orders of magnitude.," For example, the distribution of binary semi-major axes $a$ in the field star populations is proportional to $a^{-1}$ over several orders of magnitude."874 Preliminary work suggests that this may be explained as the result of Ductuations from the noisy environment found in proto-stellar clusters and molecular clouds., Preliminary work suggests that this may be explained as the result of fluctuations from the noisy environment found in proto-stellar clusters and molecular clouds.875 Other possible applications include effect of transient bar formation ancl spiral structure on overall galactic structure in the 10 billion vears since formation., Other possible applications include effect of transient bar formation and spiral structure on overall galactic structure in the 10 billion years since formation.876 ] thank Enrico Vesperini for comments and cliscussion., I thank Enrico Vesperini for comments and discussion.877 This work was support in part bv. NSP AST-90529328., This work was support in part by NSF AST-9529328.878of considering a polytropic gas model can also be applied when the spatial information of the SZ data is poor.,of considering a polytropic gas model can also be applied when the spatial information of the SZ data is poor.879" The simulations have been performed using the IBM-SP4 machine at the ""Consorzio Interuniversitario del Nord-Est per il Caleolo Elettronico” (CCINECA. Bologna). with CPU time assigned thanks to the INAF-CINECA grant. and the IBM-SP4 machine at the ""Rechenzentrum der Max-Planck-Gesellschaft"" at the ""Max-Planck-Institut. fürr Plasmaphysik"" with CPU time assigned to the ""Max-Planck-Institut fürr Astrophyvsik""."," The simulations have been performed using the IBM–SP4 machine at the “Consorzio Interuniversitario del Nord-Est per il Calcolo Elettronico” (CINECA, Bologna), with CPU time assigned thanks to the INAF–CINECA grant, and the IBM–SP4 machine at the “Rechenzentrum der Max-Planck-Gesellschaft” at the ``Max-Planck-Institut fürr Plasmaphysik” with CPU time assigned to the “Max-Planck-Institut fürr Astrophysik”."880 We wish to thank an anonymous referee for detailed comments. which helped improving the presentation of the results.," We wish to thank an anonymous referee for detailed comments, which helped improving the presentation of the results."881 We would like to thank Giuseppe Murante for his help in the initial phase of this project. and Stefano Ettori for enlightening discussions.," We would like to thank Giuseppe Murante for his help in the initial phase of this project, and Stefano Ettori for enlightening discussions."882 This work has been partially supported by the INFN-PD51 grant and by MIUR., This work has been partially supported by the INFN–PD51 grant and by MIUR.883" Part of this work served as the master degree thesis of S. A. at the ""Università degli Studi di Torino"".", Part of this work served as the master degree thesis of S. A. at the “Università degli Studi di Torino”.884(Marshetal.1995).,\cite{mdd95}.885. None of the four systems show a clear asvmmetry of this type in the line profiles., None of the four systems show a clear asymmetry of this type in the line profiles.886 A second. test that can be carried. out to look for the faint companion consists in shifting out the fitted racial velocity olf the spectra ancl creating a mean spectrum. by combining all the shifted spectra. subtracting this mean spectrum from the individual shifted ones ancl plotting the resulting spectra in a stack or trail.," A second test that can be carried out to look for the faint companion consists in shifting out the fitted radial velocity off the spectra and creating a mean spectrum by combining all the shifted spectra, subtracting this mean spectrum from the individual shifted ones and plotting the resulting spectra in a stack or trail."887 This aids the eve to identify any leftover absorption moving with the binary orbit., This aids the eye to identify any leftover absorption moving with the binary orbit.888 A Doppler map (Marsh.&Horne1988). can also be computed from. these stack of spectra., A Doppler map \cite{mh88} can also be computed from these stack of spectra.889" Any orbital motion leftover in the spectra would appear in the maps as a small absorption region located in the V,=0 axis of the velocity map.", Any orbital motion leftover in the spectra would appear in the maps as a small absorption region located in the $V_x = 0$ axis of the velocity map.890 We do not find any indication of the presence of the unseen component in either trails or Doppler maps in any of the four svstenis studied., We do not find any indication of the presence of the unseen component in either trails or Doppler maps in any of the four systems studied.891 We explore the question of how small the contribution of the faint component of the system has to be so as not to be detected using the methods discussed in the previous section., We explore the question of how small the contribution of the faint component of the system has to be so as not to be detected using the methods discussed in the previous section.892 To answer this question we create synthetic spectra that include the absorption corresponding to the brighter component of the svstem (in the form of three Ciaussians). scaled to the measured. value for each system. plus some extra absorption moving opposite to it (also represented by three Gaussians) and determine for what percentage of brightness. relative to the bright component. we should be able to detect the faint component by looking at the spectra aroundthe quadrature. phases (Marsh.et.al.1995).," To answer this question we create synthetic spectra that include the absorption corresponding to the brighter component of the system (in the form of three Gaussians), scaled to the measured value for each system, plus some extra absorption moving opposite to it (also represented by three Gaussians) and determine for what percentage of brightness, relative to the bright component, we should be able to detect the faint component by looking at the spectra aroundthe quadrature phases \cite{mdd95}."893.. his method assumes that the companion stars have a spectrum similar to that of the brighter component., This method assumes that the companion stars have a spectrum similar to that of the brighter component.894 Although the fainter white dwarf is cooler and its Hine will be Less deep in its spectrum. this seems like a reasonable assumption as the companions are also white cwarfs. unless of course they are not DA white cdwarls.," Although the fainter white dwarf is cooler and its line will be less deep in its spectrum, this seems like a reasonable assumption as the companions are also white dwarfs, unless of course they are not DA white dwarfs."895 Ln the case of wwe lind that the brightness of the companion must be Less than 10 per cent the brightness of the bright component for us not to detect it., In the case of we find that the brightness of the companion must be less than 10 per cent the brightness of the bright component for us not to detect it.896 The values we find for 3," The values we find for ,"897 The values we find for 37," The values we find for ,"898 The values we find for 373," The values we find for ,"899 The values we find for 373.," The values we find for ,"900 The values we find for 373..," The values we find for ,"901We can compare that with our classification of supercluster morphologies.,We can compare that with our classification of supercluster morphologies.902 Approximately. line filaments are comparable with our simple filaments.," Approximately, line filaments are comparable with our simple filaments."903 Star filaments can be compared with simple spiders., Star filaments can be compared with simple spiders.904 Grid and complex filaments may correspond either to multibranching filaments or to multispiders. although complex filaments are more similar to multispiders and grid filaments to multibranching filaments.," Grid and complex filaments may correspond either to multibranching filaments or to multispiders, although complex filaments are more similar to multispiders and grid filaments to multibranching filaments."905 This shows that the morphology of observed and simulated superclusters 1s. in general. similar. as we found earlier from much smaller samples of observed and simulated superclusters.," This shows that the morphology of observed and simulated superclusters is, in general, similar, as we found earlier from much smaller samples of observed and simulated superclusters."906 The biggest exception is the supercluster SCI 061. a very rich and high-density multibranching filament.," The biggest exception is the supercluster SCl 061, a very rich and high-density multibranching filament."907 No other supercluster with such a morphology has been found yet either in simulations in observations2)., No other supercluster with such a morphology has been found yet either in simulations in observations.908. Another difference between the observed and simulated superclusters. as quantified by Minkowski funetionals and shapefinders. is fine structure of superclusters. delineated by galaxies of different luminosity(2).," Another difference between the observed and simulated superclusters, as quantified by Minkowski functionals and shapefinders, is fine structure of superclusters, delineated by galaxies of different luminosity."909 The clumpiness of observed superclusters for galaxies of different luminosity has a much larger scatter than that of simulated superclusters., The clumpiness of observed superclusters for galaxies of different luminosity has a much larger scatter than that of simulated superclusters.910 Simulations do not yet explain all the features of observed superclusters., Simulations do not yet explain all the features of observed superclusters.911 We have presented an analysis of the large-scale distribution and morphology of superclusters from the SDSS DR7., We have presented an analysis of the large-scale distribution and morphology of superclusters from the SDSS DR7.912 While the overall shape of superclusters has been analysed earlier in several studies. our paper is the first in which the inner morphology of a large sample of observed superclusters is studied in detail.," While the overall shape of superclusters has been analysed earlier in several studies, our paper is the first in which the inner morphology of a large sample of observed superclusters is studied in detail."913 We used multidimensional normal mixture modelling to divide superclusters into two sets according to their physical and morphological properties., We used multidimensional normal mixture modelling to divide superclusters into two sets according to their physical and morphological properties.914 We present 2D and 3D distributions of galaxies and rich groups in superclusters. the clumpiness curve (the fourth Minkowski functional Vi—mf relation). as well as the morphological signature A\-K> for each supercluster in our sample.," We present 2D and 3D distributions of galaxies and rich groups in superclusters, the clumpiness curve (the fourth Minkowski functional $V_3 - mf$ relation), as well as the morphological signature $K_1$ $K_2$ for each supercluster in our sample."915 The superclusters were selected to contain at least 300 observed galaxies., The superclusters were selected to contain at least 300 observed galaxies.916 As we showed. this does not mean that all superclusters in our sample are rich — about 1/4 of our superclusters contain one rich cluster or group only (three superclusters do not contain any rich group or cluster).," As we showed, this does not mean that all superclusters in our sample are rich – about 1/4 of our superclusters contain one rich cluster or group only (three superclusters do not contain any rich group or cluster)."917 Summarising. our study showed that: Our results on the morphology of superclusters can be used to compare the properties of local and high-redshift superclusters.," Summarising, our study showed that: Our results on the morphology of superclusters can be used to compare the properties of local and high-redshift superclusters."918 Few superclusters at very high redshifts have already been discovered in deep. wide-field imaging surveys(22???).," Few superclusters at very high redshifts have already been discovered in deep, wide-field imaging surveys."919. Deep surveys like the ALHAMBRA project will provide us with data about (possible) very distant superclusters: we can analyse their structure and compare that with the local superclusters. using morphological methods.," Deep surveys like the ALHAMBRA project will provide us with data about (possible) very distant superclusters; we can analyse their structure and compare that with the local superclusters, using morphological methods."920 Our study does not give a definite answer to the question about the possible connection between the morphology of superclusters and their large-scale distribution., Our study does not give a definite answer to the question about the possible connection between the morphology of superclusters and their large-scale distribution.921 Also. there are superclusters in our sample that can be described as filaments or multibranching filaments. but none of them is as rich and has such an overall high density as the supercluster SCI 061.," Also, there are superclusters in our sample that can be described as filaments or multibranching filaments, but none of them is as rich and has such an overall high density as the supercluster SCl 061."922 Even the richest supercluster with a multispider morphology in our sample. the supercluster SCI 094. is not as rich as the very rich Sculptor supercluster in?.," Even the richest supercluster with a multispider morphology in our sample, the supercluster SCl 094, is not as rich as the very rich Sculptor supercluster in."923. This shows the need for a larger sample of superclusters to understand the morphological variety of superclusters. and to study the possible connection between the large-scale distribution of superclusters and their morphology.," This shows the need for a larger sample of superclusters to understand the morphological variety of superclusters, and to study the possible connection between the large-scale distribution of superclusters and their morphology."924 Different morphologies of superclusters suggest that their evolution has been different., Different morphologies of superclusters suggest that their evolution has been different.925 To understand the formation and evolution of superclusters of different morphology better. we need to study the properties and evolution of superclusters in simulations.," To understand the formation and evolution of superclusters of different morphology better, we need to study the properties and evolution of superclusters in simulations."926 The morphology of superclusters and its evolution may be one of the factors to distinguish between different cosmological models(??)., The morphology of superclusters and its evolution may be one of the factors to distinguish between different cosmological models.927. Especially interesting is the supercluster SC] 061 in the Sloan Great Wall., Especially interesting is the supercluster SCl 061 in the Sloan Great Wall.928 Up to now simulations have not been able to model its morphologytherein)., Up to now simulations have not been able to model its morphology.929. New simulations with larger volumes are needed to study the morphology of superclusters and the evolution of the morphology of simulated superclusters. to understand the reasons for the exceptional morphology of the supercluster SCI 061.," New simulations with larger volumes are needed to study the morphology of superclusters and the evolution of the morphology of simulated superclusters, to understand the reasons for the exceptional morphology of the supercluster SCl 061."930 In addition. very rich superclusters are rare: another reason to use simulations for large volumes comes from the demand to include as large a variety of superclusters in the simulation volume as possible.," In addition, very rich superclusters are rare; another reason to use simulations for large volumes comes from the demand to include as large a variety of superclusters in the simulation volume as possible."931Classical Cepheids have been kev objects in the long-lasting efforts to measure the extragalactic distance scale and (o probe the predictions of stellar evolution aud stellar pulsation theory (e.g. Freecdinan ancl Madore 2010. Caputo et al.,"Classical Cepheids have been key objects in the long-lasting efforts to measure the extragalactic distance scale and to probe the predictions of stellar evolution and stellar pulsation theory (e.g. Freedman and Madore 2010, Caputo et al."932 2005)., 2005).933 Given the enormous importance of Cepheids for the determination of the cosmic distance scale ancl cosmological parameters. it is of great importance to fully understand (hese stars astrophvsicallv.," Given the enormous importance of Cepheids for the determination of the cosmic distance scale and cosmological parameters, it is of great importance to fully understand these stars astrophysically."934 One of (he most nageing problems in Cepheid research has been (he dillicul(y to reliably determine (heir masses., One of the most nagging problems in Cepheid research has been the difficulty to reliably determine their masses.935 Christy (1968) ancl Stobie (1969) were the first to notice that Cepheicl masses calculated. from stellar pulsational theory were about 20 smaller than the corresponding Inasses estimated from their evolutionary tracks on the Hertzsprung-Itussell diagram., Christy (1968) and Stobie (1969) were the first to notice that Cepheid masses calculated from stellar pulsational theory were about 20 smaller than the corresponding masses estimated from their evolutionary tracks on the Hertzsprung-Russell diagram.936 In spite of the considerable progress in understanding the physics of Cepheid variable stars over the vears. (he “Cepheid mass discrepancy problem” has remained unsolved! for more (han 40 vears (Ixeller ancl Wood. 2002. IxXeller 2008. Evans οἱ al.," In spite of the considerable progress in understanding the physics of Cepheid variable stars over the years, the ""Cepheid mass discrepancy problem"" has remained unsolved for more than 40 years (Keller and Wood 2002, Keller 2008, Evans et al."937 2008. Caputo et al.," 2008, Caputo et al."938 2005. Neilson. Cantiello and Langer 2011 and references therein).," 2005, Neilson, Cantiello and Langer 2011 and references therein)."939 The obvious solution to the problem comes Iron an independent aud accurate measurement of themasses of a number of Cepheids with a range of pulsation periods. and (here have been a number of efforts to lind binary Cepheids allowing such a precise mass determination (Evans οἱ al.," The obvious solution to the problem comes from an independent and accurate measurement of the of a number of Cepheids with a range of pulsation periods, and there have been a number of efforts to find binary Cepheids allowing such a precise mass determination (Evans et al."940 1997. 2006 and 2008).," 1997, 2006 and 2008)."941 However. the lew Cepheids found in binary svstems for which masses have been estimated all occur in single-lined. non-eclipsing svstems.," However, the few Cepheids found in binary systems for which masses have been estimated all occur in single-lined, non-eclipsing systems."942 This has limited the accuracy of the best Cepheid dynamical mass measurements to less than 15%.. not sulliciently accurate to resolve the mass discrepancy. problem.," This has limited the accuracy of the best Cepheid dynamical mass measurements to less than 15, not sufficiently accurate to resolve the mass discrepancy problem."943 Recently. several eclipsing binary svstems in the LAIC have been discovered from OGLE Project data which contain candidates for classical Cepheil components (Udalski οἱ al.," Recently, several eclipsing binary systems in the LMC have been discovered from OGLE Project data which contain candidates for classical Cepheid components (Udalski et al."944 1999. Soszvnski et al.," 1999, Soszynski et al."945 2008)., 2008).946 Our group. as part of the dedicated. to ihe improvement of stellar distance indicators (Gieren et al.," Our group, as part of the dedicated to the improvement of stellar distance indicators (Gieren et al."947 2005). has been obtaining," 2005), has been obtaining"948" ""Bi. ", $^{209}$ 949"flux, a type C pop II galaxy would need to be an order of magnitude more massive than a type A object to be detectable with JWST (Fig. 4)).","flux, a type C pop II galaxy would need to be an order of magnitude more massive than a type A object to be detectable with JWST (Fig. \ref{Mmin}) )."950" While the relative contribution from nebular emission decreases at high ages for instantaneous burst models (Z10 Myr for IMF's that allow populations to remain luminous for that long), the intrinsic UV slope at the same time becomes redder (see Fig."," While the relative contribution from nebular emission decreases at high ages for instantaneous burst models $\gtrsim 10$ Myr for IMFs that allow populations to remain luminous for that long), the intrinsic UV slope at the same time becomes redder (see Fig."951" 11aa), thereby jeopardizing any chances of detecting a unique pop III signature."," \ref{typeC_colcrit}a a), thereby jeopardizing any chances of detecting a unique pop III signature."952" Adopting a more extended star formation history would make pop III galaxies retain their very blue UV slopes for longer, butalso keeps the fneb/fstars ratio up, and therefore still requires a very high f. to allow the broadband criteria to apply."," Adopting a more extended star formation history would make pop III galaxies retain their very blue UV slopes for longer, butalso keeps the $f_\mathrm{neb}/f_\mathrm{stars}$ ratio up, and therefore still requires a very high $f_\mathrm{esc}$ to allow the broadband criteria to apply."953 Switching to colours based on JWST filters at shorter central wavelengths would reduce the relative contribution from nebular emission somewhat (this is evident from Fig. ," Switching to colours based on JWST filters at shorter central wavelengths would reduce the relative contribution from nebular emission somewhat (this is evident from Fig. \ref{spectra}) ),"954"but also decreases the difference in magnitudes between1)), the intrinsic colours of pop III and pop II/L For instance, pop III galaxies at z=8 could display ™159—m2oo colours (based on fluxes in the NIRCam F150W and F200W filters at 1.5 and 2.0 wm, repspectively) redder than those of pop I and II galaxies for ~107 yr even in the case of fosc70.9 (i.e. lower than the fe.Z; 0.95-0.99 quoted above, albeit not by much), but the colour difference between these models is then <0.05 mag, which would be very difficult to measure in practice."," but also decreases the difference in magnitudes between the intrinsic colours of pop III and pop II/I. For instance, pop III galaxies at $z=8$ could display $m_{150}-m_{200}$ colours (based on fluxes in the NIRCam F150W and F200W filters at 1.5 and 2.0 $\mu$ m, repspectively) redder than those of pop I and II galaxies for $\sim 10^7$ yr even in the case of $f_\mathrm{esc}\approx 0.9$ (i.e. lower than the $f_\mathrm{esc}\gtrsim 0.95$ –0.99 quoted above, albeit not by much), but the colour difference between these models is then $\leq 0.05$ mag, which would be very difficult to measure in practice."955 Whether pop III objects with Lyman-continuum escape fractions fos:7 0.9—0.99 exist is an open question., Whether pop III objects with Lyman-continuum escape fractions $f_\mathrm{esc}\approx 0.9$ –0.99 exist is an open question.956" Recent simulations by Johnsonetal.(2009) suggest that fes. in this range may be produced if the pop III IMF is extremely top-heavy, but taken at face value, the prospects of identifying pop III galaxies through the colour signatures of type A objects appear more promising, since they are likely to hold for a wider range of escape fractions (fasc7 0-0.5)."," Recent simulations by \citet{Johnson et al. b} suggest that $f_\mathrm{esc}$ in this range may be produced if the pop III IMF is extremely top-heavy, but taken at face value, the prospects of identifying pop III galaxies through the colour signatures of type A objects appear more promising, since they are likely to hold for a wider range of escape fractions $f_\mathrm{esc}\approx 0$ –0.5)."957" In Sect. 5,"," In Sect. \ref{typeA},"958" we argued that pop III galaxies with SEDs dominated by nebular emission (type A) could potentially be identified based on their JWST colours, since a combination of strong hydrogen emission lines like Ha, yet absent metal emission lines like [OIII|A5007 would gives rise to very peculiar colours over certain redshift intervals."," we argued that pop III galaxies with SEDs dominated by nebular emission (type A) could potentially be identified based on their JWST colours, since a combination of strong hydrogen emission lines like $\alpha$, yet absent metal emission lines like $\lambda$ 5007 would gives rise to very peculiar colours over certain redshift intervals."959" Here, we discuss a couple of potential caveats with this method."," Here, we discuss a couple of potential caveats with this method."960" Our tests indicate that pop III, type A signatures based on the lack of [OIII]A5007 emission are erased as soon as the oxygen-to-hydrogen abundance relative to that of the Sun reaches [O/H] >—2.2 (or (O/H) >5x10756 in absolute numbers)."," Our tests indicate that pop III, type A signatures based on the lack of $\lambda$ 5007 emission are erased as soon as the oxygen-to-hydrogen abundance relative to that of the Sun reaches [O/H] $\geq -2.2$ (or (O/H) $\geq 5\times 10^{-6}$ in absolute numbers)."961" Depending on the metallicity threshold at which gas switches from the formation of pop III stars with a top-heavy IMF to pop II with an IMF more typical of that in the local Universe (oftenassumedtohappenatZ= 10~4tol0~°, and on the oxygen yields of the first supernovae, this 2006b),oxygen criterion may translate into a metallicity criterion for type A, pop III galaxy signatures that is either slightly lower or higher than that which governs the pop III-II transition."," Depending on the metallicity threshold at which gas switches from the formation of pop III stars with a top-heavy IMF to pop II with an IMF more typical of that in the local Universe \citep[often assumed to happen at $Z=10^{-4}$ to $10^{-6}$, and on the oxygen yields of the first supernovae, this oxygen criterion may translate into a metallicity criterion for type A, pop III galaxy signatures that is either slightly lower or higher than that which governs the pop III-II transition."962" Hence, the method proposed by us and Inoue(2011b) for detecting pop III, type A galaxies may in principle either miss a substantial fraction of galaxies that are still able to form pop III stars, or to catch galaxies that have already switched to pop II star formation."," Hence, the method proposed by us and \citet{Inoue b} for detecting pop III, type A galaxies may in principle either miss a substantial fraction of galaxies that are still able to form pop III stars, or to catch galaxies that have already switched to pop II star formation."963" Clearly, a method of this type is only meant to generate pop III galaxy candidates."," Clearly, a method of this type is only meant to generate pop III galaxy ."964 Follow-up spectroscopy will be required to further probe the exact nature of these targets., Follow-up spectroscopy will be required to further probe the exact nature of these targets.965 For objects that are already close to the detection threshold, For objects that are already close to the detection threshold966better than with three bands. it is not a dramatic improvement.,"better than with three bands, it is not a dramatic improvement."967 For σι=go0.3. the correctly classified fraction of SNe la rises from with three bands to with four.," For $\sigma_1=\sigma_2=0.3$, the correctly classified fraction of SNe Ia rises from with three bands to with four."968 The SNe II-P are only mareinally better classified. but (he sample with observations in Four bands consists of only eight such objects.," The SNe II-P are only marginally better classified, but the sample with observations in four bands consists of only eight such objects."969 We thus conclude that. when the photometric redshifts are reasonably good. observations in a fourth band. lor the sake of classification purposes. mav be an inefficient use of telescope time.," We thus conclude that, when the photometric redshifts are reasonably good, observations in a fourth band, for the sake of classification purposes, may be an inefficient use of telescope time."970 Next. we examine (he success rate of the SN-ABC when using observations only in two bands.," Next, we examine the success rate of the SN-ABC when using observations only in two bands."971 Since the best bands for high-: SN observations are the reddest. we discard the bluest band. and remain with E775W and F850LP.," Since the best bands for $z$ SN observations are the reddest, we discard the bluest band, and remain with F775W and F850LP."972 As expected. with two bands the results. shown in Figure 10.. are degraded.," As expected, with two bands the results, shown in Figure \ref{f:MCscss_2b}, are degraded."973 Nonetheless. in some regions of parameter space. (he success rale of the SN-ADC is non-negligible.," Nonetheless, in some regions of parameter space, the success rate of the SN-ABC is non-negligible."974 SNe Ia show the same change as when dropping from four bands to three., SNe Ia show the same change as when dropping from four bands to three.975 The success rates drop especially at low redshilt and [ον old ages., The success rates drop especially at low redshift and for old ages.976 On the other hand. surprisingly. the success rate for HII-P. and Ibe SNe is usually higher with two bands than with three.," On the other hand, surprisingly, the success rate for II-P and Ibc SNe is usually higher with two bands than with three."977 This could be understood in the following way., This could be understood in the following way.978 As described in refmodel.. our model for the absolute magnitude of CC-SNe includes a much greater dispersion than that of SNe Ia. in order to account for their intrinsic diversity.," As described in \\ref{model}, our model for the absolute magnitude of CC-SNe includes a much greater dispersion than that of SNe Ia, in order to account for their intrinsic diversity."979 This entails that CC-SNe can populate wider volumes of color-magnitude space. so that when observational constraints are weak (will one or (wo bands observed) stummune® (he likelihood over all parameter space makes the evidence Mer greater on average than τει and thus increases {ος for all objects. regarcless of their real (wpe.," This entails that CC-SNe can populate wider volumes of color-magnitude space, so that when observational constraints are weak (with one or two bands observed) summing the likelihood over all parameter space makes the evidence $E_{CC}$ greater on average than $E_{Ia}$, and thus increases $P_{CC}$ for all objects, regardless of their real type."980 As a consequence. SN la classifieation is hindered. while are apparently better classified.," As a consequence, SN Ia classification is hindered, while CC-SNe are apparently better classified."981 We have tested this explanation by reducing artificially ihe dispersion of CC-SNe in our model., We have tested this explanation by reducing artificially the dispersion of CC-SNe in our model.982 As a consequence. SN la classification improved dramatically. regardless of the number of observed bands. while CC-SN classification success was correspoudinely reduced. being worst with the least number of bands.," As a consequence, SN Ia classification improved dramatically, regardless of the number of observed bands, while CC-SN classification success was correspondingly reduced, being worst with the least number of bands."983 Even with only oue observed band (the reddest. F350LDP). as ean be seen in Figure 11.. ihe SN-ABC manages to classify. successfully some SNe. e.g. of all the SNe with redshifts 2>0.7. excluding SNe IIn.," Even with only one observed band (the reddest, F850LP), as can be seen in Figure \ref{f:MCscss_1b}, the SN-ABC manages to classify successfully some SNe, e.g. of all the SNe with redshifts $z>0.7$, excluding SNe IIn."984 This is mainly due to the fact that. at least in our models. SNe Ia are significantly brighter than most CC-SNe. which is enough to clifferentiate (probabilistically) between Ia and CC-SNe when the redshift is constrained.," This is mainly due to the fact that, at least in our models, SNe Ia are significantly brighter than most CC-SNe, which is enough to differentiate (probabilistically) between Ia and CC-SNe when the redshift is constrained."985 Finally. AGN rejection. while improving only mareinally when adding a fourth band. is weakened considerably when cliscarding information in one or two bands.," Finally, AGN rejection, while improving only marginally when adding a fourth band, is weakened considerably when discarding information in one or two bands."986 This comes from (he longer tail. ofB high. values that the 47L7 distributions. have in. these cases., This comes from the longer tail of high values that the $\chi^2$ distributions have in these cases.987 Such a (ail. increases. the confidence limit by a [actor of ten. when compared to the scenarios with three or four bands. and does not allow the rejection of any AGNs.," Such a tail increases the confidence limit by a factor of ten, when compared to the scenarios with three or four bands, and does not allow the rejection of any AGNs."988 Thus. while some classification can be done with one or (wo photometric bands. the biases in the resulting samples are stronger and (he success rates are rather low.," Thus, while some classification can be done with one or two photometric bands, the biases in the resulting samples are stronger and the success rates are rather low."989 On the, On the990to be 27664-2722.,to be $\pm$ 2.991 The 9.9-GHz observations were done using the global pointing model which is expected to be accurate to about 10 aresec., The 9.9-GHz observations were done using the global pointing model which is expected to be accurate to about 10 arcsec.992 The primary beam size was about 2 arcmin at 23-25 GHz and 5.1 aremin at 9.9 GHz., The primary beam size was about 2 arcmin at 23-25 GHz and 5.1 arcmin at 9.9 GHz.993 Note that pointing errors affect the accuracy of flux density measurements. while the accuracy of the obtained absolute positions depends primarily on the quality of the phase calibration and is believed to be better than 0.5 aresec.," Note that pointing errors affect the accuracy of flux density measurements, while the accuracy of the obtained absolute positions depends primarily on the quality of the phase calibration and is believed to be better than 0.5 arcsec."994 At the position of the masers. which are discussed in the following section. these pointing uncertainties correspond to flux density uncertainties of and at 9.9 and 23-25 GHz. respectively.," At the position of the masers, which are discussed in the following section, these pointing uncertainties correspond to flux density uncertainties of and at 9.9 and 23-25 GHz, respectively."995 The absolute flux density scale was bootstrapped from observations of 1934-638., The absolute flux density scale was bootstrapped from observations of 1934-638.996 We expect it to be accurate to better than and at 9.9 and 23- GHz. respectively.," We expect it to be accurate to better than and at 9.9 and 23-25 GHz, respectively."997 The assumed flux densities were 2.39 and 0.75 Jy at 9.9 and 23.4 GHz. respectively.," The assumed flux densities were 2.39 and 0.75 Jy at 9.9 and 23.4 GHz, respectively."998 The data reduction was performed using the package (CABB release) following standard procedures and ignoring wide-bandwidth effects for the continuum measurement (these effects are negligible for narrow zoom windows)., The data reduction was performed using the package (CABB release) following standard procedures and ignoring wide-bandwidth effects for the continuum measurement (these effects are negligible for narrow zoom windows).999 Each spectral window produced by CABB was processed independently. although we merged the overlapping broadband windows together for imaging after the calibration and removal of contaminating spectral lines.," Each spectral window produced by CABB was processed independently, although we merged the overlapping broadband windows together for imaging after the calibration and removal of contaminating spectral lines."1000 The imaging was performed for the whole field of view and used natural weighting., The imaging was performed for the whole field of view and used natural weighting.1001 We searched for maser emission in the image cube prior to the primary beam correction (.e. the noise across the field of view was constant)., We searched for maser emission in the image cube prior to the primary beam correction (i.e. the noise across the field of view was constant).1002 Then. the cube was divided by the primary beam model at the appropriate frequency and the spectra were extracted at the peak pixel by taking a slice along the spectral axis.," Then, the cube was divided by the primary beam model at the appropriate frequency and the spectra were extracted at the peak pixel by taking a slice along the spectral axis."1003 We followed this approach due to the rather high sidelobe level in the point spread function caused by the poor uv-coverage attained in the project., We followed this approach due to the rather high sidelobe level in the point spread function caused by the poor uv-coverage attained in the project.1004 This method reproduces the flux density correctly in the case of unresolved or barely resolved sources (1.e. smaller than the synthesised beam) and is well suited to maser observations., This method reproduces the flux density correctly in the case of unresolved or barely resolved sources (i.e. smaller than the synthesised beam) and is well suited to maser observations.1005 We detected emission in all class T maser transitions observed towards 0.16 (see Table D)., We detected emission in all class I maser transitions observed towards $-$ 0.16 (see Table \ref{obsdetails}) ).1006 This is an independent confirmation of the HOPS detections., This is an independent confirmation of the HOPS detections.1007 In addition. the search for the 9.9-GHz maser yielded a detection of only the fifth maser at this frequency.," In addition, the search for the 9.9-GHz maser yielded a detection of only the fifth maser at this frequency."1008 It has a peak flux density of around 70 Jy. exceeding that of all other known 9.9-GHz masers by an order of magnitude (c.f.Voronkovetal. 2010).," It has a peak flux density of around 70 Jy, exceeding that of all other known 9.9-GHz masers by an order of magnitude \citep[c.f.][]{vor10}."1009. The spectra of all observed transitions are shown in Figure |., The spectra of all observed transitions are shown in Figure \ref{spectra}.1010 It is clear that a number of spectral components contribute to the overall profile for each transition., It is clear that a number of spectral components contribute to the overall profile for each transition.1011" The relative flux densities of these components vary with transition which is reflected by the shapes of the spectra in Figure | and by the slightly broader appearance of the spectral profiles corresponding to the high excitation J=7 and 8 transitions of the Js T, E series in comparison to the lower J transitions.", The relative flux densities of these components vary with transition which is reflected by the shapes of the spectra in Figure \ref{spectra} and by the slightly broader appearance of the spectral profiles corresponding to the high excitation J=7 and 8 transitions of the $_2-$ $_1$ E series in comparison to the lower J transitions.1012 The apparent offset in velocity (most pronounced for the J=3 transition) is consistent with the rest frequency uncertainty., The apparent offset in velocity (most pronounced for the J=3 transition) is consistent with the rest frequency uncertainty.1013 To analyse the profiles in detail we decomposed the spectra into a number of Gaussian components listed in Table 2.., To analyse the profiles in detail we decomposed the spectra into a number of Gaussian components listed in Table \ref{fit_results}.1014 The first column shows the molecular transition in the same order as in Figure |.., The first column shows the molecular transition in the same order as in Figure \ref{spectra}.1015 The following tive columns represent the peak velocity. absolute position (except for the 9.9-GHz components. for which no position measurement was possible). line width given as the full width at half maximum (FWHM) and the flux density for," The following five columns represent the peak velocity, absolute position (except for the 9.9-GHz components, for which no position measurement was possible), line width given as the full width at half maximum (FWHM) and the flux density for"1016simultaneous observation and the follow-up observations.,simultaneous observation and the follow-up observations.1017 However. from Figures 1.. 2.. 8.. and 9 it is clear that both the total intensity and circularly polarized emission at 4.9 GHz are strongly variable.," However, from Figures \ref{fig:xc}, , \ref{fig:c}, \ref{fig:0110}, and \ref{fig:0111} it is clear that both the total intensity and circularly polarized emission at 4.9 GHz are strongly variable."1018" For the total intensity ght curve the reduced V assuming a constant flux is z2.5—7.5 for a time resolution ranging from 5 min to | hour: for the circular polarization light curve \7=L8-2,8 over the same range of time resolutions.", For the total intensity light curve the reduced $\chi^2$ assuming a constant flux is $\approx 2.5-7.5$ for a time resolution ranging from 5 min to 1 hour; for the circular polarization light curve $\chi^2_r\approx 1.8-2.8$ over the same range of time resolutions.1019 It is not clear if the variability of the weaker emission at 8.5 GHz is significant. with X7=1—I7 depending on the time resolution.," It is not clear if the variability of the weaker emission at 8.5 GHz is significant, with $\chi^2_r\approx 1-1.7$ depending on the time resolution."1020 We are confident that this variability is not an observational artifact for two reasons., We are confident that this variability is not an observational artifact for two reasons.1021 First. the light curves of two field sources. constructed in the same manner as that of ((see refsec:rad)). do not exhibit significant variability. with v7=1.2 and z1.8 for a time resolution of 10 min.," First, the light curves of two field sources, constructed in the same manner as that of (see \\ref{sec:rad}) ), do not exhibit significant variability, with $\chi^2_r\approx 1.2$ and $\approx 1.8$ for a time resolution of $10$ min."1022 In fact. the reduced v values for the field sources are over-estimated compared to those for ssince. unlike2M0036-18.. these sources are spatially extended and positioned away from the phase center.," In fact, the reduced $\chi^2$ values for the field sources are over-estimated compared to those for since, unlike, these sources are spatially extended and positioned away from the phase center."1023 As a result. changes in the synthesized beam during the observation affect their light curves more. significantly. than. that of2M0036+418.," As a result, changes in the synthesized beam during the observation affect their light curves more significantly than that of."1024. Second. the variability of lis significant in circular polarization where no field sources. which can introduce false variability. produce detectable emission.," Second, the variability of is significant in circular polarization where no field sources, which can introduce false variability, produce detectable emission."1025 [t is important to note that in the two past observations of2M0036-18.. lasting 150 and 180 minutes. the persistent emission was alsovariable (802).," It is important to note that in the two past observations of, lasting 150 and 180 minutes, the persistent emission was alsovariable (B02)."1026 In addition to the variability. 1t appears from Figures 2.. 8.. and 9 that the radio emission at 4.9 GHz is periodic.," In addition to the variability, it appears from Figures \ref{fig:c}, \ref{fig:0110}, and \ref{fig:0111} that the radio emission at 4.9 GHz is periodic."1027 The auto-correlation function CACF) of both the total intensity and cireular polarization at a wide range of time resolutions shows a clear peak at 3 hours (Figures 5. and 10))., The auto-correlation function (ACF) of both the total intensity and circular polarization at a wide range of time resolutions shows a clear peak at $3$ hours (Figures \ref{fig:acf} and \ref{fig:acf011011}) ).1028 The ACFs of the two field sources described above are flat. as expected for non-periodic sources.," The ACFs of the two field sources described above are flat, as expected for non-periodic sources."1029 We assess the statistical significance of the 3-hour periodicity using two other methods which provide a measure of the power spectrum and are therefore more easily calibrated: The Lomb-Scargle (LS) periodogram (e.g.. Pressetαἰ. 1992). and a one-dimensional CLEAN algorithm (Roberts.Lehar&Dreher 1987).," We assess the statistical significance of the 3-hour periodicity using two other methods which provide a measure of the power spectrum and are therefore more easily calibrated: The Lomb-Scargle (LS) periodogram (e.g., \citealt{ptv+92}) ), and a one-dimensional CLEAN algorithm \citep{rld87}."1030. The latter method has the added advantage that artifacts and spectral leakage which arise from the sampling function and the finite length of the observation are removed., The latter method has the added advantage that artifacts and spectral leakage which arise from the sampling function and the finite length of the observation are removed.1031 We assess the significance of the results using the Monte Carlo method., We assess the significance of the results using the Monte Carlo method.1032 Specifically. we construet both. randomized versions of the 4.9 GHz light curves. and simulated light curves with a (47) variability similar to that of2M0036+418.," Specifically, we construct both randomized versions of the 4.9 GHz light curves, and simulated light curves with a $\chi^2$ ) variability similar to that of."1033. Depending on the time resolution we use 50.000 to 100.000 light curves in each set and perform the same procedures as on the real data.," Depending on the time resolution we use $50,000$ to $100,000$ light curves in each set and perform the same procedures as on the real data."1034 The significance of peaks in the LS and CLEAN power spectra of the real light curve are determined as the fraction of simulated light curves which produce stronger peaks., The significance of peaks in the LS and CLEAN power spectra of the real light curve are determined as the fraction of simulated light curves which produce stronger peaks.1035 We find that both the randomized and simulated sets provide à similar measure of the significance. as do the LS and CLEAN procedures.," We find that both the randomized and simulated sets provide a similar measure of the significance, as do the LS and CLEAN procedures."1036 A representative LS periodogram is shown in Figure 6.., A representative LS periodogram is shown in Figure \ref{fig:ls}.1037 The significance of peaks in the LS and CLEAN power spectra does depend on the choice of time resolution., The significance of peaks in the LS and CLEAN power spectra does depend on the choice of time resolution.1038 This is expected since as the period is sampled more coarsely the strength of the signal is expected to decrease., This is expected since as the period is sampled more coarsely the strength of the signal is expected to decrease.1039 We use time resolutions from 2 to 30 min (Figure 7)). and find that the strongest peak always occurs at a frequency of 0.33 hi! ora period of 3 hours.," We use time resolutions from 2 to 30 min (Figure \ref{fig:ls_timeres}) ), and find that the strongest peak always occurs at a frequency of $0.33$ $^{-1}$, or a period of 3 hours."1040 For the simulated light curves the peaks that exceed the value for ooccur over the entire frequency range., For the simulated light curves the peaks that exceed the value for occur over the entire frequency range.1041 We also find that the significance of the periodicity in the circular polarization light curve is consistently higher than for the total intensity light curve., We also find that the significance of the periodicity in the circular polarization light curve is consistently higher than for the total intensity light curve.1042 This is expected because the contamination from field sources 1s non-existent in circular polarization., This is expected because the contamination from field sources is non-existent in circular polarization.1043" For the range of time resolutions investigated we find that the significance of the 3-hour period peaks at =99,.999% for ór2 min."," For the range of time resolutions investigated we find that the significance of the 3-hour period peaks at $\approx104499.999\%$ for $\delta t=2$ min."1045 This result is confirmed by the follow-up observations. and a phased light curve of the data from 2005. Jan. 10 and 11 UT. folded with a period of 184 min is shown in Figure 11..," This result is confirmed by the follow-up observations, and a phased light curve of the data from 2005, Jan. 10 and 11 UT, folded with a period of 184 min is shown in Figure \ref{fig:phase}."1046 Thus. the radio emission from lis periodic with P=3 hours.," Thus, the radio emission from is periodic with $P=3$ hours."1047 This period is maintained on timescales of at least two years., This period is maintained on timescales of at least two years.1048" If related to the rotation of then using R,©6.3«10° em. the inferred period indicates a surface equatorial rotation velocity vzz37 km s!."," If related to the rotation of then using $R_s\approx 6.3\times 10^9$ cm, the inferred period indicates a surface equatorial rotation velocity $v\approx 37$ km $^{-1}$."1049 This value is nearly 2.5 times higher as that inferred from high-resolution optical spectra. vsini=15E5 km s! (Schweitzererἱ.2001).. suggesting an inclination angle. /z24—8.," This value is nearly 2.5 times higher as that inferred from high-resolution optical spectra, $v{\rm1050sin}i\approx 15\pm 5$ km $^{-1}$ \citep{sgh+01}, suggesting an inclination angle, $i\approx 24\pm 8^\circ$."1051 Alternatively. ifthe period is related to the orbital motion of a companion which induces magnetic activity (see below) then the semi-major axis is about 3.1«10!° em or about five times the stellar radius: this is similar to the case of the highly active RS CVn systems (e.g.. Mutel&Lestrade 1985)).," Alternatively, ifthe period is related to the orbital motion of a companion which induces magnetic activity (see below) then the semi-major axis is about $3.1\times 10^{10}$ cm or about five times the stellar radius; this is similar to the case of the highly active RS CVn systems (e.g., \citealt{ml85}) )."1052 Finally. the periodic rise in flux may be a series of weak flares. rather than variable persistent emission. in which case the flare generation process is periodic.," Finally, the periodic rise in flux may be a series of weak flares, rather than variable persistent emission, in which case the flare generation process is periodic."1053 The results presented in the previous sections directly confirm for the first time that the relative activity patterns in late-M and L dwarfs differ from those in early-type stars and early M dwarfs., The results presented in the previous sections directly confirm for the first time that the relative activity patterns in late-M and L dwarfs differ from those in early-type stars and early M dwarfs.1054 It is therefore crucial to address the origin of the magnetic fields in the well-studied aas an example of a larger trend that is emerging in. sub-stellar objects., It is therefore crucial to address the origin of the magnetic fields in the well-studied as an example of a larger trend that is emerging in sub-stellar objects.1055 While some dynamo models for convective stars predict a reduced strength. physical scale. and lifetime of the magnetic field (e.g.. Durney.DeYoung&Roxburgh 1993)). the extent of this reduction is still not known.," While some dynamo models for convective stars predict a reduced strength, physical scale, and lifetime of the magnetic field (e.g., \citealt{ddr93}) ), the extent of this reduction is still not known."1056 Clearly. the stability of the magnetic field of oover a period of three years indicates a long-lived process.," Clearly, the stability of the magnetic field of over a period of three years indicates a long-lived process."1057 Similarly. the physical scale of the field. R~Ry. is significantly larger than the physical scale of the convection.," Similarly, the physical scale of the field, $R\sim R_s$, is significantly larger than the physical scale of the convection."1058 Finally. the inferred field strength and electron densities are similar to those inferred in early M dwarfs.," Finally, the inferred field strength and electron densities are similar to those inferred in early M dwarfs."1059 It is therefore possible that the current turbulent dynamo theories are missing some key ingredients. or that the magnetic fields are generated and amplified in another process. possibly by interaction with a close-in companion.," It is therefore possible that the current turbulent dynamo theories are missing some key ingredients, or that the magnetic fields are generated and amplified in another process, possibly by interaction with a close-in companion."1060 The enhancement of magnetic fields by a close companion may play a role in the RS CVn class of active short-period binaries. and a comparison ts therefore particularly illustrative.," The enhancement of magnetic fields by a close companion may play a role in the RS CVn class of active short-period binaries, and a comparison is therefore particularly illustrative."1061 These systems are known to produce radio gyrosynchrotron emission from magnetic fields of about 200 G. with a typical luminosity of Lyez2«10! ere s! Hz!. a factor of 10?higher than that from 2M0036+18.," These systems are known to produce radio gyrosynchrotron emission from magnetic fields of about 200 G, with a typical luminosity of $L_{\nu,R}\approx 2\times106210^{16}$ erg $^{-1}$ $^{-1}$, a factor of $10^3$higher than that from ."1063. Using the sealing for eyrosynchrotron. emission. LynB R. and taking into account the similar magnetic field strengths and. covering," Using the scaling for gyrosynchrotron emission, $L_{\nu,R}1064\propto B^{-3/4}R_s^2$ , and taking into account the similar magnetic field strengths and covering"10651n half of the cases there is no significant sign of infall.,In half of the cases there is no significant sign of infall.1066" In another (the Volume average ""behind) the rms dispersion is much larger than the average. so infall contributes only a minor part of the peculiar velocity."," In another (the Volume average “behind”) the rms dispersion is much larger than the average, so infall contributes only a minor part of the peculiar velocity."1067 There is a fairly clear sien of infall into the Milky Wav., There is a fairly clear sign of infall into the Milky Way.1068 Bul if an effect is seen in only half (or less) of the places it should be it can harclly be accepled as a general feature of the situation. aud (here is the strong possibility that the positive signs are due (o something else.," But if an effect is seen in only half (or less) of the places it should be it can hardly be accepted as a general feature of the situation, and there is the strong possibility that the positive signs are due to something else."1069 The method of computing the uncertainties here is (hat used for averages of data points. each of whieh has an assigned uncertainty 0;: which uncertainties are uncorrelated with each other.," The method of computing the uncertainties here is that used for averages of data points, each of which has an assigned uncertainty $\sigma_i$; which uncertainties are uncorrelated with each other."1070 I have used the following formula for the uncertainty of the average. op: Now. the uncertainties among satellite galaxy peculiar velocities correlated. since the largest part comes from parameters in the model and changing a parameter for one will change the parameter for all.," I have used the following formula for the uncertainty of the average, $\sigma_T$: Now, the uncertainties among satellite galaxy peculiar velocities correlated, since the largest part comes from parameters in the model and changing a parameter for one will change the parameter for all."1071 That would require. flormallv. (hat uncertainties be added. resulting in à much larger overall uncertainty.," That would require, formally, that uncertainties be added, resulting in a much larger overall uncertainty."1072 On the other hand. for satellites about the same giant any change in parameters will allect (hem all in much (he same way. causingless overall uncertainty.," On the other hand, for satellites about the same giant any change in parameters will affect them all in much the same way, causing overall uncertainty."1073 Rather (han spend more time on (his rather marginal calculation attempting to sort out. uncertainties. however. I will note that the rms dispersions alone show that infall is not a strong signal. even if present: ancl (reat the effects of changes in the model in more detail in a later section.," Rather than spend more time on this rather marginal calculation attempting to sort out uncertainties, however, I will note that the rms dispersions alone show that infall is not a strong signal, even if present; and treat the effects of changes in the model in more detail in a later section."1074 These results are surprising not least in the fact that Ixarachentsevοἱal.(2003a) ad lxarachentsevοἱal...(2003b) found frontside infall but no backside infall in Local Volume eroups.," These results are surprising not least in the fact that \citet{KSD03} and \citet{KMS03}1075 found frontside infall but no backside infall in Local Volume groups."1076 Most of this I will trace to differences in the background model. of which (again) I postpone a detailed discussion for a later section.," Most of this I will trace to differences in the background model, of which (again) I postpone a detailed discussion for a later section."1077 Part could be due to spurious signals in poor or limited data., Part could be due to spurious signals in poor or limited data.1078 As examples of the latter there is the peculiar velocity versus Supergalactie Z plot. Figure 6 in Warchentsey&Makarov.(1996)... which shows a clear signal of infall into the Superealactic Plane. a signal which clsappears wilh more and better data: and the lopsided histogram of peculiar velocities of Whiting(2003).. which led to the conclusion that many nearby galaxies of high radial velocity were being missed.a conclusion which also disappears with the present collection of data.," As examples of the latter there is the peculiar velocity versus Supergalactic Z plot, Figure 6 in \citet{KM96}, which shows a clear signal of infall into the Supergalactic Plane, a signal which disappears with more and better data; and the lopsided histogram of peculiar velocities of \citet{WH03}, which led to the conclusion that many nearby galaxies of high radial velocity were being missed–a conclusion which also disappears with the present collection of data."1079 Additionally. consider Figure (1)).," Additionally, consider Figure \ref{distance}) )."1080 It is tempting to see in il an increase in peculiar velocity dispersion around 4 Alpe. due to the M31 and Centaurus A groups.," It is tempting to see in it an increase in peculiar velocity dispersion around 4 Mpc, due to the M81 and Centaurus A groups."1081 In [act there is no significant increase in peculiar velocity dispersion., In fact there is no significant increase in peculiar velocity dispersion.1082 Within 1.5 Alpe the dispersion is 70 km ': from 3 to 5 Mpe. 84 kms |. which is statistically indistinguishable (wilh this number of data points). (," Within 1.5 Mpc the dispersion is 70 km $^{-1}$ ; from 3 to 5 Mpc, 84 km $^{-1}$, which is statistically indistinguishable (with this number of data points). ("1083Note that bothare indistinguishable from the peculiar,Note that bothare indistinguishable from the peculiar1084Hucussional smnmlatious of disks.,sional simulations of disks.1085"In this work we consider the simple model of the refraction obtained under the assumption that the plasma number density is constant within the polar cap, ie., g(0.,à»)=1.","In this work we consider the simple model of the refraction obtained under the assumption that the plasma number density is constant within the polar cap, i.e., $g(\theta_{m}, \varphi_{m}) = 1$."1086" To include refraction into consideration we introduce the ""imaginary source"" of radiation giving the same trajectory at large distances whence emitted parallel to the magnetic field line (see Fig. A1)).", To include refraction into consideration we introduce the ”imaginary source” of radiation giving the same trajectory at large distances whence emitted parallel to the magnetic field line (see Fig. \ref{figRefract}) ).1087" As the ""tearing off"" level locates deeply in the magnetosphere, i.e., rA«Ri, one can use the analytical expression (22)) for the angle 015. (BGI 1993)."," As the ”tearing off” level locates deeply in the magnetosphere, i.e., $r_{\rm A} \ll R_{\rm L}$, one can use the analytical expression \ref{angle}) ) for the angle $\theta_{\perp \infty}$ (BGI 1993)."1088 It gives for the polar angle of the emission point (for dipole magnetic field it does not depend on the radial distance)., It gives for the polar angle of the emission point (for dipole magnetic field it does not depend on the radial distance).1089" As a result, we obtain for the polar angle of my source After some algebraic calculations, one can find the trajectory Here is= the tadius|tan Qi,of iπωtanθ]οο] source, and where Finally, isa unit vector perpendicular to m(¢) lying for every pulsar phase )intheplanecontainingthemagneticm(¢) and the wave k vectors."," As a result, we obtain for the polar angle of imaginary source After some algebraic calculations, one can find the trajectory Here is the radius of imaginary source, and where Finally, isa unit vector perpendicular to ${\bf m}(\phi)$ lying for every pulsar phase in the plane containing the magnetic ${\bf m}(\phi)$ and the wave ${\bf k}$ vectors."1090" Since all the quantities in equation (28)) are proportional to exp(—iwt+ ikr), its solution can be easily obtained:"," Since all the quantities in equation \ref{euler}) ) are proportional to $\exp{(- i \omega t + i{\bf kr})}$ , its solution can be easily obtained:"1091Dohnnuser 1998) the waveletfilter (Slezak ct al.,"Bohringer 1998) –, the wavelet–filter (Slezak et al."1092 1990). the “photometric redshift” method Usodama et al.," 1990), the “photometric redshift” method (Kodama et al."1093 1999). voronoi tesscllations (Riuuclla ct al.," 1999), voronoi tessellations (Ramella et al."1094" 1998) aud the ""deusitvmorphology” relationship (Ostraucder et al.", 1998) and the “density–morphology” relationship (Ostrander et al.1095 1998)., 1998).1096 The level of sophistication of these algorithius has increased im anticipation of high quality CCD survey data the Sloan Digital Sky Survey. (SDSS: Gunn ct al., The level of sophistication of these algorithms has increased in anticipation of high quality CCD survey data the Sloan Digital Sky Survey (SDSS; Gunn et al.1097 L998). The carly automated catalogues of opticallyselected clusters have produced two nmnuportaut results.," 1998), The early automated catalogues of optically–selected clusters have produced two important results."1098 First. Postinan et al. ," First, Postman et al. ("1099{906) and Lunusdeu et al. (,1996) and Lumsden et al. (11001992) botFe fud evidence for a higher space density of clusters tha that seen in the Abell Catalogue.,1992) both find evidence for a higher space density of clusters than that seen in the Abell Catalogue.1101 For exiuupe. Postiua-FP ot al. (," For example, Postman et al. ("11021996) fiucs that the measured space deusitv of clusters in the Palomar Distant Custer Survey (PDCS) is a factor of 53 eroater than that implied frou the Abe1 catalogue.,1996) finds that the measured space density of clusters in the Palomar Distant Cluster Survey (PDCS) is a factor of $5\pm2$ greater than that implied from the Abell catalogue.1103 Second. the space deitv of PDCS clusters ronuiadns constant between ;—0.2 and τ=0.6. 1l aegreenieit with fre carher work. of Couch et al. (," Second, the space density of PDCS clusters remains constant between $z=0.2$ and $z=0.6$, in agreement with the earlier work of Couch et al. ("11041991) aud lias been coufirmed receutly w Holden e al. (,1991) and has been confirmed recently by Holden et al. (11051990).,1999).1106 If true. tjose resul scan be usec to place stroug coustraiut ou the uuderlviug ealaxy evolution1 iiodlel CDM) ancl measurements of he cosmolocica paralucters σς and OoO (see Dalicall. Fan Cen 1997: Reichart et al.," If true, these results can be used to place strong constraints on the underlying galaxy evolution model CDM) and measurements of the cosmological parameters $\sigma_8$ and $\Omega_o$ (see Bahcall, Fan Cen 1997; Reichart et al."1107 1999: Tlolden et al., 1999; Holden et al.1108 1999)., 1999).1109 To SOidifv these initial results. larger catalogues of chsters are required.," To solidify these initial results, larger catalogues of clusters are required."1110 Moreover. it is CCOMME increasinelv clear that we need to conipare these different. cluste1’ caalogues to help verity results aud. expand the redshitt range over which we can study the cluster distribution.," Moreover, it is becoming increasingly clear that we need to compare these different cluster catalogues to help verify results and expand the redshift range over which we can study the cluster distribution."1111 To date however. there has been liΠο crosscomparison beween these differcut clister cataogues.," To date however, there has been little cross–comparison between these different cluster catalogues."1112 Foremost. tlie relationship between the Xrav and optical catalogues of chsters remains unclear (see oldei et al.," Foremost, the relationship between the X–ray and optical catalogues of clusters remains unclear (see Holden et al."1113 1997: Bricl Henry 1993: Bower et al., 1997; Briel Henry 1993; Bower et al.1114 1997)., 1997).1115 In the optical domain. different catalogues lave used different cluster finding algorithius thus making it very dificult to crosscalibrate catalogues aud methods aud thus verify results.," In the optical domain, different catalogues have used different cluster finding algorithms thus making it very difficult to cross–calibrate catalogues and methods and thus verify results."1116 This is illustrated by the fact that although both Liuusclen ct al. (, This is illustrated by the fact that although both Lumsden et al. (11171992) aud Postinan et al. (,1992) and Postman et al. (11181996) find a higher space density than the Abell catalogue. the PDC'S finds 5 times as Inany clusters per unit vole. while the EdiuburghDivham Cluster Catalogue (EDCC: Liundsen et al.,"1996) find a higher space density than the Abell catalogue, the PDCS finds 5 times as many clusters per unit volume, while the Edinburgh--Durham Cluster Catalogue (EDCC; Lumdsen et al."1119 1992) only finds twice as many clusters per unit volune as Abell., 1992) only finds twice as many clusters per unit volume as Abell.1120 Therefore. it is impossible to fairly compare the EDCC and the PDCS even though they are both objective. automated catalogues of clusters.," Therefore, it is impossible to fairly compare the EDCC and the PDCS even though they are both objective, automated catalogues of clusters."1121 Tn this paper. we set out to rectify this problemi bv runnins a variant of the PDCS clusterfinding aleoritlin ou the same galaxy data as used by Luusden ct al. (," In this paper, we set out to rectify this problem by running a variant of the PDCS cluster–finding algorithm on the same galaxy data as used by Lumsden et al. ("11221992) in the construction of the EDCC.,1992) in the construction of the EDCC.1123 The main ain of this project is to provide a coherent set of cluster data that spans from :~0.05 — the lower redshift hinuüt of the EDSCC to iz0.6. the upper conipleteness Init of the PDCS., The main aim of this project is to provide a coherent set of cluster data that spans from $z\sim0.05$ – the lower redshift limit of the EDSGC – to $z\simeq 0.6$ – the upper completeness limit of the PDCS.1124 In addition to using a simular algorithi as Postman et al. (, In addition to using a similar algorithm as Postman et al. (11251996). we have performed a large uuuber of Moute Carlo simulations to assess the completeness nuit. aud contanunation rate. of this new EDCC cluster catalogue.,"1996), we have performed a large number of Monte Carlo simulations to assess the completeness limit, and contamination rate, of this new EDCC cluster catalogue."1126 This is the first major application of the matched &lter algorithia to low redshift galaxy data. however. it is ouly the first of mau such surveys presently underway the SDSS. DeepRange (Postinan et al.," This is the first major application of the matched filter algorithm to low redshift galaxy data, however, it is only the first of many such surveys presently underway the SDSS, DeepRange (Postman et al."1127 1998). DPOSS (Cal ct i.," 1998), DPOSS (Gal et al."1128 1999). COSAIOS (Schuecker Bochringer 1998) aud the CCD airvev of Ziritsky ct al. (," 1999), COSMOS (Schuecker Boehringer 1998) and the CCD survey of Zaritsky et al. ("11291991).,1997).1130 Tn Section 2.. we discuss the EDSCC catalogue id the matched filter detection algorithm.," In Section \ref{EDSGC}, we discuss the EDSGC catalogue and the matched filter detection algorithm."1131 Iu Section we outline the methodology used to detect our cluster candidates aud discuss in detail the Monte Carlo siuulatiouns we performed to determine our detection," In Section \ref{method}, we outline the methodology used to detect our cluster candidates and discuss in detail the Monte Carlo simulations we performed to determine our detection"1132"In order to marginalize any correlations with M,, we group the galaxies from both samples into bins of common median mass: logM,./Mo~ 11.6, 11.3 and 10.9.","In order to marginalize any correlations with $M_\star$, we group the galaxies from both samples into bins of common median mass: $\log M_*/M_\odot\sim 11.6$ , $11.3$ and $10.9$."1133" For the lens galaxies, the corresponding median redshifts are Zmeq=0.28,0.18,0.13."," For the lens galaxies, the corresponding median redshifts are $z_{\rm1134med}=0.28, 0.18, 0.13$."1135" The local galaxies sample extends to even lower masses (logM,/Mo 10.4) with no lens counterparts.", The local galaxies sample extends to even lower masses $\log M_*/M_\odot \sim 10.4$ ) with no lens counterparts.1136" Our first result (which we do not show for the sake of space) is that for the lenses, iincreases on average with M, (see Cardoneetal.2009 and Cardone&Tortora2010 for details)."," Our first result (which we do not show for the sake of space) is that for the lenses, increases on average with $M_\star$ (see \citealt{Cardone+09} and \citealt{CT10} for details)."1137" This result confirms that as in local galaxies (T+09), iis also a main driver of the fundamental plane tilt at z~0.2."," This result confirms that as in local galaxies (T+09), is also a main driver of the fundamental plane tilt at $z\sim 0.2$."1138" Next, following NRT10, we focus on correlations of the DM metrics with galaxy size and age."," Next, following NRT10, we focus on correlations of the DM metrics with galaxy size and age."1139 For the latter we adopt the look-back time to the formation epoch in order to put all the galaxies with different observed redshifts on a common reference frame., For the latter we adopt the look-back time to the formation epoch in order to put all the galaxies with different observed redshifts on a common reference frame.1140 Fig., Fig.1141" 1 demonstrates that there is a strong positive correlation between aandReg,, once the galaxies are divided into mass bins."," \ref{fig: fig1} demonstrates that there is a strong positive correlation between and, once the galaxies are divided into mass bins."1142" This may be understood as a larger eenclosing a bigger portion of the DM halo; this ""aperture effect"" appears to be more dominant than the ccorrelation with M,.", This may be understood as a larger enclosing a bigger portion of the DM halo; this “aperture effect” appears to be more dominant than the correlation with $M_\star$.1143" The local and lens samples appear reasonably similar, although the lens galaxies in the lowest mass bin are systematically higher, which is an issue we will discuss below."," The local and lens samples appear reasonably similar, although the lens galaxies in the lowest mass bin are systematically higher, which is an issue we will discuss below."1144 Both samples are in rough agreement with our ACDM toy model predictions (top panel)., Both samples are in rough agreement with our $\Lambda$ CDM toy model predictions (top panel).1145 Fig., Fig.1146 2 shows that (ppm) strongly anti-correlates withReg.., \ref{fig: fig2} shows that $\langle\rho_{\rm DM}\rangle$ strongly anti-correlates with.1147" Again considering the aperture effect and assuming DM halo homogeneity, the implication is that we are measuring a mean DM density profile with radius, with a best fitted log slope of ~—1.7."," Again considering the aperture effect and assuming DM halo homogeneity, the implication is that we are measuring a mean DM density profile with radius, with a best fitted log slope of $\sim -1.7$."1148" As discussed in NRT10, this steep slope is indicative of cuspy halos, perhaps as induced by AC."," As discussed in NRT10, this steep slope is indicative of cuspy halos, perhaps as induced by AC."1149" One could suspect that we are getting out what we are putting in, since our default galaxy model assumes an isothermal total density profile (with slope  —2) in order to extrapolate measurements to r=Reg, but we have shown in NRT10 that the use of an alternative profile yields similar results (modulo a difference of constant-M/L0.1—0.2 in the slope), still fully consistent with a cuspy contracted"," One could suspect that we are getting out what we are putting in, since our default galaxy model assumes an isothermal total density profile (with slope $\sim -2$ ) in order to extrapolate measurements to $r = \Re$, but we have shown in NRT10 that the use of an alternative constant-M/L profile yields similar results (modulo a difference of $0.1-0.2$ in the slope), still fully consistent with a cuspy contracted."1150"halo"".. In Fig. 2,,"," In Fig. \ref{fig: fig2},"1151" we also see that the ETGs have DM densities substantially larger than those of local spiral galaxies, which have been suggested to follow a unified halo trend with dwarf spheroidals (Donatoetal.2009;Walker"," we also see that the ETGs have DM densities substantially larger than those of local spiral galaxies, which have been suggested to follow a unified halo trend with dwarf spheroidals \citep{Donato+09,Walker+10b}."1152" This dichotomy is qualitatively consistent with other 2010)..findings (Gerhardetal.2001;Thomas 2009;; NRT10; Cardone&Tortora 2010)), and may imply different formation mechanisms."," This dichotomy is qualitatively consistent with other findings \citealt{Gerhard+01,Thomas+09}; NRT10; \citealt{CT10}) ), and may imply different formation mechanisms."1153" The difference might be assumed as simply caused by ETGs forming from denser late-type galaxies at earlier epochs, which would yield the corollary prediction that ETGs with younger stellar ages have less dense halos because their late-type progenitors were less dense."," The difference might be assumed as simply caused by ETGs forming from denser late-type galaxies at earlier epochs, which would yield the corollary prediction that ETGs with younger stellar ages have less dense halos because their late-type progenitors were less dense."1154" However, as we will see below, the opposite trend appears to be observed."," However, as we will see below, the opposite trend appears to be observed."1155" Finally we consider the fpw--age dependencies in Fig. 3,,"," Finally we consider the -age dependencies in Fig. \ref{fig:1156fig3},"1157" again using separate M, bins.", again using separate $M_\star$ bins.1158" The lens and local galaxies match up remarkably well in general, showing a clear trend for lower aat older ages."," The lens and local galaxies match up remarkably well in general, showing a clear trend for lower at older ages."1159" The low-mass lens galaxies are predominantly young, which is probably a selection effect on apparent magnitude."," The low-mass lens galaxies are predominantly young, which is probably a selection effect on apparent magnitude."1160 The fpm--age anti-correlation thencauses the overall ffor this mass bin to be high., The -age anti-correlation thencauses the overall for this mass bin to be high.1161" In summary, at a fixed galaxy age and mass, the higher-z sample does not show"," In summary, at a fixed galaxy age and mass, the $z$ sample does not show"11622009).,.1163. Second. the SER is expected to be enhanced. only ab scales at which ealaxy-galaxy interactions are relevant: bevond that scale star formation is not only not expected to be enhanced. but. should be depressed. because of the well known SEIt-density anticorrelation (c.g.Baloghetal.. 2002)..," Second, the SFR is expected to be enhanced only at scales at which galaxy-galaxy interactions are relevant; beyond that scale star formation is not only not expected to be enhanced, but should be depressed because of the well known SFR-density anticorrelation \citep[e.g., ][]{balogh}."1164 From the above mentioned works we choose to compare with Lietal.(2008). for three reasons: a) they use niarked statistics. b) their large sample allowed an accurate estimate of enhancement to be mace. and c) SDSS clustering has been shown to be similar to the one present in the Deal.(2006) mock. catalogue from the Milleniun Simulation in the local Universe (Springelοἱal..2005).," From the above mentioned works we choose to compare with \citet{li} for three reasons: a) they use marked statistics, b) their large sample allowed an accurate estimate of enhancement to be made, and c) SDSS clustering has been shown to be similar to the one present in the \citet{delucia} mock catalogue from the Millenium Simulation in the local Universe \citep{springel}."1165. Real galaxy surveys. even spectroscopic surveys. have no access to the real space separation of galaxies.," Real galaxy surveys, even spectroscopic surveys, have no access to the real space separation of galaxies."1166 Lietal.(2008) used. a projected correlation function wry) to circumvent this dillicultv. where the projected: correlation function is related to the 3D correlation function via: where x is the coordinate along the line of sight. anc ry is the projected. separation transverse to the line. of steht.," \citet{li} used a projected correlation function $w(r_P)$ to circumvent this difficulty, where the projected correlation function is related to the 3D correlation function via: where $\pi$ is the coordinate along the line of sight, and $r_p$ is the projected separation transverse to the line of sight."1167 We use for this exercise galaxics more massive than 3LOMAL. in order to match the selection citeria in Lieal. (2008).," We use for this exercise galaxies more massive than $3\times1168 10^{10}M_\odot$ in order to match the selection citeria in \citet{li}."1169. Moreover. they did not use an additive weigh but used the SSER of the primary galaxy as the weigh of the pair.," Moreover, they did not use an additive weight but used the SSFR of the primary galaxy as the weight of the pair."1170 We also use such a scheme here to. perform. our weighted analysis in the simulation., We also use such a scheme here to perform our weighted analysis in the simulation.1171 Lictal.(2008) calculated: the cross-correlation between a subsample of galaxies which are forming stars (primaries) and all the galaxies in the sample (secondaries)., \citet{li} calculated the cross-correlation between a subsample of galaxies which are forming stars (primaries) and all the galaxies in the sample (secondaries).1172 As we lack of such information we run a correlation using all the galaxies as both primaries and secondaries., As we lack of such information we run a correlation using all the galaxies as both primaries and secondaries.1173 As previously. we assign an average enhancement to all galaxies found: physically in very close pairs. but in order to mimic the the pair selection in Lietal.(2008).. who cross-correlate a sample of spectroscopically defined. star forming galaxies with a photometric catalog of all galaxies above the stellar mass limit. we run the correlation function selecting galaxy pairs with “line-of-sight” separations of less than LOO Alpe.," As previously, we assign an average enhancement to all galaxies found physically in very close pairs, but in order to mimic the the pair selection in \citet{li}, who cross-correlate a sample of spectroscopically defined star forming galaxies with a photometric catalog of all galaxies above the stellar mass limit, we run the correlation function selecting galaxy pairs with “line-of-sight” separations of less than 100 Mpc."1174 Our results ave not sensitive to this choice of maximum separation: correlations between galaxies on scales larger than 100 Alpe are extremely weak. in comparison to the strong clustering on <LALpe scales.," Our results are not sensitive to this choice of maximum separation; correlations between galaxies on scales larger than 100 Mpc are extremely weak, in comparison to the strong clustering on $<1 Mpc$ scales."1175 We choose to model the data with a constant enhancement e=LS at kr<r. with r=35 kkpe. Motivated by the star formation enhancement observed in galaxy seumples selected in a similar manner at cilferent recdshifts (Lietab.2008:Robainaal.2009) we choose to mocel the data with ο=2 for galaxies in pairs with separations rp«15 kpe and ο=1.5 for those in pairs with 15«rp40 kpc.," We choose to model the data with a constant enhancement $\epsilon=1.8$ at $r<r_c$, with $r_c = 35$ kpc, Motivated by the star formation enhancement observed in galaxy samples selected in a similar manner at different redshifts \citep{li, robaina} we choose to model the data with $\epsilon =2$ for galaxies in pairs with separations $r_P<15$ kpc and $\epsilon=1.5$ for those in pairs with $15<r_P<40$ kpc."1176" We also neglect. any environmental suppression of star formation at separations romor, (Bartonctal.2000:Baloghet."," We also neglect any environmental suppression of star formation at separations $r>r_c$ \citep{barton, balogh}."1177al...2002).. These are clearly oversimplifications. as the real dependence of enhancement (and suppression at large radii) on separation will be considerably more complex.," These are clearly oversimplifications, as the real dependence of enhancement (and suppression at large radii) on separation will be considerably more complex."1178 Yet. this simple moclel sullices to illustrate the recovered. enhancement. signature expected. from a model in which SE is enhanced. only at small raclii.," Yet, this simple model suffices to illustrate the recovered enhancement signature expected from a model in which SF is enhanced only at small radii."1179 eotwithstanding these limitations. we compare the results of our simple model with the data in reffig:sfr..," Notwithstanding these limitations, we compare the results of our simple model with the data in \\ref{fig:sfr}."1180 Strikinglv. we find that the tail of enhanced SE out to ~200kpe seen in the data may. in great. part. be a rellection of the use of marked correlation functions statistics to explore the radial. dependence of SE. enhancement. in galaxies.," Strikingly, we find that the tail of enhanced SF out to $\sim$ 200kpc seen in the data may, in great part, be a reflection of the use of marked correlation functions statistics to explore the radial dependence of SF enhancement in galaxies."1181 This has direct relevance in the interpretation of the results from Lietal.(2008)., This has direct relevance in the interpretation of the results from \citet{li}.1182. If one argued. that the enhancement at  LOOkkpe (or much of it) was real. one would. need to fulfil two criteria to produce such an ellect.," If one argued that the enhancement at $\sim 100$ kpc (or much of it) was real, one would need to fulfil two criteria to produce such an effect."1183 I'irstly. assuming that the triggering event is the first. pass. one would need an enhancement lifetime of at least 300Myr (longer than the internal dynamical time) for typical orbital velocities of 300km/s or less.," Firstly, assuming that the triggering event is the first pass, one would need an enhancement lifetime of at least 300Myr (longer than the internal dynamical time) for typical orbital velocities of 300km/s or less."1184 Secondly. a significant fraction of the seconcaries would need to have near-racial orbits in order to produce such an enhancement.," Secondly, a significant fraction of the secondaries would need to have near-radial orbits in order to produce such an enhancement."1185 If. as we suggest instead. the enhanced SE at ~ LOOkkpe is an artifact of the use of the 2 point correlation Function. then one would argue that enhancement happens only for close pairs and shorter interaction-induced. SE timescales and a greater. cliversity of orbits would. be permitted.," If, as we suggest instead, the enhanced SF at $\sim 100$ kpc is an artifact of the use of the 2 point correlation function, then one would argue that enhancement happens only for close pairs and shorter interaction-induced SF timescales and a greater diversity of orbits would be permitted."1186 While developing à model that realistically reproduces the data is bevond the scope of this Letter. one can clearly see that this ellect. needs to be accounted for in order to robustly interpret the behavior of marked. correlation functions.," While developing a model that realistically reproduces the data is beyond the scope of this Letter, one can clearly see that this effect needs to be accounted for in order to robustly interpret the behavior of marked correlation functions."1187 Weighted. correlation functions. are. an increasingly important tool for understanding how galaxy properties depend on their separation from cach other., Weighted correlation functions are an increasingly important tool for understanding how galaxy properties depend on their separation from each other.1188 We use a mock galaxy sample crawn from the Millenium. simulation. assigning weights using a simple prescription to illustrate and explore how well a weighted correlation function recovers the true radial dependence of the input weights.," We use a mock galaxy sample drawn from the Millenium simulation, assigning weights using a simple prescription to illustrate and explore how well a weighted correlation function recovers the true radial dependence of the input weights."1189 We find that the use of a weighted: correlation. function results in a cilution of the magnitude of any racial dependence of properties and a smearing out of that racial, We find that the use of a weighted correlation function results in a dilution of the magnitude of any radial dependence of properties and a smearing out of that radial1190Πονα0) cuission is the workhorse for relating quautitics of deuse gas to star formation (6.9.Gao&Solomon 2001).,HCN(1–0) emission is the workhorse for relating quantities of dense gas to star formation \citep[e.g.][]{GS04}.1191. It is interesting to compare couclisious about the dense componeut from Που with those of the more commonly used ΠοΝα0)., It is interesting to compare conclusions about the dense component from $_{3}$ N with those of the more commonly used HCN(1–0).1192 IICN(IL0) has been mapped at simular spatial resolution by Downesctal.(1992)., HCN(1–0) has been mapped at similar spatial resolution by \citet[][]{DRGGGM92}.1193. Fieure 2. compares Που 1) to Πονα0)., Figure \ref{inticont} compares $_{3}$ N(5–4) to HCN(1–0).1194 While ecuerally traces the same dense GMCs seeu in ICN their relative brightuesses are rather differcut., While $_{3}$ N generally traces the same dense GMCs seen in HCN their relative brightnesses are rather different.1195" Iu HCN(10) GAIC A. D and € are all within 10 of the sue brightuess aud GAICs D aud E are 100 and 50% weaker. respectively,"," In HCN(1–0) GMC A, B and C are all within 10 of the same brightness and GMCs D and E are 100 and 50 weaker, respectively."1196 Whereas in Που νο1) and (1615). C dominates. Bis nearly abseut aud A is not signi&cantlv different frou: D and E. Comparisons with IIC4N. clearly demonstrate that there ds larger varlatious in deuse gas properties than IICN incicates.," Whereas in $_{3}$ N(5–4) and (16–15), C dominates, B is nearly absent and A is not significantly different from D and E. Comparisons with $_{3}$ N clearly demonstrate that there is larger variations in dense gas properties than HCN indicates."1197 The dominate difference is cuhanced ΠΟ towards the starburst and GAIC A relative to GMC ΝC. Uulixe the WCsN transitions. IICN(10) is optically thick aud has sheltly larger (25 - 50% 4) filling factors (Downesctal. 1992).," The dominate difference is enhanced HCN towards the starburst and GMC A relative to GMC C. Unlike the $_{3}$ N transitions, HCN(1–0) is optically thick and has slightly larger (25 - 50 ) filling factors \citep[][]{DRGGGM92}."1198. As kinetic temperatures increase optically thick transitions brighten more rapidly than (lower excitation) optically thin transitions., As kinetic temperatures increase optically thick transitions brighten more rapidly than (lower excitation) optically thin transitions.1199 Hence it is expected that the TICN emissiou should favor somewhat svariicr dense gas., Hence it is expected that the HCN emission should favor somewhat warmer dense gas.1200 Likely this effect results in the much brighter relative IICN(10) inteusities towards the starburst., Likely this effect results in the much brighter relative HCN(1–0) intensities towards the starburst.

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