ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2" In the present work we will consider two possible choices for cach of these two functions. namely an exponential 1985:Wetterich1988). and a SUGRA (Brax&Martin potential. where à is a positive constant and where for simplicity the field ó has been expressed in units of the reduced Planck mass Aij. as well as both a constant and an exponentially erowing coupling function 3,(0): characterized by 4,=0 and 2,z0. respectively."," In the present work we will consider two possible choices for each of these two functions, namely an exponential \citep[][]{Lucchin_Matarrese_1984,Wetterich_1988} and a SUGRA \citep[][]{Brax_Martin_1999}3 potential, where $\alpha $ is a positive constant and where for simplicity the field $\phi $ has been expressed in units of the reduced Planck mass $M_{\rm Pl}$, as well as both a constant and an exponentially growing coupling function $\beta _{c}(\phi )$: characterized by $\beta _{1}=0$ and $\beta _{1}>0$, respectively."4 The most relevant difference between the exponential potential and the SUGRA potential relies. on the facet that. the latter features a global minimum at finite scalar field values: this allows for a change of direction of the scalar lield motion. which is the main feature of the recently proposed “Bouncing cDIT scenario (Baldi 2011a)..," The most relevant difference between the exponential potential and the SUGRA potential relies on the fact that the latter features a global minimum at finite scalar field values; this allows for a change of direction of the scalar field motion, which is the main feature of the recently proposed “Bouncing cDE"" scenario \citep[][]{Baldi_2011c}. ."5 One should also notice that the notation introduced in Eqs. (1- -5)), One should also notice that the notation introduced in Eqs. \ref{klein_gordon}- \ref{friedmann}) )6 corresponds to the original convention proposed. by Amendola(2000). and has been adopted. by several other studies. including the project. considered. in the present work. but it dilfers bv a constant factor y/3 [rom what is used in another part of the related. literature. (ase.g.Pettorino&Baccigalupi2008:Baldietal. 2010).," corresponds to the original convention proposed by \citet{Amendola_2000}7 and has been adopted by several other studies, including the project considered in the present work, but it differs by a constant factor $\sqrt{2/3}$ from what is used in another part of the related literature \citep[as \eg][]{Pettorino_Baccigalupi_2008,Baldi_etal_2010}."8. The specific models considered. in the present work have been described in full detail by Baldi(2011a). and Baleli(2011b):: we summarize them in Table L.. where the features and the specific parameters of cach model are outlined.," The specific models considered in the present work have been described in full detail by \citet{Baldi_2011c} and \citet{CoDECS}; we summarize them in Table \ref{tab:models}, where the features and the specific parameters of each model are outlined."9 The evolution equations for linear density perturbations in the context of a cDIZ cosmology have been derived in the literature (seee.g.Amencola2004:Pettorino&Baccigalupi 2008).. and in the Newtonian limit of sub-horizon scales can be expressed as follows: where 6.4=δρρω are the relative density perturbations of the coupled CDAL and uncoupled barvonic ILuicls. respectively. and where the scalar field dependence of the coupling function :2.(6) has been omitted Lorsimplicity.," The evolution equations for linear density perturbations in the context of a cDE cosmology have been derived in the literature \citep[see \eg][]{Amendola_2004,Pettorino_Baccigalupi_2008}, and in the Newtonian limit of sub-horizon scales can be expressed as follows: where $\delta _{c,b}\equiv \delta \rho _{c,b,}/\rho _{c,b}$ are the relative density perturbations of the coupled CDM and uncoupled baryonic fluids, respectively, and where the scalar field dependence of the coupling function $\beta _{c}(\phi )$ has been omitted forsimplicity."10 In Eq. (9).," In Eq. \ref{gf_c}) ),"11 the factor Pe—1|44(5)/3 represents an additional fifth-Force. mediated. by the DLE scalar field © for CDM perturbations. while the second. term in the first square bracket at. the. right-hand-side of Eq. (9))," the factor $\Gamma _{c}\equiv 1 + 4\beta _{c}^{2}(\phi )/3$ represents an additional fifth-force mediated by the DE scalar field $\phi $ for CDM perturbations, while the second term in the first square bracket at the right-hand-side of Eq. \ref{gf_c}) )"12 is an extra friction term on C'DAL Uuctuations arising as a consequence of momentum conservation (1--5..9..10)) and for a detailed: discussion. of the extra friction and fifth. force corrections to the evolution of linear.," is an extra friction term on CDM fluctuations arising as a consequence of momentum conservation \ref{friedmann}, \ref{gf_c}, \ref{gf_b}) ) and for a detailed discussion of the extra friction and fifth force corrections to the evolution of linear."13perturbations). As a consequence of these two additional terms in the perturbed dynamic equations. CDM fluctuations will grow faster in cDIS models with respect to à standard ACDAL cosmology. thereby reaching a higher σ normalization at 2=Q0 if starting from the same amplitude at the last scattering surface σος=1100. as shown in the last column of ‘Table 1..," As a consequence of these two additional terms in the perturbed dynamic equations, CDM fluctuations will grow faster in cDE models with respect to a standard $\Lambda $ CDM cosmology, thereby reaching a higher $\sigma _{8}$ normalization at $z=0$ if starting from the same amplitude at the last scattering surface $z_{\rm CMB}\approx 1100$, as shown in the last column of Table \ref{tab:models}."14 Llowever. in the nonlinear regime the interplay between the friction term anc the fifth force is not so straightforward. as for the case of linear perturbations. due to the fact that as a consequence of virialization processes. the local velocity field will not necessarily be aligned to the local gradient of the gravitational potential. as one can sec from the three-cimentional generalization of Eq. (9))," However, in the nonlinear regime the interplay between the friction term and the fifth force is not so straightforward as for the case of linear perturbations, due to the fact that as a consequence of virialization processes, the local velocity field will not necessarily be aligned to the local gradient of the gravitational potential, as one can see from the three-dimentional generalization of Eq. \ref{gf_c}) )"15 to a system of point-like massive particles: where ry is the physical distance of the target coupled particle. from the other CDAL ancl barvonic particles. respectively.," to a system of point-like massive particles: where $r_{c,b}$ is the physical distance of the target coupled particle from the other CDM and baryonic particles, respectively."16 The effect of the frietion term in the nonlinear regime has been shown to induce a suppression of small-scale power in the ¢DE models with respect to the nonlinear power that would be inferred based. on the large-scale σε normalization in the context of a ACDAL universe (Baldi 2011b)..," The effect of the friction term in the nonlinear regime has been shown to induce a suppression of small-scale power in the cDE models with respect to the nonlinear power that would be inferred based on the large-scale $\sigma _{8}$ normalization in the context of a $\Lambda $ CDM universe \citep[][]{Baldi_2011b,CoDECS}."17 Such suppression will have important consequences on the weak lensing constraints on CDE models that we want to address in the present work., Such suppression will have important consequences on the weak lensing constraints on cDE models that we want to address in the present work.18 Therefore. although it is possible to estimate the full matter power in cDIS scenarios by applying nonlinear corrections (calibrated on ACDAL simulations) to the re-normalized. linear. power spectrum (asrecentlydonee.g.bx.Amencolactal.2011).. in order to reach high accuracy at scales relevant for present and future laree lensing surveys it is necessaryto rely on a fully nonlinear treatment of cDIS scenarios via specific N- simulations.," Therefore, although it is possible to estimate the full matter power in cDE scenarios by applying nonlinear corrections (calibrated on $\Lambda $ CDM simulations) to the re-normalized linear power spectrum \citep[as recently done e.g. by][]{Amendola_etal_2011}, in order to reach high accuracy at scales relevant for present and future large lensing surveys it is necessaryto rely on a fully nonlinear treatment of cDE scenarios via specific N-body simulations."19 A cliscussion on the comparison between these two approaches is presented in Section 5.3.., A discussion on the comparison between these two approaches is presented in Section \ref{comparison}. .20" Figure 1. shows the power spectra for cach ofthe constant coupling (3,= 0) models normalised bv WALADPT.", Figure \ref{fig:PowerspectrumConstant} shows the power spectra for each ofthe constant coupling $\beta_1=0$ ) models normalised by WMAP7.21 The values of these couplings were chosen since CDE models, The values of these couplings were chosen since cDE models22The spectroscopic detection of the energetic supernova SN 2003dh coincident with GRB 030329 (Hjorth et al.,The spectroscopic detection of the energetic supernova SN 2003dh coincident with GRB 030329 (Hjorth et al.23 2003: Stanek et al., 2003; Stanek et al.24 2003) has firmly established that - at least some - long GRBs accompany the core collapse of massive stars. as it was first suggested by the spatial and temporal coincidence of GRB 980425 and SN 1998bw (Galama et al.," 2003) has firmly established that - at least some - long GRBs accompany the core collapse of massive stars, as it was first suggested by the spatial and temporal coincidence of GRB 980425 and SN 1998bw (Galama et al."25 1998)., 1998).26 Such spectroscopic signatures of supernovae (SNae) associated with GRBs have been detected in a handful of cases during the last years. eg. GRB 031203/SN 20031Iw (Malesani et al.," Such spectroscopic signatures of supernovae (SNae) associated with GRBs have been detected in a handful of cases during the last years, e.g. GRB 031203/SN 2003lw (Malesani et al."27 2004). GRB 021211/ SN 200511 (Della Valle et al.," 2004), GRB 021211/ SN 2002lt (Della Valle et al."28 2003). GRB O50525A/SN 2005ne (Della Valle et al.," 2003), GRB 050525A/SN 2005nc (Della Valle et al."29" 2006). and the recent case of GRB 060218/SN 2006a, (Campana et al."," 2006), and the recent case of GRB 060218/SN 2006aj (Campana et al."30 2006. Modjaz et al.," 2006, Modjaz et al."31 2006)., 2006).32 The possibility that core-collapse SNae are progenitors of GRBs has been further supported by the detection of re-brightening in the late-time afterglow light curves. interpreted as a contribution of accompanying SNae (Bloom et al.," The possibility that core-collapse SNae are progenitors of GRBs has been further supported by the detection of re-brightening in the late-time afterglow light curves, interpreted as a contribution of accompanying SNae (Bloom et al."33 1999. Zeh et al.," 1999, Zeh et al."34 2004. Castro-Tirado Gorosabel 1999) and the localizations of afterglows in star forming regions (e.g. Djorgovski et al.," 2004, Castro-Tirado Gorosabel 1999) and the localizations of afterglows in star forming regions (e.g. Djorgovski et al."35 2001. Bloom et al.," 2001, Bloom et al."36 2002. Fynbo et al.," 2002, Fynbo et al."37 2000. Fruchter et al.," 2000, Fruchter et al."38 1999. Holland Hjorth 1999).," 1999, Holland Hjorth 1999)."39" Indeed. the currently mostly favored scenario for the origin of long GRBs involves the collapse of a massive Wolf-Rayet star endowed with rotation (Woosley 1993. MacFadyen Woosley 1999, Woosley Heger 2004)."," Indeed, the currently mostly favored scenario for the origin of long GRBs involves the collapse of a massive Wolf-Rayet star endowed with rotation (Woosley 1993, MacFadyen Woosley 1999, Woosley Heger 2004)."40 Recently. Yoon Langer (2005) considered the evolution of massive. magnetized stars where rapid rotation induces an almost chemically homogeneous evolution. and found that the requirements of this collapsar model are satistied if the metallicity is sufficiently small. namely less than 0.1Z. ," Recently, Yoon Langer (2005) considered the evolution of massive, magnetized stars where rapid rotation induces an almost chemically homogeneous evolution, and found that the requirements of this collapsar model are satisfied if the metallicity is sufficiently small, namely less than $0.1\, Z_{\odot}$ "41Since we expect the motion of the planetesimal to be tightly coupled to the gas. we define a new set of regular variables GN.H)=(khkyofhfy) (Paardekooper et al.,"Since we expect the motion of the planetesimal to be tightly coupled to the gas, we define a new set of regular variables $(K,H)=(k-k_g, h-h_g)$ (Paardekooper et al."42 2008) and write equations (18)) as dt UH IN gy 4— CHK? where er ΞσοπornJT.," 2008) and re-write equations \ref{eq20}) ) as = ' K + g_g = ' H - g_g k_g, where ' =."43" In the case of a static disk where g,,=0. equations (19)) can be solved analytically to give Kt)-Koq - Ht)-2H"," In the case of a static disk where $g_g=0$, equations \ref{eq21}) ) can be solved analytically to give K(t) = ; H(t) =."44"ol—Re Here A, and //y are the values of A and // at /=0. and L5=WAG|ΠΠ."," Here $K_0$ and $H_0$ are the values of $K$ and $H$ at $t=0$, and $E_0^2 = K_0^2 + H_0^2$."45 The circularization time is thus proportional to 11. unlike the exponential decay time associated with the lineardrag regime.," The circularization time is thus proportional to $1/t$, unlike the exponential decay time associated with the lineardrag regime."46 The final equilibrium solution is given by ἐν=ff=O implying that. at equilibrium cCy and weσι.," The final equilibrium solution is given by $K=H=0$ implying that, at equilibrium $e \rightarrow e_g$ and $\varpi \rightarrow \varpi_g$."47 Thus. the overall dynamical behavior of the planetesimal in a static eccentric disk is very similar to the circular ease. except that the final equilibrium trajectory is now an ellipse.," Thus, the overall dynamical behavior of the planetesimal in a static eccentric disk is very similar to the circular case, except that the final equilibrium trajectory is now an ellipse."48 Neglecting terms proportional to the eccentricity. the rate of the change of the semimajor axis of the planetesimal can be written as WTIE where L= is the Delaunay momentum associated to a.," Neglecting terms proportional to the eccentricity, the rate of the change of the semimajor axis of the planetesimal can be written as = )^2, where $L=\sqrt{\mu a}$ is the Delaunay momentum associated to $a$."49 Since(1a)«\/jra1. equation (22)) suggests that the orbital decay of the planetesimal is much slower than the circularization time.," Since $(1-\alpha) \ll 1$, equation \ref{eq24}) ) suggests that the orbital decay of the planetesimal is much slower than the circularization time."50 In the limiting case where a=1. this equations indicates that no secular change exists in the semimajor axis ofthe planetesimal once the eccentricity and longitude of the pericenter have reached their equilibrium values.," In the limiting case where $\alpha=1$, this equations indicates that no secular change exists in the semimajor axis of the planetesimal once the eccentricity and longitude of the pericenter have reached their equilibrium values."51 In the case of a precessing disk. system (19)) is much more complicated to solve analytically.," In the case of a precessing disk, system \ref{eq21}) ) is much more complicated to solve analytically."52 We can. however. focus on the equilibrium solutions.," We can, however, focus on the equilibrium solutions."53 Figure 2. shows a typical example of the orbital evolution of a one-kilometer planetesimal in a retrograde oecessing disk with period of 1000 yrs., Figure \ref{fig2} shows a typical example of the orbital evolution of a one-kilometer planetesimal in a retrograde precessing disk with period of $1000$ yrs.54 The solution was obtained solving numerically the secular equations (19))., The solution was obtained solving numerically the secular equations \ref{eq21}) ).55" Due to the disk oecession. (A./1) no longer reach a stationarypoint but exhibit oscillations with frequency g, around a center located. near the origin."," Due to the disk precession, $(K,H)$ no longer reach a stationarypoint but exhibit oscillations with frequency $g_g$ around a center located near the origin."56 The same behavior isalso noted for the time evolution of he original variables (A.) (middle plot).," The same behavior isalso noted for the time evolution of the original variables $(k,h)$ (middle plot)."57 However. the system still retains an equilibrium solution in a new set of variables defined as (IN.1)=(ecoszNze.esinAx). where Acc=my.," However, the system still retains an equilibrium solution in a new set of variables defined as $({\bar K},{\bar H})=(e\cos{\Delta \varpi},e\sin{\Delta \varpi})$, where $\Delta \varpi = \varpi -\varpi_g$."58 This behavior has been noted for all values of s and as well as for any initial condition., This behavior has been noted for all values of $s$ and as well as for any initial condition.59" To obtain analytical expressions for the equilibrium solutions in this case. we note that from the definitions of (&.Ph) and (Ay. fy). it is possible to write eu Ξ kb, | hhq(23) ell — hk, kh,"," To obtain analytical expressions for the equilibrium solutions in this case, we note that from the definitions of $(k,h)$ and $({k_g},{h_g})$ , it is possible to write e_g = k k_g + h h_g e_g = h k_g - k h_g."60" The corresponding variational equations of A and // are then given by ep ""RTSy| Py due HO) gy, ↴⊳ ", The corresponding variational equations of $\bar K$ and $\bar H$ are then given by e_g = k_g+ h_g - g_g e_g e_g = k_g - h_g - g_g e_g .61In an equilibrium state. the values of (A.//) are constant and equations (243) can be simplify to," In an equilibrium state, the values of $({\bar K},{\bar H})$ are constant and equations \ref{eq26}) ) can be simplify to"62The svunmetry of the interaction between the heliosphere and interstellar material is determined by three fundamental phenomena: the solar wind (which loosely (races ecliptic,The symmetry of the interaction between the heliosphere and interstellar material is determined by three fundamental phenomena: the solar wind (which loosely traces ecliptic63tax the servers.,tax the servers.64 The extraction of 25.000 stuceut 'ecords ouly required an evening of interaction.," The extraction of 25,000 student records only required an evening of interaction."65 Whereas the se‘ipts could have obtained tliis iiorivation iu only a few teus of nmiuutes. (he process was deliberatey slowed aud ook several hours.," Whereas the scripts could have obtained this information in only a few tens of minutes, the process was deliberately slowed and took several hours."66Ss The last sage of our alalysis d1volvec| »arsiig the HTML files on each stude| into some ineaniug‘ul daaset (e.g...e) NNL forma| or raWw ASCIT).," The last stage of our analysis involved parsing the HTML files on each student into some meaningful dataset (e.g., XML format or raw ASCII)."67 Once in a usable formal. we continued our analysis IslngsandarL tools for astro101nical 'esea‘ch (neais. correlations. plottiig.€) lilear fitting).," Once in a usable format, we continued our analysis using standard tools for astronomical research (means, correlations, plotting, linear fitting)."68 Often HTML )ages contain eim)edded. infornatiol aes which facilitate converti18oO ile pages into XML fornat., Often HTML pages contain embedded information tags which facilitate converting the pages into XML format.69 Li Dickweb web ¢ata. tie HTML tag:« are only used for browser foriwatt]ie.," In Duckweb web data, the HTML tags are only used for browser formatting."70 A simple Python (regilar expression) command stips al he HTIL tags ron the page., A simple Python (regular expression) command strips all the HTML tags from the page.71 Te remaluing ext Is sluple to p'Ocess for cotrses. grades. dates. etc.," The remaining text is simple to process for courses, grades, dates, etc."72 All of these seps were accelerated by he Pytion scripting laieuage., All of these steps were accelerated by the Python scripting language.73 The Pyhou laugu: las several acvantageous featu‘es., The Python language has several advantageous features.74 For exaltuple. Python's unique leature allows ukuown Conditions in the datasets to be haiclled without crashing the analysis.," For example, Python's unique feature allows for unknown conditions in the datasets to be handled without crashing the analysis."75" Pvt101's mod iature allows for jietwork. statistical auc plotting leatures to be seamlessly integ""ated. witl ooduciug au umunanageable amount of code."," Python's modular nature allows for network, statistical and plotting features to be seamlessly integrated without producing an unmanageable amount of code."76 In this studs. none of the scripts were over 50 li in leneth. giviug us the ability to cousider a range of research questions without beiue limite oe-existiug software tools.," In this study, none of the scripts were over 50 lines in length, giving us the ability to consider a range of research questions without being limited by pre-existing software tools."77 lin L.6pt, 1 in 1.6pt78are given for the intensity. the wavelength. aud the width of the decay line postulated to be emitted by neutrinos in the vicinity (~4pe) of the sun.,"are given for the intensity, the wavelength, and the width of the decay line postulated to be emitted by neutrinos in the vicinity $(\sim{1\over2}\,{\rm pc})$ of the sun."79" An upper limit on 7 will now be derived from receut estimates of the maximum permitted deusitv of dark latter near the sun and of the free electron deusitv ο, Which is here Όσιο attributed to the ionisation of hydrogen by decay photons.", An upper limit on $\tau$ will now be derived from recent estimates of the maximum permitted density of dark matter near the sun and of the free electron density $n_e$ which is here being attributed to the ionisation of hydrogen by decay photons.80 Iu section 2.2 a lower hit on r will be determined from receut observational upper Πες on the extragalactic diffuse backeround at 15004. which impose an upper limit ou the flux of red shifted decay photons ciuitted by the cosinological distribution of neutrinos.," In section $2.2$ a lower limit on $\tau$ will be determined from recent observational upper limits on the extragalactic diffuse background at $1500\,\AA$, which impose an upper limit on the flux of red shifted decay photons emitted by the cosmological distribution of neutrinos."81 Ow derived upper aud lower limits ou 7 are only just consistent with one another. and so lead to a lighly constrained value for this quantity.," Our derived upper and lower limits on $\tau$ are only just consistent with one another, and so lead to a highly constrained value for this quantity."82 To derive the upper limit ou 7 consider à region near the suu whose atomic hydrogen deusity makes it opaque to ionisine decay photons., To derive the upper limit on $\tau$ consider a region near the sun whose atomic hydrogen density makes it opaque to ionising decay photons.83" Iu iouisation equilibrium one would have where i, is the local πασος deusitv of neutrinos aud à is the recombination coeffiicieut (excluding recombinations directly to the eround state).", In ionisation equilibrium one would have where $n_{\nu}$ is the local number density of neutrinos and $\alpha$ is the recombination coefficient (excluding recombinations directly to the ground state).84" The value of η, which the theorv attributes to iouisatiou by decay photons has been receutlv rediscussed by Sciama (19972).", The value of $n_e$ which the theory attributes to ionisation by decay photons has been recently rediscussed by Sciama (1997a).85 Using observations of dispersion measures for nearby pulsars with known radio parallaxes (Gwinn et al 1986. Bailes et al 1990). and IIST observatious of the absorption προςντ of the halo star WD93521 (Spitzer Fitzpatrick 1993) Gvhich are somewhat less straightforward to interpret). the result obtained was i=0.05+0.01011.P (Reynolds 1990. Selama 1990 b. 19972).," Using observations of dispersion measures for nearby pulsars with known radio parallaxes (Gwinn et al 1986, Bailes et al 1990), and HST observations of the absorption spectrum of the halo star HD93521 (Spitzer Fitzpatrick 1993) (which are somewhat less straightforward to interpret), the result obtained was $n_e=0.05\pm0.01\rm {cm}^{-3}$ (Reynolds 1990, Sciama 1990 b, 1997a)."86 The value of a depeuds on the temperature T of the eas., The value of $\alpha$ depends on the temperature T of the gas.87" For the relevant regions of the iuterstellar iuecdiui with the better determined values of η, oue has T< 2x104A (Reynolds 1985)."," For the relevant regions of the interstellar medium with the better determined values of $n_e$ one has $T<2$ $10^4\,K$ (Reynolds 1985)."88 IHeuce a>1.3410.Pen?sect (Ferland ct al 1992).," Hence $\alpha>1.3\times10^{-13}\rm{cm}^3\,\rm{sec}^{-1}$ (Ferland et al 1992)."89" Finally. to derive an upper lait on r an upper luit ou the nuuber deusitv 0, must be established."," Finally, to derive an upper limit on $\tau$ an upper limit on the number density $n_\nu$ must be established."90" This cau be obtained from an upper lait on the local mass densitv of neutrinos p,. suce carlicr discussions of the decaxiug neutrino theory lave already provided a sufficiently accurate value for i,. namely ~2&eV (Scimua 1990 a. 1995)."," This can be obtained from an upper limit on the local mass density of neutrinos $\rho_{\nu}$, since earlier discussions of the decaying neutrino theory have already provided a sufficiently accurate value for $m_\nu$, namely $\sim28 \rm{eV}$ (Sciama 1990 a, 1995)."91 Au upper liit on py rear the sun was recently derived by Sciama (1997 b) dun connexion with values for the largest permitted fiatteniug of the neutrino halo aud for the rotational velocity of he Galaxy at the suns position., An upper limit on $\rho_\nu$ near the sun was recently derived by Sciama (1997 b) in connexion with values for the largest permitted flattening of the neutrino halo and for the rotational velocity of the Galaxy at the sun's position.92" By taking mto account various estimates for column deusities of material near the sun au upper limit for p, of 0.03 Ape: P was obtained.", By taking into account various estimates for column densities of material near the sun an upper limit for $\rho_{\nu}$ of $0.03$ $M_{\odot}$ $^{-3}$ was obtained.93 This upper limit would be associated with the largest permitted flattening of the dark halo (Delnen Binney 1997). correspoudine to an axial ratio of 0.2 (shape Es).," This upper limit would be associated with the largest permitted flattening of the dark halo (Dehnen Binney 1997), corresponding to an axial ratio of 0.2 (shape E8)."94 It is reassuring that some other galaxies do ποσα to exhibit a similar flattening (Sackett et al 1991. Olling 1996. Decquaert Combes 1997).," It is reassuring that some other galaxies do seem to exhibit a similar flattening (Sackett et al 1994, Olling 1996, Becquaert Combes 1997)."95" The local mass density p, can also be determined V comparing clvuamical estimates of the total denusitv p, near the sun (the Oort limit) with the deusities of kuown stars and gas.", The local mass density $\rho_{\nu}$ can also be determined by comparing dynamical estimates of the total density $\rho_o$ near the sun (the Oort limit) with the densities of known stars and gas.96" The value of p, has been controversial: an estimate will be used here which is based on receut Ilipparcos observations of F stars. and so may lead to a more reliable result."," The value of $\rho_o$ has been controversial; an estimate will be used here which is based on recent Hipparcos observations of F stars, and so may lead to a more reliable result."97" This result is p,=0.11+0.0147. ? (Pham 1996. 1997)."," This result is $\rho_o=0.11\pm0.01 M_\odot$ $^{-3}$ (Pham 1996, 1997)."98 IIowever. a lower value for Po has recently been obtained from Iipparcos data by Crézzé ct al (1998). namely 0.076+0.015M.. ὃς," However, a lower value for $\rho_o$ has recently been obtained from Hipparcos data by Crézzé et al (1998), namely $0.076\pm0.015 M_\odot$ $^{-3}$."99 This result seenis rather low when compared to the deusitv of known matter (see below) aud the disagreement remains to be clarified., This result seems rather low when compared to the density of known matter (see below) and the disagreement remains to be clarified.100 Hore we provisionally adopt Plhiuu's value., Here we provisionally adopt Pham's value.101 The contribution of known stars aud gas to f ds itself somewhat uncertain., The contribution of known stars and gas to $\rho_o$ is itself somewhat uncertain.102 Often quoted values for cach are O.OLAL. ? (e.g. Dienaviné.. Robin Crézzé 1987. Crézzé et al 1998).," Often quoted values for each are $0.04 M_\odot$ $^{-3}$ (e.g. Bienaymé,, Robin Crézzé 1987, Crézzé et al 1998)."103 The stellar contribution nav have to be increased to allow for the existence of faint stars. but the OST deep survey suggests that this additional contribution may be sinall (0.8. Gould et al 1996).," The stellar contribution may have to be increased to allow for the existence of faint stars, but the HST deep survey suggests that this additional contribution may be small (e.g. Gould et al 1996)."104" If this is correct. one again obtains an upper limit for p, of 0.03AZ.. >."," If this is correct, one again obtains an upper limit for $\rho_{\nu}$ of $0.03 M_\odot$ $^{-3}$."105 This upper limit was previously derived by Bienavine et al (1987)., This upper limit was previously derived by Bienaymé et al (1987).106" If now ii,=27.beV. as derived in section 2.2. there follows au upper limit for a, near the sun of L1G«10%5m "," If now $m_{\nu}=27.4\,{\rm eV}$, as derived in section 2.2, there follows an upper limit for $n_\nu$ near the sun of $4.16\times 10^7{\rm cm}^{-3}$."107Our limits on the values of ii. a aud p.(0.0lem7) now lead. iu conjunction with (1). to the conclusion that This result can be shown to be compatible with our interpretation of Revnolds (1981) global Ta data for the Galaxy (Sciam 1997).," Our limits on the values of $n_\nu$, $\alpha$ and $n_e(\geq 0.04 {\rm cm}^{-3})$ now lead, in conjunction with (1), to the conclusion that This result can be shown to be compatible with our interpretation of Reynolds' (1984) global $\alpha$ data for the Galaxy (Sciama 1997b)."108 Some of the earliest lower limits On 7r (for a decavius neutrino not then related to the iouisation of the interstellar iuediumi) were based on observational estimates of the cosmic backeround in the far ultra-violet. which was compared with the red shifted decay fiux produced by the cosmological distribution of ueutriuos (Stecker 1980. Inuble. Bowyer Jakobsen 1981).," Some of the earliest lower limits on $\tau$ (for a decaying neutrino not then related to the ionisation of the interstellar medium) were based on observational estimates of the cosmic background in the far ultra-violet, which was compared with the red shifted decay flux produced by the cosmological distribution of neutrinos (Stecker 1980, Kimble, Bowyer Jakobsen 1981)."109 Estimates of this background are still controversial (compare Bowyer 1991 with IHeurx 1991)., Estimates of this background are still controversial (compare Bowyer 1991 with Henry 1991).110 Recent coutributions to the discussion have heen mace bv Παν Murthy (1993). Witt οσο (1991) and Witt. Friedmann Sasseeu (1997).," Recent contributions to the discussion have been made by Henry Murthy (1993), Witt Petersohn (1994) and Witt, Friedmann Sasseen (1997)."111 We adopt from their discussions an upper lit of about 2300 photons, We adopt from their discussions an upper limit of about 300 photons112Zhang&MacFadyen(2009).. and a zoom into these details is provided in Fig. 1..,"\cite{ZhangMacFadyen09}, and a zoom into these details is provided in Fig. \ref{Figall}."113 This Kelvin-Helmholtz development does not affect shell dynamics. since the characteristic time for the lateral flow is longer than the timescale found for the radial deceleration.," This Kelvin-Helmholtz development does not affect shell dynamics, since the characteristic time for the lateral flow is longer than the timescale found for the radial deceleration."114 The rarefaction wave that forms propagates inside the shell at the fluid's rest-frame sound speed., The rarefaction wave that forms propagates inside the shell at the fluid's rest-frame sound speed.115 This wave extracts energy gradually. first from the edge and ultimately from the axial region.," This wave extracts energy gradually, first from the edge and ultimately from the axial region."116 During the relativistic phase. the shell becomes structured neridionally. and energy. pressure. and density ultimately decrease from axis to edge.," During the relativistic phase, the shell becomes structured meridionally, and energy, pressure, and density ultimately decrease from axis to edge."117 Deceleration occurs on the meridionally growing part of the shell affected by the wave. as quantified in Fig. 2..," Deceleration occurs on the meridionally growing part of the shell affected by the wave, as quantified in Fig. \ref{Figlfac}."118 This meridional stratification of the blast wave makes the edge of the shell decelerate faster thaαυ] the inner part. bending the shell away from its spherical shape. as shown in Fig. 3..," This meridional stratification of the blast wave makes the edge of the shell decelerate faster than the inner part, bending the shell away from its spherical shape, as shown in Fig. \ref{Blast_R}."119 This deformation becomes pronounced when the radial speed drops to about of the lateral speed. and increases the blast-wave working surface and the distance traversed by spreading matter.," This deformation becomes pronounced when the radial speed drops to about of the lateral speed, and increases the blast-wave working surface and the distance traversed by spreading matter."120 This 15 all in full agreement with previous simulations (Granotetal.2001:Cannizzo2004:Zhang&MacFadyen 2009).," This is all in full agreement with previous simulations \citep{Granotetal01,cannizzoetal04,ZhangMacFadyen09}."121 The rarefaction front reachesPA the axis after Moca=115.536days.," The rarefaction front reaches the axis after $t_{\rm local}\,\simeq\, 115.536\, {\rm days}$."122 By this time. the blastwave has decelerated to y=1.09 at the axis (near-Newtonian phase).," By this time, the blast-wave has decelerated to $\gamma=1.09$ at the axis (near-Newtonian phase)."123 In Fig. 4..," In Fig. \ref{Vtheta},"124 we quantify the meridional speed at the front of the shell for several times. to illustrate the propagation of the rarefaction wave.," we quantify the meridional speed at the front of the shell for several times, to illustrate the propagation of the rarefaction wave."125 The meridional stratification of the blast wave decays when the Lorentz factor decreases to the point that causality links all parts of the shell together., The meridional stratification of the blast wave decays when the Lorentz factor decreases to the point that causality links all parts of the shell together.126 In this near-Newtonian phase. energy becomes uniformly distributed throughout the shell.," In this near-Newtonian phase, energy becomes uniformly distributed throughout the shell."127 labepiesultct novel discoveries of our simulation are from the details of the mitial evolutionary phase. where we now demonstrate that during the blast-wave deceleration. a ram pressure instability develops.," The most novel discoveries of our simulation are from the details of the initial evolutionary phase, where we now demonstrate that during the blast-wave deceleration, a ram pressure instability develops."128" This instability is found only while the blast wave speed remains relativistic. and disappears when its Lorentz factor becomes y<3 at time fj,4;=187days (or observer time fap,=S3hours. as determined from Δίας=Attocal— AR/c)."," This instability is found only while the blast wave speed remains relativistic, and disappears when its Lorentz factor becomes $\gamma< 3$ at time $t_{\rm local}\,\simeq\, 187 \,{\rm days}$ (or observer time $t_{\rm obs}\,\simeq \,53\, {\rm hours}$, as determined from $\Delta t_{\rm obs}=\Delta t_{\rm local}-\Delta R/c$ )."129 Figure 5 shows its spontaneous appearance and disappearance. manifesting itself during some 100 days (local time).," Figure \ref{Fig1} shows its spontaneous appearance and disappearance, manifesting itself during some 100 days (local time)."130 This instability induces small-scale bending of the blast front at wavelengths ο=0.2° (500 times larger than our cell meridional size. hence more than resolved properly)," This instability induces small-scale bending of the blast front at wavelengths $\delta \theta \,\simeq\, 0.2^{\circ}$ (500 times larger than our cell meridional size, hence more than resolved properly)."131 Detailed analysis indicates that each local front merely affects the minute region that is causally linked at this time. with causality angles around Quay=7° initially that increase during the evolution.," Detailed analysis indicates that each local front merely affects the minute region that is causally linked at this time, with causality angles around $\theta_{\rm causality} \simeq 7^\circ$ initially that increase during the evolution."132 The radial size of these ripples is given by δυο~107+pe at local time 67.5days.," The radial size of these ripples is given by $R\,\delta\theta \,\simeq\, 10^{-4}\, {\rm pc}$ at local time $67.5\,{\rm days}$."133 This is smaller than the thickness of the shell OR~3.7x10-7pe.," This is smaller than the thickness of the shell $\delta R \,\simeq \,3.7 \,\times\, 10^{-3}\, {\rm pc}$."134 The astabilities develop as small-scale ripples at the shock front. and the higher thermal pressure inside them pushes the newly shocked external medium sideways to their left and right upstream.," The instabilities develop as small-scale ripples at the shock front, and the higher thermal pressure inside them pushes the newly shocked external medium sideways to their left and right upstream."135 Fluid within the shell (behind the shock) is pushed downstream., Fluid within the shell (behind the shock) is pushed downstream.136 This local structure generates vorticity in the post shock region. and is a prime candidate that can contribute to magnetic field amplification.," This local structure generates vorticity in the post shock region, and is a prime candidate that can contribute to magnetic field amplification."137 The instabilities depend. as in the classical case (Vishniac1983).. on internal pressure within the shell being thermal and isotropic. while external pressure is mainly ram pressure in the direction. perpendicular to the shock front.," The instabilities depend, as in the classical case \citep{Vishniac83}, on internal pressure within the shell being thermal and isotropic, while external pressure is mainly ram pressure in the direction perpendicular to the shock front."138 This induces ripples. which grow in size as time proceeds. leading to shell fragmentation.," This induces ripples, which grow in size as time proceeds, leading to shell fragmentation."139 This fragmentation appears at a local time offset Ooear9LIS hours after the start of our simulation. which is of the same order as the sound crossing time of the shell.," This fragmentation appears at a local time offset $\delta t_{\rm local}\approx 115$ hours after the start of our simulation, which is of the same order as the sound crossing time of the shell."140 At this time the shell has already decelerated to a Lorentz factor of order 10 and the local causality angle is reduced to about 7 degrees., At this time the shell has already decelerated to a Lorentz factor of order 10 and the local causality angle is reduced to about 7 degrees.141 This instability appears initially at the outer edge (see Fig., This instability appears initially at the outer edge (see Fig.142 5 bottom). which is where the rarefaction wave first affects the shell.," \ref{Fig1} bottom), which is where the rarefaction wave first affects the shell."143 The edge thereby decelerates more quickly than the centre. is first to bend away from spherical shape and to reach the lower Lorentz factors.," The edge thereby decelerates more quickly than the centre, is first to bend away from spherical shape and to reach the lower Lorentz factors."144 This ts seen in the bottom panel of Fig. 5..," This is seen in the bottom panel of Fig. \ref{Fig1},"145 while the second panel upwards shows that later the entire shell develops local instabilities (even before the rarefaction wave has affected its evolution)., while the second panel upwards shows that later the entire shell develops local instabilities (even before the rarefaction wave has affected its evolution).146 The size of the fragments increase because of the spherical expansion., The size of the fragments increase because of the spherical expansion.147 Moreover. the density and. Lorentz factor contrast between fragments and surroundings increase and more energy become concentrated in these the fragments.," Moreover, the density and Lorentz factor contrast between fragments and surroundings increase and more energy become concentrated in these the fragments."148 They appear as independent shells propagating downstream. until the Lorentz factor of the entire blast wave becomes smaller then y<43. or when they are reached by the inward propagating rarefaction wave.," They appear as independent shells propagating downstream, until the Lorentz factor of the entire blast wave becomes smaller then $\gamma \leq 3$, or when they are reached by the inward propagating rarefaction wave."149 As the Lorentz factor of the shell gradually decreases. as well as the compression rate 7=I-n. the sound crossing time for the shell increases.," As the Lorentz factor of the shell gradually decreases, as well as the compression rate $\tau=\frac{\gamma \Gamma+1}{\Gamma-1}$, the sound crossing time for the shell increases."150 The shell ultinately returns to a configuration that is stable against these pressure-ram pressure aoastabilities., The shell ultimately returns to a configuration that is stable against these pressure-ram pressure instabilities.151 In this. near-Newtonian phase. the fragments iffuse and disappear. in a way that is consistent with linear analysis predictions (Vishniae.1983).," In this near-Newtonian phase, the fragments diffuse and disappear, in a way that is consistent with linear analysis predictions \citep{Vishniac83}."152. During this phase. the blast wave propagates adiabatically with effective polytropic index of Pay=5/3>1.3.," During this phase, the blast wave propagates adiabatically with effective polytropic index of $\Gamma_{\rm eff}\;\simeq\; 5/3\,>\,1.3$."153 As the fragments are forced to move. they form tails in the rear of the BM shell.," As the fragments are forced to move, they form tails in the rear of the BM shell."154 Our result is the first to show clearly that some of the as yet unexpected instability modes in BM solutions exist. decay slowly as the system evolves.," Our result is the first to show clearly that some of the as yet unexpected instability modes in BM solutions exist, decay slowly as the system evolves."155 In this case. small-scale structure appears when the Lorentz factor is 10. and disappears when it reaches 3," In this case, small-scale structure appears when the Lorentz factor is $10$, and disappears when it reaches $3$."156 As the rarefaction wave propagates towards the axis. 1t not only forces the fluid to spread towards the edge. but dampens these pressure-ram pressure instabilities.," As the rarefaction wave propagates towards the axis, it not only forces the fluid to spread towards the edge, but dampens these pressure-ram pressure instabilities."157 In the relativistic phase. the instabilities persist all the way to the axis.," In the relativistic phase, the instabilities persist all the way to the axis."158 The, The159BAT light curve. we use the lieht. curve in whole BAT bind. i.e. 15-150 keV. The first orbit of the NRT data is fully in the Windowed Timine (WT) mode.,"BAT light curve, we use the light curve in whole BAT band, i.e., 15-150 keV. The first orbit of the XRT data is fully in the Windowed Timing (WT) mode."160 We extract the light. curves aud spectrum of the NRT data with the Nselect package., We extract the light curves and spectrum of the XRT data with the Xselect package.161 The spectra is erouped with the toolgrppha. auc the spectral fitting is carried out with theXspec package.," The spectrum is grouped with the tool, and the spectral fitting is carried out with the package."162 Following Campana et al. (, Following Campana et al. (1632006) we fit the NRT spectra in the first orbit with a iiodel combining a black body component with temperature AL aud a cut-off power lav (PxETe ΕΤ} component.,"2006) we fit the XRT spectrum in the first orbit with a model combining a black body component with temperature $kT$ and a cut-off power law $F\propto164E^{-\Gamma}e^{-E/E_{c}}$ ) component."165 The absorption in both Milky and the GRB host ealaxy CV.pest) is nmcorporated., The absorption in both Milky and the GRB host galaxy $N_H^{host}$ ) is incorporated.166" We obtain hy=(63!0«107 om2, T= ""mkeV, P9LIS dUm and E,218!PS keV (correspo ο E,~5 keV). with reduced 155 for 769 degrees of freedom."," We obtain $N_H^{host}=0.63^{+0.03}_{-0.03}\times 10^{22}$ $^{-2}$, $kT=0.122^{+0.003}_{-0.004}$ keV, $\Gamma=1.78^{+0.08}_{-0.08}$ , and $E_{c}=21.8^{+15.8}_{-6.7}$ keV (corresponding to $E_p\sim 5$ keV), with reduced $\chi^2=1.55$ for 769 degrees of freedom."167 We derive the unabsorbed light curves in the 0.3-2 keV. 2-5 keV. and 5-10 keV bands from the NRT data.," We derive the unabsorbed light curves in the 0.3-2 keV, 2-5 keV, and 5-10 keV bands from the XRT data."168 As reported by Campana et al. (, As reported by Campana et al. (1692006). a thermal component exists. and is likely of different orem (e.g. the shock enissjon associated with SN 2006aj: cf.,"2006), a thermal component exists, and is likely of different origin (e.g. the shock breakout emission associated with SN 2006aj; c.f."170 Li 2006: breakoutClüselliui et al., Li 2006; Ghisellini et al.171 2006b) from he non-thermial conrponeut., 2006b) from the non-thermal component.172 We therefore subtract the contribution of this compoucut from the observed light curves., We therefore subtract the contribution of this component from the observed light curves.173 The ET aud the radiation radii (Rap) evolve with nue during the first orbit., The $kT$ and the radiation radii $R_{BB}$ ) evolve with time during the first orbit.174 We road the values of AL and Apps from Campana ct al.(2006). and caleulate the ight curves of this component m 03-2. 2-5. aud5-10 keV xuids.," We read the values of $kT$ and $R_{BB}$ from Campana et al.(2006) and calculate the light curves of this component in 0.3-2, 2-5, and 5-10 keV bands."175 Since the temperature ofthe black body component is below 0.2 keV. the light curves in the euergv baud üeher than 2 keV is esseutiallv not contaminated by the hermal compoueut.," Since the temperature of the black body component is below $0.2$ keV, the light curves in the energy band higher than 2 keV is essentially not contaminated by the thermal component."176 Du the 0.3-2 keV band. the derived ight curve of the thermal compoucnut continuously increase with time. which could be well fitted bv logF52=(10.6940.09)|(0.66£0.03)log iu ces units.," In the 0.3-2 keV band, the derived light curve of the thermal component continuously increase with time, which could be well fitted by $\log F_{0.3-2}=(-10.69\pm 0.09)+(0.66\pm 0.03)\log t$ in cgs units."177 We thus subtract the contribution ofthis componentf from the 0.5-2 keV baud light curve according to this fitting result., We thus subtract the contribution of this component from the 0.3-2 keV band light curve according to this fitting result.178 The derived uou-thermal light curves in the three NRT bands as well as the oue in the BAT band are shown in Fie.l((aj., The derived non-thermal light curves in the three XRT bands as well as the one in the BAT band are shown in \ref{LC}( (a).179 To clearly view the pulse width and spectral lag dependences with cuerey. we also plot in Έπος) the normalized lighteurves.," To clearly view the pulse width and spectral lag dependences with energy, we also plot in \ref{LC}( (b) the normalized lightcurves."180 The characteristics of the light curves along with the average photon enerev CE) of cach energv baud are reported in Table 1, The characteristics of the light curves along with the average photon energy $\bar{E}$ ) of each energy band are reported in Table 1.181 One important question is whether the NRT uon-thermal cussion aud the BAT ciission are of the same origin., One important question is whether the XRT non-thermal emission and the BAT emission are of the same origin.182 In order to clarify this we first study the spectral enerev distribution (SED) of the burst using joint BAT-NRT data., In order to clarify this we first study the spectral energy distribution (SED) of the burst using joint BAT-XRT data.183 Since this event is image trigger. the BAT event file contains ouly the data in the first 300 seconds since the BAT trigger.," Since this event is image trigger, the BAT event file contains only the data in the first 300 seconds since the BAT trigger."184 NRT began collecting data 159 seconds after the DAT trigger., XRT began collecting data 159 seconds after the BAT trigger.185 We thus only obtain siuultzueous observations of the two iustruuents from 160 to 300 seconds with the eveut files., We thus only obtain simultaneous observations of the two instruments from 160 to 300 seconds with the event files.186 The joiut-5t SED in this period is shown iu Fie.2.. which is well fitted by the DD|CPL inodel(Campana et al.," The joint-fit SED in this period is shown in \ref{SED}, which is well fitted by the BB+CPL model (Campana et al."187" 2006) with the following Nit1=d65Qss107 7. KT—043""m00 keV. parsunetersT—5tJUS Lsaud E,=E122!10?( keT (corresponding to E,frc~51 keV). with reduced 4?=0.97 or 327 degrees of edoin."," 2006) with the following parameters: $N_H^{host}=0.65^{+0.03}_{-0.03}\times 10^{22}$ $^{-2}$, $kT=0.13^{+0.01}_{-0.01}$ keV, $\Gamma=1.56^{+0.08}_{-0.07}$ and $E_{c}=122^{+160}_{-46}$ keV (corresponding to $E_p\sim 54$ keV), with reduced $\chi^2=0.97$ for 327 degrees of freedom."188" The E, strongly evolves with iue. from Sl keV at the begiuuiug down to ~5 keV at later times,"," The $E_p$ strongly evolves with time, from $54$ keV at the beginning down to $\sim1895$ keV at later times."190 This is consistent with that reported bv Campana et al. (, This is consistent with that reported by Campana et al. (1912006) and Cchiscllini et al. (,2006) and Ghisellini et al. (19220062).,2006a).193 The nodel fitting results are shown in Fig.2..ext, The model fitting results are shown in \ref{SED}.194raOne cau observe hat the DAT-coniponeut is a good xlatiou of the NRT non-thermal component., One can observe that the BAT-component is a good extrapolation of the XRT non-thermal component.195 This result iuplies that the ron-thermal chussious detected bv. NRT aud BAT are of he same origin., This result implies that the non-thermal emissions detected by XRT and BAT are of the same origin.196 As shown in Fie... the light curves in different cucrey bauds can be all modeled by a single FRED-pulse.," As shown in \ref{LC}, the light curves in different energy bands can be all modeled by a single FRED-pulse."197 Ikocevski et al. (, Kocevski et al. (198"2003) developed an empirical expression to fit à FRED-like pulse. which reads. where f, is the time of the παπι flux C£,,). ty is the offset time. aud r aud d are the rising aud decaving power-law iudices. respectively.","2003) developed an empirical expression to fit a FRED-like pulse, which reads, where $t_{m}$ is the time of the maximum flux $F_{m}$ ), $t_0$ is the offset time, and $r$ and $d$ are the rising and decaying power-law indices, respectively."199 We fit the Πο curves with Eq.(1)) and then measure the pulse width. rising aud decaving times at the fullwwidth halfinaxiunun (FWIIM) of the fitting lizht curves. aud the risine-to-decaving time ratio (47).," We fit the light curves with \ref{Kocevski}) ) and then measure the pulse width, rising and decaying times at the full-width half-maximum (FWHM) of the fitting light curves, and the rising-to-decaying time ratio $\varphi$ )."200 The errors of these quantities are derived from sinulatious by assinuiue a normal distribution of the errors of the Πες paraimcters., The errors of these quantities are derived from simulations by assuming a normal distribution of the errors of the fitting parameters.201 The reported errors are at lo coufidence level., The reported errors are at $1\sigma$ confidence level.202 The results are in Table 1., The results are tabulated in Table 1.203 We show zw as a function of £ iu Fie.3((a)., We show $\omega$ as a function of $\bar{E}$ in \ref{FWHM_LAG}( (a).204atAM Appareutly the Io quantities are correlated., Apparently the two quantities are correlated.205 A best viclds wxEΤΟfound , A best fit yields $\omega\propto E^{-0.31\pm 0.03}$.206The y parzimeter ranges from 0.13 to 0.59., The $\varphi$ parameter ranges from $0.43$ to 0.59.207 It is that NRF 060218 roughly satisfies the same wFE relation (Fenimore et al., It is found that XRF 060218 roughly satisfies the same $\omega - E$ relation (Fenimore et al.208 1995: Norris et al., 1995; Norris et al.209" 2005) aud its 42 values are also well consistent with that observed in typical GRBs (οιο, Norris et al.", 2005) and its $\varphi$ values are also well consistent with that observed in typical GRBs (e.g. Norris et al.210 1996: Liang et al., 1996; Liang et al.211 2002). although it las a much longer pulse width than other single-pulse GRBs.," 2002), although it has a much longer pulse width than other single-pulse GRBs."212 These results imply that NRF 060218 may be an extension of CRBs to the extremely long aud soft regime., These results imply that XRF 060218 may be an extension of GRBs to the extremely long and soft regime.213 The light curves shown in Fig.l((a) display a siguificaut spectral lag (7). with soft photons lageineg behind the hard photons. as usually seen in long CRBs(Norris et al.," The light curves shown in \ref{LC}( (a) display a significant spectral lag $\tau$ ), with soft photons lagging behind the hard photons, as usually seen in long GRBs (Norris et al."214 2000: Yi ct al., 2000; Yi et al.215 2006)., 2006).216 We illustrate this lag behavior with the intensitv-normalized light curves in Fige.l((b)., We illustrate this lag behavior with the intensity-normalized light curves in \ref{LC}( (b).217 The light curves peak at 105+25. 735x9. 919+7. aud 1082+13 seconds. respectively. ina sequence of high euergy baud to low energy band as shown in Fie. 3((," The light curves peak at $405\pm 25$, $735\pm 9$, $919\pm 7$, and $1082\pm 13$ seconds, respectively, in a sequence of high energy band to low energy band as shown in Fig. \ref{FWHM_LAG}( ("218b).,b).219" The best fit to the correlation between the peak tine (£,:,:) aud the average photoneuergy vields. A simple estimate of the lags between any pairs of the I light curves obtaius Tra,=163~677 seconds.boiug cousisteut with that shown im Celrels et al. ("," The best fit to the correlation between the peak time $t_{peak} $ ) and the average photonenergy yields, A simple estimate of the lags between any pairs of the 4 light curves obtains $\tau_{peak}=163\sim 677$ seconds,being consistent with that shown in Gehrels et al. ("2202007).,2007).221 We note NRF 060218 becomes the new record-holder of the lone-lae. wide-pulse CRBs.," We note XRF 060218 becomes the new record-holder of the long-lag, wide-pulse GRBs."222 The previous record holder was CRB 971208. with 7—58 secouds and i=395 seconds (Norris et al.," The previous record holder was GRB 971208, with $\tau\sim 58$ seconds and $\omega=395$ seconds (Norris et al."223 2005)., 2005).224brightness is proportional to the number density. of Hà knots.,brightness is proportional to the number density of $_2$ knots.225 New observations of Ils 2.12 jun line reveal several new aspects to the molecular knots ol the Helix nebula., New observations of $_2$ 2.12 $\mu$ m line reveal several new aspects to the molecular knots of the Helix nebula.226 The II» images reveal that the knots have arcuate structures with the apex pointing towards (he central star., The $_2$ images reveal that the knots have arcuate structures with the apex pointing towards the central star.227 These molecular hydrogen knots are most highly structured in the [field positions closest to the central star ancl become increasinely less structured with increasing radius., These molecular hydrogen knots are most highly structured in the field positions closest to the central star and become increasingly less structured with increasing radius.228 All of the HH» emission is confined to knots., All of the $_2$ emission is confined to knots.229 In contrast the ionized eas (racers have a signilicant component of diffuse ionized eas emission., In contrast the ionized gas tracers have a significant component of diffuse ionized gas emission.230 Using the nunmber densitv of molecular hydrogen knots in the 5 NICMOS fieldl positions. we estimate the total number of knots to be 223.000. a [actor of 6.5 more than previous estimates based on optical images.," Using the number density of molecular hydrogen knots in the 5 NICMOS field positions, we estimate the total number of knots to be $\sim$ 23,000, a factor of 6.5 more than previous estimates based on optical images."231 The total neutral gas mass in the Helix based on these new knots estimates is 0.35 M. assuming an average mass of 1.5x10? M. [or the individual knots based on previous work by O'Dell&Iandron(1996)., The total neutral gas mass in the Helix based on these new knots estimates is 0.35 $_\odot$ assuming an average mass of $\sim$$1.5\times10^{-5}$ $_\odot$ for the individual knots based on previous work by \cite{odell96}.232. The Is emission structure of the entire Ielix nebula supports (he recent interpretation of the Helix as a nearly pole-on poly-polar planetary nebula., The $_2$ emission structure of the entire Helix nebula supports the recent interpretation of the Helix as a nearly pole-on poly-polar planetary nebula.233 The average intensity is 9xLO? erg | ? sr| remains relatively constant with projected distance [rom the central star., The average intensity is $9\times10^{-5}$ erg $^{-1}$ $^{-2}$ $^{-1}$ remains relatively constant with projected distance from the central star.234 The temperature and IH» 2.12 jan intensity of the knots suggest an origin in the photodissociation regions (PDRs) of the individual knots: however. theoretical models for the PDIs in planetary nebulae do not adecquately reproduce the Il» intensitv.," The temperature and $_2$ 2.12 $\mu$ m intensity of the knots suggest an origin in the photodissociation regions (PDRs) of the individual knots; however, theoretical models for the PDRs in planetary nebulae do not adequately reproduce the $_2$ intensity."235 The brightest knots appear in regions of more numerous knots and may be exposed to direct starlight that may cause rapid photoevaporation in comparison to the more embedded knots of the clisk., The brightest knots appear in regions of more numerous knots and may be exposed to direct starlight that may cause rapid photoevaporation in comparison to the more embedded knots of the disk.236 We gratefully acknowledge the work of mauv STS9clI colleagues who contributed to this observational setup of this project., We gratefully acknowledge the work of many STScI colleagues who contributed to this observational setup of this project.237 Zoltan Levay who superposed the NICMOS fields on the combined CTIO and ACS image., Zoltan Levay who superposed the NICMOS fields on the combined CTIO and ACS image.238 This work was supported in part bv an οοί grant. GO OIO041 and bv the internal STSel funds. DDRF D0001.32319.," This work was supported in part by an STScI grant GO 01041 and by the internal STScI funds, DDRF D0001.82319."239the CMR of Perseus has slope and zero point consistent with those reported for Fornax (Mieskeetal.20071. II (Misgeldet and Centaurus (Misgeldetal.2009).,"the CMR of Perseus has slope and zero point consistent with those reported for Fornax \citep{M07}, I \citep{M08} and Centaurus \citep{M09}."240. Such linearity and universality led several authors to use the CMR as a reliable distance indicator (Sandage1972) and to suggest that the origin of this relation in galaxy clusters is independent of the environment II: Misgeldetal.2008:DeRijcke 2009).," Such linearity and universality led several authors to use the CMR as a reliable distance indicator \citep{S72} and to suggest that the origin of this relation in galaxy clusters is independent of the environment I; \citealp{M08,deRij09}) )."241 However. for the Virgo cluster. Janz&Lisker(2009). have obtained an S-shaped CMR that seems to be consistent with the non-linear relation found by Ferrareseetal.(2006) for the same cluster.," However, for the Virgo cluster, \citet{JL09} have obtained an S-shaped CMR that seems to be consistent with the non-linear relation found by \citet{F06} for the same cluster."242 In addition. it is still under discussion whether there is a genuine (ie. with a physical origin) increase in the scatter of the CMR towards its faint end or. instead. the larger scatter can be accounted for by photometric or classification errors and/or background galaxies contamination.," In addition, it is still under discussion whether there is a genuine (i.e., with a physical origin) increase in the scatter of the CMR towards its faint end or, instead, the larger scatter can be accounted for by photometric or classification errors and/or background galaxies contamination."243" In the Perseus cluster. Conseliceetal.(2002) have found a significant spread σιoy, 0.5 mag) around the mean CMR. in the colours of galaxies with Ag=16 mag."," In the Perseus cluster, \citet{C02} have found a significant spread $\sigma_{(B-R)}\sim$ 0.5 mag) around the mean CMR, in the colours of galaxies with $M_B > -16$ mag."244 They argued in favor of a physical origin of this scatter. —pointing to differences in metal abundances and formation scenarios among blue and red low mass cluster galaxies.," They argued in favor of a physical origin of this scatter, pointing to differences in metal abundances and formation scenarios among blue and red low mass cluster galaxies."245 From a more recent spectroscopic study of the faint population of Perseus. Penny&Conselice(2008). have found that most of the red and blue galaxies responsible of the scatter are in the background.," From a more recent spectroscopic study of the faint population of Perseus, \citet{PC08} have found that most of the red and blue galaxies responsible of the scatter are in the background."246 However. there is still an increase in the colour dispersion of contirmed members with Ag>15 mag. in comparison with brighter ones.," However, there is still an increase in the colour dispersion of confirmed members with $M_B > -15$ mag, in comparison with brighter ones."247 Janz&Lisker(2009) found an increase of the scatter about the CMR at intermediate brightness. while for the brighter and fainter galaxies the scatter is interpreted as due to photometric errors.," \citet{JL09} found an increase of the scatter about the CMR at intermediate brightness, while for the brighter and fainter galaxies the scatter is interpreted as due to photometric errors."248 The authors conclude that the increase at intermediate luminosities confirms the fact that. in Virgo. dwarf and bright early-type galaxies do not share one common linear CMR.," The authors conclude that the increase at intermediate luminosities confirms the fact that, in Virgo, dwarf and bright early-type galaxies do not share one common linear CMR."249 On the contrary. from a thorough morphological identification of the galaxies included in the Coma CMR. Terlevichetal.(2001) have found no detectable increase in the colour dispersion all along the early-type galaxies” relation.," On the contrary, from a thorough morphological identification of the galaxies included in the Coma CMR, \citet{T01} have found no detectable increase in the colour dispersion all along the early-type galaxies' relation."250 When spiral and irregular galaxies. as well as unclassified objects. are plotted in the same colour-magnitude diagram. they introduce a considerable scatter towards the blue side of the relation at intermediate and ow luminosities.," When spiral and irregular galaxies, as well as unclassified objects, are plotted in the same colour–magnitude diagram, they introduce a considerable scatter towards the blue side of the relation at intermediate and low luminosities."251 Andreonetal.(2006). have obtained a thin (σιpym 0404 mag) CMR in 11185. with a scatter that does not increase with magnitude.," \citet{An06} have obtained a thin $\sigma_{(B-R)}=$ 0.04 mag) CMR in 1185, with a scatter that does not increase with magnitude."252 López-Cruzetal.(2004) have found. or 57 X-ray detected Abell clusters in the redshift range 0.02<>= OLS. a universal CMR with an average colour dispersion of Tpqn=0.074 mag.," \citet{LC04} have found, for 57 X-ray detected Abell clusters in the redshift range $0.02\leq z \leq 0.18$ , a universal CMR with an average colour dispersion of $\sigma_{(B-R)}=0.074$ mag."253 They noticed that the cluster displaying he largest scatter in its CMR (0.5 mag at //=1S mag) presents background contamination from higher redshift clusters., They noticed that the cluster displaying the largest scatter in its CMR (0.5 mag at $R=18$ mag) presents background contamination from higher redshift clusters.254 These authors also pointed out that photometric errors could become an important source of dispersion in the relation (see.also.Seckeretal. 1997).," These authors also pointed out that photometric errors could become an important source of dispersion in the relation \citep[see, also,][]{S97}."255. In the Hydra (Misgeldetal.2008). and Centaurus (Misgeldetal.2009) clusters a larger colour scatter has also been found for faint early-type galaxies. in comparison to luminous ones.," In the Hydra \citep{M08} and Centaurus \citep{M09} clusters a larger colour scatter has also been found for faint early-type galaxies, in comparison to luminous ones."256 However. such increase is considered as due to photometric errors and it is shown that dubious members of the cluster and background galaxies can introduce significant dispersion in the relation.," However, such increase is considered as due to photometric errors and it is shown that dubious members of the cluster and background galaxies can introduce significant dispersion in the relation."257" Recently. Jafféetal.(2011). have found that 172 early-type confirmed members of 13 clusters and groups with redshifts 0.4>OLS. define tight CMRs with a small intrinsic colour seatter(a,7°V,= 0.076)."," Recently, \citet{J11} have found that 172 early-type confirmed members of 13 clusters and groups with redshifts $0.4 \lesssim z \lesssim 0.8$, define tight CMRs with a small intrinsic colour scatter $\sigma_{(U-V)}=0.076$ )."258 The CMR of spectroscopically contirmed Antlia members displays the most common features found for this relation in other nearby and distant clusters of galaxies., The CMR of spectroscopically confirmed Antlia members displays the most common features found for this relation in other nearby and distant clusters of galaxies.259 That is. it spans almost 10 magnitudes with no perceptible change of slope or increase in its scatter towards faint luminosities.," That is, it spans almost 10 magnitudes with no perceptible change of slope or increase in its scatter towards faint luminosities."260 When uncontirmed members and confirmed background galaxies are introduced in the relation. it displays a larger colour dispersion. not only in its faint end but also at intermediate luminosities.," When unconfirmed members and confirmed background galaxies are introduced in the relation, it displays a larger colour dispersion, not only in its faint end but also at intermediate luminosities."261 In 22b of PaperII we included in the same colour-magnitude diagram FS90 galaxies with spiral and irregular morphologies. some of them with spectroscopically confirmed membership.," In 2b of I we included in the same colour–magnitude diagram FS90 galaxies with spiral and irregular morphologies, some of them with spectroscopically confirmed membership."262 These objects introduced considerable dispersion towards the blue side of the relation. in agreement with the results of Terlevichetal.(2001).," These objects introduced considerable dispersion towards the blue side of the relation, in agreement with the results of \citet{T01}."263 The revised slope of the relation for all definite members is steeper than that found in PaperII. However. this value is in agreement with the one found in that paper for the bright end of the relation.," The revised slope of the relation for all definite members is steeper than that found in I. However, this value is in agreement with the one found in that paper for the bright end of the relation."264 Therefore. the bright galaxies seem to define the slope of the relation and when confirmed early-type dwarf members are included in the analysis. the faint galaxies follow a relation with a similar slope and scatter.," Therefore, the bright galaxies seem to define the slope of the relation and when confirmed early-type dwarf members are included in the analysis, the faint galaxies follow a relation with a similar slope and scatter."265 This steeper value for the slope of the CMR of Antlia is still consistent with those reported for other galaxy clusters., This steeper value for the slope of the CMR of Antlia is still consistent with those reported for other galaxy clusters.266 The computed intrinsic scatter of the relation is ae.p;c0.08 when only confirmed members are considered., The computed intrinsic scatter of the relation is $\sigma_{(C-T_1)}\sim0.08$ when only confirmed members are considered.267" Following Terlevichetal.(2001.seetheireq.D)... we calculate the intrinsic seatter as m;,;,=;(7. where £6 is the mean colour error of the sample."," Following \citet[][see their eq.\,1]{T01}, we calculate the intrinsic scatter as $\sigma_{intr}=\sqrt{\sigma_{obs}^2-\langle\epsilon\rangle^2}$, where $\langle\epsilon\rangle$ is the mean colour error of the sample."268" If we translate our intrinsic dispersion to 15HR) colours through e;4;=0.704ae.gp, (Seeeq;8inForte.Faifer&Geisler 2007)..5. we obtain σιjj,~0.06 which is similar to the mean value obtained by López-Cruzetal.(2004) for clusters with+«0.04. and consistent with the value obtained by Penny&Conselice(2008) for the CMR of Perseus at the bright end(eo,gιν 0.05)."," If we translate our intrinsic dispersion to $(B-R)$ colours through $\sigma_{(B-R)}=0.704~\sigma_{(C-T_1)}$ \citep*[see eq.\,8 in][]{FFG07}, we obtain $\sigma_{(B-R)}\sim0.06$ which is similar to the mean value obtained by \citet{LC04} for clusters with$z<0.04$, and consistent with the value obtained by \citet{PC08} for the CMR of Perseus at the bright end $\sigma_{(B-R)}\sim0.05$ )."269" If we take into account that 71Ho0.02 (Geisler1900). we can use the relation ayp,=Oygg,02560,0 (eeeq.|inHarrisetal.2002). and we obtain m,5,~0.02 which is a lower value than that obtained by Andreonetal.(2006). in 11185 (7,47.2)= 0.086)."," If we take into account that $T_1-R\simeq0.02$ \citep{gei96}, we can use the relation $\sigma_{(V-T_1)}=\sigma_{(V-R)}=0.256~\sigma_{(C-T_1)}$ \citep[see eq.\,1 in][]{HH02b} and we obtain $\sigma_{(V-R)}\sim0.02$ which is a lower value than that obtained by \citet{An06} in 1185 $\sigma_{(V-R)}=0.036$ )."270" In the Centaurus cluster. Misgeld(2009) have found intrinsic scatters of σι4, —0.06. 0.09 and 0.14 in three different magnitude intervals."," In the Centaurus cluster, \citet{M09} have found intrinsic scatters of $\sigma_{(V-I)}=$ 0.06, 0.09 and 0.14 in three different magnitude intervals."271" Using m,;,=0.490,0.p,, (seethefirstequationinForbes&Forte2001). these values translate in oe.μι —0.12. 0.18 and 0.28. much higher than our common value for the whole Antlia CMR."," Using $\sigma_{(V-I)}=0.49~\sigma_{(C-T_1)}$ \citep[see the first equation in][]{FF01}, these values translate in $\sigma_{(C-T_1)}=$ 0.12, 0.18 and 0.28, much higher than our common value for the whole Antlia CMR."272 For the Hydra cluster. Misgeldetal.(2008) have found a mean scatter for the relation of σεν7;=0.12 which is equivalent to σοςμι=0.24.," For the Hydra cluster, \citet{M08} have found a mean scatter for the relation of $\sigma_{(V-I)}=0.12$ which is equivalent to $\sigma_{(C-T_1)}=0.24$."273 Regarding the positions in the colour-magnitude diagram of the confirmed Antlia cEs. they can be compared with those displayed by the cE galaxies recently. identified in Centaurus al.2009). and Coma (Priceetal.2009.. see also Chiboucasal. 20100).," Regarding the positions in the colour-magnitude diagram of the confirmed Antlia cEs, they can be compared with those displayed by the cE galaxies recently identified in Centaurus \citep{M09} and Coma \citealp{P09}, see also \citealp{Chi10}) )."274 Centaurus” cEs are located within the CMR on its red side. in a similar manner to Antlia’s cEs (seefig.3inMisgeldet 2009)..," Centaurus' cEs are located within the CMR on its red side, in a similar manner to Antlia's cEs \citep[see fig.\,3 in][]{M09}. ."275 Despite all confident Coma's cEs (namely. CeGV9a. CeGV19a and CeGV[9b) are found on the red side of Coma's mean CMR. only one of them shows a similar location to those found in Antlia and Centaurus (that is. within or near the general trend). while the other two display a considerable offset from the," Despite all confident Coma's cEs (namely, CcGV9a, CcGV19a and CcGV19b) are found on the red side of Coma's mean CMR, only one of them shows a similar location to those found in Antlia and Centaurus (that is, within or near the general trend), while the other two display a considerable offset from the"276the quiescent (first) exposure obtained for each star from the fIare exposure.,the quiescent (first) exposure obtained for each star from the flare exposure.277 We found that the continuum flux represented and of the total flare radiation. respectively. with ihe remainder of the enerev coming from the line radiation.," We found that the continuum flux represented and of the total flare radiation, respectively, with the remainder of the energy coming from the line radiation."278 Lawley&Pettersen(1991) found that the continuum emitted of the flare flux during the impulsive phase of their very large flare. and averaged over the course of the flare.," \citet{Hawley1991} found that the continuum emitted of the flare flux during the impulsive phase of their very large flare, and averaged over the course of the flare."279 This suggests that our flare exposures may have included the impulsive phase aud part of the decay phase of each flare., This suggests that our flare exposures may have included the impulsive phase and part of the decay phase of each flare.280 The existence of these continuum flare spectra in our sample. ancl (he relative strength of the lines and continua. give us additional confidence Chat we are correctly identilving [lares by our automatic algorithms.," The existence of these continuum flare spectra in our sample, and the relative strength of the lines and continua, give us additional confidence that we are correctly identifying flares by our automatic algorithms."281 Figure 10. shows our observed flare duty excle as a function of spectral type., Figure \ref{fig:flares_spt} shows our observed flare duty cycle as a function of spectral type.282 The duty evele increases with later spectral tvpe. from for MO stars to for M9 stars.," The duty cycle increases with later spectral type, from for M0 stars to for M9 stars."283 The error bars were calculated. [rom binomial statistics. ancl the number of flares identified at each spectral type is noted.," The error bars were calculated from binomial statistics, and the number of flares identified at each spectral type is noted."284 The numbers in parentheses are the number of flares identified by the variability criteria., The numbers in parentheses are the number of flares identified by the variability criteria.285 The much larger duty eveles lor MY and later are based on a small number of stars. and although there are many (thousands of objects in the MO-M3 bins. there ave very few flares.," The much larger duty cycles for M7 and later are based on a small number of stars, and although there are many thousands of objects in the M0-M3 bins, there are very few flares."286 In order to improve the statistics. we binned by spectral type ancl found the duty eveles to be 0.022+0.01675 of MO-1 stars: 0.077&0.023% for M2-3 stars: 0.56+0.09% for M4Á-G stars: and 34156 of MT-9 stars.," In order to improve the statistics, we binned by spectral type and found the duty cycles to be $0.022\pm0.016\%$ of M0-1 stars; $0.077\pm0.023\%$ for M2-3 stars; $0.56\pm0.09\%$ for M4-6 stars; and $3\pm1\%$ of M7-9 stars."287 ]xowalskietal.(2009) investigated Πάνος in a large SDSS photometric sample., \citet{Kowalski2009} investigated flares in a large SDSS photometric sample.288 Thev required near simultaneous photometric enhancements in both the uw and g Tillers. and emploved a threshold of |Au|> 0.7 to define a flare.," They required near simultaneous photometric enhancements in both the $u$ and $g$ filters, and employed a threshold of $|\Delta u| >$ 0.7 to define a flare."289 Figure 11 compares their flare duty evele with our results for the binned data., Figure \ref{fig:ejh_afk_rates} compares their flare duty cycle with our results for the binned data.290 We find a higher duty. evele. by a factor of ~ 4.5. but (he duty evele as a function of spectral type has a similar trend in both studies.," We find a higher duty cycle, by a factor of $\sim$ 4.5, but the duty cycle as a function of spectral type has a similar trend in both studies."291 It is nol surprising that the duty eveles are different. since the two studies use such clilferent observations and threshold criteria.," It is not surprising that the duty cycles are different, since the two studies use such different observations and threshold criteria."292 llowever. we can qualitatively estimate (he effect. of observing line versus conünuunm enhancements. and (he effect of exposure time.," However, we can qualitatively estimate the effect of observing line versus continuum enhancements, and the effect of exposure time."293 The line emission remains enhanced for much longer than the continuum emission leading to a higher probability of observing Hares in line emission., The line emission remains enhanced for much longer than the continuum emission leading to a higher probability of observing flares in line emission.294 Longer exposure times increase the chance of a flare occurring during the exposure., Longer exposure times increase the chance of a flare occurring during the exposure.295 Both of these factors lead to the observed hieher duty evele seen im our spectroscopic observations., Both of these factors lead to the observed higher duty cycle seen in our spectroscopic observations.296keep the subframe as small as possible to keep anisoplanatic effects to a minimum.,keep the subframe as small as possible to keep anisoplanatic effects to a minimum.297 The subframe size used in this work was found after experimenting with various sizes., The subframe size used in this work was found after experimenting with various sizes.298 It is difficult to find an objective measure for this quantity., It is difficult to find an objective measure for this quantity.299" Nevertheless, the experiments showed that there is a significant tolerance in the results in terms of the exact frame-size chosen, which can vary by several arcseconds."," Nevertheless, the experiments showed that there is a significant tolerance in the results in terms of the exact frame-size chosen, which can vary by several arcseconds."300" The positions and fluxes of each star as well as the correspondingformal uncertainties were computed by taking the mean of the multiple measurements and the corresponding formal uncertainties from overlapping frames (byuncertainty we refer in this work to the uncertainty estimated by the algorithm for each fit, based on the given PSF and Gaussian and photon noise)."," The positions and fluxes of each star as well as the corresponding uncertainties were computed by taking the mean of the multiple measurements and the corresponding formal uncertainties from overlapping frames (by we refer in this work to the uncertainty estimated by the algorithm for each fit, based on the given PSF and Gaussian and photon noise)."301 The astrometric and photometric uncertainties caused by the uncertainty in the estimated PSF were estimated from the standard deviation of the multiple measurements from the overlapping frames (We refer to this source of uncertainty in this work as uncertainty.)., The astrometric and photometric uncertainties caused by the uncertainty in the estimated PSF were estimated from the standard deviation of the multiple measurements from the overlapping frames (We refer to this source of uncertainty in this work as .).302" Since the PSFs of the different subframes are not strictly statistically independent (common PSF reference stars in overlapping subframes), the uncertainty in the mean was computed by dividing the standard deviation by (N73) instead of /(N), where N is the number of measurements for a given star."," Since the PSFs of the different subframes are not strictly statistically independent (common PSF reference stars in overlapping subframes), the uncertainty in the mean was computed by dividing the standard deviation by $\sqrt{(N/3)}$ instead of $\sqrt{(N)}$ , where $N$ is the number of measurements for a given star."303 The factor 3 here is not strictlymathematically, The factor $3$ here is not strictlymathematically304picture of FRAIL jet. deceleration on kiloparsec scales has emerged. [rom these. studies.,picture of I jet deceleration on kiloparsec scales has emerged from these studies.305 The How. velocities are 3=rie8 OS 0.9 where the jets first. brighten abruptly. typically at ~Lkkpe from the nucleus.," The flow velocities are $\beta = v/c \approx$ 0.8 – 0.9 where the jets first brighten abruptly, typically at $\sim$ kpc from the nucleus."306 The jets tare and then recollimate. decelerating rapidly to speeds of .32 0.1 0.4.," The jets flare and then recollimate, decelerating rapidly to speeds of $\beta \approx$ 0.1 – 0.4."307 The best-fitting transverse velocity. profiles appear to be approximately self-similar., The best-fitting transverse velocity profiles appear to be approximately self-similar.308 At least in the 4/5 cases where the jets appear to be propagating in contact with the interstellar medium: of the host galaxy rather than inside racio lobes. they are roughly faster on-axis than at their edges.," At least in the 4/5 cases where the jets appear to be propagating in contact with the interstellar medium of the host galaxy rather than inside radio lobes, they are roughly faster on-axis than at their edges."309 Nevertheless. an evolution of the velocity profiles with distance from the nucleus is not excluded.," Nevertheless, an evolution of the velocity profiles with distance from the nucleus is not excluded."310 In particular. the transverse velocity. variations are poorly constrained where the jets first brighten abruptly and a top-hat profile would also be consistent with the observations in these regions of all five sources.," In particular, the transverse velocity variations are poorly constrained where the jets first brighten abruptly and a top-hat profile would also be consistent with the observations in these regions of all five sources."311ga In order to decelerate. a jet must entrain matter. either rom stars within its volume (??) or by ingestion of the surrounding material at its boundary. as originally suggested »w 72. ? and 7?..," In order to decelerate, a jet must entrain matter, either from stars within its volume \citep{Phinney83,komi94} or by ingestion of the surrounding material at its boundary, as originally suggested by \citet{baan80}, \citet{deyoung81} and \citet{begelman82}."312 In the latter case. the transverse velocity oolile almost inevitably evolves with distance from the nucleus.," In the latter case, the transverse velocity profile almost inevitably evolves with distance from the nucleus."313 X-rav observations can be used to infer the emperature. density ancl pressure profiles of the hot eas associated with the host galaxies of PIRI radio galaxies (c.g.???)..," X-ray observations can be used to infer the temperature, density and pressure profiles of the hot gas associated with the host galaxies of I radio galaxies \citep[e.g.][]{hardcastle02,worrall03,hardcastle05}."314 Together with the velocity distributions derived rom mocdelling of the radio emission. these can be used in a conservation-law analysis (2.hereafter.B94) to. derive jet energy. fluxes and the variations of mass (lux. pressure. internal density ancl entrainment rate with distance from he nucleus (?.hereafterLBO2b)..," Together with the velocity distributions derived from modelling of the radio emission, these can be used in a conservation-law analysis \citep[hereafter B94]{bick94} to derive jet energy fluxes and the variations of mass flux, pressure, internal density and entrainment rate with distance from the nucleus \citep[hereafter LB02b]{lb02b}."315 Such an analysis is quasi-one-dimensional and therefore adopts. values for the [Low variables (in particular the velocity) averaged: across. the jet cross-section., Such an analysis is quasi-one-dimensional and therefore adopts values for the flow variables (in particular the velocity) averaged across the jet cross-section.316 This is reasonable if the velocity. profiles rave restricted. ranges ancl do not evolve significantly with distance down the jets. as is consistent. with the observations of 331 (LBO2b).," This is reasonable if the velocity profiles have restricted ranges and do not evolve significantly with distance down the jets, as is consistent with the observations of 31 (LB02b)."317 LE ETCIE jets are in pressure equilibrium. with their surroundings after they recollimate. this analysis requires that a significant overpressure drives the initial Ularine.," If I jets are in pressure equilibrium with their surroundings after they recollimate, this analysis requires that a significant overpressure drives the initial flaring."318 An alternative approach. which would also be consistent with the observations. is to postulate that the transverse velocity. profiles evolve. significantly as the jets interact with the external medium.," An alternative approach, which would also be consistent with the observations, is to postulate that the transverse velocity profiles evolve significantly as the jets interact with the external medium."319 Phe first approximation is then Oo assume pressure equilibrium between the jet and. its surrouncines and to take explicit account of the interaction oetween the jets and their surroundings using a simple mixine-laver model., The first approximation is then to assume pressure equilibrium between the jet and its surroundings and to take explicit account of the interaction between the jets and their surroundings using a simple mixing-layer model.320 Fhis is the subject of the present paper., This is the subject of the present paper.321 The key assumption is that there is a turbulent mixing aver between the jet and its environment. produced by the interaction of the two components.," The key assumption is that there is a turbulent mixing layer between the jet and its environment, produced by the interaction of the two components."322 The mixing laver grows roth into the jet and into the environment. and the initially aminar jet eventually becomes fully turbulent.," The mixing layer grows both into the jet and into the environment, and the initially laminar jet eventually becomes fully turbulent."323 As in the quasi-one-dimensional analysis of 2.. we use the relativistic ormulation of the laws of conservation of mass. ΠιοΠΙΟΩΙunm. and energy given by D94.," As in the quasi-one-dimensional analysis of \citet{lb02b}, we use the relativistic formulation of the laws of conservation of mass, momentum and energy given by B94."324 We deseribe the ecometry of the jet-laver model in Section 2.., We describe the geometry of the jet-layer model in Section \ref{structure}.325 Phe relativistic conservation laws are introduced in Section 3.., The relativistic conservation laws are introduced in Section \ref{laws}.326 We derive. and. discuss the solutions for our model in Section. d4.., We derive and discuss the solutions for our model in Section \ref{solutions}.327 In. Section r5... we apply our moclel to observations of 331.," In Section \ref{3c31}, we apply our model to observations of 31."328 We discuss the effects of varving model parameters in Section G and summarize our conclusions in Section 7.., We discuss the effects of varying model parameters in Section \ref{discussion} and summarize our conclusions in Section \ref{conclusion}.329 The basic structure of an FRU jet in our model is shown in Figure 1.., The basic structure of an I jet in our model is shown in Figure \ref{cartoon}.330 Following the definition given by LBO2a. we divide the jet into andregions! Close to the nucleus in the Haring region. the outer isophotes have small. but increasing opening angles.," Following the definition given by LB02a, we divide the jet into and Close to the nucleus in the flaring region, the outer isophotes have small, but increasing opening angles."331 Further out. they spread. rapidly and then recollimate.," Further out, they spread rapidly and then recollimate."332 In the outer region. the expansion is conical.," In the outer region, the expansion is conical."333 “Phe radio emission close to the base of the Daring region is usually faint ancl it is always possible to identify a distance from the nucleus where the jet brightens abruptly., The radio emission close to the base of the flaring region is usually faint and it is always possible to identify a distance from the nucleus where the jet brightens abruptly.334 We refer to this location as thepoint., We refer to this location as the.335 We assume pressure equilibrium with the surroundings ab all distances from the nucleus and. adopt the simplest ;xossible prescription for velocity variations following ?.., We assume pressure equilibrium with the surroundings at all distances from the nucleus and adopt the simplest possible prescription for velocity variations following \citet{cr91}.336 Wherever possible. we approximate the velocity of a component of the flow by its spatially averaged: value.," Wherever possible, we approximate the velocity of a component of the flow by its spatially averaged value."337 We xostulate that the [ow close to the axis of the Daring region is laminar. with a constant relativistic bulk velocity i; and hat this occupies the full width of the jet at the brightening volt. where interaction with the external medium becomes significant. for the first time.," We postulate that the flow close to the axis of the flaring region is laminar, with a constant relativistic bulk velocity $v_{j}$ and that this occupies the full width of the jet at the brightening point, where interaction with the external medium becomes significant for the first time."338 As a result. of cntrainment of external material. a slowerlayer forms between he laminar jet and the environment.," As a result of entrainment of external material, a slower forms between the laminar jet and the environment."339 The bulk velocity of the shear laver should. vary continuously in the racial (r) direction from ve; at dts boundary. with the laminar core to Oat its outer edge., The bulk velocity of the shear layer should vary continuously in the radial $r$ ) direction from $v_j$ at its boundary with the laminar core to 0 at its outer edge.340 The models derived by LBO2a show. however. that the ratio of edge to centre velocity or the svnchrotron-emitting material is 20.7 throughout he Hlaring and outer regions. so the velocity range within he mixing [aver is lah narrow.," The models derived by LB02a show, however, that the ratio of edge to centre velocity for the synchrotron-emitting material is $\approx$ 0.7 throughout the flaring and outer regions, so the velocity range within the mixing layer is fairly narrow."341 Thus we assume that the steacdv-state [low in this laver has a constant bulk velocity DScj., Thus we assume that the steady-state flow in this layer has a constant bulk velocity $v_{s}<v_{j}$.342 Material from both the environment. and. the aminar jet is continuously injected into the shear laver. the alter component supplving encrey and momentum as well as mass.," Material from both the environment and the laminar jet is continuously injected into the shear layer, the latter component supplying energy and momentum as well as mass."343 Integrated across the jet. the fraction of slower material then increases with distance from the nucleus: this would be interpreted as deceleration of the entire [ow in fits to observations with poor transverse resolution.," Integrated across the jet, the fraction of slower material then increases with distance from the nucleus; this would be interpreted as deceleration of the entire flow in fits to observations with poor transverse resolution."344 The laminar jet in the centre eventually vanishes. so no more energv or momentum can be injected into the shear laver from the inside.," The laminar jet in the centre eventually vanishes, so no more energy or momentum can be injected into the shear layer from the inside."345 Motivated by the analysis of 331 (LDBO2a). we assume that this transition occurs. precisely at the end of the Haring region.," Motivated by the analysis of 31 (LB02a), we assume that this transition occurs precisely at the end of the flaring region."346 This may not be general: modelling of other sources suggests that the bulk of the jet deceleration occurs in the first part of the Haring region, This may not be general: modelling of other sources suggests that the bulk of the jet deceleration occurs in the first part of the flaring region347If the ἐν are calculated at the mean position 2D—4ul:2)/2. the delay for a single sky. position becomes If the 7; ave caleulated at the mean position +=Cap| typ)/2. the differential delay is to lowest orders iu 7 The leading term 2A:7/5 contains With (05) aud (32)). we may expand. P? in a power series of Ac. We do the same for D? via ((50)). and eventually combine these power series of A+ at the oof ((7)).,"If the $l_i$ are calculated at the mean position $\bar z=(z_1+z_2)/2$, the delay for a single sky position becomes If the $l_i$ are calculated at the mean position $\bar z=(z_{1\textrm{P}}+z_{2\textrm{P}})/2$ , the differential delay is to lowest orders in $\tau$ The leading term $2\Delta z \tau l_2$ contains With \ref{eq.PofIs}) ) and \ref{eq.rtayl}) ), we may expand $P^2$ in a power series of $\Delta z$, We do the same for $D^2$ via \ref{eq.Dofl}) ), and eventually combine these power series of $\Delta z$ at the of \ref{eq.beff}) ),"348D ids found. suggesting that the large values of the break frequeney found in the case of low-power LISs is most likely due to the elect of B on the cooling of the electrons.,"$B$ is found, suggesting that the large values of the break frequency found in the case of low-power HSs is most likely due to the effect of $B$ on the cooling of the electrons."349 Indeed. assuming a roughly constant emitting volume (or 7 for à const.," Indeed, assuming a roughly constant emitting volume (or $\tau$ for a const."350 velocity in the post shock region). Fig.," velocity in the post shock region), Fig."351 4 also shows the zeroth-order approximation (no acdiabatie losses) of Iq., 4 also shows the zeroth-order approximation (no adiabatic losses) of Eq.352" 7 G,xD.7. solid lino)."," \ref{nub} $\nu_b\propto B^{-3}$, solid line)."353 The slope of this approximation is surprisingly close to that observed., The slope of this approximation is surprisingly close to that observed.354 With the aim to compare the behaviour of our VET sample with other ος selected to match the same range of £j. we extracted all the [ux densities of optical svnchrotron Ls from the literature.," With the aim to compare the behaviour of our VLT sample with other HSs selected to match the same range of $\nu_b$, we extracted all the flux densities of optical synchrotron HSs from the literature."355 In Fig., In Fig.356 4 we display the break frequeney and the equipartition magnetic field. strength derived: with the same procedure cleseribecl below for these S additional optical svnchrotron Liss (Tab., 4 we display the break frequency and the equipartition magnetic field strength derived with the same procedure described below for these 8 additional optical synchrotron HSs (Tab.357 1)., 1).358 The radio and optical data from the literature have been combined with archive LIST data when available., The radio and optical data from the literature have been combined with archive HST data when available.359 1n this Letter we do not include. the case of 2263E since it has been shown that the broad. banc spectrum of this HS might. result from a combination of two cillerent spectral components (Llardeastle et al., In this Letter we do not include the case of 263E since it has been shown that the broad band spectrum of this HS might result from a combination of two different spectral components (Hardcastle et al.360 2002). ancl the cases of 1196N and 3€2295N whose optical emission is best interpreted. as. due to. svnchro-selt-Compton. (Hardcastle 2001: Brunetti 2000).," 2002), and the cases of 196N and 295N whose optical emission is best interpreted as due to synchro-self-Compton (Hardcastle 2001; Brunetti 2000)."361" We notice that the xehaviour followed bv the LISs from the literature is consistent with that of the VLT ones ancl thus strengthen the derived 5j By., trend.", We notice that the behaviour followed by the HSs from the literature is consistent with that of the VLT ones and thus strengthen the derived $\nu_b - B_{eq}$ trend.362 lt is clear that such a trend should be tested combining the VETE sample with a sample of Liss with relatively high values of the magnetic field. and thus with anerpeched svnehrotron break frequencies below ~1077 Hz (Fig., It is clear that such a trend should be tested combining the VLT sample with a sample of HSs with relatively high values of the magnetic field and thus with an synchrotron break frequencies below $\sim 10^{12}$ Hz (Fig.363 4)., 4).364 YEP observations of a sample of relatively low-raclio power LSs has led to an unprecedented detection rate of these regions in the optical., VLT observations of a sample of relatively low-radio power HSs has led to an unprecedented detection rate of these regions in the optical.365 Prom a theoretical point of. view. this result is the natural consequence of optical emitting electrons surviving longer in low power. io. low-/3 field. regions than in bright and strong-licld LISs.," From a theoretical point of view, this result is the natural consequence of optical emitting electrons surviving longer in low power, i.e. $B$ field, regions than in bright and strong-field HSs."366 We have shown that the combination of low magnetic fields and laree distances from the core of the Liss in our VLTI sample indicates the need for in-situ particle acceleration. in these regions: under physically realible hypotheses. the emitting electrons. are too energetic aud distant from the core to be transported. from the nucleus to the LIS region.," We have shown that the combination of low magnetic fields and large distances from the core of the HSs in our VLT sample indicates the need for in-situ particle acceleration in these regions: under physically realible hypotheses, the emitting electrons are too energetic and distant from the core to be transported from the nucleus to the HS region."367 We have shown that there is a trend between the magnetic field. strength (equipartition) in the IIS. volume and the measured synchrotron break frequency for the ος in our VET sample., We have shown that there is a trend between the magnetic field strength (equipartition) in the HS volume and the measured synchrotron break frequency for the HSs in our VLT sample.368 In addition. we also have shown tha he behaviour of optical svnchrotron ος taken from the iLerature is consistent with that of our VET Liss.," In addition, we also have shown that the behaviour of optical synchrotron HSs taken from the literature is consistent with that of our VLT HSs."369 This tren ws the inferred within the framework of the in-situ acceleration scenario in which the break cnerey of he acceleratedinjected electrons is driven by the cooling in the post-shock region., This trend has the inferred within the framework of the in-situ acceleration scenario in which the break energy of the accelerated/injected electrons is driven by the cooling in the post-shock region.370 The combination of our low power sample with statistical samples of high power HSs will tes he reported trend: the break frequency of high power Liss is in general expected to be below 107 Hz., The combination of our low power sample with statistical samples of high power HSs will test the reported trend: the break frequency of high power HSs is in general expected to be below $\sim 10^{12}$ Hz.371 We thank Ix. Meisenheimer. J. kirk and €i. Setti for useful discussions and the anonymous referee for helpful advice on the presentation of the paper.," We thank K. Meisenheimer, J. Kirk and G. Setti for useful discussions and the anonymous referee for helpful advice on the presentation of the paper."372 GB ancl IXKIIM. acknowledge the MPLA for their warm hospitality. ancl partial financial support., GB and KHM acknowledge the MPIA for their warm hospitality and partial financial support.373 GB and SV acknowledge partial financial support from MIUI under grant. COLIN 2001-02-8773., GB and SV acknowledge partial financial support from MIUR under grant COFIN 2001-02-8773.374. ΙΙΝΤΕ was, KHM was375A-type supergiants are important probes of metallicity in nearby galaxies (ο...???)..,"A-type supergiants are important probes of metallicity in nearby galaxies \citep[e.g.,][]{ml95, venn00b, bg02}."376 Phis is because of their intrinsic uminositv anc relatively small bolometric corrections (ensuring that they are among the visually brightest. stars in anv galaxy: e.g.. 2)). and their spatial isolation (which contrasts with O- and. B-type stars. which are frequently ound in clusters. or associations. or in binary svstenis with companions of comparable brightness).," This is because of their intrinsic luminosity and relatively small bolometric corrections (ensuring that they are among the visually brightest stars in any galaxy; e.g., \citealt{hum83}) ), and their spatial isolation (which contrasts with O- and B-type stars, which are frequently found in clusters or associations, or in binary systems with companions of comparable brightness)."377 Moreover. not only are the optical spectra of A-type supergiants tvpically ree of significant contamination from spatially unresolved companions. but they also exhibit. lines from a relatively wide range of elements. which can be modeled: reasonably satisfactorily using relatively simple LTE atmospheres (cf. 7)..," Moreover, not only are the optical spectra of A-type supergiants typically free of significant contamination from spatially unresolved companions, but they also exhibit lines from a relatively wide range of elements, which can be modeled reasonably satisfactorily using relatively simple LTE atmospheres \citep[cf.][]{venn95}."378 A-type stars can also. be important occasionally dominant contributors to the integrated light of more distant. unresolved. galactic svstems (c.g...7).," A-type stars can also be important – occasionally dominant – contributors to the integrated light of more distant, unresolved galactic systems \citep[e.g.,][]{bb99}."379 In the interpretation of such unresolved. svstems. as well as the spectra of individual stars. the correspondence between spectral morphology ancl funcamental stellar parameters is a Κον issue.," In the interpretation of such unresolved systems, as well as the spectra of individual stars, the correspondence between spectral morphology and fundamental stellar parameters is a key issue."380 We address this issue in the present paper. motivated by the need to classify the A-type stars observed in our forthcoming 2db survey of the luminous-star content of the SAIC (7).. ancl to assign consistent ancl accurate ellective temperatures to them.," We address this issue in the present paper, motivated by the need to classify the A-type stars observed in our forthcoming 2dF survey of the luminous-star content of the SMC \citep{ehi}, and to assign consistent and accurate effective temperatures to them."381 By way of introduction. to. the philosophy of spectral classification which we adopt. we can do no better than craw on the discussion given by 2? in his seminal paper on the classification of XIx-tvpe spectra: Thus. to quote a more recent doven of classification.," By way of introduction to the philosophy of spectral classification which we adopt, we can do no better than draw on the discussion given by \citet{m37} in his seminal paper on the classification of A–K-type spectra: Thus, to quote a more recent doyen of classification,"382simulations will be useful in studying uncollapsecl gas outside of virialized halos and determining its contribution to absorption svstenis.,simulations will be useful in studying uncollapsed gas outside of virialized halos and determining its contribution to absorption systems.383 We have illustrated that absorption systems comprise a powerful probe of galaxy formation., We have illustrated that absorption systems comprise a powerful probe of galaxy formation.384 Acquiring more data of this kind. and developing more detailed models of these systems. will help in forming a complete picture of the properties of the gas present in the early epochs of galaxy formation. which form the building blocks of the galaxies that we see today.," Acquiring more data of this kind, and developing more detailed models of these systems, will help in forming a complete picture of the properties of the gas present in the early epochs of galaxy formation, which form the building blocks of the galaxies that we see today."385 We thank Celine Pérroux for stimulating conversations., We thank Celine Pérroux for stimulating conversations.386 AHAL acknowledges support. from. NASA ΑΔ. erant NAG5-3525 and NSE grant AST-9802568., AHM acknowledges support from NASA LTSA grant NAG5-3525 and NSF grant AST-9802568.387 INP was partially supported by NASA through a Hubble Fellowship grant ΕΙ-01142.01-A awarded by STSCL and JAP was supported by NASA and NSP grants at UCSC., JXP was partially supported by NASA through a Hubble Fellowship grant HF-01142.01-A awarded by STSCI and JRP was supported by NASA and NSF grants at UCSC.388Only the SED data at frequencies near and below the dust peak are used [ον (he model fit because the mid- (to near-It data points clearly require additional. higher temperature dust components.,"Only the SED data at frequencies near and below the dust peak are used for the model fit because the mid- to near-IR data points clearly require additional, higher temperature dust components."389" The SED fit for Arp 220 is shown in Figure 1.. and it demonstrates the effects of chaneine 7, while holding ;» constant."," The SED fit for Arp 220 is shown in Figure \ref{fig:a220sed}, and it demonstrates the effects of changing $T_d$ while holding $\beta$ constant."390 The scatter of data points about. various models suggests that there are svstematic scaling differences among different flix density nmeasurenienis. generally larger (han the nominal uncertainties reported. especially in the subanillimeter wavelengths.," The scatter of data points about various models suggests that there are systematic scaling differences among different flux density measurements, generally larger than the nominal uncertainties reported, especially in the submillimeter wavelengths."391 At a glance. all three dust temperature models plotted seem to do an adequate job of fitting the submun and FIR. data points qualitatively.," At a glance, all three dust temperature models plotted seem to do an adequate job of fitting the submm and FIR data points qualitatively."392 However. a closer examination reveals that the 7)=74 Ix model fails to matehi the subiimn points.," However, a closer examination reveals that the $T_d=74$ K model fails to match the submm points."393 The Ty=43 Ix model matches the submunm data points reasonably well. but it clearly Falls short on predicting the FIR data points.," The $T_d=43$ K model matches the submm data points reasonably well, but it clearly falls short on predicting the FIR data points."394 Previous studies of subi dust properties For Iuminous infrared galaxies generally. favored. cold dust temperature between 40 and 50 Ix for Arp 2202000b)., Previous studies of submm dust properties for luminous infrared galaxies generally favored cold dust temperature between 40 and 50 K for Arp 220.395. I we were to choose a dust SED model that best fits all observed data points between. Imm and 60 jan. however. a slightly warmer dust model is favored.," If we were to choose a dust SED model that best fits all observed data points between 1mm and 60 $\mu$ m, however, a slightly warmer dust model is favored."396 Our starburst SED model analvsis is applied to 23 IR-selected starburst galaxies (hat are selected for (1) their Lj45 exceeding LO!L.: and (2) having at least (wo measurements covering (heir subi part of the spectrum., Our starburst SED model analysis is applied to 23 IR-selected starburst galaxies that are selected for (1) their $L_{FIR}$ exceeding $10^{11}~L_\odot$; and (2) having at least two measurements covering their submm part of the spectrum.397 The SED data are primarily drawn trom the IRAS Faint Source Catalog. NRAO/VLA Sky Survey 1998)..(1991)..(1992).. (1996).. (1999)... (2000).. (2000b).. and (2001).," The SED data are primarily drawn from the IRAS Faint Source Catalog, NRAO/VLA Sky Survey , , and ."398. As stummarized in Table IL.. the characteristic dust temperature 7; ranges between 46 Ix and 74 Ix. with a mean of 58x9 Kk. Dust emissivity ο also ranges widely. between 1.05 and 1.70. with à mean of 1.3240.17 and a median of 1.35 (see Figure 2)).," As summarized in Table \ref{tab:23gals}, the characteristic dust temperature $T_d$ ranges between 46 K and 74 K, with a mean of $58\pm9$ K. Dust emissivity $\beta$ also ranges widely, between 1.05 and 1.70, with a mean of $1.32\pm0.17$ and a median of 1.35 (see Figure \ref{fig:betaTd}) )."399 It is likely that all galaxies consist of an ensemble of dust clouds with a range of temperature2001).. ancl single temperature SED models tend to favor a smaller 2 (flatter subi dust spectrum) and higher dust temperature (han tvpically found in giant molecular clouds (10-20 IX).," It is likely that all galaxies consist of an ensemble of dust clouds with a range of temperature, and single temperature SED models tend to favor a smaller $\beta$ (flatter submm dust spectrum) and higher dust temperature than typically found in giant molecular clouds (10-20 K)."400 Since available SED measurements are generally sparse in practice. we accept these limitations of a single temperature dust model lor the purpose of keeping the number ol [ree parameters manageably small.," Since available SED measurements are generally sparse in practice, we accept these limitations of a single temperature dust model for the purpose of keeping the number of free parameters manageably small."401 Thermal Bremsstrahilung (Iree-Iree) emission makes significant contribution only in the bottom of the SED trough between the non-thermal svnchrotron aud thermal dust feature. and it plays essentially no role in defining the starburst SED template.," Thermal Bremsstrahlung (free-free) emission makes significant contribution only in the bottom of the SED trough between the non-thermal synchrotron and thermal dust feature, and it plays essentially no role in defining the starburst SED template."402" Variations in (hie svnchrotron emission are (tracked by a parameter fy, (see Eq. 13)).", Variations in the non-thermal synchrotron emission are tracked by a parameter $f_{nth}$ (see Eq. \ref{eq:nth2}) ).403" The dispersion in (he radio-FIR. correlation is measured to be about 0.25 in a logarithmic scale2001).. and a rather broad range of fy), lound (see Figure 3)) is consistent with this expectation."," The dispersion in the radio-FIR correlation is measured to be about 0.25 in a logarithmic scale, and a rather broad range of $f_{nth}$ found (see Figure \ref{fig:fnth}) ) is consistent with this expectation."404 Presence of a radio AGN (e.g. Mrk 231. NGC! 6240)ean account for the increase," Presence of a radio AGN (e.g. Mrk 231, NGC 6240)can account for the increase"405mean energy per unit mass and spatial frequency existing in the resolved scales. so that for κ227/L. The Sapexponentοπή. « is also imposed by continuity arguments.,"mean energy per unit mass and spatial frequency existing in the resolved scales, so that for $k=2\pi/L$, The exponent $\alpha$ is also imposed by continuity arguments."406 When the inertial range begins. re. at A=22/A. then Ej is given by equation (2)).," When the inertial range begins, i.e. at $k=2\pi/\Lambda$, then $E_k$ is given by equation \ref{kolmo}) )."407" This constraint leads to The definition of In)E, in equation (4) implies. where weSxzp have assumed aw>| and Lo>A, ("," This constraint leads to The definition of $E_t$ in equation \ref{eq4}) ) implies, where we have assumed $\alpha> 1$ and $L \gg \Lambda$. ("408Intermediate values of A provide magnetic energies in between equation [11]] and the limit considered here.),Intermediate values of $\Lambda$ provide magnetic energies in between equation \ref{3ck}] ] and the limit considered here.)409 The expression (21)). together with equation (10)). render Once more the unsigned flux in unresolved fields turns out to be significant.," The expression \ref{myalpha}) ), together with equation \ref{this}) ), render Once more the unsigned flux in unresolved fields turns out to be significant."410 The ratio in equation (22)) has been evaluated using equation (20)) with the same parameters leading to equation (13)). which provide an exponent e varying from 2.1 to 1.8 when A goes from 10 km to 0.1 km.," The ratio in equation \ref{add_fau}) ) has been evaluated using equation \ref{crazy}) ) with the same parameters leading to equation \ref{this_other}) ), which provide an exponent $\alpha$ varying from 2.1 to 1.8 when $\Lambda$ goes from 10 km to 0.1 km."411 Equations (13). (17)) and (22)) suggest that the implicit turbulent field accounting for the used magnetic. diffusivity has a magnetic flux similar to that explicitly shown in. the simulations.," Equations \ref{this_other}) ), \ref{tttt}) ) and \ref{add_fau}) ) suggest that the implicit turbulent field accounting for the used magnetic diffusivity has a magnetic flux similar to that explicitly shown in the simulations."412 Some numerical simulations of turbulent nagneto-convection show a range of wavenumbers where the magnetic energy exceeds the kinetic energy (super equipartition range: see Biskamp2003:Maronetal.2004;Brandenburg 2005).," Some numerical simulations of turbulent magneto-convection show a range of wavenumbers where the magnetic energy exceeds the kinetic energy (super equipartition range; see \citealt{bis03,mar04,bra05}) )."413 The magnetic energy densities used above are much smaller than the kinetic energy density of the solar granulation., The magnetic energy densities used above are much smaller than the kinetic energy density of the solar granulation.414 If this super equipartition range would have to be included in our estimate. one needs to increase & with respect to the values employed above.," If this super equipartition range would have to be included in our estimate, one needs to increase $\varepsilon$ with respect to the values employed above."415" The turbulent magnetic. energy would increase accordingly. leading to (B,) larger than the values in equations (13)) and C17))."," The turbulent magnetic energy would increase accordingly, leading to $\langle B_t\rangle$ larger than the values in equations \ref{this_other}) ) and \ref{tttt}) )."416 Consequently. the estimates above are probably conservative. a conclusion reinforcing the importance of the unresolved magnetic fields.," Consequently, the estimates above are probably conservative, a conclusion reinforcing the importance of the unresolved magnetic fields."417 The numerical simulations of solar magneto-convection require artificially large magnetic diffusion. which smears out all the spectrum of magnetic structures smaller than the grid scale.," The numerical simulations of solar magneto-convection require artificially large magnetic diffusion, which smears out all the spectrum of magnetic structures smaller than the grid scale."418 The use of such high magnetic diffusivity can be understood as the effect of a complex unresolved turbulent magnetic field with spatial scales so small that the diffusion time scale for the true small Ohmie diffusivity is similar to the diffusion time scale for the structures in the simulation., The use of such high magnetic diffusivity can be understood as the effect of a complex unresolved turbulent magnetic field with spatial scales so small that the diffusion time scale for the true small Ohmic diffusivity is similar to the diffusion time scale for the structures in the simulation.419 Such ài implicit magnetic field does not contribute to the polarimetric signals synthesized by Khomenkoetal.(2005)., Such an implicit magnetic field does not contribute to the polarimetric signals synthesized by \citet{kho05}.420. Assuming à turbulent cascade for the unresolved artificially smeared magnetic fields. we find that their unsigned magnetic flux is at least as important as that explicitly shown in the simulation.," Assuming a turbulent cascade for the unresolved artificially smeared magnetic fields, we find that their unsigned magnetic flux is at least as important as that explicitly shown in the simulation."421 Should this magnetic flux is considered. the Zeeman polarization signals measured by Khomenkoetal. are consistent with an unsigned flux of 2x20G (Le.. (B)=(By; equations [13]]. [17]] and [22]] ).," Should this magnetic flux is considered, the Zeeman polarization signals measured by \citeauthor{kho05}422 are consistent with an unsigned flux of $2\times 20~{\rm G}$ (i.e., $\langle B_t\rangle \simeq\langle B\rangle$; equations \ref{this_other}] ], \ref{tttt}] ] and \ref{add_fau}] ] )."423 In other words the unsigned flux assigned by Khomenkoetal.(2005) must be regarded as a conservative lower limit., In other words the unsigned flux assigned by \citet{kho05} must be regarded as a conservative lower limit.424 This conclusion is not specific of the simulations analyzed here., This conclusion is not specific of the simulations analyzed here.425" A bias is to be expected whenever the quiet Sun unsigned magnetic flux is inferred as the unsigned flux of numerical simulations reproducing observed Zeeman polarization signals,", A bias is to be expected whenever the quiet Sun unsigned magnetic flux is inferred as the unsigned flux of numerical simulations reproducing observed Zeeman polarization signals.426 The calculations that we describe represent only a first approximation to estimating the bias., The calculations that we describe represent only a first approximation to estimating the bias.427 They are based on the theory of MHD turbulence. which remains to be completed.," They are based on the theory of MHD turbulence, which remains to be completed."428 The conclusions have to be backed up or rejected by numerical simulations with realistic Ohmie diffusivities., The conclusions have to be backed up or rejected by numerical simulations with realistic Ohmic diffusivities.429 HPRN-CT-2002-003313., 313.430 The spatial discretization of the MHD equations solved by Vógler(2003) is based on a four-order finite difference scheme.," The spatial discretization of the MHD equations solved by \citet{vog03b}431 is based on a four-order finite difference scheme."432 Then the components of the magnetic field are approximated by a four-order polynomial. so that the first and second partial derivatives appearing in the MHD equations are represented by a third-order polynomial and a second-order polynomial. respectively.," Then the components of the magnetic field are approximated by a four-order polynomial, so that the first and second partial derivatives appearing in the MHD equations are represented by a third-order polynomial and a second-order polynomial, respectively."433 We will estimate L as the smallest wavelength of a sinusoidal magnetic field for which the error involved in these polynomial approximations is insignificant., We will estimate $L$ as the smallest wavelength of a sinusoidal magnetic field for which the error involved in these polynomial approximations is insignificant.434 Let us denote by /Εν) one of the components of the magnetic field vector. with & the wavenumber along the spatial coordinate x. The numerical code represents it in the surroundings of i as the polynomial f;Co. The fifth order term in the Taylor expansion of /€v) provides the error of the approximation. AJGo. As usual. the symbol /*'η] denotes the n-th derivative of //C0.," Let us denote by $f(x)$ one of the components of the magnetic field vector, with $k$ the wavenumber along the spatial coordinate $x$, The numerical code represents it in the surroundings of $x_0$ as the polynomial $f_a(x)$, The fifth order term in the Taylor expansion of $f(x)$ provides the error of the approximation, $\Delta f(x)$, As usual, the symbol $f^{(n)}$ denotes the $n$ -th derivative of $f(x)$."435 The approximation CÀ2)) is carried out at each pixel. so that with Av the pixel size.," The approximation \ref{approximation}) ) is carried out at each pixel, so that with $\Delta x$ the pixel size."436 Among the various polynomials used to represent the MHD equations. the computation of the second derivatives. corresponds to the lowest order and. therefore. it is the worst approximation.," Among the various polynomials used to represent the MHD equations, the computation of the second derivatives, corresponds to the lowest order and, therefore, it is the worst approximation."437 If the error associated. with the computation of the second derivatives is tolerable. then the polynomial approximation is tolerable.," If the error associated with the computation of the second derivatives is tolerable, then the polynomial approximation is tolerable."438 According to equation (A3}). the error Af7G) is," According to equation \ref{delta}) ), the error $\Delta f^{(2)}(x)$ is"439transform the data covariance matrix. we add the constraint ACBCBYP). where J is the unit matrix and A is a Lagrangian multiplier.,"transform the data covariance matrix, we add the constraint $\lambda(BCB^\dag-I)$, where $I$ is the unit matrix and $\lambda$ is a Lagrangian multiplier."440 It can be shown (TTID)) that this is equivalent to a ecucralised Wwarlamen-Loevve cigenvalie problem. which has a unique solution 2 for cach parameter.," It can be shown \cite{TTH}) ) that this is equivalent to a generalised Karhunen-Loèvve eigenvalue problem, which has a unique solution $B$ for each parameter."441" These solutions have the property that DB2 CB""t N17) where Aj=Lf; are the cigeuvalies of the transformed data set and the inverse errors associated with cach eigeumiode of the new data set."," These solutions have the property that 	B C) _i I, where $\lambda_i=1/\sigma'_i$ are the eigenvalues of the transformed data set and the inverse errors associated with each eigenmode of the new data set."442 The new. compressed data set. 4. can uow be ordered bv decreasing eigenvalue. so that the first clectinode contains the most information about the desired parameter. the second slightly less iuforiiatiou. and so on.," The new, compressed data set, $\x'$, can now be ordered by decreasing eigenvalue, so that the first eigenmode contains the most information about the desired parameter, the second slightly less information, and so on."443 The total error on the paraieter is then simply eiven by the iuverse of the 1«1. Fisher matrix D ες) κ), The total error on the parameter is then simply given by the inverse of the $1\times1$ Fisher matrix 	F' = 	 ( ).444 We are now free to choose how many eigeunmodes to include in the Likelihood analysis., We are now free to choose how many eigenmodes to include in the likelihood analysis.445 A compression of LO will lead to a time saving of 107., A compression of 10 will lead to a time saving of $10^3$.446 Tlowever this is only exact if we now the true value of the parameters used to calculate 5., However this is only exact if we know the true value of the parameters used to calculate $B$.447 But if we are near the maxi likelihood solution then we cau iterate towards the exact solution., But if we are near the maximum likelihood solution then we can iterate towards the exact solution.448 This procedure is optimal for all parameters — linear aud nonlinear in the model., This procedure is optimal for all parameters – linear and nonlinear – in the model.449" In the special case of lincar paraiucters that are just proportional to the signal part of the data covariance matrix (for example the amplitude of ο, if the data are the 0;,,). the eigenmodes reduce to signal-to-noise clgcnimodes (Boud199L.. Bunn&Sueivama 1995))."," In the special case of linear parameters that are just proportional to the signal part of the data covariance matrix (for example the amplitude of $C_\ell$, if the data are the $a_{\ell m}$ ), the eigenmodes reduce to signal-to-noise eigenmodes \cite{bond}, \cite{bunn}) )."450 Ποιος our cigenmodes are more ecneral than cigcuimodes., Hence our eigenmodes are more general than signal-to-noise eigenmodes.451 Furthermore. as our eieeunmodes satisfv the condition that the Fisher matrix is a maxinmun.thev are the optimal oues for data compression.," Furthermore, as our eigenmodes satisfy the condition that the Fisher matrix is a maximum, they are the optimal ones for data compression."452 Aux other choice. iucludius sigual-to-noise eieeniodes. would eive a higher variance.," Any other choice, including signal-to-noise eigenmodes, would give a higher variance."453 Iu Figure 1 we plot the nucertainty on 3 parameters for COBE-type data. the quadrupole. Q. the spectral iudex of scalar perturbations. 1 aud the re-ionization optical depth. 7.," In Figure 1 we plot the uncertainty on 3 parameters for COBE-type data, the quadrupole, $Q$, the spectral index of scalar perturbations, $n$ and the re-ionization optical depth, $\tau$."454 The analysis preseuted so far is strictly optimal only for the coucitional likelihood — the estimation of oue parameter when all others are known., The analysis presented so far is strictly optimal only for the conditional likelihood – the estimation of one parameter when all others are known.455 A far more challenging task is to optimise the data compression when all parameters are to be estimated from the data., A far more challenging task is to optimise the data compression when all parameters are to be estimated from the data.456" In this case. the mareinal error on a sinele paralucter 0; rises above the conditional error L/YF}; to \F,,>."," In this case, the marginal error on a single parameter $\theta_i$ rises above the conditional error $1/\sqrt{F_{ii}}$ to $\sqrt{F_{ii}^{-1}}$."457 As far as we are aware. there is uo general solution kuown to this problem. but here we preseut some methods which have intuitive motivation aud appear successful in practice.," As far as we are aware, there is no general solution known to this problem, but here we present some methods which have intuitive motivation and appear successful in practice."458 Suppose that we repeat the optimusation procedure. outlined above. i times. ouce for cach parameter.," Suppose that we repeat the optimisation procedure, outlined above, $m$ times, once for each parameter."459 The union of these sets should do well at estimating all parameters. but the size may he larec.," The union of these sets should do well at estimating all parameters, but the size may be large."460 However.," However,"461 (lasinger&vanderIlis1989).," \citep[see][for a recent review]{va2006}. \citep{hava1989},"462. have huninosities close to the Eddinetoji huuainositv (~0.5 oor more). Whereas atoll sources Lave luΠω in the range ~O.0Lledd.," have luminosities close to the Eddington luminosity $\sim$ or more), whereas atoll sources have luminosities in the range $\sim$."463. An exaple of the variety in shapes that is observed in the CD/IIID tracks of the Z ancl atoll subclasses is shown in Figure 1.., An example of the variety in shapes that is observed in the CD/HID tracks of the Z and atoll subclasses is shown in Figure \ref{fig:overview}.464 The Z source tracks typically show three branches. which from top to bottom are called the horizoutal brauch. the normal branch. aud the faring brauch.," The Z source tracks typically show three branches, which from top to bottom are called the horizontal branch, the normal branch, and the flaring branch."465 Based on the presence and oricutation of these branches. the Z sources can be further divided iuto f “Cre-like” Z sources (Cve N-2. CN 5I. aud GNX 31010) and the ‘Sco-like’ Z sources (Sco N-1. CN 1712. aud CX 319|2). with the former showing Z-shaped tracks in t IID refüe:overviewaa) and the latter more ον -s*haped tracks refiic:overviewhb.c: see also I&uulkersetal.199E:Womanetal.2007b (hereafter HOT).," Based on the presence and orientation of these branches, the Z sources can be further divided into the `Cyg-like' Z sources (Cyg X-2, GX 5–1, and GX 340+0) and the `Sco-like' Z sources (Sco X-1, GX 17+2, and GX 349+2), with the former showing `Z'-shaped tracks in the HID \\ref{fig:overview}a a) and the latter more $\nu$ '-shaped tracks \\ref{fig:overview}b b,c; see also \citealt{kuvaoo1994,hovawi2007} (hereafter H07))."466 The atoll sources can show Z-haped tracks as well rofüe:overviewee). although the individual branches are thought to have a different plysical nature than the Z source brauches," The atoll sources can show `Z'-shaped tracks as well \\ref{fig:overview}g g), although the individual branches are thought to have a different physical nature than the Z source branches"467a [function of position over 1ie sky) over an area of 2151 square degrees.,a function of position over the sky) over an area of 2151 square degrees.468" “Phe survey. ος'ometry consists of two broad declination strips. à Larger one in the SGP covering the area 3307alantxeRA(2000)=2 ""AQ. 37.57Xdec(2000)220==.)n. and a smaller one se in the NGP with 950""*<RA(2000)< 14""50'"". 2.5f£dec(2000)£zτον plus 100 random. 2-degree fields spread: uniformly over the 7000 square degrees. of the APA catalogue in the southern Galactic hemisphere."," The survey geometry consists of two broad declination strips, a larger one in the SGP covering the area $3^h 30^m\simlt {\rm RA}({\rm 2000})\simlt46921^h40^m$ , $-37.5^\circ \simlt {\rm dec}({\rm 2000})\simlt -22.5^\circ$ and a smaller one set in the NGP with $9^h 50^m\simlt {\rm RA}({\rm 2000})\simlt 47014^h50^m$ , $2.5^\circ \simlt{\rm dec}({\rm 2000}) \simlt -7.5^\circ$, plus 100 random 2-degree fields spread uniformly over the 7000 square degrees of the APM catalogue in the southern Galactic hemisphere."471 Phe niccian redshift’ of the galaxies is 0.11 ancl the great majority have z«0.3., The median redshift of the galaxies is 0.11 and the great majority have $z<0.3$.472 The completion of the 2415 has allowed us. to obtain 271 new spectroscopic counterparts for 5146Hs= mJy radio objects to be added to the sample presented in Magliocchetti et al. (, The completion of the 2dFGRS has allowed us to obtain 271 new spectroscopic counterparts for $S_{1.4 \rm GHz}\ge 1$ mJy radio objects to be added to the sample presented in Magliocchetti et al. (4732002).,2002).474 As in. Maegliocchetti οἱ al. (, As in Magliocchetti et al. (4752002). the parent radio dataset comes from. matching ogether sources in the FIRST (Becker et al.,"2002), the parent radio dataset comes from matching together sources in the FIRST (Becker et al."476" 1995) and APAL catalogues over the region of the sky between 048""*<LA(2000)Zo1432"" and 2.777<dec(2000)2.357. where these two surveys overlap."," 1995) and APM catalogues over the region of the sky between $9^h 48^m \simlt {\rm RA}({\rm 2000})477\simlt 14^h 32^m$ and $-2.77^\circ \simlt {\rm dec}({\rm 2000}) 478\simlt 2.25^\circ$, where these two surveys overlap."479" Magliocchetti Maddox (2002) find 4075 identifications corresponding to 16.7 per cent of the original radio sample in the APAIL catalogue OL b,22 and fora matching radius of 2 arcsec. value"," Magliocchetti Maddox (2002) find 4075 identifications – corresponding to 16.7 per cent of the original radio sample – in the APM catalogue for $\bj\le 22$ and fora matching radius of 2 arcsec, value"480"The light profiles of spiral galaxies consist of two principal components: an inner, bulge-dominated component; and an outer exponentially declining disc with some minor deviations related to spiral arms(??)..","The light profiles of spiral galaxies consist of two principal components: an inner, bulge-dominated component; and an outer exponentially declining disc with some minor deviations related to spiral arms\citep{deVaucouleurs:1959, Freeman:1970}."481" However, since ? we have known that this 'classical picture fails for most spiral galaxies, particularly at the faint surface brightness µ of the outer stellar disc."," However, since \cite{vanderKruit:1979} we have known that this `classical' picture fails for most spiral galaxies, particularly at the faint surface brightness $\mu$ of the outer stellar disc."482" We now know that most disc profiles are best described by a two slope model (broken exponential), characterised by an inner and outer exponential scalelength separated by a relatively well defined break radius rpu (?).."," We now know that most disc profiles are best described by a two slope model (broken exponential), characterised by an inner and outer exponential scalelength separated by a relatively well defined break radius $r_{\rm brk}$ \citep{Pohlen_etal:2002}."483" Many studies have now reported (mainly using surface photometry) the existence of broken exponential discs, or and distant z«1 Universe (???).."," Many studies have now reported (mainly using surface photometry) the existence of broken exponential discs, or, in spiral galaxies in both the local \citep{Pohlen_etal:2002, Pohlen_etal:2007, Pohlen_Trujillo:2006, Bakos_etal:2008,484Erwin_etal:2008, Gutierrez_etal:2011, Maltby_etal:2011} and distant $z<1$ Universe \citep{Perez:2004,485Trujillo_Pohlen:2005, Azzollini_etal:2008}."486 Broken exponential discs have also been reported using resolved star counts on some nearby galaxies (??)..," Broken exponential discs have also been reported using resolved star counts on some nearby galaxies \citep{Ibata_etal:2005,Ferguson_etal:2007}."487 These studies have resulted in a comprehensive classification scheme for disc galaxies based on break features in the outer disc component of their radial µ profiles (seee.g.???)..," These studies have resulted in a comprehensive classification scheme for disc galaxies based on break features in the outer disc component of their radial $\mu$ profiles \citep[see e.g.][]{Erwin_etal:2005,488Erwin_etal:2008, Pohlen_Trujillo:2006}."489" This scheme consists of three broad profile types (Type I, II and III): Type I (no break) - a single exponential disc extending out to several scalelengths (e.g. ?);; Type II (down-bending break, truncation) — a broken exponential disc with a shallow inner and steeper outer region (??); Type III (up-bending break, antitruncation) — à broken exponential disc with a shallower region beyond the break radius rprk (?).."," This scheme consists of three broad profile types (Type I, II and III): Type I (no break) – a single exponential disc extending out to several scalelengths \citep[e.g.][]{BlandHawthorn_etal:2005}; Type II (down-bending break, ) – a broken exponential disc with a shallow inner and steeper outer region \citep{vanderKruit:1979,Pohlen_etal:2002}; Type III (up-bending break, ) – a broken exponential disc with a shallower region beyond the break radius $r_{\rm brk}$ \citep{Erwin_etal:2005}. ."490" In the classical picture (simple bulge and disc), the de"," In the classical picture (simple bulge and disc), the de"491The shearing sheet. (Goldreich LyncenBell 1965. Julian Poomre 1966) model has been developed. as a tool to study the dynamics of galactic clises and is particularly well suited to describe theoretically the dynamical mechanisms responsible for the formation of spiral arms.,"The shearing sheet (Goldreich Lynden–Bell 1965, Julian Toomre 1966) model has been developed as a tool to study the dynamics of galactic discs and is particularly well suited to describe theoretically the dynamical mechanisms responsible for the formation of spiral arms."492 For the sake of simplicity the mocel describes only the dynamics of a patch of a galactic disc., For the sake of simplicity the model describes only the dynamics of a patch of a galactic disc.493 Ht is assumed to be infinitesimally thin and its radial size is assumed to be much smaller than the disc., It is assumed to be infinitesimally thin and its radial size is assumed to be much smaller than the disc.494 Polar coordinates can be therefore rectified to pseucdo-cartesian coordinates and the velocity Gelcl of the cilferentia rotation of the disc can be approximated by a linear shear low., Polar coordinates can be therefore rectified to pseudo-cartesian coordinates and the velocity field of the differential rotation of the disc can be approximated by a linear shear flow.495" ""These simplifications allow an analytical treatment of he problem. which helps to clarify the underlving physica »rocesses operating in the disc."," These simplifications allow an analytical treatment of the problem, which helps to clarify the underlying physical processes operating in the disc."496 ln two previous papers (Fuchs 2001a. b. referre jiereafter to as papers Lo and 4D LE considered the stellardyvnamical model of a shearing sheet ancl discusse he unbounded sheet and then the dynamical consequences. when inner boundary conditions are applied.," In two previous papers (Fuchs 2001a, b, referred hereafter to as papers I and II) I considered the stellardynamical model of a shearing sheet and discussed the unbounded sheet and then the dynamical consequences, when inner boundary conditions are applied."497 “Phe aim was to give a consistent. theoretical description. of pure swing amplification (Loonwe 1981) as well as exponentially. erowing mocdes in the framework of the same moclel., The aim was to give a consistent theoretical description of pure swing amplification (Toomre 1981) as well as exponentially growing modes in the framework of the same model.498 lt is well known from numerous studies that. if a star disc is perturbed by a succession of spiral density waves. the stars are scattered. randomly by the spiral arms anc their velocity. dispersion. grows steadily so that the background states of the disces are evolving. (Julian 1967... Carlbere Sellwood 1985. Binney Lacey LOSS. Jenkins Binney 1990).," It is well known from numerous studies that, if a star disc is perturbed by a succession of spiral density waves, the stars are scattered randomly by the spiral arms and their velocity dispersion grows steadily so that the background states of the discs are evolving (Julian 1967, Carlberg Sellwood 1985, Binney Lacey 1988, Jenkins Binney 1990)."499 Dynamical disc heating has also been demonstrated in numerical simulations of the cvnamical evolution of star discs such as by Sellwood /Carlberg (1984) or Toomre (1990)., Dynamical disc heating has also been demonstrated in numerical simulations of the dynamical evolution of star discs such as by Sellwood Carlberg (1984) or Toomre (1990).500 In the present paper L discuss disc heating of the shearing sheet., In the present paper I discuss disc heating of the shearing sheet.501 LE follow in particular the theory of dilfusion of stars in the twodimensional action integral space due O wave star scattering. developed. by Dekker (1976)., I follow in particular the theory of diffusion of stars in the two–dimensional action integral space due to wave – star scattering developed by Dekker (1976).502 In section (2) 1 briclly describe the formal. clerivation of the diffusion equation. in the framework of quasiinear theory (Llall Sturrock 1967) and. in section (3) 1 calculate dilfusion coelIicients for scattering of stars by swing amplified density waves., In section (2) I briefly describe the formal derivation of the diffusion equation in the framework of quasi--linear theory (Hall Sturrock 1967) and in section (3) I calculate diffusion coefficients for scattering of stars by swing amplified density waves.503 This kind. of spiral density waves ws been shown to be relevant for disc heating by Toomre (1990). wheras modelike density waves. on the other hand. do not heat cllectively (Barbanis Woltjer 1967. Dell Ixalnajs 1972).," This kind of spiral density waves has been shown to be relevant for disc heating by Toomre (1990), wheras mode–like density waves, on the other hand, do not heat effectively (Barbanis Woltjer 1967, Lynden--Bell Kalnajs 1972)."504 When describing the dise heating effects. of a succession of transient spiral density waves. one has to distinguish between the long time scales. on which the overall distribution function of stars in. phase space is evolving. i.c. the dynamical heating time scale. from the shorter time scales. on whieh the individual density waves develop.," When describing the disc heating effects of a succession of transient spiral density waves, one has to distinguish between the long time scales, on which the overall distribution function of stars in phase space is evolving, i.e. the dynamical heating time scale, from the shorter time scales, on which the individual density waves develop."505 As is well known from plasma physics (Hall Sturrock 1967) this concept allows to derive from the Boltzmann equation, As is well known from plasma physics (Hall Sturrock 1967) this concept allows to derive from the Boltzmann equation506If the drop were larger. then using samples without this region removed could bias our estimate of e. upwards.,"If the drop were larger, then using samples without this region removed could bias our estimate of $\sigma_8$ upwards."507 More likely. the supercluster may cause a slight underestimate of the size of our error bars. since the jackknife samples used to calculate the covariance matrie are smaller than the supercluster.," More likely, the supercluster may cause a slight underestimate of the size of our error bars, since the jackknife samples used to calculate the covariance matric are smaller than the supercluster."508 This prevents the jackknife method from fully capturing the variance in the density field., This prevents the jackknife method from fully capturing the variance in the density field.509" We have chosen to use the (--band selected) SDSS rather than the (5,;-band. selected) 2dFGRS for our main constraint on ox. since the prediction for the luminosity of galaxies in bluer bands depends more heavily on recent star formation."," We have chosen to use the $r$ -band selected) SDSS rather than the $b_J$ -band selected) 2dFGRS for our main constraint on $\sigma_8$, since the prediction for the luminosity of galaxies in bluer bands depends more heavily on recent star formation."510 It therefore tends to be more model-dependent than the prediction for redder bands. where there is a larger dependence on total stellar mass.," It therefore tends to be more model-dependent than the prediction for redder bands, where there is a larger dependence on total stellar mass."511 None the less. the 2dFGRS provides very valuable data on galaxy clustering. and an accurate galaxy formation model should give constraints on σκ Which are consistent between the two datasets.," None the less, the 2dFGRS provides very valuable data on galaxy clustering, and an accurate galaxy formation model should give constraints on $\sigma_8$ which are consistent between the two datasets."512 In addition. the analysis of satellite fractions in the 2dFGRS by ?. suggested. if somewhat indirectly. that the 2dF data prefer a relatively low ox.," In addition, the analysis of satellite fractions in the 2dFGRS by \citet{VAN05} suggested, if somewhat indirectly, that the 2dF data prefer a relatively low $\sigma_8$."513 In a similar spirit to the analysis we perform here. this constraint on σκ came about independently of other datasets.," In a similar spirit to the analysis we perform here, this constraint on $\sigma_8$ came about independently of other datasets."514 It may therefore be interesting to see whether our relatively high value of σε coming from galaxy clustering data alone is driven by the data (in. which case our estimate for c; when using 2dFGRS data should. be consistent with theirs) or by other factors., It may therefore be interesting to see whether our relatively high value of $\sigma_8$ coming from galaxy clustering data alone is driven by the data (in which case our estimate for $\sigma_8$ when using 2dFGRS data should be consistent with theirs) or by other factors.515 Note. for example. that ? quote a high preferred value for ox in their 2dFGRS clustering," Note, for example, that \citet{PAN05} quote a high preferred value for $\sigma_8$ in their 2dFGRS clustering"516path corresponding to this collision frequency is 5x10P em = 1.5x10* parsee = 330 AU.,path corresponding to this collision frequency is $5 \times 10^{15}$ cm = $1.5 \times 10^{-3}$ parsec = 330 AU.517 For the case of - charge exchange. the collision [requeney would be a few (mes higher. and the collisional mean [ree path a few times smaller than the numbers given immediately above.," For the case of $^+$ -H charge exchange, the collision frequency would be a few times higher, and the collisional mean free path a few times smaller than the numbers given immediately above."518 In anv case. we conclude that the Local Clouds are highly collisional by Uzdenskvys second criterion.," In any case, we conclude that the Local Clouds are highly collisional by Uzdensky's second criterion."519 li seems likely that collisions between ions taking part in the Alfvénnic waves and turbulence in the local clouds. and neutral atoms which are not. is responsible [for the removal of temperature anisotropy. and ion-specilio heating.," It seems likely that collisions between ions taking part in the Alfvénnic waves and turbulence in the local clouds, and neutral atoms which are not, is responsible for the removal of temperature anisotropy and ion-specific heating."520 Ib would be worthwhile to conduct a theoretical study of ion and neutral atom cyvnamics in the presence of Alfvénnie turbulence. including collisions due to both charge exchange and induced dipole scattering.," It would be worthwhile to conduct a theoretical study of ion and neutral atom dynamics in the presence of Alfvénnic turbulence, including collisions due to both charge exchange and induced dipole scattering."521 such calculations could determine if the collisions do indeed remove temperature anisotropy and ion-specifie temperatures. by taking the energv which is preferentially input to one or a ew ious. and distributing it to all ion and neutral atoms species.," Such calculations could determine if the collisions do indeed remove temperature anisotropy and ion-specific temperatures, by taking the energy which is preferentially input to one or a few ions, and distributing it to all ion and neutral atom species."522 Introducinge Uzdenskvs first criterion of eollisionalitv has provided interestinge insightex in (he present context., Introducing Uzdensky's first criterion of collisionality has provided interesting insight in the present context.523 The fact that the collision Irequency. is approximately 8 orders οἱ nagnitude smaller (han (he evrolrequency means (hat plasma instabilities and quasilinear nodification of ion distribution functions would have aumple time to develop. unencumbered by collisions. if conditions for instabilities were present.," The fact that the collision frequency is approximately 8 orders of magnitude smaller than the gyrofrequency means that plasma instabilities and quasilinear modification of ion distribution functions would have ample time to develop, unencumbered by collisions, if conditions for instabilities were present."524 The absence of “collisionless” observational signalures suggests thal energelic processes on ion temporal and spatial scales are nol occurring in the Local Clouds., The absence of “collisionless” observational signatures suggests that energetic processes on ion temporal and spatial scales are not occurring in the Local Clouds.525 The conclusions of this paper are as follows., The conclusions of this paper are as follows.526Canuna ray bursts (CRBs) were discovered in 1969 (IKlebesadel. Strong aud Olsou 1973) by America satellites of the class aimed at verifving Russian compliance with the unclear atmospheric test ban treaty.,"Gamma ray bursts (GRBs) were discovered in 1969 (Klebesadel, Strong and Olson 1973) by American satellites of the class aimed at verifying Russian compliance with the nuclear atmospheric test ban treaty."527 Though the discovery was made m 1969. the paper appeared ouly four vears later because the authors had lingering doubts about the reality of the effects they had discovered.," Though the discovery was made in 1969, the paper appeared only four years later because the authors had lingering doubts about the reality of the effects they had discovered."528 Since then. several thousands of bursts have been observed by amore than a dozen different satellites. but it is remarkable that the basic burst features outlined in the abstract of the 1969 paper (photons in the range 0.2.—1.5MeV. duratious of 0.1.305. flneuces ntherange 10—2410bergseii 7) have remained substautiall: unchanged.," Since then, several thousands of bursts have been observed by a more than a dozen different satellites, but it is remarkable that the basic burst features outlined in the abstract of the 1969 paper (photons in the range $0.2-1.5\; MeV$, durations of $0.1-30\; s$, fluences inthe range $10^{-5}-2\times 10^{-4}\; ergs\; cm^{-2}$ ) have remained substantially unchanged."529 Ciuvenut evidence (Fishinan and \lecean 1995) has highlishted a wide 5) duration distribution. with hiuts of a bimodality which is claimed to correlate (at the 2.50 level) with spectral properties.," Current evidence (Fishman and Meegan 1995) has highlighted a wide $0.01-100\; 530s$ ) duration distribution, with hints of a bimodality which is claimed to correlate (at the $2.5\sigma$ level) with spectral properties."531 All bursts spectra observed so far are strictly nonthermal. and there has never been any confirmation by BATSE of a supposed thermal coumponent (nor of cyclotron lines or precursors. for this natter) claimed in previous reports.," All bursts' spectra observed so far are strictly non–thermal, and there has never been any confirmation by BATSE of a supposed thermal component (nor of cyclotron lines or precursors, for this matter) claimed in previous reports."532 A remarkable feature reported by BATSE is the οασπιο diversity of light curves. ranging from inpulsive ones (a spike followed wea slower decay. nicknamed FREDs for Fast Rise-Exponenutial Decay). to smootli oues. to long ones with amazingly sharp fluctuations. including even some with a strongly periodic appearance (two such examples are the “hand? aud the ‘comb’. so licknamed from the nuuber of hichQ. regularly repeating sharp spikes).," A remarkable feature reported by BATSE is the bewildering diversity of light curves, ranging from impulsive ones (a spike followed by a slower decay, nicknamed FREDs for Fast Rise-Exponential Decay), to smooth ones, to long ones with amazingly sharp fluctuations, including even some with a strongly periodic appearance (two such examples are the `hand' and the `comb', so nicknamed from the number of high–Q, regularly repeating sharp spikes)."533 The most exceptional result from DATSE. though. was the sky distribution of he bursts CFig.1).," The most exceptional result from BATSE, though, was the sky distribution of the bursts (Fig.1)."534 It was obvious frou it that the bursts led to be extragalactic.," It was obvious from it that the bursts to be extragalactic,"535The dynamical evolutiou of galaxies in our sinulatious is diiven by the joiut action of several plivsical processes such as the star formation mechanisin. gas infall aac ealactic outflows.,"The dynamical evolution of galaxies in our simulations is driven by the joint action of several physical processes such as the star formation mechanism, gas infall and galactic outflows."536 Tle star formation process is trigecrec jiunulv when the eas ects cold aud deuse., The star formation process is triggered mainly when the gas gets cold and dense.537 As a consequence of star formation. SN energy is released heating up the surrounding cold aud deuse ISN which. when appropriated (see section 2)). is promoted to the hot phase.," As a consequence of star formation, SN energy is released heating up the surrounding cold and dense ISM which, when appropriated (see section \ref{sec:simus}) ), is promoted to the hot phase."538 This generates a stronger decrease in the star formation activity in svstems with shallower poteutia wells because it is easier for the cold aud deuse gas im smal systems to match the eutropv of the hot and/or diffuse ohase residing within their siiall dark matter haloes., This generates a stronger decrease in the star formation activity in systems with shallower potential wells because it is easier for the cold and dense gas in small systems to match the entropy of the hot and/or diffuse phase residing within their small dark matter haloes.539" But. he cooling times (f£5,,4) of the promoted particles are too short compared to their dvnamiucal times (fq) to allow his hot phase to be stable for a long time""."," But, the cooling times $t_{\rm cool}$ ) of the promoted particles are too short compared to their dynamical times $t_{\rm dyn}$ ) to allow this hot phase to be stable for a long time."540. ence. he eas which has just reached the hot phase due to SN heating miüeht cool down again iu short timescales. returning to the cold phase.," Hence, the gas which has just reached the hot phase due to SN heating might cool down again in short timescales, returning to the cold phase."541 Therefore. SN feedback leads ο a self-regulated evcle of heating aud cooling exerting au Huportant infiuence on the regulation of the star formation xocess in low-mass ealaxies.," Therefore, SN feedback leads to a self-regulated cycle of heating and cooling exerting an important influence on the regulation of the star formation process in low-mass galaxies."542 As the svstems get larger. i6 hot phase is established at a higher teniperature due to the joint effect of the continuous punipius of SN ¢wrev iuto the hot environment aud the increase of je vindal temperature of the dark haloes hosting them.," As the systems get larger, the hot phase is established at a higher temperature due to the joint effect of the continuous pumping of SN energy into the hot environment and the increase of the virial temperature of the dark haloes hosting them."543 Hence. as the cooling times ect longer compared to the dynamical time scales. the hot gas is able to remain iu us phase.," Hence, as the cooling times get longer compared to the dynamical time scales, the hot gas is able to remain in this phase."544 While the hot cuviroument is able to build up as galaxies ect more massive. galactic winds would be nore difficult to he triggered in these galaxies. siuce more SN enerey would be required by the cold phase iu order o match the eutropy of its nearby hot environment aud. herefore. to be promoted generating outflows.," While the hot environment is able to build up as galaxies get more massive, galactic winds would be more difficult to be triggered in these galaxies, since more SN energy would be required by the cold phase in order to match the entropy of its nearby hot environment and, therefore, to be promoted generating outflows."545 \eamwhile. he cold gas remains available for star formation.," Meanwhile, the cold gas remains available for star formation."546 It is also true that as the svstenis erows. their gas reservoir decreases. also decreasing their star formation activity and consequently. the source of SN energy.," It is also true that as the systems grows, their gas reservoir decreases, also decreasing their star formation activity and consequently, the source of SN energy."547 Therefore. the action of SN feedback is mich less important at regulating he transformation of the remaining gas iuto stars iu these aree systems.," Therefore, the action of SN feedback is much less important at regulating the transformation of the remaining gas into stars in these large systems."548 Iu order to quantitatively probe that these behaviours are taking place inour systems. we estimated the relations vetween the dynamical and the cooling times of the cold eas that has joined the ho phase by the action of SN ceedback G.e. promoted particles). along the evolution of our simulated volumes.," In order to quantitatively probe that these behaviours are taking place in our systems, we estimated the relations between the dynamical and the cooling times of the cold gas that has joined the hot phase by the action of SN feedback (i.e. promoted particles), along the evolution of our simulated volumes."549" The fraction of gas-phase uou-available for ctiicicu cooling within simulated galaxies (PY?) is defined as the eas mass within 2,4, which satisfies he couditiou ρωανα20.1 (Navarro&White1993).", The fraction of gas-phase non-available for efficient cooling within simulated galaxies $F^{\rm vir}_{\rm gas}$ ) is defined as the gas mass within $R_{\rm vir}$ which satisfies the condition $t_{\rm cool}/t_{\rm dyn} > 0.1$ \citep{navarro1993}.550. Iu Fie. 9.. ," In Fig. \ref{fig:tcool}, ,"551we plot FEln as a function oVere dn 8230 at 2= (left panel) and +=2 (wight paucl)., we plot $F^{\rm vir}_{\rm gas}$ as a function of $V_{\rm circ}$ in S230 at $z=0$ (left panel) and $z=2$ (right panel).552 As expected. FEE Is an increasing funcjon of Vigo.," As expected, $F^{\rm vir}_{\rm gas}$ is an increasing function of $V_{\rm circ}$."553 At z= 0. systems with Vaso1009.+ has an important fraction of their easshase (>90 per cent) subject to an efficieut cooling.," At $z=0$ , systems with $V_{\rm circ} < 100 {\rm \ km \ s^{-1}}$ has an important fraction of their gas-phase $> 90 $ per cent) subject to an efficient cooling."554 Oulv at Vie>100kins+. PSE starts to increase reaching Sat Vane 250]aus|.," Only at $V_{\rm circ} > 100 {\rm \ km \ s^{-1}}$, $F^{\rm vir}_{\rm gas}$ starts to increase reaching 0.8 at $V_{\rm circ} \sim 250 {\rm \ km \ s^{-1}}$."555 The same trends are present at ;=2. albeit with a larger dispersion at the high-velocity cud.," The same trends are present at $z =2$, albeit with a larger dispersion at the high-velocity end."556 Iuterestiuehv our model predicts that the ransition from efficieut to inefficient eas cooling occurs at around the characteristic velocity V.100kunst where he TER bends.," Interestingly, our model predicts that the transition from efficient to inefficient gas cooling occurs at around the characteristic velocity $V_{\rm c} \sim 100 {\rm \ km \ s^{-1}}$ where the TFR bends."557 This velocity is also in agreenmieut with he theoretical expectations frou Dekel&Silk(L986) who concluded that only for svstems with ων larger than 41 ∿↓∩≼⊔↘↽⋯↴∖↴∙↑↕∐∖↸⊳∪∪∐↕∶↴⋁↑∐⊔↸∖↴∖↴∪↕↑↕∐∖≼∐↕−⊓↕↴∖↴↸∖⋜↧∐≼↧∐∪↑. : : ⋅⋅ ∶↴∙⊾⋜↧↴∖↴⋜∐⋅↸∖⋜↧↑↕↸∖⋜↧↴∖↴↑∪∐↸∖∪↥⋅≼∐∖↥⋅∪↕≯↕⊔⋜↧∶↴∙⊾∐↕↑∏≺∐∖↕∪∐∶↴∙⊾↸∖↥⋅↑∐⋜⋯↑∐↸∖ ≼↧⋅↖↽∐⋜↧⋯↕↸⊳⋜↧↕↑↕∐∐∖↴∖↴⋜⋯≼↧∙↑↕∐∖↥⋅↸∖↕≯∪↥⋅↸∖∙↑∐↸∖∶↴∙⊾⋜↧↴∖," This velocity is also in agreement with the theoretical expectations from \citet{ds86} who concluded that only for systems with $V_{\rm cir}$ larger than $\sim 100 \ {\rm km \ s}^{-1}$, the cooling times of the diffuse and hot gas are at least one order of magnitude longer than the dynamical times and, therefore,the gas could remain hot."558↴↸⊳∪∏↕≼⊔⋅↸∖⋯⋜↧↕∐∐∪↑∙ We have studied the «ΤΕΙ and bTFR by performing lydrodvuamiuical simulations iun a cosmological scenario iucluding the action of the combined multiphase aud SN feedback model of Scaunapiecoctal.(2005.2006).," We have studied the sTFR and bTFR by performing hydrodynamical simulations in a cosmological scenario including the action of the combined multiphase and SN feedback model of \citet{scan05, scan06}."559. Our results suggest the existence of a change iu the slope of the STERand bTER produced by the action of SN feedback., Our results suggest the existence of a change in the slope of the sTFRand bTFR produced by the action of SN feedback.560 At ;— 0. the simulated «ΤΕΙ is very tightly definedand, At $z=0$ the simulated sTFR is very tightly definedand561= 12p = 12p,= 12pt = 12pt562"Observations of nou-thermal astroplivsical sources upou the utinost diverse spatial scales and Iuninosity ranges. from Supernova remnants to Active Galactic Nuclei. aud energy bands. from radio frequencies up to > Lave, require electron acceleration up to ultra-relativistic energies when interpreted via svuchrotron or seltComXtou CLUISSIOLL.","Observations of non-thermal astrophysical sources upon the utmost diverse spatial scales and luminosity ranges, from Supernova remnants to Active Galactic Nuclei, and energy bands, from radio frequencies up to $\gamma-$ rays, require electron acceleration up to ultra-relativistic energies when interpreted via synchrotron or self-Compton emission."563 Relativistic particles can also be directly deected as in 16 case of the streams of particles fron soar flares or the cosmic radiation., Relativistic particles can also be directly detected as in the case of the streams of particles from solar flares or the cosmic radiation.564 ALultiwaveleust1 studies of extragalactic |jets. μις by combining observations fous rac1ο arravs. UST inthe optical baud and X-ray satellites. showed that many extragalactic jets cuit uou-thermal raclatioji extend18o rou radio to N-ravs. aud that spectral auk morphological catures roin. m Wau instances. ucarly coustaut alo18o he jet frou radio up to optical frequencies.," Multi-wavelength studies of extragalactic jets, med by combining observations from radio arrays, HST in the optical band and X-ray satellites, showed that many extragalactic jets emit non-thermal radiation extending from radio to X-rays, and that spectral and morphological features remain, in many instances, nearly constant along the jet from radio up to optical frequencies."565 TUs iniplies a constancy of the relativistic electron distrimtion fiction over at least five decades in euergv. that reeds to be interpreted (see discussions in Aleisculeier. Rosser Schlóttelbure 1996 aud Meiseibenuer. Netunmamn Rosser 1996 for ΙΣΤ).," This implies a constancy of the relativistic electron distribution function over at least five decades in energy, that needs to be interpreted (see discussions in Meisenheimer, Rösser Schlöttelburg 1996 and Meisenheimer, Neumann Rösser 1996 for M87)."566" Mauyv physical mechanisnas of particle acceleration have been studied. and Fermi-likse processes occmring at ΑΠΟ shocks have been particularly visited since they automatically lead to power-law particle distri""tions. as dictated by obscrvatious (sec. e.c... Bell 1978. Drm 1982. Dlaudford Eichler 1987. Achterbere 1990. Kirk 1991)."," Many physical mechanisms of particle acceleration have been studied, and Fermi-like processes occurring at MHD shocks have been particularly visited since they automatically lead to power-law particle distributions, as dictated by observations (see, e.g., Bell 1978, Drury 1983, Blandford Eichler 1987, Achterberg 1990, Kirk 1994)."567 Other mechanisms of particle acceleration iiclude the cüffusive particle acceleration at a tangential discontinuity ju] a velocity feld involving relativistic velocities (Osrowski. 1990. 1908).," Other mechanisms of particle acceleration include the diffusive particle acceleration at a tangential discontinuity in a velocity field involving relativistic velocities (Ostrowski, 1990, 1998)."568 Continuous reacceleration of aLicles could take place bw conversion of magnetic cherey into particle cherey via magnetic reconnection. as proposed bv Lesch Birk ©008): mechanisms of ouwticle acceCL‘ation bv turbulent plasma waves (Li ct al.," Continuous reacceleration of particles could take place by conversion of magnetic energy into particle energy via magnetic reconnection, as proposed by Lesch Birk (1998); mechanisms of particle acceleration by turbulent plasma waves (Li et al."569 1997) or w intense lowavelength electromagnetic ποια» (Disuovatvi-Kogan lacce 1995) have also )en considered., 1997) or by intense long-wavelength electromagnetic fields (Bisnovatyi-Kogan ce 1995) have also been considered.570" Each of these miechiaudsius leads different valies for the aN enerev attained by he accelerated particles, and differen xedietious on the observed radiation spectrun."," Each of these mechanisms leads to different values for the maximum energy attained by the accelerated particles, and different predictions on the observed radiation spectrum."571 A possible «lue to build a “universal spectrum” is the ciffusive shock acceleration (DSÀ) by uultiple shoocks. as ciscussed in M«‘rose Pope (1993) aid Ferrari Melrose (1997). under very geuera conditions.," A possible clue to build a “universal spectrum"" is the diffusive shock acceleration (DSA) by multiple ocks, as discussed in Melrose Pope (1993) and Ferrari Melrose (1997), under very general conditions."572 Iu this pa]x owe concentrate on the diffusive particle acceleration at shocks. and we treat. iu a consistent wav by incaus of a uunerncal hvdrocode. the jet instabilities that wield shock formation. the particle acceleration ii these shocks. and the temporal evolution of the distribution function. subject to adiabatic effects and svuchrotron losses.," In this paper we concentrate on the diffusive particle acceleration at shocks, and we treat, in a consistent way by means of a numerical hydrocode, the jet instabilities that yield shock formation, the particle acceleration in these shocks, and the temporal evolution of the distribution function, subject to adiabatic effects and synchrotron losses."573 In our model the magneic field aud the relativistic particles are advected passively by the thermal fluid. as du previous studies by Matthews aud Scheucr (1990) who treated acdabatic expansion axl svuchrotron losses without including particle acceleration. aud by AMassaglia et a. (," In our model the magnetic field and the relativistic particles are advected passively by the thermal fluid, as in previous studies by Matthews and Scheuer (1990) who treated adiabatic expansion and synchrotron losses without including particle acceleration, and by Massaglia et al. ("5741996) who modeled shock acceleration as an adiabatic compression of fixed strength.,1996) who modeled shock acceleration as an adiabatic compression of fixed strength.575 Iu our study the equation for the evolution of the particle distribution fuwction is solved in a selfconsisteut wav. and particle acceleration at shocks is treated in the ‘test-particle’ approxination. 16. ueelecting the effects of cuerey subraction from the shocks.," In our study the equation for the evolution of the particle distribution function is solved in a self-consistent way, and particle acceleration at shocks is treated in the `test-particle' approximation, i.e. neglecting the effects of energy subtraction from the shocks."576 Moreover we, Moreover we577magnitudes in the required bands and to compare them with the observed values to estimate the distance.,magnitudes in the required bands and to compare them with the observed values to estimate the distance.578 Absolute bolometric and V magnitudes were calculated with JKTABSDIM in two cases: with and without spots., Absolute bolometric and $V$ magnitudes were calculated with JKTABSDIM in two cases: with and without spots.579" In the first case we follow the concept presented by López-MoralesRibas(2005) and calculate a value that we name an — T» Which is actually a temperature related to the true luminosity through the Stefan-Boltzman law: Spotted areas of the stellar surface emit less radiation than ""clean"" photosphere. thus T, is not equal to the photospherte temperature — 7,4."," In the first case we follow the concept presented by \citet{lop05} and calculate a value that we name an – $T_{eff}^S$, which is actually a temperature related to the true luminosity through the Stefan-Boltzman law: Spotted areas of the stellar surface emit less radiation than ”clean” photosphere, thus $T_{eff}^S$ is not equal to the photospheric temperature – $T_{phot}$."580 The effective temperature is actually the temperature of à homogeneous. spherical blackbody of the same size as the spotted star and radiating the same amount of light as the star with a given photospheric temperature and a spot with given parameters.," The effective temperature is actually the temperature of a homogeneous, spherical blackbody of the same size as the spotted star and radiating the same amount of light as the star with a given photospheric temperature and a spot with given parameters."581" It can be calculated from the relation: where 7—Pepor/Tyna, 1s à fraction of the temperature of the spot surface to the stellar photosphere temperature and 8 is an angular radius of the spot (López-Morales&Ribas2005).", It can be calculated from the relation: where $\tau = T_{spot}/T_{phot}$ is a fraction of the temperature of the spot surface to the stellar photosphere temperature and $\theta$ is an angular radius of the spot \citep{lop05}.582 The spot parameters obtained from our fit are listed in Table 3.., The spot parameters obtained from our fit are listed in Table \ref{tab_par_04}. .583 In PHOEBE the longitude of the spot is counted clockwise from 0 to 2π. and 0 means the direction towards the other star.," In PHOEBE the longitude of the spot is counted counter-clockwise from 0 to $2\pi$, and 0 means the direction towards the other star."584 The latitude is counted from 0 (the +z pole) to π (the —z pole)., The latitude is counted from 0 (the $+z$ pole) to $\pi$ (the $-z$ pole).585" Using Τὸ, we can mimic the “apparent” properties of the components. mainly absolute V magnitudes. and compare them to observed ones."," Using $T_{eff}^S$ we can mimic the ”apparent” properties of the components, mainly absolute $V$ magnitudes, and compare them to observed ones."586 Thus we can estimate the distance., Thus we can estimate the distance.587" We used the parameters from Table 5 and found the distance of 148 + 5 pe as a weighted average of eight separately calculated results. based on bolometric corrections mentioned earlier and in five bands — our (observed) V and 7. and J. H. and K, from 2MASS."," We used the parameters from Table \ref{tab_par_04} and found the distance of 148 $\pm$ 5 pc as a weighted average of eight separately calculated results, based on bolometric corrections mentioned earlier and in five bands – our (observed) $V$ and $I$, and $J$ , $H$, and $K_s$ from 2MASS."588 The best consistency between results from various bands was reached for E(B—V)=0.13., The best consistency between results from various bands was reached for $E(B-V)= 0.13$.589" The values of the apparent M,,, and My are given in Table 3. in the part.", The values of the apparent $M_{bol}$ and $M_V$ are given in Table \ref{tab_par_04} in the part.590" We ran JKTABSDIM a second time with the photospheric temperatures ρω, as derived directly by PHOEBE.", We ran JKTABSDIM a second time with the photospheric temperatures $T_{phot}$ as derived directly by PHOEBE.591" This way we can caleulate the ""true"" values of Mj; and My as if there were no spots at all.", This way we can calculate the ”true” values of $M_{bol}$ and $M_V$ as if there were no spots at all.592 They are more useful for comparison with theoretical models., They are more useful for comparison with theoretical models.593 We list them in Table 3. 1n the part., We list them in Table \ref{tab_par_04} in the part.594" Note that the values ""with"" and ""without"" spots are very close.", Note that the values ”with” and ”without” spots are very close.595" Nevertheless. we decided to use the ""rectified"" ones in our further evolutionary. status analysis and also the age determination. because models are calculated for unspotted stars."," Nevertheless, we decided to use the ”rectified” ones in our further evolutionary status analysis and also the age determination, because models are calculated for unspotted stars."596 One should remember that the total large uncertainties in colour. temperatures. and magnitudes are caused by the error in the absolute magnitude calibration.," One should remember that the total large uncertainties in colour, temperatures, and magnitudes are caused by the error in the absolute magnitude calibration."597 Formal errors dependent on the quality of the photometric data are several times lower., Formal errors dependent on the quality of the photometric data are several times lower.598 It is particularly important for the temperature ratio which ts derived with about uncertainty., It is particularly important for the temperature ratio which is derived with about uncertainty.599 In order to check how the potentials (thus radi are affected by the calibration uncertainty. we set the temperatures to be higher by about 200 K. keeping their ratio constant.," In order to check how the potentials (thus radii) are affected by the calibration uncertainty, we set the temperatures to be higher by about 200 K, keeping their ratio constant."600 We held the resulting temperatures fixed (at about 4550 and 4290 K) and repeated the fit., We held the resulting temperatures fixed (at about 4550 and 4290 K) and repeated the fit.601 The resulting. potentials in this model have not changed significantly (well below their uncertainties). therefore we concluded that this systematic error in the photometric calibration. colour. and temperatures does not affect our final results for the radii.," The resulting potentials in this model have not changed significantly (well below their uncertainties), therefore we concluded that this systematic error in the photometric calibration, colour, and temperatures does not affect our final results for the radii."602 We made the same conclusion after lowering the temperatures by 200 K from their best-fitting model values., We made the same conclusion after lowering the temperatures by 200 K from their best-fitting model values.603 However. to obtain conservative radii uncertainties. we incorporated the difference in the radi between those models into the total error of the radii.," However, to obtain conservative radii uncertainties, we incorporated the difference in the radii between those models into the total error of the radii."604 For the spot parameters. the temperature fraction and spot's angular radius are generally degeneratec and it is difficult to fit them simultaneously.," For the spot parameters, the temperature fraction and spot's angular radius are generally degenerated and it is difficult to fit them simultaneously."605 Some weak constrains are possible if the spot is eclipsed — from the eclipse's shape. and during the phases when the spot starts to be visible (larger spots are visible longer).," Some weak constrains are possible if the spot is eclipsed – from the eclipse's shape, and during the phases when the spot starts to be visible (larger spots are visible longer)."606 For of ASAS-04 (and ASAS-08 as well) we are not able to solve that problem. consequently oursolution is degenerated.," For of ASAS-04 (and ASAS-08 as well) we are not able to solve that problem, consequently oursolution is degenerated."607 Errors given in. Table 3 are formal only and are probably underestimated.," Errors given in Table \ref{tab_par_04}608 are formal only and are probably underestimated."609 In our analysis. it is more important to deduce the influence of the spot on the total flux.," In our analysis, it is more important to deduce the influence of the spot on the total flux."610 Figure 2 depicts our model light curves and SAAO measurements., Figure \ref{fig_lc_04} depicts our model light curves and SAAO measurements.611 One can easily see the out-of-eclipse variations in the system., One can easily see the out-of-eclipse variations in the system.612 According to our results. ASAS-04 consists of two slightly inflated stars.," According to our results, ASAS-04 consists of two slightly inflated stars."613 Theoretical models of the main-sequence stars of these masses predict radii around 0.74 R.. (Baratfeetal.1998)., Theoretical models of the main-sequence stars of these masses predict radii around 0.74 $_\odot$ \citep{bar98}.614. Also the temperatures exceed the values expected for main-sequence dwarfs of given masses by over 200 K for both components (e.g.Harmanec1988;Tokunaga2000) and indicate a ~G8 type for the primary and - Kl for secondary (Tokunaga2000).," Also the temperatures exceed the values expected for main-sequence dwarfs of given masses by over 200 K for both components \citep[e.g.][]{har88,tok00} and indicate a $\sim$ G8 type for the primary and $\sim$ K1 for secondary \citep{tok00}."615. This may indicate a main sequence turn-off stage. which is a unique feature among known low-mass eclipsing binaries.," This may indicate a main sequence turn-off stage, which is a unique feature among known low-mass eclipsing binaries."616 The quite large difference in the eclipses? depths observed in our light curve. especially in the V band. implicates the temperatures ratio to be significantly different from 1.," The quite large difference in the eclipses' depths observed in our light curve, especially in the $V$ band, implicates the temperatures ratio to be significantly different from 1."617 One may find it surprising. considering the nearly equal masses of the ASAS-04 components.," One may find it surprising, considering the nearly equal masses of the ASAS-04 components."618 This cannot be fully explained by the age and the evolutionary status of the system., This cannot be fully explained by the age and the evolutionary status of the system.619 The analysis of the ASAS-08 light curve was similar to ASAS-O4s., The analysis of the ASAS-08 light curve was similar to ASAS-04's.620 The light curve of ASAS-08 based on our SAAO data is shown in Fig. 3.., The light curve of ASAS-08 based on our SAAO data is shown in Fig. \ref{fig_lc_08}.621 One can see that the out-of-eclipse variation is clear and pronounced., One can see that the out-of-eclipse variation is clear and pronounced.622 To make the fitting easier and more reliable and the model more accurate. we decided to fit a two- model with one spot on each component.," To make the fitting easier and more reliable and the model more accurate, we decided to fit a two-spot model with one spot on each component."623 One large spot could not explain the modulation., One large spot could not explain the modulation.624 As previously. we firstly corrected. the ephemeris and orbital values by joining the RVs and two light curves in PHOEBE (the resulting values are given in Table 2)) and then. keeping them fixed. obtained preliminary values of the temperatures and potentials.," As previously, we firstly corrected the ephemeris and orbital values by joining the RVs and two light curves in PHOEBE (the resulting values are given in Table \ref{tab_orb}) ) and then, keeping them fixed, obtained preliminary values of the temperatures and potentials."625 The minimal eccentricity manifests itself in phasesof brightnes minima. which for ASAS-08 are @prin=—O.00018 or 0.99982 and ων= 0.50018.," The minimal eccentricity manifests itself in phasesof brightnes minima, which for ASAS-08 are $\phi_{prim} = -0.00018$ or 0.99982 and $\phi_{seco} = 0.50018$ ."626" Spots were added later ""manually"" byputting 1n their parameters and inspecting the light curve by eye.", Spots were added later ”manually” byputting in their parameters and inspecting the light curve by eye.627 The automatic, The automatic628the latter reached in A2199. which has a central value of 21 per cent).,"the latter reached in A2199, which has a central value of 21 per cent)."629 Finally. a third ingredient. probably a ICM. contributes by about 17 (0-33) per cent (and a probability to be larger than 0 of 73 per cent) with a distribution that goes from —29+15 per cent in A426 to 40412 per cent in A1795. one of the objects with the largest detected soft excess (Bonamente et al.," Finally, a third ingredient, probably a ICM, contributes by about 17 (0–33) per cent (and a probability to be larger than 0 of 73 per cent) with a distribution that goes from $\pm$ 15 per cent in A426 to $\pm$ 12 per cent in A1795, one of the objects with the largest detected soft excess (Bonamente et al."630 2002. Kaastra et al.," 2002, Kaastra et al."631 2003)., 2003).632 I am grateful to Hans Bóhhringer and Andy Fabian that pointed out à relevant weakness in the assumptions done in the original manuscript., I am grateful to Hans Böhhringer and Andy Fabian that pointed out a relevant weakness in the assumptions done in the original manuscript.633A. de,	A. de634For many years 1t was accepted that the minimum size for the column density fluctuations in the Galactic ISM ts around | pe (52x10? AU).,For many years it was accepted that the minimum size for the column density fluctuations in the Galactic ISM is around 1 pc $\sim$ $\times$ $^5$ AU).635 The common understanding was that although sub-parsee structures do exist. only a tiny fraction of the column density could be ascribed to these small scales (Dickey Lockman 1990)).," The common understanding was that although sub-parsec structures do exist, only a tiny fraction of the column density could be ascribed to these small scales (Dickey Lockman \cite{dickey}) )."636 However. the pioneering VLBI work by Dieter. Welch Romney (1976)). and the later confirmation by Diamond et al. (1989))," However, the pioneering VLBI work by Dieter, Welch Romney \cite{dieter}) ), and the later confirmation by Diamond et al. \cite{diamond}) )"637 demonstrated the existence of significant fluctuations over scales of 20 AU., demonstrated the existence of significant fluctuations over scales of 20 AU.638 These findings were confirmed by 21 em absorption measurements against high-velocity pulsars (Frail et al. 1991. 1994)).," These findings were confirmed by 21 cm absorption measurements against high-velocity pulsars (Frail et al. \cite{frail91,frail94}) ),"639 which showed that the column density varies significantly over scales between 5 and 110 AU. with of the cold neutral gas distributed in AU-sized structures (Frail et al. 1994)).," which showed that the column density varies significantly over scales between 5 and 110 AU, with of the cold neutral gas distributed in AU-sized structures (Frail et al. \cite{frail94}) )."640 However. some more recent radio observations on the same pulsars (Weisberg Stanimirovié 2007)) have shown that the variations are far smaller than those originally found by Frail et al. (1991. 1994)).," However, some more recent radio observations on the same pulsars (Weisberg Stanimirović \cite{weisberg}) ) have shown that the variations are far smaller than those originally found by Frail et al. \cite{frail91,frail94}) )."641 These studies were followed by a series of works looking at the variations of and/or column densities along the lines of sights to close binaries or high proper motion stars (see Crawford 2003 and Lauroesch 2007 for à review)., These studies were followed by a series of works looking at the variations of and/or column densities along the lines of sights to close binaries or high proper motion stars (see Crawford \cite{crawford03} and Lauroesch \cite{lauroesch07} for a review).642 Similar investigations were carried out for molecular gas (CH. CH™. and CN: Pan et al. 2004::," Similar investigations were carried out for molecular gas (CH, $^+$, and CN; Pan et al. \cite{pan};"643 Rollinde et al. 2003)).," Rollinde et al. \cite{rollinde}) ),"644 and diffuse interstellar bands (Cordiner. Sarre Fossey 2005)).," and diffuse interstellar bands (Cordiner, Sarre Fossey \cite{cordiner}) )."645 An alternative method ts the study of interstellar absorptions along the lines of sight to stellar clusters. like M92 (Andrews. Meyer Lauroesch 2001)) and w-Cen (Van Loon et al. 2009)).," An alternative method is the study of interstellar absorptions along the lines of sight to stellar clusters, like M92 (Andrews, Meyer Lauroesch \cite{andrews}) ) and $\omega$ -Cen (Van Loon et al. \cite{vanloon}) ),"646 or the Magellanic Clouds (e.g. André et al. 2004))., or the Magellanic Clouds (e.g. André et al. \cite{andre}) ).647 For a general review on the small ISM structures in our Galaxy the reader is referred to Haverkorn Goss (2007y)., For a general review on the small ISM structures in our Galaxy the reader is referred to Haverkorn Goss \cite{sins}) ).648 In this article we present an independent technique to analyze extra-galactic ISM structure on spatial scales of about 100 AU., In this article we present an independent technique to analyze extra-galactic ISM structure on spatial scales of about 100 AU.649 The proposed method is based on the extremely high expansion velocity displayed by a supernova (SN) photosphere C107 km s! or 5.7 AU day)., The proposed method is based on the extremely high expansion velocity displayed by a supernova (SN) photosphere $\sim$ $^4$ km $^{-1}$ or 5.7 AU $^{-1}$ ).650 A Type Ia SN reaches a photospheric radius of ~10 em (~100 AU) in two weeks from the explosion. and expands at a rate of 6 to 3 AU day! during the first two months of its evolution.," A Type Ia SN reaches a photospheric radius of $\sim$ $^{15}$ cm $\sim$ 100 AU) in two weeks from the explosion, and expands at a rate of 6 to 3 AU $^{-1}$ during the first two months of its evolution."651 If the typical size of the fluctuations m an intervening cloud is much larger than 10? em. then the associated absorption features will not evolve with time.," If the typical size of the fluctuations in an intervening cloud is much larger than $^{15}$ cm, then the associated absorption features will not evolve with time."652 On the contrary. if the ISM is patchy on comparable scales. the column density fluctuations will translate into measurable variations of the corresponding absorption features.," On the contrary, if the ISM is patchy on comparable scales, the column density fluctuations will translate into measurable variations of the corresponding absorption features."653 After introducing a simple model for the calculation of time-dependent line equivalent widths for a given cloud geometry (Sect. 2)).," After introducing a simple model for the calculation of time-dependent line equivalent widths for a given cloud geometry (Sect. \ref{sec:model}) ),"654 we present the results of Monte-Carlo simulations (Sect. 3)).," we present the results of Monte-Carlo simulations (Sect. \ref{sec:results}) ),"655 and discuss the applicability of the method and the effects on the observations of Type las (Sect. 4)., and discuss the applicability of the method and the effects on the observations of Type Ia's (Sect. \ref{sec:disc}) ).656 Appendix A gives the details on the derivation of the composite equivalent width., Appendix A gives the details on the derivation of the composite equivalent width.657 Let us fix a reference polar coordinates system (7.4) whose origin is located at the explosion center (see Fig. 1))., Let us fix a reference polar coordinates system $r$ $\theta$ ) whose origin is located at the explosion center (see Fig. \ref{fig:cloud}) ).658 As seen from a far observer (the distance between the SN and the observer is assumed to be much larger than that between the SN and the intervening material). the SN will appear as an expanding photodisk which extends to the ejecta boundary radius (0).," As seen from a far observer (the distance between the SN and the observer is assumed to be much larger than that between the SN and the intervening material), the SN will appear as an expanding photodisk which extends to the ejecta boundary radius $r_{\rm ej}(t)$."659 We then consider a cloud placed in front of the SN. at a distance large enough that the explosion has no effect on its physical conditions (1.6. 210 pe. see Simon et al. 2009..," We then consider a cloud placed in front of the SN, at a distance large enough that the explosion has no effect on its physical conditions (i.e. $>$ 10 pc, see Simon et al. \cite{simon09}."660 See also Sect., See also Sect.661 + here). and we indicate with N(r.6) the cloud column density in the species under consideration.," \ref{sec:disc} here), and we indicate with $N(r,\theta)$ the cloud column density in the species under consideration."662 Finally. we introduce P(t) as the time-dependent surface brightness," Finally, we introduce $\Phi(r,t)$ as the time-dependent surface brightness"663Ramsbottom C. A.. Bell Ix. L. Berrington Ix. À.. 1991. J. Phys.,"Ramsbottom C. A., Bell K. L. Berrington K. A., 1994, J. Phys."664 B. 27. Sinith M. S.. lawauo L. H. Malaney R. À.. 1993. ApJS. 85. Schleicher. D. R. C.. Galli. D.. Palla. F.. Camenzind. M.. Wlessen. B. 5.. Bartelinann. AL. Clover. S. C. 22008.AGA... 00. Uc;»ergel D. N.. et al.," B, 27, Smith M. S., Kawano L. H. Malaney R. A., 1993, ApJS, 85, Schleicher, D. R. G., Galli, D., Palla, F., Camenzind, M., Klessen, R. S., Bartelmann, M., Glover, S. C. 2008, 490, Spergel D. N., et al."665 2007. ApJS. 170. 377 Stancil P. C.. Lepp S. Dalgarno A.. 1996. ApJ. 15s. 101 Stancil P. C. Zygelinan B.. 1996. ApJ. 172. Verner D. A.. Ferland CC. J.. 1996. ApJS. 103. Vonlanthen. P.. Rauscher. T.. Winteler. C.. Puy. D.. Signore. M.. Dubrovich. V. 2009. A&AA. Wagoner BR. V.. Fowler W. A. Hovle F.. 1967. ApJ. 118. Weruli M.. Caruso D.. Bodo E. Cianturco EF. À.. 2009. J. Phys.," 2007, ApJS, 170, 377 Stancil P. C., Lepp S. Dalgarno A., 1996, ApJ, 458, 401 Stancil P. C. Zygelman B., 1996, ApJ, 472, Verner D. A., Ferland G. J., 1996, ApJS, 103, Vonlanthen, P., Rauscher, T., Winteler, C., Puy, D., Signore, M., Dubrovich, V. 2009, A, 503, Wagoner R. V., Fowler W. A. Hoyle F., 1967, ApJ, 148, Wernli M., Caruso D., Bodo E. Gianturco F. A., 2009, J. Phys."666 Chem., Chem.667 A.. 113. Zaldagarriaga M.. Loeb A.. 2002.Αρ... 561.," A., 113, Zaldagarriaga M., Loeb A., 2002, 564,"668part. this variability is due to global pulsations.,"part, this variability is due to global pulsations."669 Edmonds Gilliland (1995) proposed. radial or nonraclial pulsations as an explanation for the variability. they observed. in. [x giants in the globular cluster 47 Tuc., Edmonds Gilliland (1995) proposed radial or nonradial pulsations as an explanation for the variability they observed in K giants in the globular cluster 47 Tuc.670 They found frequencies between 3 and Gyllz with amplitudes between 5 and 15mmmaeg. (," They found frequencies between 3 and $\,\mu$ Hz with amplitudes between 5 and mmag. ("671C1997) analysecl photometric data from red stars in the LMC collected from the microlensing project ALACLIO. ancl reported that the period-Iuminosity relation comprises several ridges in the period range of 2200-davs. which may be interpreted as arising from racial modes of dilferent. η.,"1997) analysed photometric data from red stars in the LMC collected from the microlensing project MACHO, and reported that the period-luminosity relation comprises several ridges in the period range of 200-days, which may be interpreted as arising from radial modes of different $n$."672 Hatzes ancl Cochran (1998) reported that there is strong evidence from radial-velocity data for oscillations in Ix giants., Hatzes and Cochran (1998) reported that there is strong evidence from radial-velocity data for oscillations in K giants.673 Frequencies similar to those found in a UMa have been found. in à number of other objects.," Frequencies similar to those found in $\alpha\,$ UMa have been found in a number of other objects."674 In particular. Llazes and Cochran quote Ll frequencies of Arcturus LI) in the range pllz.," In particular, Hazes and Cochran quote 11 frequencies of Arcturus $\;$ III) in the range $\,\mu$ Hz."675 Evidence for short-periocd multimode pulsations in a number of M stars has been presented recently by Ixoen and Laney (2000)., Evidence for short-period multimode pulsations in a number of M stars has been presented recently by Koen and Laney (2000).676 Thus. by being a multimode pulsator à UMa appears not to be unique amongst red. giants.," Thus, by being a multimode pulsator $\alpha\,$ UMa appears not to be unique amongst red giants."677 But with its high frequencies and low amplitudes it does represent an extreme case so Far. although it is not wholly out of line with the others.," But with its high frequencies and low amplitudes it does represent an extreme case so far, although it is not wholly out of line with the others."678 This star is the hottest and the least Luminous object amongst. variable red. giants., This star is the hottest and the least luminous object amongst variable red giants.679 Lt provides. so far. the best example of possible red-giant. oscillations. but its spectrum is not as clean as that of the Sun. or of those of other main-sequence stars. or of white dwarfs.," It provides, so far, the best example of possible red-giant oscillations, but its spectrum is not as clean as that of the Sun, or of those of other main-sequence stars, or of white dwarfs."680 Nevertheless we consider the evidence to be strong enough to justify new investigations in the theory of red-giant oscillations., Nevertheless we consider the evidence to be strong enough to justify new investigations in the theory of red-giant oscillations.681 So far. only the modelling of radial pulsations in Aliras (see and references therein) and Areturus has attracted the theorists’ attention.," So far, only the modelling of radial pulsations in Miras (see and references therein) and Arcturus has attracted the theorists' attention."682 Nonraclial oscillations in red giants have been ignored almost entirely., Nonradial oscillations in red giants have been ignored almost entirely.683 Llere we review the theoretical aspects of this problem. in Section 3. ancl provide some numerical examples. of the properties of the oscillations of a model of a UMa ancl of models ofa MM. star on the red-giant branch.," Here we review the theoretical aspects of this problem, in Section 3, and provide some numerical examples of the properties of the oscillations of a model of $\alpha\,$ UMa and of models of a $_\odot$ star on the red-giant branch."684 Some data concerning these models are presented in Section 2., Some data concerning these models are presented in Section 2.685 The most intriguing issue posed by the discovery of oscillations in red giants is the identification of the mechanism by which they are. driven., The most intriguing issue posed by the discovery of oscillations in red giants is the identification of the mechanism by which they are driven.686 Possibilities to consider are (a) stochastic excitation of linearly stable modes bv convection and (b) selbexcitation of linearly unstable nmicdes., Possibilities to consider are (a) stochastic excitation of linearly stable modes by convection and (b) self-excitation of linearly unstable modes.687 We shall speak of oscillations of case (a) as being solar-like. and case (b). Mira-like.," We shall speak of oscillations of case (a) as being solar-like, and case (b), Mira-like."688 Our understanding. of the excitation mechanism in the Sun and in Miras is. not satisfactory. but the separate association of these stars with each of the two distinct possible excitation mechanisms is now generally accepted.," Our understanding of the excitation mechanism in the Sun and in Miras is not satisfactory, but the separate association of these stars with each of the two distinct possible excitation mechanisms is now generally accepted."689 In Section 4 we present results of calculations of racial-miode stability anc of the amplitudes in the case of stochastic excitation., In Section 4 we present results of calculations of radial-mode stability and of the amplitudes in the case of stochastic excitation.690 There are stringent constraints on the parameters. for defining models of a UMa.," There are stringent constraints on the parameters for defining models of $\alpha\,$ UMa."691 “Phe star is bright. and is in a visual binary system.," The star is bright, and is in a visual binary system."692 Accurate spectroscopic data. parallax. and a radius determination by means of interferometry are available.," Accurate spectroscopic data, parallax, and a radius determination by means of interferometry are available."693 After considering all the observational cata. ((2000) suggested. the following values for the stars global parameters: Al=4 los(L/L.)=2540.05. Zur=(4660+100) Ix. (0000) constructed evolutionary models with masses in this range and with an initial chemical composition Y=0.727 and Z—0.0124. which is consistent with the spectroscopic value of Fe/l and the Galactic helium enrichment.," After considering all the observational data, (2000) suggested the following values for the star's global parameters: $M$ $_\odot$, $\log(L/L_\odot)=2.5\pm0.05$ , $T_{\rm eff}=(4660\pm100)\,$ K. (2000) constructed evolutionary models with masses in this range and with an initial chemical composition $X=0.727$ and $Z=0.0124$, which is consistent with the spectroscopic value of [Fe/H] and the Galactic helium enrichment."694 They. found that only models with AZ<45M. satisfy the observational constraints., They found that only models with $M\le4.5$ $_\odot$ satisfy the observational constraints.695 We have adopted the same initial chemical composition in our model caleulations., We have adopted the same initial chemical composition in our model calculations.696 Furthermore. we have adopted the same Opacity and equation of state.," Furthermore, we have adopted the same opacity and equation of state."697 For the model of à UMa we have considered only A=ΕΔΕ. and we have adjusted the mixing-length: parameter. a. to be consistent with the values of log(L/L.) and Lig proposed by (2000).," For the model of $\alpha\,$ UMa we have considered only $M=4\,$ $_\odot$, and we have adjusted the mixing-length parameter, $\alpha$, to be consistent with the values of $\log(L/L_\odot)$ and $T_{\rm eff}$ proposed by (2000)."698 The star à UMa is a high-mass red. giant with a nondegencrate core.," The star $\alpha\,$ UMa is a high-mass red giant with a nondegenerate core."699 Such stars are very rare., Such stars are very rare.700 As seen in Lο., As seen in Fig.701 l. the red-giant branch for AJ=4M. is very. short: the star spends only My on it. which is more than two orders of magnitude shorter than the time spent by a star with a mass of AJ= 2M.. in which helium ignites in a degenerate core.," 1, the red-giant branch for $M=4\,$ $_\odot$ is very short; the star spends only My on it, which is more than two orders of magnitude shorter than the time spent by a star with a mass of $M=2\,$ $_\odot$, in which helium ignites in a degenerate core."702 We have chosen the model sequence with Al= 2M. to illustrate nonracial mode properties in red giants over a wide range of luminosity.," We have chosen the model sequence with $M=2\,$ $_\odot$ to illustrate nonradial mode properties in red giants over a wide range of luminosity."703 The most important xwameter determining nonradial mode properties 1s the ratio of the mean density of the core to the mean density of the whole star., The most important parameter determining nonradial mode properties is the ratio of the mean density of the core to the mean density of the whole star.704 In the sequence we have chosen. this xwameter increases by nearly four orders of magnitudes o*ween the bottom and the top of the giant branch.," In the sequence we have chosen, this parameter increases by nearly four orders of magnitudes between the bottom and the top of the giant branch."705 We have considered. four models for the MAL. sequence. calculated with the same values of VY. Z and à as those for he model of a UAla.," We have considered four models for the $_\odot$ sequence, calculated with the same values of $X$, $Z$ and $\alpha$ as those for the model of $\alpha\,$ UMa."706 The locations of the selected models on the evolutionary tracks are indicated. in Fig., The locations of the selected models on the evolutionary tracks are indicated in Fig.707 1: the xvwameters characterizing these models are listed in Table 1. (, 1; the parameters characterizing these models are listed in Table 1. (708(2000) considered. only racial modes. as potential candidates for explaining the peaks in the a UMa frequeney spectrum. determined. by ((2000).,"2000) considered only radial modes as potential candidates for explaining the peaks in the $\alpha\,$ UMa frequency spectrum determined by (2000)."709 They noticed that the frequencies of these peaks are much lower than the buovaney frequency deep in the star. aud presumed that a nonradial interpretation would appear to imply that the modes are ο modes of high. radial orcler.," They noticed that the frequencies of these peaks are much lower than the buoyancy frequency deep in the star, and presumed that a nonradial interpretation would appear to imply that the modes are g modes of high radial order."710 According to their estimate. the separation between the evelic frequencies of consecutive ο modes of like degree is of the order. of 2. ancl consequently. they argued. the spectrum could not be resolved. into individual modes.," According to their estimate, the separation between the cyclic frequencies of consecutive g modes of like degree is of the order of $\,\mu$ Hz, and consequently, they argued, the spectrum could not be resolved into individual modes."711 They did not. however. explain why radial modes. should," They did not, however, explain why radial modes should"712" ITO. ina ~OL 3.6«107AF. 109 101937, ", $_2$ $\sim 0.1$ $3.6 \times 10^7 M_{\odot}$ $10^6$ $10^{10} M_{\odot}$ 713assign spectral states to GN based on their power spectra (sce e.g. Uttlev Mellardy 2005. Aróvvalo et. al.,"assign spectral states to AGN based on their power spectra (see e.g. Uttley McHardy 2005, Arévvalo et al."714 2006. Alellardy et al.," 2006, McHardy et al."715 2007) can be applied only to a few best monitored objects with quality light curves., 2007) can be applied only to a few best monitored objects with quality light curves.716 Clearly. there is a need to develop indirect methods of assigning the accretion mode to the SEDs of AGN.," Clearly, there is a need to develop indirect methods of assigning the accretion mode to the SEDs of AGN."717 1n. Sobolewska. Cuerlifisski. Siemiginowska (2009. hereafter Paper ED) we defined the disc-to-power law index for Galactic black hole binaries. acp20.32(06pg.—1)|1. which corresponds to the X-ray. loudness. parameter. os. used to characterize the ACN broad-band. optical/UVX- spectra.," In Sobolewska, Gierlińsski, Siemiginowska (2009, hereafter Paper I) we defined the disc-to-power law index for Galactic black hole binaries, $\alpha^{ \prime}_{\rm GBH} \simeq 0.32(\alpha_{\rm GBH}718-1)+1$, which corresponds to the X-ray loudness parameter, $\alpha_{\rm ox}$, used to characterize the AGN broad-band optical/UV/X-ray spectra."719 The acu&0.824log(efisf(ofdoo]11 Gvhore cf. denotes the EFe flux in erg τος 4) was defined as the index of a nominal power law between the 3 keV. where the aceretion disc dominates the spectrum. of a GBIL (with the exception of the hard state) and 20 keV. where the spectrum is dominated by a power law emission. modelled as C'omptonization of the seed. cise photons in the hot corona.," The $\alpha_{\rm GBH} \simeq 0.824720\log[(ef_e)_{\rm 3}/(ef_e)_{\rm 20}] + 1$ (where $ef_e$ denotes the $EF_E$ flux in erg $^{-2}$ $^{-1}$ ) was defined as the index of a nominal power law between the 3 keV, where the accretion disc dominates the spectrum of a GBH (with the exception of the hard state) and 20 keV, where the spectrum is dominated by a power law emission, modelled as Comptonization of the seed disc photons in the hot corona."721 The ee accounts for the many orders on magnitude cillerence betweenpy the energies lor which the AcBH and os; are defined (3-00-20 keV ancl 2500A--t0-2 keV. respectively).," The $\alpha^{ \prime}_{\rm GBH}$ accounts for the many orders on magnitude difference between the energies for which the $\alpha_{\rm722 GBH}$ and $\alpha_{\rm ox}$ are defined (3-to-20 keV and -to-2 keV, respectively)."723 We showed that the distribution of ac shows three distinctive peaks around 1. 1.5 and 2. which correspond to hard. intermediate/very high and soft spectral states. respectively.," We showed that the distribution of $\alpha^{ \prime}_{\rm GBH}$ shows three distinctive peaks around $\sim$ 1, 1.5 and 2, which correspond to hard, intermediate/very high and soft spectral states, respectively."724. Hence. ae;jy and so o. together with. the X-ray. photon index. can be indicators of a spectral state of accreting black holes.," Hence, $\alpha^{\prime}_{\rm725 GBH}$ and so $\alpha_{\rm ox}$, together with the X-ray photon index, can be indicators of a spectral state of accreting black holes."726 In the present paper we develop the Paper LE idea. in more detail., In the present paper we develop the Paper I idea in more detail.727 We use the GDBII phenomenology to simulate an outburst of ACN., We use the GBH phenomenology to simulate an outburst of AGN.728 We use a physical mocel of accretion to describe the spectra of a representative GDII. GRO J1655-40. at various luminosity levels. and then we scale the seed photons temperature and bolometric Luminosity in the best fitting models with mass. as in the standard Shakura-Sunvaev dise case. to study aceretion onto a supermassive black hole.," We use a physical model of accretion to describe the spectra of a representative GBH, GRO J1655-40, at various luminosity levels, and then we scale the seed photons temperature and bolometric luminosity in the best fitting models with mass, as in the standard Shakura-Sunyaev disc case, to study accretion onto a supermassive black hole."729 Next. we separate the simulated ACGN spectral states in the ass vs. (ήν) plane for various classes. of AGN. including broad and narrow line Type 1 Sevferts and LINERs.," Next, we separate the simulated AGN spectral states in the $\alpha_{\rm ox}$ vs. $(\nu L_\nu)_o$ plane for various classes of AGN, including broad and narrow line Type 1 Seyferts and LINERs."730" We investigate if the mass spread in the observed AGN samples can contribute to the observed. correlation between the X-ray loudness. a,x.) and monochromatic luminosity at25004."," We investigate if the mass spread in the observed AGN samples can contribute to the observed correlation between the X-ray loudness, $\alpha_{\rm731 ox}$ ) and monochromatic luminosity at."732.. The structure of the paper is as follows., The structure of the paper is as follows.733 La Sec., In Sec.734 2 we describe the cata selection criteria ancl data reduction procedure as well as give details of data modeling., \ref{sec:data} we describe the data selection criteria and data reduction procedure as well as give details of data modeling.735 Section we present our method of mass scaling of a GI outburst to the case of AGN., Section \ref{sec:method} we present our method of mass scaling of a GBH outburst to the case of AGN.736 In Sec., In Sec.737 4. we present simulated spectra. resulting correlations between the parameters. and compare our work with observational sunples.," \ref{sec:res} we present simulated spectra, resulting correlations between the parameters, and compare our work with observational samples."738 Finally. in Sec.," Finally, in Sec."739 5. we discuss and conclude our results., \ref{sec:dc} we discuss and conclude our results.740 CBI binaries undergo violent events during which their luminosity may increase by more than 3 orders of magnitudo., GBH binaries undergo violent events during which their luminosity may increase by more than 3 orders of magnitude.741 During these outbursts the sources show variety of dilferent X-ray spectral shapes (c.g. Remillard AleClintock 2006: Done et al., During these outbursts the sources show variety of different X-ray spectral shapes (e.g. Remillard McClintock 2006; Done et al.742 2006)., 2006).743 This spectral variability. is relatively well understood (c.g. Ciüerlifisski Done 2004)., This spectral variability is relatively well understood (e.g. Gierlińsski Done 2004).744 Fvpical peak outburst luminosities do not exceed 0.5L/Lg (e.g. Done ct al., Typical peak outburst luminosities do not exceed $L/L_E$ (e.g. Done et al.745 2006)., 2006).746 TFhis is most probably connected to the phiysies of the aceretion disces that become unstable at. high LíLp (c.g. Alerloni 2003. Merloni Navakshin 2006).," This is most probably connected to the physics of the accretion discs that become unstable at high $L/L_E$ (e.g. Merloni 2003, Merloni Nayakshin 2006)."747 A [ow GBLIs sporacically reach the high Eddington ratios (see e.g. references in Done et al., A few GBHs sporadically reach the high Eddington ratios (see e.g. references in Done et al.748" 2006). but only CRS 1915|105 accretes steaclily at Eddington ratios 0.3JxLib,<3."," 2006), but only GRS 1915+105 accretes steadily at Eddington ratios $0.3\leq L/L_E \leq 3$."749 lt was shown in Done. Wardziuisski. Cicrlinsski (2004). however. that GRS 1915]105 occupies a dilferent. region in. their color-color diagram than the normal CGBIIs. and it never &oes into a normal hard or soft state.," It was shown in Done, Wardzińsski, Gierlińsski (2004), however, that GRS 1915+105 occupies a different region in their color-color diagram than the 'normal' GBHs, and it never goes into a 'normal' hard or soft state."750 In our study we are looking for a well monitored outburst of afypicad (11211. that would display a variety of different spectral states. and could be easily described with a standard. dise|corona model.," In our study we are looking for a well monitored outburst of a GBH, that would display a variety of different spectral states, and could be easily described with a standard disc+corona model."751 For these reasons. we have selected the 2005 outburst of a confirmed Galactic N-rav black hole binary GRO J165540 hosting a 0.381. black hole. located at the distance of 3.2 kpe. with inclination of 30° (Remillard AleClintock 2006).," For these reasons, we have selected the 2005 outburst of a confirmed Galactic X-ray black hole binary GRO J1655–40 hosting a $_{\odot}$ black hole, located at the distance of 3.2 kpc, with inclination of $^\circ$ (Remillard McClintock 2006)."752 Phe lighteurve of the outburst is presented in Fig., The lightcurve of the outburst is presented in Fig.753 laa. The X-ray bolometric luminosity (caleulated based on the extrapolated 0.01.1000 keV flux of the best fitting models) changed by more than 3 orders of magnitude. and at the peak of the outburst the system reached ~20 of the Ecelington luminosity.," \ref{fig:loop}a a. The X-ray bolometric luminosity (calculated based on the extrapolated 0.01–1000 keV flux of the best fitting models) changed by more than 3 orders of magnitude, and at the peak of the outburst the system reached $\sim$ of the Eddington luminosity."754 In 2005 GRO J1655-40 clisplaved a variety of GBLI spectral states (e.g. Brocksopp et al., In 2005 GRO J1655-40 displayed a variety of GBH spectral states (e.g. Brocksopp et al.755 2006: Done et al., 2006; Done et al.756 2007). with the spectral variations covering a typical range [for its class.," 2007), with the spectral variations covering a typical range for its class."757 This can be seen e.g. in the patterns followed. by GRO J1655-40 (Eig., This can be seen e.g. in the patterns followed by GRO J1655-40 (Fig.758 Ibb) and other GDBllIs (Sobolewska et al., \ref{fig:loop}b b) and other GBHs (Sobolewska et al.759 2009) in the ecpg vs. monochromatic luminosity at 3 keV diagrams. ancl also in the hardness-intensity. cliagranms presented for other GDBlIS (e.g. Fender. Belloni Gallo 2004. Jolloni et al.," 2009) in the $\alpha_{\rm GBH}$ vs. monochromatic luminosity at 3 keV diagrams, and also in the hardness-intensity diagrams presented for other GBHs (e.g. Fender, Belloni Gallo 2004, Belloni et al."760 2005)., 2005).761 Hlence. we argue that the 2005 data of GRO 1655-40. provide a reasonable SED template to study. aceretion mechanisms onto a black hole at various luminosity levels.," Hence, we argue that the 2005 data of GRO J1655-40 provide a reasonable SED template to study accretion mechanisms onto a black hole at various luminosity levels."762 We note. however. that the Bhard-to-soft state transition in 2005 outburst ofGRO 1655-40 happened aboO.02LJLe. while it was shown that such a transition mav also happen in DII at much higher ratios. Z0.3L/ Lr (Cierliisski Newton 2006).," We note, however, that the hard-to-soft state transition in 2005 outburst of GRO J1655-40 happened at $\sim0.02L/L_{\rm E}$, while it was shown that such a transition may also happen in GBH at much higher ratios, $\geq$ $L/L_{E}$ (Gierlińsski Newton 2006)."763 Thus our template may lack luminous hard state SEDs. and. we discuss its implications later on.," Thus our template may lack luminous hard state SEDs, and we discuss its implications later on."764 We reduced all data of the 2005 outburst found in the public using vor., We reduced all data of the 2005 outburst found in the public using ver.765 6.2., 6.2.766 We extracted speetra for detector 2. top laver only and spectra [from both clusters: one spectrum. per pointed observation (see Paper E for the details of data reduction).," We extracted spectra for detector 2, top layer only and spectra from both clusters; one spectrum per pointed observation (see Paper I for the details of data reduction)."767 For modeling we used ver., For modeling we used ver.768 11.3 (Arnaud 1996)., 11.3 (Arnaud 1996).769 It has been shown (e.g. Gicrlifsski et al., It has been shown (e.g. Gierlińsski et al.770 1999. Done CGierlinsski 2003) that the spectral evolution of C:BIL during an outburst can be explained. in terms of variations of the soft photons temperature ancl hard-to-soft compactness ratio. which depends mostly on the geometry. of the disc- system.," 1999, Done Gierlińsski 2003) that the spectral evolution of GBH during an outburst can be explained in terms of variations of the soft photons temperature and hard-to-soft compactness ratio, which depends mostly on the geometry of the disc-corona system."771 Following these authors. we described. the," Following these authors, we described the"772and pulsation is needed.,and pulsation is needed.773 These works have shown that a 2D approach tends to produce a larger effect on the frequencies than 1D perturbative methods., These works have shown that a 2D approach tends to produce a larger effect on the frequencies than 1D perturbative methods.774" As discussed above, rotation and overshoot change the unscaled frequencies in opposite directions."," As discussed above, rotation and overshoot change the unscaled frequencies in opposite directions."775" While increasing rotation decreases the frequencies, increasing core overshoot increases the frequencies."," While increasing rotation decreases the frequencies, increasing core overshoot increases the frequencies."776" According to ??,, 1D calculations will not find as large a shift from rotation as 2D models, and hence will need a smaller overshoot to match the observed frequency in rapidly rotating stars."," According to \citet{lignieres, me08}, 1D calculations will not find as large a shift from rotation as 2D models, and hence will need a smaller overshoot to match the observed frequency in rapidly rotating stars."777" Finally, we decided to test the technique discussed in Section 5 on 0 Oph."," Finally, we decided to test the technique discussed in Section \ref{idit} on $\theta$ Oph."778" As discussed in Section 5,, our resolution in both velocity and overshoot is quite coarse, so we do not expect to place tight constraints on 0 Oph in this exploratory calculation."," As discussed in Section \ref{idit}, our resolution in both velocity and overshoot is quite coarse, so we do not expect to place tight constraints on $\theta$ Oph in this exploratory calculation."779" We fixed the metallicity of our models at Z = 0.02, using the ? abundances."," We fixed the metallicity of our models at Z = 0.02, using the \citet{GS} abundances."780" For our asteroseismic comparison, we fixed the mass at 9.5Mo,, after calculating the evolutionary tracks of 8.5, 9 and 9.5 Mamodels and determining which models gave the best match to the observed location of 0 Oph."," For our asteroseismic comparison, we fixed the mass at 9.5, after calculating the evolutionary tracks of 8.5, 9 and 9.5 models and determining which models gave the best match to the observed location of $\theta$ Oph."781" The seven observed frequencies of 0 Oph were compared against the 9.5 mmodels shown in Figure 1,, evolved to an age of 15.6 Myr."," The seven observed frequencies of $\theta$ Oph were compared against the 9.5 models shown in Figure \ref{fig:HR}, evolved to an age of 15.6 Myr."782" We used the spectroscopic mode identifications given by ?,, but used only the given 6 values as constraints."," We used the spectroscopic mode identifications given by \citet{briquet05}, but used only the given $\ell$ values as constraints."783" As for the calculations performed in Section 5,, we found that the best results were obtained when each frequency is compared only to model frequencies of the same έο."," As for the calculations performed in Section \ref{idit}, we found that the best results were obtained when each frequency is compared only to model frequencies of the same $\ell_o$."784" When we do this comparison for 0 Oph, we find the best fit model has a rotation and overshoot of (35 + 35s!, 0.28 + 0.1H,)."," When we do this comparison for $\theta$ Oph, we find the best fit model has a rotation and overshoot of (35 $\pm$ 35, 0.28 $\pm$ $_p$ )."785" This model is located within the observed photometric errors for 6 Oph, with a luminosity of log(L/Lo)=3.75 and an effective temperature Τε;=22590K."," This model is located within the observed photometric errors for $\theta$ Oph, with a luminosity of $log(L/L_{\odot}) = 3.75$ and an effective temperature $T_{eff} = 22590 K$."786" The rotation velocity found in our best solution is in good agreement with the rotation velocity as determined from both the vsini and the observed mode splitting, 29 + 7 citepbriquet05,briquet07.."," The rotation velocity found in our best solution is in good agreement with the rotation velocity as determined from both the $vsini$ and the observed mode splitting, 29 $\pm$ 7 \\citep{briquet05,briquet07}."787" The convective core overshoot determined here is slightly lower than that determined by ?,, although the two results do agree within the errors."," The convective core overshoot determined here is slightly lower than that determined by \citet{briquet07}, although the two results do agree within the errors."788" It seems that when a more accurate treatment of rotation is taken into account, at least for slowly rotating stars, this does indeed reduce the need for convective core overshooting."," It seems that when a more accurate treatment of rotation is taken into account, at least for slowly rotating stars, this does indeed reduce the need for convective core overshooting."789" Our new estimate is still higher than the results determined for other f Cephei stars (typically 0.1-0.2), although again, the results agree to within our uncertainties."," Our new estimate is still higher than the results determined for other $\beta$ Cephei stars (typically 0.1-0.2), although again, the results agree to within our uncertainties."790" Our models for 0 Oph have been calculated using a metallicity of Z = 0.02 at the composition of ?,, considerably higher than that determined by ?.."," Our models for $\theta$ Oph have been calculated using a metallicity of Z = 0.02 at the composition of \citet{GS}, considerably higher than that determined by \citet{briquet07}."791" As discussed in their work, higher metallicity is correlated to lower convective core overshoot, so one would expect our models to have a lower overshoot."," As discussed in their work, higher metallicity is correlated to lower convective core overshoot, so one would expect our models to have a lower overshoot."792" In fact, based on the results given in their Table 4, we would expect a 1D model with our metallicity to have an overshoot of a, = 0.32."," In fact, based on the results given in their Table 4, we would expect a 1D model with our metallicity to have an overshoot of $\alpha_{ov}$ = 0.32."793" As is expected, this is lower than the overshoot calculated by ?,, and is much closer to the value obtained with our 2D models."," As is expected, this is lower than the overshoot calculated by \citet{briquet07}, and is much closer to the value obtained with our 2D models."794" Nevertheless, our models also show the need for an unusually high convective core overshoot in this star."," Nevertheless, our models also show the need for an unusually high convective core overshoot in this star."795" Although our models have shown some indications that rotation and overshoot can be complimentary effects, it appears that more rapid rotation is required in order to influence the frequencies."," Although our models have shown some indications that rotation and overshoot can be complimentary effects, it appears that more rapid rotation is required in order to influence the frequencies."796 Another limitation of our models is the restriction to fixed mass and age., Another limitation of our models is the restriction to fixed mass and age.797" This is of course not realistic, and has been introduced to limit the computations required."," This is of course not realistic, and has been introduced to limit the computations required."798" As mentioned in Section 2,, we initially calculated models at three different masses, 8.5, 9 and 9.5Mo."," As mentioned in Section \ref{method}, we initially calculated models at three different masses, 8.5, 9 and 9.5."799". All of these models were close to the observed error box of 0 Oph, although the lower mass models needed to be evolved to a higher age."," All of these models were close to the observed error box of $\theta$ Oph, although the lower mass models needed to be evolved to a higher age."800" Although detailed frequency calculations were not performed for these models, it seems likely that matching models could be found."," Although detailed frequency calculations were not performed for these models, it seems likely that matching models could be found."801 Including mass and age as free parameters is currently under investigation and will be included in future work., Including mass and age as free parameters is currently under investigation and will be included in future work.802" We have found that both rotation and overshoot do have an effect on stellar frequencies, although this is predominately through the effects of changing stellar radius."," We have found that both rotation and overshoot do have an effect on stellar frequencies, although this is predominately through the effects of changing stellar radius."803" Increasing convective core overshoot increases the unscaled frequencies, while rotation causes the unscaled frequencies to decrease, although certain choices of scaling can minimize this effect for rotation."," Increasing convective core overshoot increases the unscaled frequencies, while rotation causes the unscaled frequencies to decrease, although certain choices of scaling can minimize this effect for rotation."804" Although the frequencies themselves may change, as expected we find that the overshoot has no effect on the mode splitting."," Although the frequencies themselves may change, as expected we find that the overshoot has no effect on the mode splitting."805 We also investigated the effect of overshooting on the large and small separations., We also investigated the effect of overshooting on the large and small separations.806" We find that increasing convective core overshoot decreases the large separations, but increases the small separation."," We find that increasing convective core overshoot decreases the large separations, but increases the small separation."807" Unfortunately, both of these effects are"," Unfortunately, both of these effects are"808(e.g. Spruit et al.,(e.g. Spruit et al.809 2001: Drenkhahn Spruit 2002: Zhang Mésszárros 2002: Giannios Spruit 2007)., 2001; Drenkhahn Spruit 2002; Zhang Mésszárros 2002; Giannios Spruit 2007).810" In both of the above two non-internal shock models for GRB prompt emissions. it is possible to argue that the emission radius ος»uld be in principle related to the Lorentz factor EL and variability ἐν in a non-trivial (e.g. other than r.=L7c£,) manner."," In both of the above two non-internal shock models for GRB prompt emissions, it is possible to argue that the emission radius $r$ could be in principle related to the Lorentz factor $\Gamma$ and variability $t_v$ in a non-trivial (e.g. other than $r=\Gamma^2 ct_v$ ) manner."811 For example. in the photosphere model. + is detined by the optically-thin condition. and is not directly related to ἐν which is related to the time history of the GRB central engine.," For example, in the photosphere model, $r$ is defined by the optically-thin condition, and is not directly related to $t_v$ which is related to the time history of the GRB central engine."812" In the magnetic dissipation model. if the energy dissipation occurs locally (i.e. the emission region scale is much smaller than the emission radius). it is possible to have r>L7cf,.."," In the magnetic dissipation model, if the energy dissipation occurs locally (i.e. the emission region scale is much smaller than the emission radius), it is possible to have $r>\Gamma^2813ct_v$."814 In general. it is reasonable to treat r :is an independent quantity with respect to Land /...," In general, it is reasonable to treat $r$ as an independent quantity with respect to $\Gamma$ and $t_v$."815 High energy photons produced in the prompt emission region are expected to interact with lower energy photons before escaping as a result of two photon attenuation., High energy photons produced in the prompt emission region are expected to interact with lower energy photons before escaping as a result of two photon attenuation.816 In general. the internal optical depth of  interactions depends on LL. ἐς. and the radius of the emission region.," In general, the internal optical depth of $\gamma\gamma$ interactions depends on $\Gamma$, $t_v$, and the radius of the emission region."817" Traditionally. internal shocks have been taken as the default model of GRB prompt emission. and he pair attenuation optical depth has been expressed as a function of EL and /,. only (e.g. Piran 1999: Lihwick Sari 2001)."," Traditionally, internal shocks have been taken as the default model of GRB prompt emission, and the pair attenuation optical depth has been expressed as a function of $\Gamma$ and $t_v$ only (e.g. Piran 1999; Lithwick Sari 2001)."818 The »uüir attenuation process is expected to leave a cutoff spectral feature in the prompt emission spectrum. and detecting such a spectral cutoff by high energy missions such as GLAST has been discussed as an important method toestimate the bulk Lorentz factor L of he fireball (Baring&Harding1997:Baring2006).," The pair attenuation process is expected to leave a cutoff spectral feature in the prompt emission spectrum, and detecting such a spectral cutoff by high energy missions such as GLAST has been discussed as an important method toestimate the bulk Lorentz factor $\Gamma$ of the fireball \citep{math1,math2}."819. The issue of unknown emission radius + makes the yicture more complicated., The issue of unknown emission radius $r$ makes the picture more complicated.820 It is no longer straightforward to estimate LP with an observed spectral cutoffenergy., It is no longer straightforward to estimate $\Gamma$ with an observed spectral cutoff energy.821 On the other hand. tljere are other independent methods of estimating L using early afterglow (e.g. Sari Piran 1999: Zhang. Kobayashi Mésszárros 2003) or prompt emission (Pe'er et al.," On the other hand, there are other independent methods of estimating $\Gamma$ using early afterglow (e.g. Sari Piran 1999; Zhang, Kobayashi Mésszárros 2003) or prompt emission (Pe'er et al."822 2007) data and there have been cases of such measurements (Molinari et al., 2007) data and there have been cases of such measurements (Molinari et al.823 2007: Pe'er et a., 2007; Pe'er et al.824 2007)., 2007).825 It is then possible ο use the observed spectral cutoff energy to diagnose the unknown GRB emission site if Lis measured by other means., It is then possible to use the observed spectral cutoff energy to diagnose the unknown GRB emission site if $\Gamma$ is measured by other means.826 In this yaper we release the internal shock assumption and re-express the cutoff energy more generally as a function of rand ['., In this paper we release the internal shock assumption and re-express the cutoff energy more generally as a function of $r$ and $\Gamma$.827 We then discuss an approach of diagnosing the GRB prompt emission site using the future cutoff energy data retrieved by GLAST and other missions., We then discuss an approach of diagnosing the GRB prompt emission site using the future cutoff energy data retrieved by GLAST and other missions.828 Lately Murase Ioka (2007. see also Murase Nagataki 2006) also independently discuissed to use the pair cutoff signature to diagnose whether the emission site is the pair/baryonic photosphere.," Lately Murase Ioka (2007, see also Murase Nagataki 2006) also independently discussed to use the pair cutoff signature to diagnose whether the emission site is the pair/baryonic photosphere."829 We discuss this topic nqore generally to diagnose any emission site., We discuss this topic more generally to diagnose any emission site.830 We emphasise that our method can be used to constrain i only when a clear cut-off is observed in the high energy photon spectrum from a GRB., We emphasise that our method can be used to constrain $r$ only when a clear cut-off is observed in the high energy photon spectrum from a GRB.831" The cross section of two-photon interaction can be generally expressed as (Gould Schreder 1967) where oy .is the Thomson cross section.. b=-1GETunE,)] Lip:is the center of. mass dimen.sionless speed of the pair produced. {νι ££., and 0 are the high- and low-energy photon energies and their incident angles in the comoving frame of the GRB ejecta."," The cross section of two-photon interaction can be generally expressed as (Gould Schreder 1967) )= ], where $\sigma_T$ is the Thomson cross section, $b=832[1-(E_{\gamma_l,th}^{\prime}/E_{\gamma_l}^{\prime})]^{1/2}$ is the center of mass dimensionless speed of the pair produced, $E_{\gamma h}^{'}$, $E_{\gamma l}^{'}$ and $\theta'$ are the high- and low-energy photon energies and their incident angles in the comoving frame of the GRB ejecta."833 The threshold energy of pair production for a high energy photon with energy Loo is, The threshold energy of pair production for a high energy photon with energy $E_{\gamma_h}^{\prime}$ is.834 In the comoving frame. the relative velocity of the high energy and low energy photons along the direction of the former is c(l|cos0).," In the comoving frame, the relative velocity of the high energy and low energy photons along the direction of the former is $c(1-\cos{\theta'})$."835 For an isotropic distribution the fraction of low energy photons moving in the differential cone at an angle between 9 and (8|dé’) is Esin dd’., For an isotropic distribution the fraction of low energy photons moving in the differential cone at an angle between $\theta'$ and $(\theta'+d\theta')$ is $\frac{1}{2}\sin\theta'd{\theta'}$ .836" The inverse of the mean free path for >, , interactions P,-GET, )can be calculated as ΓΕek(EL,89) where", The inverse of the mean free path for $\gamma_h$ $\gamma_l$ interactions $l_{\gamma_h\gamma_l}^{-1}(E_{\gamma_h}^{\prime})$ can be calculated as ) where837Lewis 2002) as a possible alternative to explain. the acceleration of the universe.,Lewis 2002) as a possible alternative to explain the acceleration of the universe.838 They modified the Friedmann equation as This model has no energy component besides ordinary matter., They modified the Friedmann equation as This model has no energy component besides ordinary matter.839 If we consider a spatially flat FRW universe. the Friedmann equation is modified as Eq. (," If we consider a spatially flat FRW universe, the Friedmann equation is modified as Eq. ("84039).,39).841 The universe undergoes acceleration requires η<2/3., The universe undergoes acceleration requires $n < 2/3$.842 If n=0. itis the same as the cosmological constant universe.," If $n=0$, it is the same as the cosmological constant universe."843 We can obtain H(z)by using Eq. (40)), We can obtain $H(z)$ by using Eq. \ref{Carda}) )844" and pj,Ξρμων+zb)2Ojo(17Lj. wherep,=3H;distance ;/8nGis the critical density of the universe."," and $\rho_m=\rho_{m}(1+z)^3=\Omega_{m}\rho_c(1+z)^3$, where $\rho_c=3H_0^2/8\pi G$ is the critical density of the universe."845" The luminosity ini this modelts For the Cardassian expansion model. we obtain nYQ,a, sifred3 Qo. πασά Qo, yo, In the DGP model the modified Friedmann equation due to the presence of an infinite-volume extra dimension is (Deffayet et al."," The luminosity distance in this model is For the Cardassian expansion model, we obtain _M-1), (n-1)^2 _M) _M, = (n-1)^2 _M n, _M)) In the DGP model the modified Friedmann equation due to the presence of an infinite-volume extra dimension is (Deffayet et al."846" 2002) where the bulk-induced term. €. is defined as For a flat universe. OQ,=0."," 2002) where the bulk-induced term, $\Omega_{r_c}$, is defined as For a flat universe, $\Omega_k=0$."847 In the above equation. ος is the crossover scale beyond which the gravitational force follows the 5-dimensional 1/r behavior.," In the above equation, $r_c$ is the crossover scale beyond which the gravitational force follows the 5-dimensional $1/r^3$ behavior."848" Note that on short length scales r«r, (at early times) the gravitational force follows the usual four-dimensional 1/77 behavior."," Note that on short length scales $r849\ll r_c$ (at early times) the gravitational force follows the usual four-dimensional $1/r^2$ behavior."850" For a spatially flat universe. O,=(1—Q,,)2/4."," For a spatially flat universe, $\Omega_{r_c}=(1-\Omega_m)^2/4$."851 We obtain - TR) gravity models. in which the gravitational Lagrangian is a function. of the curvature scalar R. also can explain current cosmic acceleration (Vollick 2003: Carroll et al.," We obtain = $f(R)$ gravity models, in which the gravitational Lagrangian is a function of the curvature scalar $R$, also can explain current cosmic acceleration (Vollick 2003; Carroll et al."852 2004: Capozziello et al., 2004; Capozziello et al.853 2009)., 2009).854 Poplawski (2006) derived a quite complicated expression of jerk parameter in. (ΑΔ)=R—£5 (Poplawski 2006): The snap parameter in this model is (Poplawski 2007) Poplawski (2007) calculated goΞ-0.6704. jo=πα. ," Poplawski (2006) derived a quite complicated expression of jerk parameter in $f(R)=R-\frac{\alpha^2}{3R}$ (Poplawski 2006): The snap parameter in this model is (Poplawski 2007) Poplawski (2007) calculated $q_0=-0.67^{+0.06}_{-0.03}$, $j_0=1.01^{+0.08}_{-0.21}$ and $s_0=-0.22^{+0.21}_{-0.19}$."855These expressions of the jerk and snap parameters are only valid in Palatini variational principle., These expressions of the jerk and snap parameters are only valid in Palatini variational principle.856 A generic formulae of cosmographic parameter are derived by Capozziello. Cardone Salzano (2008) (for more details. see Equations (23)-(33) in their paper).," A generic formulae of cosmographic parameter are derived by Capozziello, Cardone Salzano (2008) (for more details, see Equations (23)-(33) in their paper)."857 They also gave the best fitted value: go=—0.55+0.38. jj=1.045.4 and sy=—0.35+28.1 using SNe Ia. In this paper. we only use Poplawski (2006) as an example for the ΤΑ) gravity.," They also gave the best fitted value: $q_0=-0.55\pm0.38$, $j_0=1.0\pm5.4$ and $s_0=-0.35\pm28.1$ using SNe Ia. In this paper, we only use Poplawski (2006) as an example for the $f(R)$ gravity."858 Davis et al. (, Davis et al. (8592007) fitted the SNe Ia dataset that include 60 ESSENCE SNe la (WoodVasey et al.,2007) fitted the SNe Ia dataset that include 60 ESSENCE SNe Ia (WoodVasey et al.860 2007). 57 SNe la from Super-Nova Legacy Survey (SNLS) (Astier et al.," 2007), 57 SNe Ia from Super-Nova Legacy Survey (SNLS) (Astier et al."861 2006). 45 nearby SNe Ia and 30 SNe Ia detected by HST (Riess et al.," 2006), 45 nearby SNe Ia and 30 SNe Ia detected by HST (Riess et al."862 2007) with the MCLS2K2 method., 2007) with the MCLS2K2 method.863" With the luminosity distance d; in units of megaparsecs. the predicted distance modulus ts The likelihood functions can be determined from y statistic. where ο is the dispersion in the supernova redshift (transformed to distance modulus) due to peculiar velocities. Ho; is the observational distance modulus. and σσ, is the uncertainty in the individual distance moduli."," With the luminosity distance $d_{L}$ in units of megaparsecs, the predicted distance modulus is The likelihood functions can be determined from $\chi^{2}$ statistic, where $\sigma_{\nu}$ is the dispersion in the supernova redshift (transformed to distance modulus) due to peculiar velocities, $\mu_{0,i}$ is the observational distance modulus, and $\sigma_{\mu_{0,i}}$ is the uncertainty in the individual distance moduli."864 The confidence regions can be found through marginalizing the likelihood functions over Πρ (.e.. integrating the probability density exp)* for all values of Ho).," The confidence regions can be found through marginalizing the likelihood functions over $H_{0}$ (i.e., integrating the probability density $p\propto\exp^{-\chi^{2}/2}$ for all values of $H_{0}$ )."865 We use the calibration results obtained by using the interpolation methods directly from SNe Ia data (Liang et al., We use the calibration results obtained by using the interpolation methods directly from SNe Ia data (Liang et al.866 2008)., 2008).867 The calibrated luminosity relations are completely cosmology independent., The calibrated luminosity relations are completely cosmology independent.868 We assume these relations do not, We assume these relations do not869shows a sample of data generated by the above procedure.,shows a sample of data generated by the above procedure.870" Having verified that generating sources from our model can accurately mimic the relevant UKIDSS data, the model can now be used with confidence as the prior needed to perform Bayesian cclassification."," Having verified that generating sources from our model can accurately mimic the relevant UKIDSS data, the model can now be used with confidence as the prior needed to perform Bayesian classification."871 A first test of our Bayesian cclassification method is to analyse the simulated UKIDSS data described in4., A first test of our Bayesian classification method is to analyse the simulated UKIDSS data described in.872"6.. As the input star and galaxies distributions are known, the resultant stellar probabilities are, given the deliberately imposed restrictions on the use of colour information, optimal."," As the input star and galaxies distributions are known, the resultant stellar probabilities are, given the deliberately imposed restrictions on the use of colour information, optimal."873" In particular, the numbers and properties of the sources which cannot be classified decisively are of interest, as any real sources with such properties will have P;~0.5."," In particular, the numbers and properties of the sources which cannot be classified decisively are of interest, as any real sources with such properties will have $\ps \simeq 0.5$."874 The distribution of posterior star probabilities for all sources is shown in and the distribution in Y cy space is shown in8., The distribution of posterior star probabilities for all sources is shown in and the distribution in $Y$ $\stat_Y$ space is shown in.875". These results from simulated data can be compared to (left) and 12 (left), which show the results when our method is applied to real UKIDSS data."," These results from simulated data can be compared to (left) and \ref{figure:PostClassProbasUKIDSSus-pipe} (left), which show the results when our method is applied to real UKIDSS data."876" While there is not much difference between and 12 (left), there are two noticeable differences between and 11 (left): there are more simulated sources with low star probabilities and there are more sources with P clearly different from 0 and 1(i.e.,, not classified with certainty)."," While there is not much difference between and \ref{figure:PostClassProbasUKIDSSus-pipe} (left), there are two noticeable differences between and \ref{figure:HistPostStarVectors} (left): there are more simulated sources with low star probabilities and there are more sources with $\ps$ clearly different from $0$ and $1$, not classified with certainty)."877" In particular there are many more sources with P,<0.4, yet clearly non-zero."," In particular there are many more sources with $\ps\la0.4$, yet clearly non-zero."878 The former difference can be explained by the fact that there are fewer bright sources (which are, The former difference can be explained by the fact that there are fewer bright sources (which are879lines are a viable velocity reference [or planet searches. including ?.. ?.. ?.. and ?..,"lines are a viable velocity reference for planet searches, including \citet{seifahrt2008}, , \citet{blake2010}, \citet{figueira2010harps}, and \citet{figueira2010crires}."880 This technique requires an excellent model of Z(À). which can be derived empirically from observations of the Sun (?) or calculated directly. based on assumptions about (he composition aud structure of Earth's atmosphere (?)..," This technique requires an excellent model of $T(\lambda)$, which can be derived empirically from high-resolution observations of the Sun \citep{blake2010} or calculated directly based on assumptions about the composition and structure of Earth's atmosphere \citep{seifahrt2010}."881 Atmospheric constituents like Cll). COs. and Os are well-mixed from Earth's surface through the mesosphere and have seasonal variations in total column density.," Atmospheric constituents like $_{4}$, $_{2}$, and $_{2}$ are well-mixed from Earth's surface through the mesosphere and have seasonal variations in total column density."882 For wavelengths 900<A«2500 nm. absorption bv Π.Ο becomes very important. having large optical depth al some wavelengths.," For wavelengths $900<\lambda<2500$ nm, absorption by $_{2}$ O becomes very important, having large optical depth at some wavelengths."883 Modeling these absorption features poses a significant challenge since the total water column can have large ancl rapid variations., Modeling these absorption features poses a significant challenge since the total water column can have large and rapid variations.884 We demonstrate that Precipitable Water Vapor (PWV) estimates derived from a Global Positioning System (GPS) receiver can be used to calculate theoretical transmission spectra having no free parameters and resulting in excellent [its to astronomical spectra in the wavelength: range 900<A«1000 nm., We demonstrate that Precipitable Water Vapor (PWV) estimates derived from a Global Positioning System (GPS) receiver can be used to calculate theoretical transmission spectra having no free parameters and resulting in excellent fits to astronomical spectra in the wavelength range $900<\lambda<1000$ nm.885 In a region of non-saturated IO. lines we find fit residuals <2%. likely dominated by residual fringing signals in our spectra.," In a region of non-saturated $_2$ O lines we find fit residuals $<2\%$, likely dominated by residual fringing signals in our spectra."886 We find that GPS-based PWV estimates are also useful [or estimating total transmission in the SDSS z band and demonstrate that changes in PWV bias photometric measurements of mid-M stars and determine an empirical correction factor for the z-band photometric measurements in the SDSS database., We find that GPS-based PWV estimates are also useful for estimating total transmission in the SDSS z band and demonstrate that changes in PWV bias photometric measurements of mid-M stars and determine an empirical correction factor for the z-band photometric measurements in the SDSS database.887 As part of an ongoing program {ο measure the radial velocities of M stars. we observed T4 A star telluric standards with the ARCES echelle spectrograph (72). on the 3.5 m telescope ab Apache Point Observatory (APO).," As part of an ongoing program to measure the radial velocities of M stars, we observed 74 A star telluric standards with the ARCES echelle spectrograph \citep{wang2003} on the 3.5 m telescope at Apache Point Observatory (APO)."888 A single ARCES observation contains data in more than 100 spectral orders spanning 360 nm to LOLO nm at a resolution of R~30.000.," A single ARCES observation contains data in more than 100 spectral orders spanning 360 nm to 1010 nm at a resolution of $\sim$ 30,000."889 These A star observations were collected during 2010 under a wide range of observing conditions and ab airmass (AM) up to AM-2.0., These A star observations were collected during 2010 under a wide range of observing conditions and at airmass (AM) up to AM=2.0.890 Exposure times were tailored so that S/N per pixel in the extracted spectra would be ~500 at A~800 nm., Exposure times were tailored so that S/N per pixel in the extracted spectra would be $\sim500$ at $\lambda\sim800$ nm.891 The ARCES spectral orders are closely spaced and mareinally sampled in the spatial direction. requiring special care in (he spectral ex(raction process so as not to induce aliasing.," The ARCES spectral orders are closely spaced and marginally sampled in the spatial direction, requiring special care in the spectral extraction process so as not to induce aliasing."892 We collected a large number of bias and «quartz lamp frames on each night and used the quartz lamp frames to define the positions of the centers of each of 15 spectral orders. which run approximately parallel to the detector rows.," We collected a large number of bias and quartz lamp frames on each night and used the quartz lamp frames to define the positions of the centers of each of 75 spectral orders, which run approximately parallel to the detector rows."893 Alter subtracting an average nightly bias. we estimated scattered light in both the stellar spectra and (quartz lamp spectra bv fitting a Ilow-order polynomial surface to the 74 inter-order minima of each column.," After subtracting an average nightly bias, we estimated scattered light in both the stellar spectra and quartz lamp spectra by fitting a low-order polynomial surface to the 74 inter-order minima of each column."894 Next. we extracted the stellar and quartz lamp spectra using an aperture extraction algorithm with fractional pixel weighting at the edges of the aperture.," Next, we extracted the stellar and quartz lamp spectra using an aperture extraction algorithm with fractional pixel weighting at the edges of the aperture."895 Since the orders are so narrow. it was necessaryto flat field the ARCES data using," Since the orders are so narrow, it was necessaryto flat field the ARCES data using"896conumuunitv.,community.897 Iu particular. we have introduced and described: απ alternative. off-the-shelf. casy wav fo POCuce ligh quality stereo pairs withTUON.. which we refer to as the imethod.," In particular, we have introduced and described an alternative, off-the-shelf, easy way to produce high quality stereo pairs with, which we refer to as the method."898. This echuique acapts he Toc-in procedure taking inte account the current μπατοι of plotting abilities. without affecting on the quality of the stereo ors.," This technique adapts the Toe-in procedure taking into account the current limitation of plotting abilities, without affecting on the quality of the stereo pairs."899 Specifically. no vertical parallax cau boe detected in the resulting stereo pairs.," Specifically, no vertical parallax can be detected in the resulting stereo pairs."900 Testing our sTi stereo airs on several studeuts aud astrouoimers at the Mouut Stromlo Observatory revealed that they represeut a eood trade-off. by being able to convey a satisfactory ecling of depth from any viewpoint. aud by being as effective as standard Toe-in stereo pairs with an elevation lower that ||~507.," Testing our sTi stereo pairs on several students and astronomers at the Mount Stromlo Observatory revealed that they represent a good trade-off, by being able to convey a satisfactory feeling of depth from any viewpoint, and by being as effective as standard Toe-in stereo pairs with an elevation lower that $|\theta_0|\sim50^{\circ}$."901 The tests also revealed hat sTi stereo pairs provide more depth structure around the data itself as compared to their equivalent Offset stereo pairs. and that the sTi method is in that respect more appropriate for creating stereo pairs iu Astrophysics. a fact already. observed by Peterkactal. (2009).," The tests also revealed that sTi stereo pairs provide more depth structure around the data itself as compared to their equivalent Offset stereo pairs, and that the sTi method is in that respect more appropriate for creating stereo pairs in Astrophysics, a fact already observed by \cite{Peterka09}."902. We have then used three examples. one idealized and two realistic. with which we have presented various vpes of stereo pairs. liehliehted. several aspects of stereoscopie visualization. and identified the main vcnehts of using stereo pairs as a complement to wore «andard plotting techniques in a publication.," We have then used three examples, one idealized and two realistic, with which we have presented various types of stereo pairs, highlighted several aspects of stereoscopic visualization, and identified the main benefits of using stereo pairs as a complement to more standard plotting techniques in a publication."903 First. they are a polyvalent tool that is adaptable ο one’s needs: them shape. size. aud color cau be adapted to best reveal the 3D data set witlout iupacting the ability to trausnüt a depth perception o the viewer.," First, they are a polyvalent tool that is adaptable to one's needs; their shape, size, and color can be adapted to best reveal the 3D data set without impacting the ability to transmit a depth perception to the viewer."904 Secoud. they profit amy multivariate a set. observational or theoretical. aud potentially onefit different genres of studies (e.g.. of both the heoretical and observational kind).," Second, they profit any multivariate data set, observational or theoretical, and potentially benefit different genres of studies (e.g., of both the theoretical and observational kind)."905 Third. they excatlv acilitate he communicaion of complex 23D shapes.," Third, they greatly facilitate the communication of complex 3D shapes."906" Especially, where a text description might be subject o interpretation. stereo pairs can force upon the viewer a unique view of the data set. thereby. avoiding ulsconceptions."," Especially, where a text description might be subject to interpretation, stereo pairs can force upon the viewer a unique view of the data set, thereby avoiding misconceptions."907 This is possibly the main factor that should dictate the use of stereoscopy in publications and preseutatious., This is possibly the main factor that should dictate the use of stereoscopy in publications and presentations.908 Foral hese reasons. stereo pairs should be cousidercd a valuable tool for the Ástroplivsiecs comunumuitv - a Ποια where most data sets are nultidinensional and nultivariate. and where stereo pairs cau be applied o inanv different sub-topics. but always with the conumion aim of simplifving. clarifving. aud eliuinatiug ulsconceptious.," For all these reasons, stereo pairs should be considered a valuable tool for the Astrophysics community - a field where most data sets are multidimensional and multivariate, and where stereo pairs can be applied to many different sub-topics, but always with the common aim of simplifying, clarifying, and eliminating misconceptions."909 The evolutiou of informatics las made stereo pairs aesthetic. useful. and straightforward to xoduce.," The evolution of informatics has made stereo pairs aesthetic, useful, and straightforward to produce."910 We are convinced that they have a promising uture. given the rapid evolution of 3D visualization αχσταο aud tecliniques. e.g.o 3D televisions.," We are convinced that they have a promising future, given the rapid evolution of 3D visualization hardware and techniques, e.g. 3D televisions."911 Although we «till ack a standardized API aud user-friendly software to couple the stereo images to the cisplav devices. these will likely be provided as soon as the need is identified.," Although we still lack a standardized API and user-friendly software to couple the stereo images to the display devices, these will likely be provided as soon as the need is identified."912 Shiniug astroplivsical data sets in 3D ou hand-held devices might sound futuristic., Sharing astrophysical data sets in 3D on hand-held devices might sound futuristic.913 Nonetheless. stereo pairs can already be casily stacked iuto a movie. and plaved ching a talk in a lecture theatre equipped with 3D xojection abilities. enabliug the audience to experience a elinipse of the 3D future for Astroplivsics.," Nonetheless, stereo pairs can already be easily stacked into a movie, and played during a talk in a lecture theatre equipped with 3D projection abilities, enabling the audience to experience a glimpse of the 3D future for Astrophysics."914 Iu couclusion. we are convinced that the ideas conceived through the ougoiug 3D trend currently: occurmiug iu the non-scientific community can aud ought to be used in Astrophysics.," In conclusion, we are convinced that the ideas conceived through the ongoing 3D trend currently occurring in the non-scientific community can and ought to be used in Astrophysics."915 Stereo pairs are a good wav to start opening our minds today., Stereo pairs are a good way to start opening our minds today.916 We thauk the referee for his/her comuueuts that helped ereatlv iuprove this paper., We thank the referee for his/her comments that helped greatly improve this paper.917 This research has made use of NASA’s Astroplivsics Data System., This research has made use of NASA's Astrophysics Data System.918 Part of this research was uudertakeun ou the NCT National Facility at the Australian National University aud some software used iu this work were in part developed by the DOE-supported ASC Alliance Ceuter for Ay.rophysical Thermonuclear Flashes at the University of Chicago., Part of this research was undertaken on the NCI National Facility at the Australian National University and some software used in this work were in part developed by the DOE-supported ASC / Alliance Center for Astrophysical Thermonuclear Flashes at the University of Chicago.919The formation epoch of galaxies has long been the of cosmology.,The formation epoch of galaxies has long been the of cosmology.920 Traditionally one of the most. popular and. successful wavs of elimpsing this epoch has been the analvsis of cxtragalactic source counts or more Commonly ealaxy number counts., Traditionally one of the most popular and successful ways of glimpsing this epoch has been the analysis of extragalactic source counts or more commonly galaxy number counts.921 Although originally intended. as a means of determining the geometry of the Universe this ool has shown to be much more viable ancl useful in the study of the evolutionary and star formation history of galaxies (Ixirshner ct al.(1981).. Ellis( LOs7))).," Although originally intended as a means of determining the geometry of the Universe this tool has shown to be much more viable and useful in the study of the evolutionary and star formation history of galaxies (Kirshner et \shortcite{kirshner81}, , \shortcite{ellis87}) )."922 In particular. he large dust. content of galaxies cliscovered by LAS and he strong Ix-corrections have mace the infra-red and more recently. the sub-mm. extremely important. wavebancds Lor he study. of galaxy evolution ancl cosmic star formation.," In particular, the large dust content of galaxies discovered by IRAS and the strong K-corrections have made the infra-red and more recently, the sub-mm, extremely important wavebands for the study of galaxy evolution and cosmic star formation."923 By modelling the counts of galaxies it has become possible to analyze the evolution of the galaxy population out to redshifts of unity ancl higher., By modelling the counts of galaxies it has become possible to analyze the evolution of the galaxy population out to redshifts of unity and higher.924 Coupled with the advent. of new observational data. galaxy number counts are poised to discriminate between rivalling evolutionary theories.," Coupled with the advent of new observational data, galaxy number counts are poised to discriminate between rivalling evolutionary theories."925 ]tecentIy. it has become the vogue to tackle the problem of the number distribution of galaxies in the Universe via one of two methods.," Recently, it has become the vogue to tackle the problem of the number distribution of galaxies in the Universe via one of two methods."926 The first (often called. the evolution approach (Lonsdale 1996))). takes the observed. present dav (2= 0) luminosity function. ancl evolves it in luminosity and/or density back out to higher redshifts assuming some paramoeterization of the evolution (Beichman Helou (1991).. Blain Longair (1993).. Pearson Robinson (1996).. Nu et al. (1998).," The first (often called the approach \cite{lonsdale96}) ), takes the observed, present day $z=0$ ) luminosity function and evolves it in luminosity and/or density back out to higher redshifts assuming some parameterization of the evolution (Beichman Helou \shortcite{beich91}, , Blain Longair \shortcite{blain93}, , Pearson Rowan-Robinson \shortcite{cpp96}, Xu et al. \shortcite{xu98},"927.. Takeuchi et al. (1999)))., Takeuchi et al. \shortcite{take99}) ).928 This method has the advantages that it is both direct. and relatively simple to implement with few [ree parameters ancl assumptions about the Universe at earlier times., This method has the advantages that it is both direct and relatively simple to implement with few free parameters and assumptions about the Universe at earlier times.929 The disadvantage inthepast was thattheinformation on which, The disadvantage inthepast was thattheinformation on which930We discuss the evolution of QSO/AGN activities uncer the Uv-wheel (rotation. driven). model which ⋠⋠is one of∙ the plausible models. for the powerful. engine of the ACGNs includingincludi a rotating‘.be central [blackholeblackhole (BIL.(BIL).,We discuss the evolution of QSO/AGN activities under the fly-wheel (rotation driven) model which is one of the plausible models for the powerful engine of the AGNs including a rotating central blackhole (BH).931| ‘ThisThis llv-wheellvcwheel engine. might- not be f.familiarii| comparingp: o.with: thehe f£fuel| enginev: (accretion IEEEdriven engine). however. this is very attractive becauseMUN this model can| explainbe the evolution ‘and the lifetime ol AGN activities- very naturally.," This fly-wheel engine might not be familiar comparing with the fuel engine (accretion driven engine), however, this is very attractive because this model can explain the evolution and the lifetime of AGN activities very naturally."932" [tism widely“1ly believedbelieve thatp recent""QUO discoveryISCOVOLY oft the Στοred tailEM of[omissionemission lines (Ee Ie) romfrom the central region of AGNAXCGNs SUGsuggestsECSIS thati the"" central.Cent xackblackholes ""woabesve. quickly ∙rotating Le. the monster BLE should be the IXerr. 1911. (see Tanaka et al."," It is widely believed that recent discovery of the red tail of emission lines (Fe $\alpha$ ) from the central region of AGNs suggests that the central blackholes are quickly rotating, i.e., the monster BH should be the Kerr BH (see Tanaka et al."933 1905. Lwasawa et al.," 1995, Iwasawa et al."934 19060. Dabrowski ct al.," 1996, Dabrowski et al."935 1997)., 1997).936 The innermost stable circular orbit around the Ixerr DII can intrudeintrucle more closeclo tc» the. horizonIv than: the| SchwartzschildSchwartzschi hole (non-rotating DII) of the same mass., The innermost stable circular orbit around the Kerr BH can intrude more close to the horizon than the Schwartzschild hole (non-rotating BH) of the same mass.937 Hence the line emission from the innermost region of the accretion disk should be considerably. red-shifted by the eravitation. and makes the red tail.," Hence the line emission from the innermost region of the accretion disk should be considerably red-shifted by the gravitation, and makes the red tail."938 From the theoretical point of view. the majority believes that the central DIE presumably. gets an enormous angular momenttun at the formation stage of the monster.," From the theoretical point of view, the majority believes that the central BH presumably gets an enormous angular momentum at the formation stage of the monster."939 For example. Sasaki Umoemura (1996) showed the formation scenario. by using. the Compton. crag process as follows.," For example, Sasaki Umemura (1996) showed the formation scenario by using the Compton drag process as follows."940⋅ After⋅ the neutralization⊀. of⋅ universe. at z~4107. density. Iluctuations. grow to form⋅ the proto-galactic⋠ cloud. and each Iluctuation. obtains. the angular momentum through the tical. interaction. among them.," After the neutralization of universe at $z \sim 10^3$, density fluctuations grow to form the proto-galactic cloud, and each fluctuation obtains the angular momentum through the tidal interaction among them."941 At the era z~2105. nuclear reactions. occur in. the central region. of⋅ the rotating. proto-galactie+ cloud. and the matters are reionized. by stellar WYEV radiation.," At the era $z \sim 10^2$, nuclear reactions occur in the central region of the rotating proto-galactic cloud, and the matters are reionized by stellar UV radiation."942"Dari EEThe rotating; reionized""E matters must interact; again. with. the uniformlylp distributed.. cosmic.. background radiation from the last scattered. surface.", The rotating reionized matters must interact again with the uniformly distributed cosmic background radiation from the last scattered surface.943 This interaction clliciently extracts the angular. momentum of the cloud material to the radiation field by the Compton scattering. then the angular momentum of the matter decreases. and when it gocs just below a critical value of the angular momentum. the matter suddenly. collapses ancl makes the quickly rotating monster blackho," This interaction efficiently extracts the angular momentum of the cloud material to the radiation field by the Compton scattering, then the angular momentum of the matter decreases, and when it goes just below a critical value of the angular momentum, the matter suddenly collapses and makes the quickly rotating monster blackhole."944accuracy.,accuracy.945" While the period of the transiting planet is constrained by the transits timing themselves, the mass is not well constrained because, to a good approximation, the amplitude of the TTVs does not depend on the mass of the transiting planet itself (Equation ??))regime."," While the period of the transiting planet is constrained by the transits timing themselves, the mass is not well constrained because, to a good approximation, the amplitude of the TTVs does not depend on the mass of the transiting planet itself (Equation \ref{eqn:ttv}) )."946" Finally, we remark that although the y? landscape allowed for several, well-separated local minima, both the SA and the MCMC algorithms were able to efficiently sample the parameter space."," Finally, we remark that although the $\chi^2$ landscape allowed for several, well-separated local minima, both the SA and the MCMC algorithms were able to efficiently sample the parameter space."947" Therefore, it is likely that global minimization routines will be part of the standard toolset to analyze the future ttransit datasets."," Therefore, it is likely that global minimization routines will be part of the standard toolset to analyze the future transit datasets."948" The bright nearby dwarf HAT-P-7 hosts a transiting hot Jupiter, first characterized by the HATNet project (Paletal.2008)."," The bright nearby dwarf HAT-P-7 hosts a transiting hot Jupiter, first characterized by the HATNet project \citep{Pal08}."949". The star is in the field of view of one of the ddetectors; ten days of photometric data, as processed by the pipeline, were obtained during the commissioning phase (Boruckietal.2009)."," The star is in the field of view of one of the detectors; ten days of photometric data, as processed by the pipeline, were obtained during the commissioning phase \citep{Borucki09_2}."950". Additional primary transits and a number of secondary eclipses were observed using and (Christiansenetal. 2010),, with the intent of studying the atmospheric properties of the planet."," Additional primary transits and a number of secondary eclipses were observed using and \citep{Christiansen10}, with the intent of studying the atmospheric properties of the planet."951 The EPOXI best-fit central times achieved an accuracy of σε.&1073 d (m1.5 minutes)., The EPOXI best-fit central times achieved an accuracy of $\sigma_{tr} \approx 10^{-3}$ d $\approx 1.5$ minutes).952" Given its extensive and diverse coverage, and the inclusion of this planet in the star list, we chose this system as a prototype of the class of massive transiting planets that will be monitored by the mission and may reveal TTVs."," Given its extensive and diverse coverage, and the inclusion of this planet in the star list, we chose this system as a prototype of the class of massive transiting planets that will be monitored by the mission and may reveal TTVs."953" In particular, we are interested in assessing the secure detection of a low-mass planet in a 2:1 MMR with the transiting gas giant (we consider only the case of an external perturber in the present analysis)."," In particular, we are interested in assessing the secure detection of a low-mass planet in a 2:1 MMR with the transiting gas giant (we consider only the case of an external perturber in the present analysis)."954magnetic field detection for the star. it might also be that this frequency detected in both the photometry and spectroscopy originates from low-amplitude surface inhomogeneities.,"magnetic field detection for the star, it might also be that this frequency detected in both the photometry and spectroscopy originates from low-amplitude surface inhomogeneities."955 We are unable to discriminate between these two options., We are unable to discriminate between these two options.956 In any case. we interpret the detection of all these modes with combination frequencies that are not excited by the heat mechanism in terms on a non-linear resonant mode excitation by the dominant radial mode. as already proposed in perll. That this mechanism seems to be at work and results in frequencies beyond the usual frequency regime of the 8 Cep stars Is supported by the low inertia of these modes refinertia)). which makes it much easier to excite them than low-order ¢ modes.," In any case, we interpret the detection of all these modes with combination frequencies that are not excited by the heat mechanism in terms on a non-linear resonant mode excitation by the dominant radial mode, as already proposed in I. That this mechanism seems to be at work and results in frequencies beyond the usual frequency regime of the $\beta\,$ Cep stars is supported by the low inertia of these modes \\ref{inertia}) ), which makes it much easier to excite them than low-order g modes."957 The high amplitude of the radial mode thus seems to trigger the excitation of p modes at frequencies between [8.5.20]cd.. which would otherwise be stable.," The high amplitude of the radial mode thus seems to trigger the excitation of p modes at frequencies between $[8.5,20]$, which would otherwise be stable."958 The results discussed for the model with M.= ΠΜ. remain qualitatively the same for the four other models listed in the upper part of refmodels..," The results discussed for the model with $M=11.4\,$ $_\odot$ remain qualitatively the same for the four other models listed in the upper part of \\ref{models}."959 We used the set of models that fulfil all the seismic requirements of the Cep-type modes. as well as the combination frequencies. to revisit the claim. of. solar-like oscillations in the star (Belkacem et 22009).," We used the set of models that fulfil all the seismic requirements of the $\beta\,$ Cep-type modes, as well as the combination frequencies, to revisit the claim of solar-like oscillations in the star (Belkacem et 2009)."960 In II. the authors already pointed out that the value found for a possible frequency spacing depends on the prewhitening procedure adopted to model the light curve.," In I, the authors already pointed out that the value found for a possible frequency spacing depends on the prewhitening procedure adopted to model the light curve."961 Moreover. it was found in PaperII that several of the modes with combination frequencies considered by Belkacem et ((2009). who made their computations for the frequency range 11.26]d.. are phase-locked. which is not what is expected for stochastic! forcing.," Moreover, it was found in I that several of the modes with combination frequencies considered by Belkacem et (2009), who made their computations for the frequency range $[11,26]\,$, are phase-locked, which is not what is expected for stochastic forcing."962 The interpretation of the residual light curve in terms of solar-like oscillations was also questioned by Balona et ((2011). in view of the lack of such oscillations inKepler data of B-type pulsators. because these data have higher precision than the CoRoT data.," The interpretation of the residual light curve in terms of solar-like oscillations was also questioned by Balona et (2011), in view of the lack of such oscillations in data of B-type pulsators, because these data have higher precision than the CoRoT data."963 One expects solar-like oscillations in stars with similar fundamental parameters than 1180642 to have comparable amplitudes. and these amplitudes would be far above the detection limit of data.," One expects solar-like oscillations in stars with similar fundamental parameters than 180642 to have comparable amplitudes, and these amplitudes would be far above the detection limit of data."964 In the sample of Balona et (2011). seven stars have an effective temperature above KK and are positioned in the joint part of the p Cep and SPB instability strips. but only one of these seven has a temperature close to the one of 1180642.," In the sample of Balona et (2011), seven stars have an effective temperature above K and are positioned in the joint part of the $\beta\,$ Cep and SPB instability strips, but only one of these seven has a temperature close to the one of 180642."965 This star’s variability is probably due to rotation and at the mmag level. Le.. a factor of more than ten below the one of our target. so the comparison between the Kepler stars and 1180642 in terms of solar-like oscillations is premature.," This star's variability is probably due to rotation and at the mmag level, i.e., a factor of more than ten below the one of our target, so the comparison between the Kepler stars and 180642 in terms of solar-like oscillations is premature."966 On the observational side. we made an extensive search for ridges in écchelle diagrams constructed for the CoRoT residual light curve of 1180642 discussed in PaperIL. adopting the same method as in the case of the CoRoT data of the OS.5V pulsator 446149 (Degroote et 22010b).," On the observational side, we made an extensive search for ridges in écchelle diagrams constructed for the CoRoT residual light curve of 180642 discussed in I, adopting the same method as in the case of the CoRoT data of the O8.5V pulsator 46149 (Degroote et 2010b)."967 In doing so. we considered numerous values for a large frequency spacing.," In doing so, we considered numerous values for a large frequency spacing."968 We failed to identify any ridges. in particular also for the value of the spacing reported in Belkacem et ((2009).," We failed to identify any ridges, in particular also for the value of the spacing reported in Belkacem et (2009)."969 This model-independent result stands in contrast to the clear ridges present in the écchelle diagram of 446149., This model-independent result stands in contrast to the clear ridges present in the écchelle diagram of 46149.970 A comparison between the écchelle diagram of 446149 and two for 1180642. one based on the large spacing by Belkacem et ((2009) and the most likely one reported in IL. is shown in refechelle..," A comparison between the écchelle diagram of 46149 and two for 180642, one based on the large spacing by Belkacem et (2009) and the most likely one reported in I, is shown in \\ref{echelle}."971 The recently discovered solar-like oscillations in the frequency regime above that of the heat-driven modes in a ὁ Sct star observed with the satellite did lead to clear ridges in the écchelle diagram of that star (Antochi et 22011). as is the case for 446149.," The recently discovered solar-like oscillations in the frequency regime above that of the heat-driven modes in a $\delta\,$ Sct star observed with the satellite did lead to clear ridges in the écchelle diagram of that star (Antochi et 2011), as is the case for 46149."972 We then considered our seismic models that explain all the modes of 1180642 in the frequency regime [0.20] in terms of heat-driven modes with non-linear mode couplings (listed in refmodels)).," We then considered our seismic models that explain all the modes of 180642 in the frequency regime $[0,20]\,$ in terms of heat-driven modes with non-linear mode couplings (listed in \\ref{models}) )."973 Irrespective of the cause of the power in the range [11.26]d ... we first computed all frequency differences between the axisymmetric mode frequencies of consecutive radial order for the same degree £ in that interval and compared all these spacing values with the one reported by Belkacem et (2009). with an allowed uncertainty ofed.," Irrespective of the cause of the power in the range $[11,26]\,$ , we first computed all frequency differences between the axisymmetric mode frequencies of consecutive radial order for the same degree $\ell$ in that interval and compared all these spacing values with the one reported by Belkacem et (2009), with an allowed uncertainty of."974. For themodel with M=11.4 Mes. this spacing occurs only once. Le.. between the £=3.710. σι and g» modes.," For themodel with $M=11.4\,$ $_\odot$, this spacing occurs only once, i.e., between the $\ell=3,m=0$, $_1$ and $_2$ modes."975 It also occurs once between the (=3.71=0. ps and py modes of the model with M—11.8 M. while it never occurs for the three other models in the upper part of refmodels..," It also occurs once between the $\ell=3,m=0$, $_3$ and $_4$ modes of the model with $M=11.8\,$ $_\odot$, while it never occurs for the three other models in the upper part of \\ref{models}. ."976 Subsequently. we computed all frequency differences for all the axisymmetric modes of £=0.....4 in the frequency interval |11.26]d.. to test) whether any particular spacing occurred.," Subsequently, we computed all frequency differences for all the axisymmetric modes of $\ell=0,\ldots,4$ in the frequency interval $[11,26]\,$, to test whether any particular spacing occurred."977 The outcome of these computations is shown in refspacingfie for the two models indicated in italics in refmodels.., The outcome of these computations is shown in \\ref{spacingfig} for the two models indicated in italics in \\ref{models}.978 It can be seen that no frequency spacing can be discerned among the model frequencies., It can be seen that no frequency spacing can be discerned among the model frequencies.979 We have managed to explain the extensive observational seismic input deduced from CoRoT and ground-based photometry along with high-resolution spectroscopy of the pCep star HD1180642 by means of present-day models.," We have managed to explain the extensive observational seismic input deduced from CoRoT and ground-based photometry along with high-resolution spectroscopy of the $\beta\,$ Cep star 180642 by means of present-day models."980 All of the 30 detected frequencies are fitted by model frequencies. of which 16 are predicted to be excited and 13 are combination frequencies that can be linked to the dominant radial fundamental mode with an extremely large amplitude for this type of pulsator.," All of the 30 detected frequencies are fitted by model frequencies, of which 16 are predicted to be excited and 13 are combination frequencies that can be linked to the dominant radial fundamental mode with an extremely large amplitude for this type of pulsator."981 Our modelling resulted in a mass between 11.4 and ΜΜ. and a zero or very low core overshooting parameter. along with an age of between 12 and 13 million years (corresponding to a central hydrogen fraction between 0.2] and 0.25) if we allow an excitation problem for only one of the independentoscillation modes. namely for the £62 3. py mode with a frequency cd.. This is a frequency regime where similar excitation problems have been found for this type ofpulsator (e.g.. Dziembowski," Our modelling resulted in a mass between 11.4 and $_\odot$ and a zero or very low core overshooting parameter, along with an age of between 12 and 13 million years (corresponding to a central hydrogen fraction between 0.21 and 0.25) if we allow an excitation problem for only one of the independentoscillation modes, namely for the $\ell=3$ , $_1$ mode with a frequency This is a frequency regime where similar excitation problems have been found for this type ofpulsator (e.g., Dziembowski"982the November/December 2006 eclipse.,the November/December 2006 eclipse.983 We suggest that this is the reason for the rapid increase in emission of the Balmer lines. particularly in Πα. observed in the second half of 2006.," We suggest that this is the reason for the rapid increase in emission of the Balmer lines, particularly in $\alpha$, observed in the second half of 2006."984 We note that the luminosity in the Balmer emission lines. ϱominated by Πα. as observed by Munarietal.(2007a) c=ring the eclipse. was ~3.5L« (assuming Epg-\=0.9 and a 8 kpe distance to V838 Mon).," We note that the luminosity in the Balmer emission lines, dominated by $\alpha$, as observed by \cite{mun07} during the eclipse, was $\sim 3.5\,L_\odot$ (assuming $E_{B-V} = 0.9$ and a 8 kpc distance to V838 Mon)."985" Thus. the accretion, as estimated above. can provide enough energy to explain the observed luminosity in the Balmer lines."," Thus, the accretion, as estimated above, can provide enough energy to explain the observed luminosity in the Balmer lines."986"relsec:resu relsec:dise Vy. p, Po. of bo! AZ!=AZ(1—f) //r7.eGoD c ez>=5p/p/ 7? (5=1). py=pele)Vy=Vielrir M,. [2]]) p,(rr)=M,/tare?τή).yeas ar>7 [3]]) Parker(1958). ",\\ref{sec:resu} \\ref{sec:disc} $\vct{V_w}$ $\rho_w$ $\Phi_\ast^{\rm eff}$ $\Phi_\ast^{\rm eff}$ $M_\ast^{\rm eff}=M_\ast(1-f)$ $f/r^2$ $\cs$ $\cs^2=\gamma p/\rho$ $\gamma$ $\gamma=1$ $\rho_w=\rho_w(r)$$\vct{V_w}=V_w(r)\het{r}$ $\dot{M}_\ast$ \ref{equ:conw}] $\rho_w(r)=\dot{M}_\ast/4\pi r^2 V_w(r)$ $r^{-2}$ \ref{equ:momw}] \citet{par58} 987(2000).,(2000).988 By comparing this number with that found. with the same aperture ancl colour selection. applied. to olfset Gelds we determine that roughly of these are Ποιά ealaxies. and correct Noy by this factor.," By comparing this number with that found with the same aperture and colour selection applied to offset fields we determine that roughly of these are field galaxies, and correct $N_{\rm cl}$ by this factor."989 Using Kk-corrections of Menanteau (1999) we may determine what //- and I-band magnitudes these cluster galaxies would have if the cluster were shifted to higher redshift. and what [raction of those galaxies would then be brighter than the limiting magnitudes of //=22 and J= 24.5.," Using $k$ -corrections of Menanteau (1999) we may determine what $H$ - and $I$ -band magnitudes these cluster galaxies would have if the cluster were shifted to higher redshift, and what fraction of those galaxies would then be brighter than the limiting magnitudes of $H=22$ and $I=24.5$ ."990 At each redshift. we measure σ of the field counts in an aperture corresponding to the angular size of the physical aperture at that redshift. and calculate the contrast. m...," At each redshift we measure $\sigma_f$ of the field counts in an aperture corresponding to the angular size of the physical aperture at that redshift, and calculate the contrast, $\sigma_c$."991 Fig., Fig.992 1 shows the results ofthis calculation., \ref{fig-contrast} shows the results of this calculation.993 Abell 2219 itself at 2=0.22 vields a do detection in the and à Se detection in the Z/-band., Abell 2219 itself at $z=0.22$ yields a $4\sigma$ detection in the and a $5\sigma$ detection in the $H$ -band.994 To the 36 level we would be able to see such a cluster to z=0.9 in / and z=L4 in 441., To the $3\sigma$ level we would be able to see such a cluster to $z=0.9$ in $I$ and $z=1.4$ in $H$.995 This demonstrates the advantage of searching for clusters in the infrared: for a given cluster. the contrast is ercater and remains greater to much higher redshift. due to the advantageous elfects of the and reduce numbers of field galaxies.," This demonstrates the advantage of searching for clusters in the infrared: for a given cluster, the contrast is greater and remains greater to much higher redshift due to the advantageous effects of the and reduced numbers of field galaxies."996 ΕΕ the unexplained mass detection of Erben (2000) were the result. of a high-redshif cluster similar to Abell 1942 or Abell 2219. then for a limiting magnitude Jf=22 we would expect to be able to make a 0>4 detection in the to the redshif limit they present for such a cluster.," If the unexplained mass detection of Erben (2000) were the result of a high-redshift cluster similar to Abell 1942 or Abell 2219, then for a limiting magnitude $H=22$ we would expect to be able to make a $\sigma>4$ detection in the to the redshift limit they present for such a cluster."997 For such à magnitude limit we may also determine how poor a cluster we could. detect., For such a magnitude limit we may also determine how poor a cluster we could detect.998 For a cluster at 2= Fig., For a cluster at $z=1$ Fig.999 1 shows that a richness class HE cluster has o.75., \ref{fig-contrast} shows that a richness class III cluster has $\sigma_c \simeq 5$.1000 We would therefore. detect a cluster at that redshift) with 3/5 as many galaxies at the 36 level., We would therefore detect a cluster at that redshift with 3/5 as many galaxies at the $3 \sigma$ level.1001 Using the relations between numbers. richness. and. mass of van. lINampen Ixatgert. (1997) this means that to ff=22 we would. be able to detect a cluster with roughly the mass of Abell 2219. or a richness class LL cluster.," Using the relations between numbers, richness, and mass of van Kampen Katgert (1997) this means that to $H=22$ we would be able to detect a cluster with roughly the mass of Abell 2219, or a richness class II cluster."1002 Infrared. imaging data for the rich cluster Abell 1942 (2= 0.224) were taken over four nights in February ancl March 2000 using the Cambridge Infrared. Survey Instrument (CIRSL. Beekett 1998) on the 2.5m du Pont telescope at Las Campanas. Chile.," Infrared imaging data for the rich cluster Abell 1942 $z=0.224$ ) were taken over four nights in February and March 2000 using the Cambridge Infrared Survey Instrument (CIRSI, Beckett 1998) on the 2.5m du Pont telescope at Las Campanas, Chile."1003 CIRSE is a wide-field: infrared imager composed of four Ly 1 Rockwell Hawai HegCd'Ie detectors. with a gap of approximately one cetector width between cach array.," CIRSI is a wide-field infrared imager composed of four 1K $\times$ 1K Rockwell Hawaii HgCdTe detectors, with a gap of approximately one detector width between each array."1004 On the Dupont telescope the pixel scale is 0.2 aresec/pixel. corresponding to a field of view of 3.4.3.4 arcmin for each detector.," On the Dupont telescope the pixel scale is 0.2 arcsec/pixel, corresponding to a field of view of $3.4 \times 3.4$ arcmin for each detector."1005 The instrument pointing was arranged so that one chip inmaged the core of Abell 1942. one chip imaged the dark lump region as indicated by the mass maps of Erben (2000). and the remaining two chips covered adjacent blank skv regions.," The instrument pointing was arranged so that one chip imaged the core of Abell 1942, one chip imaged the dark lump region as indicated by the mass maps of Erben (2000), and the remaining two chips covered adjacent blank sky regions."1006 This configuration ensured. that. the infrared data would overlap the existing CELT UlISI image (whieh has a similar pixel size of 0.24 arcesec/pixel) whilst providing essential background field count data., This configuration ensured that the infrared data would overlap the existing CFHT UH8K image (which has a similar pixel size of 0.24 arcsec/pixel) whilst providing essential background field count data.1007 The deep CLIE observations were mace using 45 second exposures with a nine-point dither pattern., The deep CIRSI observations were made using 45 second exposures with a nine-point dither pattern.1008 Typically three or four exposures were taken at cach dither position. followed. by an ollset of 9 or 15 arcsec.," Typically three or four exposures were taken at each dither position, followed by an offset of 9 or 15 arcsec."1009 Table 1 summzrizes the observations., Table \ref{tab-obs} summarizes the observations.1010 The CIRSL data were reduced. using the pipeline developed. by one of us (JRL) for the Las Campanas lnfrared Survey (Alarzke 1999. Firth 2000).," The CIRSI data were reduced using the pipeline developed by one of us (JRL) for the Las Campanas Infrared Survey (Marzke 1999, Firth 2000)."1011 Flat Ποια. frames. were created from. come Lats ancl back pixel masks constructed. from the data., Flat field frames were created from dome flats and bad pixel masks constructed from the data.1012 The images at cach dither position were coadcdecl and Gat fielded. followed: by a first-pass sky subtraction.," The images at each dither position were coadded and flat fielded, followed by a first-pass sky subtraction."1013 Object masks were constructed for the sky-subtracted images and these masks were used to perform a second-pass running sky subtraction on the original images., Object masks were constructed for the sky-subtracted images and these masks were used to perform a second-pass running sky subtraction on the original images.1014 A reset anomaly present in the data was corrected by median filtering the rowsand columns of cach quacrant of cach image., A reset anomaly present in the data was corrected by median filtering the rowsand columns of each quadrant of each image.1015 The olfscts between images due to the dithering pattern were calculated. and a tangent plane," The offsets between images due to the dithering pattern were calculated, and a tangent plane"1016We applied. our methods to the erouncd-basecl data of he “Pres Lyrl field. which is also observed by the satellite.,"We applied our methods to the ground-based data of the TrES Lyr1 field, which is also observed by the satellite."1017 We found non-radial pulsators such as 3 Cop stars. ὃ Set stars. SPB stars. and ~ Dor stars.," We found non-radial pulsators such as $\beta$ Cep stars, $\delta$ Sct stars, SPB stars, and $\gamma$ Dor stars."1018 Because of lack of »ecise and dereddened information. and because of overlap in frequency range we could. however. sometimes not avoic confusion between 3 Cep and 9 Set stars. on one hand. ane οποσα SPB and > Dor stars on the other hand.," Because of lack of precise and dereddened information, and because of overlap in frequency range we could, however, sometimes not avoid confusion between $\beta$ Cep and $\delta$ Sct stars, on one hand, and between SPB and $\gamma$ Dor stars on the other hand."1019 Besides non-racdial pulsators we also mention the detection of binary stars and some classical racial pulsators., Besides non-radial pulsators we also mention the detection of binary stars and some classical radial pulsators.1020 The results of his classification will be made available through electronic ables., The results of this classification will be made available through electronic tables.1021 The research leading to these results has received. funding rom the European Research Council under the European Communitys Seventh Framework Programme (PPT/2007POLIS)AERC grant agreement n 227224 (PROSPERITY). rom the Research Council of KULeuven (GOA/2008(0-4). rom the Lund for Scientific Research of Flanders (€.0332.06). trom the Beleian federal science policy οσο (C90309: CoRoT Data Lxploitation. C90291. Caia-DPAC). and from the Spanish Ministerio de Educacionn v Ciencia through grant AYA2005-04286.," The research leading to these results has received funding from the European Research Council under the European Community's Seventh Framework Programme (FP7/2007--2013)/ERC grant agreement $^\circ$ 227224 (PROSPERITY), from the Research Council of K.U.Leuven (GOA/2008/04), from the Fund for Scientific Research of Flanders (G.0332.06), from the Belgian federal science policy office (C90309: CoRoT Data Exploitation, C90291 Gaia-DPAC), and from the Spanish Ministerio de Educaciónn y Ciencia through grant AYA2005-04286."1022 Public access o the Tres cata were provided to the through he NASA Star and. Exoplanct Database (ΝΟ). Περι/nsted.ipac.caltech.edu)," Public access to the TrES data were provided to the through the NASA Star and Exoplanet Database (NStED, http://nsted.ipac.caltech.edu)."1023ns stand for relativistic object and optical star mass. respectively).,"$m_v$ stand for relativistic object and optical star mass, respectively)."1024" Taken at face value. these q.A, values would lead to the optical star nass function f,z312M. and the binary component masses ni,=18M.. 2LM.."," Taken at face value, these $q, K_v$ values would lead to the optical star mass function $f_v\approx 3.12 M_\odot$ and the binary component masses $m_x=18 M_\odot$, $m_v=24 M_\odot$ ."1025 However. such a large mass ratio ix dn a strong disagreenient with the observed duration of the N-ray eclipse. which sugeests a nmmuch sualler mass ratio 4~(20 0.3.," However, such a large mass ratio is in a strong disagreement with the observed duration of the X-ray eclipse, which suggests a much smaller mass ratio $q\sim 0.2-0.3$ ."1026" We stress that the binary inclination angle iu SS133 (;/= TN"".S) is fixcc frou the analysis of moving Chussion lines.", We stress that the binary inclination angle in SS433 $i=78^o.8$ ) is fixed from the analysis of moving emission lines.1027" There are two possibilitics: (1) either the model we used to fit Nav. eclipses should »» mnocdified. or (2) the value of A, and A, are mflueuce by additional plivsical effects."," There are two possibilities: (1) either the model we used to fit X-ray eclipses should be modified, or (2) the value of $K_x$ and $K_v$ are influenced by additional physical effects."1028 Although there are some reasons to modify the uodel (e.g.. the asvunuetric shape of the hard N-rav eclipse. which may sueecst an asvuuuetric wind outflow roni the ilhuninated part of the optical star aud wiud-wind collision). we shall consider here oulv the second yossibilitv.," Although there are some reasons to modify the model (e.g., the asymmetric shape of the hard X-ray eclipse, which may suggest an asymmetric wind outflow from the illuminated part of the optical star and wind-wind collision), we shall consider here only the second possibility."1029" The reason is that the actual value of A, should be decreased in order to account for the observed jcatiug effect.", The reason is that the actual value of $K_v$ should be decreased in order to account for the observed heating effect.1030 Let us assume the ass ratio iu the system to be 4— L3. as with this value we can satisfactorily describe the width of X-ray eclipse aud the observed X-ray precessio- wuplitude (see Fie. 103).," Let us assume the mass ratio in the system to be $q=0.3$ , as with this value we can satisfactorily describe the width of X-ray eclipse and the observed X-ray precession amplitude (see Fig. \ref{fig:jthick}) )."1031" Taliug A,=132 |au/s vicld:4. focBAAL.. aud in,=GAL... in,=206M.. IK,=Ll aus. Clearly this is an unacceptable model."," Taking $K_v=132$ km/s yields $f_v\approx 3.1 M_\odot$ and $m_x=62 M_\odot$, $m_v=206 M_\odot$, $K_x=440$ km/s. Clearly, this is an unacceptable model."1032" Now let ww4. decrease A, down to 85 kms. the lower lait hat follow:μα roni a more accurate treatment of the heating effect in he racial velocity curve analysis (Wade aud Iorue Loss. Autokhina et al."," Now let us decrease $K_v$ down to 85 km/s, the lower limit that follows from a more accurate treatment of the heating effect in the radial velocity curve analysis (Wade and Horne 1988, Antokhina et al."1033 2005)., 2005).1034" This would vield a better fit with my=AL. ny,=OAL... aud A,=283 lau/s. still too Hel to be acceptable."," This would yield a better fit with $m_x=17 M_\odot$, $m_v=55 M_\odot$, and $K_x=283$ km/s, still too high to be acceptable."1035 Less than half of the stellar surface is sufficiently cool to eive the absorption lines πιο: study (e.g. due to sideway heating from scattered UV radiation in the strong accretion disk wind)., Less than half of the stellar surface is sufficiently cool to give the absorption lines under study (e.g. due to sideway heating from scattered UV radiation in the strong accretion disk wind).1036 This additionally decreases the value of the actual radial velocity wuplitude., This additionally decreases the value of the actual radial velocity semi-amplitude.1037 Fie., Fig.1038 19. illustrates these considerations., \ref{fig:illum} illustrates these considerations.1039" So taking. for cxample. A,=TO lkin/s aud 4= vields the optical star mass functiou f,=0.16A... Dinary lasses iy=OAL... Ny.=2041, and the optical star radius δρ~LOR..."," So taking, for example, $K_v=70$ km/s and $q=0.3$ yields the optical star mass function $f_v=0.46 M_\odot$, binary masses $m_x=9 M_\odot$, $m_v=30 M_\odot$ and the optical star radius $R_v\sim 401040R_\odot$."1041" This radius is compatible with a typical bolometyic huniuositv of a 30... A5-AT supereiant with Ty,8500 Is. Iu this solution. A,2233 kan/s. larger than the measured value 175 ans. but the true value of A, iav be affected by the strong accretion disk wiud."," This radius is compatible with a typical bolometric luminosity of a $30 M_\odot$ A5-A7 supergiant with $T_{eff}\sim 8500$ K. In this solution, $K_x\simeq 233$ km/s, larger than the measured value 175 km/s, but the true value of $K_x$ may be affected by the strong accretion disk wind."1042" The interpretation of the binary parameters presented above is stronely based on the binary mass ratio q=0.3 as inferred frou, modeling the observatious of the hard XN-rav eclipse with account of the observed auplitude (~ 1) of the hard N-vav precessional variability of the system.", The interpretation of the binary parameters presented above is strongly based on the binary mass ratio $q=0.3$ as inferred from modeling the observations of the hard X-ray eclipse with account of the observed amplitude $\sim 4$ ) of the hard X-ray precessional variability of the system.1043 The model we use (an optical star filling its Roche lobe | thick accretion disk with a hot corona) is sniplistic and cannot perfectly reproduce the appareut asvuuuetric shape of the N-rav eclipse., The model we use (an optical star filling its Roche lobe + thick accretion disk with a hot corona) is simplistic and cannot perfectly reproduce the apparent asymmetric shape of the X-ray eclipse.1044 Iu the real situation. an adcditiona N-rav absorption bv outflowing eascous streams. exteuded stella: envelope or wind secs quite plausible.," In the real situation, an additional X-ray absorption by outflowing gaseous streams, extended stellar envelope or wind seems quite plausible."1045 If we interpret the complex shape of the hard N-ray ceressC» as beue[m] due to additional variable absorption effects. we obtain the geometry of the hard N-ray cluitting region m the form of au exteuded oblate corona over the accretion disk.," If we interpret the complex shape of the hard X-ray egress as being due to additional variable absorption effects, we obtain the geometry of the hard X-ray emitting region in the form of an extended oblate corona over the accretion disk."1046 IHToscever. a straightforward interpretation of the join spectrum of the source observed in March: 2001 is also possible by a single thermal cussion with a temperature of ~30 keV. No additional cutting region is required to fit this broadband Nay spectrin.," However, a straightforward interpretation of the joint spectrum of the source observed in March 2004 is also possible by a single thermal emission with a temperature of $\sim 30$ keV. No additional emitting region is required to fit this broadband X-ray spectrum."1047 There are two possible solutions., There are two possible solutions.1048 First. we could trv to describe the observed hard N-rav spectrum. by a more coniplex model involving two components. a hot corona | cooler thin jet radiatius5 in the standard N-rav baud.," First, we could try to describe the observed hard X-ray spectrum by a more complex model involving two components, a hot corona + cooler thin jet radiating in the standard X-ray band."1049 Second. we could try to accept the thin cooling jet interpretation of the XN-rav spectra. but then would wave to adiuit a differcut shape of the N-rav eclipse.," Second, we could try to accept the thin cooling jet interpretation of the X-ray spectrum, but then would have to admit a different shape of the X-ray eclipse."1050 Our nodeling shows that a thin short jet could reproduce he observed amplitude (—1) of lard N-rav precessional variability in SS133., Our modeling shows that a thin short jet could reproduce the observed amplitude $\sim 4$ ) of hard X-ray precessional variability in SS433.1051 Iun that case. the shape of the N-rav eclipse inust be more sharp. with shorter ineress/ceress iues than actually observed (cf.," In that case, the shape of the X-ray eclipse must be more sharp, with shorter ingress/egress times than actually observed (cf."1052 Fig. 9))., Fig. \ref{fig:jthin_s}) ).1053 Tf we look at 1ο data. such a shape cau indeed be found at the egress ase of the eclipse (see Fig. 6)).," If we look at the data, such a shape can indeed be found at the egress phase of the eclipse (see Fig. \ref{fig:eclips_Xop}) )."1054 The (apparently longer) ineress fine could be due to additional (apart from the opaque star body) absorption of hard X-ray cussion by au optically thick gascous stream outfowine from the optical star., The (apparently longer) ingress time could be due to additional (apart from the opaque star body) absorption of hard X-ray emission by an optically thick gaseous stream outflowing from the optical star.1055 Apparently the same smooth ingress aud egress shape of the eclipse in softer N-ravs (the aud data) in that case coul be due to the soft X-ray ciitting region located urther upstream of the jets., Apparently the same smooth ingress and egress shape of the eclipse in softer X-rays (the and data) in that case could be due to the soft X-ray emitting region located further upstream of the jets.1056 This interpretation also explains the shallower soft N-rav. eclipse., This interpretation also explains the shallower soft X-ray eclipse.1057 Clearly im this situation we need more observations of the hard XN-rav eclipse to confini the asvuuuctric Ineress/ceress eclipse shape aud flatuess of its bottoni.," Clearly, in this situation we need more observations of the hard X-ray eclipse to confirm the asymmetric ingress/egress eclipse shape and flatness of its bottom."1058 We hope to do this in future obscrvatious of SS133., We hope to do this in future observations of SS433.1059 The results of the observations of the peculiar diunrv svstem S$133 in 2003-2001 can be stmarized as ollows., The results of the observations of the peculiar binary system SS433 in 2003-2004 can be summarized as follows.1060 1l., 1.1061" Ward X-ray eaission up to LOO keV was discovered roni this superaccretiug nücroquasar with uneclipsed jud Xaay luminosity close to the maximum opening xecessjon phase L£,.(18GÜkeV)~Ls1075 erg/s. L.(GO—120keV)~2«107 erg/s (assuming the 5 kpe distance to SS133). which is about of tle soft N-ray jet luminosity."," Hard X-ray emission up to $\sim 100$ keV was discovered from this superaccreting microquasar with uneclipsed hard X-ray luminosity close to the maximum opening precession phase $L_x(18-60 \hbox{keV})\sim 4\times 10^{35}$ erg/s, $L_x(60-120 \hbox{keV})\sim 2\times 10^{35}$ erg/s (assuming the 5 kpc distance to SS433), which is about of the soft X-ray jet luminosity."1062total magnification of a point source with one image at the same location as the RBA] image is shown as the dashed. line.,total magnification of a point source with one image at the same location as the RBM image is shown as the dashed line.1063 Bunelle positions within ας=0.5 produce magnifications slat1., Bundle positions within $x=0.5$ produce magnifications $\mu_{\rm RBM} \ll 1$.1064 For these bundles we actually selected the fainter of the images. as opposed to the case considered. previously. where we purposefully. selected. the bundle corresponding to the brighter image.," For these bundles we actually selected the fainter of the images, as opposed to the case considered previously, where we purposefully selected the bundle corresponding to the brighter image."1065 Solutions of the lens equation.x3).. which produce an image near the lens (Ge.5 1) correspond. to total magnifications near ye=1l. as the source is far from the caustic point (ycLer» 1).," Solutions of the lens equation, which produce an image near the lens $x_- \lesim 1$ ) correspond to total magnifications near $\mu = 1$, as the source is far from the caustic point $y \simeq - 1/x_- > 1$ )."1066 This is demonstrated with the thin solid line inFigure4.. where we plot rav. bundles with jjx1 within the Einstein radius as j/—ye|I.," This is demonstrated with the thin solid line in, where we plot ray bundles with $\mu \leq 1$ within the Einstein radius as $\mu^{\prime} = \mu + 1$."1067 Lt is clear that à small strip of image locations near the critical curve is responsible for the high magnification region of the MPLI. for which the Ray Bundle method is not well sulted.," It is clear that a small strip of image locations near the critical curve is responsible for the high magnification region of the MPH, for which the Ray Bundle method is not well suited."1068 Images well within the Einstein radius correspond. to sources [ar from the lens axis., Images well within the Einstein radius correspond to sources far from the lens axis.1069 Such images are the faint images described in (at arai). and so there will be à second image at zug which contributes the majority of the Lux.," Such images are the faint images described in (at $\bvec{x}_{\rm faint}$ ), and so there will be a second image at $\bvec{x}_{\rm bright}$ which contributes the majority of the flux."1070 Although it is not. possible to solve for amisi GIVEN Bian. d£ the entire image plane is well sampled. with rav bundles. then we can expect that another bundle will pass through wien and the source magnification will be calculated on the basis of this second. bundle only.," Although it is not possible to solve for $\bvec{x}_{\rm bright}$ given $\bvec{x}_{\rm faint}$, if the entire image plane is well sampled with ray bundles, then we can expect that another bundle will pass through $\bvec{x}_{\rm bright}$ and the source magnification will be calculated on the basis of this second bundle only."1071 Two restrictions are now imposed on the Ray Bunelle method for its later application to ensembles of lenses. which serve to complete the definition of the method.," Two restrictions are now imposed on the Ray Bundle method for its later application to ensembles of lenses, which serve to complete the definition of the method."1072 Firstly. image positions within the Einstein radius. or equivalentIv. any magnifications which arecalculated to be jp<1 are discarded.," Firstly, image positions within the Einstein radius, or equivalently, any magnifications which arecalculated to be $\mu < 1$ are discarded."1073 Secondly. after selecting a relative error for fist. we do not include images which fall within cau Einstein radii of any given lens.," Secondly, after selecting a relative error for $\mu_{\rm RBM}$, we do not include images which fall within $x_{\rm cut}$ Einstein radii of any given lens."1074 Having shown that in the ‘weak’ lensing limit (Jar-| 222). we can be sure of caleulating the magnification to within 5 per cent (or better) using Nya.zcd we can now proceed. to a statistical comparison between the Ray Shooting and Rav A3undle methods.," Having shown that in the `weak' lensing limit $\vert \bvec{x}_{\rm c} 1075\vert \gesim 2$ ), we can be sure of calculating the magnification to within $5$ per cent (or better) using $N_{\rm ray} \ge 4$ we can now proceed to a statistical comparison between the Ray Shooting and Ray Bundle methods."1076 Next we compare the ALPL obtained with the BAL and the 15M., Next we compare the MPH obtained with the RBM and the RSM.1077 A number of subtle cdilferences exist between the two methods. even when applied to the same lens model.," A number of subtle differences exist between the two methods, even when applied to the same lens model."1078 The source size investigated is limited by the number of pixels in the source plane for the RSAL, The source size investigated is limited by the number of pixels in the source plane for the RSM.1079" For a grid of ΑνNyis Covering a square region PifuasoZyhuax. the source ""radius? is αν=fux/Npis-"," For a grid of $N_{\rm pix} \times N_{\rm pix}$ covering a square region $2 y_{\rm max} \times 2 y_{\rm max}$, the source `radius' is $R_{\rm s} = y_{\rm max}/N_{\rm pix}$."1080 We choose the RSAL sources to be squares with a side-length. equal to the diameter of the circular. RBAL image bundles., We choose the RSM sources to be squares with a side-length equal to the diameter of the circular RBM image bundles.1081 Since the magnification decreases as the source area ds increased. we expect each RSAL source to have a systematically smaller magnification than the corresponding RBAL image.," Since the magnification decreases as the source area is increased, we expect each RSM source to have a systematically smaller magnification than the corresponding RBM image."1082 Lt is possible to use a much finer resolution &erid lor the rav shooting. and then integrate over a larger source size. but we have elected not to do this.," It is possible to use a much finer resolution grid for the ray shooting, and then integrate over a larger source size, but we have elected not to do this."1083 This decision was based on a comparison of the computation time: for our implementation of the RSAL a grid. of 1000100ῦ pixels. with an average of No=25O ravs per pixels took approximately eight. hours of computation time.," This decision was based on a comparison of the computation time: for our implementation of the RSM, a grid of $1000 \times 1000$ pixels, with an average of $\bar{N} = 250$ rays per pixels took approximately eight hours of computation time."1084" An equivalent number of images (where IN,4,—8) is completed in 1 minute with the Due to the distortion of ravs near the boundary. as shown in5.. we actually shoot ravs with the IM hrough a larger angular region in the image plane."," An equivalent number of images (where $N_{\rm ray} =8$ ) is completed in 1 minute with the Due to the distortion of rays near the boundary, as shown in, we actually shoot rays with the RSM through a larger angular region in the image plane."1085 This events us from including source pixels which are not well sampled by ravs., This prevents us from including source pixels which are not well sampled by rays.1086 The accuracy of the RSAL magnifications depends on he average number of ravs collected in each pixel. NV.," The accuracy of the RSM magnifications depends on the average number of rays collected in each pixel, $\bar{N}$."1087" Since we are not implementing a (fast) hierarchical method. the ime required. to obtain the magnification distribution is ooportional to the total number of ravs. Nasa,=NN pin: "," Since we are not implementing a (fast) hierarchical method, the time required to obtain the magnification distribution is proportional to the total number of rays, $N_{\rm RSM} = \bar{N} N_{\rm pix}^2$ ."1088The RSAL does not fully sample the highest. magnification region (ff7fhyax) due to the regularplacement of sources on a grid., The RSM does not fully sample the highest magnification region $(\mu \approx \mu_{\rm max})$ due to the regularplacement of sources on a grid.1089" With the RBAI image size fixed by A,=£F. we are left to choose the number of ravs which make up the ray bundle. Nive. and the number of images."," With the RBM image size fixed by $R_{\rm i} = R_{\rm s}$, we are left to choose the number of rays which make up the ray bundle, $N_{\rm ray}$, and the number of images."1090 Ideally we want the images to completely cover the image plane (which again has a slightly larger angular size than the source plane due to the dellection of light ravs near the boundaries) which requires where f is (approximately) the fraction of the sourceplane covered by sources., Ideally we want the images to completely cover the image plane (which again has a slightly larger angular size than the source plane due to the deflection of light rays near the boundaries) which requires where $f$ is (approximately) the fraction of the sourceplane covered by sources.1091 For the RBAL then. the total number of ravs required is Αν—Nuusc New.," For the RBM then, the total number of rays required is $N_{\rm RBM} = N_{\rm image} \times N_{\rm ray}$ ."1092 The comparative computational speed. ancl resulting magnification. accuracy may be obtained by requiring Nip=Nps., The comparative computational speed and resulting magnification accuracy may be obtained by requiring $N_{\rm RBM} = N_{\rm RSM}$.1093 Setting f—1 and 2— Ro. we have," Setting $f = 1$ and $R_{\rm i} = R_{\rm s}$ , we have"1094mid-2009. revealing in exquisite new detail the abundance of low surface brightness substructure present in the M31 halo (MeConnachieetal.2009.seealsoFig.1)..,"mid-2009, revealing in exquisite new detail the abundance of low surface brightness substructure present in the M31 halo \citep[][see also Fig. 1]{mcconnachie:09}."1095 We consider a globular cluster. ensemble defined by confirmed objects in V3.5 of the Revised Bologna Catalogue (RBC:e.g..Galletietal.2007) plus newly-discovered clusters from the first semester of PAndAS imaging.," We consider a globular cluster ensemble defined by confirmed objects in V3.5 of the Revised Bologna Catalogue \citep[RBC; e.g.,][]{galleti:07} plus newly-discovered clusters from the first semester of PAndAS imaging."1096 In this work we are primarily interested in globular clusters lying outside Ry=30 kpe (see below)., In this work we are primarily interested in globular clusters lying outside $R_{{\rm p}}=30$ kpc (see below).1097 The RBC list of confirmed globular clusters includes 41 objects discovered in our pre-PAndAS ΜΟΙ surveys (Martinetal.2006:Huxor 2008).. of which 31 fall beyond 30 kpc.," The RBC list of confirmed globular clusters includes $41$ objects discovered in our pre-PAndAS M31 surveys \citep{martin:06,huxor:08}, of which $31$ fall beyond $30$ kpc."1098 The RBC also contains three clusters outside 30 kpe not discovered by us., The RBC also contains three clusters outside $30$ kpc not discovered by us.1099"We retain all RBC entries defined as ""extended clusters” (Huxoretal.2005.2008).","We retain all RBC entries defined as “extended clusters” \citep{huxor:05,huxor:08}."1100. At present there is little evidence that these are anything other than globular clusters with peculiarly diffuse structures (Huxoretal.2010a).. at least in terms of their constituent stellar populations (Mackeyetal.2006) and internal dynamics (Collinsetal.2009).," At present there is little evidence that these are anything other than globular clusters with peculiarly diffuse structures \citep{huxor:10}, at least in terms of their constituent stellar populations \citep{mackey:06} and internal dynamics \citep{collins:09}."1101. The extension provided by first-semester PAndAS imaging over the region previously surveyed for globular clusters by Huxoretal.(2008) consists of nearly complete coverage of the inner parts of M31 together with a large halo area to the west and north-west., The extension provided by first-semester PAndAS imaging over the region previously surveyed for globular clusters by \citet{huxor:08} consists of nearly complete coverage of the inner parts of M31 together with a large halo area to the west and north-west.1102 We have searched all fields at =30 kpe as well as many fields interior to this. using Ryprocedures similar to those described by Huxoretal.(2008).," We have searched all fields at $R_{{\rm p}}\ge30$ kpc as well as many fields interior to this, using procedures similar to those described by \citet{huxor:08}."1103 This has resulted in a catalogue of 43 previously unknown globular clusters. the properties of which will be detailed in a forthcoming paper (Huxor et al.," This has resulted in a catalogue of $43$ previously unknown globular clusters, the properties of which will be detailed in a forthcoming paper (Huxor et al."1104 2010b. in prep.).," 2010b, in prep.)."1105 For now it is sufficient to note that 33 of these objects fall at projected radii beyond 30 kpe. including 12 between 50—100 kpe and four outside 100 kpe.," For now it is sufficient to note that $33$ of these objects fall at projected radii beyond $30$ kpc, including $12$ between $50-100$ kpc and four outside $100$ kpc."1106 Sixteen of our newly-discovered clusters appear to be of the extended variety., Sixteen of our newly-discovered clusters appear to be of the extended variety.1107" In summary. our sample contains 67 clusters with A,=30 kpc. although only 61 of these lie within the present PAndAS footprint."," In summary, our sample contains $67$ clusters with $R_{{\rm p}}\ge30$ kpc, although only $61$ of these lie within the present PAndAS footprint."1108" All PAndAS imaging is taken during dark sky conditions with seeing better than 0.7"".", All PAndAS imaging is taken during dark sky conditions with seeing better than $0.7\arcsec$.1109 Under such circumstances globular clusters in. the M31 halo partially resolve into stars. meaning that identification 18. straightforward and unambiguous (see Fig.," Under such circumstances globular clusters in the M31 halo partially resolve into stars, meaning that identification is straightforward and unambiguous (see Fig."1110 1)., 1).1111 Following the analysis of Huxoretal. (2010a).. we believe our search procedure does not lead to significant bias or incompleteness in the overall cluster selection function down to Myz—5.," Following the analysis of \citet{huxor:10}, we believe our search procedure does not lead to significant bias or incompleteness in the overall cluster selection function down to $M_{{\rm V}}\approx-5$."1112 Furthermore. away from the very innermost M31 fields where crowding is non-negligible we expect no significant spatial variation in completeness.," Furthermore, away from the very innermost M31 fields where crowding is non-negligible we expect no significant spatial variation in completeness."1113 Figure | shows the positions of all globular clusters in our sample overlaid on the PAndAS metal-poor ({Fe/H] —1.4) stellar density map., Figure 1 shows the positions of all globular clusters in our sample overlaid on the PAndAS metal-poor $[$ $/$ $]\la-1.4$ ) stellar density map.1114 In the outer parts of the M31 halo where large tidal debris streams are readily distinguished (RyZ30 kpe). there is a striking correlation between these features and the positions of many globular clusters.," In the outer parts of the M31 halo where large tidal debris streams are readily distinguished $R_{{\rm p}}\ga30$ kpc), there is a striking correlation between these features and the positions of many globular clusters."1115 Indeed. close inspection of Fig.," Indeed, close inspection of Fig."1116 1 reveals very few remote clusters that do not project onto some kind of underlying field overdensity. even though these substructures clearly occupy only a relatively small fraction of the overall survey footprint.," 1 reveals very few remote clusters that do not project onto some kind of underlying field overdensity, even though these substructures clearly occupy only a relatively small fraction of the overall survey footprint."1117 In order to put this result on more quantitative ground we undertake several calculations aimed at estimating the probability that the apparent association between clusters and debris streams could be due to chance alignment., In order to put this result on more quantitative ground we undertake several calculations aimed at estimating the probability that the apparent association between clusters and debris streams could be due to chance alignment.1118 That is. we aim to compute the level of significance at which similar substructures exist in both the globular cluster and field star distributions beyond Δρz30 kpc.," That is, we aim to compute the level of significance at which similar substructures exist in both the globular cluster and field star distributions beyond $R_{{\rm p}}\approx30$ kpc."1119 We base our analysis on a simple Monte Carlo methodology utilizing a set of 1.5«10? random realizations of a smoothly-distributed M31 globular cluster system., We base our analysis on a simple Monte Carlo methodology utilizing a set of $1.5\times10^5$ random realizations of a smoothly-distributed M31 globular cluster system.1120 These represent the null case where globular clusters constitute a well-mixed. unstructured halo population.," These represent the null case where globular clusters constitute a well-mixed, unstructured halo population."1121 Comparing the properties of these mock systems to those of the real M31. system then allows us to assess whether the observed globular clusters are indeed spatially correlated with underlying field overdensities. or whether the apparent association can be ascribed to stochastic effects.," Comparing the properties of these mock systems to those of the real M31 system then allows us to assess whether the observed globular clusters are indeed spatially correlated with underlying field overdensities, or whether the apparent association can be ascribed to stochastic effects."1122" In each mock system we randomly generated cluster galactocentric radii between A,=30—130 kpe using a probability distribution function. defined by the observed globular cluster radial surface-density profile. and selected position angles randomly from a uniform distribution such that each individual cluster fell within the PAndAS footprint."," In each mock system we randomly generated cluster galactocentric radii between $R_{{\rm p}}=30-130$ kpc using a probability distribution function defined by the observed globular cluster radial surface-density profile, and selected position angles randomly from a uniform distribution such that each individual cluster fell within the PAndAS footprint."1123 Our outer limit is the maximum radius with nearly complete coverage over the presently-observed area. while our inner limit is the approximate radius interior to which there are many overlapping halo features (e.g..Fergusonetal.2002) and it becomes meaningless to associate clusters with field substructure via spatial coincidence alone.," Our outer limit is the maximum radius with nearly complete coverage over the presently-observed area, while our inner limit is the approximate radius interior to which there are many overlapping halo features \citep[e.g.,][]{ferguson:02} and it becomes meaningless to associate clusters with field substructure via spatial coincidence alone."1124 We set the total number of clusters in each mock system equal to the size of the known M31 sample between =30—130 kpe within the PAndAS area (61 objects)., We set the total number of clusters in each mock system equal to the size of the known M31 sample between $R_{{\rm p}}=30-130$ kpc within the PAndAS area $61$ objects).1125" Our derivedRy, cluster surface-density profile closely matches that obtained by Huxoretal.(2010a).", Our derived cluster surface-density profile closely matches that obtained by \citet{huxor:10}.1126. We utilized a FITS version of the PAndAS stellar density map to test whether the observed M31 globular clusters are preferentially projected against regions with higher densities of metal-poor red giant stars., We utilized a FITS version of the PAndAS stellar density map to test whether the observed M31 globular clusters are preferentially projected against regions with higher densities of metal-poor red giant stars.1127 The FITS map has an embedded World Coordinate System. which allowed us to easily calculate the mean value in à 7« pixel box about the position of each cluster.," The FITS map has an embedded World Coordinate System, which allowed us to easily calculate the mean value in a $7\times7$ pixel box about the position of each cluster."1128 The clusters themselves are not generally visible on the map since they are usually unresolved by the cataloguing software., The clusters themselves are not generally visible on the map since they are usually unresolved by the cataloguing software.1129 To be sure. we omitted the central (cluster) pixel from the average (one ~350 pe).," To be sure, we omitted the central (cluster) pixel from the average (one $\approx350$ pc)."1130 Our box corresponds to a ~2.5« kpe region on the sky. representing an adequate compromise in obtaining enough pixels without considering an unreasonably broad area about each cluster.," Our box corresponds to a $\sim2.5\times2.5$ kpc region on the sky, representing an adequate compromise in obtaining enough pixels without considering an unreasonably broad area about each cluster."1131 It is also sufficiently larger than the ~2.5 pixel Gaussian smoothing kernel used while generating the map., It is also sufficiently larger than the $\sim2.5$ pixel Gaussian smoothing kernel used while generating the map.1132 We considered the mean value in each box. rather than all pixels individually. because this smoothing means that adjacent pixel values are not independent.," We considered the mean value in each box, rather than all pixels individually, because this smoothing means that adjacent pixel values are not independent."1133 We repeated this process for all real and mock globular clusters. and formed the results into two cumulative distributions (Fig.," We repeated this process for all real and mock globular clusters, and formed the results into two cumulative distributions (Fig."1134 2)., 2).1135 These have quite different shapes — m particular. that for the real cluster system clearly contains fewer low values than does the distribution for the mock systems.," These have quite different shapes – in particular, that for the real cluster system clearly contains fewer low values than does the distribution for the mock systems."1136 In other words. the observed M31 globular clusters preferentially project onto regions of higher field star density than would be expected if they constituted an," In other words, the observed M31 globular clusters preferentially project onto regions of higher field star density than would be expected if they constituted an"1137age. considering other facts (see next section) we adopt 5 Gyr as the lower limit.,"age, considering other facts (see next section) we adopt 5 Gyr as the lower limit."1138 If ASAS-04 ts older than 8 Gyr it would mean that it is currently close to the turn-off point and ends its Main-sequence evolution. which makes it a very interesting object for more research.," If ASAS-04 is older than 8 Gyr it would mean that it is currently close to the turn-off point and ends its main-sequence evolution, which makes it a very interesting object for more research."1139 On the contrary. ASAS-08 is a younger. likely a main-sequence binary.," On the contrary, ASAS-08 is a younger, likely a main-sequence binary."1140 With our value of the systemic radial velocity. the distance. and the PPMX proper motion —]83.7 mas/yr and py=15.49 mas/yr) we obtained Uo=-30.9 40.8. V=-20.640.3 and W=-18.0+1.2 km κ.," With our value of the systemic radial velocity, the distance, and the PPMX proper motion $\mu_{\alpha}=-183.7$ mas/yr and $\mu_{\delta}=15.49$ mas/yr) we obtained $U=-26.9 \pm 0.8$ , $V = -20.6 \pm 0.3$ and $W = -18.0 \pm 1.2$ km $^{-1}$."1141 Those values put ASAS-08 exactly in the thin disc regime. but it is hard to associate the binary with any young moving group. so we can conclude that its age is more than ~| Gyr.," Those values put ASAS-08 exactly in the thin disc regime, but it is hard to associate the binary with any young moving group, so we can conclude that its age is more than $\sim 1$ Gyr."1142 The level of activity supports this conclusion., The level of activity supports this conclusion.1143" Hawleyetal.(1999) have proven that M dwarfs in voung open clusters have a well defined V—J colour at which their activity. measured from the H, emission. becomes ubiquitous."," \citet{haw99} have proven that M dwarfs in young open clusters have a well defined $V-I$ colour at which their activity, measured from the $_\alpha$ emission, becomes ubiquitous."1144 Active stars (which have Ελ >| A)) from a certain cluster are redder than this characteristic V—7., Active stars (which have $_{H_\alpha}$ $\ge 1$ ) from a certain cluster are redder than this characteristic $V-I$.1145" Hawleyetal.(1999) gave a relation between the age rjj, of the cluster and this “H,,-limit™ colour at which M dwarfs have ΕΝ~|As Later Gizisetal.(2002) also used this relation for field M dwarfs.", \citet{haw99} gave a relation between the age $t_{H_\alpha}$ of the cluster and this $_\alpha$ -limit” colour at which M dwarfs have $_{H_\alpha} \simeq 1$: Later \citet{giz02} also used this relation for field M dwarfs.1146" Both ASAS-08 components have EW;;, =0.6 A(whichagreeswithChristian&Mathioudakis 2002).. consequently we can estimate the lower limit for the system's age with Eq. 4.."," Both ASAS-08 components have $_{H_\alpha}$ $\simeq 0.6$ \citep[which agrees with ][]{chr02}, consequently we can estimate the lower limit for the system's age with Eq. \ref{eq_vi}."1147 With our value of the secondary's V—/ we conclude that the system must be much older thàn 85 Myr., With our value of the secondary's $V-I$ we conclude that the system must be much older than 85 Myr.1148" If we further assume that the third component is inactive. in the meaning of EW;,. weget a lower limit for the age of the system to be about 290 Myr."," If we further assume that the third component is inactive, in the meaning of $_{H_\alpha}$, weget a lower limit for the age of the system to be about 290 Myr."1149" As for ASAS-04. according to the definition by Hawleyetal.(1999).. we consider ASAS-08. as well as ASAS-04. as “weakly active"" in terms of H, equivalent width (and in those terms only)."," As for ASAS-04, according to the definition by \citet{haw99}, we consider ASAS-08, as well as ASAS-04, as ”weakly active” in terms of $_\alpha$ equivalent width (and in those terms only)."1150" ASAS-08 was also observed by Parihanetal. (2009).. who recorded substantial emission in the H,, line at a level similar to the one presented here."," ASAS-08 was also observed by \citet{par09}, who recorded substantial emission in the $_\alpha$ line at a level similar to the one presented here."1151 Other activity indicators are also detected i1 emission. especially the caleium H and K lines are very strong (see Fig.," Other activity indicators are also detected in emission, especially the calcium H and K lines are very strong (see Fig."1152 5 and Table 6)., \ref{fig_spec} and Table \ref{tab_eqw}) ).1153 As for ASAS-04. other Balmer lines are also seen in emission. including weak He (out of the range of Fig. 5).," As for ASAS-04, other Balmer lines are also seen in emission, including weak $_6$ (out of the range of Fig. \ref{fig_spec}) )."1154" Other lines. such as sodium D or He | 5877Á.. were not found in emission. but Parthanetal.(2009) noted them to have ""comparable levels of emission"". which presumably may indicate their variability."," Other lines, such as sodium D or He I 5877, were not found in emission, but \citet{par09} noted them to have ”comparable levels of emission”, which presumably may indicate their variability."1155 This implicates the level of activity is higher than for ASAS-04 and is consistent with the presence of larger spots., This implicates the level of activity is higher than for ASAS-04 and is consistent with the presence of larger spots.1156 Also the X-ray-to-bolometric luminosity ratio is higher than for the former system., Also the X-ray-to-bolometric luminosity ratio is higher than for the former system.1157" When we incorporated the data for from ROSAT (Vogesetal.1999) and assumed a linear correlation between Ly and ¥,,,;. we found (ονοι=7-6£3.5-107 and (Ly/Lage=9544.0:1077 for the primary and secondary respectively."," When we incorporated the data for from ROSAT \citep{vog99} and assumed a linear correlation between $L_X$ and $v_{rot}$, we found $(L_X/L_{bol})_1 = 7.6\pm3.5 \cdot 10^{-4}$ and $(L_X/L_{bol})_2 = 9.5\pm4.0 \cdot 10^{-4}$ for the primary and secondary respectively."1158 The excess of the radit. measured in the same manner as previously. is 816 and 10.5706; respectively.," The excess of the radii, measured in the same manner as previously, is $8^{+1}_{-2}$ and $10.5^{+2.0}_{-1.5}$ respectively."1159 Those numbers agree within errors with the relation found by López-Morales (2007). but place ASAS-08 above it.," Those numbers agree within errors with the relation found by \citet{lop07}, , but place ASAS-08 above it."1160 In this section we compare our results with several popular and widely used sets of theoretical evolutionary models and isochrones — Y (Yietal.2001:Demarque2004). BCAH98 (Baratfeetal.1998).. PADOVA (Girardietal.2000:Marigoetal.2008) and GENEVA (Lejeune&Shaerer2001).," In this section we compare our results with several popular and widely used sets of theoretical evolutionary models and isochrones — $^2$ \citep{yi01,dem04}, BCAH98 \citep{bar98}, PADOVA \citep{gir00,mar08} and GENEVA \citep{lej01}."1161. In Fig., In Fig.1162" 6 we show the results for ASAS-04 together with several isochrones on the mass versus bolometric magnitude Mp. radius R. logarithm of temperature log(,5,). absolute V magnitude M, and observed (V—/) colour planes."," \ref{fig_evo_04} we show the results for ASAS-04 together with several isochrones on the mass versus bolometric magnitude $M_{bol}$, radius $R$, logarithm of temperature $\log(T_{phot})$, absolute $V$ magnitude $M_V$ and observed $(V-I)$ colour planes."1163 We compare our results with theoretical predictions for three scenarios: (1) the early main-sequence stage and solar composition (/eft)): (2) late main-sequence stage and reduced metallicity (21iddle)) (3) main sequence turn-off and solar metallicity (Ισ)., We compare our results with theoretical predictions for three scenarios: (1) the early main-sequence stage and solar composition ); (2) late main-sequence stage and reduced metallicity ); (3) main sequence turn-off and solar metallicity ).1164 Because of the limited availability our sets are not uniform for the scenario (2) and (3) — slightly different metallicities were used for the GENEVA and BCAH98 sets in (2) and a differet age for BCAH98 in the scenario (3)., Because of the limited availability our sets are not uniform for the scenario (2) and (3) – slightly different metallicities were used for the GENEVA and BCAH98 sets in (2) and a different age for BCAH98 in the scenario (3).1165 In this case we may cosider this tsochrone as a lower limit for the age estimate as 1t usually lies close to one of the errorbars., In this case we may consider this isochrone as a lower limit for the age estimate as it usually lies close to one of the errorbars.1166" [sochrones for the scenarios (2) and (3) were selected to fit our measurements in the M/M;,; plane.", Isochrones for the scenarios (2) and (3) were selected to fit our measurements in the $M/M_{bol}$ plane.1167 We chose this plane as a reference since recent findings show that although radit and temperatures are not particularly well reproduced. the lumimosity (hence Mj) is and one can then fit an isochrone to the data if the radius is scaled by a factor B and the temperature by 87? (Chabrieretal.2007:Moralesetal. 2009b).," We chose this plane as a reference since recent findings show that although radii and temperatures are not particularly well reproduced, the luminosity (hence $M_{bol}$ ) is and one can then fit an isochrone to the data if the radius is scaled by a factor $\beta$ and the temperature by $\beta^{-0.5}$ \citep{cha07,mor09b}."1168. The left column clearly shows that ASAS-04 cannot be at the early main sequence stage., The left column clearly shows that ASAS-04 cannot be at the early main sequence stage.1169 The observed properties are not reproduced in any of the panels. except for M/(V—D.," The observed properties are not reproduced in any of the panels, except for $M/(V-I)$."1170 As was mentioned above. both the radit temperatures exceed predictions.," As was mentioned above, both the radii temperatures exceed predictions."1171 One could fit a | Gyr isochrone to our data if Z«0.006 was assumed., One could fit a 1 Gyr isochrone to our data if $Z<0.006$ was assumed.1172 However. considering the activity-radius relation (López-Morales2007) and kinematies. we find this scenario very unlikely.," However, considering the activity-radius relation \citep{lop07}1173 and kinematics, we find this scenario very unlikely."1174 The degeneration between ageand metallicity of models that fit the data is already well known (Lastennet&Valls-Gabaud2002) and ASAS-04 is no exception., The degeneration between ageand metallicity of models that fit the data is already well known \citep{las02} and ASAS-04 is no exception.1175" Our measurements of mass and Mj, are well reproduced not only by models from Fig. 6.."," Our measurements of mass and $M_{bol}$ are well reproduced not only by models from Fig. \ref{fig_evo_04},"1176 but also for example for t=8 Gyr. Z=0.012.," but also for example for $t = 8$ Gyr, $Z = 0.012$."1177 One ean also see how BCAH98 for t=6 Gyr and Z=0.006 varies from the other isochrones., One can also see how BCAH98 for $t=6$ Gyr and $Z=0.006$ varies from the other isochrones.1178 For the presented case oft=6 Gyr. we observe the aforementioned discrepancies in the radii and temperatures (except for BCAH98. which is for smaller Z).," For the presented case of $t=6$ Gyr, we observe the aforementioned discrepancies in the radii and temperatures (except for BCAH98, which is for smaller $Z$ )."1179 Thus we find this age/metallicity set a probableone., Thus we find this age/metallicity set a probableone.1180 We observed the same behaviour but with smaller discrepancies for sets with f=8 Gyr and Z= 0.012., We observed the same behaviour but with smaller discrepancies for sets with $t = 8$ Gyr and $Z=0.012$ .1181 For the case of 6 Gyr and Z=0.01 a single correction factor p=Roose!Ryo can be found for both components and would be8- 1.055., For the case of 6 Gyr and $Z=0.01$ a single correction factor $\beta\equiv R_{obs}/R_{mod}$ can be found for both components and would be $\beta\simeq 1.055$ .1182 This corresponds to the shift in Alog(Type.)= 0.012. which would allow for fitting a single isochrone.," This corresponds to the shift in $\Delta\log(T_{phot}) \simeq 0.012$ , which would allow for fitting a single isochrone."1183 The discrepancies diminish. around ¢~10—11 Gyr. where the," The discrepancies diminish around $t \sim 10-11$ Gyr, where the"1184ltecent high-resolution spectral studies byChandra. ancl have revealed that emission lines at 6.7 or 6.0 keV (probably emitted. by highly. ionized. iron) are common features in the X-ray spectra of active galactic nuclei. CXGNs. e.g.. Poundsetal.2003:Reeves2004:2010:Patricketal. 2010)).,"Recent high-resolution spectral studies by, and have revealed that emission lines at 6.7 or 6.9 keV (probably emitted by highly ionized iron) are common features in the X-ray spectra of active galactic nuclei (AGNs, e.g., \citealt{Pounds2003,Reeves2004,Yaqoob2004,Bianchi2009,Shu2010,Patrick2010}) )."1185 The emission lines produced by ionized iron in optically thin. photoionized material in AGNs have been studied by Bianchi&Matt(2002).," The emission lines produced by ionized iron in optically thin, photoionized material in AGNs have been studied by \citet[]{Bianchi2002}."1186.. Their results may require an iron overabundance by a factor of a few to account for the observed linc strength., Their results may require an iron overabundance by a factor of a few to account for the observed line strength.1187 The energy and ionization balance at the surface of an accretion disk can change due to the X-ray. illumination. and this alfects the line emission.," The energy and ionization balance at the surface of an accretion disk can change due to the X-ray illumination, and this affects the line emission."1188 Thus. it is important to determine the radial ionization structure of X-ray photoionized accretion disks. in order to study the reflected spectra and the associated iron emission.," Thus, it is important to determine the radial ionization structure of X-ray photoionized accretion disks, in order to study the reflected spectra and the associated iron emission."1189 The energy of the iron line generally increases as iron. becomes more stripped. from GA keV. for to 6.97 keV for (Ixaspietal.2002:Paerels&Ixahn2003 )).," The energy of the iron line generally increases as iron becomes more stripped, from 6.4 keV for to 6.97 keV for \citealt{Kaspi2002,Paerels2003}) )."1190 This provides à diagnostic of the accretion disk structure: we can compare the caleulated photoionization structure of the disk with the observed energy of the iron line. assuming that the line was emitted from the disk.," This provides a diagnostic of the accretion disk structure: we can compare the calculated photoionization structure of the disk with the observed energy of the iron line, assuming that the line was emitted from the disk."1191 In this letter. we calculate. the radial ionization structure of an X-ray illuminated AGN accretion. clisk as a function of Eddington ratio. ApiTMLiviLett: where Lig. is the bolometric luminosity and Lea is the Eddington Luminosity.," In this letter, we calculate the radial ionization structure of an X-ray illuminated AGN accretion disk as a function of Eddington ratio, $\lambda_{\rm Edd} \equiv \lb/\ledd$, where $\lb$ is the bolometric luminosity and $\ledd$ is the Eddington luminosity."1192 We then compare the precictec range of ionization parameters and iron line energies with a sample of recent. line observations., We then compare the predicted range of ionization parameters and iron line energies with a sample of recent line observations.1193" We plot the predicted and observed line energies ZZ, as a function ofAgqqa.", We plot the predicted and observed line energies $E_{\rm \alpha}$ as a function of.1194. This gives us clues on the origin of the iron lines., This gives us clues on the origin of the iron lines.1195 Phroughout this Letter. we assume standard cosmological parameters ο =7T0kms + DOOq=0.27. and Ὃν=0.73.," Throughout this Letter, we assume standard cosmological parameters $h_0$ = 70 km $^{-1}$ $^{-1}$, $\Omega_{\rm m} = 0.27$, and $\Omega_{\rm \Lambda} = 0.73$."1196 X-ray rellection from the surface. of cold. matter around compact accreting objects has been studied by many authors, X-ray reflection from the surface of cold matter around compact accreting objects has been studied by many authors1197In order to use the above formulations of the accretion rate to determine the resultant mass spectrum. we need a basic model of a stellar cluster.,"In order to use the above formulations of the accretion rate to determine the resultant mass spectrum, we need a basic model of a stellar cluster."1198 Phe cluster is initially gas dominated. in order to provide the mass reservoir [or accretion., The cluster is initially gas dominated in order to provide the mass reservoir for accretion.1199 Observations of the voungest clusters estimate that up to 90 per cent of the mass is in gas (Lada 1991)., Observations of the youngest clusters estimate that up to 90 per cent of the mass is in gas (Lada 1991).1200 Such systems are unlikely to be in equilibrium. and regardless of their initial configurations. will collapse towards a clensity distribution (Larson 1969: Llunter 1977).," Such systems are unlikely to be in equilibrium, and regardless of their initial configurations, will collapse towards a density distribution (Larson 1969; Hunter 1977)."

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