ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 In order to keep the discussion of the various IC processes as clear as possible. we concentrate on the EUV excess. aud explain the consequences of the TEX excess for the different inodels iu separate subsectious.," In order to keep the discussion of the various IC processes as clear as possible, we concentrate on the EUV excess, and explain the consequences of the HEX excess for the different models in separate subsections."3 Sec., Sec.4" 5.r, contains a concise discussion of our results."," \ref{sec:disc}5 contains a concise discussion of our results."6The column density distribution of absorbing gas is expected to be related to the facing law: gas both feeds the DII and obscures the radiation released.,The column density distribution of absorbing gas is expected to be related to the fading law; gas both feeds the BH and obscures the radiation released.7 Llowever the astrophysical relationship is complicated ancl depends on. for example. the surrounding star formation and the geometry. of the accretion disc.," However the astrophysical relationship is complicated and depends on, for example, the surrounding star formation and the geometry of the accretion disc."8 ? have used the numerical simulations of quasars fucllecl by gas accretion by 2? to construct a parametrised Luminosity and time dependent mocel for the obscuring column density.," \citet{hopkins2005b}9 have used the numerical simulations of quasars fuelled by gas accretion by \citet{dimatteo2005} to construct a parametrised luminosity and time dependent model for the obscuring column density."10 Ehe probability £2 that a quasar is obscured by a given total hydrogen column density Ny depends on the amount of time a quasar remains in a given accretion phase., The probability $P$ that a quasar is obscured by a given total hydrogen column density $N_{\rm H}$ depends on the amount of time a quasar remains in a given accretion phase.11 Phe simulated data is fit with a log-normal distribution vote that the mean column density. Ny. ancl dispersion. ON. are predominantly. determined by the instantaneousxlometric Luminosity of the quasar £L.," The simulated data is fit with a log-normal distribution Note that the mean column density, $\bar{N}_{\rm H}$, and dispersion, $\sigma_{\rm N_{\rm H}}$, are predominantly determined by the instantaneousbolometric luminosity of the quasar $L$."12 7 also demonstrated that the shape of this distribution or quasars. with a D-band. luminosity above 10! L. is consistent with a statistical analvsis of the reddening found oward SDSS quasars in 2.., \citet{hopkins2005b} also demonstrated that the shape of this distribution for quasars with a B-band luminosity above $10^{11}$ $_{\sun}$ is consistent with a statistical analysis of the reddening found toward SDSS quasars in \citet{hopkins2004}.13 Phis analytic fit is derived from simulations of gaseous disc galaxies. and of course may not (e representative of the typical accretion rate onto black voles at all redshifts.," This analytic fit is derived from simulations of gaseous disc galaxies, and of course may not be representative of the typical accretion rate onto black holes at all redshifts."14 However at the redshifts that we are applying it (z2 2) galaxies are expected to be gas rich., However at the redshifts that we are applying it $z>2$ ) galaxies are expected to be gas rich.15 Since we are predominantly comparing our model to optical dataquoted in UV magnitudes we have used the reddening law presented in ? to model cust ancl gas absorption., Since we are predominantly comparing our model to optical dataquoted in UV magnitudes we have used the reddening law presented in \citet{gaskell2004} to model dust and gas absorption.16 The reddening law is normalised such that the optical depth in the V-bancl (5500 A)) is the same as for an SAIC-like reddening curve taken from (?)]] for a galaxy with the metallicity of the Milky Was., The reddening law is normalised such that the optical depth in the V-band $5500$ ) is the same as for an SMC-like reddening curve [taken from \citep{pei1992}] ] for a galaxy with the metallicity of the Milky Way.17 Phis results in a V-band optical depth identical to that adopted by 2? who assumed a ΛΙκο reddening curve with a gas-to-dust ratio as [or the Milky Way., This results in a V-band optical depth identical to that adopted by \citet{hopkins2005d} who assumed a SMC-like reddening curve with a gas-to-dust ratio as for the Milky Way.18 At X-ray. wavelengths the absorption is dominated by photo-clectric absorption and C'ompton scattering by hvdrogen., At X-ray wavelengths the absorption is dominated by photo-electric absorption and Compton scattering by hydrogen.19 Following ? we assume an average neutral eas [fraction of 0.352r and assume Chat the tonisect component contributes to the photoclectrie absorption. but not the optical reddening or Compton scattering.," Following \citet{hopkins2005d} we assume an average neutral gas fraction of $0.35$ and assume that the ionised component contributes to the photoelectric absorption, but not the optical reddening or Compton scattering."20 We note that this model makes the simplistic assumption that the distribution of gas and cust is spatially uniform., We note that this model makes the simplistic assumption that the distribution of gas and dust is spatially uniform.21" We now turn to calculating the observed luminosity function for a given redshift z and observed. wavelength v (or more usefullv for comparison with X-ray. observations. wave-band £6, ο)."," We now turn to calculating the observed luminosity function for a given redshift $z$ and observed wavelength $\nu$ (or more usefully for comparison with X-ray observations, wave-band $\nu_a \rightarrow22\nu_b$ )."23" Given the probability that a quasar with a given intrinsic bolometric Luminosity £ is obscured. by a given column density. the probability that the intrinsic specific luminosity L5 is observed to have a specific luminosity L,.. PUL.[LIlog! he thay be written"," Given the probability that a quasar with a given intrinsic bolometric luminosity $L^{\prime}$ is obscured by a given column density, the probability that the intrinsic specific luminosity $L^{\prime}_{\nu}$ is observed to have a specific luminosity $L_{\nu}$ , $P(L_{\nu}|L^{\prime}_{\nu})d{\rm log}L^{\prime}_{\nu}$ , may be written"24either of two possible regimes.,either of two possible regimes.25 If the observations are above the cooling frequeucy. for the burst. the electron spectral slope tudes p is giveu by p=22 aud the tine decay slope is either p—22 (lor an ofl-axis orphan) or 3p/1—1/2=33/2 (for an ou-axis dirty fireball).," If the observations are above the cooling frequency for the burst, the electron spectral slope index $p$ is given by $p = 2 \beta$ and the time decay slope is either $p=2\beta$ (for an off-axis orphan) or $3p/4 - 1/2 = 3\beta/2 - 1/2$ (for an on-axis dirty fireball)."26 On the other hanc. if the observations are below the cooling frequency. we have p=229+1 ancl decay slopes of eitler p=2094+] or 3p/l—3/1=32/2.," On the other hand, if the observations are below the cooling frequency, we have $p = 2 \beta + 1$ and decay slopes of either $p = 2\beta+1$ or $3p/4 - 3/4 = 3 \beta/2$."27 To distinguish the two afterglow regimes. we therefore need to tell apart two time decay slopes a diflering by either p/l+1/2=9/24+1/2 or by p/1-o-3/1—2/241.," To distinguish the two afterglow regimes, we therefore need to tell apart two time decay slopes $\alpha$ differing by either $p/4+1/2 = \beta/2 +1/2$ or by $p/4 + 3/4 =28\beta/2 + 1$."29 Since pzz2 is typical we will be satisfied with any observational strategy that cau measure a toa olle-sigina accuracy of £0.3. sullicient to distiuguisli tle above two scenarios at a 3o level.," Since $p \approx 2$ is typical we will be satisfied with any observational strategy that can measure $\alpha$ to a one-sigma accuracy of $\pm 0.3$, sufficient to distinguish the above two scenarios at a $3\sigma$ level."30 To determine the error iu à. Eliave generated artificial power law liglit curves sampled accordiug to an assumed observing strategy. aud with artificial nolse added.," To determine the error in $\alpha$, I have generated artificial power law light curves sampled according to an assumed observing strategy and with artificial noise added."31" I then fit each simulated. light curve with a model f=fil!4-14)//4]."". where iis the time elapsed since the first observation."," I then fit each simulated light curve with a model $f = f_1 [( \that + t_1) / t_1]^{-\alpha}$, where is the time elapsed since the first observation."32 The first numerical experiments were used to demonstrate that the accuracy. of the recovered spectral slope a5; does not. vary substantially with the intrinsic slope a over the range 1xaX3 [or a wide range of observing strategies., The first numerical experiments were used to demonstrate that the accuracy of the recovered spectral slope $\alphobs$ does not vary substantially with the intrinsic slope $\alpha$ over the range $1 \la \alpha \la 3$ for a wide range of observing strategies.33 The remainineOm simulations therefore used a uniform value of a=1.85. near the midpoint of the interesting[n] range.," The remaining simulations therefore used a uniform value of $\alpha = 1.8$, near the midpoint of the interesting range."34 Because we model the light curves to be power law decays after the first detection at time fy. there is only one characteristic tinescale in the light curve (/4).," Because we model the light curves to be power law decays after the first detection at time $t_1$, there is only one characteristic timescale in the light curve $t_1$ )."35 Only the ratio 5///4 need be considered in studsius the accuracy of light curve fitting., Only the ratio $\delta t / t_1$ need be considered in studying the accuracy of light curve fitting.36 I have therelore fixed 6/=1 day in the slinulaticis while allowing /; to vary., I have therefore fixed $\delta t = 1$ day in the simulations while allowing $t_1$ to vary.37 Results for 0/=& days can be inferred by replacing /4 with fy/h in the figures., Results for $\delta t = k$ days can be inferred by replacing $t_1$ with $t_1 / k$ in the figures.38 Figure 1. shows how the uncertainty in a varies with photometric accuracy. lor a baseline strategy of nightly samples (d/=1 day) contiuued for 7 nights total aud [or /4=0.5.1.2 cays.," Figure \ref{merr} shows how the uncertainty in $\alpha$ varies with photometric accuracy, for a baseline strategy of nightly samples $\delta39t = 1$ day) continued for 7 nights total and for $t_1 = 0.5, 1, 2$ days."40 Figure 2. shows the variation of da with the total duration A/=(CN—1)94 of monitoring. for the two cases where we (a) fix δή=1 and vary NV. and (b) fix IN=7 and vary 9///4.," Figure \ref{dur} shows the variation of $\delta \alpha$ with the total duration $\Delta t = (N-1) \delta t$ of monitoring, for the two cases where we (a) fix $\delta t / t_1 = 1$ and vary $N$, and (b) fix $N=7$ and vary $\delta t / t_1$."41 The observational error ou each iueasurement is held coustaut at 0i=0.05 throughout., The observational error on each measurement is held constant at $\delta m = 0.05$ throughout.42 The uncertainties iu the measured values of a aud { are strougly. correlated., The uncertainties in the measured values of $\alpha$ and $t_1$ are strongly correlated.43 The slope of the correlation can be estimated easily by notiug that This implies that the expected error ὁ=—óa/(dlogf/dl). where we can evaluate the observable quantity dlogf/d! near the midpoint of the observations.," The slope of the correlation can be estimated easily by noting that This implies that the expected error $\delta t_1 \approx -\delta \alpha /44(d\log f/dt)$, where we can evaluate the observable quantity $d\log f45/ dt$ near the midpoint of the observations."46 The age of an orphan afterglow at first discovery is a key [actor in how well we can determine its decay slope., The age of an orphan afterglow at first discovery is a key factor in how well we can determine its decay slope.47 In this section we predict this distribution in a simple orphan afterglow mocel., In this section we predict this distribution in a simple orphan afterglow model.48second order Feri process (Ixoniue'ets 1956: Suuvaev Titarchulk 1980).,second order Fermi process (Kompane'ets 1956; Sunyaev Titarchuk 1980).49 The spectral shape iu the limit of unsaturated Comptonization by a thermal plasma Is primarily determined by the Couptou y-paramcter eiven by yf(lkpT.fine?yr.un in the limit that the corona is optically thin., The spectral shape in the limit of un-saturated Comptonization by a thermal plasma is primarily determined by the Compton parameter given by $y=(4k_BT_e/m_ec^2)\tau_{c}$ in the limit that the corona is optically thin.50 A potential source of seed photons is the transitional region between the corona aud the deuse disk (Ross Fabian 1993: Ross et al., A potential source of seed photons is the transitional region between the corona and the dense disk (Ross Fabian 1993; Ross et al.51 1999: Dallautvue et al., 1999; Ballantyne et al.52 2001: Navakshin et al., 2001; Nayakshin et al.53 2000: Navakshin IWallmian 2001)., 2000; Nayakshin Kallman 2001).54 The cold dense disk is uot a perfect reflector and downward Courptonized N-rays serve as a source of heat due to non-zero albedo., The cold dense disk is not a perfect reflector and down-ward Comptonized X-rays serve as a source of heat due to non-zero albedo.55 Above photon energies of 30 keV. Compton dowu-scatterine donünates the albedo while at lower energies. photo-clectric absorption mainly contributes to the albedo.," Above photon energies of 30 keV, Compton down-scattering dominates the albedo while at lower energies, photo-electric absorption mainly contributes to the albedo."56 These caleulatious show that for high values of ionizing flux. which is XL.. fluorescence and absorption features iu the N-rav spectruni persist. though at a highly suppressed level.," These calculations show that for high values of ionizing flux, which is $\propto L_c$, fluorescence and absorption features in the X-ray spectrum persist, though at a highly suppressed level."57 The outgoing spectrum is roughly represented by a fat power law that exteuds to the cut-off energv eiven by kp., The outgoing spectrum is roughly represented by a flat power law that extends to the cut-off energy given by $k_BT_e$.58" For AGN. the power law spans from tens of eV. all the way to several Lundreds of The bhrielest ULNs with interred »olonmietric DIuunosities ~LOL, for a stellar inass black hole are dominate by hard power-law X-rays."," For AGN, the power law spans from tens of eV all the way to several hundreds of The brightest ULXs with inferred bolometric luminosities $\sim 10L_{_{\rm Edd}}$ for a stellar mass black hole are dominated by hard power-law X-rays."59" Such behavior Is in line wih the theoretical expectations outlined above,", Such behavior is in line with the theoretical expectations outlined above.60 Iu sub-Ecddiieton black hole accretion flows that power black hole bivaries (BITBs) and ACN. the fraction of energv dissipated in the corona fis roughly eiven by the ratio of Compouized to bolometric power.," In sub-Eddington black hole accretion flows that power black hole binaries (BHBs) and AGN, the fraction of energy dissipated in the corona is roughly given by the ratio of Comptonized to bolometric power."61" Table 1. shows that for DIIDs. the ratio L./E is correlated with £/L,.,,."," Table \ref{t: states} shows that for BHBs, the ratio $L_c/L$ is correlated with $L/L_{_{\rm Edd}}$."62" For the ""ULX state” (SDOG). the black hole mass is not measured aud is taken to have a characteristic value of LOAL..."," For the “ULX state” (SD06), the black hole mass is not measured and is taken to have a characteristic value of $10\,M_{\odot}$."63 Finthermore. Cot et al. (," Furthermore, Grimm et al. ("642003) coustruct the colmbined luminosity function of local star-forming ealaxies.,2003) construct the combined luminosity function of local star-forming galaxies.65 When they restrict their study to high mass N-rav binaries (IIAINBs: companion mass 25 M.). they fud tha the huuinosiv function is well-described by a sinele ]xywer-law up to Qurestrapolated) huuinosities of 3o10 ores Le. 30 times the Eddinetou Limit for a 1044.. )black hole (see t111 figure 5).," When they restrict their study to high mass X-ray binaries (HMXBs; companion mass $> 5\,M_{\odot}$ ), they find that the luminosity function is well-described by a single power-law up to (un-extrapolated) luminosities of $3\times 10^{40}$ erg/s i.e., 30 times the Eddington Limit for a $M_{\odot}$ black hole (see their figure 5)."66 If these spectra were modeled aud extrapol:ited to higher energies (100 keV). then their huuinositv would exteud to 1011 ere/s. Both properties of their luminosity function simultancously dictate that super-Edcdineton accretion is at work aud that it is radiativelv efücient.," If these spectra were modeled and extrapolated to higher energies (100 keV), then their luminosity would extend to $\sim 10^{41}$ erg/s. Both properties of their luminosity function simultaneously dictate that super-Eddington accretion is at work and that it is radiatively efficient."67 If intermeciate imass black holes {1[BUs) ave responsible for the population of extra-galactie IINENDs above the characteristic Eddington Limit. then one would expect a break in the luminosity function.," If intermediate mass black holes (IMBHs) are responsible for the population of extra-galactic HMXBs above the characteristic Eddington Limit, then one would expect a break in the luminosity function."68 It is unreasonable to expect that IMDIIS are members of binary svstenis in the same muuber as stellar mass black holes., It is unreasonable to expect that IMBHs are members of binary systems in the same number as stellar mass black holes.69" If the high end of the TAUINB Iunuiuositv function signals super-Eddington bhuuinositfies from radiativelvHi-cfficient accretion. then luminosity function would exhibit a break above L,,, "," If the high end of the HMXB luminosity function signals super-Eddington luminosities from radiatively accretion, then luminosity function would exhibit a break above $L_{_{\rm Edd}}$."70Stuilarly. a bonnedjet explanation for the high eud of the TAINB luminosity function would produce a break in the lunuinositv function.," Similarly, a beamed-jet explanation for the high end of the HMXB luminosity function would produce a break in the luminosity function."71 The fact that the huninositv function is a power-law is most easily interpreted by realizing that the central sources of IININDs are wind-fed aud the rate at which high mass stars donate mass to their compact colupalious is set bv stellar evolution., The fact that the luminosity function is a power-law is most easily interpreted by realizing that the central sources of HMXBs are wind-fed and the rate at which high mass stars donate mass to their compact companions is set by stellar evolution.72 The fact that the spectral energy. distributiois of the bright ULXs possess the same properties from basic theoretical arguineuts and observational expectations as that of super-Eddiugtou radiatively effideut accretion flows is suggestive., The fact that the spectral energy distributions of the bright ULXs possess the same properties – from basic theoretical arguments and observational expectations – as that of super-Eddington radiatively efficient accretion flows is suggestive.73 In addition. the luminosity function of the extra-ealactic TAINBs reinforces the motion that bright ULXs represcut a mode of black hole accretion that is both super-Eddineton aud rachatively ctiicicut.," In addition, the luminosity function of the extra-galactic HMXBs reinforces the notion that bright ULXs represent a mode of black hole accretion that is both super-Eddington and radiatively efficient."74 Iu its observational appearance as seen through its spectral energy distribution. Sw 1611157 can be thought of as a scaled-up bright ULX.," In its observational appearance as seen through its spectral energy distribution, Sw 1644+57 can be thought of as a scaled-up bright ULX."75 Aeain. the bright ULNs represent a class of stellar mass sources objects that persistently cuit well above the Eddington Limit with lieh radiative cfficicncy.," Again, the bright ULXs represent a class of stellar mass sources objects that persistently emit well above the Eddington Limit with high radiative efficiency."76" Therefore. it seenis natural to construct an accretion model of Sw J161L157 that resclubles those of bright ULX. multiplied bv a factor of ~10%LO"" du mass,"," Therefore, it seems natural to construct an accretion model of Sw J1644+57 that resembles those of bright ULX, multiplied by a factor of $\sim 10^6-10^7$ in mass."77 Rather than steady feeding from a companion star. the source of fuel results from the tidal disruption of an ordinary star (Rees 1988).," Rather than steady feeding from a companion star, the source of fuel results from the tidal disruption of an ordinary star (Rees 1988)."78 There las been receut theoretical progress on this topic (Rosswoe Raiirez-Ruiz 2009). vet the resulting spatial distribution of the debris is remains uncertain.," There has been recent theoretical progress on this topic (Rosswog Ramirez-Ruiz 2009), yet the resulting spatial distribution of the debris is remains uncertain."79 Assume that ~τν of stellar eas is placed iu a circular orbit at radius Ry that, Assume that $\sim 1 M_{\odot}$ of stellar gas is placed in a circular orbit at radius $R_0$ that80observations was roughly 1.5 areseconds.,observations was roughly 1.5 arcseconds.81 Figure 1. shows the resulting VLA images al 4.99 Gllz: a few details of the images are listed in Table 6..," Figure \ref{fig:vla}82 shows the resulting VLA images at 4.99 GHz; a few details of the images are listed in Table \ref{tab:vla}."83 The VLBA images were made with “natural” weighting of the visibility data in order to achieve (he best possible sensitivity., The VLBA images were made with “natural” weighting of the visibility data in order to achieve the best possible sensitivity.84 The imaging was carried out over a number of 4096 by 4096 pixel fields. with pixel sizes of 0.40.5 milliareseconds.," The imaging was carried out over a number of 4096 by 4096 pixel fields, with pixel sizes of 0.4–0.5 milliarcseconds."85 The resolution of the images was sub-parsec (see Table 1)). twpically with better resolution in (he east-west direction since the sources were at low cleclination and the VLBI array had a significant east-west elongation.," The resolution of the images was sub-parsec (see Table \ref{tab:obs}) ), typically with better resolution in the east-west direction since the sources were at low declination and the VLBI array had a significant east-west elongation."86 spectral and (me averaging in the correlation and imagine were set so that the peak flux densities in the relatively wide fields imaged were not degraded by averaging of the data (see Bridle Schwab 1999 [or discussion of this effect)., Spectral and time averaging in the correlation and imaging were set so that the peak flux densities in the relatively wide fields imaged were not degraded by averaging of the data (see Bridle Schwab 1999 for discussion of this effect).87 The total area imaged at milliarcsecond resolution is shown lor each galaxy in Figure 1.., The total area imaged at milliarcsecond resolution is shown for each galaxy in Figure \ref{fig:vla}.88 Although these relatively low resolution VLA images display some radio emission outside the areas imaged with HSA. higher resolution images of all galaxies (published. or made [rom archival VLA data) confirm that all regions with sub-aresecond 5 GIIz emission were included in the IISA imaging.," Although these relatively low resolution VLA images display some radio emission outside the areas imaged with HSA, higher resolution images of all galaxies (published, or made from archival VLA data) confirm that all regions with sub-arcsecond 5 GHz emission were included in the HSA imaging."89 For each galaxy. between 10 and 10? pixels were included in the wide-field IISA images.," For each galaxy, between $10^8$ and $10^9$ pixels were included in the wide-field HSA images."90" Thus. in (he absence of a-priori information about the location of milliareseconcl radio sources, setting a 36 source detection threshold clearly is inadequate."," Thus, in the absence of a-priori information about the location of milliarcsecond radio sources, setting a $3\sigma$ source detection threshold clearly is inadequate."91 Most individual images contained pixels between 5 and 6 times the rms noise. and a fex fields had pixels above 6 times the noise. in seemingly random locations.," Most individual images contained pixels between 5 and 6 times the rms noise, and a few fields had pixels above 6 times the noise, in seemingly random locations."92 Therefore. we set conservative upper limits for each ealaxy ol 7 (mes (lie rms noises given in Table 1..," Therefore, we set conservative upper limits for each galaxy of 7 times the rms noises given in Table \ref{tab:obs}."93 To get (rue upper limits. it also is necessary to account for possible losses of interferometer coherence in the pliase-referencing process.," To get true upper limits, it also is necessary to account for possible losses of interferometer coherence in the phase-referencing process."94 To estimate this coherence loss. we observed the “check” source J0826—2230 occasionally in place of Ile 2-10 and J1316—3338 in place of NGC 5253. (," To estimate this coherence loss, we observed the “check” source $-$ 2230 occasionally in place of He 2-10 and $-$ 3338 in place of NGC 5253. ("95No check source was observed for IL Zw 40 because of the long slew times that would have been recquired for the Arecibo telescope).,No check source was observed for II Zw 40 because of the long slew times that would have been required for the Arecibo telescope).96 Comparing (he peak [lux densities of JOS826—2230 and J1316—3338 in phase- images to those derived after sell-calibration indicates respective coherence loss factors o£ 2 and 3 at ealibrator-galaxy separations of 5:99 and 2288., Comparing the peak flux densities of $-$ 2230 and $-$ 3338 in phase-referenced images to those derived after self-calibration indicates respective coherence loss factors of 2 and 3 at calibrator-galaxy separations of 9 and 8.97 Coherence losses tvpically increase approximately linearly with the calibrator-ealaxy separation 1995).. so we infer reductions in the peak amplitudes by a factor of 1.4 for He 2-10 and a factor of 2.0 for NGC 5253.," Coherence losses typically increase approximately linearly with the calibrator-galaxy separation \citep{bea95}, so we infer reductions in the peak amplitudes by a factor of 1.4 for He 2-10 and a factor of 2.0 for NGC 5253."98 II Zw 40 was observed at à much smaller switching angle of 0277., II Zw 40 was observed at a much smaller switching angle of 7.99 and αἱ a higher elevation Chan the other two galaxies: averaging (he interpolated values [or the other (wo ealaxies. we estimate a reduction factor of 1.2 for the peak amplitudes of anv real sources in II Zw 40.," and at a higher elevation than the other two galaxies; averaging the interpolated values for the other two galaxies, we estimate a reduction factor of 1.2 for the peak amplitudes of any real sources in II Zw 40."100 Thus. we arrive at the final upper limits lor each galaxy which are given in Table 4..," Thus, we arrive at the final upper limits for each galaxy which are given in Table \ref{tab:limits}. ."101In recent years. it has become increasingly clear that the most infraredIR)-Iuminous galaxies pay an important role in the star ormation history of the Universe.,"In recent years, it has become increasingly clear that the most infrared(IR)-luminous galaxies pay an important role in the star formation history of the Universe."102 Though they provide only a rivial contribution in the local Universe. both theory (??) and observations (2227). have shown that by z2:1 the total IR uminosity density is dominated by luminous (10<LipL. 1047: LIRGs). and at higher redshifts by ultralumious systems (Lip~»107 L. ULIRGs).," Though they provide only a trivial contribution in the local Universe, both theory \citep{hopkins2009.ulirg,hopkins2010.sfh} and observations \citep{lefloch2005,perezgonzalez2005,magnelli2009,goto2010} have shown that by $z\gsim 1$ the total IR luminosity density is dominated by luminous $10^{11} < L_{IR}/L_\odot < 10^{12}$ ; LIRGs), and at higher redshifts by ultralumious systems $L_{IR} > 10^{12}$ $L_\odot$ ULIRGs)."103 Thus detailed study of these »opulations. and the processes driving their tremendous radiative output is critical to a thorough understanding of galaxy formation more generally.," Thus detailed study of these populations, and the processes driving their tremendous radiative output is critical to a thorough understanding of galaxy formation more generally."104 Submillimetre-selected galaxies (SMGs). discovered in the first deep cosmological surveys at.(22?) by the Submillimetre Common User Bolometer Array (SCUBA:?).. represent some of the most extreme objects in the high-redshift Universe (forareview.see ?)..," Submillimetre-selected galaxies (SMGs), discovered in the first deep cosmological surveys at\citep{smail1997,hughes1998,barger1998} by the Submillimetre Common User Bolometer Array \citep[SCUBA:][]{holland1999}, represent some of the most extreme objects in the high-redshift Universe \citep[for a review, see][]{blain2002}. ."105 Owing to a strong negative À-correction. the selection function at zzSOQ—I000;:m is flat from 2] 10. and therefore provdes an unbiased view of star formation out to very high redshift (2)..," Owing to a strong negative $k$ -correction, the selection function at $\approx 800-1000$ is flat from $z\sim 1-10$ , and therefore provdes an unbiased view of star formation out to very high redshift \citep{blain1993}."106 Though their bolometric energy output rivals that of luminous quasars. SMOs are several orders of magnitude more numerous at comparable redshifts (2~2.5: 2). ," Though their bolometric energy output rivals that of luminous quasars, SMGs are several orders of magnitude more numerous at comparable redshifts \citep[$z\sim 2.5$;][]{chapman2005}. ."107At the same time. these two extreme populations are thought to be connected via an evolutionary sequence (222?) driving the formation of the most massive galaxies (22222)...," At the same time, these two extreme populations are thought to be connected via an evolutionary sequence \citep[][]{hopkins2009.ulirg,narayanan2009.smg,narayanan2009.co,narayanan2009.dog} driving the formation of the most massive galaxies \citep{scott2002,blain2004,swinbank2006,swinbank2008,viero2009}. ."108" Thus. in the context of a merger-driven cosmic cycle (e.g...2222), SMGs represent the transition objects between star formation and AGN-dominated systems. and as such a compelling laboratory for testing models of galaxy formation and evolution in the most extreme environments."," Thus, in the context of a merger-driven cosmic cycle \citep[e.g.,][]{sanders1988a,hopkins2006,hopkins2007a,hopkins2007b}, SMGs represent the transition objects between star formation and AGN-dominated systems, and as such a compelling laboratory for testing models of galaxy formation and evolution in the most extreme environments."109 While their bolometric luminosity is thought to be primarily poweredby star formation €222222222).. SMGs couldinprinciple represent one of two verydifferent channels: a steady-state mode," While their bolometric luminosity is thought to be primarily poweredby star formation \citep{alexander2005,alexander2005b,alexander2008,valiante2007,menendez2007,menendez2009,pope2008b,momjian2010,serjeant2010}, , SMGs couldinprinciple represent one of two verydifferent channels: a steady-state mode"110be the product of small and unrecognized svstematic errors.,be the product of small and unrecognized systematic errors.111" However. Alcocketal.(2001) argued that the parallax measurement could not be so easily dismissed because the direction of v derived from (his measurement agreed with the measured direction of 44,4 to within about 67."," However, \citet{alcock01} argued that the parallax measurement could not be so easily dismissed because the direction of $\tilde \bv$ derived from this measurement agreed with the measured direction of $\bmu_\rel$ to within about $6^\circ$."112 The chance of such an agreement. if the parallax measurement were indeed spurious. is only about3%.," The chance of such an agreement, if the parallax measurement were indeed spurious, is only about."113. Thus. a decade after its discovery. the event remains truly a puzzle.," Thus, a decade after its discovery, the event remains truly a puzzle."114" llere I show that the parallax solution flor MACIIO-LMC-5 is subject to a four-fold degeneracy,", Here I show that the parallax solution for MACHO-LMC-5 is subject to a four-fold degeneracy.115 While two of these solutions are virtually identical to their counterparts. the other (wo lead to quite different estimates of the mass and distance.," While two of these solutions are virtually identical to their counterparts, the other two lead to quite different estimates of the mass and distance."116 One pair of solutions is equivalent to (the solution reported by Aleocketal.(2001)., One pair of solutions is equivalent to the solution reported by \citet{alcock01}.117. The other pair vields both a larger mass and larger distance., The other pair yields both a larger mass and larger distance.118 I show that these are consistent wilh the photometric determinations., I show that these are consistent with the photometric determinations.119 While it is customary to fit for microlens parallaxes in the Irae of the Sun. itis actually possible to stav much closer to the data if one adopts the geocentric point of view. which is illustrated in Figure 2..," While it is customary to fit for microlens parallaxes in the frame of the Sun, it is actually possible to stay much closer to the data if one adopts the geocentric point of view, which is illustrated in Figure \ref{fig:geo}."120 This can be important. especially in cases like the present one in which the parallax is only weakly detected.," This can be important, especially in cases like the present one in which the parallax is only weakly detected."121 Let s(/) be the Earth-to-Sun vector in units of AU in the heliocentric frame., Let $\bs(t)$ be the Earth-to-Sun vector in units of AU in the heliocentric frame.122" Let /,, be sone fixed (ime. in practice a time very close to the time fy of the peak of the event as seen from the Earth. and evaluate the derivative of s(/) at this time. Then in the geocentric [rame (and relative to its position at /,). the Sun has a positional olfset (see inset to Fig. 2))."," Let $t_p$ be some fixed time, in practice a time very close to the time $t_0$ of the peak of the event as seen from the Earth, and evaluate the derivative of $\bs(t)$ at this time, Then in the geocentric frame (and relative to its position at $t_p$ ), the Sun has a positional offset (see inset to Fig. \ref{fig:geo}) ),"123 Consider now observations toward an event at some given celestial coordinates. aud deline A and é as (he unit vectors pointing north and east.," Consider now observations toward an event at some given celestial coordinates, and define $\bn$ and $\be$ as the unit vectors pointing north and east."124 The projected position of the sun in the adopted frame will then be Note that this coordinate svstem is right-hancdec., The projected position of the Sun in the adopted frame will then be Note that this coordinate system is right-handed.125presence of a more smoothly distributed. population of clusters.,presence of a more smoothly distributed population of clusters.126 Parameters of oscillation and the scale of the net can be determined from observations if the number of clusters is sullicient to get an error corridor of the correlation function which is smaller than the amplitude of oscillations., Parameters of oscillation and the scale of the net can be determined from observations if the number of clusters is sufficient to get an error corridor of the correlation function which is smaller than the amplitude of oscillations.127 For a quasiregular population this minimal number of objects is about 30. and for a heterogeneous. population it is about 1000. depending on the fraction of the quasiregular component in the whole population of clusters.," For a quasiregular population this minimal number of objects is about 30, and for a heterogeneous population it is about 1000, depending on the fraction of the quasiregular component in the whole population of clusters."128 If superclusters are located in the corners of a random. cellular void network (Voronoi model) then the correlation function has a minimum. and its location corresponds to the mean separation between superclusters ancl voids.," If superclusters are located in the corners of a random cellular void network (Voronoi model) then the correlation function has a minimum, and its location corresponds to the mean separation between superclusters and voids."129 There follows a secondary maximunr corresponding to the clustering of clusters on opposite sides of voids., There follows a secondary maximum corresponding to the clustering of clusters on opposite sides of voids.130 Η the distribution of superclusters is random then the correlation function is featureless and becomes Iat after the initial highly. positive value., If the distribution of superclusters is random then the correlation function is featureless and becomes flat after the initial highly positive value.131 Oscillating properties of the correlation function are related to the shape of the power spectrum. near. the maximum of the spectrum., Oscillating properties of the correlation function are related to the shape of the power spectrum near the maximum of the spectrum.132 Oscillations occur only in the case when the spectrum has a sharp maximum ancl sudden transition of the spectral index from a positive value on large wavelengths and a negative one on short wavelengths., Oscillations occur only in the case when the spectrum has a sharp maximum and sudden transition of the spectral index from a positive value on large wavelengths and a negative one on short wavelengths.133 Thus we see that the correlation function is indeed a useful statistic of the geometry of [large scale. structures., Thus we see that the correlation function is indeed a useful statistic of the geometry of large scale structures.134 Observationallv. we have. emplovecd the larec scale correlation. Function. of a sample of Abell clusters (1297. Paper HD: we have exploited these results in a study. of the correlation function of Las Campanas Redshift Survey galaxies (Tucker 1995. 1997).," Observationally, we have employed the large scale correlation function of a sample of Abell clusters (E97, Paper II); we have exploited these results in a study of the correlation function of Las Campanas Redshift Survey galaxies (Tucker 1995, 1997)."135 This work was supported by Estonian Science Foundation erant 182 and International Science Foundation grant LLIE100., This work was supported by Estonian Science Foundation grant 182 and International Science Foundation grant LLF100.136 JE and AS were supported. in. Potsdam by the Deutsche Forschungseemeinschaft: AS was supported by the Russian Foundation for Basie Research Grant 96202-17591., JE and AS were supported in Potsdam by the Deutsche Forschungsgemeinschaft; AS was supported by the Russian Foundation for Basic Research Grant 96-02-17591.137 We thank It. van de Weveacrt for his Voronoi tessellation model program. and Ix.-H1. Bóhhning for his help to prepare figures.," We thank R. van de Weygaert for his Voronoi tessellation model program, and K.-H. Böhhning for his help to prepare figures."138"If, on the other hand, there a bend in the flux tube ([]~0). the only way to satisfy ((3)) is for the pre-factor to vanish.","If, on the other hand, there a bend in the flux tube $\disc{\that}\ne0$ ), the only way to satisfy \ref{eq:bend_eq}) ) is for the pre-factor to vanish."139" Since the non-trivial solution of all three Rankine-Hugoniot conditions would over-determine the system, they must be satisfied trivially, without discontinuity."," Since the non-trivial solution of all three Rankine-Hugoniot conditions would over-determine the system, they must be satisfied trivially, without discontinuity."140" In other words p;. and v are continuous at {η and satisfy the relation e,=0,/Anyvy the Altvénn speed."," In other words $\rho_i$, and $\vpar$ are continuous at $\mu_0$ and satisfy the relation $\vpar=B_e/\sqrt{4\pi\rho_i}=\va$ the Alfvénn speed."141 This is similar to an intermediate shock2000).. but includes the influence of fast magnetosonic waves assumed to be maintaining pressure balance across the tube.," This is similar to an intermediate shock, but includes the influence of fast magnetosonic waves assumed to be maintaining pressure balance across the tube."142 The A-shaped bend in the post-reconnection flux tube shown in reffig:geom will immediately decompose into four ditferent shocks of the kinds deseribed above., The $\Lambda$ -shaped bend in the post-reconnection flux tube shown in \\ref{fig:geom} will immediately decompose into four different shocks of the kinds described above.143" Two intermediate shocks (bends, B) propagate along the field lines, forming a straight horizontal section between them (see reffig:bend)), as previously found by(2006)."," Two intermediate shocks (bends, B) propagate along the field lines, forming a straight horizontal section between them (see \\ref{fig:bend}) ), as previously found by."144". Two GDSs propagate away from the center, at -Εὖ,, along the horizontal section."," Two GDSs propagate away from the center, at $\pm v_s$, along the horizontal section."145" This symmetric arrangement divides the tube into sections labeled, 2. 2 and 1. outward fromthe center."," This symmetric arrangement divides the tube into sections labeled, $3$, $2$ and $1$, outward fromthe center."146" Section 1 consists of the flux tube at restand in its initial state: vy=0, py=p, and py=υ.."," Section $1$ consists of the flux tube at restand in its initial state: $\vvec_1=0$, $\rho_1=\rho_e$ and $p_1=p_e$."147" The initial field lines are inclined at angle ¢, so t,—€&coscC-ZsinC. while ts= Xin the horizontal section."," The initial field lines are inclined at angle $\zeta$, so $\that_1=\xhat\cos\zeta-\zhat\sin\zeta$, while $\that_2=\xhat$ in the horizontal section."148" The bend propagates along the initial field at the Alfvénn speed: τα=ὃν,t4.", The bend propagates along the initial field at the Alfvénn speed: $\uvec=\vae\that_1$.149" The relative parallel flow is continuous across the bend ej,=6i»—0,;."," The relative parallel flow is continuous across the bend $v_{\parallel,1}=v_{\parallel,2}=-\vae$."150 These facts can be combined into the post-bend fluid velocity Vo=u 27 (7) directed along the bisector of the bend (the mean direction of the curvature force).," These facts can be combined into the post-bend fluid velocity _2 = + _2 = , directed along the bisector of the bend (the mean direction of the curvature force)."151" Internal quantities are continuous across the bends, so p»=pyp, andpo=pyp,."," Internal quantities are continuous across the bends, so $\rho_2=\rho_1=\rho_e$ and $p_2=p_1=p_e$."152" Froma reference frame moving downward at —Zv,,sinC. sections 2 and 3 appear to form a classic shock tube. with inflow at M, = _ sinr(Q//2) .(8) where 4=5/3 is the ratio ofspecific heats."," From a reference frame moving downward at $-\zhat\vae\sin\zeta$ sections $2$ and $3$ appear to form a classic shock tube, with inflow at M_2 = = /2) , where $\gamma=5/3$ is the ratio ofspecific heats."153 Since 9.« 1.this Alfvénnic inflow can have," Since $\beta_e\ll1$ ,this Alfvénnic inflow can have"154"Mmin increases, as shown in the left hand plot.","$M_{\rm min}$ increases, as shown in the left hand plot."155" Weighting halos by their masses is a poorer approximation to the optimal weight when Mi,>101°A!Mgo.", Weighting halos by their masses is a poorer approximation to the optimal weight when $M_{\rm min} >10^{13}~h^{-1}M_{\odot}$.156 The halo model prediction of the optimal weight is generally in good agreement with the measurements., The halo model prediction of the optimal weight is generally in good agreement with the measurements.157" The agreement is not perfect, however, especially when M approaches Myin."," The agreement is not perfect, however, especially when $M$ approaches $M_{\rm min}$."158" Figure 2 shows the stochasticity E associated with these linear estimators dm of the mass distribution, as a function of the minimum mass Mii, of halos included in the sample."," Figure \ref{evsm} shows the stochasticity $E$ associated with these linear estimators $\hat \delta_m$ of the mass distribution, as a function of the minimum mass $M_{\rm min}$ of halos included in the sample."159" Black, purple, blue, and red solid curves show E derived from optimal, mass, bias and uniform weighting of the halos."," Black, purple, blue, and red solid curves show $E$ derived from optimal, mass, bias and uniform weighting of the halos."160" Weighting halos by their masses yields lower E than bias weighting or equal weighting, but is significantly worse than the optimal when the halo catalog has Mmin©10?-!Mg or lower."," Weighting halos by their masses yields lower $E$ than bias weighting or equal weighting, but is significantly worse than the optimal when the halo catalog has $M_{\rm min}\approx 10^{13}h^{-1}M_\odot$ or lower."161" Bias weighting would be optimal if the standard biased Poisson model were correct, but is"," Bias weighting would be optimal if the standard biased Poisson model were correct, but is"162We present here contour maps and major axis photometric profiles for the sample of edge-on galaxies in the HIDE (Table 1).,We present here contour maps and major axis photometric profiles for the sample of edge-on galaxies in the HDF (Table 1).163would contain the Lo emission line at this redshift and the detected emission could be at least partially a result of this.,would contain the $\alpha$ emission line at this redshift and the detected emission could be at least partially a result of this.164 The discovery of such a distant. radio source from our initial spectroscopic observations demonstrate the promise of our survey for finding the most distant radio sources., The discovery of such a distant radio source from our initial spectroscopic observations demonstrate the promise of our survey for finding the most distant radio sources.165 We did not observe all of our candidates LRGs in this observing run due to poor weather. as à consequence the elective area surveyed. was only 74.5 square degrees.," We did not observe all of our candidates HzRGs in this observing run due to poor weather, as a consequence the effective area surveyed was only $\sim$ 4.5 square degrees."166 With further observations over the rest of the SWIRL and UIXIDSS DNS regions. we will certainly be able to make the most accurate measurements of the space density of radio sources at z>3 and hopefully discover the first radio source appropriate for 21 em absorption studies within the epoch of reionization.," With further observations over the rest of the SWIRE and UKIDSS DXS regions, we will certainly be able to make the most accurate measurements of the space density of radio sources at $z>3$ and hopefully discover the first radio source appropriate for 21 cm absorption studies within the epoch of reionization."167" ""This discovery also shows that samples constructed. on the basis of steepespectral index may miss a signilicant [fraction of high-redshift sources (see also Waddington et al.", This discovery also shows that samples constructed on the basis of steep-spectral index may miss a significant fraction of high-redshift sources (see also Waddington et al.168 1999)., 1999).169" Future observations of the rest of he 9,469;>10 mJy sources in the SWIRL/DNS fields will allow us to quantify the distribution of spectral indices fcr hese distant sources and aid in defining the search. criteria or distant radio sources with future radio continuum surveys made possible with LOPAR. EVLA and the SKA oecursor telescopes."," Future observations of the rest of the $S_{1.4\rm GHz}>10$ mJy sources in the SWIRE/DXS fields will allow us to quantify the distribution of spectral indices for these distant sources and aid in defining the search criteria for distant radio sources with future radio continuum surveys made possible with LOFAR, EVLA and the SKA precursor telescopes."170 Furthermore. future observations with he VISTA Deep Extragalactic Observations (VIDEO) survey /star-www.herts.ac.uk/-mjarvis/video) and the Spitzer Representative Volume survey (SIEBWVs: its.caltech.ecuy~mlacy/servs.btml) will not only allow to make an extremely selective sample of Hz: candidates but also allow us to measure the environmental density around these distant radio sources in the same wav that has been attempted around. the most. distant. QSOs (e.g. Willott et al.," Furthermore, future observations with the VISTA Deep Extragalactic Observations (VIDEO) survey $\sim$ mjarvis/video/) and the Spitzer Representative Volume survey (SERVs; $\sim$ mlacy/servs.html) will not only allow to make an extremely selective sample of HzRG candidates but also allow us to measure the environmental density around these distant radio sources in the same way that has been attempted around the most distant QSOs (e.g. Willott et al."171 2005: Stiavelli et al., 2005; Stiavelli et al.172 2005)., 2005).173 ALJJ acknowledges the support of an BRCUI fellowship., MJJ acknowledges the support of an RCUK fellowship.174 The WIPE is operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Itoque cde los Muchachos of the Instituto de Astrofisica de Canarias., The WHT is operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias.175and the maximum amplitude of the fluctuating field can exceed this values.,and the maximum amplitude of the fluctuating field can exceed this values.176 The parallel electric force associated with the Alfven wave dynamies could play an important role in a number of cases., The parallel electric force associated with the Alfven wave dynamics could play an important role in a number of cases.177 First. as the primary source of thermal electron acceleration. where waves and turbulence are triggered by the reconnection process(??) or as a result of the twisting of the field lines anchored in the photosphere.," First, as the primary source of thermal electron acceleration, where waves and turbulence are triggered by the reconnection \citep{Bellan1998,LongcopePriest2007} or as a result of the twisting of the field lines anchored in the photosphere."178 It has also been proposed that part of the energy released during magnetic. reconnection is transported by Alfven waves to the chromosphere(??).," It has also been proposed that part of the energy released during magnetic reconnection is transported by Alfven waves to the \citep{Emslie1982,Fletcher2008}."179. Therefore. in a situation where Alfvenic turbulence fills the loop. the waves will affect the transport of the energetic electrons to the chromosphere.," Therefore, in a situation where Alfvenic turbulence fills the loop, the waves will affect the transport of the energetic electrons to the chromosphere."180 Acceleration occurs along the field lines which are perturbed by the Alfven dynamics. hence the pace of the acceleration along Bo=By+dB_ also controls the cross-By transport.," Acceleration occurs along the field lines which are perturbed by the Alfven dynamics, hence the pace of the acceleration along $\mathbf{B}=\mathbf{B}_{0}+\mathbf{\delta B}_{\perp}$ also controls the $\mathbf{B}_{0}$ transport."181 Finally. as already mentioned in the Introduction. we note that if the electric field produced by Alfven turbulence can re-accelerate non-thermal electrons injected into the chromosphere this revision. of the standard Thick Target Model may resolve existing problems with it.," Finally, as already mentioned in the Introduction, we note that if the electric field produced by Alfven turbulence can re-accelerate non-thermal electrons injected into the chromosphere this revision of the standard Thick Target Model may resolve existing problems with it."182 Whether this 15 really the case depends on the detailed nature of the interaction between the parallel electric field and the electrons which requires a kinetic description. the subject of a future publication.," Whether this is really the case depends on the detailed nature of the interaction between the parallel electric field and the electrons which requires a kinetic description, the subject of a future publication."183The real positive solution corresponds to the physical image.,The real positive solution corresponds to the physical image.184" The discriminant of Equation (11)) is 4Jj97,", The discriminant of Equation \ref{eqn:poly2}) ) is $4\hat{\beta}^3 - 27$.185" Thus it has a real solution if 3<WV27/4: where. with. w=οσσο,"," Thus it has a real solution if $\hat{\beta} < \sqrt[3]{27/4}$ : where, with $\omega = e^{(2\pi/3)i}$."186 1This. solution. corresponds. to a physical. image. inside. the Einstein. rng., This solution corresponds to a physical image inside the Einstein ring.187 For 3q/27/4. Equation (11)) has three real solutions.," For $\hat{\beta} > \sqrt[3]{27/4}$, Equation \ref{eqn:poly2}) ) has three real solutions."188 However. two of them are not physical because (μον do not satisfy 9«0.," However, two of them are not physical because they do not satisfy $\hat{\theta} < 0$."189 Only the solution corresponds to aphysical image inside the Einstein ring., Only the solution corresponds to aphysical image inside the Einstein ring.190 Figure 2 shows the calculated images for source stars al various positions on a straight line (source trajectory)., Figure \ref{fig2} shows the calculated images for source stars at various positions on a straight line (source trajectory).191 The motion of the images are similar to those of the Seliwirzschild lensing., The motion of the images are similar to those of the Schwarzschild lensing.192" Table 1. shows the Einstein radii and angular Einstein radii [or a bulge star (Dy=Spe and D,=4hpe are assumed) and a star in the Large Magellanic Cloud (LMC. Ds=50lps and Dp=25/pe are assumed) for various throat radii."," Table \ref{tbl-1} shows the Einstein radii and angular Einstein radii for a bulge star $D_S = 8 kpc$ and $D_L = 4 kpc$ are assumed) and a star in the Large Magellanic Cloud (LMC, $D_S = 50 kps$ and $D_L = 25 kpc$ are assumed) for various throat radii."193 The detection of a lens [or which the Einstein radius is smaller than the star radius (z 105/75) is very difficult because most of the features of the gravitational lensing are smeared out by the finite-source effect., The detection of a lens for which the Einstein radius is smaller than the star radius $\thickapprox 10^6 km$ ) is very difficult because most of the features of the gravitational lensing are smeared out by the finite-source effect.194 Thus. detecting a wormhole with a throat radius less (han 14» from the Galactic gravitational lensing of a star is very difficult.," Thus, detecting a wormhole with a throat radius less than $1 km$ from the Galactic gravitational lensing of a star is very difficult."195The light curve of Schwarzschild lensing was derived by Paczviski (1936)...,The light curve of Schwarzschild lensing was derived by \citet{Pacz86}. .196 The same, The same197with a low mass SN component Ushimaruet.al.2004:Qian&Wasserbure2007).,"with a low mass SN component \citep{ish04,qw07}."198. Although the initial conditions of Ning.Qian.&Mever(2007) were taken from a stellar evolution model (Nomoto1984.1987).. the evolution of temperature and density in (he mass-shell trajectories was derived in a semi-analvtücal fashion assuming a shock speed in the region of interest approaching LOM em |.," Although the initial conditions of \cite{nqm07} were taken from a stellar evolution model \citep{nom84,nom87}, the evolution of temperature and density in the mass-shell trajectories was derived in a semi-analytical fashion assuming a shock speed in the region of interest approaching $10^{10}$ cm $^{-1}$ ."199 Using shock jump relations (Matzner 1999).. (hey derived the entropy and expansion (inmescale and obtained resulting nucleosvithesis that did exhibit characteristics reminiscent of r—process abundances.," Using shock jump relations \citep{mm99}, they derived the entropy and expansion timescale and obtained resulting nucleosynthesis that did exhibit characteristics reminiscent of $r-$ process abundances."200 The authors conclude by imploring further research (o test their assertions in modern finely zoned supernova explosion simulations of progenitors in (he same mass range., The authors conclude by imploring further research to test their assertions in modern finely zoned supernova explosion simulations of progenitors in the same mass range.201 Recently. Nitaura.Janka.&IHillebrandt:(2006) have calculated supernovae explosions in (his mass range. considering an AL. progenitor star with an O-Ne-Mg core (Nomoto and using a sophisticated treatment of neutrino transport.," Recently, \cite{kjh06} have calculated supernovae explosions in this mass range, considering an $\,M_\odot$ progenitor star with an O-Ne-Mg core \citep{nom84} and using a sophisticated treatment of neutrino transport."202 The nucleosvnthesis studies presented here are based on an update of these (spherically svannmietric) simulations for a revised progenitor model. in which the outer lavers of the helium shell and a dilute hydrogen envelope were added (Ix. Nomoto. private communication).," The nucleosynthesis studies presented here are based on an update of these (spherically symmetric) simulations for a revised progenitor model, in which the outer layers of the helium shell and a dilute hydrogen envelope were added (K. Nomoto, private communication)."203 The new simulations also include an improved treatment of electron captures and inelastic neutrino scattering by nuclei in NSE (Langankeet.al.2003.2007)..," The new simulations also include an improved treatment of electron captures and inelastic neutrino scattering by nuclei in NSE \citep{lmp03, lmp07}."204 The principle results of these simulations will be discussed in a separate publication (Müller&Janka|2008)., The principle results of these simulations will be discussed in a separate publication \citep{mj08}.205". Some relevant inlormation about the explosion dvnanies can be found in Jankaοἱ,al.(2007).", Some relevant information about the explosion dynamics can be found in \cite{jmkb07}.206. Our results survey explosive nucleosynthesis in 32 zones extracted [rom an 8.5 M. SN model starting at the edge of the O-Ne-Mg core ancl extending though the C-O and IIe lavers., Our results survey explosive nucleosynthesis in 32 zones extracted from an 8.8 $\Msun$ SN model starting at the edge of the O-Ne-Mg core and extending though the C-O and He layers.207 The mass-cut that. defined our inner most zone had an initial (pre-collapse) radius of 7.717x10* em with an enclosed mass of 1.363 M.., The mass-cut that defined our inner most zone had an initial (pre-collapse) radius of $7.717 \times 10^7$ cm with an enclosed mass of 1.363 $\Msun$.208 The last zone studied had a radius at the onset of core-collapse of 1.1306x105 em with an enclosed mass of 1.376 M.., The last zone studied had a radius at the onset of core-collapse of $1.1306 \times 10^8$ cm with an enclosed mass of 1.376 $\Msun$.209 The amount of processed ejecta is 0.013 M.., The amount of processed ejecta is 0.013 $\Msun$.210 Exterior to this was a hvdrogen envelope IH. He) whose outermost zone αἱ core-collapse was ab radius 6.414xLO! em with an enclosed mass ol 2.626 M...," Exterior to this was a hydrogen envelope H, He) whose outermost zone at core-collapse was at radius $6.414\times 10^{13}$ cm with an enclosed mass of 2.626 $\Msun$."211 The amount to total ejecta is the difference. 1.263 M...," The amount to total ejecta is the difference, 1.263 $\Msun$."212 During shock wave passage. (he temperature increased dramatically and in most οἱ ihe zones exceeded Jy=7.," During shock wave passage, the temperature increased dramatically and in most of the zones exceeded $T_9 = 7$."213 As such photo-disintegration will disassemble any C or O into a—particles and nucleons., As such photo-disintegration will disassemble any C or O into $\alpha-$ particles and nucleons.214 Each nucleosvnthesis caleulation started at a point in the expansion when (he temperature had declined to To=9.0 (or ils maxinnm value if it never achieved this). with the starting values of density and Y; also taken fromthe SN model.," Each nucleosynthesis calculation started at a point in the expansion when the temperature had declined to $_9=9.0$ (or its maximum value if it never achieved this), with the starting values of density and $Y_e$ also taken fromthe SN model,"215high inclination. of the northern component is confirmed by our measurements.,high inclination of the northern component is confirmed by our measurements.216 In particular. the almost face-on dise could explain why the emission of the spatially resolved Bry emission is observed blueshifted: the corresponding redshifted emission might be covered by the face-on disc.," In particular, the almost face-on disc could explain why the emission of the spatially resolved $\gamma$ emission is observed blueshifted: the corresponding redshifted emission might be covered by the face-on disc."217 Since the position angles of the disces can not be well constrained by our new data. we did our modelling (Section 4.3.2)) with fixed positiot angles (T. Beck. private communication) as well as with the position angles as free parameters.," Since the position angles of the discs can not be well constrained by our new data, we did our modelling (Section \ref{2bbm}) ) with fixed position angles (T. Beck, private communication) as well as with the position angles as free parameters."218 Both approaches lead to the same results., Both approaches lead to the same results.219 The main results of our study are that Haro 6-10 ts embedded in a common envelope (which causes the mid-infrared absorption feature in both components of the binary system). and that the two discs of the binary system are misaligned.," The main results of our study are that Haro 6-10 is embedded in a common envelope (which causes the mid-infrared absorption feature in both components of the binary system), and that the two discs of the binary system are misaligned."220 Observational studies of the dise. inclinations in. young binary systems have been carried out in the last years. using different techniques: polarimetric and direct observations of protoplanetary dises or indirect observations via the position of the jet from the protostellar object. which is expected to be perpendicular to the disc.," Observational studies of the disc inclinations in young binary systems have been carried out in the last years, using different techniques: polarimetric and direct observations of protoplanetary discs or indirect observations via the position of the jet from the protostellar object, which is expected to be perpendicular to the disc."221 Recently. also long-baseline infrared interferometry was used to measure the geometrical properties of circumstellar dises in binary systems.," Recently, also long-baseline infrared interferometry was used to measure the geometrical properties of circumstellar discs in binary systems."222 Polarimetric studies on the dise orientations have been carried out by. e.g.. 22?..," Polarimetric studies on the disc orientations have been carried out by, e.g., \citet{Moninetal1998, Wolfetal2001, Moninetal2006}."223 They all observed T Tauri stars and found that dises tend to be aligned in young binaries. ?..," They all observed T Tauri stars and found that discs tend to be aligned in young binaries. \cite{Jensenetal2004},"224 in particular. found a tendency for binary system dises to be nearly (but not exactly) aligned with each other. and for those in triple and quadruple systems to be There are also cases of misaligned discs found by observations of misaligned jets from protostellar objects (e.g.. ?).. Inferred jet precession (e.g..22).. and direct observations (e.g..22).," in particular, found a tendency for binary system discs to be nearly (but not exactly) aligned with each other, and for those in triple and quadruple systems to be There are also cases of misaligned discs found by observations of misaligned jets from protostellar objects \citep[e.g.,][]{Davisetal1994}, inferred jet precession \citep[e.g.,][]{Eisloffeletal1996, Davisetal1997}, and direct observations \citep[e.g.,][]{Koresko1998, Stapelfeldtetal1998a}."225 A recent interferometric study of T Tau showed that the dises in this triple system are misaligned (?):: The circumstellar dise of the northern component is seen almost face-on. while the southern components are surrounded by higher inclined discs.," A recent interferometric study of T Tau showed that the discs in this triple system are misaligned \citep{Ratzkaetal2009}: The circumstellar disc of the northern component is seen almost face-on, while the southern components are surrounded by higher inclined discs."226 Especially the dise around T Tau Sa. the most massive star in the system and a prototypical IRC. is seen almost edge-on.," Especially the disc around T Tau Sa, the most massive star in the system and a prototypical IRC, is seen almost edge-on."227 The formation process of T Tau thus has to have been highly dynamic., The formation process of T Tau thus has to have been highly dynamic.228 However. these cases of misaligned discs do not represent yet a statistical significant sample.," However, these cases of misaligned discs do not represent yet a statistical significant sample."229The ionization fraction for hyclrogen is defined. as For any svstem (he ionization fraction depends on the net recombination rate in the svstem.,The ionization fraction for hydrogen is defined as For any system the ionization fraction depends on the net recombination rate in the system.230 For a svstem in LTE. the ionization fraction can be calculated using the Saha equation wilh knowledge of the electron density and temperature.," For a system in LTE, the ionization fraction can be calculated using the Saha equation with knowledge of the electron density and temperature."231 On the other hand. for svstems not in LTE. it is important to solve the radiative transler equation and the rate equations simultaneously.," On the other hand, for systems not in LTE, it is important to solve the radiative transfer equation and the rate equations simultaneously."232 The recombination rate of a system is dependent on the munuber of angular momentum sub-states of the svstem. aud also on the presence of other elements in the environment that can contribute to the free electron density., The recombination rate of a system is dependent on the number of angular momentum sub-states of the system and also on the presence of other elements in the environment that can contribute to the free electron density.233 The recombination process in a svstem is determined bv the net rate of photo-ionization and iis inverse process (recombination) which are modified due to line transitions., The recombination process in a system is determined by the net rate of photo-ionization and its inverse process (recombination) which are modified due to line transitions.234 The effectiveness (towards recombination) of a resonant transition depends on the escape probability of the line., The effectiveness (towards recombination) of a resonant transition depends on the escape probability of the line.235 Also there are transitions (hat take place such as the collisional de-excitation of electrons to lower energy levels., Also there are non-radiative transitions that take place such as the collisional de-excitation of electrons to lower energy levels.236 In addition to these there is the downward 25. process that connects states of (he same parity while the corresponding upward transition rate is verv low., In addition to these there is the downward $\gamma$ process that connects states of the same parity while the corresponding upward transition rate is very low.237 Therefore i( is important to study all these quantities to determine the correct nature of recombination., Therefore it is important to study all these quantities to determine the correct nature of recombination.238 We investigate the 25 process. the photo-ionization rale. (he escape probability and the collisional de-excitation rates of svstems with different hycrogen atom models and metallicities of the environment.," We investigate the $\gamma$ process, the photo-ionization rate, the escape probability and the collisional de-excitation rates of systems with different hydrogen atom models and metallicities of the environment."239 We denote 15; as (he photo-ionizalion rate [from a state with index » (which is not its principal «quantum number)., We denote $P_{\textit{n}}$ as the photo-ionization rate from a state with index $n$ (which is not its principal quantum number).240" Similarly. we define the escape probability as ;2,, which is the escape probability. for the resonant line photon between the level 15 and the level characterized by index »."," Similarly, we define the escape probability as $\beta_{n1}$ which is the escape probability for the resonant line photon between the level $1s$ and the level characterized by index $n$."241 The collisional cle-excitation rate is defimed as the rate of, The collisional de-excitation rate is defined as the rate of242open field lines defining the outer gap. anc calculate the emission direction in the observer's frame at cach point on the field lines.,"open field lines defining the outer gap, and calculate the emission direction in the observer's frame at each point on the field lines."243 In Tang et al. (, In Tang et al. (2442008). the emission direction coincides with the direction of the rotating vacuum dipole field defined in the co-rotating frame.,"2008), the emission direction coincides with the direction of the rotating vacuum dipole field defined in the co-rotating frame."245 In the present three-dimensional model. on the other hand. the emission direction calculated in only observer's frame with the computation method. employed. by Takata et al. (," In the present three-dimensional model, on the other hand, the emission direction calculated in only observer's frame with the computation method employed by Takata et al. ("2462007).,2007).247 The curvature photons are assumed to be emitted in the direction of the particle motion. which can be described as where the first term represents the motion along the magnetic field line. ον is calculated from the condition that π—c. and the second term is the drift motion.," The curvature photons are assumed to be emitted in the direction of the particle motion, which can be described as where the first term represents the motion along the magnetic field line, $v_p$ is calculated from the condition that $|\vec{v}|=c$, and the second term is the drift motion."248 The polar anele to the rotation axis ὁ of the emission direction and the pulse phase c are calculated from (Yacligaroglueo 1997)., The polar angle to the rotation axis $\zeta$ of the emission direction and the pulse phase $\psi$ are calculated from (Yadigaroglu 1997).249 Wa point in a field line satisfies le3<ofr). the radiation. of that. point can be seen by the observer. where 3 is the viewing angle. and yor)=ANP)μὴ.," If a point in a field line satisfies $|\zeta-\beta|<\varphi(r)$, the radiation of that point can be seen by the observer, where $\beta$ is the viewing angle and $\varphi(\vec{r})=\Delta{l}(\vec{r})/s(\vec{r})$."250 Because the positions of the first and second. peaks in the light curve is also. determined. by viewing ecomoetry. the predicted inclination angle a and the viewing angle 3 are uniquely determined by comparing the calculated peak separation with the observations.," Because the positions of the first and second peaks in the light curve is also determined by viewing geometry, the predicted inclination angle $\alpha$ and the viewing angle $\beta$ are uniquely determined by comparing the calculated peak separation with the observations."251 In this section. we apply our model to the Vela pulsar.," In this section, we apply our model to the Vela pulsar."252 In our two-laver model. the general. properties. of. 5-rav emissions from the outer gap are characterized by. f. gy and fifhe.," In our two-layer model, the general properties of $\gamma$ -ray emissions from the outer gap are characterized by $f$, $g_1$ and $h_1/h_2$."253 Specifically. the gap fraction f£. mainly. determines the cut-olf energy in the spectrum.," Specifically, the gap fraction $f$ mainly determines the cut-off energy in the spectrum."254 Zhang Cheng (1997) suggested. a scll-consistent mechanism provided by the ravs emitted by the polar cap that is heated by the return current to restrict the gap., Zhang Cheng (1997) suggested a self-consistent mechanism provided by the X-rays emitted by the polar cap that is heated by the return current to restrict the gap.255" Their fractional size of the gap. [zo=0.42477""qugs prediets that of the Vela. pulsar is 0.15."," Their fractional size of the gap, $f_{ZC}=0.32P^{26/21}_{-1}B^{-4/7}_{12}$, predicts that of the Vela pulsar is 0.15."256 In the two-dimensional model (Wang ct al., In the two-dimensional model (Wang et al.257 2010). f=1.16 was used for fitting the phase-averaged spectrum of the Vela pulsar.," 2010), $f=0.16$ was used for fitting the phase-averaged spectrum of the Vela pulsar."258 Ehe current in the main acceleration region. 1gy. and the ratio between the thicknesses of the main acceleration region and that of the whole gap. by fhe. determine the photon index of the spectrum together.," The current in the main acceleration region, $1-g_1$, and the ratio between the thicknesses of the main acceleration region and that of the whole gap, $h_1/h_2$ , determine the photon index of the spectrum together."259 For the Vela pulsar. the fitting of the two-dimensional two-Laver model gives 1gy=0.)s and byfhe.=0.927 (Wane ct al.," For the Vela pulsar, the fitting of the two-dimensional two-layer model gives $1-g_1=0.08$ and $h_1/h_2=0.927$ (Wang et al."260 2010)., 2010).261 The position of the upper boundary. ανν is treated as à model parameter. because it is alfected hy the actual magnetic field. structure. which is not understood well.," The position of the upper boundary $a_{min}$ is treated as a model parameter, because it is affected by the actual magnetic field structure, which is not understood well."262 ‘Together with the inclination angle a and the viewing angle 3. the position of the upper boundary ην can be constrained by the detailed structure of pulsed. profile.," Together with the inclination angle $\alpha$ and the viewing angle $\beta$, the position of the upper boundary $a_{min}$ can be constrained by the detailed structure of pulsed profile."263 As we show in the following section. we find that the set of (o.0.(uis)=(Y.SOT. 0.935) reproduces well both the light curves and the spectra.," As we show in the following section, we find that the set of $\alpha,~\beta,~a_{min})=(57^{\circ},~80^{\circ},~0.935$ ) reproduces well both the light curves and the spectra."264 Figure 2. shows the skv-map of the emitted photons from the magnetic surface of a=0.95 with a—57 and 93=SO., Figure \ref{skymap} shows the sky-map of the emitted photons from the magnetic surface of $a=0.95$ with $\alpha=57^{\circ}$ and $\beta=80^{\circ}$.265 Although there are many sets of the inclination angle and the viewing angle that can provide the observed. peak separation. our choice of these two angles is not arbitrary.," Although there are many sets of the inclination angle and the viewing angle that can provide the observed peak separation, our choice of these two angles is not arbitrary."266 The reason for this will be discussed later., The reason for this will be discussed later.267 Firstly. we assume constant 1ο and f in the azimuthal direction.," Firstly, we assume constant $1-g_1$, $h_1/h_2$ and $f$ in the azimuthal direction."268 By fitting the phase-averaged spectrum [or the Vela pulsar. we obtain 1 and f=0.2 for the present threc-dimensional mocdel.," By fitting the phase-averaged spectrum for the Vela pulsar, we obtain $1-g_1=0.05$, $h_1/h_2=0.927$ and $f=0.2$ for the present three-dimensional model."269 Lere we assume the distance of 2=325 pe., Here we assume the distance of $D=325$ pc.270 ligure 3. compares the caleulated (histograms) and the observes. (solid. lines) pulse profiles in six cillerent. energy bands., Figure \ref{edlc_nd} compares the calculated (histograms) and the observes (solid lines) pulse profiles in six different energy bands.271 We can see in Figure 3. that the model provided pulse profiles ave generally. consistent with the observations., We can see in Figure \ref{edlc_nd} that the model provided pulse profiles are generally consistent with the observations.272 For example. the pulsed. profiles in wide energy bands have two main peaks with the separation of about 0.42.," For example, the pulsed profiles in wide energy bands have two main peaks with the separation of about 0.42."273 Phe positions of the two peaks in the light curves are determined by the ecometry of the magnetic field., The positions of the two peaks in the light curves are determined by the geometry of the magnetic field.274 In the present. simple model. however. the caleulated pulse profile can not explain the existence of the observed third peak between (wo main peaks. as we can see in Figure 3..," In the present simple model, however, the calculated pulse profile can not explain the existence of the observed third peak between two main peaks, as we can see in Figure \ref{edlc_nd}."275 The peaks emerging in the calculated: pulse profiles of Figure 3. are caused bv so called: caustic effects (Yadigaloglu and Romani 1995: Cheng. Ruderman and Zhang5 2000: Dyks. Harding5 and Rucdak 2004). in which more photons are observed at narrow width of the rotation phase ue to the specialerelativistie elfect (that is. the aberration X the emission direction and. photon's travel time).," The peaks emerging in the calculated pulse profiles of Figure \ref{edlc_nd}276 are caused by so called caustic effects (Yadigaloglu and Romani 1995; Cheng, Ruderman and Zhang 2000; Dyks, Harding and Rudak 2004), in which more photons are observed at narrow width of the rotation phase due to the special-relativistic effect (that is, the aberration of the emission direction and photon's travel time)."277" In the ""austic model. the phases of the peaks are determined. by 1e magnetic field structure. and they do not. depend: on 1f energy. band."," In the caustic model, the phases of the peaks are determined by the magnetic field structure and they do not depend on the energy band."278 On the other hand. the observed: phase X the third peak shifts with the energy bands.," On the other hand, the observed phase of the third peak shifts with the energy bands."279 Lhe simple caustic model can not explain the phase shift of the observed ird peak., The simple caustic model can not explain the phase shift of the observed third peak.280 On theseground. we speculate that the existence of the third peak and its phase shift is related with more complex structure of the emission region.," On theseground, we speculate that the existence of the third peak and its phase shift is related with more complex structure of the emission region."281"radius is then given bv ri,στ(Le,2x04)!?T,> where ay is the Stefan-Boltzimann constant.","radius is then given by $r_{in} \simeq (L_{th}/2\pi \sigma_S)^{1/2} T_d^{-2}$, where $\sigma_S$ is the Stefan-Boltzmann constant."282 There is still some debate over whether the data from. hard state NRBs προς a truncated mner disk radius or uot. with often couflicting results from continuum fitting of the thermal accretion disk. aud the modeling of the potentially broadened irou fluorescence line atalle 6.1 keV. Several groups claim an inner radius of typic Vin13 1055 where ry=2GALIpy ©?is the Sclavarzschild radius of a nou-rotating black hole (Esinc£al2001:Tousickctal2009:Done&DiazTrigo 2010).," There is still some debate over whether the data from hard state XRBs implies a truncated inner disk radius or not, with often conflicting results from continuum fitting of the thermal accretion disk, and the modeling of the potentially broadened iron fluorescence line at 6.4 keV. Several groups claim an inner radius of typically $r_{in}283\sim 10^{2} - 10^3 \, r_s$ , where $r_s =2G M_{BH}/c^2$ is the Schwarzschild radius of a non-rotating black hole \citep{Esin01,284 Tomsick+09, DDT10}."285" Ou the other haud. several recent works argue that the data iuplv a lower iunuer radius. ~10—1002,74. (Reynoldsetal, 2010)... or even against the need for a recessed disk to explain the data ίσιο,Reisetal2009:Revuolds&Aliller 2010)."," On the other hand, several recent works argue that the data imply a lower inner radius, $\sim 10 - 10^{1.5} \, r_s$, \citep{RMHM10}, or even against the need for a recessed disk to explain the data \citep[e.g.,][]{RMF09, RM10}."286. Regardless of the exact radius where it occurs. eencrallv we do expect a trausition of properties iu the iuflow/outflow of the accreting plasma.," Regardless of the exact radius where it occurs, generally we do expect a transition of properties in the inflow/outflow of the accreting plasma."287" Once the gas approaches the disk tuner radius r;,. if is expected to become eeomoetricallvy thicker aud optically thin. aud also radiativelv inefficicut."," Once the gas approaches the disk inner radius $r_{in}$, it is expected to become geometrically thicker and optically thin, and also radiatively inefficient."288 Several variations of the original acivection-domiuated accretion flaw (ADAF:seeNarawau&MeClintock.2008.forarecentreview) scenario. nore eoncrally referred to as radiatively inefficient accretion flows (RIAFs) now exist.," Several variations of the original advection-dominated accretion flow \citep[ADAF; see][for a recent289review]{NM08} scenario, more generally referred to as radiatively inefficient accretion flows (RIAFs) now exist."290 Because RIAFSs are likely necessary to support jet lanuchine (see.e.g..Livioctαἱ.1999:Meier. 2001).. we here assume such a transition is likely.," Because RIAFs are likely necessary to support jet launching \citep[see, e.g.,][]{LOP99,291 Meier01}, we here assume such a transition is likely."292" Towever. since emission from RIAFs las becu extensively studied in the past(e.e..jets,Esiuetal1997. 2001).. we currently focus ou the ubssi"," However, since emission from RIAFs has been extensively studied in the past \citep[e.g.,][]{Esin97, Esin01}, we currently focus on the jets."293on!While we assume here that thejets dominate the. we note that a possible coutributiou from the RIAF may alter our final results.," While we assume here that the jets dominate the, we note that a possible contribution from the RIAF may alter our final results."294 We thus asstmuc that at some radius rj). part of the plasima is ejected outward from sviuuuctric nozzles into a jet outflow.," We thus assume that at some radius $r_j$, part of the plasma is ejected outward from symmetric nozzles into a jet outflow."295" Iu the caleulatious presented. is taken as an independent variable. that is not necessarily7; equal to +;,."," In the calculations presented, $r_j$ is taken as an independent variable, that is not necessarily equal to $r_{in}$."296 During the ejection process. the clectrous are accelerated.," During the ejection process, the electrons are accelerated."297 Such an acceleration can result from Fermi acceleration iu shock waves (Ellisonetal.1990:Spitkovskv 2008).. or perhaps in reconnection lavers of strong magnetized outflows(c.g.Dreukhalin.&Spruit 2002).," Such an acceleration can result from Fermi acceleration in shock waves \citep{EJR90, Spit08}, or perhaps in reconnection layers of strong magnetized outflows \citep[e.g.,][]{DS02}."298". We paraimcterize the current uncertainties about the details of the acceleration process by siniply assis that a fraction £j of the clectrous are accelerated to a power law distribution with power law index p above a characteristic Lorentz factor 5,,. likely set bv the thermal temperature of the innermost accretion flow."," We parameterize the current uncertainties about the details of the acceleration process by simply assuming that a fraction $\xi_{pl}$ of the electrons are accelerated to a power law distribution with power law index $p$ above a characteristic Lorentz factor $\gamma_m$, likely set by the thermal temperature of the innermost accretion flow."299" The remaining electrous (a fraction Lo £,/) asstuc a Maxwellian distribution. with tempcrature mapa0—kTClawine?—5,/2. amie smooth connection with the power at higher energies."," The remaining electrons (a fraction $1-\xi_{pl}$ ) assume a relativistic Maxwellian distribution, with temperature $\theta \equiv kT/m_e c^2 = \gamma_m/2$, ensuring smooth connection with the power law at higher energies."300" Iu order to connect the acceleration microplivsies to the system euergeties, we further asstuue that a fraction e, of the jet kinetic luminosityLj is dissipated away. carried bv the energetic electrous."," In order to connect the acceleration microphysics to the system energetics, we further assume that a fraction $\epsilon_e$ of the jet kinetic luminosity$L_k$ is dissipated away, carried by the energetic electrons."301 This assumption therefore resultsin the coustraiut (0...Peer&Waxiian2001):: CURE uds be—we dU ( 9922.," This assumption therefore results in the constraint \citep[e.g.,][]{PW04}: _m = _e ) ), p=2, _e ) 2."302 Tere. éuas CGuin) Is the maxima (nuünnuun)euergv of the accelerated electrous .," Here, $\epsilon_{\max}$ $\epsilon_{\min}$ ) is the maximum (minimum)energy of the accelerated electrons ."303" The πλακα. energv is calculated bv equating the acceleration time to the cooling time οι, via svuchrotrou cussion). aud the Wun euerev. for power law index p—2 is calculated Heratively, AS Guinμυiterativel"," The maximum energy is calculated by equating the acceleration time to the cooling time (e.g., via synchrotron emission), and the minimum energy, for power law index $p=2$ is calculated iteratively, as $\epsilon_{\min} = \gamma_m m_e304c^2$."305yFollowing the calculation of στων it is corrected to account for the fraction 1.£4 of the electrous that asstime a Maxwellian distribution. so that the energy density iu the combined (Maxwellian | power law) electron population exactly equals a fraction e. of the enerev density in theide jet.," Following the calculation of $\gamma_{m}$, it is corrected iteratively to account for the fraction $1-\xi_{pl}$ of the electrons that assume a Maxwellian distribution, so that the energy density in the combined (Maxwellian + power law) electron population exactly equals a fraction $\epsilon_e$ of the energy density in the jet."306 The particles propagate at bulls velocity 3j«¢ he jet. diving a (comoving) dyuamnical time tyne2ΜΗ)oie. where 5;=(1H)1/2 is the Lorentz factor associated with the bulk motion of the plasma.," The particles propagate at bulk velocity $\beta_j c$ inside the jet, during a (comoving) dynamical time $t_{dyn} \simeq \gamma_j307r_j/\beta_j c$ , where $\gamma_j = (1-\beta_j^2)^{-1/2}$ is the Lorentz factor associated with the bulk motion of the plasma."308 During this time. a continuous injection (and acceleration) of particles at the base of the jet is assumed.," During this time, a continuous injection (and acceleration) of particles at the base of the jet is assumed."309 We assume the existence of a steady maguetic field of strength B inside the jet., We assume the existence of a steady magnetic field of strength $B$ inside the jet.310" While iu some works the magnetic οπσον density is described as a fraction ερ of the thatjet energy. (analogue to the definition of €,.). we note as the source of the magnetic field may be attached to the immer parts of the disk. it is possible that epl."," While in some works the magnetic energy density is described as a fraction $\epsilon_B$ of the jet energy (analogue to the definition of $\epsilon_e$ ), we note that as the source of the magnetic field may be attached to the inner parts of the disk, it is possible that $\epsilon_B \geq 1$."311 Therefore. here we consider B to be a free parameter.," Therefore, here we consider $B$ to be a free parameter."312 As a result. once introduced iuton the jet. the particles lose thei energv via radiatively Πιο cherectic photons.," As a result, once introduced into the jet, the particles lose their energy via radiatively producing energetic photons."313 This energy loss results from svuchnrotrou enuüssiou aud by inverse Compton scattering of both the thermal disk photons as well as the svuchrotron emitted photous (SSC)., This energy loss results from synchrotron emission and by inverse Compton scattering of both the thermal disk photons as well as the synchrotron emitted photons (SSC).314" The existence of characteristic plivsical scale (5j (correspouding to characteristic time ty, ) iuplies that the physical quautitics the(0... the magnetic field DB the energv deusitv in photon field) do not vary sjenificautlv over this scale."," The existence of a characteristic physical scale $r_j$ (corresponding to characteristic time $t_{dyn}$ ) implies that the physical quantities (e.g., the magnetic field $B$ or the energy density in the photon field) do not vary significantly over this scale."315 In particular. we neglect adiabatic cnereyv losses over ts scale. as its contribution to the electrons cooling is(bv definition) mach weaker than the radiative cooling(scefurtherdiscussionin&Casella 2009).," In particular, we neglect adiabatic energy losses over this scale, as its contribution to the electrons cooling is (by definition) much weaker than the radiative cooling \citep[see further discussion in][]{PC09}."316. The radiative cooling time of electrons at cucrey oc? ds eiven by (n the Thourpson regine): ΕΠΕdup) wherehere ty={πο Lufsées?and up=[PssBoyer axwo the (comoving) cucrey deusities of the thermal photous (asstine evliudrical eeoietry) aud the maguetic field. respectively.," The radiative cooling time of electrons at energy $E = \gamma m_e c^2$ is given by (in the Thompson regime): =, where $u_{th} = L_{th}/\pi r_j^2 \beta_j c \gamma_j^2$ and $u_B =317B^2/8 \pi$ are the (comoving) energy densities of the thermal photons (assuming cylindrical geometry) and the magnetic field, respectively."318" We denote bv +, the Loreutz factor of the clectrous for which the cooliug time is comparable to the chyπας time. 2.=(ολBeary,| ο: "," We denote by $\gamma_c$ the Lorentz factor of the electrons for which the cooling time is comparable to the dynamical time, $\gamma_c = (m_e319c^2)/(4/3) c \sigma_T (u_{th} + u_B) t_{dyn}$ ."320"For 5.al« +,,. theelectron energy distribution iu the range5.«Rm3,» Yeaches a steady state; which is calculatedby solving the rate equation. ωσεί= --Since the power emitted ly both svuchrotrou and Compton scattering is Dae7XO05/0tx 27. the steady state electron distribution at the range 5,«+SLOWw"" ∙↴ IT)xw2 7."," For $\gamma_c \ll321\gamma_m$ , theelectron energy distribution in the range$\gamma_c \ll322\gamma \ll \gamma_m$ reaches a steady state, which is calculated by solving the rate equation, ${dn_{el}(\gamma,t) / dt} = (\partial323/ \partial \gamma) \left[ n_{el}(\gamma) {\partial \gamma / \partial324 t} \right] = 0.$ Since the power emitted by both synchrotron radiation and Compton scattering is $P_{syn, IC} \propto \partial325\gamma /\partial t \propto \gamma^2$ , the steady state electron distribution at the range $\gamma_c \ll \gamma \ll \gamma_m$ is $n_{el} (\gamma) \propto \gamma^{-2}$ ."326is proportional to the total optical luminosity of the cluster galaxies. (Songaila et al.,is proportional to the total optical luminosity of the cluster galaxies (Songaila et al.327 1990: Ciotti et al., 1990; Ciotti et al.328 LOOL: Arnaud et al., 1991; Arnaud et al.329 1992: Renzini et al., 1992; Renzini et al.330 1993)., 1993).331 This strongly. argues for the iron (metals) now in the ICM having been produced. by the (massive) stars of the same stellar population to which belong the low-mass stars now producing the bulk of the cluster optical light., This strongly argues for the iron (metals) now in the ICM having been produced by the (massive) stars of the same stellar population to which belong the low-mass stars now producing the bulk of the cluster optical light.332 As well known. much of the cluster light comes from the old spheroidals (cllipticals and bulges). hence one can sav thatyoung.," As well known, much of the cluster light comes from the old spheroidals (ellipticals and bulges), hence one can say that."333 lt is now well established. that the stellar populations in spheroicals — in clusters as well in the field are very old. with the bulk of stars having formed at 223 (for a recent review with extensive references see Renzini Cimatti 1999).," It is now well established that the stellar populations in spheroidals – in clusters as well in the field – are very old, with the bulk of stars having formed at $z\gsim 3$ (for a recent review with extensive references see Renzini Cimatti 1999)."334 Therefore. the simplest. interpretation of the data suggests that the bulk of the heavy elements. in the ICM. were produced. and. expelled. (rom. galaxies a long lime ago. Le. al zzz3.," Therefore, the simplest interpretation of the data suggests that the bulk of the heavy elements in the ICM were produced and expelled from galaxies a long time ago, i.e. at $z\gsim 3$."335 Iso. the ICM abundances should not show any significant evolution all the wav to very high redshifts.," If so, the ICM abundances should not show any significant evolution all the way to very high redshifts."336 Existing data are in agreement with this prediction (see Fig., Existing data are in agreement with this prediction (see Fig.337 1). but do not reach much bevond z20.5.," 1), but do not reach much beyond $z\simeq 0.5$."338 Future X-ray observatories could check this prediction., Future X-ray observatories could check this prediction.339 Lt is also interesting to adcdress the question of which galaxies have produced the bulk of the iron and the other heavy elements. ie. the relative contribution as a function of the present-day luminosity of cluster galaxies.," It is also interesting to address the question of which galaxies have produced the bulk of the iron and the other heavy elements, i.e. the relative contribution as a function of the present-day luminosity of cluster galaxies."340 This has been recently, This has been recently341ol light: so the contribution of line radiation to the energy and momentum budgets is not included. which is a weakness of the procedure.,"of light; so the contribution of line radiation to the energy and momentum budgets is not included, which is a weakness of the procedure."342 However. CIL [or instance. has onlv 3 resonance lines. all of order 3 to 4 eV (Radzie and Smirnov (1985))). not enough to play a significant role in the reaction budget.," However, CH, for instance, has only 3 resonance lines, all of order 3 to 4 eV (Radzig and Smirnov \cite{rad}) ), not enough to play a significant role in the reaction budget."343 The computations were perlormed [or impact parameters p—0. 1. 2. 3. 4. 5 A and I velocities. V. between 5 and 110 24 per picosecond (5104 and 1.1109 1).," The computations were performed for impact parameters p=0, 1, 2, 3, 4, 5 $\AA{\ }$ and H velocities, V, between 5 and 110 $\AA{\ }$ per picosecond $5\,10^{4}$ and $1.1\, 10^{6}$ $^{-1}$ )."344 No association was observed [for p>3 A. nor for V higher than 510° ! (which corresponds to a L gas temperature of 21200 IN).," No association was observed for $>$ 3 $\AA{\ }$, nor for V higher than $5\, 10^{5}$ $^{-1}$ (which corresponds to a H gas temperature of $\sim$ 1200 K)."345 For p=3 21. association occured [or all velocities lower than 510enis !Í ," For p=3 $\AA{\ }$, association occured for all velocities lower than $5\, 10^{5}$ $^{-1}$ ."346No activation energy. was detectable., No activation energy was detectable.347" Lf the cross-section radius is taken as 3 1. the area becomes 27.2LO19 οι”,"," If the cross-section radius is taken as 3 $\AA{\ }$, the area becomes $27.2\,\,10^{-16}$ $^{2}$."348 At a gas temperature of 300 IX (reference temperature for rates in Rate06). the relative velocity of C and ILis 2.410? ! and k126.6101 emis. !F.," At a gas temperature of 300 K (reference temperature for rates in Rate06), the relative velocity of C and H is $2.4\,\,10^{5}$ $^{-1}$ and $6.6\,\,10^{-10}$ $^{3}$ $^{-1}$."349 However. caution is in orderhere. because the dependence on temperature of neutral-neutral reaction rates in general is not vet. fully documented experimentally (see Smith et al. (2004))):," However, caution is in orderhere, because the dependence on temperature of neutral-neutral reaction rates in general is not yet fully documented experimentally (see Smith et al. \cite{smi}) );"350 so kl was set at 10.P ems | in Table 1. but computations were also mace for0.1 and 6.6 10.1 em?s. +. [or comparison.," so k1 was set at $10^{-10}$ $^{3}$ $^{-1}$ in Table 1, but computations were also made for0.1 and 6.6 $10^{-10}$ $^{3}$ $^{-1}$, for comparison."351 Similar computations were made for CII+CII- Coll., Similar computations were made for $\to$ $_{2}$ $_{2}$ .352ollscts from the centre by integrating the emission. along the lines of sight.,offsets from the centre by integrating the emission along the lines of sight.353" It is then possible to regrid the data in the map plane and convolve with the (tvpically Gaussian) beam pattern of the telescope. which for the JCM'T is 15""."," It is then possible to regrid the data in the map plane and convolve with the (typically Gaussian) beam pattern of the telescope, which for the JCMT is $15\arcsec$."354 The spectra are computed with a frequency resolution of Q.01kms5.," The spectra are computed with a frequency resolution of $0.01~{\rm355km~s^{-1}}$."356 Once a plausible general model has been set up. observational data can be read directly into the code and multiple models. with varvine parameters can be calculated and the dillerence. between the mocel and the cata minimized.," Once a plausible general model has been set up, observational data can be read directly into the code and multiple models with varying parameters can be calculated and the difference between the model and the data minimized."357 The dimension of the model cube is selected so that the data points are positioned at integer values of the cube spacing., The dimension of the model cube is selected so that the data points are positioned at integer values of the cube spacing.358 The data is regridded so that the cata channels match those of the model output., The data is regridded so that the data channels match those of the model output.359 After generating a model cube. the code compares the model with the data and calculates 47 for that fit.," After generating a model cube, the code compares the model with the data and calculates $\chi^2$ for that fit."360 Phe numerical techniques of simplex and simulated. annealing are usec to drive the refining process where the code adopts new parameters and calculates a new cube: full details are given in νουctal. (2003)., The numerical techniques of simplex and simulated annealing are used to drive the refining process where the code adopts new parameters and calculates a new cube; full details are given in \citet{keto.et.al03}.361. X tvpical fitting run may require the caleulation of several hundred model cubes., A typical fitting run may require the calculation of several hundred model cubes.362 The model parameters are Listed in Table 4.3. along with either the fixed. adopted: values used. in the code or the range over which a parameter was allowed to vary., The model parameters are listed in Table \ref{parameters} along with either the fixed adopted values used in the code or the range over which a parameter was allowed to vary.363 The number of mocdel runs required to explore the parameter space increases rapidly with the number of free parameters so those parameters which have the best empirical contraints were given fixed. values., The number of model runs required to explore the parameter space increases rapidly with the number of free parameters so those parameters which have the best empirical contraints were given fixed values.364 The density profile used is that of a Plummer sphere which is ceLlinecl as where po is the central density anc ry is the Plummer radius., The density profile used is that of a Plummer sphere which is defined as where $\rho_0$ is the central density and $r_0$ is the Plummer radius.365 This simple density law has the property that as rosQ. ptr)po while for laree r. podspofi? ," This simple density law has the property that as $r\rightarrow3660$, $\rho(r)\rightarrow \rho_0$ while for large $r$, $\rho(r)\rightarrow {\rho_0 / r^2}$."367The outer radius of the cloud is defined. as 6000 AU., The outer radius of the cloud is defined as 6000 AU.368 The Plummer profile is also a reasonable approximation to (and easier to deal with than) the Bonner-Ebert sphere density distribution., The Plummer profile is also a reasonable approximation to (and easier to deal with than) the Bonner-Ebert sphere density distribution.369 This latter distribution appears to describe the density profile of pre-stellar cores and is begining to be used routinely in modelling work., This latter distribution appears to describe the density profile of pre-stellar cores and is begining to be used routinely in modelling work.370" Phe adopted values of ro and po were 1000AU and 10""emi. respectively.", The adopted values of $r_0$ and $\rho_0$ were $1000~{\rm AU}$ and $10^6~{\rm cm^{-3}}$ respectively.371 These values were chosen to approximate the Donner-IZbert sphere fit to the density. distribution of LIGSOB carried out by Evansctal.(2001)., These values were chosen to approximate the Bonner-Ebert sphere fit to the density distribution of L1689B carried out by \citet{evans.et.al01}.372. Similarly. an empirical approximation to the dust temperature profile fit of Evansetal.(2001) was emploved to trace the gas temperature (the eas density is sullicientLy high that the two temperatures can be considered: well coupled).," Similarly, an empirical approximation to the dust temperature profile fit of \citet{evans.et.al01} was employed to trace the gas temperature (the gas density is sufficiently high that the two temperatures can be considered well coupled)."373 The temperature is 10 Ix in most of the cloud and then drops. over a short distance. to 7 lx in the centre.," The temperature is 10 K in most of the cloud and then drops, over a short distance, to 7 K in the centre."374 In fact. trial runs with a constant temperature of 10 Ix throughout the cloud vield very similar results to this temperature profile.," In fact, trial runs with a constant temperature of 10 K throughout the cloud yield very similar results to this temperature profile."375 The fractional abundance of HOO was taken to have a constant. value from the range 5.010οLo.7., The fractional abundance of ${\rm HCO^+}$ was taken to have a constant value from the range $5.0\times 10^{-10}-1.0\times 10^{-8}$.376 The assumption of a constant abundance is of course a crude approximation ancl a self-consistent chemistry. should be included in the cloud., The assumption of a constant abundance is of course a crude approximation and a self-consistent chemistry should be included in the cloud.377 Llowever. the chemistry of αςο is complicated. ancl Rawlingsetal.(1992). show that its abundance intially rises as depletion. ensues.," However, the chemistry of ${\rm HCO^+}$ is complicated and \citet{rawlings.et.al92} show that its abundance intially rises as depletion ensues."378 The sticking coellicient of HCO on to charged and neutral dust. grains is also not well known., The sticking coefficient of ${\rm HCO^+}$ on to charged and neutral dust grains is also not well known.379 Vherefore an attempt to include the chemistry does not vet seem worthwhile., Therefore an attempt to include the chemistry does not yet seem worthwhile.380 A simple. solid. body. rotation law was adopted. for the inner regions of the model cloud., A simple solid body rotation law was adopted for the inner regions of the model cloud.381 X rotation axis that matches the dividing line between the red ancl blue asvmmetrie profiles was imposed., A rotation axis that matches the dividing line between the red and blue asymmetric profiles was imposed.382 The range of projected velocities. investigated is O10.4kmsJ|..., The range of projected velocities investigated is $0.1-0.4~{\rm km~s^{-1}}$ .383 The. rotation radius is an estimate of where the inner regions stop rotating and is estimated. as being at 3000AU 5000AU for the CO depleted. “hole? Redmanetal. 2002))., The rotation radius is an estimate of where the inner regions stop rotating and is estimated as being at $3000~{\rm AU}$ $5000~{\rm AU}$ for the CO depleted 'hole' \citealt{redman.et.al02b}) ).384 Finally. the uncertain turbulent velocity width was allowed to vary over the range 0.12O18kms+," Finally, the uncertain turbulent velocity width was allowed to vary over the range $0.12-0.18~{\rm km~s^{-1}}$."385 The full set of svnthesised ICOJ—3:2 line profiles for he best ft model is cisplaved in Figure 3.., The full set of synthesised ${\rm HCO^+} J=3\rightarrow 2$ line profiles for the best fit model is displayed in Figure \ref{modelonly}.386 For clarity. the rotation axis points vertically.," For clarity, the rotation axis points vertically."387 The line profiles show clear asvinmetrics with the sense of the asvmunetry switching tween. red. and. blue on either side of the rotation axis., The line profiles show clear asymmetries with the sense of the asymmetry switching between red and blue on either side of the rotation axis.388 The sel-absorption is strongest towards the centre of the model cloud. anc the asvounetry is strongest. there., The self-absorption is strongest towards the centre of the model cloud and the asymmetry is strongest there.389 Away rom the centre of the cloud. the drop in column density ancl self-absorption results in a reduced line strength and less onounced asymmetry. (the dillerence in strength. between rec. and blue peak: the relative magnitude of the absorption rough).," Away from the centre of the cloud, the drop in column density and self-absorption results in a reduced line strength and less pronounced asymmetry (the difference in strength between red and blue peak; the relative magnitude of the absorption trough)."390 These results confirm that it is possible to generate roth red ancl blue asymmetric line profiles entirely in the absence of any infall or outflow. motions., These results confirm that it is possible to generate both red and blue asymmetric line profiles entirely in the absence of any infall or outflow motions.391 Figure 4. is an overlay of the best fit model described above with the ΙΟΔΙ cata of Recman et al (2004)., Figure \ref{hcocompare} is an overlay of the best fit model described above with the JCMT data of Redman et al (2004).392 The rotation axis is marked on the figure., The rotation axis is marked on the figure.393 Given the simplicity of the model. the fit is excellent. with the sense of the asvmmetry in the line profiles. their shape and the fall-oll in line strength away from the centre being reproduced well.," Given the simplicity of the model, the fit is excellent with the sense of the asymmetry in the line profiles, their shape and the fall-off in line strength away from the centre being reproduced well."394 Phe most obvious of the discrepancies is that the line strengths are overestimated for the brightest lines near the centre of the cloud., The most obvious of the discrepancies is that the line strengths are overestimated for the brightest lines near the centre of the cloud.395 One explanation for this may be due to the freezing out of HCO onto grains., One explanation for this may be due to the freezing out of ${\rm HCO^+}$ onto grains.396 Any [reeze-out of the HICO— is likely to occur first in the centre of the cloud. where the density is highest. and progress outwards.," Any freeze-out of the ${\rm HCO^+}$ is likely to occur first in the centre of the cloud, where the density is highest, and progress outwards."397 Lf iere is significant [reeze-out inthe very centre of the cloud.," If there is significant freeze-out inthe very centre of the cloud,"398to 715%.,to $\sim15\%$.399 Lt is interesting to note that simulation MIO. the only case of a minor merger. was less cllicient in converting gas to stars than the other simulations.. with. fi“Lined=sn-0.297.," It is interesting to note that simulation M110, the only case of a minor merger, was less efficient in converting gas to stars than the other simulations, with $f_{\rm gas}^{\rm final}=0.297$."400 Following the approach of Robertsonetal.(2006)... we iive computed the SER: for all the simulations. ancl used hese results to identify stellar populations.," Following the approach of \citet{robertsonetal06}, we have computed the SFR for all the simulations, and used these results to identify stellar populations."401 Some examples of them are shown in the top left. panels of Figs. 6- 9.., Some examples of them are shown in the top left panels of Figs. \ref{M12_kin}- \ref{M13_kin}.402 οσα that the simulations start at /=0., Notice that the simulations start at $t=0$.403 The results are quite similar. for all simulations., The results are quite similar for all simulations.404 A major starburst invariably occurs during the merger., A major starburst invariably occurs during the merger.405 This starburst peaks γαποσα ~6087.vr and 500A.vr comparable to hat seen in igh-redshift. Lyman-break galaxies. (Erbetal. 2006).," This starburst peaks between $\sim60M_\odot\,{\rm yr}^{-1}$ and $500M_\odot\,{\rm yr}^{-1}$, comparable to that seen in high-redshift Lyman-break galaxies \citep{erbetal06}."406. The results are qualitatively similar to recent work involving similar gas ratio but cdillerent feodhack assumptions (Johanssonetal.2009) or clillerent gus ratio and dillerent. feedback. (Coxetal.2008)., The results are qualitatively similar to recent work involving similar gas ratio but different feedback assumptions \citep{jnb09} or different gas ratio and different feedback \citep{coxetal08}.407.. The main quantitative difference come from the amount of gas available during the merger., The main quantitative difference come from the amount of gas available during the merger.408 As stated in Johanssonctal.(2009.scetheirFigs.1and 3).. there is a huge dillerence in the maximum. value of the SER depending on gas mass fraction.," As stated in \citet[][see their Figs.~1 and 3]{jnb09}, there is a huge difference in the maximum value of the SFR depending on gas mass fraction."409 The SEI. is also dependent of the numerical methods used. for feedback in case of major mergers (Coxetal. 2006)., The SFR is also dependent of the numerical methods used for feedback in case of major mergers \citep{coxetal06}.410. After the starburst. the star formation steaclily drops. as the system relaxes aud a dise forms.," After the starburst, the star formation steadily drops, as the system relaxes and a disc forms."411 We identify the beginning and the end of the merger with the beginning and the end of the starburst. respectively.," We identify the beginning and the end of the merger with the beginning and the end of the starburst, respectively."412 We then define two populations of stars:slars. which include stars already present in the galaxies before the merger and stars formed during the merger by the starburst. andstars. which include all stars formed after the merger. when the starburst is completed.," We then define two populations of stars:, which include stars already present in the galaxies before the merger and stars formed during the merger by the starburst, and, which include all stars formed after the merger, when the starburst is completed."413 The definitions for voung and old stars remain the same throughout the paper., The definitions for young and old stars remain the same throughout the paper.414 The dashed vertical lines in the top-left panels of Figs. 6-, The dashed vertical lines in the top-left panels of Figs. \ref{M12_kin}-415 9. indicate the beginning and end of the starburst. identified by eve as the merger boundaries are not crucial for the subsequent analysis.," \ref{M13_kin} indicate the beginning and end of the starburst, identified by eye as the merger boundaries are not crucial for the subsequent analysis."416 The time when the starburst begins is listed in Table 2.., The time when the starburst begins is listed in Table \ref{table-times}.417 For most simulations. the starburst lasts 0.20.3 Cave.," For most simulations, the starburst lasts 0.2–0.3 Gyr."418 The simulation All2z (Fig. 7)), The simulation M12z (Fig. \ref{M12z_kin}) )419 is a notable exception. with a starburst that is weaker and lasts for 0.5 Civr.," is a notable exception, with a starburst that is weaker and lasts for 0.5 Gyr."420 We use the term to designate the final state of each simulation., We use the term to designate the final state of each simulation.421 Our simulations are meant to represent the interactions occurring at high redshift. when the gas content is very high.," Our simulations are meant to represent the interactions occurring at high redshift, when the gas content is very high."422 In this sense. the merger remnant represents objects at 272.3 and the galaxies still have time to form more stars until >=0.," In this sense, the merger remnant represents objects at $z\sim2-3$ and the galaxies still have time to form more stars until $z=0$."423 The subsequent infall of extragalactic gas may also produce more stars at z=0 and help to reform à clise (Brooksοἱal.2009)., The subsequent infall of extragalactic gas may also produce more stars at $z=0$ and help to reform a disc \citep{brooksetal09}.424. At the end of cach simulation. we calculated the V-band luminosity of the merger remnant. using the stellar svnthesis model of Kodama&Arimoto(1997).," At the end of each simulation, we calculated the V-band luminosity of the merger remnant, using the stellar synthesis model of \citet{ka97}."425. From this. we produced: mock V-band. luminosity maps (modulo the lack of dust extinction).," From this, we produced mock V-band luminosity maps (modulo the lack of dust extinction)."426 Figs. 2-, Figs. \ref{M12}-427 4 show the luminosity. maps for 3 remnants., \ref{M1290} show the luminosity maps for 3 remnants.428 On cach figure. the left panels show the stars born after the merger (voung stars). the micelle panels show the stars born before or during the merger (old stars) and the right panels show all stars.," On each figure, the left panels show the stars born after the merger (young stars), the middle panels show the stars born before or during the merger (old stars) and the right panels show all stars."429 We immediately see that old and voung stars have very cillerent distributions., We immediately see that old and young stars have very different distributions.430 In simulation M12 (Fig. 2)).," In simulation M12 (Fig. \ref{M12}) ),"431 voung ancl old. stars form. dises that have comparable radii. but the edge-on views (bottom. panels) clearly shows that the voung disc is thin. while the old clise is thick.," young and old stars form discs that have comparable radii, but the edge-on views (bottom panels) clearly shows that the young disc is thin, while the old disc is thick."432 Phe presence of two distinct discs. a thin one and a thick one. is in remarkable agreement. with observations (Yoachim&Dal-canton 2006).. and this motivated us to publish the results of tha particular simulation in an earlier paper (BOT).," The presence of two distinct discs, a thin one and a thick one, is in remarkable agreement with observations \citep{yd06}, and this motivated us to publish the results of that particular simulation in an earlier paper (B07)."433 We found that all he simulations except for simulations M12z ancl A11 do result in the formation of a thin disc mace of voung stars. and a thick disc mace of old stars that were alreacly present before the merger. or formed. during the mergers.," We found that all the simulations except for simulations M12z and M11 do result in the formation of a thin disc made of young stars, and a thick disc made of old stars that were already present before the merger, or formed during the mergers."434 These stars end up either in the thick disc or in the halo., These stars end up either in the thick disc or in the halo.435 Simulations M12z and ALLL show more elliptical like remnants., Simulations M12z and M11 show more elliptical like remnants.436 Simulation MI2z (Fig. 3)), Simulation M12z (Fig. \ref{M12z}) )437 produced. a remnant that has a very complex structure., produced a remnant that has a very complex structure.438 Even though we find a small cise mace of voung stars. the overall structure resembles more an elliptical galaxy than a disc galaxy.," Even though we find a small disc made of young stars, the overall structure resembles more an elliptical galaxy than a disc galaxy."439 Simulation ALLL also shows a small voung disc., Simulation M11 also shows a small young disc.440 Compared with the other simulations. the initial galaxies Gall and Gal2," Compared with the other simulations, the initial galaxies Gal1 and Gal2"441than that observed for wider separated pairs or isolated SVSTCLUS.,than that observed for wider separated pairs or isolated systems.442 More receutly. Peeplesetal.(2008.2009) have studied. respectively. a sample of low-mass. lieh-metallicity auc high-mass. low-1uetallicity outhers from the mass-moetallicity relation of star-forming galaxies from selected from the Sloan Digital Sky Survey (8DSS).They showed that the low-mass. hiegh-metallicity outlicrs are ustly isolated galaxies. with no evident conrpanion or stroug interactions.," More recently, \citet{peeples08, peeples09} have studied, respectively, a sample of low-mass, high-metallicity and high-mass, low-metallicity outliers from the mass-metallicity relation of star-forming galaxies from selected from the Sloan Digital Sky Survey (SDSS).They showed that the low-mass, high-metallicity outliers are usually isolated galaxies, with no evident companion or strong interactions."443 Ou the other haud. the high-iuass. low-unctallicity outherts typically consist of systems that have high star formation rates aud evidence for disturbed morphologics.," On the other hand, the high-mass, low-metallicity outlierts typically consist of systems that have high star formation rates and evidence for disturbed morphologies."444 ILowever. Cooperetal.(2008) found a stroug motallicity-censity relation for star forming galaxies iu the local universe. with the more iauetalarich galaxies apparently favouring regious of hieher galaxy overdcusity (seealsoEllisonetal.2009).," However, \citet{cooper08} found a strong metallicity-density relation for star forming galaxies in the local universe, with the more metal-rich galaxies apparently favouring regions of higher galaxy overdensity \citep[see also][]{ellison09}."445. They conclude that the discrepancy ound with the outer studies (ncludiug those just discussed) is due to the fact that the number of close airs (s «100kpeh i3 in the SDSS sample constitutes ouly a tiny fraction of the whole sample (less than of galaxies)., They conclude that the discrepancy found with the outer studies (including those just discussed) is due to the fact that the number of close pairs (s $< 100\; \mathrm{kpc\;h^{-1}}$ ) in the SDSS sample constitutes only a tiny fraction of the whole sample (less than of galaxies).446 In this case. close ors with low central netallicity could not contribute siguificautly to the scatter ouch in the inassanetallicitv relation.," In this case, close pairs with low central metallicity could not contribute significantly to the scatter found in the mass-metallicity relation."447 Of course it can be difficult to discern trends in the gas phase netallicity during a merger when studviue huge samples of galaxies in SDSS as other factors Lay douinate he overall iass-netalliity. relationship and its scatter., Of course it can be difficult to discern trends in the gas phase metallicity during a merger when studying large samples of galaxies in SDSS as other factors may dominate the overall mass-metallicity relationship and its scatter.448 A confirmation that the mass-imetallicity relation is affected by interactions onlv for close pairs showing sieus of strong disturbances has been found by MicheDausacetal.x (2008).. who pointed out that. iu such ours. the gas metallicity depends ou the mass ratio of he two interacting svstenis: less iuassive members are systematically enriched. while a galaxy im interaction with a comparable stellar mass companion shows a ietallicity ower than that of a galaxy in isolation.," A confirmation that the mass-metallicity relation is affected by interactions only for close pairs showing signs of strong disturbances has been found by \citet{dansac08}, who pointed out that, in such pairs, the gas metallicity depends on the mass ratio of the two interacting systems: less massive members are systematically enriched, while a galaxy in interaction with a comparable stellar mass companion shows a metallicity lower than that of a galaxy in isolation."449 So while merecrs aud interactions alone may not drive the overall scatter iu je luass-luctallicity relationship. itf may © a contributingo actor.," So while mergers and interactions alone may not drive the overall scatter in the mass-metallicity relationship, it may be a contributing factor."450 All these studies suggest that he dilution aud enriclineut of the ISM in he central regions of oealaxics stronsglv depend on the exac timine of the different processes at play: gas inflows. -iteractiou-drivenu star formation. eas consuniptiou. feedback aud subsequeut enrichment.," All these studies suggest that the dilution and enrichment of the ISM in the central regions of disk galaxies strongly depend on the exact timing of the different processes at play: gas inflows, interaction-driven star formation, gas consumption, feedback and subsequent enrichment."451 While a amber of wunerical studies have investigated the respouse of the gascous componcut of ealaxies during tidal interactions aud the subsequent star formation such interactions induce (Iounoctal.2001:Mibhos&ITeruquistal.2005:DiMatteoet2007. 2008).. little attention has been given to the detailed evolution of the metal content during galaxy eucounters," While a number of numerical studies have investigated the response of the gaseous component of galaxies during tidal interactions and the subsequent star formation such interactions induce \citep{iono04,452mihos94a, springel00, cox06, cox08, kapferer05, dimatteo07, dimatteo08}, little attention has been given to the detailed evolution of the metal content during galaxy encounters."453 Using a galaxw pair catalogue from costuological simulations. Perezetal.(2006) have shown that the O/T abundance ratio in the central reeions of close ealaxy pairs (s «50kpeh ‘) shows a lower level of eurichineut than the mean O/II abundance ratio of a control sample. thus confirming the role plaved by eas inflow in diluting the metal content of the uuclear regions.," Using a galaxy pair catalogue from cosmological simulations, \citet{perez06} have shown that the O/H abundance ratio in the central regions of close galaxy pairs (s $< 50\; \mathrm{kpc\;h^{-1}}$ ) shows a lower level of enrichment than the mean O/H abundance ratio of a control sample, thus confirming the role played by gas inflow in diluting the metal content of the nuclear regions."454 Receutly. Bupkeetal.(2010) have analysed sinulatious of major galaxy mergers. studving the dilution of the gas metallicity in the unclear regions due to eas inflow.," Recently, \citet{rupke10} have analysed simulations of major galaxy mergers, studying the dilution of the gas metallicity in the nuclear regions due to gas inflow."455 They found a dilution of about 0.1 - 0.3 dex. happening shortly after the first poricentre passage between the two galaxies.," They found a dilution of about 0.1 - 0.3 dex, happening shortly after the first pericentre passage between the two galaxies."456 Iowever. their models do uot iuclude either star formation prescriptions or metal enriclineut. so that while it has been possible to give predictions about the strength of the dilution. nothing is still known about the role plaved. bx interaction-induced star formation iu the metal dilution and then subsequent eurchemenut.," However, their models do not include either star formation prescriptions or metal enrichment, so that while it has been possible to give predictions about the strength of the dilution, nothing is still known about the role played by interaction-induced star formation in the metal dilution and then subsequent enrichement."457 Moreover. the exact tiniug of the dilution peak aud its correlation with the increase in the amplitude of the star formation have not been studied vet im amy detail.," Moreover, the exact timing of the dilution peak and its correlation with the increase in the amplitude of the star formation have not been studied yet in any detail."458 Tere we study imiergers and fivbvs involving two massive She galaxies. having a mass ratio l:l.," Here we study mergers and flybys involving two massive Sbc galaxies, having a mass ratio 1:1."459 The She galaxies (hereafter called eSb) are coniposed of a. spherical dark matter halo aud a spherical bulge. represented by Plunuuer spheres (Binney&TremaineL987) with total lüasses μι=1.7ςlottAL: and Afp=11.5ς109AL: and core radi ry=12kpc aud rp=1kpc respectively.," The Sbc galaxies (hereafter called gSb) are composed of a spherical dark matter halo and a spherical bulge, represented by Plummer spheres \citep{bt1} with total masses $M_H=1.7\times10^{11}\;\mathrm{M_{\sun}}$ and $M_B=11.5\times10^9\;\mathrm{M_{\sun}}$ and core radii $r_H=12\;\mathrm{kpc}$ and $r_B=1\;\mathrm{kpc}$ respectively."460" The stellar disk is represented bv ai ATivamoto-Nagai density profile (Binney&Tremaine1987) with nass AL,=10.6«109AL... vertical and radial scale leueths eiven respectively by ὃς=0.5rkpe and e,=5kpe."," The stellar disk is represented by a Miyamoto-Nagai density profile \citep{bt1} with mass $M_{*}=40.6\times10^9\;\mathrm{M_{\sun}}$, vertical and radial scale lengths given respectively by $h_{*}=0.5\;\mathrm{kpc}$ and $a_{*}=5\;\mathrm{kpc}$."461" The galaxies initially coutai a gas nass Mj,=0.2M... redistributed im a \livamoto-Nagai disk with vertical aux radial scale lengths given respectively by ρω=0.2kpe aud (444=6προ"," The galaxies initially contain a gas mass $M_{gas}=0.2 \; M_{*}$, redistributed in a Miyamoto-Nagai disk with vertical and radial scale lengths given respectively by $h_{gas}=0.2\;\mathrm{kpc}$ and $a_{gas}=6\;\mathrm{kpc}$."462 For cach pair of interacting galaxies. we performed 21 simulations. varvine the galaxies orbita initial conditions Guitial orbital cncrey E and aneular momentum L) aud taking into account both direct iux retrograde orbits.," For each pair of interacting galaxies, we performed 24 simulations, varying the galaxies orbital initial conditions (initial orbital energy E and angular momentum L) and taking into account both direct and retrograde orbits."463 The initial orbital parameters (initia distance between the two galaxies. initial relative velocity. specific aneular momentum. orbital energev aud spin) or the different ruus are fully described iu Table 7 of Chiliugari:vetal.2010)... aud we refer the reader to this oper for heir complete description.," The initial orbital parameters (initial distance between the two galaxies, initial relative velocity, specific angular momentum, orbital energy and spin) for the different runs are fully described in Table 7 of \citet{chili10}, and we refer the reader to this paper for their complete description."464 We chose a reference frame with its origi at the xuvcentre of the system and x-v plane corresponding to he orbital plaue., We chose a reference frame with its origin at the barycentre of the system and x-y plane corresponding to the orbital plane.465 For cach interacting pair. we have kept he disk of one of the two galaxies iu the orbital plane (G4= 07). and varied the inclination /» of the companion disk. considerius: ο=(Q7. jo=1. ji)=75. aud fy=907.," For each interacting pair, we have kept the disk of one of the two galaxies in the orbital plane $i_1 = 0 \degr$ ), and varied the inclination $i_2$ of the companion disk, considering: $i_2 = 0 \degr$, $i_2 = 45 \degr$, $i_2 =46675 \degr$, and $i_2 = 90\degr$."467 Theorbital angular 1io1mieutuni can be parallel (direct orbit) or anti-parallel (retrograde orbit) to the of the reference frame., Theorbital angular momentum can be parallel (direct orbit) or anti-parallel (retrograde orbit) to the z-axis of the reference frame.468 All the simulations (96 in total) were run usiug the Tree-SPID code cescribed iu Semelin&Combes (2002).., All the simulations (96 in total) were run using the Tree-SPH code described in \citet{benoit02}. .469 Each galaxy contains a total of Nror=120000 particles.," Each galaxy contains a total of $N_{TOT}=120000$ particles,"470establishing the chronology of star clusters in the Galaxy and nearby systems. core overshoot allects (he spectral dating of voung aud intermediate age galaxies observed at large recdshifts.,"establishing the chronology of star clusters in the Galaxy and nearby systems, core overshoot affects the spectral dating of young and intermediate age galaxies observed at large redshifts."471 Convective core overshoot is loosely understood here as the presence of material motions and/or mixing bevonid (he formal boundary for convection set by the classical Schwarzschild criterion (1906)., Convective core overshoot is loosely understood here as the presence of material motions and/or mixing beyond the formal boundary for convection set by the classical Schwarzschild criterion (1906).472 An early study bv Saslaw Schwarzschild (1965). based on thermodynamic erounds (i.e. the edge of the convective core in massive stars is sharply defined in an entropy diagram). suggested that little overshoot takes place at the edge of convective cores.," An early study by Saslaw Schwarzschild (1965), based on thermodynamic grounds (i.e. the edge of the convective core in massive stars is sharply defined in an entropy diagram), suggested that little overshoot takes place at the edge of convective cores."473 For this reason. il was believed that the presence of a gap in the CMD of open star clusters and its magnitude could be used as indicators of the age and chemical composition of the cluster (Aizenman. Demarque Miller 1966).," For this reason, it was believed that the presence of a gap in the CMD of open star clusters and it's magnitude could be used as indicators of the age and chemical composition of the cluster (Aizenman, Demarque Miller 1966)."474 ILowever. Shaviv Salpeter (1973) pointed out that if one takes into account the presence of hvdrodyenamic motions and turbulence. one might expect some non-negligible amount of overshoot.," However, Shaviv Salpeter (1973) pointed out that if one takes into account the presence of hydrodynamic motions and turbulence, one might expect some non-negligible amount of overshoot."475 In fact. observational studies of the size of gaps near the turnoff in open star cluster CMID's suggest better agreement with theoretical isochrones which adimit some amount of core overshoot (Maecder Mermilliod 1981: Stothers Chin 1991: Carraro et al.," In fact, observational studies of the size of gaps near the turnoff in open star cluster CMD's suggest better agreement with theoretical isochrones which admit some amount of core overshoot (Maeder Mermilliod 1981; Stothers Chin 1991; Carraro et al."476 1993: Daniel et al., 1993; Daniel et al.477 1994: Demarque. Sarajedini Guo 1994: Nozhurina-Platais et al.," 1994; Demarque, Sarajedini Guo 1994; Kozhurina-Platais et al."478 1997; Nordstrómumn. Andersen Andersen 1997).," 1997; Nordströmm, Andersen Andersen 1997)."479 Several computational schemes of various degrees of sophistication in (reating (he physics of overshoot have been developed [ον stellar evolution codes (Prather Demarque 1974: Cogan 1975: Maeder 1975: Maeder Meynet 1988: Bertelli et al., Several computational schemes of various degrees of sophistication in treating the physics of overshoot have been developed for stellar evolution codes (Prather Demarque 1974; Cogan 1975; Maeder 1975; Maeder Meynet 1988; Bertelli et al.480 1990)., 1990).481 As well. studies of detached eclipsing binaries in which the components have convective cores suggest some core overshoot of the order of 0.2 pressure scale height (Ribas. Jordi Gimenez 2000).," As well, studies of detached eclipsing binaries in which the components have convective cores suggest some core overshoot of the order of 0.2 pressure scale height (Ribas, Jordi Gimenez 2000)."482 sStothers Chin (1991) pointed out the high sensitivity of the amount of convective core overshoot to the adopted opacities., Stothers Chin (1991) pointed out the high sensitivity of the amount of convective core overshoot to the adopted opacities.483 For example. increases in radiative opacities [rom ihe OPAL eroup (Iglesias Rogers 1996) over the previous generation Los Alamos Opacity Library (IIuebner et al.," For example, increases in radiative opacities from the OPAL group (Iglesias Rogers 1996) over the previous generation Los Alamos Opacity Library (Huebner et al."484 1977). decrease the need for overshoot in comparison will observational data.," 1977), decrease the need for overshoot in comparison with observational data."485 In fact. the nature of the overshoot depends on the details of the local plwsics ad the convective core edge.," In fact, the nature of the overshoot depends on the details of the local physics at the convective core edge."486 As pointed out by Zahn (1991). the local Pécclet number. which characterizes (he relative importance of radiative and turbulent diffusivity. determines whether in the mixed overshoot region. penetration takes place (i.e. the temperature eradient is the adiabatie gradient). or rather the local radiative transfer dominates (he enerev transport (overmiximg).," As pointed out by Zahn (1991), the local Pécclet number, which characterizes the relative importance of radiative and turbulent diffusivity, determines whether in the mixed overshoot region, penetration takes place (i.e. the temperature gradient is the adiabatic gradient), or rather the local radiative transfer dominates the energy transport (overmixing)."487 In the latter case. the stable temperature gradient is unallected by the mixing.," In the latter case, the stable temperature gradient is unaffected by the mixing."488 Roxburgh (1989. 1992) also considered the plvsics of convective core overshoot [rom a different point of view.," Roxburgh (1989, 1992) also considered the physics of convective core overshoot from a different point of view."489 Ilis integral constraint argument places an upper limit on the amount of core overshoot which can take place in the stellar interior., His integral constraint argument places an upper limit on the amount of core overshoot which can take place in the stellar interior.490 Zahn (1991) argued that overshoot is practically adiabatic at the edge of the convective core. except in a thin," Zahn (1991) argued that overshoot is practically adiabatic at the edge of the convective core, except in a thin"491parameters are given in Table 1..,parameters are given in Table \ref{tab-specparams}.492" We found significant diffuse excess emission above the particle background in all rings and derived the surface brightness for each region by dividing the model flux by the effective extraction area, which is the geometric ring area inside the FoV minus excluded regions and bad pixels."," We found significant diffuse excess emission above the particle background in all rings and derived the surface brightness for each region by dividing the model flux by the effective extraction area, which is the geometric ring area inside the FoV minus excluded regions and bad pixels."493" Due to limited statistics, we fixed the column density at a default value ofcm."," Due to limited statistics, we fixed the column density at a default value of."494". Therefore, we list the observed surface fluxes in Table 1,, as opposed to the intrinsic fluxes we provide for all other spectra."," Therefore, we list the observed surface fluxes in Table \ref{tab-specparams}, as opposed to the intrinsic fluxes we provide for all other spectra."495" The diffuse surface flux shows a clear radial dependence (Fig. 2)),"," The diffuse surface flux shows a clear radial dependence (Fig. \ref{fig-radial-flux}) ),"496 which indicates that a significant part of the excess is connected to the cluster., which indicates that a significant part of the excess is connected to the cluster.497" At distances greater than ~170” from the GC core, the observed surface flux seems to reach a base level of = slaarcsec? (1—7 keV)."," At distances greater than $\sim$ 170"" from the GC core, the observed surface flux seems to reach a base level of $\approx$ $^{-2}$ (1–7 keV)."498 In the following section we derive the unabsorbed surface flux for the outer region by applying a more realistic physical model., In the following section we derive the unabsorbed surface flux for the outer region by applying a more realistic physical model.499 lis close to the Galactic plane where diffuse Galactic emission becomes an important component., is close to the Galactic plane where diffuse Galactic emission becomes an important component.500" However, the bblank-sky datasets are composed of observations towards high Galactic latitudes, which would underestimate the sky background in our case."," However, the blank-sky datasets are composed of observations towards high Galactic latitudes, which would underestimate the sky background in our case."501" To test whether the spectrum observed from the outer three rings is compatible with thermal Galactic diffuse emission, we used a more physically reasonable model."," To test whether the spectrum observed from the outer three rings is compatible with thermal Galactic diffuse emission, we used a more physically reasonable model."502" Similar to ? and ?,, who modeled the diffuse Galactic ridge emission as observed with andChandra, respectively, we describe the Galactic diffuse component using a (2-T) non-equilibrium ionization model (NED) (?).."," Similar to \citet{1997ApJ...491..638K} and \citet{2005ApJ...635..214E}, who modeled the diffuse Galactic ridge emission as observed with and, respectively, we describe the Galactic diffuse component using a (2-T) non-equilibrium ionization model (NEI) \citep{1984Ap&SS..98..367M}."503" To improve the statistical quality, we combined the outer three (175-246”) rings into a single spectrum."," To improve the statistical quality, we combined the outer three (175–246"") rings into a single spectrum."504 The spectrum was adaptively binned to a minimum of 20 excess counts per bin., The spectrum was adaptively binned to a minimum of 20 excess counts per bin.505 As background we again used the spectrum extracted from the same region in the NXB dataset., As background we again used the spectrum extracted from the same region in the NXB dataset.506" We fitted a 2-T NEI model to the outer spectrum, freezing most of the parameters to the fit values from Table 8 in ?.."," We fitted a 2-T NEI model to the outer spectrum, freezing most of the parameters to the best-fit values from Table 8 in \citet{2005ApJ...635..214E}."507 We left the surface brightnesses of the two components and the ffree to vary to account for the difference in flux and column density between the region around aand the area observed by ?.., We left the surface brightnesses of the two components and the free to vary to account for the difference in flux and column density between the region around and the area observed by \citet{2005ApJ...635..214E}.508" In addition, we allowed the Si-abundance of the soft component as a free fit-parameter, because the low-ionized Si line at ~1.8 keV (??) was otherwise underestimated."," In addition, we allowed the Si-abundance of the soft component as a free fit-parameter, because the low-ionized Si line at $\sim$ 1.8 keV \citep{1997ApJ...491..638K,2005ApJ...635..214E} was otherwise underestimated."509 The spectrum of the outer region together with the model fit is shown in Fig., The spectrum of the outer region together with the model fit is shown in Fig.510 3 (Top))., \ref{fig-spectra} ).511" To be able to compare our results to the analysis of ?,, we chose an energy range of 0.7— keV in this specific case."," To be able to compare our results to the analysis of \citet{2005ApJ...635..214E}, we chose an energy range of 0.7--10 keV in this specific case."512 The best-fit values are given in Table 1 region)., The best-fit values are given in Table \ref{tab-specparams} region).513 The total intrinsic surface flux of the two components is a factor of three lower than the value for the Galactic region observed by ?.., The total intrinsic surface flux of the two components is a factor of three lower than the value for the Galactic region observed by \citet{2005ApJ...635..214E}.514" This relation is in good agreement with the ratio between the column densities for both regions, which is ~4 (?).."," This relation is in good agreement with the ratio between the column densities for both regions, which is $\sim$ 4 \citep{1990ARAA...28..215D}."515" Assuming that the Galactic column density seen from a certain direction is directly related to the expected flux from a diffuse Galactic component, we conclude that at least ~3/4 of the total excess above particle background observed from the outer region comes from Galactic diffuse emission."," Assuming that the Galactic column density seen from a certain direction is directly related to the expected flux from a diffuse Galactic component, we conclude that at least $\sim$ 3/4 of the total excess above particle background observed from the outer region comes from Galactic diffuse emission."516" In this section we focus on the diffuse emission observed from the inner five rings (55-175"")."," In this section we focus on the diffuse emission observed from the inner five rings (55–175"")."517" In addition to the radial dependence of the diffuse excess emission, Fig."," In addition to the radial dependence of the diffuse excess emission, Fig."518 2 shows the infrared surface brightness profile (?) and the X-ray point-source distribution (King-profilefrom?).., \ref{fig-radial-flux} shows the infrared surface brightness profile \citep{1995AJ....109..218T} and the X-ray point-source distribution \citep[King-profile from ][]{2006ApJ...651.1098H}.519" Both profiles are scaled to match the first diffuse X-ray data point, using an exponential fit in the case of the infrared data."," Both profiles are scaled to match the first diffuse X-ray data point, using an exponential fit in the case of the infrared data."520" To investigate the nature of the diffuse excess emission observed from the inner region in more detail and to improve the statistical quality, we extracted the combined spectrum from the inner five rings (55-175"")."," To investigate the nature of the diffuse excess emission observed from the inner region in more detail and to improve the statistical quality, we extracted the combined spectrum from the inner five rings (55–175"")."521" As a first step we fitted the same 2-T NEI model to the NXB subtracted inner spectrum, binned to a minimum of 20 excess counts per bin, as was done for the outer region in the previous section."," As a first step we fitted the same 2-T NEI model to the NXB subtracted inner spectrum, binned to a minimum of 20 excess counts per bin, as was done for the outer region in the previous section."522 The resulting surface fluxes of the two components are listed in Table 1. region)., The resulting surface fluxes of the two components are listed in Table \ref{tab-specparams} region).523" Following the same argument as in the previous section, we estimate that in this case only ~1/3 of the total observed emission is of diffuse Galactic origin."," Following the same argument as in the previous section, we estimate that in this case only $\sim$ 1/3 of the total observed emission is of diffuse Galactic origin."524" Together with the surface brightness showing a clear radial dependence with respect to the core of5, we conclude that a significant part of the observed flux is connected to the GC."," Together with the surface brightness showing a clear radial dependence with respect to the core of, we conclude that a significant part of the observed flux is connected to the GC."525" As an estimate for the Galactic diffuse background component, we subtracted the outer (175—246"", see previous section) from the inner spectrum."," As an estimate for the Galactic diffuse background component, we subtracted the outer (175–246"", see previous section) from the inner spectrum."526 Figure 3 (Bottom)) shows, Figure \ref{fig-spectra} ) shows527"in terms of the convective cucrev flux with IV,FeoE, for pressure scale height 7,aud adiabatic eradieut Vag=(dlufidlniP).",in terms of the convective energy flux with $W_b = F_C\nabla_{ad}/H_p$ for pressure scale height $H_p$and adiabatic gradient $\nabla_{ad} = (d\ln T/d\ln P)_s$ .528" This expression for T, can be calculated directly from the backerouud structure (Eq.", This expression for $W_b$ can be calculated directly from the background structure (Eq.529 3) aud is appropriate for small density fluctuations that cau be linearly related to temperature fluctuations using the isobaric thermodynamic derivative a good approximation nm iunost cases of deep. nearly adiabatic convection.," 3) and is appropriate for small density fluctuations that can be linearly related to temperature fluctuations using the isobaric thermodynamic derivative, a good approximation in most cases of deep, nearly adiabatic convection."530 From Eq., From Eq.531 1 we see that Globally. je integrated dissipation feyd is coistraincedffortcomings by both the werimal state evolution. Z5 (Eq.," \ref{eq:ltot} we see that Globally, the integrated dissipation $\int\epsilon_K dm$ is constrained by both the thermal state evolution, $T\dot{s}$ (Eq."532 2. 3). and the balance with buovancy driviug (Eq.," 2, 3), and the balance with buoyancy driving (Eq."533 |. noting that ΓΕτομ)Lui(rna)= 0).," 4, noting that $L_K(r_{\rm top}) = L_K(r_{\rm bot}) = 0$ )."534 The radial profile of εις is determined by the topology of the couvective flow., The radial profile of $\epsilon_K$ is determined by the topology of the convective flow.535" Arnettetal.(20094). show that the dissipation is wel described by the properties of the component of. turbulence. ez,)Segay|02)24 with egyoef190afT where fis the largest scale of iiotion iu the flow and. eg ae ο, are the nou-radial velocity fluctuations."," \citet{arnett2009a} show that the dissipation is well described by the properties of the component of turbulence, $v_{\rm iso}^2 \sim \frac{3}{2}(v_{\theta}^2 + v_{\phi}^2)$ with $\epsilon_K \sim v_{\rm iso}^3/l_d$ where $l_d$ is the largest scale of motion in the flow and $v_{\theta}$ and $v_{\phi}$ are the non-radial velocity fluctuations."536 Iu Fig., In Fig.537 3 we present the radial distribution of the sinetic cherey frou the simulation data., 3 we present the radial distribution of the kinetic energy from the simulation data.538 The first pane shows the total Ly: aud the second panel shows the rorizoutal component scaled to au equivalent isotropic value. EySER," The first panel shows the total $E_K$ and the second panel shows the horizontal component scaled to an equivalent isotropic value, $E_{K,{\rm iso}} = \frac{3}{2}E_{K,H}$."539" The increase in £g at the )onndaries of the convection zones are due to the rorizoutal deflection of the large scale flow and wave notions excited in stable lavers (e.g.Meakin&Ar-τοι2006.2007a}) and should be corrected for whem identifving £i, with the convective turbulence."," The increase in $E_{K,H}$ at the boundaries of the convection zones are due to the horizontal deflection of the large scale flow and wave motions excited in stable layers \citep[e.g.][]{meakin2006,meakin2007a} and should be corrected for when identifying $E_{K,{\rm iso}}$ with the convective turbulence."540 Iu Fig., In Fig.541 3 (right) we over plot two approximatious o τω one based on a wniform distribution of dissipation and one based ou a dissipation that decreases ineatly with enclosed mass.," 3 (right) we over plot two approximations to $E_{K,{\rm iso}}$ : one based on a uniform distribution of dissipation and one based on a dissipation that decreases linearly with enclosed mass."542" The relationship ει=(QEpaoo/l with FyIT, is used."," The relationship $\epsilon_K = (2 E_{K,{\rm iso}})^{3/2}/l_d$ with $l_d = H_p$ is used."543 The absolute scale of the dissipation aud kinetic energv profiles are xovided by the coustraint that the elobal dissipation rate nist balance the elobal rate of buovaucy driving., The absolute scale of the dissipation and kinetic energy profiles are provided by the constraint that the global dissipation rate must balance the global rate of buoyancy driving.544 The amplitude of the kinetic energv that satisfies lis elobal balance is found by varving it until the voundary conditions on Ly are satisfied (6. Lg=0 at the boundaries of the convection zone).," The amplitude of the kinetic energy that satisfies this global balance is found by varying it until the boundary conditions on $L_K$ are satisfied (i.e., $L_K=0$ at the boundaries of the convection zone)."545" Egi,LCFfp? provides a good first approximation."," $E_{K,{\rm iso}} \sim \frac{1}{2}(F_c/\rho)^{2/3}$ provides a good first approximation."546 The kinetic energy fluxes found using this procedure are compared to the simulation data in Fie., The kinetic energy fluxes found using this procedure are compared to the simulation data in Fig.547 | for the two assumed dissipation profiles., 4 for the two assumed dissipation profiles.548 We have provided a basic overview of the counectiou between turbulent dissipation aud the kinetic cucrey flux iu cfiicicnt Caigh Pécclet uuuber) couvection., We have provided a basic overview of the connection between turbulent dissipation and the kinetic energy flux in efficient (high Pécclet number) convection.549 The oulv asstuption made in our analysis involved the radial profile of the dissipation εἰς which we will discuss in a future publication., The only assumption made in our analysis involved the radial profile of the dissipation $\epsilon_K$ which we will discuss in a future publication.550 For now we shall suffice to sav that the dissipation can be derived directly frou. the stellar model by adopting certain constraints ou the topology of the convective flow., For now we shall suffice to say that the dissipation can be derived directly from the stellar model by adopting certain constraints on the topology of the convective flow.551 In particular. a two component flow model consisting of a backeround isotropic turbulent state and a laree scale. plame-lke flow is a promising approach.," In particular, a two component flow model consisting of a background isotropic turbulent state and a large scale, plume-like flow is a promising approach."552 The data presented in Figs., The data presented in Figs.553 3 and { illustrate the of the commonly used closure relation referred to as theapprocimatian!., 3 and 4 illustrate the shortcomings of the commonly used closure relation referred to as the.554. \Lost illustrative is the fact tha while the y distributions are nearly identical in models aud the Ly: profiles are roughly imurror nuages., Most illustrative is the fact that while the $E_K$ distributions are nearly identical in models and the $L_K$ profiles are roughly mirror images.555 The locally defined down eracdicut approximation flux fails because tle properties of the turbulent transport are strongly shaped by global constraints. a feature that is captured by the analysis presented in ," The locally defined down gradient approximation flux fails because the properties of the turbulent transport are strongly shaped by global constraints, a feature that is captured by the analysis presented in \\ref{sec:keflux}. ."556Anothercousequence of the distribution of kinetic energv within the convection zoue is the rate of boundary laver mixing (see Fig., Anotherconsequence of the distribution of kinetic energy within the convection zone is the rate of boundary layer mixing (see Fig.557 2). which can significantly modifv thestellar structure on evolutionary timescales (see87inMeakin&Arnett 2007b)..," 2), which can significantly modify thestellar structure on evolutionary timescales \citep[see \S7 in][]{meakin2007b}. ."558then the mass ratio of the binary responsible for the blue and red absorption components would be close to unity.,then the mass ratio of the binary responsible for the blue and red absorption components would be close to unity.559 This in turn would be at odds with the light curve. which implies that there is a rather large difference in surface brightness between the components of the eclipsing binary.," This in turn would be at odds with the light curve, which implies that there is a rather large difference in surface brightness between the components of the eclipsing binary."560 The most likely interpretation of this line morphology therefore seems that it represents the very broad absorption line of only one star. but either deformed by pulsations such as in 6 CCep-type variables TTelting et citeTelting)) or partially filled in. by some circumstellar emission or chromospheric emission from. a low-mass companion heated by the tradiation from the B-star.," The most likely interpretation of this line morphology therefore seems that it represents the very broad absorption line of only one star, but either deformed by pulsations such as in $\beta$ Cep-type variables Telting et \\cite{Telting}) ) or partially filled in by some circumstellar emission or chromospheric emission from a low-mass companion heated by the irradiation from the B-star."561 In the case of the former interpretation. it must be stressed that our photometry does not reveal the signature of typical BCCep variations (see Paper D.," In the case of the former interpretation, it must be stressed that our photometry does not reveal the signature of typical $\beta$ Cep variations (see Paper I)."562 As to the circumstellar emission interpretation. we note that neither HP nor Ha have emission above the continuum. but both lines have a somewhat similar morphology to that of 55876. in the sense that they exhibit a rather narrow core anc more extended wings (especially the red wing).," As to the circumstellar emission interpretation, we note that neither $\beta$ nor $\alpha$ have emission above the continuum, but both lines have a somewhat similar morphology to that of $\lambda$ 5876, in the sense that they exhibit a rather narrow core and more extended wings (especially the red wing)."563 In the absence of an unambiguous interpretation of the spectral morphology of 444. we choose to use the RVs of the 244921 line. which is less complex than 255876. to derive some constraints on the orbital motion of the main component.," In the absence of an unambiguous interpretation of the spectral morphology of 44, we choose to use the RVs of the $\lambda$ 4921 line, which is less complex than $\lambda$ 5876, to derive some constraints on the orbital motion of the main component."564" Assuming that the RVs of this line indeed reflect orbital motion. a circular SBI orbital solution yields Ty=2454531.774+0.285. y,=(42+O) kkmss. Κι=(34x l6ykkmss7!. and a)sini=3.5Νο."," Assuming that the RVs of this line indeed reflect orbital motion, a circular SB1 orbital solution yields $T_0 = 2454531.774 \pm 0.285$, $\gamma_1 = (42 \pm 9)$ $^{-1}$, $K_1 = (34 \pm 16)$ $^{-1}$, and $a_1\,\sin{i} = 3.5\,R_{\odot}$."565 This yields a very low mass-function of fim)=Unj—msv55(0.021+0.030)M...," This yields a very low mass-function of $f(m) = \frac{m_2^3\,\sin^3{i}}{(m_1 + m_2)^2} = (0.021 \pm 0.030)\,M_{\odot}$."566 Here. To stands for the time of primary minimum.," Here, $T_0$ stands for the time of primary minimum."567 Compared to the photometric ephemerides. there is a shift in phase by 0.116 or 1.116.," Compared to the photometric ephemerides, there is a shift in phase by $0.116$ or 1.116."568 Since the number of orbital cycles between our photometric and spectroscopic campaigns amounts to 224. this phase shift implies an error in the orbital period of either 0.003 or ddays. well within or consistent with the estimated error in the orbital period as inferred from the photometric data ddays. see above).," Since the number of orbital cycles between our photometric and spectroscopic campaigns amounts to 224, this phase shift implies an error in the orbital period of either 0.003 or days, well within or consistent with the estimated error in the orbital period as inferred from the photometric data days, see above)."569 Since the system is eclipsing. we can to first order approximate the sin’/ term in the mass function to be unity.," Since the system is eclipsing, we can to first order approximate the $\sin^3{i}$ term in the mass function to be unity."570 Assuming a mass of 10 — 12Μ. for the BI primary. we find that the secondary should have a mass of about 1.4 — M... which implies that the companion might be an early F-type star.," Assuming a mass of 10 – $M_{\odot}$ for the B1 primary, we find that the secondary should have a mass of about 1.4 – $M_{\odot}$, which implies that the companion might be an early F-type star."571 But would this result be reasonable?, But would this result be reasonable?572 To answer this question. we return to the photometric light curve of the system.," To answer this question, we return to the photometric light curve of the system."573 We first recall that the latter displays variations outside the eclipses that are quite large., We first recall that the latter displays variations outside the eclipses that are quite large.574 In Paper I. we attributed them to spots. but our current knowledge of the system allows us to be a bit more specific.," In Paper I, we attributed them to spots, but our current knowledge of the system allows us to be a bit more specific."575 If we are indeed dealing with an F star closely orbiting around a VV primary. it seems unavoidable that there will be a strong heating effect of part of the secondary’s surface by the primary’s raciation.," If we are indeed dealing with an F star closely orbiting around a V primary, it seems unavoidable that there will be a strong heating effect of part of the secondary's surface by the primary's radiation."576 Test calculations carried out with the code 1ndicate that the light curve of the system can be explained by assuming that the hemisphere of the secondary facing the primary 15 significantly hotter than the rear side., Test calculations carried out with the code indicate that the light curve of the system can be explained by assuming that the hemisphere of the secondary facing the primary is significantly hotter than the rear side.577 However. the solution of the light curve is certainly not unique. because we ignore the actual mass ratio of the system and this parameter cannot be well-constrained from the photometric data alone.," However, the solution of the light curve is certainly not unique, because we ignore the actual mass ratio of the system and this parameter cannot be well-constrained from the photometric data alone."578 As an illustration. we show below the best-fit solution obtained for mj/nm»=8.," As an illustration, we show below the best-fit solution obtained for $m_1/m_2 = 8$."579 We note in addition that the radius of the secondary inferred from the light curve solution (5.6R« in the case of the best- solution shown below) is actually much larger than the expected radius of an early-F main-sequence star. but closer to what one would expect for a giant.," We note in addition that the radius of the secondary inferred from the light curve solution $R_{\odot}$ in the case of the best-fit solution shown below) is actually much larger than the expected radius of an early-F main-sequence star, but closer to what one would expect for a giant."580 Given the youth of the 22 cluster. the most straightforward explanation ts that the secondary star of 444 Is not a genuine giant. but rather a pre-main sequence (PMS) object.," Given the youth of the 2 cluster, the most straightforward explanation is that the secondary star of 44 is not a genuine giant, but rather a pre-main sequence (PMS) object."581 A PMS nature of the secondary would also provide a very natural explanation of the rather bright and hard X-ray emission of this system., A PMS nature of the secondary would also provide a very natural explanation of the rather bright and hard X-ray emission of this system.582 In summary. our analysis of the spectroscopic and photometric data of MSP444 leaves a number of open questions about the exact nature of the primary component.," In summary, our analysis of the spectroscopic and photometric data of 44 leaves a number of open questions about the exact nature of the primary component."583 The most likely scenario seems to be that this system consists of a BI main-sequence star and a low-mass PMS companion., The most likely scenario seems to be that this system consists of a B1 main-sequence star and a low-mass PMS companion.584 The physical parameters of the system are admittedly too uncertain to attempt a self-consistent determination of the distance of 22. although we note that the parameters of the fit in refMSP44sol are consistent with a distance of 8.4kkpe.," The physical parameters of the system are admittedly too uncertain to attempt a self-consistent determination of the distance of 2, although we note that the parameters of the fit in \\ref{MSP44sol} are consistent with a distance of kpc."585 If the VV spectral type of the 444 primary were correct and the companion contributed little to the integrated light of the, If the V spectral type of the 44 primary were correct and the companion contributed little to the integrated light of the586observed and confirmed compact groups. with the classification for each group ts listed in Table 1.,"observed and confirmed compact groups, with the classification for each group is listed in Table 1."587 To understand how our distant CGs. be them isolated or closer to a large-scale structure. compare with nearby ones. we proceed to measure the characteristic properties. 1.8. the three-dimensional (3D) velocity dispersion. crossing time. and mass. mass-to-light ratio. using the luminosities derived as explained in Sect.," To understand how our distant CGs, be them isolated or closer to a large-scale structure, compare with nearby ones, we proceed to measure the characteristic properties, i.e. the three-dimensional (3D) velocity dispersion, crossing time, and mass, mass-to-light ratio, using the luminosities derived as explained in Sect."588 2.3., 2.3.589 For the 3D velocity dispersion. we use the same equation used in Hickson et al. (," For the 3D velocity dispersion, we use the same equation used in Hickson et al. ("5901992). the crossing time being defined as: whereπου R is the median of galaxy-galaxy separations and σερ Is the 3D velocity dispersion.,"1992), the crossing time being defined as: where R is the median of galaxy-galaxy separations and $\sigma_{3D}$ is the 3D velocity dispersion."591 The dimensionless crossing time. shown in column 5 of Table 2. Πως. spans from 0.002 to 0.135. with a median value of 0.020. which ts slightly larger than the value measured for HCGs. 0.016.," The dimensionless crossing time, shown in column 5 of Table 2, $H_\mathrm{o}t_\mathrm{c}$, spans from 0.002 to 0.135, with a median value of 0.020, which is slightly larger than the value measured for HCGs, 0.016."592 The median observed velocity dispersion is 273s!.. while the 3D velocity dispersion is 382!.. substantially larger than that found for the HCGs (Hickson et al..," The median observed velocity dispersion is 273, while the 3D velocity dispersion is 382, substantially larger than that found for the HCGs (Hickson et al.,"593 92)., 92).594" If we restrict ourselves only to isolated groups. re. the ones. the median crossing time becomes Hr, = 0.024. 50% longer than the crossing time measured for HCGs but still half of the median value measured for SCGs. 0.051."," If we restrict ourselves only to isolated groups, i.e. the ones, the median crossing time becomes $H_\mathrm{o}t_\mathrm{c}$ = 0.024, $\%$ longer than the crossing time measured for HCGs but still half of the median value measured for SCGs, 0.051."595" The median radial velocity dispersion is c, = I88kms!.. while the 3D velocity dispersion is 73, =.. Very similar to that found for nearby If we consider the groups associated to larger structures. excluding those in the middle of a cluster. we measure a median radial velocity dispersion of c, =310kms7!.. while the 3D velocity dispersion is σερ =... which is about 1.6 times larger than the value measured for the isolated groups. in agreement with the result of Einasto et al."," The median radial velocity dispersion is $\sigma_{r}$ = , while the 3D velocity dispersion is $\sigma_{3D}$ =, very similar to that found for nearby If we consider the groups associated to larger structures, excluding those in the middle of a cluster, we measure a median radial velocity dispersion of $\sigma_{r}$ =, while the 3D velocity dispersion is $\sigma_{3D}$ =, which is about 1.6 times larger than the value measured for the isolated groups, in agreement with the result of Einasto et al."596 for loose groups closer to large-scale structures on the sky., for loose groups closer to large-scale structures on the sky.597 A comparison of the crossing time and velocity dispersion of the whole DPOSS sample and the isolated DPOSS compact groups is shown in Figure 5., A comparison of the crossing time and velocity dispersion of the whole DPOSS sample and the isolated DPOSS compact groups is shown in Figure 5.598 A test shows that the two populations are different at a confidence level of 97%., A test shows that the two populations are different at a confidence level of $\%$.599 For the mass estimate. we use different estimators. the virial and the projected mass.," For the mass estimate, we use different estimators, the virial and the projected mass."600 The expression for the virial mass is given in Equation 4. which is valid only under the assumption of spherical symmetry.," The expression for the virial mass is given in Equation 4, which is valid only under the assumption of spherical symmetry."601 where Aj; is the projected separation between galaxies 1 and j. here assumed to be the median length of the 2D galaxy-galaxy separation vector. corrected for cosmological effects; N is the number of concordant galaxies in the system. and V= is the velocity component along the line of sight of the galaxy with respect to the centre of mass of the group.," where $R_{ij}$ is the projected separation between galaxies i and j, here assumed to be the median length of the 2D galaxy-galaxy separation vector, corrected for cosmological effects; N is the number of concordant galaxies in the system, and $V_{zi}^2$ is the velocity component along the line of sight of the galaxy with respect to the centre of mass of the group."602 As observed by Heisler et al. (, As observed by Heisler et al. (6031985) and Perea et al. (,1985) and Perea et al. (6041990). the use of the virial theorem produces the best mass estimates. provided that there are no interlopers or projection effects.,"1990), the use of the virial theorem produces the best mass estimates, provided that there are no interlopers or projection effects."605 In case one of these two effects Is present. the current values should be considered as upper limits to the real mass.," In case one of these two effects is present, the current values should be considered as upper limits to the real mass."606 Another good mass estimate ts given by the projected mass estimator. which is defined as where R; is the projected separation from the centroid of the system. and fp is a numerical factor depending on the distribution of the orbits around the centre of mass of the system.," Another good mass estimate is given by the projected mass estimator, which is defined as where $R_{i}$ is the projected separation from the centroid of the system, and $_{P}$ is a numerical factor depending on the distribution of the orbits around the centre of mass of the system."607 Assuming a spherically symmetric system for which the Jeans hydrostatic equilibrium applies. we can express in an explicit form (Perea et al..," Assuming a spherically symmetric system for which the Jeans hydrostatic equilibrium applies, we can express in an explicit form (Perea et al.,"608 1990)., 1990).609 Since we lack information about the orbit eccentricities. we estimate the mass for radial. circular. and isotropic orbits and the corresponding expressions for Mp are given in Equations 6. 7. and 8 respectively as where2nG R is the median length of the 2D galaxy-galaxy separation The results for the four estimators all agree quite well with each other. and the reported value for the mass in column 6 of Table 2 is the average of all four estimates.," Since we lack information about the orbit eccentricities, we estimate the mass for radial, circular, and isotropic orbits and the corresponding expressions for $_{P}$ are given in Equations 6, 7, and 8 respectively as where R is the median length of the 2D galaxy-galaxy separation The results for the four estimators all agree quite well with each other, and the reported value for the mass in column 6 of Table 2 is the average of all four estimates."610 The averaged values havebeen used for the estimate of the M/L ratio in column 8, The averaged values havebeen used for the estimate of the M/L ratio in column 8611The compact radio source Sagittarius A* is suggested to be associated with a supermassive black hole al the Galactic Center (Eckart Genzel 1997. Ghez 1998. Backer Sramek 1999. Reid 1999).,"The compact radio source Sagittarius A* is suggested to be associated with a supermassive black hole at the Galactic Center (Eckart Genzel 1997, Ghez 1998, Backer Sramek 1999, Reid 1999)."612 The flux density variability of Ser A* has been puzzling since (he discovery. of this intriguing radio compact source at the center, The flux density variability of Sgr A* has been puzzling since the discovery of this intriguing radio compact source at the center613in which fy can physically be seen to represent the “echo time” — the two-way travel time for the wave. corresponding to a vertical reflection from the subsurface reflector.,"in which $t_0$ can physically be seen to represent the “echo time"" — the two-way travel time for the wave, corresponding to a vertical reflection from the subsurface reflector."614 The term under the square root sign is themoveout factor. which appears because the wave reaching the receiver at a distance . from the shot point (1.9. the location of the source). has not been reflected vertically (Lowrie1997).," The term under the square root sign is the factor, which appears because the wave reaching the receiver at a distance $x$ from the shot point (i.e. the location of the source), has not been reflected vertically \citep{lowrie}."615. Under the condition that the receiver distance. .c. is much less than the reflector depth. d. i.e. .c«d. itis à matter of some simple algebraic steps to arrive at an approximate solution (through a binomial expansion) for the normal moveout. Af=f—fy. as The primary objective here is to determine the depth. 4. of the reflector.," Under the condition that the receiver distance, $x$, is much less than the reflector depth, $d$, i.e. $x \ll d$, it is a matter of some simple algebraic steps to arrive at an approximate solution (through a binomial expansion) for the normal moveout, $\Delta t = t - t_0$, as The primary objective here is to determine the depth, $d$ , of the reflector."616 The vertical echo time. fy. and the normal moveout time. Af. can be obtained from the reflection data.," The vertical echo time, $t_0$, and the normal moveout time, $\Delta t$, can be obtained from the reflection data."617" The corresponding receiver distance. ο”, will also be known from the data."," The corresponding receiver distance, $x$, will also be known from the data."618 Taken together. all of these will allow for determining the value of e from Eq. (3)).," Taken together, all of these will allow for determining the value of $v$ from Eq. \ref{nmo}) )."619 This. with the help of the definition of £y. will subsequently also allow for the determination of 4.," This, with the help of the definition of $t_0$, will subsequently also allow for the determination of $d$."620 In all of this there is a clear signal that a precise extraction of the value of ο from the reflection data is a principal necessity in determining the reflector depth accurately., In all of this there is a clear signal that a precise extraction of the value of $v$ from the reflection data is a principal necessity in determining the reflector depth accurately.621 Even the simplest possible case that is being studied here emphasises this fact., Even the simplest possible case that is being studied here emphasises this fact.622 Knowing the precise value of the velocity will be an equally important issue when one considers more complicated instances of reflection seismology involving non-horizontal reflectors of continually varying gradients., Knowing the precise value of the velocity will be an equally important issue when one considers more complicated instances of reflection seismology involving non-horizontal reflectors of continually varying gradients.623" Besides this. with ο being dependent on the elastic properties of the material through which the wave propagates 1999)., getting a correct measure of the velocity also conveys an impression of the true nature of the subsurface material."," Besides this, with $v$ being dependent on the elastic properties of the material through which the wave propagates \citep{ll, mgc}, getting a correct measure of the velocity also conveys an impression of the true nature of the subsurface material."624 It is scarcely to be expected that the layeringof actual geological strata will conform to the neat and orderly, It is scarcely to be expected that the layeringof actual geological strata will conform to the neat and orderly625purity.,purity.626 This choice resulted in a catalogue that was 9896 complete and 52 96 pure., This choice resulted in a catalogue that was $\%$ complete and 52 $\%$ pure.627 Fig., Fig.628" 5 shows that clipping groups and clusters with the lowest richnesses will improve the purity, but will reduce the completeness."," \ref{fig:pure_test} shows that clipping groups and clusters with the lowest richnesses will improve the purity, but will reduce the completeness."629" This plot also shows that the purity is much higher for lower values of Rgriena(z=0.5), which would correspond to structures that have smaller radial sizes."," This plot also shows that the purity is much higher for lower values of $R_{friend}(z=0.5)$, which would correspond to structures that have smaller radial sizes."630" Therefore, it appears that the purity is mainly affected by the size and richness of the groups and clusters."," Therefore, it appears that the purity is mainly affected by the size and richness of the groups and clusters."631" In an attempt to improve the purity while preserving the completeness, several new catalogues were made by clipping out groups and clusters with sizes larger than some threshold for a given richness from the original 25LAQ mock cluster catalogue."," In an attempt to improve the purity while preserving the completeness, several new catalogues were made by clipping out groups and clusters with sizes larger than some threshold for a given richness from the original 2SLAQ mock cluster catalogue."632 Table 3 shows the total number of groups and clusters with 3 and 4 members for various radial cuts., Table \ref{tab:clips} shows the total number of groups and clusters with 3 and 4 members for various radial cuts.633" Reip is the size threshold in Mpc 1-1 above which all groups and clusters will be removed, No: is the total number of groups and clusters for a given Retip, Neue is the number of groups and clusters that are matched to 28LAQ mock haloes for a given Rai? and the ratio Nirue/Niot gives a measure for the purity for a given Rep."," $_{clip}$ is the size threshold in Mpc $h^{-1}$ above which all groups and clusters will be removed, $_{tot}$ is the total number of groups and clusters for a given $_{clip}$, $_{true}$ is the number of groups and clusters that are matched to 2SLAQ mock haloes for a given $_{clip}$ and the ratio $_{true}$ $_{tot}$ gives a measure for the purity for a given $_{clip}$."634" As can been seen in the table, when no cuts are made groups of 3 and 4 members are only 3896 and 5796 pure respectively."," As can been seen in the table, when no cuts are made groups of 3 and 4 members are only $\%$ and $\%$ pure respectively."635 Above richness of 4 all groups and clusters are above 80% pure., Above richness of 4 all groups and clusters are above $\%$ pure.636" Therefore, the majority of the contamination in the cluster catalogue arises from these small groups."," Therefore, the majority of the contamination in the cluster catalogue arises from these small groups."637Observations have so far led to a large number of discovered high-mass X-ray binaries. both in the Milky Way and other ealaxies (overLOOintheMilkyWayalone:Liuetal.2006).,"Observations have so far led to a large number of discovered high-mass X-ray binaries, both in the Milky Way and other galaxies \citep[over 100 in the Milky Way alone;][]{liu06}."638. However. only a handful of these are believed to harbor black holes.," However, only a handful of these are believed to harbor black holes."639 Two of these. €vgnus X-1 and Cvenus X-3. are found in our own Galaxy.," Two of these, Cygnus X-1 and Cygnus X-3, are found in our own Galaxy."640 The most well-known and. well-stucdied of the black hole binaries is Cvgnus X-1., The most well-known and well-studied of the black hole binaries is Cygnus X-1.641 In parallel with the discoverv of more sources. new techniques have given estimates of the spin parameter. of the black hole.," In parallel with the discovery of more sources, new techniques have given estimates of the spin parameter of the black hole."642 The two main techniques rely on spectral fitting of the thermal component (e.g..Shaleeetal.2006) or relativistically broadened. iron line (c.g...Miller2007).," The two main techniques rely on spectral fitting of the thermal component \citep[e.g.,][]{sha06} or relativistically broadened iron line \citep[e.g.,][]{mil07}."643. Llowever. these results are quite sensitive as spectral fitting is prone to a certain amount of degeneracy ancl mocel dependency.," However, these results are quite sensitive as spectral fitting is prone to a certain amount of degeneracy and model dependency."644 Phe technique is also dependent on the spectral state of the source. making it dillicult to apply to certain sources which do not show this state. e.g. Cvg X-1.," The technique is also dependent on the spectral state of the source, making it difficult to apply to certain sources which do not show this state, e.g. Cyg X-1."645 Axelssonetal.(2005) presented an alternative technique for determining the spin parameter in (νο X-1., \cite{axe05} presented an alternative technique for determining the spin parameter in Cyg X-1.646 By studying the evolution of quasi-periodic oscillations (QPOs). they were able to give support to the idea that the oscillations are connected to the relativistic precession frequencies predicted: by general relativity in the strong eravitational field close to the black hole.," By studying the evolution of quasi-periodic oscillations (QPOs), they were able to give support to the idea that the oscillations are connected to the relativistic precession frequencies predicted by general relativity in the strong gravitational field close to the black hole."647 Based. on this identification. the spin parameter was measured to be0:01. assuming the black hole mass to beM.," Based on this identification, the spin parameter was measured to be, assuming the black hole mass to be."648.. While still dependent on the theoretical interpretation. this method allows for a much more precise determination of the spin than the spectral modelling techniques.," While still dependent on the theoretical interpretation, this method allows for a much more precise determination of the spin than the spectral modelling techniques."649 As several of the black hole svstems discovered. so far are tight svstenis. a possible source of spin may be tidal locking (see.e.g.Podsiadlowskietal.2004:Levanct 2006).," As several of the black hole systems discovered so far are tight systems, a possible source of spin may be tidal locking \citep[see, e.g.,][]{pod04,ldk06}."650. Upon collapse of the black hole progenitor. the angular momenttu is preserved in the spin parameter of the black hole.," Upon collapse of the black hole progenitor, the angular momentum is preserved in the spin parameter of the black hole."651 In this paper. we will investigate whether such a scenario can explain the measured spin parameter of (νο X-1.," In this paper, we will investigate whether such a scenario can explain the measured spin parameter of Cyg X-1."652 This system is a good candidate for such an investigation: it is bright and thereby. well stucied. ancl observations by Mirabel&Itodrigues(2003) indicate that the mass loss in the formation of the black hole was low.," This system is a good candidate for such an investigation: it is bright and thereby well studied, and observations by \cite{mir03} indicate that the mass loss in the formation of the black hole was low."653 1n the rest of this section. we motivate our choice for the system. parameters such as the mass of the compact object.," In the rest of this section, we motivate our choice for the system parameters such as the mass of the compact object."654 Based on this. in the following section we investigate whether svstems similar to (νο X-1 can acquire sullicient angular momentum via tidal locking to explain the current spin parameter.," Based on this, in the following section we investigate whether systems similar to Cyg X-1 can acquire sufficient angular momentum via tidal locking to explain the current spin parameter."655 In Sect., In Sect.656 2. we discuss the evolution of the system in the past. including possible processes which may cause the spin measured todav to diller from the natal one.," \ref{evolution} we discuss the evolution of the system in the past, including possible processes which may cause the spin measured today to differ from the natal one."657 Although one of the best. studied: black hole candidate sources. estimates of the current parameters of the (νο," Although one of the best studied black hole candidate sources, estimates of the current parameters of the Cyg"658"phase error of one cycle, the maximum bin size in the k- derivative is v is Av)=(k+DTE, implying Ny&pU)[AO) templates in that derivative and Ni=Ne templates overall.","phase error of one cycle, the maximum bin size in the $k$ -th derivative is $\nu^{(k)}$ is $\Delta \nu^{(k)} = (k + 1)!/\Tlag^{k+1}$, implying $N_{k} \approx \nu^{(k)}/ \Delta \nu^{(k)}$ templates in that derivative and $N_\text{total} = \prod^s_{k=0} N_k$ templates overall."659 We discuss this matter further in IlioSection 6.2.., We discuss this matter further in Section \ref{sec:templates}.660" To improve on the above situation, we recognize that 7 for an isolated neutron star is the sum of gravitational-wave and electromagnetic torque contributions: where R, is the neutron star radius, D is the polar magnetic field, n is the electromagnetic braking index (theoreticallyequalto3,butcouldbeaslow1.8;Melatos 2005)."," To improve on the above situation, we recognize that $\dot{\nu}$ for an isolated neutron star is the sum of gravitational-wave and electromagnetic torque contributions: where $R_{\star}$ is the neutron star radius, $B$ is the polar magnetic field, $n$ is the electromagnetic braking index \citep[theoretically equal to 3, but could be as low as 1.8;][]{melatos97, palomba05}."661". Assuming that the electromagnetic torque is proportional to a power of v, then v must enter the torque in the combination R,v/c, (i.e. the ratio of R, to the characteristic lever arm, the light cylinder distance, c/27v) on dimensional grounds."," Assuming that the electromagnetic torque is proportional to a power of $\nu$, then $\nu$ must enter the torque in the combination $R_\star \nu/c$, (i.e. the ratio of $R_\star$ to the characteristic lever arm, the light cylinder distance, $c/2 \pi \nu$ ) on dimensional grounds."662" In terms of an arbitrary reference frequency, 144r, we write 7=—Qi(v/ret)”—Qa(v/viet)"", with Qi=Qiv3., and Q»=Q5v?,."," In terms of an arbitrary reference frequency, $\nu_{\rm{ref}}$, we write $\dot{\nu} = - Q_1 \left(\nu/\nu_{\rm{ref}}\right)^5 - Q_2 \left(\nu/\nu_{\rm{ref}}\right)^n$, with $Q_1 = Q_1' \nu_{\rm{ref}}^5$ and $Q_2 = Q_2' \nu_{\rm{ref}}^n$."663" Throughout this paper, we set rec=1 HHz for simplicity."," Throughout this paper, we set $\nu_\text{ref} = 1$ Hz for simplicity."664" There may, of course, be other torques acting on a newly born neutron star."," There may, of course, be other torques acting on a newly born neutron star."665" For example, nonlinear r-mode instabilities can emit a significant amount of gravitational radiation under certain conditions (Owenetal.1998)."," For example, nonlinear r-mode instabilities can emit a significant amount of gravitational radiation under certain conditions \citep{owen98}."666". If there is a rapidly rotating pulsar with B<10!! GG in SNR 19874, its instability time scale (27 years) would exceed its age, and the gravitational radiation from the instabilities alone should be detectable by Advanced LIGO (Brinketal.2004;Bondarescuetal. 2009)."," If there is a rapidly rotating pulsar with $B \leq 10^{11}$ G in SNR 1987A, its instability time scale (27 years) would exceed its age, and the gravitational radiation from the instabilities alone should be detectable by Advanced LIGO \citep{brink04, bondarescu09}."667". However, for the purposes of our search, we assume that the spin down is described by (25))."," However, for the purposes of our search, we assume that the spin down is described by \ref{eq:numodel}) )."668" An equally serious issue is that n may change over the lyyr integration period, although in (25)), we assume that n is constant."," An equally serious issue is that $n$ may change over the yr integration period, although in \ref{eq:numodel}) ), we assume that $n$ is constant."669" Young pulsars have n« 3, and it can be argued that n approaches 3 over the spin-down time-scale (Melatos1997)."," Young pulsars have $n < 3$ , and it can be argued that $n$ approaches 3 over the spin-down time-scale \citep{melatos97}."670". In this search, we maintain the assumption of constant n."," In this search, we maintain the assumption of constant $n$."671" However, it is possible to extend (25)) to include time-dependent n in future searches."," However, it is possible to extend \ref{eq:numodel}) ) to include time-dependent $n$ in future searches."672" We aim, in the first instance, to exclude the simplest astrophysical model while recognizing that it covers only a small fraction of the total parameter space."," We aim, in the first instance, to exclude the simplest astrophysical model while recognizing that it covers only a small fraction of the total parameter space."673" When implementing the search, instead of stepping through a grid of frequency derivatives, we search instead over V,Qi1,Q2, and m."," When implementing the search, instead of stepping through a grid of frequency derivatives, we search instead over $\nu, Q_1, Q_2$, and $n$."674" This reduces the number of parameters and allows one to track the phase more accurately for a given computational cost, as errors stemming from incorrect choices of (v,Q1,Qo,n) grow more slowly with observation time than errors stemmingfrom higher-order frequency derivatives."," This reduces the number of parameters and allows one to track the phase more accurately for a given computational cost, as errors stemming from incorrect choices of $(\nu, Q_1, Q_2, n)$ grow more slowly with observation time than errors stemmingfrom higher-order frequency derivatives."675 The improvement is quantified in Section 6.2.., The improvement is quantified in Section \ref{sec:templates}. .676 We note that the search targets, We note that the search targets677"to regions of the secondary star on the trailing hemisphere away from the £4, point.",to regions of the secondary star on the trailing hemisphere away from the $L_1$ point.678 This obscuration of the accretion stream by the secondary star itself may explain the observed shadow on the trailing hemisphere., This obscuration of the accretion stream by the secondary star itself may explain the observed shadow on the trailing hemisphere.679 This feature could also be explained if svstematic errors were able to produce a greater line lux in the centres of the lines. corresponding to artificially brighter polar regions in the Roche tomograms and giving the illusion of a shadow at lower latitudes.," This feature could also be explained if systematic errors were able to produce a greater line flux in the centres of the lines, corresponding to artificially brighter polar regions in the Roche tomograms and giving the illusion of a shadow at lower latitudes."680 It was first thought that the assumption of a Gaussian profile for the emission from the secondary star could. introduce such an artefact. since the actual profile from the secondary star is expected to be Hatter. especially around equadrature.," It was first thought that the assumption of a Gaussian profile for the emission from the secondary star could introduce such an artefact, since the actual profile from the secondary star is expected to be flatter, especially around quadrature."681 We found. however. that at low spectra resolutions the emission. profile from the secondary. is wel approximated by a Gaussian.," We found, however, that at low spectral resolutions the emission profile from the secondary is well approximated by a Gaussian."682 Artefacts could be generate if the emission. from the various components of HU. Aqr (e.g. from the secondary star and the accretion stream) are incorrectly disentangled. which is especially dillicul ab phases where the individual components are crossing each other.," Artefacts could be generated if the emission from the various components of HU Aqr (e.g. from the secondary star and the accretion stream) are incorrectly disentangled, which is especially difficult at phases where the individual components are crossing each other."683 This situation is more cdillicult to assess ane emphasises the importance of mapping lines that are known to originate solely from the secondary star., This situation is more difficult to assess and emphasises the importance of mapping lines that are known to originate solely from the secondary star.684BETP 2008/06 Pom 1.5em 0.5cm 2.5cnm This is an introduction to the study of strongly interacting matter.,BI-TP 2008/06 2cm 1.5cm 0.5cm 2.5cm This is an introduction to the study of strongly interacting matter.685 We survey its different possible states and discuss the transition from hadronic matter to a plasma of deconfined quarks ancl gluons., We survey its different possible states and discuss the transition from hadronic matter to a plasma of deconfined quarks and gluons.686 Following this. we sunmiarze (he results provided bv lattice QCD linite temperature and density. aud (then investigate the nature of the deconfinement transilion.," Following this, we summarize the results provided by lattice QCD finite temperature and density, and then investigate the nature of the deconfinement transition."687", Finally we give a schematic overview of possible wavs (o study (he properties of the quark-gluon plasma. *", Finally we give a schematic overview of possible ways to study the properties of the quark-gluon plasma. *688 Lecture given at theSchool. Jaipur/India. 11. 2008: to appear in," Lecture given at the, Jaipur/India, 1, 2008; to appear in"689at 10.5 pm for the diffuse sightlines.,at 10.5 $\mu$ m for the diffuse sightlines.690 From an eyeball comparison of the 9.7 jm silicate features in Fig., From an eyeball comparison of the 9.7 $\mu$ m silicate features in Fig.691 11 we conclude that these features in molecular sightlines differ substantially from the absorption feature observed towards theCentre., \ref{fig:earlymol} we conclude that these features in molecular sightlines differ substantially from the absorption feature observed towards the.692 The slopes of the long wavelength side of the features (1.6. 4L» 10.5 μπι) are the same as that of the GalacticCentre., The slopes of the long wavelength side of the features (i.e. $\lambda >$ 10.5 $\mu$ m) are the same as that of the Galactic.693 If we assume that the profiles are indeed the same from 10.5 um onward. then the molecular sightlines show excess absorption between 7.5 and 10.5 jm. In Fig.," If we assume that the profiles are indeed the same from 10.5 $\mu$ m onward, then the molecular sightlines show excess absorption between 7.5 and 10.5 $\mu$ m. In Fig."694 12. the difference is plotted between the observed features in the molecular sightlines in our sample and the feature., \ref{fig:mol_galcent} the difference is plotted between the observed features in the molecular sightlines in our sample and the feature.695 The observed difference between the 9.7 jm silicate profiles in molecular sightlines and the Galactic sightline can be caused by three effects: (1) The presence of a photospheric gas phase SiO band in the spectrum of the background star. (, The observed difference between the 9.7 $\mu$ m silicate profiles in molecular sightlines and the Galactic sightline can be caused by three effects: (i) The presence of a photospheric gas phase SiO band in the spectrum of the background star. (69611) The presence of ices along the line-of-sight. (,ii) The presence of ices along the line-of-sight. (697iit) A change in the dust properties of the amorphous silicates.,iii) A change in the dust properties of the amorphous silicates.698 We will discuss these three effects separately below., We will discuss these three effects separately below.699 Since the spectral type for 3 of the 4+ sources is unknown. there might be a small photospheric gas phase SiO band in the spectra.," Since the spectral type for 3 of the 4 sources is unknown, there might be a small photospheric gas phase SiO band in the spectra."700spectroscopy observations of M cwarfs should allow for the possibility of variable stellar IT I liue flux at the level with a dutv evele of ~3%..,"spectroscopy observations of M dwarfs should allow for the possibility of variable stellar H I line flux at the level, with a duty cycle of $\sim$."701 If observed.in broad- filters. these line flax enhancements would produce chhancements of 0.L nmüllianags(J--band) to 0.3 iuilli-maes (As--band). siguificauth below the upper limits of the IR photometric stability preseuted in Section 3.2..," If observedin broad-band filters, these line flux enhancements would produce enhancements of 0.4 milli-mags-band) to 0.3 milli-mags -band), significantly below the upper limits of the IR photometric stability presented in Section \ref{irflares}."702 We have presented ~17 hows of high cadeuce. lieh precision. simultaneous optical and IR photometric monitoring of 3 active AL dwarfs.," We have presented $\sim$ 47 hours of high cadence, high precision, simultaneous optical and IR photometric monitoring of 3 active M dwarfs."703 We detected and characterized four highly cnerectic optical flares having U-baud total cnereies of ~7.8 x 109 to —1.3 x 107? ores. and fouud no correspouding response iu theJ..JL. or baudpasses at the precision of our data.," We detected and characterized four highly energetic optical flares having U-band total energies of $\sim$ 7.8 x $^{30}$ to $\sim$ 1.3 x $^{32}$ ergs, and found no corresponding response in the, or bandpasses at the precision of our data."704 To sunuuarize our results: We thank the referee. Rachel Osteu. for providius comunenuts which helped to improve the content aud clarity of this paper.," To summarize our results: We thank the referee, Rachel Osten, for providing comments which helped to improve the content and clarity of this paper."705 BAIT acknowledges support from a Maury Gates Research Scholarship., BMT acknowledges support from a Mary Gates Research Scholarship.706 We acknowledge support πο NSF AST erauts 08-02230 (JPW). 08-07205 (AFI. ELII. SLU). and 06-15116 (PIs).," We acknowledge support from NSF AST grants 08-02230 (JPW), 08-07205 (AFK, ELH, SLH), and 06-45416 (PK)."707 ΔΕΝ and SJS thaws NOAÀO for supporting their travel to KPNO to carry out portions of these observations., AFK and SJS thank NOAO for supporting their travel to KPNO to carry out portions of these observations.708 Observations from the NMSU lin were supported in part by NSF AST 05-1939s., Observations from the NMSU 1m were supported in part by NSF AST 05-19398.709 We thauk J. Irwin for sharing \[Earth detections of a YZ CAG flare with us. and J. Daveuport for providing access to his model results aud discussion on the topic.," We thank J. Irwin for sharing MEarth detections of a YZ CMi flare with us, and J. Davenport for providing access to his model results and discussion on the topic."710 BAIT aud JPW thank the Iailuc-Ikoua shark. which was hiking iu uearby waters during the preparation of this niauuscript. for not cating them. ARC.. Lin. I," BMT and JPW thank the Kailua-Kona shark, which was lurking in nearby waters during the preparation of this manuscript, for not eating them. , , ,"711 BAIT aud JPW thank the Iailuc-Ikoua shark. which was hiking iu uearby waters during the preparation of this niauuscript. for not cating them. ARC.. Lin. IK," BMT and JPW thank the Kailua-Kona shark, which was lurking in nearby waters during the preparation of this manuscript, for not eating them. , , ,"712 BAIT aud JPW thank the Iailuc-Ikoua shark. which was hiking iu uearby waters during the preparation of this niauuscript. for not cating them. ARC.. Lin. IKD," BMT and JPW thank the Kailua-Kona shark, which was lurking in nearby waters during the preparation of this manuscript, for not eating them. , , ,"713 BAIT aud JPW thank the Iailuc-Ikoua shark. which was hiking iu uearby waters during the preparation of this niauuscript. for not cating them. ARC.. Lin. IKDP," BMT and JPW thank the Kailua-Kona shark, which was lurking in nearby waters during the preparation of this manuscript, for not eating them. , , ,"714 BAIT aud JPW thank the Iailuc-Ikoua shark. which was hiking iu uearby waters during the preparation of this niauuscript. for not cating them. ARC.. Lin. IKDPN," BMT and JPW thank the Kailua-Kona shark, which was lurking in nearby waters during the preparation of this manuscript, for not eating them. , , ,"715 BAIT aud JPW thank the Iailuc-Ikoua shark. which was hiking iu uearby waters during the preparation of this niauuscript. for not cating them. ARC.. Lin. IKDPNO," BMT and JPW thank the Kailua-Kona shark, which was lurking in nearby waters during the preparation of this manuscript, for not eating them. , , ,"716 BAIT aud JPW thank the Iailuc-Ikoua shark. which was hiking iu uearby waters during the preparation of this niauuscript. for not cating them. ARC.. Lin. IKDPNO:," BMT and JPW thank the Kailua-Kona shark, which was lurking in nearby waters during the preparation of this manuscript, for not eating them. , , ,"717 BAIT aud JPW thank the Iailuc-Ikoua shark. which was hiking iu uearby waters during the preparation of this niauuscript. for not cating them. ARC.. Lin. IKDPNO:2," BMT and JPW thank the Kailua-Kona shark, which was lurking in nearby waters during the preparation of this manuscript, for not eating them. , , ,"718 BAIT aud JPW thank the Iailuc-Ikoua shark. which was hiking iu uearby waters during the preparation of this niauuscript. for not cating them. ARC.. Lin. IKDPNO:2.," BMT and JPW thank the Kailua-Kona shark, which was lurking in nearby waters during the preparation of this manuscript, for not eating them. , , ,"719 BAIT aud JPW thank the Iailuc-Ikoua shark. which was hiking iu uearby waters during the preparation of this niauuscript. for not cating them. ARC.. Lin. IKDPNO:2.1," BMT and JPW thank the Kailua-Kona shark, which was lurking in nearby waters during the preparation of this manuscript, for not eating them. , , ,"720 BAIT aud JPW thank the Iailuc-Ikoua shark. which was hiking iu uearby waters during the preparation of this niauuscript. for not cating them. ARC.. Lin. IKDPNO:2.11," BMT and JPW thank the Kailua-Kona shark, which was lurking in nearby waters during the preparation of this manuscript, for not eating them. , , ,"721 BAIT aud JPW thank the Iailuc-Ikoua shark. which was hiking iu uearby waters during the preparation of this niauuscript. for not cating them. ARC.. Lin. IKDPNO:2.11.," BMT and JPW thank the Kailua-Kona shark, which was lurking in nearby waters during the preparation of this manuscript, for not eating them. , , ,"722 BAIT aud JPW thank the Iailuc-Ikoua shark. which was hiking iu uearby waters during the preparation of this niauuscript. for not cating them. ARC.. Lin. IKDPNO:2.11..," BMT and JPW thank the Kailua-Kona shark, which was lurking in nearby waters during the preparation of this manuscript, for not eating them. , , ,"723the distance measure Dy does not lead to an equivalently good estimate of the cosmic parameters.,the distance measure $D_{V}$ does not lead to an equivalently good estimate of the cosmic parameters.724" Clearly, the systematic uncertainty that we calculated is only a minor effect compared with the errors intrinsic to the actual measurement of the acoustic scale, as a comparison of the three solid (green) lines in Fig."," Clearly, the systematic uncertainty that we calculated is only a minor effect compared with the errors intrinsic to the actual measurement of the acoustic scale, as a comparison of the three solid (green) lines in Fig."725 9 shows., \ref{fig:dDVcomp} shows.726 The lowest one is the fluctuation of the scale Dy for full spheres of the corresponding size at different places in the universe., The lowest one is the fluctuation of the scale $D_{V}$ for full spheres of the corresponding size at different places in the universe.727 It is therefore the possible local deformation caused by statistical over- or underdensities., It is therefore the possible local deformation caused by statistical over- or underdensities.728" The possible precision of a measurement of Dy by BAOs, however, also depends on the number of observable modes."," The possible precision of a measurement of $D_{V}$ by BAOs, however, also depends on the number of observable modes."729" This induces an error if the volume is too small, and in particular when it is smaller than the BAO scale a reasonable measurement is no longer possible."," This induces an error if the volume is too small, and in particular when it is smaller than the BAO scale a reasonable measurement is no longer possible."730" Accordingly, even for a perfect sampling of the observed volume, the error will not be smaller than the solid (green) lines in the middle."," Accordingly, even for a perfect sampling of the observed volume, the error will not be smaller than the solid (green) lines in the middle."731" If one adds shot noise caused by imperfect sampling by a galaxy density of n=3x 107n?Mpc, typical for SDSS and BOSS, the error increases even more."," If one adds shot noise caused by imperfect sampling by a galaxy density of $n=3\times10^{-4} h^3 \mathrm{Mpc^{-3}}$ , typical for SDSS and BOSS, the error increases even more."732" This means that for the realistic situation where we do not have a sufficiently small perfect ruler to allow for large statistics already for the small volumes considered here, the deformation uncertainty that we calculated remains completely subdominant."," This means that for the realistic situation where we do not have a sufficiently small perfect ruler to allow for large statistics already for the small volumes considered here, the deformation uncertainty that we calculated remains completely subdominant."733" Local fluctuations of the Hubble expansion rate have already been considered in the literature (Turneretal.,1992;Shi1996;Wangetal.,1998;Umeh 2010)."," Local fluctuations of the Hubble expansion rate have already been considered in the literature \citep{hubble:turner,hubble:shiturner,hubble:wangturner,clarkson:hubble}."734. Here we wish to add two new aspects., Here we wish to add two new aspects.735 The first one is on the measurement of A(z) itself., The first one is on the measurement of $H(z)$ itself.736" Experiments that try to measure H as a function of z, like the WiggleZ survey (Blakeetal.,2011),, do this by measuring a “local” average H(z,,) in a region around the redshift z,,."," Experiments that try to measure $H$ as a function of $z$, like the WiggleZ survey \citep{hubbleofz}, do this by measuring a “local” average $H(z_{m})$ in a region around the redshift $z_{m}$."737 These regions should not be too small to keep the effects of local fluctuations small., These regions should not be too small to keep the effects of local fluctuations small.738" On the other hand they cannot be enlarged in an arbitrary way because then the redshift z,, becomes less and less characteristic for the averaging domain.", On the other hand they cannot be enlarged in an arbitrary way because then the redshift $z_{m}$ becomes less and less characteristic for the averaging domain.739" In other words, for an increasingly thicker shell Az, the evolution of H(z) begins to play a role."," In other words, for an increasingly thicker shell $\Delta z$, the evolution of $H(z)$ begins to play a role."740" Therefore, one may find the optimal thickness of the averaging shells over which the variation in the expansion rate equals the variance imposed by the inhomogeneous matter distribution."," Therefore, one may find the optimal thickness of the averaging shells over which the variation in the expansion rate equals the variance imposed by the inhomogeneous matter distribution."741 The corresponding shells are shown in Fig. 10.., The corresponding shells are shown in Fig. \ref{fig:VarVerg}.742" It should be noted that the error for the first bin is certainly underestimated in our treatment, which rests on linear perturbation theory."," It should be noted that the error for the first bin is certainly underestimated in our treatment, which rests on linear perturbation theory."743" Taking into account higher orders, which become dominant at small scales, will certainly increase it."," Taking into account higher orders, which become dominant at small scales, will certainly increase it."744" Of course, in these measurements the survey geometries will not necessarily be close to the SDSS or the 2dF geometry, but they are shown to illustrate survey geometries that do not cover the full sky."," Of course, in these measurements the survey geometries will not necessarily be close to the SDSS or the 2dF geometry, but they are shown to illustrate survey geometries that do not cover the full sky."745" Secondly, we wish to note that the relation between fluctuations in the Hubble expansion rate and fluctuations in the matter density offers the interesting possibility to determine the evolution of the growth function for matter perturbations from the variances of the Hubble rate measured at different redshifts."," Secondly, we wish to note that the relation between fluctuations in the Hubble expansion rate and fluctuations in the matter density offers the interesting possibility to determine the evolution of the growth function for matter perturbations from the variances of the Hubble rate measured at different redshifts."746" A direct measurement of the growth function by a determination of og at different epochs is difficult, because one never examines the underlying dark matter distribution."," A direct measurement of the growth function by a determination of $\sigma_{8}$ at different epochs is difficult, because one never examines the underlying dark matter distribution."747 Therefore one has to assume that the observed objects represent the same clustering pattern as the underlying dark matter (this is the problem of bias)., Therefore one has to assume that the observed objects represent the same clustering pattern as the underlying dark matter (this is the problem of bias).748 It is well known that there is bias and its modeling typically has to rely on assumptions., It is well known that there is bias and its modeling typically has to rely on assumptions.749 An interesting bypass is to look at the variation of local expansion rates at different redshifts., An interesting bypass is to look at the variation of local expansion rates at different redshifts.750 The assumption that the luminous objects follow the local flow is more likely and the assumption that this local flow is generated by the inhomogeneities of the underlying dark matter distribution is also reasonable., The assumption that the luminous objects follow the local flow is more likely and the assumption that this local flow is generated by the inhomogeneities of the underlying dark matter distribution is also reasonable.751" A similar idea leads to the attempt to use redshift-space distortions to do so(Percival&White,2009).", A similar idea leads to the attempt to use redshift-space distortions to do so\citep{percival:bao}.752". The fact that one considers fluctuations means that we would not have to know the actual value of H(z), but only the local variation at different redshifts."," The fact that one considers fluctuations means that we would not have to know the actual value of $H\left(z\right)$, but only the local variation at different redshifts."753" This variation, defined as has the fluctuations of Eq. (47))"," This variation, defined as has the fluctuations of Eq. \ref{eq:sigH}) )"754" If we were to measure this quantity at different redshifts, we could, without knowledge of the absolute normalization of Ho (z), determine fp(ap) only from the variance and therefore the constant c=Qa /Qyy."," If we were to measure this quantity at different redshifts, we could, without knowledge of the absolute normalization of $H_{\cD}\left(z\right)$ , determine $f_\cD\left(a_{\cD}\right)$ only from the variance and therefore the constant $c=\Omega_{\Lambda}/\Omega_{m}$ ."755set of vector harmonic terms bevond (he Ogorodnikov-Milne model.,set of vector harmonic terms beyond the Ogorodnikov-Milne model.756 The detected pattern of tangential velocities of Hipparcos stars consistent with this interpretation is shown in Fig. 2.., The detected pattern of tangential velocities of Hipparcos stars consistent with this interpretation is shown in Fig. \ref{Gamma.fig}.757 The Milkv Wax disk is warped. as has been established from the distribution of stars and neutral hydrogen.," The Milky Way disk is warped, as has been established from the distribution of stars and neutral hydrogen."758 In (his respect. our Galaxy is not different [rom many other spiral ealaxies exhibiting a range of warp distorüons.," In this respect, our Galaxy is not different from many other spiral galaxies exhibiting a range of warp distortions."759 The origin of galactic warps is not clear: a number of hypotheses have been proposed. including the tidal interaction of the disk with the dark matter halo. the influence of the bar. and the perturbation from a major satellite ealaxv.," The origin of galactic warps is not clear; a number of hypotheses have been proposed, including the tidal interaction of the disk with the dark matter halo, the influence of the bar, and the perturbation from a major satellite galaxy."760 The Sun appears to be close to the line of nodes of the Milky Way warp. and the upper rim of the disk is at (=90° (in the rotation direction).," The Sun appears to be close to the line of nodes of the Milky Way warp, and the upper rim of the disk is at $\ell=90\degr$ (in the rotation direction)."761 The height of the midsection above the plane is «quadratic wilh galactocentric distance in the modelof (2000).. wp)=(p—p/15 kpe lor p>py. and zero lor p«py.," The height of the midsection above the plane is quadratic with galactocentric distance in the modelof \citet{dri}, $w(\rho)=(\rho-\rho_w)^2/15$ kpc for $\rho > \rho_w$, and zero for $\rho < \rho_w$."762" According to (2006).. the warp begins well within the solar circle (p,«p. ). and the line of nodes deviates [rom the solar radius by 157."," According to \citet{mom}, , the warp begins well within the solar circle $\rho_w < \rho_{\sun}$ ), and the line of nodes deviates from the solar radius by $15\degr$."763" The single most unexpected result of our analvsis is the strong model parameter Ly, (Table 2)). represented by the coefficient of the first-degree magnetic harmonic ff,‘that ds. a rigid rotation around the direction —Y (see Eqs. A7))."," The single most unexpected result of our analysis is the strong model parameter $L_{13}$ (Table \ref{om.tab}) ), represented by the coefficient of the first-degree magnetic harmonic $\vec{H}_1^{-1}$, that is, a rigid rotation around the direction $-Y$ (see Eqs. \ref{mag.eq}) )."764 The sign of this parameter implies that the stars move upward in the direction of the Galactic center. downward in the opposite direction. away [rom the center at the north pole. and toward the center at the south pole.," The sign of this parameter implies that the stars move upward in the direction of the Galactic center, downward in the opposite direction, away from the center at the north pole, and toward the center at the south pole."765 The signal-to-noise ratio on this parameter is about 6., The signal-to-noise ratio on this parameter is about 6.766 The extra statistically significant term -. detected by us in the local velocity field may be related to the former., The extra statistically significant term $h_2^{-1}$ detected by us in the local velocity field may be related to the former.767" The pattern οἱ tangential velocities generated bv these (wo magnetic harmonics. 6.21rll,|120DIEtis shown in Fig. 4.."," The pattern of tangential velocities generated by these two magnetic harmonics, $6.21\,r\vec{H}_1^{-1}-1.20\,r\vec{H}_2^{-1}$, is shown in Fig. \ref{tt.fig}."768" The main effect of the higher degree harmonic is that the axis of rotation lies below the plane al roughly b=—20. nearly obliterating the motion in the north pole region, but retaining the galactocentric motion near (he south pole."," The main effect of the higher degree harmonic is that the axis of rotation lies below the plane at roughly $b=-20\degr$, nearly obliterating the motion in the north pole region, but retaining the galactocentric motion near the south pole."769 The most conspicuous features are (he general upward motion of stars in (he direction of the galactic center. ancl the downward motion of stars at 6=1807.," The most conspicuous features are the general upward motion of stars in the direction of the galactic center, and the downward motion of stars at $\ell = 180\degr$."770 It dis tempting to relate these (wo unexpected components (o a kinematic signature of the Galactic warp., It is tempting to relate these two unexpected components to a kinematic signature of the Galactic warp.771" The shape of the warp. as traced by the distribution of neutral hydrogen. ancl dust. implies that the stars in (he solar region are involved in a general upward motion. since the starting rim of the warp is within the solar circle (pj,=6.5 kpe)."," The shape of the warp, as traced by the distribution of neutral hydrogen and dust, implies that the stars in the solar region are involved in a general upward motion, since the starting rim of the warp is within the solar circle $\rho_w = 6.5 $ kpc)."772 This common motion is indistinguishable from (he vertical solar rellex motion. but the model also implies a radial gradient of the upward velocity. Vzipx(p— pi). Which is detectablein the proper motion field.," This common motion is indistinguishable from the vertical solar reflex motion, but the model also implies a radial gradient of the upward velocity, $V_{Z,{\rm warp}} \propto (\rho-\rho_w)$ , which is detectablein the proper motion field."773 In the near-plane zone. the differential warp motion manilests itself as a dowuwarc," In the near-plane zone, the differential warp motion manifests itself as a downward"774 In the near-plane zone. the differential warp motion manilests itself as a dowuwarcl," In the near-plane zone, the differential warp motion manifests itself as a downward"775themselves when correlated features cannot be directly seen in the lighteurves and the correlation only emerges when averaging many features in a cross-correlation function.,themselves when correlated features cannot be directly seen in the lightcurves and the correlation only emerges when averaging many features in a cross-correlation function.776 We show the results in Fig. 7.., We show the results in Fig. \ref{ModelCCFFig}.777 Note that both model CCFs show an oscillatory character., Note that both model CCFs show an oscillatory character.778 This is a feature of the X-ray ACF. and is a consequence of the QPO in the X-ray lightcurves.," This is a feature of the X-ray ACF, and is a consequence of the QPO in the X-ray lightcurves."779 Overall. the agreement between model and observed CCFs is good. supporting the interpretation of the correlation as arising from disc reprocessing.," Overall, the agreement between model and observed CCFs is good, supporting the interpretation of the correlation as arising from disc reprocessing."780 We have interpreted correlations seen at the outburst peak as due to thermal reprocessing and those on the decline as instead associated with synchrotron emission as inferred for XTE JI1151450., We have interpreted correlations seen at the outburst peak as due to thermal reprocessing and those on the decline as instead associated with synchrotron emission as inferred for XTE J1118+480.781 These interpretations are obviously rather speculative and uncertain., These interpretations are obviously rather speculative and uncertain.782 Thermal reprocessing at the outburst peak is eminently plausible and the lags are in the range expected give the proposed orbital period of the binary., Thermal reprocessing at the outburst peak is eminently plausible and the lags are in the range expected give the proposed orbital period of the binary.783 Other X-ray binaries have shown correlations consistent with reprocessing in the disk citetHynes:1998a.Hynes:2006a.Hynes:2007a.. and. the spectral energy distribution at outburst peak could be successfully modelled as due to an accretion disk (Stilletal.2005).," Other X-ray binaries have shown correlations consistent with reprocessing in the disk \\citet{Hynes:1998a,Hynes:2006a,Hynes:2007a}, and the spectral energy distribution at outburst peak could be successfully modelled as due to an accretion disk \citep{Still:2005a}."784 This ean be considered the most natural interpretation., This can be considered the most natural interpretation.785 Associating the correlations seen on the decline with synchrotron emission is more tentative., Associating the correlations seen on the decline with synchrotron emission is more tentative.786 Primarily we are interpreting the presence of the dip in the CCF: had this not been present. we would not have been led to this conclusion.," Primarily we are interpreting the presence of the dip in the CCF; had this not been present, we would not have been led to this conclusion."787 In XTE JI1184-480. the presence of optical synchrotron could be associated with a very flat spectral energy distribution extending into the IR.," In XTE J1118+480, the presence of optical synchrotron could be associated with a very flat spectral energy distribution extending into the IR."788 This was clearly not the case early in the outburst of aas the SED was modelled as a disk., This was clearly not the case early in the outburst of as the SED was modelled as a disk.789 In fact our SMARTS monitoring data shows no evidence for a change in the shape of the SED during the period observed. with the V// colour remaining approximately constant to within the accuracy of our measurements.," In fact our SMARTS monitoring data shows no evidence for a change in the shape of the SED during the period observed, with the $V-H$ colour remaining approximately constant to within the accuracy of our measurements."790" The absence of a change in the optical/IR colour does call a synchrotron interpretation into question,", The absence of a change in the optical/IR colour does call a synchrotron interpretation into question.791 Given the evolution of the source between the two epochs there is no reason to expect that the origin of the correlated variability should be different., Given the evolution of the source between the two epochs there is no reason to expect that the origin of the correlated variability should be different.792 Nonetheless. the CCFs clearly are different very different. and so a change must have occurred.," Nonetheless, the CCFs clearly are different very different, and so a change must have occurred."793" Of course. if the decline data are associated with synchrotron emission, and the SED has not changed. we cannot rule out synchrotron emission at the peak as well."," Of course, if the decline data are associated with synchrotron emission, and the SED has not changed, we cannot rule out synchrotron emission at the peak as well."794 This seems less likely. as argued above. but this possibility cannot be completely rejected.," This seems less likely, as argued above, but this possibility cannot be completely rejected."795 We have presented a study of the correlated X-ray and optical variability in the black hole candidate aat two epochs. one at the peak of the outburst (2005 July 6—7) and the other on the decline phase (2005 August 9).," We have presented a study of the correlated X-ray and optical variability in the black hole candidate at two epochs, one at the peak of the outburst (2005 July 6–7) and the other on the decline phase (2005 August 9)."796 Data from July shows a smeared and lagged correlation that can be readily interpreted as arising from thermal reprocessing in the accretion disk., Data from July shows a smeared and lagged correlation that can be readily interpreted as arising from thermal reprocessing in the accretion disk.797 Data in August show a dip and peak structure similar to that seen in XTE ΤΙ118-480., Data in August show a dip and peak structure similar to that seen in XTE J1118+480.798 Much later in the outburst sshowed a strong dip followed by a weak peak (Durantetal.2008) indicating that the CCF morphology varies with the source state., Much later in the outburst showed a strong dip followed by a weak peak \citep{Durant:2008a} indicating that the CCF morphology varies with the source state.799 If it arises in the same way as in XTE ΤΙ1184-480. we should interpret it as due to optical synchrotron emission possibly associated with a jet. but in the absence of spectral evidence for a jet contribution in the optical this remains a somewhat unsatisfving explanation.," If it arises in the same way as in XTE J1118+480, we should interpret it as due to optical synchrotron emission possibly associated with a jet, but in the absence of spectral evidence for a jet contribution in the optical this remains a somewhat unsatisfying explanation."800 As suggested by Durantetal.(2008)... it is possible that the origin is synchrotron or cyclotron emission from above the disk rather than from a jet.," As suggested by \citet{Durant:2008a}, it is possible that the origin is synchrotron or cyclotron emission from above the disk rather than from a jet."801 These observations would not have been possible without accommodations from several directions., These observations would not have been possible without accommodations from several directions.802 We are grateful to the Argos team for allowing us to use some of their time on very short notice to obtain the first epoch of observations., We are grateful to the Argos team for allowing us to use some of their time on very short notice to obtain the first epoch of observations.803 The second epoch was facilitated through an award of VLT Director's Discretionary Time., The second epoch was facilitated through an award of VLT Director's Discretionary Time.804 Finally we are once again indebted to Jean Swank and the tteam for fitting the public ToO observation schedule around these serendipitous observing opportunities., Finally we are once again indebted to Jean Swank and the team for fitting the public ToO observation schedule around these serendipitous observing opportunities.805helm. with hydrogen being (he most abundant species bv. mass (Ixuulkers2004).,"helium, with hydrogen being the most abundant species by mass \citep{K04}."806.. The svstem εἰ; 1820-30 (Strohmaver2000:Strolinmaver&Brown2002) is the exception.," The system 4U 1820-30 \citep{S00,SB02} is the exception."807 Several studies (Fedorova&Ergma1989:Podsiaclowskietal.2002:Cumming2003) imply that (he compact star in this svstem accretes a heliumn-rich mixture will a small hydrogen mass fraction XN~0.1.," Several studies \citep{FE89,PRP02,C03} imply that the compact star in this system accretes a helium-rich mixture with a small hydrogen mass fraction $X \sim 0.1$."808" Observationallv. the superburst from εἰ, 1820-30 is distinct. with a larger fluence. Iuminositv. and peak temperature than everv other superburst observed Caius [ar (νικουςοἱal.2002b:INuuülkers.2004)."," Observationally, the superburst from 4U 1820-30 is distinct, with a larger fluence, luminosity, and peak temperature than every other superburst observed thus far \citep{Ketal02,K04}."809".. Therefore. to determine the effects of accreted eas composition on superbursts. we choose two different elemental abundances: (4) mixed hvdrogen/helium. for which the mass fractionsof the accreted gas are (X—0.7. Y=0.28. and Ζονο=0.016. and Gi) ""helium. for which X=0.1. Y—0.83. and Zexo=0.016."," Therefore, to determine the effects of accreted gas composition on superbursts, we choose two different elemental abundances: (i) “mixed hydrogen/helium”, for which the mass fractionsof the accreted gas are $X = 0.7$, $Y = 0.28$, and $Z_{\mathrm{CNO}} = 0.016$, and (ii) “helium”, for which $X = 0.1$, $Y = 0.88$, and $Z_{\mathrm{CNO}} = 0.016$."810 Figure 8 shows the superburst energies and recurrence (times as a function of accretion rale. as calculated by our model.," Figure 8 shows the superburst energies and recurrence times as a function of accretion rate, as calculated by our model."811 All other parameters being equal. helium accretors require a larger column density. of accreted. eas before a superburst is triggered.," All other parameters being equal, helium accretors require a larger column density of accreted gas before a superburst is triggered."812 Therefore. (heir superbursis are more energetic and have longer recurrence (mes. in agreement with the observations of AU 1820-30.," Therefore, their superbursts are more energetic and have longer recurrence times, in agreement with the observations of 4U 1820-30."813 Helin burning releases less energv per eram than hydrogen burning by approximately one order of magnitude., Helium burning releases less energy per gram than hydrogen burning by approximately one order of magnitude.814 Consequently. lor a given column density. (he temperature at the base of the laver is lower (see 33). so a larger column of fuel must accumulate before a superburst can occur.," Consequently, for a given column density, the temperature at the base of the layer is lower (see 3), so a larger column of fuel must accumulate before a superburst can occur."815 This clisparily is greater at. high accretion rates. for which a lower column density is required for an instabilitv.," This disparity is greater at high accretion rates, for which a lower column density is required for an instability."816 Less matter exists between the hvdrogen/helium burning region aud (he base of the laver. so tlie base is less insulated from the burninge regionreg and therefore more sensitive to the energvay ὃgenerated there.," Less matter exists between the hydrogen/helium burning region and the base of the layer, so the base is less insulated from the burning region and therefore more sensitive to the energy generated there."817 As we have shown. the composition of the accreted gas affects superburst characteristics bv its effect upon the thermal profile of (he outer crust where superbursts are triggered.," As we have shown, the composition of the accreted gas affects superburst characteristics by its effect upon the thermal profile of the outer crust where superbursts are triggered."818 llowever. the composition may have an even greater influence on superburst characteristics through the carbon vield resulting from both the stable and unstable burning of the gas.," However, the composition may have an even greater influence on superburst characteristics through the carbon yield resulting from both the stable and unstable burning of the gas."819 Unfortunately. we cannot investigate Chis aspect of the problem with our model since we do not solve for the carbon vield sell-consistently. butset it through the parameter Cy.," Unfortunately, we cannot investigate this aspect of the problem with our model since we do not solve for the carbon yield self-consistently, butset it through the parameter $C_{\mathrm{f}}$."820 We assume the fiducial value Cy)=0.3 for all caleulations unless notified otherwise., We assume the fiducial value $C_{\mathrm{f}} = 0.3$ for all calculations unless notified otherwise.821 The composition of the accreted laver where superbursts are triggered is uncertain., The composition of the accreted layer where superbursts are triggered is uncertain.822 In parücular. (he mass Iraction of carbon produced via stable and uustable hydrogen and helium burning is unknown. but it most likely has to be 2LOY for mixed hvdrogen/helim accretors (Cumming&Bildsten2001) and 230% for helium accretors (Strohmaver&Brown 2002)..," In particular, the mass fraction of carbon produced via stable and unstable hydrogen and helium burning is unknown, but it most likely has to be $\gtrsim10\%$ for mixed hydrogen/helium accretors \citep{CB01} and $\gtrsim30\%$ for helium accretors \citep{SB02}. ."823 These authors find that. for A/<0.3 Αμ. a smaller mass fraction of carbon than these limits," These authors find that, for $\dot{M} \lesssim 0.3824\dot{M}_{\mathrm{Edd}}$ , a smaller mass fraction of carbon than these limits"825intrinsic redshift distributions considered below.,intrinsic redshift distributions considered below.826 Although some of the predicted redshifts coincide with the three regions of high density. several do not.," Although some of the predicted redshifts coincide with the three regions of high density, several do not."827 Tn a previous analysis of the distribution of QSOs around the Sevfert II ealaxy NGC 1068 it was found that. when combined with the results of DurbidgeaudDewitt(1990).. it appears to be possible to fit QSO intrinsic redshifts bv the relation where GN ds an integer. and Aly can have ouly certain well-defined values determuned bv a quanti muuber » (Bell2002a.b.c.d:BellaudComean2003a.b)..," In a previous analysis of the distribution of QSOs around the Seyfert II galaxy NGC 1068 it was found that, when combined with the results of \citet{bur90}, it appears to be possible to fit QSO intrinsic redshifts by the relation where $N$ is an integer, and $M_{N}$ can have only certain well-defined values determined by a quantum number $n$ \citep{bel02a,bel02b,bel02c,bel02d,bel03a,bel03b}."828 For N= 1. the predicted values are eiven by the relation where s = 0.12.3..9.," For $N$ = 1, the predicted values are given by the relation where $n$ = 0,1,2,3..,9."829 This equation has a naxinmni redshift value of 0.62., This equation has a maximum redshift value of 0.62.830 For NV = 2 the oedieted values axe 0.31. 0.62. 0:868. 1.05L. 1.178. and 1.21.," For $N$ = 2 the predicted values are 0.31, 0.62, 0.868, 1.054, 1.178, and 1.24."831 For No = 3 the predicted values are 1.558. T.188. 1.798. aud 1.56.," For $N$ = 3 the predicted values are 0.558, 1.488, 1.798, and 1.86."832 The NV — 3 values are otted in Fig 2 at level -1. aud are indicated by the vertical lines.," The $N$ = 3 values are plotted in Fig 2 at level -1, and are indicated by the vertical lines."833 These redshifts correspond closely to he regions of high density in Fig 2., These redshifts correspond closely to the regions of high density in Fig 2.834 For Vo — | the xedieted iutriusie redshift values are 2.ls. 2.Ls. and 1.178.," For $N$ = 4 the predicted intrinsic redshift values are 2.48, 2.418, and 1.178."835 For all ligher N-states. zi> herefore caunot νο correlated with either of the observed redshift distributions considered here.," For all higher $N$ -states, $_{iQ} > 3$ and therefore cannot be correlated with either of the observed redshift distributions considered here."836 Equ lL predicts the intrinsic redshifts that uake up the second intrinsic redshift distribution considered below aud is hereafter referred to as he zi; relation., Eqn 4 predicts the intrinsic redshifts that make up the second intrinsic redshift distribution considered below and is hereafter referred to as the $_{iQ}$ relation.837 It was found previously that the QSOs near NGC LOGS were all in the V = 2 state., It was found previously that the QSOs near NGC 1068 were all in the $N$ = 2 state.838 Since all. or at least most. of the QSOs around NGC 6212 are asstuuned bere to have been ejected from the same parent ealaxy. it is assunued that they too will all be in the same N-state.," Since all, or at least most, of the QSOs around NGC 6212 are assumed here to have been ejected from the same parent galaxy, it is assumed that they too will all be in the same $N$ -state."839 From Fig 2. that state appears to be the N = 3 state.," From Fig 2, that state appears to be the $N$ = 3 state."840 If the widths of the deuse regions iu the QSO redshift distribution are due to Ίο ejection velocity smnieariug. as sugeested above. clearly isolated redshift values caunot be expected to correlate well with individual intrinsic redshift values that are spaced apart by a distance less than. or the order of. this smearing. unless the," If the widths of the dense regions in the QSO redshift distribution are due to l-o-s ejection velocity smearing, as suggested above, clearly isolated redshift values cannot be expected to correlate well with individual intrinsic redshift values that are spaced apart by a distance less than, or the order of, this smearing, unless the"841Now. we will show that it is possible to formulate a new zumilv of stellar models hy performing a linear combination of generalized. Ixalnajs dises. in such a wav that the new surface densities can be written as polynomials of the new »otentials.,"Now, we will show that it is possible to formulate a new family of stellar models by performing a linear combination of generalized Kalnajs discs, in such a way that the new surface densities can be written as polynomials of the new potentials."842 As ib was quoted. this is a basic requirement or the derivation of equilibrium DEs through the Ixalnajs ormatism sketched above.," As it was quoted, this is a basic requirement for the derivation of equilibrium DFs through the Kalnajs formalism sketched above."843 In. particular. we are interested on to derive a simple relation between the relative potential on the disc and the surface density.," In particular, we are interested on to derive a simple relation between the relative potential on the disc and the surface density."844" At first. note that ,(0.7). given by (3)). can. be pewrltten as where ci. are constants defined as and the relation (5)) was derived. by introducing the identity GXrfken (2005))) From (5)) we note that the maximum. value of the eravitational potential on the nth disc is 9,(0.0)."," At first, note that $\Phi_n(0,\eta)$, given by \ref{dk}) ), can be rewritten as where $A_{sr}$ are constants defined as and the relation \ref{eq:phi1}) ) was derived by introducing the identity \cite{arf}) ) From \ref{eq:phi1}) ) we note that the maximum value of the gravitational potential on the $n$ th disc is $\Phi_n(0,0)$."845" Pherefore. we define the relative potential on such a disc as Now. suppose that we can choose a [linear combination of those W,, leading to a new relative potential W,,, of the [orm where D, are constants that canbe determined from chy, and C4, (see section ??))."," Therefore, we define the relative potential on such a disc as Now, suppose that we can choose a linear combination of those $\Psi_n$ leading to a new relative potential $\tilde{\Psi}_m$ of the form where $B_{n}$ are constants that canbe determined from $A_{nr}$ and $C_{n}$ (see section \ref{sec:Bn}) )."846" The new relative potential W,,, is eencrated by a new mass distribution clescribecl by a surface density Ns that is also a linear combination of generalized. Ixalnajs cliscs ο", The new relative potential $\tilde{\Psi}_m$ is generated by a new mass distribution described by a surface density $\tilde{\Sigma}_m$ that is also a linear combination of generalized Kalnajs discs $\Sigma_{m}$.847" ‘That is From this relation and (0)). we can note that X, can be rewritten as Thus. we can see that this new Lamily of disces is characterized by the fact that the surface density can be split as a combination of powers of the relativepotential."," That is From this relation and \ref{potnew}) ), we can note that $\tilde{\Sigma}_m$ can be rewritten as Thus, we can see that this new family of discs is characterized by the fact that the surface density can be split as a combination of powers of the relativepotential."848 This important fact makes viable the further derivation of two integral Ds for the whole lamily (see section ??)). that can be considered as a set of self-consistent galactic moclels.," This important fact makes viable the further derivation of two integral DFs for the whole family (see section \ref{sec:DFs}) ), that can be considered as a set of self-consistent galactic models."849" Now. the above statements are only true if we can determinate the constants D,. introduced in (9))."," Now, the above statements are only true if we can determinate the constants $B_{n}$, introduced in \ref{potnew}) )."850" In the next subsection. we show a procedure that. by using the orthogonality properties of £5,. leads to à recurrence relation expressing {2 in terms of st, and €."," In the next subsection, we show a procedure that, by using the orthogonality properties of $P_{n}$, leads to a recurrence relation expressing $B_{n}$ in terms of $A_{nr}$ and $C_{n}$."851" According to definitions (S)) and (3)). the relative potential associated to the generalized Ixalnajs clises can be written as where €, are constants defined by So. bv introducing (12)) into (0)). W,, can also be written in terms of Legendre polynomials as where D, are constants to be determined."," According to definitions \ref{eq:psidef}) ) and \ref{dk}) ), the relative potential associated to the generalized Kalnajs discs can be written as where $\tilde{C}_n$ are constants defined by So, by introducing \ref{eq:psileg}) ) into \ref{potnew}) ), $\tilde{\Psi}_m$ can also be written in terms of Legendre polynomials as where $D_n$ are constants to be determined."852" Lore. it is important to note that these D, are suchthat The above equations can be written in a compact way which sununarizes the previous series of recurrence relations."," Here, it is important to note that these $D_n$ are suchthat The above equations can be written in a compact way as which summarizes the previous series of recurrence relations."853 Now. let us come to the problem of calculating D.," Now, let us come to the problem of calculating $D_{n}$ ."854" According to (9)) and (14)). we have and by using the orthogonality properties of Legendre polynomials. we obtain that reduces to in such away that. by using (16)). we can determine the constants 2,,."," According to \ref{potnew}) ) and \ref{eq:psir}) ), we have and by using the orthogonality properties of Legendre polynomials, we obtain that reduces to in such a way that, by using \ref{eq:4.25a}) ), we can determine the constants $B_n$ ."855" In order to do this. note that equations (15a))- (15d)) give us recurrencerelations: from (15a)) we obtain D. trom (15b)) we obtain D,, ,. and so on."," In order to do this, note that equations \ref{eq:4.22}) \ref{eq:4.25}) ) give us recurrencerelations: from \ref{eq:4.22}) ) we obtain $B_m$ , from \ref{eq:4.23}) ) we obtain $B_{m-1}$ , and so on."856 In general. we," In general, we"857"using number counting, as the integral under the derived best fit function is just the number of galaxies: The uncertainty on the parameters of the luminosity function - derived using either method - can be difficult to estimate.","using number counting, as the integral under the derived best fit function is just the number of galaxies: The uncertainty on the parameters of the luminosity function - derived using either method - can be difficult to estimate."858" A major source of potential error, particularly at the faint end, is uncertainty on the distance."," A major source of potential error, particularly at the faint end, is uncertainty on the distance."859" ? discuss the distance estimates for the Local Volume galaxies in detail: direct distance estimators are used wherever possible (Cepheids, red giant branch, Tully-Fisher relation, supernovae), and when a distance from one of these methods is not available distances are estimated from the Hubble velocity, corrected for a local group dipole effect as derived by ?.."," \cite{2008ApJS..178..247K} discuss the distance estimates for the Local Volume galaxies in detail: direct distance estimators are used wherever possible (Cepheids, red giant branch, Tully-Fisher relation, supernovae), and when a distance from one of these methods is not available distances are estimated from the Hubble velocity, corrected for a local group dipole effect as derived by \cite{1996AJ....111..794K}."860" The uncertainties on the distance (both random, and systematic to the flow model) are typically 7—15%."," The uncertainties on the distance (both random, and systematic to the flow model) are typically $7 - 15 \%$."861 The effect of this distance uncertainty (and the effect of the photometric flux uncertainty) will be to shift galaxies into neighbouring bins of luminosity (or SFR)., The effect of this distance uncertainty (and the effect of the photometric flux uncertainty) will be to shift galaxies into neighbouring bins of luminosity (or SFR).862" As a result, the errors on the various luminosity function parameters are highly correlated, and have a complex dependence on the errors in the raw data."," As a result, the errors on the various luminosity function parameters are highly correlated, and have a complex dependence on the errors in the raw data."863" We deal with these errors using a Monte Carlo resampling method, by creating a large number of realisations of the luminosity function drawn - with replacement - from the parent sample."," We deal with these errors using a Monte Carlo resampling method, by creating a large number of realisations of the luminosity function drawn - with replacement - from the parent sample."864" Parameters with well defined errors (i.e. flux) were allowed to vary randomly according to a Gaussian likelihood function defined by the lo parameter error, and the standard deviation in the resultant luminosity functions in each bin was taken to be an estimate of the error."," Parameters with well defined errors (i.e. flux) were allowed to vary randomly according to a Gaussian likelihood function defined by the $\sigma$ parameter error, and the standard deviation in the resultant luminosity functions in each bin was taken to be an estimate of the error."865" Obscured Active Galactic Nuclei (AGN), are a potential source of contamination for our sample, if we want to interpret the emission in terms of pure star formation."," Obscured Active Galactic Nuclei (AGN), are a potential source of contamination for our sample, if we want to interpret the emission in terms of pure star formation."866" Unified models of AGN assume a dusty torus - which emits strongly in the IR - surrounding a central engine; this bright IR emission can be falsely interpreted as originating from dust heated by star forming regions, which leads to an overestimation of the star formation rate of the galaxy."," Unified models of AGN assume a dusty torus - which emits strongly in the IR - surrounding a central engine; this bright IR emission can be falsely interpreted as originating from dust heated by star forming regions, which leads to an overestimation of the star formation rate of the galaxy."867" If we are to accurately estimate the star formation rate density of the volume containing our sample, it is important to remove such sources of possible contamination."," If we are to accurately estimate the star formation rate density of the volume containing our sample, it is important to remove such sources of possible contamination."868" AGN number amongst the most extreme objects in the Universe, and, when active, have prodigious bolometric outputs."," AGN number amongst the most extreme objects in the Universe, and, when active, have prodigious bolometric outputs."869" The effect of AGN subtraction will, therefore, be to reduce the very upper end of the luminosity function, while leaving the behaviour at L«107197Le relatively unchanged (see e.g. ?;; ?))."," The effect of AGN subtraction will, therefore, be to reduce the very upper end of the luminosity function, while leaving the behaviour at $\mathrm{L}<10^{\sim10 - 11}\; \mathrm{L}_{\sun}$ relatively unchanged (see e.g. \citealt{2010ApJ...709..884Y}; \citealt{2010MNRAS.402.1693H}) )."870" At the upper end, star formation occurs almost entirely in highly extincted, dusty environments (? and references therein), where IR is by far the best SFR tracer: we therefore consider the effect of AGN contamination on our IR-selected sample only, as the UV-selected and LVL datasets will have a negligible AGN contribution (?).."," At the upper end, star formation occurs almost entirely in highly extincted, dusty environments \citealt{Calzetti:2010aa} and references therein), where IR is by far the best SFR tracer: we therefore consider the effect of AGN contamination on our IR-selected sample only, as the UV-selected and LVL datasets will have a negligible AGN contribution \citep{2007tS..173..267S}."871" It is difficult to perfectly remove all AGN on a galaxy-by-galaxy basis without detailed spectroscopy being available for the entire sample, using which the AGN component can be separated from the star forming component (see e.g. ?))."," It is difficult to perfectly remove all AGN on a galaxy-by-galaxy basis without detailed spectroscopy being available for the entire sample, using which the AGN component can be separated from the star forming component (see e.g. \citealt{2010arXiv1008.2932F}) )."872" In the absence of spectral data for our entire sample, a better method is to remove the AGN component statistically from the sample as a whole."," In the absence of spectral data for our entire sample, a better method is to remove the AGN component statistically from the sample as a whole."873" This requires a knowledge of the global behaviour of the AGN population, in the form of an AGN luminosity function which can then be subtracted from our original ‘total’ luminosity function, leaving only the star forming component."," This requires a knowledge of the global behaviour of the AGN population, in the form of an AGN luminosity function which can then be subtracted from our original `total' luminosity function, leaving only the star forming component."874" To this end, we use the data in the work by ?,, a spectroscopic study of a subset of the 24um selected 5mJy Unbiased Spitzer Extragalactic Survey (5MUSES) sample ?.."," To this end, we use the data in the work by \cite{2010b_Wu}, a spectroscopic study of a subset of the 24um selected 5mJy Unbiased Spitzer Extragalactic Survey (5MUSES) sample \cite{2010arXiv1009.1633W}."875" This subset focused on galaxies with z<0.3 from 5MUSES, with <z>~0.12."," This subset focused on galaxies with $z<0.3$ from 5MUSES, with $<z>\sim0.12$."876" The 226 objects in this subsample were analysed with mid- and far-IR photometry (allowing a full characterisation of their IR SED), and mid-IR spectroscopy - allowing each source’s luminosity to be decomposed into AGN and star-forming components."," The 226 objects in this subsample were analysed with mid- and far-IR photometry (allowing a full characterisation of their IR SED), and mid-IR spectroscopy - allowing each source's luminosity to be decomposed into AGN and star-forming components."877" For the purpose of this analysis, we will examine the IR luminosity function of their sample and use the relations given in their work to derive the contribution to the IR LF from AGN."," For the purpose of this analysis, we will examine the IR luminosity function of their sample and use the relations given in their work to derive the contribution to the IR LF from AGN."878" We then take this fractional AGN contribution (as a function of IR luminosity) and subtract it from our data, leaving us with IR data for our galaxies which can be interpreted in terms of pure star formation."," We then take this fractional AGN contribution (as a function of IR luminosity) and subtract it from our data, leaving us with IR data for our galaxies which can be interpreted in terms of pure star formation."879 Figure 1 shows the luminosity function for our IR-selected sample., Figure \ref{fig:agn_lf} shows the luminosity function for our IR-selected sample.880" Also plotted is the total IR luminosity function for the galaxies reported in ?,, derived by taking their 15um LF and transforming into an IR LF using the average luminosity conversion given."," Also plotted is the total IR luminosity function for the galaxies reported in \cite{2010arXiv1009.1633W}, derived by taking their $\mu m$ LF and transforming into an IR LF using the average luminosity conversion given."881 The AGN component of their IR LF is also shown., The AGN component of their IR LF is also shown.882" As expected, their SED fitting shows that the bolometric IR luminosity for AGN sources"," As expected, their SED fitting shows that the bolometric IR luminosity for AGN sources"883uniform weighting of the visibiliües. which optimizes resolution at the expense of sensitivity.,"uniform weighting of the visibilities, which optimizes resolution at the expense of sensitivity."884" The result is shown in Figure te. with a rms noise of 0.14 mJy ancl resolution of about 1.3""."," The result is shown in Figure 4c, with a rms noise of 0.14 mJy and resolution of about $1.3''$."885 The source is comprised of two components separated by 1.3”., The source is comprised of two components separated by $''$.886" Gaussian fitting to each component shows that they are unresolved. with upper limits to their sizes of about 1.1""."," Gaussian fitting to each component shows that they are unresolved, with upper limits to their sizes of about $''$."887 Table 2 lists the component positions and flux densities., Table 2 lists the component positions and flux densities.888" The position of the 1.35mm continuum peak is located within 0.2"" of the southern CO component. and the mm continuum source also shows marginal evidence for a north-south extension on the scale of 1"" (Guilloteau et al."," The position of the 1.35mm continuum peak is located within $''$ of the southern CO component, and the mm continuum source also shows marginal evidence for a north-south extension on the scale of $''$ (Guilloteau et al."889 1997)., 1997).890" The optical QSO position is within 0.1"" of the southern source position.", The optical QSO position is within $''$ of the southern source position.891 Figure 5 shows the high resolution (D. array) image of the CO(2-1) emission from 13350417., Figure 5 shows the high resolution (B array) image of the CO(2-1) emission from 1335–0417.892" The naturally weighted beam is roughly cireular with EWIIM = 0.17"".", The naturally weighted beam is roughly circular with FWHM = $0.17''$.893 Nothing is detected in this high resolution image to a 20 surface brightness limit of 0.13 mJv +., Nothing is detected in this high resolution image to a $\sigma$ surface brightness limit of 0.18 mJy $^{-1}$.894" Non-detection at high resolution could mean that the emission is diffuse on scales larger (han the resolution with a (redshift corrected) brightness temperature <921. On the other hand. a number of compact components distributed over 1"" with higher brightness temperature is certainly not precluded. eg."," Non-detection at high resolution could mean that the emission is diffuse on scales larger than the resolution with a (redshift corrected) brightness temperature $\le 22$ K. On the other hand, a number of compact components distributed over $''$ with higher brightness temperature is certainly not precluded, eg."895" the data allow lor four small (0.17) components each with brightness temperatures > 22 Ix, The HH» gas masses can be calculated from the values of £Z/ in Table 1 assuming a value of X = the IH» mass-to-CO(1-0) luminosity conversion factor in M. (IX km ! pc?) |.", the data allow for four small $\le 0.17''$ ) components each with brightness temperatures $\ge$ 22 K. The $_2$ gas masses can be calculated from the values of $L'$ in Table 1 assuming a value of X = the $_2$ mass-to-CO(1-0) luminosity conversion factor in $_\odot$ (K km $^{-1}$ $^2$ $^{-1}$.896 A value of X~4.6 is applicable to Galactic Giant Molecular Clouds (Dame οἱ al., A value of $\rm X \simeq 4.6$ is applicable to Galactic Giant Molecular Clouds (Dame et al.897 1937: Strong et al., 1987; Strong et al.898 1983: Brontiman et al., 1988; Bronfman et al.899 1983). while for ULIBGs Downes ancl Solomon (1998)," 1988), while for ULIRGs Downes and Solomon (1998)"900where Pi;=P/(L0Mes ty) ,"where $\dot{P}_{15}\equiv \dot{P}/(10^{-15}{\rm901s}~{\rm s}^{-1})$ ."902"DL=0.5 and op,=1.4 represent the position and lateral extent of the death band. respectively."," $= 0.5$ and $\sigma_{\rm DL}= 1.4$ represent the position and lateral extent of the death band, respectively."903 For the pulsar velocity distribution at. birth. we adopt the clouble-gaussian model of ACC deseribed above.," For the pulsar velocity distribution at birth, we adopt the double-gaussian model of ACC described above."904 The orientation of the pulsar kick at birth is assumed to be random. and the Galactic rotational velocity (220 kin 1) is added: veetorially to the initial kick velociv.," The orientation of the pulsar kick at birth is assumed to be random, and the Galactic rotational velocity (220 km $^{-1}$ ) is added vectorially to the initial kick velocity."905" Finally. we compute the detector sensitivity using the standard detector equation DDewev et 11934): — In the above equation. & is a loss lactor. 5 is the signal-to-noise ratio for a detection (assumed to be 8). Zi. is the svstem temperature. G the telescope gain. D the receiver bandwidth. NV, the number of polarizations and των, (he observation time."," Finally, we compute the detector sensitivity using the standard detector equation Dewey et 1984): =, In the above equation, $\sigma$ is a loss factor, $\beta$ is the signal-to-noise ratio for a detection (assumed to be 8), $T_{\rm sys}$ is the system temperature, $G$ the telescope gain, $B$ the receiver bandwidth, $N_p$ the number of polarizations and $\tau_{\rm obs}$ the observation time."906" The specilic values of these parameters for (he various surveys we consider can be found in the papers referenced D QE D MM ,""241.", The specific values of these parameters for the various surveys we consider can be found in the papers referenced in 3 below.9072E⋅p-2↕∐⋅⋝∖↘≊↽≻≡↽⊃∣≻≼↲↥∪∖∖⋅⊺↥∐↲∪∣≻⊳∖≼↲↕∖≼↲≼⊔≻∏↥⋝∖≼↲∖∖∐∐↥⊔⊳∖≸↔↴↕∖≼↲∐∣≻∡∖⊓≓⋜⋝⊓⊽⊐∣∣↴∣⋝∖⋮⋯↓↓⋝↴∣⊓∖↓↴∣⋝∖∙⊲⋮≖∩∣IE2 ⋅⊓⊽⊽⊳↗∣∣↕⋟∖⊽ ⊔∐↲↕∐⊔⋅↕∐⋟∖⇁↕≺∢↕↽≻∏↥⋟∖⊽≼↲∖∖⇁↕≼∐∐⋅≀↕⊍∖⊽⋟∖⊽∏∐∐↲≺⇂≼↲≺⇂∏≀↧↴↥↥∪↶↱≻↖∕⊓∣↙∪↓⋟⊔∐↲↕↽≻≼↲↕⋅↕⋯⇂⋅⊤⋝∖⋮⋯↓↓⋝↕⋟∖⊽⊔∐↲⋟∖⊽≀↧↴∐↕↕↽≻∐∐≸≟↕∐∩↲↕⋅∖↽≀↧↴↥⋅ ⊤↓≽⋋↓↕⋟∖⊽⊔∐↲≺∐⋟∖⊽↕↽≻≼↲↕∷∖⊽↕∪∐⋟∖⊽∐∐↲≀↧↴↕⋅↕∐↖↳↴≀↕↴≺∢↕⋅∪⋟∖⊽⋟∖⊽∪∐≼↲∐⋅≼↲≺⇂⋯↲∐≺↕∖↽≺∢↥⋯↴∐∐≼↲↥⋅≀↧↴∐≺⇂⊤⋝∖∙⊲⊓↿↿↕⋟∖⊽⊔∐↲∣↽≻↕⋅∪≀↕↴≺⇂≼↲↕∐∐≸≟ ol the pulse due to interstellar scattering.," The observed pulse width is given by $W=(W^2_{50}+\tau_{\rm samp}^2 + \tau_{\rm DM}^2 + \tau_{\rm908scatt}^2)^{1/2}$ $W_{50}$ is the intrinsic pulse width, assumed equal to of the period, $\tau_{\rm samp}$ is the sampling interval, $\tau_{\rm DM}$ is the dispersion smearing across one frequency channel, and $\tau_{\rm scatt}$ is the broadening of the pulse due to interstellar scattering."909 The dispersion measure and scattering measure of each pulsar (needed to calculate the above ceuantities) are computed using the public by Cordes Lazio (2003). while the all-sky data are from the 408 MIIz compilation of Haslam et al (1982). scaled to other [frequencies assuming a spectral index of 2.6 [or the brightness temperature of the diffuse Galactic svnchrotron background.," The dispersion measure and scattering measure of each pulsar (needed to calculate the above quantities) are computed using the public by Cordes Lazio (2003), while the all-sky data are from the 408 MHz compilation of Haslam et al (1982), scaled to other frequencies assuming a spectral index of –2.6 for the brightness temperature of the diffuse Galactic synchrotron background."910 We neglect the ellects of eut-offs in harmonie summing and [filtering of the data (see e.g. Manchester et al., We neglect the effects of cut-offs in harmonic summing and filtering of the data (see e.g. Manchester et al.911 POOL). which has a small effect on the sensitivity for periodswhich are not very short and for large DMs (E. Crawford 2003.private communication).," 2001), which has a small effect on the sensitivity for periodswhich are not very short and for large DMs (F. Crawford 2003,private communication)."912transformation.,transformation.913" In ideal MHD, the three fields are related to each other in the mean solar wind frame by E,2—óvxB and putting this into Equation (1)) gives Since the mean solar wind speed is much larger than the fluctuations, |Vsy|>|óv|, and is mostly in the x (radial) direction, iis dominatedEy scby the magnetic field fluctuations convected by the mean solar wind flow and therefore follows their scaling."," In ideal MHD, the three fields are related to each other in the mean solar wind frame by $\mathbf{E}_{\text{sw}}=-\delta\mathbf{v}\times\mathbf{B}$ and putting this into Equation \ref{eq:lorentz}) ) gives Since the mean solar wind speed is much larger than the fluctuations, $|\mathbf{v}_{\text{sw}}|>|\delta\mathbf{v}|$, and is mostly in the $x$ (radial) direction, is dominated by the magnetic field fluctuations convected by the mean solar wind flow and therefore follows their scaling."914" The of the spectra in Figure 1 agree with this interpretation: amplitudesthe sspectrum is an orderEy scof magnitude larger than the sspectrum, showing that for the y-component, the secondEy. term on the right-hand side of Equation (2)) is than the first."," The amplitudes of the spectra in Figure \ref{fig:spectra} agree with this interpretation: the spectrum is an order of magnitude larger than the spectrum, showing that for the $y$ -component, the second term on the right-hand side of Equation \ref{eq:ideallorentz}) ) is larger than the first."915 The x-component of Eq., The $x$ -component of Eq.916" 2 does not depend on largerthe radial solar wind velocity, so scaling of ddoes not depend only on the scaling of B and indeed is different to that of Brace."," \ref{eq:ideallorentz} does not depend on the radial solar wind velocity, so scaling of does not depend only on the scaling of $\mathbf{B}$ and indeed is different to that of $B_{\text{trace}}$."917" hhas Egy,a scaling closer to that of Virace, which can also be shown to be consistent with ffluctuations in ideal MHD."," has a scaling closer to that of $v_{\text{trace}}$, which can also be shown to be consistent with fluctuations in ideal MHD."918" Splitting the magnetic field into a constant mean value plus fluctuations, B=Bo--óB, the electric field in the mean solar wind frame is given by The mean value of |5B|/|Bo| is between 0.1 and 0.4 for the of scales to which indices were fitted."," Splitting the magnetic field into a constant mean value plus fluctuations, $\mathbf{B}=\mathbf{B}_0+\delta\mathbf{B}$, the electric field in the mean solar wind frame is given by The mean value of $|\delta\mathbf{B}|/|\mathbf{B}_0|$ is between 0.1 and 0.4 for the range of scales to which spectral indices were fitted."919" Since at rangethese small scales in the solar spectralwind Bo>OB, the electric field spectrum in the mean solar wind frame is dominated by the velocity fluctuations, and therefore has a similar scaling."," Since at these small scales in the solar wind $\mathbf{B}_0>\delta\mathbf{B}$, the electric field spectrum in the mean solar wind frame is dominated by the velocity fluctuations, and therefore has a similar scaling."920 Similar arguments can be made for the ffluctuations in gyrokinetic theory (Schekochihinetal.2009)., Similar arguments can be made for the fluctuations in gyrokinetic theory \citep{schekochihin09}.921". The fact that we observe a spectral index close to 23/2 in aand aalso Eysuggestssw that the perpendicular velocity component has this scaling, which is in agreement with the results of Chapman&Hnat(2007).."," The fact that we observe a spectral index close to $-3/2$ in and also suggests that the perpendicular velocity component has this scaling, which is in agreement with the results of \citet{chapman07}. ."922" The electric field scaling is also in agreement with previous measurements of the velocity trace spectral index (e.g.,Tesseinetal.2009;Podesta&Borovsky2010).."," The electric field scaling is also in agreement with previous measurements of the velocity trace spectral index \citep[e.g.,][]{tessein09,podesta10d}."923" The scaling of the compressive fluctuations (|B| and n) is close to —5/3, matching the trace magnetic field spectrum, rather than the velocity spectrum."," The scaling of the compressive fluctuations $|\mathbf{B}|$ and $n$ ) is close to $-5/3$, matching the trace magnetic field spectrum, rather than the velocity spectrum."924" Previous observations (e.g.,2010) could not distinguish between —5/3 and —3/2 in the compressive fluctuations so this scaling is consistent with those observations."," Previous observations \citep[e.g.,][]{marsch90b,bellamy05,issautier10} could not distinguish between $-5/3$ and $-3/2$ in the compressive fluctuations so this scaling is consistent with those observations."925 The compressive fluctuations are mainly due to the slow mode (Howesetal.2011) and are sometimes thought to be passive to the tturbulence., The compressive fluctuations are mainly due to the slow mode \citep{howes11b} and are sometimes thought to be passive to the turbulence.926" Since their scaling matches the magnetic field, rather than the velocity, the cannot be due solely to passive convection and maynonlinearity include nonlinearities with the magnetic field."," Since their scaling matches the magnetic field, rather than the velocity, the nonlinearity cannot be due solely to passive convection and may include nonlinearities with the magnetic field."927" This supports the theories of compressible reduced MHD and kinetic reduced MHD (Schekochihinetal.2009),, in which the compressive fluctuations interact nonlinearly with both the magnetic field and velocity."," This supports the theories of compressible reduced MHD and kinetic reduced MHD \citep{schekochihin09}, , in which the compressive fluctuations interact nonlinearly with both the magnetic field and velocity."928" To test the significance of the difference between the mean spectral index values in Table 1,, the t-test was applied."," To test the significance of the difference between the mean spectral index values in Table \ref{tab:scaling}, the $t$ -test was applied."929 This is appropriate since the spectral indices appear to be normally distributed and are independent measurements., This is appropriate since the spectral indices appear to be normally distributed and are independent measurements.930 The { value for differentiating between the spectral indices of Brace and iis f=0.41., The $t$ value for differentiating between the spectral indices of $B_{\text{trace}}$ and is $t=0.41$.931" This is smaller than the value of Ey,1.96sc for infinite degrees of freedom, showing that there is no statistically significant difference between the scaling of these two fields."," This is smaller than the value of 1.96 for infinite degrees of freedom, showing that there is no statistically significant difference between the scaling of these two fields."932" For differentiating between the spectral indices of Eyaandsw tthe { Eyscvalue is f=15, larger than the value, showing that these two fields have significantly different spectral indices."," For differentiating between the spectral indices of and the $t$ value is $t=15$, larger than the value, showing that these two fields have significantly different spectral indices."933 This confirms that the —5/3 and —3/2 difference is a statistically robust result., This confirms that the $-5/3$ and $-3/2$ difference is a statistically robust result.934" To examine the cause of the spread of spectral index values, the correlation between the different spectral indices was measured."," To examine the cause of the spread of spectral index values, the correlation between the different spectral indices was measured."935" The linear correlation coefficients, calculated from various pairs of sets of the 272 spectral index values of each field, are shown in Table 2.."," The linear correlation coefficients, calculated from various pairs of sets of the 272 spectral index values of each field, are shown in Table \ref{tab:correlations}."936" It can be seen that the spectral indices of most pairs of fields are poorly correlated, having correlation coefficients lower than 0.4."," It can be seen that the spectral indices of most pairs of fields are poorly correlated, having correlation coefficients lower than 0.4."937" This suggests that the spread of values is mostly due to random, rather than systematic, variation, although the fact that the correlation coefficients are all slightly positive suggests perhaps some small underlying systematic variation."," This suggests that the spread of values is mostly due to random, rather than systematic, variation, although the fact that the correlation coefficients are all slightly positive suggests perhaps some small underlying systematic variation."938 The exceptions are correlations between Bac; and aand between aand whichEy have correlation coefficients larger than 0.8.," The exceptions are correlations between $B_{\text{trace}}$ and and between and, which have correlation coefficients larger than 0.8."939" This is E,sw,,due to the reasons discussed above: the sspectrum is essentially a measure of the Brace E,spectrumsy because the y-component of the last term in Equation (2)) is large and aand aare similarsw because the x-component of the last term in Equation (2)) is not (since iismostly in the x-direction).", This is due to the reasons discussed above: the spectrum is essentially a measure of the $B_{\text{trace}}$ spectrum because the $y$ -component of the last term in Equation \ref{eq:ideallorentz}) ) is large and and are similar because the $x$ -component of the last term in Equation\ref{eq:ideallorentz}) ) is not large (since ismostly in the $x$ -direction).940" This is E,sw,,due to the reasons discussed above: the sspectrum is essentially a measure of the Brace E,spectrumsy because the y-component of the last term in Equation (2)) is large and aand aare similarsw because the x-component of the last term in Equation (2)) is not (since iismostly in the x-direction).l", This is due to the reasons discussed above: the spectrum is essentially a measure of the $B_{\text{trace}}$ spectrum because the $y$ -component of the last term in Equation \ref{eq:ideallorentz}) ) is large and and are similar because the $x$ -component of the last term in Equation\ref{eq:ideallorentz}) ) is not large (since ismostly in the $x$ -direction).941" This is E,sw,,due to the reasons discussed above: the sspectrum is essentially a measure of the Brace E,spectrumsy because the y-component of the last term in Equation (2)) is large and aand aare similarsw because the x-component of the last term in Equation (2)) is not (since iismostly in the x-direction).la", This is due to the reasons discussed above: the spectrum is essentially a measure of the $B_{\text{trace}}$ spectrum because the $y$ -component of the last term in Equation \ref{eq:ideallorentz}) ) is large and and are similar because the $x$ -component of the last term in Equation\ref{eq:ideallorentz}) ) is not large (since ismostly in the $x$ -direction).942" This is E,sw,,due to the reasons discussed above: the sspectrum is essentially a measure of the Brace E,spectrumsy because the y-component of the last term in Equation (2)) is large and aand aare similarsw because the x-component of the last term in Equation (2)) is not (since iismostly in the x-direction).lar", This is due to the reasons discussed above: the spectrum is essentially a measure of the $B_{\text{trace}}$ spectrum because the $y$ -component of the last term in Equation \ref{eq:ideallorentz}) ) is large and and are similar because the $x$ -component of the last term in Equation\ref{eq:ideallorentz}) ) is not large (since ismostly in the $x$ -direction).943" This is E,sw,,due to the reasons discussed above: the sspectrum is essentially a measure of the Brace E,spectrumsy because the y-component of the last term in Equation (2)) is large and aand aare similarsw because the x-component of the last term in Equation (2)) is not (since iismostly in the x-direction).larg", This is due to the reasons discussed above: the spectrum is essentially a measure of the $B_{\text{trace}}$ spectrum because the $y$ -component of the last term in Equation \ref{eq:ideallorentz}) ) is large and and are similar because the $x$ -component of the last term in Equation\ref{eq:ideallorentz}) ) is not large (since ismostly in the $x$ -direction).944" This is E,sw,,due to the reasons discussed above: the sspectrum is essentially a measure of the Brace E,spectrumsy because the y-component of the last term in Equation (2)) is large and aand aare similarsw because the x-component of the last term in Equation (2)) is not (since iismostly in the x-direction).large", This is due to the reasons discussed above: the spectrum is essentially a measure of the $B_{\text{trace}}$ spectrum because the $y$ -component of the last term in Equation \ref{eq:ideallorentz}) ) is large and and are similar because the $x$ -component of the last term in Equation\ref{eq:ideallorentz}) ) is not large (since ismostly in the $x$ -direction).945"In simulations involving radiative cooling and turbulence resulting from acoustic-gravity waves, Fujita et al. (","In simulations involving radiative cooling and turbulence resulting from acoustic-gravity waves, Fujita et al. ("9462004) found that cooling catastrophe can be prevented even in the absence of thermal conduction.,2004) found that cooling catastrophe can be prevented even in the absence of thermal conduction.947" However, the level of turbulence in those simulations was higher then in the cases that we Figure 7 is the analog of Figure 3 (right panel) and shows the behavior of the Spitzer fraction (solid line)."," However, the level of turbulence in those simulations was higher then in the cases that we Figure 7 is the analog of Figure 3 (right panel) and shows the behavior of the Spitzer fraction (solid line)."948" As in the adiabatic case, the ratio evolves asymptotically toward an approximately constant level but in this case the saturated level is slightly lower (~30% of the Spitzer-Braginskii value)."," As in the adiabatic case, the ratio evolves asymptotically toward an approximately constant level but in this case the saturated level is slightly lower $\sim 30$ of the Spitzer-Braginskii value)."949 The unperturbed HBI case is shown for reference (dashed line)., The unperturbed HBI case is shown for reference (dashed line).950" We attribute the small offset between the theoretical maximum Spitzer fraction of and the simulated one to the fact that the HBI is 1/3marginally more competitive in the cooling case, due to the steeper temperature profile."," We attribute the small offset between the theoretical maximum Spitzer fraction of 1/3 and the simulated one to the fact that the HBI is marginally more competitive in the cooling case, due to the steeper temperature profile."951 We note that the cooling results described above come with possible caveats., We note that the cooling results described above come with possible caveats.952 The above examples of cooling runs may not carry over to higher ICM densities., The above examples of cooling runs may not carry over to higher ICM densities.953 We, We954the Galaxy at the time of lormation of the population under study.,the Galaxy at the time of formation of the population under study.955 From the observational viewpoint. (he metallicity gradient depends on the galaxy. (wpe. the population utilized. the method of calculating the o-element abundanuces. the distances of the probes from the Galactic center. and also on the uncertainties associated (o all these variables.," From the observational viewpoint, the metallicity gradient depends on the galaxy type, the population utilized, the method of calculating the $\alpha$ -element abundances, the distances of the probes from the Galactic center, and also on the uncertainties associated to all these variables."956 Planetary nebulae well encompass several generations οἱ stars in galaxies. (hus are essential probes ol metallicity gradient: their a-elemental abundances are relatively easily determined. ancl the samples are sizable.," Planetary nebulae well encompass several generations of stars in galaxies, thus are essential probes of metallicity gradient: their $\alpha$ -elemental abundances are relatively easily determined, and the samples are sizable."957 On the other hand. historically it has been difficult to reach an agreement on the value of the 1D eradient slope from Galactic PNe. due to two factors: the unreliabilitv of the distance scale. and the selection of the PN population.," On the other hand, historically it has been difficult to reach an agreement on the value of the 1D gradient slope from Galactic PNe, due to two factors: the unreliability of the distance scale, and the selection of the PN population."958 It is in fact essential (hat the eradients do not depend on the distance scale. but also that the disk population selected for this calculation is as complete and homogeneous as possible.," It is in fact essential that the gradients do not depend on the distance scale, but also that the disk population selected for this calculation is as complete and homogeneous as possible."959 The use of oxvgen and neon sees (o be aclequate in Galactic studies. where oxveen production through the AGB is marginal. while in low-metallicitv galaxies oxvgen might not be the ideal choice. since oxvgen nueht be carried at the LIMS surface by the third dredge-up (Ixarakas et al.," The use of oxygen and neon seems to be adequate in Galactic studies, where oxygen production through the AGB is marginal, while in low-metallicity galaxies oxygen might not be the ideal choice, since oxygen might be carried at the LIMS surface by the third dredge-up (Karakas et al."960 2002)., 2002).961 In Figures 4 through 6 we show the oxvgen and neon abundances. in the usual form ol A(X)2log(X/I1)2-12. versus the ealactocentric distances of the PNe for the three PN Types.," In Figures 4 through 6 we show the oxygen and neon abundances, in the usual form of A(X)=log(X/H)+12, versus the galactocentric distances of the PNe for the three PN Types."962 The samples have been selected against both bulge and halo PNe. following the prescriptions of 62.4.," The samples have been selected against both bulge and halo PNe, following the prescriptions of $\S$ 2.4."963 Bipolar PNe have not been included in the gradient plots to minimize (he distance uncertainties of the disk PNe., Bipolar PNe have not been included in the gradient plots to minimize the distance uncertainties of the disk PNe.964 Note that (he bump around (he solar vicinity in Figure 5 is due (ο the historical selection of nearby PNe as spectral targets., Note that the bump around the solar vicinity in Figure 5 is due to the historical selection of nearby PNe as spectral targets.965 In Table 3 we give the abundance averages ancl gradient. resulting from our analysis with. in column (1) the a-element considered. in column (2) the PN type included in the statistics. in column (3) (he number of PNe in the sample (n parenthesis the sample size excluding bipolar PNe. i. e.. (he sample size used for exadients and plots). in column (4) the average linear abundance with its dispersion. in column (5) the dispersion of the v-axis distributions. in," In Table 3 we give the abundance averages and gradient resulting from our analysis with, in column (1) the $\alpha$ -element considered, in column (2) the PN type included in the statistics, in column (3) the number of PNe in the sample (in parenthesis the sample size excluding bipolar PNe, i. e., the sample size used for gradients and plots), in column (4) the average linear abundance with its dispersion, in column (5) the dispersion of the y-axis distributions, in"966These limitations force us to consider treating the differential background matching separately from PSF matching.,These limitations force us to consider treating the differential background matching separately from PSF matching.967 We have seen towards high surface brightness targets such as M31 systematic effects such as scattered or reflected light can imprint complex time-variable signatures upon the differential background that the OIS algorithm cannot deal with adequately., We have seen towards high surface brightness targets such as M31 systematic effects such as scattered or reflected light can imprint complex time-variable signatures upon the differential background that the OIS algorithm cannot deal with adequately.968" The OIS algorithm performs PSF and background flux matching simultaneously, whilst prior to OIS these were treated separately by various M31 variable photometry pipelines (Tomaney&Crotts1996;Ansarietal. 1997)."," The OIS algorithm performs PSF and background flux matching simultaneously, whilst prior to OIS these were treated separately by various M31 variable photometry pipelines \citep{tom96,ans97}."969". However, the OIS algorithm provides clear advantages over earlier schemes due to its flexibility in modelling the PSF."," However, the OIS algorithm provides clear advantages over earlier schemes due to its flexibility in modelling the PSF."970 Ideally we would like to combine the best of the old and current approaches., Ideally we would like to combine the best of the old and current approaches.971" To this end we choose to separate out the photometric and PSF matching stages, as in earlier approaches."," To this end we choose to separate out the photometric and PSF matching stages, as in earlier approaches."972 Then we run ISIS with differential background matching effectively turned off by setting the background polynomial to order zero [i.e. setting My=0 in Equation (3))]., Then we run ISIS with differential background matching effectively turned off by setting the background polynomial to order zero [i.e. setting $M_b = 0$ in Equation \ref{bgbasis}) )].973 In this case the least squares minimization of D? in Equation (1)) should be driven by the quality of the PSF transformation kernel A rather than potentially having to trade between the quality of PSF and background matching., In this case the least squares minimization of $D^2$ in Equation \ref{dia}) ) should be driven by the quality of the PSF transformation kernel $K$ rather than potentially having to trade between the quality of PSF and background matching.974 We begin by determining a gross linear photometric scaling to match the image flux., We begin by determining a gross linear photometric scaling to match the image flux.975 Due to large telescope pointing errors in the first two seasons of the Angstrom survey the sky area common to, Due to large telescope pointing errors in the first two seasons of the Angstrom survey the sky area common to976The mareinal PDF of J. hielliehts the source of the Galactic tidal torque.,The marginal PDF of $\vec J'_x$ highlights the source of the Galactic tidal torque.977 However. it remaius to describe how this manifests iu the time-dependent distribution fuuctiou of the comets aueular uomentum.," However, it remains to describe how this manifests in the time-dependent distribution function of the comet's angular momentum."978 InSection 3.. we used the Boltzmann equation (Equation 5)) to relate the axisvuuuetric single perturbation PDF (pC7/)) to the distribution of aneular momentum (£(J(f3)).," InSection \ref{secLevy}, we used the Boltzmann equation (Equation \ref{eqBoltzmann}) ) to relate the axisymmetric single perturbation PDF $p(J')$ ) to the distribution of angular momentum $f(\vec J(t))$ )."979" That derivation. however. depends on the simplifications afforded by the single power law form of p(.J"")."," That derivation, however, depends on the simplifications afforded by the single power law form of $p(J')$."980 For the nou-axisvuuuctric single perturbation PDF depicted in Fieure 1. an analytic solution to the corresponding Doltzuiuum equation would be much more diffieult to calculate.," For the non-axisymmetric single perturbation PDF depicted in Figure \ref{figContours}, an analytic solution to the corresponding Boltzmann equation would be much more difficult to calculate."981 Tusteack we use a bootstrap techuique to estimate the distribution function from a sample of single perturbations.," Instead, we use a bootstrap technique to estimate the distribution function from a sample of single perturbations."982" The velocity of the perturbers. e,. their inuuboer deusity. à». aud the area sampled when generating the single interaction PDF. wie. pAset the average time associated with cach perturbation. 1/7=i02,ον."," The velocity of the perturbers, $v_p$, their number density, $n$, and the area sampled when generating the single interaction PDF, $\pi b_{\rm max}^2$, set the average time associated with each perturbation, $1/\tau = n \pi b_{\rm max}^2 v_p$."983 The angular moment at a time tis then the sum of t/7 single perturbations., The angular momentum at a time $t$ is then the sum of $t/\tau$ single perturbations.984 By randomly choosing f/r perturbations from the PDF aud addiug them vectoriallv. we ecucrate a sample of angular momentum vectors that reflect the distribution function at that time f.," By randomly choosing $t/\tau$ perturbations from the PDF and adding them vectorially, we generate a sample of angular momentum vectors that reflect the distribution function at that time $t$."985 To accurately probe the evolution over many orders of magnitude. several sónele interaction PDFs with different Όμως Were used.," To accurately probe the evolution over many orders of magnitude, several single interaction PDFs with different $b_{\rm max}$ were used."986 Ignoring large impact parameters iucreases 7. or equivaleutly. samples the close encounters more often over a fixed uunber of perturbations.," Ignoring large impact parameters increases $\tau$, or equivalently, samples the close encounters more often over a fixed number of perturbations."987 We verified that the distribution fictions caleulated with large 7 (sinall Όμως) ire not sienificautly affected bv ignoring the frequeut perturbations of smaller 7’., We verified that the distribution functions calculated with large $\tau$ (small $b_{\rm max}$ ) are not significantly affected by ignoring the frequent perturbations of smaller $J'$.988 The mareinal distribution functions at four different times are shown in Fieure 2., The marginal distribution functions at four different times are shown in Figure \ref{fig4Hists}.989 Each histogram contains 10° iootstrapped. Jtt). generated from the stm of between Laud 1000 single perturbations.," Each histogram contains $10^6$ bootstrapped $\vec990J(t)$, generated from the sum of between 4 and 1000 single perturbations."991" The distribution of J,(f) is slotted in the dotted lines for J,(4)>0 aud dash-dotted for J,(t)<0.", The distribution of $J_y(t)$ is plotted in the dotted lines for $J_y(t)>0$ and dash-dotted for $J_y(t)<0$.992" For J,(f). the solid line represcuts the negative rturbatious and the dashed line the positive oues."," For $J_x(t)$, the solid line represents the negative perturbations and the dashed line the positive ones."993 The top panel shows the augular momentum distribution at early times. or equivaleutlv. at low typical augular uonieuta.," The top panel shows the angular momentum distribution at early times, or equivalently, at low typical angular momenta."994 For reference. we denote this time ty.," For reference, we denote this time $t_0$."995 Since the single interaction PDF for perturbations of this magnitude ix axisymmetric. all four fictions are identical.," Since the single interaction PDF for perturbations of this magnitude is axisymmetric, all four functions are identical."996 The excess of perturbations to negative J is not visible as the Uselihood for those eucounters is too low to be sampled in the 10° vectors generated for tle plot., The excess of perturbations to negative $J'_x$ is not visible as the likelihood for those encounters is too low to be sampled in the $10^6$ vectors generated for the plot.997 The second panel depicts the four distribution fictions 100 times later than the time of the top panel., The second panel depicts the four distribution functions 100 times later than the time of the top panel.998 Again both πιοΊος show a simular shape. aud the typical value for all four has erown linearly with time as predicted by Equation S.," Again both functions show a similar shape, and the typical value for all four has grown linearly with time as predicted by Equation \ref{eqODE}."999 The trajectories passing between the sun aud the comet have been sampled iu a small fraction of the generated J(f). and the contribution from the spike of Figure lec is apparent.," The trajectories passing between the sun and the comet have been sampled in a small fraction of the generated $\vec J(t)$, and the contribution from the spike of Figure \ref{figContours}c c is apparent."1000" Additionally the normalization of the positive distribution of J,(f) has fallen to reflect the breaking of the svuuuetry around J,= 0.", Additionally the normalization of the positive distribution of $J_x(t)$ has fallen to reflect the breaking of the symmetry around $J_x=0$ .1001 The distributions iu the first, The distributions in the first1002 z-6 z—20. z6-8 0.910ες) Lz0.1L. boost for the discovery power of and large ground-based telescopes., $z{\simeq}6$ $z{\simeq}20$ $z{\sim}6{-}8$ $L{\gs}0.3L^{\star}_{z{=}3.8}$ $L{\ls}0.1L^{\star}$ boost for the discovery power of and large ground-based telescopes.1003 Indeed. the galaxy redshift record has been broken on several occasions with the help of the gravitational magnification of distant galaxies by foreground galaxy clusters (Mellier et 11991; Franx et 11997; Hu et 22002: Kneib et 22004).," Indeed, the galaxy redshift record has been broken on several occasions with the help of the gravitational magnification of distant galaxies by foreground galaxy clusters (Mellier et 1991; Franx et 1997; Hu et 2002; Kneib et 2004)."1004 The faint end of the luminosity function of Lyman-o emitters at z25 has also been constrained with the help of gravitational lensing (Santos et 22004: Ellis et 22001)., The faint end of the luminosity function of ${\alpha}$ emitters at $z{=}5$ has also been constrained with the help of gravitational lensing (Santos et 2004; Ellis et 2001).1005 Extension of these techniques to zz:7 Is therefore an important element of observational studies of cosmic re-ionization., Extension of these techniques to $z{\gs}7$ is therefore an important element of observational studies of cosmic re-ionization.1006 Pelló et ((2004 - hereafter PO4) reported a gravitationally magnified (j/025—100) galaxy at -ΞΙ0 (hereafter #11916. following PO4s nomenclature) behind the foreground galaxy cluster 11835. (050.25).," Pelló et (2004 – hereafter P04) reported a gravitationally magnified ${\mu}{\sim}25{-}100$ ) galaxy at $z{=}10$ (hereafter 1916, following P04's nomenclature) behind the foreground galaxy cluster 1835 $z{=}0.25$ )."1007" This interpretation is based on nor-detection in optical imaging from the ground (3o limits in a 0.6"" diameter aperture: V227.4. R227.5. 126.9) αιd space (30 limit in a 0.2” diameter aperture: R05727. 2) and the shape of the continuum at An,tym (using a 1.5” aperture: (J-H)>0.6. (H—-K )=—-0.5+0.4) which ts reminiscent of the Lyman-break selection technique (Steidel et 11996)."," This interpretation is based on non-detection in optical imaging from the ground $3{\sigma}$ limits in a $0.6''$ diameter aperture: $V{\ge}27.4$, $R{\ge}27.5$ , $I{\ge}26.9$ ) and space $3{\sigma}$ limit in a $0.2''$ diameter aperture: $R_{702}{\ge}27.2$ ), and the shape of the continuum at ${\lambda}_{\rm obs}{\ge}1{\mu}{\rm m}$ (using a $1.5''$ aperture: $(J{-}H){\ge}0.6$, $(H{-}K){=}{-}0.5{\pm}0.4$ ) which is reminiscent of the Lyman-break selection technique (Steidel et 1996)."1008" PO4 corroborated the putative Lyman-break redshifted to Ao,21.37//m. with an emission line at. Ao4,21.33754/m. with integrated flux of (4.140.5)<107ergem™~s7!. which they interpret. as Lyman-o."," P04 corroborated the putative Lyman-break redshifted to ${\lambda}_{\rm1009obs}{\simeq}1.3{\mu}{\rm m}$ with an emission line at ${\lambda}_{\rm1010obs}{=}1.3375{\mu}{\rm m}$ with integrated flux of $(4.1{\pm}0.5){\times}10^{-18}{\rm erg\,cm^{-2}\,s^{-1}}$, which they interpret as ${\alpha}$."1011 Lower redshift interpretations of the line ([OII] at z22.59; [OIII] at zz1.68: Hea at zz1.04) were discarded by ΡΟΗ largely on the basis of the low probability of solutions at zz;7 when fitting synthetic spectral energy distributions (SEDs) to their photometric data., Lower redshift interpretations of the line ([OII] at $z{=}2.59$; [OIII] at $z{=}1.68$; ${\alpha}$ at $z{=}1.04$ ) were discarded by P04 largely on the basis of the low probability of solutions at $z{\ls}7$ when fitting synthetic spectral energy distributions (SEDs) to their photometric data.1012 The most likely ofthese lower-redshift solutions (222.59) was further excluded on the basis of the dust extinction required to fitthe photometric data (Ay 22). and the absence of doublet structure in the observed emission line.," The most likely ofthese lower-redshift solutions $z{=}2.59$ ) was further excluded on the basis of the dust extinction required to fitthe photometric data $A_V{\ge}2$ ), and the absence of doublet structure in the observed emission line."1013reviews of the existing coustraiuts aud the seuxitivitv of future experiments. seo Ref. [G]..,"reviews of the existing constraints and the sensitivity of future experiments, see Ref. \cite{EDreviews}."1014 The host of experimental measurements conducted to date have larecly disfavored only the case of two or less aree ED: for auv larger umber of them. the lower luit ou the fundamental Planck scale is only ~1 Τον. hardly probing the most natural range of scaleκ expected in the ADD model.," The host of experimental measurements conducted to date have largely disfavored only the case of two or less large ED; for any larger number of them, the lower limit on the fundamental Planck scale is only $\sim 1$ TeV, hardly probing the most natural range of scales expected in the ADD model."1015 As was pointed out a decade ago [τι aji exciting consequence of TeV- quantum eravitv is the possibility of producing black holes (BIT) in ligh-cuerey interactions. accessible at colliders or by ultva-high-cucrey cosmic ravs.," As was pointed out a decade ago \cite{BHearly}, an exciting consequence of TeV-scale quantum gravity is the possibility of producing black holes (BH) in high-energy interactions, accessible at colliders or by ultra-high-energy cosmic rays."1016 More recently. this phenomenon has bee1 quantified for the case of TeV- particle collisions|s]. resulting iu a njicnuerizimeg prediction that the LUC would produce miui black holes at au ¢unonuous rate (ce. 1 Wz for Mp=1 TeV). thus becoming a black-hole actorv.," More recently, this phenomenon has been quantified for the case of TeV-scale particle \cite{dlgt}, resulting in a mesmerizing prediction that the LHC would produce mini black holes at an enormous rate (e.g., $\sim 1$ Hz for $M_D = 1$ TeV), thus becoming a black-hole factory."1017 This observation led to an explosion of follow-up publications ou the| properties of nini-black holes produced in the lab aud made this subject οne of the most actively studied aspects of phenomenologyo of models with exra dimensions., This observation led to an explosion of follow-up publications on the properties of mini-black holes produced in the lab and made this subject one of the most actively studied aspects of phenomenology of models with extra dimensions.1018 Tere we review oulv some of the basic facts iu phenomenology of black holes., Here we review only some of the basic facts in phenomenology of black holes.1019 For more extensive reviews. including the latest developments. sce Ref. |9]..," For more extensive reviews, including the latest developments, see Ref. \cite{BHreviews}."1020 The most experimentally interesting feature of the above models with ED is rich low-enerev plienomenology that originates from the Wik spectrum of various particles propagating in ED., The most experimentally interesting feature of the above models with ED is rich low-energy phenomenology that originates from the KK spectrum of various particles propagating in ED.1021 Iu what follows we compare the KIN) spectiua observed in the ADD.1. and RS models aud discuss various experimental constraints on the model parameters.," In what follows we compare the KK spectrum observed in the ADD, and RS models and discuss various experimental constraints on the model parameters."1022 Iu the ADD inodel. the ouly particle that propagates in ED aud acquires IIS anodes is the eravitou.," In the ADD model, the only particle that propagates in ED and acquires KK modes is the graviton."1023 Given the size of ED (~10? 10i» ni). Onorgv spacing between the KI excitations of the eraviton is ~1 meV 0 MeV. Consequently. the adjacent modes are hard to resolve au in mosty. of the experiments the KIS spectrum would appear coutiuuous. from zero to a certain ultraviolet cutoff above which quantum eravity effects would modify this seimi-classical picture.," Given the size of ED $\sim 10^{-3}$ $10^{-15}$ m), energy spacing between the KK excitations of the graviton is $\sim 1$ meV – 100 MeV. Consequently, the adjacent modes are hard to resolve and in most of the experiments the KK spectrum would appear continuous, from zero to a certain ultraviolet cutoff above which quantum gravity effects would modify this semi-classical picture."1024 Since the fuudamental Planck scale in the ADD model is Mp~ Τον. it’s natural to expect this cutoff. Ma. to be of the same order: MsgMp.," Since the fundamental Planck scale in the ADD model is $M_D \sim 1$ TeV, it's natural to expect this cutoff, $M_S$, to be of the same order: $M_S \sim M_D$."1025 While cach KI mode couples to the energv-1iomoenutun tensor witli the exavitational streugth Gy. the sheer umber of tre available IWIN modes is sufficient to enliauce eravitational attraction tremeously.," While each KK mode couples to the energy-momentum tensor with the gravitational strength $G_N$, the sheer number of the available KK modes is sufficient to enhance gravitational attraction tremendously."1026 In the nunodel with a singleextra dimension of the size :. the zeroth KIX mode of a gauge boson is the SM. particle of mass My.," In the model with a singleextra dimension of the size $R$ , the zeroth KK mode of a gauge boson is the SM particle of mass $M_V$."1027 TUs mass can be either 0 (photon. οποια) or >0 (1. Z).," This mass can be either $0$ (photon, gluon) or $>0$ $W$, $Z$ )."1028 The mass of the i-lh IIS anode is eiven by M;=(AR|PY R?., The mass of the $i$ -th KK mode is given by $M_i = \sqrt{M_V^2 + i^2/R^2}$ .1029 Forthe coupactification scale Me=BR~1 Τον. l/RmMy and hence the nou-zeroth WI modes or all gauge bosons are," Forthe compactification scale $M_C \equiv 1/R \sim 1$ TeV, $1/R \gg M_V$ and hence the non-zeroth KK modes for all gauge bosons are"10304.,4.1031" All calculations were done using (Qm,0Q,a,h,08,Ms)= (0.27,0.73,0.72,0.8,0.96), consistent with WMAP 7-year data (Komatsuetal.2011)."," All calculations were done using $(\Omega_m,\Omega_\Lambda,h,\sigma_8,n_s)=(0.27,0.73,0.72,0.8,0.96)$ , consistent with WMAP 7-year data \citep{komatsu/etal:2011}."1032. All distances are comoving., All distances are comoving.1033" Table 1 shows our simulation parameters: C, the ionizing efficiency, Aj, the comoving absorption system mean free path, t.y, the photoevaporation time for the evolving Aaps models, and Mnin, the minimum halo mass of galaxies."," Table 1 shows our simulation parameters: $\zeta$ , the ionizing efficiency, $\mfp$, the comoving absorption system mean free path, $t_{\rm ev}$, the photoevaporation time for the evolving $\mfp$ models, and $M_{\rm min}$, the minimum halo mass of galaxies."1034" Also shown are the redshifts when the global ionized fraction equals 0.5, 0.9, and 1 -- zos, zoo, and ze, respectively, and the bubble mean free path when the neutral fraction is 0.1, Ao=A»@ur 0.1)."," Also shown are the redshifts when the global ionized fraction equals 0.5, 0.9, and 1 – $z_{0.5}$, $z_{0.9}$, and $z_{\rm ov}$, respectively, and the bubble mean free path when the neutral fraction is 0.1, $\lambda_0\equiv1035\lambda_{\rm b}(x_{\rm HI}=0.1)$ ."1036" The parameters were varied to give a Thomson scattering optical depth of(7_,79, T+)=(0.06,0.09,0.12), corresponding to the 2-0 constraint from (Komatsuetal.2011),, with the He I fraction tracking I, and instantaneous He II reionization at z=3."," The parameters were varied to give a Thomson scattering optical depth $\tau_-,\tau_0,\tau_+$ $=$ $0.06,0.09,0.12$ ), corresponding to the $\sigma$ constraint from \citep{komatsu/etal:2011}, with the He I fraction tracking H I, and instantaneous He II reionization at $z=3$."1037 All simulationsH used 4096? cells in a 2 Gpc/h box., All simulations used $4096^3$ cells in a 2 $/h$ box.1038" We model the mean reionization history wtih two spatially uniform mean free paths: that corresponding to ionized bubbles, Ap, and Lyman-limit systems, λαυς."," We model the mean reionization history wtih two spatially uniform mean free paths: that corresponding to ionized bubbles, $\lambda_{\rm b}$, and Lyman-limit systems, $\mfp$."1039" Ionizing radiation is attenuated by their superposition, so that Ac,=Ap!-Aj. The spatially flux is F(z)=Amrp(z)e(z), where e(z) is the averagedionizing ionizingphoton emissivity."," Ionizing radiation is attenuated by their superposition, so that $\lambda^{-1}_{\rm mfp}=\lambda^{-1}_{\rm b}+\mfp^{-1}.$ The spatially averaged ionizing flux is $F(z)=\lambda_{\rm mfp}(z)\epsilon(z)$, where $\epsilon(z)$ is the ionizing photon emissivity."1040" We set e(z)—CHo. feou(Z)s where ¢ is number of per collapsed hydrogen atom, corrected for ionizingrecombinationsphotons outside of absorption systems."," We set $\epsilon(z)=\zeta n_{H,0} \dot{f}_{\rm coll}(z)$ , where $\zeta$ is number of ionizing photons per collapsed hydrogen atom, corrected for recombinations outside of absorption systems."1041" The mean ionization rate is When λαυς>Av, photons typically reach the edges of bubbles without being absorbed by intervening Lyman-limit systems, and the photoionization rate is equal to the emission rate."," The mean ionization rate is When $\mfp\gg \lambda_{\rm b}$, photons typically reach the edges of bubbles without being absorbed by intervening Lyman-limit systems, and the photoionization rate is equal to the emission rate."1042" When Aaps< Ap, the probability of a photon reaching the edge of a bubble is λιυς/λυ, and the ionization rate is suppressed."," When $\mfp\ll \lambda_{\rm b}$ , the probability of a photon reaching the edge of a bubble is $\mfp/\lambda_{\rm1043 b}$, and the ionization rate is suppressed."1044" A more realistic treatment would involve allowing F, Aj, and Ἆαυς to vary spatially, obtaining a spatially-dependent solution of equation (1)), which can then be averaged to find the global reionization history."," A more realistic treatment would involve allowing $F$, $\lambda_b$, and $\lambda_{\rm abs}$ to vary spatially, obtaining a spatially-dependent solution of equation \ref{dxdt}) ), which can then be averaged to find the global reionization history."1045 We have chosen the simpler uniform model of equation (1)) as a starting point., We have chosen the simpler uniform model of equation \ref{dxdt}) ) as a starting point.1046" Although this choice does not affect our results on the morphology of the ionization field at fixed ionized fraction, the assumptions underlying equation (1)) should be kept in mind when interpreting the reionization history and photon consumption rates we find."," Although this choice does not affect our results on the morphology of the ionization field at fixed ionized fraction, the assumptions underlying equation \ref{dxdt}) ) should be kept in mind when interpreting the reionization history and photon consumption rates we find."1047" Our three-dimensional model is based on that of Furlanettoal. (2004),, later extended to three dimensions by Zahnal. (2007)."," Our three-dimensional model is based on that of \citet{furlanetto/etal:2004}, later extended to three dimensions by \citet{zahn/etal:2007}."1048". Its main assumption is that a region is fully ionized if its collapsed fraction is greater than some threshold, Cfeon>1."," Its main assumption is that a region is fully ionized if its collapsed fraction is greater than some threshold, $\zeta f_{\rm coll} > 1$."1049" As shown in Alvarezetal.(2009),, by smoothing the linear density field over a range of scales, one can efficiently determine when each point is first reionized, z,."," As shown in \citet{alvarez/etal:2009}, by smoothing the linear density field over a range of scales, one can efficiently determine when each point is first reionized, $z_r$."1050" We do not smooth over scales with radii larger than Aaps, since absorption systems shield radiation from these distances."," We do not smooth over scales with radii larger than $\mfp$, since absorption systems shield radiation from these distances."1051" We assume that the absorption systems contribute a spatially uniform opacity, and therefore the scale beyond which we do notsmooth is the same everywhere."," We assume that the absorption systems contribute a spatially uniform opacity, and therefore the scale beyond which we do notsmooth is the same everywhere."1052 This approach is desirable becausethe orderin which points are ionized is the same as that in which the Furlanettoetal.criterion is first met around each point., This approach is desirable becausethe orderin which points are ionized is the same as that in which the \citet{furlanetto/etal:2004} criterion is first met around each point.1053" However, the reionization redshifts do not generally result in the correct"," However, the reionization redshifts do not generally result in the correct"1054within the 68% contour. however this may be scattered light [rom the X-ray binary X1721-308. just over 1 degree away.,"within the $68\%$ contour, however this may be scattered light from the X-ray binary X1724-308, just over 1 degree away."1055 We measured a peak within this area (src3). and two sources uear the edges of the FOV (srcl.src2).," We measured a peak within this area (src3), and two sources near the edges of the FOV (src1,src2)."1056 We could find no other X-ray images of this field., We could find no other X-ray images of this field.1057J1800-2327 This unage shows au X- complex with possible point sources (sp2 aud sp3) iu the southern portion coincident with inassive voung stars in the Sharpless 32 HII region., This image shows an X-ray complex with possible point sources (sp2 and sp3) in the southern portion coincident with massive young stars in the Sharpless 32 HII region.1058 There is also a coincident 60 fe source seen in the IRAS survey with a yeak at 18h 09m 58s. -23«d [1m Lis (uear sp3).," There is also a coincident 60 $\mu$ source seen in the IRAS survey with a peak at 18h 09m 58s, -23d 41m 14s (near sp3)."1059 However. the y-ray contours favor he northeru part of the complex. which las a larder spectrum.," However, the $\gamma-$ ray contours favor the northern part of the complex, which has a harder spectrum."1060 This exteuded X-uy enmdsson ds surrouuded by molecular eas in the Lyuds 227 dark nebula. aud. has )eeu sugeestedMOD to be a synelirotron. nebula ualuntaluiuig pressure equilibrium with the cloud by means of a pulsar wind (see Oka et al.," This extended X-ray emission is surrounded by molecular gas in the Lynds 227 dark nebula, and has been suggested to be a synchrotron nebula maintaining pressure equilibrium with the cloud by means of a pulsar wind (see Oka et al."1061 1999 for details)., 1999 for details).1062 This sou‘ce also seems o be moderately variable in 5—rays., This source also seems to be moderately variable in $\gamma-$ rays.1063 The xight[n] point source to the south (src2) is lear a weak. radio point source.," The bright point source to the south (src2) is near a weak, radio point source."1064 Such X-av/radio sources are frequently associated with Sevfert galaxies. which are common ckground sources in hard N-rays (Gioiaetal. 1990).," Such X-ray/radio sources are frequently associated with Seyfert galaxies, which are common background sources in hard X-rays \citep{g90}."1065.41825-1310 This source is near the young pulsar PSR B1823-13., This source is near the young pulsar PSR B1823-13.1066 However. our GeV source position is not consistent. with it at the 95% conlideuce level.," However, our GeV source position is not consistent with it at the $95\%$ confidence level."1067 The new image. based ou the GeV positiou. reveals a previously uuknowu exteuded X-ray. source with a spectrum suggestive of a pulsar wind uebula.," The new image, based on the GeV position, reveals a previously unknown extended X-ray source with a spectrum suggestive of a pulsar wind nebula."1068 Near the conjunction of our field with the archival GPS fields is some apparently thermal diffuse X-ray. emission near a noln-thermal radio source iu the Sharpless 53 HII cluster. which may be a superuova remuaut (15.102. marked as such in figure. also source F of Ixassii et al.," Near the conjunction of our field with the archival GPS fields is some apparently thermal diffuse X-ray emission near a non-thermal radio source in the Sharpless 53 HII cluster, which may be a supernova remnant (G18.1-0.2, marked as such in figure, also source F of Kassim et al."1069 1989)., 1989).1070 This latter source is also cousistent with tlie soft 2? —ray source (D—2.60£0.19) δα J1823-131I., This latter source is also consistent with the soft $\gamma-$ ray source $\Gamma = 2.69 \pm 0.19$ ) 3EG J1823-1314.1071 This source is the ouly uuideutiliel GeV source that made our flux cut at high Calactic latitude (6~25°)., This source is the only unidentified GeV source that made our flux cut at high Galactic latitude $b\sim 25^{\circ}$ ).1072 Due to its hard spectrum. small error contour. aud uuicque position resulting in low absorption. it has been the subject of au extensive observing campaign with ROSAT and ASCA. as well as radio auc optical studies (Mirabaletal.2000).," Due to its hard spectrum, small error contour, and unique position resulting in low absorption, it has been the subject of an extensive observing campaign with ROSAT and ASCA, as well as radio and optical studies \citep{m00}."1073. Ouly a few. very faint point sources are in the field.," Only a few, very faint point sources are in the field."1074 Mirabaletal.(2000). suggest oue variable soft. N-ray source observed. by ROSAT as a potential counterpart., \citet{m00} suggest one variable soft X-ray source observed by ROSAT as a potential counterpart.1075 Stroug upper limits on the optical flux suggest a neutron star identification., Strong upper limits on the optical flux suggest a neutron star identification.1076 However. the relative N-ray to 5—ray. [flux is remarkably low assumiug tle X-rays are due to thermal eimission from a neutron star surlace.," However, the relative X-ray to $\gamma-$ ray flux is remarkably low assuming the X-rays are due to thermal emission from a neutron star surface."1077 This may indicate au agiug isolated. pulsar with ouly weak maguetospheric X-ray. emission., This may indicate an aging isolated pulsar with only weak magnetospheric X-ray emission.1078 Lu our image. mace from the archival daa. the most sigeuilicaut peak cosistent with the GeV source is at. 18h36109.2s. £59d2809s. which is a μιαθα. source with a 2-10 keV [lus of ouly ~10.Pergsem7s+.," In our image, made from the archival data, the most significant peak consistent with the GeV source is at 18h36m9.2s, +59d28m09s, which is a marginal source with a 2-10 keV flux of only $\sim 10^{-13}{\rm ergs}\,{\rm cm}^{-2}1079\,{\rm s}^{-1}$."1080 This is not one of the sources listed by Mirabaletal.(2000)., This is not one of the sources listed by \citet{m00}.1081. However. we use this as the X-ray [lux iu Figure 2. aud Figure 3..J1937-0010.," However, we use this as the X-ray flux in Figure \ref{FXfg} and Figure \ref{AXtau}."1082 This field contalus a single point source in a small. well constrained error contour.," This field contains a single point source in a small, well constrained error contour."1083 The field was observed twice. with slightly different poiutiugs. aud the poiut source was seen at the same sky coordinates in both.," The field was observed twice, with slightly different pointings, and the point source was seen at the same sky coordinates in both."1084 The Parkes multi-beam survey has clicoverecl a [ast pulsar within the contour (D'Amicoοἱal.2000) which is not consistent with the X-ray source.," The Parkes multi-beam survey has dicovered a fast pulsar within the contour \citep{dam00}1085 which is not consistent with the X-ray source."1086J190740557 This source ids listed as 3EC 190320550 in the third EGRET catalog. even though the center of the LM ellipse was 1° away with hardly αν overlap with the very large 95% contour.," This source is listed as 3EG J1903+0550 in the third EGRET catalog, even though the center of the LM ellipse was $\sim 1^{\circ}$ away with hardly any overlap with the very large $95\%$ contour."1087 Lt sees likely that 3EG J1903+0550 is associated with the SNR C0.5-0.5. in which case it las uo," It seems likely that 3EG J1903+0550 is associated with the SNR G40.5-0.5, in which case it has no"1088the generation of 2-rays in evolved SNRs.,the generation of $\gamma$ -rays in evolved SNRs.1089 TUS considered the case of hadronic particle acceleration iu au SNR shock eucouuterue a dense molecular cloud. based on the theoretical model (Yamazakictal.2006).. but conclusion remained to be drawn due to limitation of the data explored in their paper. ic.. low counting statistics of the observation aud the lack of highiaesolutiou |? CO maps.," T08 considered the case of hadronic particle acceleration in an SNR shock encountering a dense molecular cloud, based on the theoretical model \citep{yam06}, but conclusion remained to be drawn due to limitation of the data explored in their paper, i.e., low counting statistics of the observation and the lack of high-resolution $^{12}$ CO maps."1090 Iu this paper. we report new results obtained from audSnzaki N-rav observations and CO spectral-liue data from Delinha 13.7 um radio telescope. and examine the theoretical 1iodel.," In this paper, we report new results obtained from and X-ray observations and CO spectral-line data from Delinha 13.7 m radio telescope, and examine the theoretical model."1091 TESS J1731-317 was observed by ou March 21. 2007 (οΤΟ 01056850201: PT: GC. Puehlilbofor). with a 25 ksec exposure.," HESS J1731-347 was observed by on March 21, 2007 (ObsID 0405680201; PI: G. Puehlhofer), with a 25 ksec exposure."1092 We reduced the data obtained from the European Photon Imaging Camera (EPIC). using the Scicuce Aualvsis Svsteii (SAS). version 8.0.," We reduced the data obtained from the European Photon Imaging Camera (EPIC), using the Science Analysis System (SAS), version 8.0."1093 We selected EPIC-MOS aud EPIC-pu eveuts with patteus 0-12 and 0-1. respectively.," We selected EPIC-MOS and EPIC-pn events with pattens 0-12 and 0-4, respectively."1094 Au examination of the light curve indicated that the observation was contanunated by background flares., An examination of the light curve indicated that the observation was contaminated by background flares.1095 Cleaning of the laugh particle backeround results iu effective exposure of 15.0. 11.5 and 6.2 ks for the MOS1. MOS2 and pu detectors. respectively.," Cleaning of the high particle background results in effective exposure of 15.9, 11.8 and 6.2 ks for the MOS1, MOS2 and pn detectors, respectively."1096" Moreover. the observation was also contaminated by xesunablv from a bright source. IRNS ""J173157.7-335007.starlight (Νους 1999).. located at 50 axis to the north aud outside the feld of view (FoV)."," Moreover, the observation was also contaminated by, presumably from a bright source, 1RXS J173157.7-335007 \citep{vog99}, located at $\sim$ $^\prime$ off axis to the north and outside the field of view (FoV)."1097 Cousequently a substantial portion ofthe upper (northern) FoV of the MOS1 aud pu detectors was contaminated (contamination iu the NOS2 FoV is appareutlv iiunual) and thus masked out from subsequent analysis.," Consequently, a substantial portion of the upper (northern) FoV of the MOS1 and pn detectors was contaminated (contamination in the MOS2 FoV is apparently minimal) and thus masked out from subsequent analysis."1098 We produced couuts and exposure uaps for the three detectors. iu the O.8-1.5. 1.5-2.2 and 2.2-7 keV bands.," We produced counts and exposure maps for the three detectors, in the 0.8-1.5, 1.5-2.2 and 2.2-7 keV bands."1099 The low euergy cutoff is justified by the relatively high foreground absorption near the Calactic aue., The low energy cutoff is justified by the relatively high foreground absorption near the Galactic plane.1100 We then merged the counts aud exposure maps. accounting for the difference in the effective area amoue he three detectors.," We then merged the counts and exposure maps, accounting for the difference in the effective area among the three detectors."1101 We also produced correspouding vackeround niaps. using the Filter Wheel Closed data hat characterizes the quiescent particle background.," We also produced corresponding background maps, using the Filter Wheel Closed data that characterizes the quiescent particle background."1102 TESS JL731-317 was observed by Suzaku on Fe 25. 2007 (ObsID 101099010: PL G. Puehlhofer). with both N-rav huaging Spectrometers (XIS) (Ikoviunaetal.2007) aud Ihud X-ray Detector (Takahashietal.2007).," HESS J1731-347 was observed by Suzaku on Feb. 23, 2007 (ObsID 401099010; PI: G. Puehlhofer), with both X-ray Imaging Spectrometers (XIS) \citep{koy07} and Hard X-ray Detector \citep{tak07}."1103. The uct exposure time is about 33 ks., The net exposure time is about 33 ks.1104 In this work. we focus on the NIS. Frout-Tlluuinated (FI) CCDs that have very high efficiency. and low backeround especially around 5 keV. Since the NIS2 became inoperable since Noveniber 2002. onlv data from NISO is used here.," In this work, we focus on the XIS Front-Illuminated (FI) CCDs that have very high efficiency and low background especially around 5 keV. Since the XIS2 became inoperable since November 2002, only data from XIS0 is used here."1105 We used cleaned versio 2.0 data (reductionby ITEADAS software versionViet6.5)., We used cleaned version 2.0 data (reduction by HEADAS software version 6.5).1106" The Suzaku FoV is « 18 arcmin?. centered at a compact source ThBQ LP, LG ‘|."," The Suzaku FoV is $\times$ 18 $^{2}$, centered at a bright compact source $^{\rm h}$ $^{\rm m}$ $^{\rm s}$, $^\circ$ $^{\prime}$ ]."1107 The Suzaku spectra were extracted from|] a cireular-source reeion with offsource aunulus backerouud region in the sale observation so that possible contamination by SNR enission is reduced to the minima., The Suzaku spectra were extracted from a circular-source region with off-source annulus background region in the same observation so that possible contamination by SNR emission is reduced to the minimum.1108" In order to merease the statistics, the spectra from NISO and NIS3 were jointly fitted for subsequent analysis."," In order to increase the statistics, the spectra from XIS0 and XIS3 were jointly fitted for subsequent analysis."1109 We observe the 6353.6-0.7/ITESS J1731-217 system by cluploving the 13.7 meter Delinha uullimeter telescope at the Purple Mountain Observatory in March 2005., We observe the G353.6-0.7/HESS J1731-347 system by employing the 13.7 meter Delinha millimeter telescope at the Purple Mountain Observatory in March 2008.1110 The telescope has an angular resolution of 55” at the observing frequencies., The telescope has an angular resolution of $''$ at the observing frequencies.1111" Simultancously the three J=1-0 CO isotopic lines (e. PCO, PCO. andCO} were observed by using a cryogenic superconductius SIS receiver and a multi-line backend. spectroscopic svsteni (Zouctal.2001).. but only the ""CO was bright enough for significant detection."," Simultaneously the three J=1-0 CO isotopic lines (i.e., $^{12}$ CO, $^{13}$ CO, and$^{18}$ CO) were observed by using a cryogenic superconducting SIS receiver and a multi-line backend spectroscopic system \citep{zuo04}, but only the $^{12}$ CO was bright enough for significant detection."1112 The system provides a velocity coverage from Vrsg-— D90 to GO laa  and velocity resolution of0.37 kindoe1 iuof CO., The system provides a velocity coverage from $_{LSR}$ = -150 to 60 km $^{-1}$ and velocity resolution of 0.37 $^{-1}$ in $^{12}$ CO.1113" Three target spots (sec Fig.1b). each with a nfIndes. were selected over the €1353.6-0.7.TeV area. which iuc the ceuter position at the s-vay peak [RA=17:32:00. Dec=-3Lb:12:00]). and theROSAT N-ray(SL: peak sites ($2: |173220. -315100]. S3:[173250.. respectively,"," Three target spots (see Fig.1b), each with a size of $'\times5'$, were selected over the G353.6-0.7 area, which includes the center position at the TeV $\gamma$ -ray peak (S1:[RA=17:32:00, Dec=-34:42:00]), and the X-ray peak sites (S2: [173220, -345400], S3:[173250, -344600]), respectively."1114 These regions were inapped with-311600[|). a erid size of 1'&10., These regions were mapped with a grid size of $1'\times1'$.1115 Each point was integrated up to 6 nünutes. resulting an average rus noise level iu the spectra to be 0.2-0.3 K. Spectral line data were processed by the CLASS package of GILDAS software developed by IRAAL," Each point was integrated up to 6 minutes, resulting an average rms noise level in the spectra to be 0.2-0.3 K. Spectral line data were processed by the CLASS package of GILDAS software developed by IRAM."1116 Fie., Fig.1117 1 shows the overall X-ray iiorphologv revealed byNewton. along with the radio coutiuuuun enmissiou of €1353.6-0.7LT (Fig.," 1 shows the overall X-ray morphology revealed by, along with the radio continuum emission of G353.6-0.7 (Fig."1118 la) and the x-ray ciission of IIESS JATBL3 (Fig., 1a) and the $\gamma$ -ray emission of HESS J1731-347 (Fig.1119 Ib)., 1b).1120 The radio SNR has a shell-like inorpholosv aud an extent of —230/ in diameter. hugely overlapping the extended TESS source.," The radio SNR has a shell-like morphology and an extent of $\sim$ $^\prime$ in diameter, largely overlapping the extended HESS source."1121 On the castern half of the SNR. N-ray ciission coimcideut with the radio chussion was detected in an carlyROSAT observation (TOs).," On the eastern half of the SNR, X-ray emission coincident with the radio emission was detected in an early observation (T08)."1122 This is confirmed by the present observation. although the lower (southern) part of the radio shell falls outside the EoV. It is also evident that N-rav emission is present along the western half of the radio shell. which was not detected iu theROSAT observation albeit its larger FoV. This can be unuderstood. as the cussion is detected onlv iu the 2.2-T keV baud that is almost eutirelv bevoud theROSAT energev coveraeo.," This is confirmed by the present observation, although the lower (southern) part of the radio shell falls outside the FoV. It is also evident that X-ray emission is present along the western half of the radio shell, which was not detected in the observation albeit its larger FoV. This can be understood, as the emission is detected only in the 2.2-7 keV band that is almost entirely beyond the energy coverage."1123 A uunber of N-rav substructures are revealed uuder the moderate spatial resolution ofNewton., A number of X-ray substructures are revealed under the moderate spatial resolution of.1124 Iu particular. a prominent filament is present within the shell. passing through the brightest Guner) part of the TESS source (Fig.," In particular, a prominent filament is present within the shell, passing through the brightest (inner) part of the HESS source (Fig."1125 1b) and partially coincident with radio contiuuunn enuüsson (Fie., 1b) and partially coincident with radio continuum emission (Fig.1126 la)., 1a).1127 With comparable widths of ~2’. the filament aud the eastern N-rav shel ogether define a ring-like feature (enclosed by the two dotted circles in Fig.," With comparable widths of $\sim$$2^\prime$, the filament and the eastern X-ray shell together define a ring-like feature (enclosed by the two dotted circles in Fig."1128 la: hereafter referred to as the rime). along which there are several bright knots (lighlighte w the small ellipses in Fie.," 1a; hereafter referred to as the ring), along which there are several bright knots (highlighted by the small ellipses in Fig."1129 laj., 1a).1130 Several plumes are xeseut northwest of the ring. where the radio shel apparently breaks.," Several plumes are present northwest of the ring, where the radio shell apparently breaks."1131 From their projected positions. it is rot clear whether the plumes are the natural extent of he shell or the flameut.," From their projected positions, it is not clear whether the plumes are the natural extent of the shell or the filament."1132" Furthermore. there is a bright conipact source centeriug at (RA. Dec.) = adie (179329. 15/18""). showing no counterpart on the |nuage."," Furthermore, there is a bright compact source centering at (R.A., Dec.) = $^{\rm h}$ $^{\rm m}$ $^{\rm s}$ , $^\circ$ $^\prime$ $^{\prime\prime}$ ), showing no counterpart on the radio image."1133 This source is named NMMS J173203-311518 hereafter., This source is named XMMS J173203-344518 hereafter.1134 The rius is not necessarily a coherent feature., The ring is not necessarily a coherent feature.1135Neglecting the viscous effects. ancl by assuming again that the neutron matter is described by a polviropic equation of state. while the quark phase obevs the simple bag model equation of state. one obtains lor (he conversion time The volume V(/) of the neutron matter converted to quark matter after a time interval |leony IS given. in Chis simple model. by If (he transition [rom neutron to quark phase is driven bv viscous processes only. then and In the previous Sections we have considered (he process of nucleation of quark bubbles in neutron star cores. and we have derived the conditions for quark matter formation in an astrophysical context.,"Neglecting the viscous effects, and by assuming again that the neutron matter is described by a polytropic equation of state, while the quark phase obeys the simple bag model equation of state, one obtains for the conversion time The volume $V(t)$ of the neutron matter converted to quark matter after a time interval $t<t_{conv}$ is given, in this simple model, by If the transition from neutron to quark phase is driven by viscous processes only, then and In the previous Sections we have considered the process of nucleation of quark bubbles in neutron star cores, and we have derived the conditions for quark matter formation in an astrophysical context."1136 In the present Section we shall apply the results previously obtained to analvze the possibility of the transition from neutron (o quark phase curing (he spinning down of a rapidly rotating neutron star., In the present Section we shall apply the results previously obtained to analyze the possibility of the transition from neutron to quark phase during the spinning down of a rapidly rotating neutron star.1137 In (his case the rotational energy of the star can be used to (rigger the phase transition., In this case the rotational energy of the star can be used to trigger the phase transition.1138 The minimum energy density required to create a quark bubble is, The minimum energy density required to create a quark bubble is1139The solid line in Figure 3) illustrates the maguetic s»ectra Ayfh) obtained from the nunerical sinulations for Case 1.,The solid line in Figure \ref{fig:mag_spec_1} illustrates the magnetic spectra $\hat E_B(k)$ obtained from the numerical simulations for Case 1.1140 Tie. left-haud. pauels of Figure { aud Figure 5 show the correspoudiug results for Cases 2 ancl 3. 'espectively.," The left-hand panels of Figure \ref{fig:mag_spec_2} and Figure \ref{fig:mag_spec_3} show the corresponding results for Cases 2 and 3, respectively."1141 We note that the magnetic energy peaks at vyLERI1l. 5$στ aud Ayee12.," We note that the magnetic energy peaks at $k_1^*\approx 11$, $k_2^*\approx 7$ and $k_3^*\approx 12$."1142 The dotted lines denote the converged clilusivity spectra. 2242E(k). calculated by USiLο equation (15)).," The dotted lines denote the converged diffusivity spectra, $2 \pi k^2F(k)$, calculated by using equation \ref{eq:corr_v_int}) )."1143 The velocity energy spectra (defined analogously to Ep(&)) are shown by the clashecl-clotted lines., The velocity energy spectra (defined analogously to $\hat E_B(k)$ ) are shown by the dashed-dotted lines.1144 We now turni to the solutions of the Ixazantsev model., We now turn to the solutions of the Kazantsev model.1145 For each of the three cases. using relation (5) to calculate wy(r) from the diffusivity spectrum. we solve equation (5)) Dor the fastest growing eigenmode.," For each of the three cases, using relation \ref{eq:kappa_L_F}) ) to calculate $\kappa_L(r)$ from the diffusivity spectrum, we solve equation \ref{eq:M_L}) ) for the fastest growing eigenmode."1146 We find Ay=0.017I. Ao=0.2576 aud Ax=1.3053.," We find $\lambda_{1}=0.0174$, $\lambda_{2}=0.2576$ and $\lambda_{3}=1.3053$."1147 The Ixazautsev maguetic spectra are shown by the cashed lines in Figure 3. (Case 1) aud the left-Iaud panels of Figure { (Case 2) aud Figure 5. (Case 3)., The Kazantsev magnetic spectra are shown by the dashed lines in Figure \ref{fig:mag_spec_1} (Case 1) and the left-hand panels of Figure \ref{fig:mag_spec_2} (Case 2) and Figure \ref{fig:mag_spec_3} (Case 3).1148 As expected. tlie agreemer| between the iuuerical simula10is and Ixazantsev results is good for Case 1.," As expected, the agreement between the numerical simulations and Kazantsev results is good for Case 1."1149 The egrowth rates agree[we within the error bounds auc ile spectra peak at approximately the same wavenumber., The growth rates agree within the error bounds and the spectra peak at approximately the same wavenumber.1150 Howeve much less cai be said for cases 2 aud 3.," However, much less can be said for cases 2 and 3."1151 The erowtl rates disagree by [actors of approximately 11 (Case 2 aud 5 (Case 3) αιd tlie peak in the lxazantsev inagnetic euergy spectra are shifted towads larger waveiuubers (smaller scales) by factors of approximately 2.6b (Case 2) and 2.7 (Case 3)., The growth rates disagree by factors of approximately $11$ (Case 2) and $5$ (Case 3) and the peak in the Kazantsev magnetic energy spectra are shifted towards larger wavenumbers (smaller scales) by factors of approximately 2.6 (Case 2) and 2.7 (Case 3).1152 \Vliat is striking however Is tiat the shape of the spectra are similar., What is striking however is that the shape of the spectra are similar.1153 Iudeed. it appears as though tje ]xazantsev sj)ectrunmb COUd be matched to that of the numerical simulations by a simple trauslalion.," Indeed, it appears as though the Kazantsev spectrum could be matched to that of the numerical simulations by a simple translation."1154 In an attempt to cletermine a possible reasou [or tle apparent translation. we proceed to investigate the sensitivity of the Ixazautsev dyuaimo to tlie energy containiug scales of the velocity," In an attempt to determine a possible reason for the apparent translation, we proceed to investigate the sensitivity of the Kazantsev dynamo to the energy containing scales of the velocity"1155Ilieh resolution observations of wari absorbers have resulted in beautiful spectra.,High resolution observations of warm absorbers have resulted in beautiful spectra.1156 Iloxves«y. they have not vet eiveu us additional insight iuto the properties/ kinematics of the absorber.," However, they have not yet given us additional insight into the properties/ kinematics of the absorber."1157 This is because most of the absorption line spectra have low signal to noise ratio (S/N): the measured absorption line equivalent widths are uucertaiu to £L06. laveer than those from scusitive ASCA observations.," This is because most of the absorption line spectra have low signal to noise ratio (S/N): the measured absorption line equivalent widths are uncertain to $\pm 40\%$, larger than those from sensitive ASCA observations."1158 Hieh resolution spectra should be viewed more as a proof of concept than diagnostic tools., High resolution spectra should be viewed more as a proof of concept than diagnostic tools.1159 Moreover. iiost of the modeling efforts are preliminary.," Moreover, most of the modeling efforts are preliminary."1160 So interpretations should be iule with caution. especially if the results are unexpected.," So interpretations should be made with caution, especially if the results are unexpected."1161 Ouly when we obtain well constrained piriuueters can we hope to build and test models of AGN structre and physics., Only when we obtain well constrained parameters can we hope to build and test models of AGN structure and physics.1162 One such effort is lead by Tan Ceorge and Mike Crceushaw in obtamune nmultmweaveleugth. high S/N spectra of a nearby Sevfert galaxy with a warn absorber.," One such effort is lead by Ian George and Mike Crenshaw in obtaining multiwavelength, high S/N spectra of a nearby Seyfert galaxy with a warm absorber."1163 Our team has observed NGC 3783 with WETC/ACTIS-S for 900. scS with IIST/STIS for 31 orbits and also with FUSE aud NTE.," Our team has observed NGC 3783 with HETG/ACIS-S for 900 ksec, with HST/STIS for 34 orbits and also with FUSE and XTE."1164 These observations wave resulted in one of the best high resolution spectra of ACNS (fieure 5)., These observations have resulted in one of the best high resolution spectra of AGNs (figure 5).1165" Modeling efforts are under way (Netzerανν, in preparation)."," Modeling efforts are under way (Netzer, in preparation)."1166 Within next vear or so. we will know whether or not our view of the nuclear region of AGNs ects alered dramatically.," Within next year or so, we will know whether or not our view of the nuclear region of AGNs gets altered dramatically."1167 Because of space limitations. I could uot cover the subject fully.," Because of space limitations, I could not cover the subject fully."1168" Iuterested readers are referred to conference proceedings: ""Mass Ejection from ACN” aud ""Mass Outflow in Active Galactic Nuclei: New Perspectives”."," Interested readers are referred to conference proceedings: “Mass Ejection from AGN” and “Mass Outflow in Active Galactic Nuclei: New Perspectives""."1169" I thank the organizers of the mecting for inviting me to eive a review talk on wari absorbers in ACNs,", I thank the organizers of the meeting for inviting me to give a review talk on warm absorbers in AGNs.1170 This has been a very nice meeting aud it is always wonderful to be back home., This has been a very nice meeting and it is always wonderful to be back home.1171" Baheall. JN. 1993. ÀpJS. 87. 1 Crenshaw. M. 1997 in ""Mass Ejection from AGUNT. Ed: N. Arav. L. Slilos man. BR. Wevmann [ASP Conf."," Bahcall, J.N. 1993, ApJS, 87, 1 Crenshaw, M. 1997 in “Mass Ejection from AGN”, Ed: N. Arav, I., Shlos man, R. Weymann [ASP Conf."1172 Series Vol., Series Vol.1173 125] Elvis. M. 2010. ApJ. 515. 63 Fiore. F.. Elvis. M.. Math. S.. Wilkes. D.. McDowell J. 1993. ApJ. 115. 129 George. Lo 2000. ApJ. 531. 52 IIalpern. J. 1982. Ph.D. Thesis. Warvarcd University.," 128] Elvis, M. 2000, ApJ, 545, 63 Fiore, F., Elvis, M., Mathur, S., Wilkes, B., McDowell J. 1993, ApJ, 415, 129 George, I. 2000, ApJ, 531, 52 Halpern, J. 1982, Ph.D. Thesis, Harvard University."1174" Kaastra. J. 2000. AA νο,"," Kaastra, J. 2000, A Lett.,"1175 351. 83 Ikas]X. S. 2002. ApJ. subinitted ]xiss. Ge. 20HN. dn “Probing the Physics of Active Galactic Nuclei”. Ed: BAL Peterson. RAV. Posee. aid R.S. Polidan. [," 354, 83 Kaspi, S. 2002, ApJ, submitted Kriss, G. 2001, in “Probing the Physics of Active Galactic Nuclei”, Ed: B.M. Peterson, R.W. Pogge, and R.S. Polidan. ["1176San Francisco: ASP (vol 221)| Irolik. J. EIxiss. Ci. 1995. ApJ. LL7. 512 Masnoto. CL. Leighlv. IKK. Marshall. IH. 2001. in “X-ray Einission from Accretiou onto Dlack Ποes. Eds: T. Yacooh.,"San Francisco: ASP (vol 224)] Krolik, J, Kriss, G. 1995, ApJ, 447, 512 Mastumoto, C., Leighly, K. Marshall, H. 2001, in “X-ray Emission from Accretion onto Black Holes”, Eds: T. Yaqoob."1177" iu. S.. Wilkes. D.. Elvis. M. Ficπο, EF. 1991. ΑΡ. 131. 193 jur. S.. Elvis. M. Wilkes. D. 1995 ApJ. 152. 230 iur. S. 1997 in 7ass Ejection frou AGN”. Ed: N. Aray. L. Shlos mam. vinann [ASP Conf."," Mathur, S., Wilkes, B., Elvis, M. Fiore, F. 1994, ApJ, 434, 493 Mathur, S., Elvis, M. Wilkes, B. 1995 ApJ, 452, 230 Mathur, S. 1997 in “Mass Ejection from AGN”, Ed: N. Arav, I., Shlos man, R. Weymann [ASP Conf."1178 Series Vol., Series Vol.1179 128] iur. S. 2001. in “The Ilhieh Enerev Universe at Sharp Focus: Cliuidra Svinposium. Ed: E. Schοσο] aud S. Vitiek [ASP Conf.," 128] Mathur, S. 2001, in “The High Energy Universe at Sharp Focus: Chandra Symposium"", Ed: E. Schlegel and S. Vrtilek [ASP Conf."1180 Series], Series]1181and none with smaller £-). so that where Nor ix the total ummber of objects in the sample.,"and none with smaller $F_\gamma$ ), so that where $N_{\rm tot}$ is the total number of objects in the sample."1182 However. this is not the SID pr(o)that euters Eq. 8..," However, this is not the SID $p_L(\alpha)$that enters Eq. \ref{theone}."1183 The latter is defined by Eq. (1)), The latter is defined by Eq. \ref{fe}) )1184 aud is the distribution of spectral iudices for blazars iu à Iunuinositv interval between L- and L.|dL.., and is the distribution of spectral indices for blazars in a luminosity interval between $L_\gamma$ and $L_\gamma+dL_\gamma$.1185 A flux-limited sample will be biased toward harder spectral indices than a fixed eamuna-rav luminosity interval. because not all blazars with the same £. have the same flux: harder blazars have higher fiuxes in the band and are more easy to detect.," A flux-limited sample will be biased toward harder spectral indices than a fixed gamma-ray luminosity interval, because not all blazars with the same $L_\gamma$ have the same flux: harder blazars have higher fluxes in the high-energy band and are more easy to detect."1186 A relation can be derived between pla} and prtao). starting from a relation between d?N/4F.da aud ΜΗ”... L. is proportional to Εν inultiplied by a function of : aud à (see Eq. BD1)).," A relation can be derived between $\hat{p}(\alpha)$ and $p_L(\alpha)$, starting from a relation between $d^2N/dF_\gamma d\alpha$ and $d^3N/dL_\gamma dV_{\rm com} d\alpha$: $L_\gamma$ is proportional to $F_\gamma$ multiplied by a function of $z$ and $\alpha$ (see Eq. \ref{lfrelation}) )."1187 In addition. in writing Eq. CL)).," In addition, in writing Eq. \ref{fe}) ),"1188 we lave asstuned that à is independent of £L. aud +., we have assumed that $\alpha$ is independent of $L_\gamma$ and $z$.1189 Thus. we obtain snce Eq. CÀ3))," Thus, we obtain since Eq. \ref{step2}) )"1190 combined with Eqs. (A2)), combined with Eqs. \ref{step1}) )1191 aud (1)). ¢ives Substituting iuto Eq. CÀT))," and \ref{fe}) ), gives Substituting into Eq. \ref{a1}) )"1192 we obtain where the last equality gives the definition of tho sample correction bias Af(a): the normalization. τον is obtained by requiring that pr(a) integrates to 1.," we obtain where the last equality gives the definition of the sample correction bias $\hat{M}(\alpha)$; the normalization, $N_{\rm tot}$, is obtained by requiring that $p_L(\alpha)$ integrates to 1."1193" The isotropic gamuna-ray luninosity of a blazar at some fiducial rest-frame energy. £y (the energy cuutted iu pliotous of energy. £y per uiuit time. assuming that the blazar eiits isotropically). is related to its iuteerated photon flux. F- (the nuuber of photous euütted iu energies abovevy frame energy E, por unit time per unit area). through where dg ds the huninosity distance. aud we have asstmed that the blazar las a singlepower-law energy. spectrum GEN.dE.XE. 7)."," The isotropic gamma-ray luminosity of a blazar at some fiducial rest-frame energy, $E_f$ (the energy emitted in photons of energy $E_f$ per unit time, assuming that the blazar emits isotropically), is related to its integrated photon flux, $F_\gamma$ (the number of photons emitted in energies above frame energy $E_f$ per unit time per unit area), through where $d_L$ is the luminosity distance, and we have assumed that the blazar has a single–power-law energy spectrum $dN_{\gamma}/dE_{\gamma} \propto E_{\gamma}^{-\alpha}$ )."1194 Tu turn. the differeutial sugle-blazar flux. FijiτςEo) (ΠΟΥ of photous per uut energy per unit time per uut area eitted at observer-fraime cuerey. £g). is velated to F. through Having assumed a power-law spectra. FL becomes Substituting the above into the equation for L. aud solving for Puy τε). we get Thus. neglecting absorption. Fiji4(E9) is given by," In turn, the differential single-blazar flux, $F_{\rm ph,1}(E_0)$ (number of photons per unit energy per unit time per unit area emitted at observer-frame energy, $E_0$ ), is related to $F_\gamma$ through Having assumed a power-law spectrum, $F_{\gamma}$ becomes Substituting the above into the equation for $L_{\gamma}$ and solving for $F_{\rm ph,1}(E_f)$ , we get Thus, neglecting absorption, $F_{\rm ph,1}(E_0)$ is given by"1195the limited angular momeutum budget combined with relatively rapid horizoual branch rotation sets stringent limits ou the post-inaiu sequence angilar momentum evolution.,the limited angular momentum budget combined with relatively rapid horizontal branch rotation sets stringent limits on the post-main sequence angular momentum evolution.1196 Tlere are some otter interesting possibilities that should be mentionect., There are some other interesting possibilities that should be mentioned.1197" First. there is the possibility hat maiLL sequeice stars could contain rapiον rotating co""es."," First, there is the possibility that main sequence stars could contain rapidly rotating cores."1198 Even the most recen helioseisimic in1versiolis do not rue out rapid rotation in the deep solar iuteriOr. although they also |srovidle no supyort for the existeice of rotation rapid euoieh toc ontributea large amount ol anglar momenttu," Even the most recent helioseismic inversions do not rule out rapid rotation in the deep solar interior, although they also provide no support for the existence of rotation rapid enough to contribute a large amount of angular momentum."1199 il sonne Wail sedquenuce stars retain rapidly rotating cores. he most likely possibiiy is therefore that a rsuige of iuerual rotation rates survives in stars to late ages: In. this case the internal LOlatiol of tlje Sul would simjy be one of a range of possibilitieS.," If some main sequence stars retain rapidly rotating cores, the most likely possibility is therefore that a range of internal rotation rates survives in stars to late ages; in this case the internal rotation of the Sun would simply be one of a range of possibilities."1200" Tlis is possidle if 5ars have a rauge of overal inagnetic fied morphologies. with the Sun being closer to a fieda tla strougly couples the raciative core aud couvective envelope aud the progeuiOs of he rapidls “rotating horizor1al branch sta""p οσον beiig stars with weak coupling."," This is possible if stars have a range of overall magnetic field morphologies, with the Sun being closer to a field that strongly couples the radiative core and convective envelope and the progenitors of the rapidly rotating horizontal branch stars presumably being stars with weak coupling."

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