ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 Seeing couditious varied from 0.5 to 0.6 arcsec between suele exposures. with an average airniass of 1.06.," Seeing conditions varied from 0.5 to 0.6 arcsec between single exposures, with an average airmass of 1.06."3 Data reduction las been performed in Carching bv ↕⋯∖∐∐⋈∖↥⋅↴∖↴∪↕≯∏∐∖⊏≋↻≋∖⊽↑↸∖, Data reduction has been performed in Garching by members of the ESO SV team.4⋜⋯↕∙↕⋟⋜∐⋅↑↕↸⊳∏↕⋜∐⋅↸⊳⋜∐⋅↸∖↖↖↽⋜↧↴∖↴∏↴∖↴↸∖≼↧ for the basic reduction steps since the CCD suffered for color dependent blemishes. with the largest one located practically at the ceuter.," Particular care was used for the basic reduction steps since the CCD suffered for color dependent blemishes, with the largest one located practically at the center."5 Variations in the CCD sensitivity caused by dust erains were also noted by coluparing flat field nuages taken iu different nights, Variations in the CCD sensitivity caused by dust grains were also noted by comparing flat field images taken in different nights.6 All these problems made dathelding werv tricky and requested a non-stancdad mrocedure., All these problems made flatfielding very tricky and requested a non-standard procedure.7 Data were thus flatiiclded using flats obtained directle from the sky by inediau-combining several science exposures taken im different niehts., Data were thus flatfielded using flats obtained directly from the sky by median-combining several science exposures taken in different nights.8 The use of these lead finally to a flatfieldine accuracy for wide-baud filters down to I much higher than achievable either with dome or twilight fats.," The use of these lead finally to a flatfielding accuracy for wide-band filters down to $1\%$, much higher than achievable either with dome or twilight flats."9 Bias frames were obtained nearly every dav and show no noticeable structure or changes with iue., Bias frames were obtained nearly every day and show no noticeable structure or changes with time.10 Bias subtraction and flatfielding were porfonnued usus the ΠΑΕ package., Bias subtraction and flatfielding were performed using the IRAF package.11 huages were then corrected for the CCD dithering and combined using he IRAF tasks audincombine., Images were then corrected for the CCD dithering and combined using the IRAF tasks and.12 Photometric calibrations have been performed by imaging the staudard star PO1633009 from a Landolt field., Photometric calibrations have been performed by imaging the standard star PG1633+099 from a Landolt field.13 The zero-poiut was computed applving the IRAF photometry packagedigiphot. with a final accuracy of 0.03 inagnuitudes.," The zero-point was computed applying the IRAF photometry package, with a final accuracy of 0.03 magnitudes."14 Astrometry on the image has been performed using as a reference the coordinates of a few field stars extracted from the USNO catalogue using the ESO Skycat tool., Astrometry on the image has been performed using as a reference the coordinates of a few field stars extracted from the USNO catalogue using the ESO Skycat tool.15 The pixel-to-sky coordinates transformation has been thus computed using the UN STARLINK software ASTROM (Wallace. 1990). leadius to a final accuracy of &0.5 arcsec on our absolute astrometry after takiug in the consideration both the raus.," The pixel-to-sky coordinates transformation has been thus computed using the UK STARLINK software ASTROM (Wallace, 1990), leading to a final accuracy of $\simeq 0.5$ arcsec on our absolute astrometry after taking in the consideration both the r.m.s."16 of the astrometric fit (+0.3 aresec] and the average uncertainty on the USNO coordinates (270.25 arcsec)., of the astrometric fit $(\simeq 0.3$ arcsec) and the average uncertainty on the USNO coordinates $(\simeq 0.25$ arcsec).17 The most recent radio position of Ll. also reported in Tab.2 of the paper of Chakrabarty Kaspi," The most recent radio position of $-$ 44, also reported in Tab.2 of the paper of Chakrabarty Kaspi"18"Jandthe —module Jaregivenbyto ZT El= Furthermore, let r:=00)..(4.1) A grading function is defined by delta((Z!):= and thus, Define for any AA:— Here is a graded vector space according to 17 and denotes the set of all formal sums T;),where and[10&,.","and the -module are given by Z^m_n E^l_k:=. Furthermore, let r:=. A grading function is defined by (Z^l_k):= and thus, Define for any A:= Here is a graded vector space according to \cite{GazorYuFormal,GazorYuSpec} and denotes the set of all formal sums where and."19". The action of on Jisgivenby((S, for any ((S,T) and We first remove the linear part from the system with a linear change of state variable5."," The action of on is given by for any (S, and We first remove the linear part from the system with a linear change of state variable."20"3.6].. Therefore, we may assume Since d??(0,Z1)= d??(0,Z9) —(,—,89* both terms of and are eliminated from the second level extended partial orbital normal form, = 8*P* Now let min{kk|, 00, (In case is not finite, an arbitrary choice for trivially completes the proof.)"," Therefore, we may assume Since (0,Z^1_1)= (0,Z^0_1) ^0_1) both terms of and are eliminated from the second level extended partial orbital normal form, = ^0_k Now let k| 0, (In case is not finite, an arbitrary choice for trivially completes the proof.)"21" Denote = ((0,...,,0,ZB,m where the number of zeros is 22k--times for1."," Denote := ,0, Z^0_m, where the number of zeros is -times for."22". Then, = ((0,0, 20, Επι) pr(4.2)dimer)=z—Lm-—1PER for any By Theorem there exist transformations that send the vector field into the infinite level orbital normal form πο Μο... For any 1, there exists a nonzero state solution JandatimesolutionTT )suchthat((T, S)*u=—Zlu."," Then, = (0,0, Z^0_m, ^0_r }, for any By Theorem \ref{LNF} there exist transformations that send the vector field into the infinite level orbital normal form ^0_r for some 2, ^0_1, For any 1, there exists a nonzero state solution and a time solution such that (T, S)*u=-Z^l_ku."23" Therefore, the symmetry group for is not finitely generated."," Therefore, the symmetry group for is not finitely generated."24 Now the linear change of state variable )inEquation(4.2) )isobtained., Now the linear change of state variable in Equation \ref{inftONF}) ) is obtained.25T hecompositionofthismapwiththesymmetrygroupassociatedwithuu results in a symmetry group for The rest of the proof follows Theorem ∙, The composition of this map with the symmetry group associated with results in a symmetry group for The rest of the proof follows Theorem \ref{SNF}. .26Iu the following models of several extragalactic SSC aud ΑΠΟΤΟ sources are discussed.,In the following models of several extragalactic SSC and CMB-IC sources are discussed.27 The exact definitions of the model parameters can be found in the Appendix., The exact definitions of the model parameters can be found in the Appendix.28 We eive lints on the detectability of theses sources by the iustruineuts listed iu Tab., We give hints on the detectability of theses sources by the instruments listed in Tab.29 d. based on rough detection sienificance estimates as described in Sect. 3..," \ref{tab:sensitivity}30 based on rough detection significance estimates as described in Sect. \ref{sec:newinstruments}."31" Our high huuinositv radio galaxy is assuned to have spherical lobes with a diameter of LO kpc. ae ainagnctic field strength of 35 pC. The clectrou population is a single power-law with spectral iudex of s= 2.1. which extends frou py=10 to po=3105 aud which is normalized by C=6.63-10temὉ, "," Our high luminosity radio galaxy is assumed to have spherical lobes with a diameter of 40 kpc, and a magnetic field strength of 35 $\mu$ G. The electron population is a single power-law with spectral index of $s = 2.4$ , which extends from $p_{1} = 10$ to $p_{2} =323\,\cdot 10^4$ and which is normalized by $C = 6.63\cdot10^{-4}\, {\rm33cm}^{-3}$."34This corresponds to an cherey content iu relativistic electronsof 19-1p? cre and in maenetic fields of L8:1077 ere., This corresponds to an energy content in relativistic electronsof $4.9\cdot 10^{59}$ erg and in magnetic fields of $4.8\cdot 10^{58}$ erg.35 The energy ratio of electronic to magnetic euergv is LO. aud therefore by onlv a factor of a few above what racio-astronomers call equipartition. for which the energy of clectrous racliating above LO MIIz equals that of the magnetic fields.," The energy ratio of electronic to magnetic energy is 10, and therefore by only a factor of a few above what radio-astronomers call equipartition, for which the energy of electrons radiating above 10 MHz equals that of the magnetic fields."36 The Iuuinositv at 1 GIIz is 3.9-10°ore/TIz/s.," The luminosity at 1 GHz is $3.9\cdot10^{34}\,{\rm37erg/Hz/s}$."38 τος A. for exaluple. has a flux of 211 Jv at 5 GIIz (Stull.1971).. as two of our model cocoons if they are placed at the Iuimuinositv distance of 265 Mpc. similar to that of Cveuus A for Hy=ODkan/s/AIpe and gy=0.5 (Owenetal.1997.forthe redshift)...," Cygnus A, for example, has a flux of 214 Jy at 8 GHz \cite{1971AJ.....76....1S}, as two of our model cocoons if they are placed at the luminosity distance of 265 Mpc, similar to that of Cygnus A for $H_0 = 65\,{\rm km/s/Mpc}$ and $q_0 = 0.5$ \cite[for the39redshift]{1997ApJ...488L..15O}."40 The svuchrotrou aud SSC ceutra surface brightuess of our radio cocoons are shown in Fie. 0.., The synchrotron and SSC central surface brightness of our radio cocoons are shown in Fig. \ref{fig:CygAexp}.41 Iu this figure possible later stages in the evolution of the radio source. after the supplv with fresh electrons was shut down. are also shown.," In this figure possible later stages in the evolution of the radio source, after the supply with fresh electrons was shut down, are also shown."42 In order to model these stages we asstuue that the radio cocoons will expat adiabatically while they vise buovautlv in the cluster atmosphere (Clurazovetal.2001:Briigecu&Ixaiscr. 2001)..," In order to model these stages we assume that the radio cocoons will expand adiabatically while they rise buoyantly in the cluster atmosphere \cite{2001ApJ...554..261C,2001MNRAS.325..676B}."43 Iu our illustrating example we assume that the jet supply of fresh radio plasima shuts down at the preseut evolutionary stage of Cyeguus A. The two radio cocoons are assuned to expand with hb=3/2 aud ty=75 Myr (see Eq. A3))., In our illustrating example we assume that the jet supply of fresh radio plasma shuts down at the present evolutionary stage of Cygnus A. The two radio cocoons are assumed to expand with $b = 3/2$ and $t_0= 75$ Myr (see Eq. \ref{eq:expansion}) ).44" This should serve as a rough model for a rise with half sonic velocity in a sineular isothermal cluster atmosphere (cluster density * cluster 3], ", This should serve as a rough model for a rise with half sonic velocity in a singular isothermal cluster atmosphere (cluster density $\propto$ cluster $^{-2}$ ).45We note that he evolution of the electron spectra is not corrected. or the reduced svuchrotron cooling at self absorbed frequencies., We note that the evolution of the electron spectra is not corrected for the reduced synchrotron cooling at self absorbed frequencies.46 An investigation of this more complicated problem was doue by Rees (1967) ]t is obvious. that a radio cocoon of a powerful. conipact radio galaxy produces a detectable SSC flux for a long time after the the svuchrotrou radio emission vanished from the radio observable frequency band.," An investigation of this more complicated problem was done by Rees \cite*{1967MNRAS.136..279R}47 It is obvious, that a radio cocoon of a powerful, compact radio galaxy produces a detectable SSC flux for a long time after the the synchrotron radio emission vanished from the radio observable frequency band."48 At low radio frequencies the SSC fux remains even for a few Cor. due to the slow cuerev losses by sclfabsorbed svuchrotrou chussion.," At low radio frequencies the SSC flux remains even for a few Gyr, due to the slow energy losses by self-absorbed synchrotron emission."49 But adiabatic losses due the expansion of the source are able to reduce the SSC fiux substautiallv., But adiabatic losses due the expansion of the source are able to reduce the SSC flux substantially.50 The typical angular area is of the order of arcani., The typical angular area is of the order of $^2$.51 Therefore all of the instruments listed in Tab., Therefore all of the instruments listed in Tab.52 1. should be able to detect a Cyeuus-Á like radio cocoon., \ref{tab:sensitivity} should be able to detect a Cygnus-A like radio cocoon.53 All but LOFAR aud CAIRT see it best shortly after he decay of the svuchrotron emission., All but LOFAR and GMRT see it best shortly after the decay of the synchrotron emission.54 The latter is because at below CGIIz frequencies the source clission is risiue with time during the first few 100 Myr., The latter is because at below GHz frequencies the source emission is rising with time during the first few 100 Myr.55 PLANCTS and HERSCTIEL should eive oulv relative week detection of carly stages., PLANCK and HERSCHEL should give only relative week detection of early stages.56" Iowever. if such a very powerful radio ghost would be much: closer. e.g. located iu the Virgo cluster. even later PAages may be detectable with these ιβαποτς,"," However, if such a very powerful radio ghost would be much closer, e.g. located in the Virgo cluster, even later stages may be detectable with these instruments."57 GPS are believed to be the τον carly stage of radio ealaxies. im which a small (< kpc) radio cocoon is working its wav through the dense interstellar medimu of a radioealaxy (Suellenetal.2000:DeZottiab.2000.and therem)..," GPS are believed to be the very early stage of radio galaxies, in which a small $<$ kpc) radio cocoon is working its way through the dense interstellar medium of a radiogalaxy \cite[and references58therein]{2000MNRAS.319..445S,2000A&A...354..467D}. ."59 The spectral peak at typically a CIIz is likely due to svuchrotron-solf-absorptiou at lower frequencies., The spectral peak at typically a GHz is likely due to synchrotron-self-absorption at lower frequencies.60 Although it turns out that SSC emission, Although it turns out that SSC emission61Solar flare iupuldve clectrou events present an alternative to the more traditional hard N-ray diagnostics of poorly understood acceleration and transport of solar cuereetic electrons.,Solar flare impulsive electron events present an alternative to the more traditional hard X-ray diagnostics of poorly understood acceleration and transport of solar energetic electrons.62 While hard X-rav observations provide insight mto energetic electrous ij the lower deuse solar atinosphere (es.—777). nupulsive solar olectrou eveuts (e.g.77) provide crucial information about escapiug electrons from the acceleration region.," While hard X-ray observations provide insight into energetic electrons in the lower dense solar atmosphere \citep[e.g.][]{Arnoldy_etal1968,DennisSchwartz1989,BrownKontar05}, impulsive solar electron events \citep[e.g.][]{Lin1985,Krucker_etal07} provide crucial information about escaping electrons from the acceleration region."63 Because of the rather Buited spatial resolution of past and current hard X-ray. observatious. even the spatially resolved lard ταν spectrum of energetic electrons with RITESSI(c.g.2) electronisa convolution of transport effects aud possibly acceleration (?)..," Because of the rather limited spatial resolution of past and current hard X-ray observations, even the spatially resolved hard X-ray spectrum of energetic electrons with RHESSI \citep[e.g.][]{Emslie_etal2003} is a convolution of transport effects and possibly electron acceleration \citep{Brown_etal2009}."64" Ποσο, de-convolution of the electron accelerated spectrum aud accelerator properties from hard N-ravs is a non-trivial task using both forwarcd-anodelling (?7?) and modoel-àiudepeudenut techniques (??).."," Hence, de-convolution of the electron accelerated spectrum and accelerator properties from hard X-rays \citep{Brown_etal2006} is a non-trivial task using both forward-modelling \citep{Holman_etal2003,Kasparova_etal2005} and model-independent techniques \citep{Piana_etal2003,Kontar_etal2005}."65 Solar electron iupulsve events propagate outward through the aliiost collisionless plasina of the solar corona and solar wind (?).., Solar electron impulsive events propagate outward through the almost collisionless plasma of the solar corona and solar wind \citep{Lin1985}.66 Even with this collixiouless regie the energetic electrous cau interact with plasma via generation aud isorption of electrostatic plasima waves., Even with this collisionless regime the energetic electrons can interact with plasma via generation and absorption of electrostatic plasma waves.67 Iu the standard scenario (?).. the non-linear interaction of beam-driven plasma waves leads to the appearance of rather strong radio enüsson - type 1 solar/iuterplauctary radio bursts.," In the standard scenario \citep{GinzburgZhelezniakov1958}, the non-linear interaction of beam-driven plasma waves leads to the appearance of rather strong radio emission - type III solar/interplanetary radio bursts."68 The observatious of type III solar bursts aud energetic particles (2777). as well as theoretical (2???) iid nuncerical investieatious (2°222222?) provide strong support to the standard type ITE model.," The observations of type III solar bursts and energetic particles \citep{Linetal1981,Ergun_etal98,Gosling_etal2003,Krucker_etal07} as well as theoretical \citep{ZheleznyakovZaitsev1970,Zaitsev_etal72,Melnik1995} and numerical investigations \citep{MagelssenSmith1977,Grognard1982,Kontar_etal1998,Yoon_etal2000,Kontar2001_a,Li_etal2006a,Ledenev04,Krasnoselskikh_etal2007} provide strong support to the standard type III model."69 The plaua of the solar corona aud the solar wind is a ποπο turbulent medium with density perturbations at various leugth scales., The plasma of the solar corona and the solar wind is a non-uniform turbulent medium with density perturbations at various length scales.70 The structure of the solar wind density fluctuations have been analyses using sciutillatious of siaLsize radio sources (6.8.TT). ," The structure of the solar wind density fluctuations have been analysed using scintillations of small-size radio sources \citep[e.g.][]{Hollweg1970,Young1971}. ."71Iu-situ measurements have :uso been used to determine the deusitv spectrum near 1e Earth aud between 0.3 ane LAU withMelos (2).., In-situ measurements have also been used to determine the density spectrum near the Earth and between $0.3$ and $1$ AU with \citep{MarschTu1990}.72 While the detailed structre of the density turbulence iu the àmer lieliosplere is not wel established. the density fluctuation spectrum rear the Earth seciis close to a power-law spectrum with spectra index about 5/3. sinular to earlier observations.," While the detailed structure of the density turbulence in the inner heliosphere is not well established, the density fluctuation spectrum near the Earth seems close to a power-law spectrum with spectral index about $5/3$, similar to earlier observations."73 It has been recognized {7T) that beanicdriven Langulr Waves cal be effectively altered by even weak density eradicuts.," It has been recognized \citep{Ryutov1969,KarpmanIstomin1974} that beam-driven Langmuir waves can be effectively altered by even weak density gradients."74 Therefore the effect of density fluctuations ο1 beali-driven plasma waves responsible for type III radio bursts has been considered both uuuercallv. arc analytically (0?7)..," Therefore the effect of density fluctuations on beam-driven plasma waves responsible for type III radio bursts has been considered both numerically and analytically \citep{Melroseetal1986,Robinsonetal1992,Kontar2001_solphys}."75" Density fluctuations are believed. to SUppress plasma wave growth (77) aud|IC τοspousidle for 1C chuupy plasiua. wave distrinition observec ""msiti near the Earth(?7).."," Density fluctuations are believed to suppress plasma wave growth \citep{SmithSime1979,Muschiettietal1985} and be responsible for the clumpy plasma wave distribution observed in-situ near the Earth \citep{Gurnettetal1978,Linetal1981}."76 The fluctuations. whils changing 1C distribution of plasma waves significantly. ive a rather weak modulation effect on t10 lustantancous «istribution of electrous. (?)..," The fluctuations, whilst changing the distribution of plasma waves significantly, have a rather weak modulation effect on the instantaneous distribution of electrons \citep{Kontar2001_a}."77 Receutly. ? have shown that 1C electron beam plasma interaction via Laugniuir waves in the non-uniform solar corona leacs to he appeara1ος of a break energy in t16 obscved spectruu a the Earth and can explain the oISCTVCL Lappareut carlyinjection of ow-enerev electrons.," Recently, \citet{KontarReid2009} have shown that the electron beam plasma interaction via Langmuir waves in the non-uniform solar corona leads to the appearance of a break energy in the observed spectrum at the Earth and can explain the observed apparent early injection of low-energy electrons."78 Towever. the net effec of deusitv fluctuations in the solar wind on the electro) spectrin detected near 1 AU has not been addressed before.," However, the net effect of density fluctuations in the solar wind on the electron spectrum detected near 1 AU has not been addressed before."79 Iu this paper. we investigate the effects of ckerounud ράσα deusitv Πιοuation ou the generation ancl absorption of plasma waves from a high ejergw solar electron. beam travelling fixnu the Sun to the Earth.," In this paper, we investigate the effects of background plasma density fluctuation on the generation and absorption of plasma waves from a high energy solar electron beam travelling from the Sun to the Earth."80 We demoustrate the ccpendence of plasina waves on the evelof deusitv fluctuations. with hieh levels dampine εινα waves too much to be πι accordance wih detected ype II radio ciission.," We demonstrate the dependence of plasma waves on the levelof density fluctuations, with high levels damping plasma waves too much to be in accordance with detected type III radio emission."81 We also show how he level of, We also show how the level of82the flux calibration we extracted a 1-D spectrum of the standare star to find the calibration function: then we extracted a set of I-D spectra of the galaxy summing up a number of lines corresponding to the slit width.,the flux calibration we extracted a 1-D spectrum of the standard star to find the calibration function; then we extracted a set of 1-D spectra of the galaxy summing up a number of lines corresponding to the slit width.83" Since the slit width was 2 anc the scale of the instrument was /0.252""pix. we collapsed eight lines to obtain each. 1-D spectrum."," Since the slit width was $2 ''$ and the scale of the instrument was $0.252 ''/pix$, we collapsed eight lines to obtain each 1-D spectrum."84 Finally we applied the flux calibration to this collection of spectra., Finally we applied the flux calibration to this collection of spectra.85 The wavelength and flux-calibrated spectra are shown in Fig., The wavelength and flux-calibrated spectra are shown in Fig.86 4. and Fig. 5.., \ref{spec1} and Fig. \ref{spec2}.87 The fluxes of the above mentioned emission lines were measured using the IRAF routine. that provides an interactive facility to display and analyze spectra.," The fluxes of the above mentioned emission lines were measured using the IRAF routine, that provides an interactive facility to display and analyze spectra."88 We evaluated flux and equivalent width by marking two continuum points around the line to be measured., We evaluated flux and equivalent width by marking two continuum points around the line to be measured.89 The linear continuum ts, The linear continuum is90any of the other bolometer-based LDBs. such as Boomerang (Lange 1997) or NLANINLA. (Richarels 1997) or even HENE-based LDBs. such as BEAST (Lubin 1997) and derived similar error forecasts.,"any of the other bolometer-based LDBs, such as Boomerang (Lange 1997) or MAXIMA (Richards 1997) or even HEMT-based LDBs, such as BEAST (Lubin 1997) and derived similar error forecasts."91 For most parameters the inclusion of prior constraints on their variation have no effect. particularly for a high precision experiment like Planck.," For most parameters the inclusion of prior constraints on their variation have no effect, particularly for a high precision experiment like Planck."92 Even for MAP the inclusion of priors has little impact. except for variables such as Va. which are poorly constrained. [rom the experiment ione.," Even for MAP the inclusion of priors has little impact, except for variables such as $Y_{He}$ which are poorly constrained from the experiment alone."93 I£ the helium abundance is allowed to float. freely. it has a substantial effect on the other parameters: however. limiting its value to be 0.2300.02 results in little impact on the other numbers.," If the helium abundance is allowed to float freely, it has a substantial effect on the other parameters; however, limiting its value to be $0.23 \pm 0.02$ results in little impact on the other numbers."94 For the LDB|DMIEE case. the errors are susbstantially larger with no controlling priors.," For the LDB+DMR case, the errors are susbstantially larger with no controlling priors."95 As expected. the parameters have correlations among rwemsclyes that range from weak to very strong in all models. anc can dilfer from experiment to experiment as well as model to model.," As expected, the parameters have correlations among themselves that range from weak to very strong in all models, and can differ from experiment to experiment as well as model to model."96 The power amplitude: £C1/2p3 oaud τι. have à correlation coellicient about for SCDAL lor Planck and ALAR., The power amplitude $\avrg{{\cal C}_\ell}_B^{1/2}$ and $\tau_C$ have a correlation coefficient about for SCDM for Planck and MAP.97 The most highly. correlated. are oj and wa. as expected from. the anele-cistance near-degeneracy.," The most highly correlated are $\omega_{k}$ and $\omega_{\Lambda}$, as expected from the angle-distance near-degeneracy."98" In the ENTables. the O4h7.2 numbers are. determined.. with. O.h fixed. and the £,h numbers are determined. with OXh fixed: the other 1parameters are relatively insensitive o fixing either. or neither."," In the Tables, the $\Omega_{\Lambda}{\rm h}^2$ numbers are determined with $\Omega_k{\rm99h}^2$ fixed, and the $\Omega_k{\rm h}^2$ numbers are determined with $\Omega_{\Lambda}{\rm h}^2$ fixed; the other parameters are relatively insensitive to fixing either, or neither."100 Thus. although. our. estimates of errors after. mareinalization are gratifvinglv small for many parameters. especially for the specifications of Planck. hey are large in other cases δν].," Thus, although our estimates of errors after marginalization are gratifyingly small for many parameters, especially for the specifications of Planck, they are large in other cases $\delta \Omega_{\Lambda}{\rm101h}^2$ )."102 Error estimates in square brackets are those obtained when the most correlated component for that. variable is constrained. to of the target value., Error estimates in square brackets are those obtained when the most correlated component for that variable is constrained to be the target value.103 A more natural way to deal with strong correlations between variables is. to perform a xinciple component analysis in parameter space. rank-ordering linear combinations of parameters. as described in Section ??:: some linear combinations are determined exquisitely well and some are less well determined because of near-degeneracies as is illustrated in the Tables.," A more natural way to deal with strong correlations between variables is to perform a principle component analysis in parameter space, rank-ordering linear combinations of parameters, as described in Section \ref{sec:prior}: some linear combinations are determined exquisitely well and some are less well determined because of near-degeneracies as is illustrated in the Tables."104 The Tables also show values obtained in round brackets when positivity constraints on parameters such as 7c: are used., The Tables also show values obtained in round brackets when positivity constraints on parameters such as $\tau_C$ are used.105 The àh/h shown are determined [rom h?=Mw hence it is a derived. rather than fundamental quantity.," The $\delta {\rm h}/ {\rm h}$ shown are determined from ${\rm h}^2 =106\sum_j \omega_j$, hence it is a derived rather than fundamental quantity."107 However. b errors depend upon what is kept fixed and what is varied.," However, ${\rm h}$ errors depend upon what is kept fixed and what is varied."108 Thus we can use h to replace one of d. c. wy. with the other two to be marginalized.," Thus we can use ${\rm h}$ to replace one of $\omega_{m}$, $\omega_{\Lambda}$, $\omega_k$, with the other two to be marginalized."109" In that case. the error estimate would be ób/h=0.50,fh?"," In that case, the error estimate would be $\delta {\rm h}/{\rm h} = 0.5110\delta \omega_j /{\rm h}^2$."111 We find that the estimated. errors on. parameters. are sensitive to their input target-mocdel values., We find that the estimated errors on parameters are sensitive to their input target-model values.112" Table 3. shows results for two other @,=O mocels. a ACDAL model and an LICDAL model."," Table \ref{tab:satparams2} shows results for two other $\Omega_k=0$ models, a $\Lambda$ CDM model and an HCDM model."113 This illustrates the sensitivity of parameter error estimation to relatively modest. changes in the target Cy., This illustrates the sensitivity of parameter error estimation to relatively modest changes in the target ${\rm C}_\ell$.114 In interpreting these tables it is also important to take into account the restrictions that we have imposed on the models., In interpreting these tables it is also important to take into account the restrictions that we have imposed on the models.115 Phe OCDAL model error estimates are derived assuming there is no tensor component., The OCDM model error estimates are derived assuming there is no tensor component.116 Including it has little clleet on the results: even the most correlated. the amplitude. zc: and mi. are only slightly allected.," Including it has little effect on the results: even the most correlated, the amplitude, $\tau_C$ and $n_s$, are only slightly affected."117" Phe angle-distance scaling ensures that the tensor power spectrum does not fall off until hisher £ than in the ο=0 cases. and this leads to a substantial improvement in 07,."," The angle-distance scaling ensures that the tensor power spectrum does not fall off until higher $\ell$ than in the $\Omega_k=0$ cases, and this leads to a substantial improvement in $\delta r_{ts}$."118 We have also found that the errors on rm; and rj; are extremely dependent on the input εν if they are allowed to vary independentIy (ox and TFurner 1994. Ixnox. 1995. Efstathiou 1997).," We have also found that the errors on $ n_t$ and $ r_{ts}$ are extremely dependent on the input $r_{ts}$ if they are allowed to vary independently (Knox and Turner 1994, Knox 1995, Efstathiou 1997)."119" However. hand the various matter densities. &x,5,,etc... are insensitive to the tensor spectrum for reasonable values of ες£;2."," However, ${\rm h}$ and the various matter densities, $\omega_{cdm}$, are insensitive to the tensor spectrum for reasonable values of $r_{ts} \simlt 2$."120 In open universes. features in the power-speetrum shift to larger multipoles according to the angle-distance relation. roughly as (0)σος2 thus. for low Qo. high resolution is required. to determine parameters which allect the Doppler peak structure h ancl the various v).," In open universes, features in the power-spectrum shift to larger multipoles according to the angle-distance relation, roughly as $C(\ell)121\rightarrow C(\ell/\Omega_0^{1/2})$; thus, for low $\Omega_0$, high resolution is required to determine parameters which affect the Doppler peak structure ${\rm h}$ and the various $\omega$ )."122 Phe relative accuracies of the parameters are less sensitive to variations of £2; and bh., The relative accuracies of the parameters are less sensitive to variations of $\Omega_b$ and ${\rm h}$.123 In summary. we have described how το compute the errors in the estimation of cosmological parameters from measurements of the CAIB power spectrum at a number of frequencies with dillerent angular resolutions are sensitivities.," In summary, we have described how to compute the errors in the estimation of cosmological parameters from measurements of the CMB power spectrum at a number of frequencies with different angular resolutions and sensitivities."124 We have also shown how prior information on the values of parameters can be incorporated. into the analysis and. deseribed some of the pitfalls of this type of analysis that can arise if inaccurate cderivatives of the C's are used and if poor parameter choices are adopted., We have also shown how prior information on the values of parameters can be incorporated into the analysis and described some of the pitfalls of this type of analysis that can arise if inaccurate derivatives of the ${\rm C}_\ell$ 's are used and if poor parameter choices are adopted.125 We have applied. our machinery to the MAD ane Planck satellites and find that these missions are capable of determining fundamental cosmological parameters to an accuracy (that far exceeds that from conventiona astronomical techniques., We have applied our machinery to the MAP and Planck satellites and find that these missions are capable of determining fundamental cosmological parameters to an accuracy that far exceeds that from conventional astronomical techniques.126" In particular. Planck is capable of determining the Hubble constant anc the baryon density parameter O, to a precision of a few percent or better for each of the target models listed in Tables 2 and 3.."," In particular, Planck is capable of determining the Hubble constant and the baryon density parameter $\Omega_b$ to a precision of a few percent or better for each of the target models listed in Tables \ref{tab:satparams1} and \ref{tab:satparams2}."127 However. some parameter combinations are poorly determined: by CAB observations alone as described. in Section ?? and Section 3...," However, some parameter combinations are poorly determined by CMB observations alone as described in Section \ref{sec:targetmod} and Section \ref{sec:satparams}."128 Nevertheless. despite this caveat. it is evident from this work that accurate CAIB observations have the potential to revolutionize our knowledge of the kev cosmological parameters describing our Universe.," Nevertheless, despite this caveat, it is evident from this work that accurate CMB observations have the potential to revolutionize our knowledge of the key cosmological parameters describing our Universe."129 We would. like to thank Llovel Knox for. useful discussions., We would like to thank Lloyd Knox for useful discussions.130 JLB was supported by the Canadian Institute for Advanced. Research and. NSERC., JRB was supported by the Canadian Institute for Advanced Research and NSERC.131 GPE acknowledges the award of a PPARC Senior Research Fellowship., GPE acknowledges the award of a PPARC Senior Research Fellowship.132 MT was supported by NASA through a Hubble: Fellowship. 3ELIE-O01084.01-96.X. awareled by the Space Telescope Science Institute. which is operated. by AURA. Inc. uncer NASA contract NAS5-26555.," MT was supported by NASA through a Hubble Fellowship, HF-01084.01-96A, awarded by the Space Telescope Science Institute, which is operated by AURA, Inc. under NASA contract NAS5-26555."133concentrated in between the PAH cations and VSGs.,concentrated in between the PAH cations and VSGs.134 Both the spectra and spatial maps of each signal show high correlation to the results using SpitzerOs IRS-SL mode (??).. allowing us to use these results to verify our conclusions.," Both the spectra and spatial maps of each signal show high correlation to the results using SpitzerÕs IRS-SL mode \citep{Olivier, Olivier10}, allowing us to use these results to verify our conclusions."135 To further explore the origin. of the three resolved signals. we employed the NASA Ames PAH IR Spectroscopic Database.," To further explore the origin of the three resolved signals, we employed the NASA Ames PAH IR Spectroscopic Database."136 The fit shows that the component spectra resolved by BSS could be recreated by an appropriate combinatior of specific classes of PAH spectra from the database., The fit shows that the component spectra resolved by BSS could be recreated by an appropriate combination of specific classes of PAH spectra from the database.137" Then. we used a database to fit an observed spectrum and groupec the individual molecules into charge class. then compared the spectra of the combined charge classes to the BSS extractec PAH™ and PAH"" signals."," Then, we used a database to fit an observed spectrum and grouped the individual molecules into charge class, then compared the spectra of the combined charge classes to the BSS extracted $^+$ and $^0$ signals."138" The components were found to be very similar to the BSS extracted PAH™ and PAH"".", The components were found to be very similar to the BSS extracted $^+$ and $^0$.139 Specific spectral properties are found for each population: By using the BSS method and the PAH Database fit. we arrived at the above conclusions.," Specific spectral properties are found for each population: By using the BSS method and the PAH Database fit, we arrived at the above conclusions."140 Each method has unique yet complementary strengths and weaknesses., Each method has unique yet complementary strengths and weaknesses.141 The BSS method is blind. i.e. has no intrinsic assumptions about the emitting components. however since the statistical properties of the emitting components are unknown. the unmixing is not perfectly efficient.," The BSS method is blind, i.e. has no intrinsic assumptions about the emitting components, however since the statistical properties of the emitting components are unknown, the unmixing is not perfectly efficient."142 Additionally. the BSS method separates 3 mathematically distinct signals. but gives no intuition about the molecular properties of these signals.," Additionally, the BSS method separates 3 mathematically distinct signals, but gives no intuition about the molecular properties of these signals."143 The PAH Database allows for direct physical interpretation of the fit yet is biased towards smaller molecules and lacks spectral information for PAH clusters or other possible carriers of the VSG signal., The PAH Database allows for direct physical interpretation of the fit yet is biased towards smaller molecules and lacks spectral information for PAH clusters or other possible carriers of the VSG signal.144 Although both methods suffer limitations. the strengths of one compensate for the weaknesses of the other.," Although both methods suffer limitations, the strengths of one compensate for the weaknesses of the other."145" Although the database fit may be degenerated in some cases. the interpretation of the y database fit results. in terms of classes. is in agreement with the result of the BSS for PAH and PAH""."," Although the database fit may be degenerated in some cases, the interpretation of the $\chi^2$ database fit results, in terms of classes, is in agreement with the result of the BSS for $^+$ and $^0$."146 The VSG spectrum can only be obtained by BSS. and the database fit of this spectrum provide additional information on the possible chemical nature of this component.," The VSG spectrum can only be obtained by BSS, and the database fit of this spectrum provide additional information on the possible chemical nature of this component."147 Both methods. te. BSS and Database Fitting. are powerful tools. but they be used with an understanding of their limitations (described in details in Appendices A and B).," Both methods, i.e. BSS and Database Fitting, are powerful tools, but they be used with an understanding of their limitations (described in details in Appendices A and B)."148 The efficiency of NMF ts subject to two main limitations: 1) the possible non-unicity of solutions 2) the inaccuracy of the unmixing in the presence of noise., The efficiency of NMF is subject to two main limitations: 1) the possible non-unicity of solutions 2) the inaccuracy of the unmixing in the presence of noise.149 These two problems are the subject of intensive theoretical research in the field of signal processing (see e.g. ? and ?))., These two problems are the subject of intensive theoretical research in the field of signal processing (see e.g. \citealt{donoho} and \citealt{hans}) ).150 If the statistical properties of the source matrix are known. then one can determine whether NMP will function properly.," If the statistical properties of the source matrix are known, then one can determine whether NMF will function properly."151" In a ""real life” case like here however. since the matrix is not knownpriori.. we cannot verify these statistical properties."," In a “real life"" case like here however, since the matrix is not known, we cannot verify these statistical properties."152 We therefore rely on some empirical considerations., We therefore rely on some empirical considerations.153 Procuring the. component. spectra (Figure 3)). the most prominent unmixing artifact is located at 11.0 um and reveals itself with a sharp drop in Signal 3.," Procuring the component spectra (Figure \ref{fig:weightfactors}) ), the most prominent unmixing artifact is located at 11.0 $\mu$ m and reveals itself with a sharp drop in Signal 3."154 Some less discernible artifacts can be found at 11.2 jm as an added peak of Signal 2 (seen in the grey envelope of Figure 3)) and at 12.7um as a dip in intensity of Signal 3. roughly resembling an absorption feature.," Some less discernible artifacts can be found at 11.2 $\mu$ m as an added peak of Signal 2 (seen in the grey envelope of Figure \ref{fig:weightfactors}) ) and at $\mu$ m as a dip in intensity of Signal 3, roughly resembling an absorption feature."155 We suggest that the unmixing artifacts seen in some signals are compensated for by an increase or decrease of intensity. at the same wavelength. in other signals.," We suggest that the unmixing artifacts seen in some signals are compensated for by an increase or decrease of intensity, at the same wavelength, in other signals."156 This is most clearly seen at the 11.0 gam wavelength., This is most clearly seen at the 11.0 $\mu$ m wavelength.157 The sharp drop to 0 of Signal 3 is compensated by the weak satellite feature of Signal |., The sharp drop to 0 of Signal 3 is compensated by the weak satellite feature of Signal 1.158 Similarly. the absorption-type feature seen at 12.7 is compensated by a slightly increased intensity of Signal 2 at 12.7 im. In order to better understand the unmixing efficiency. two tests were conceived:," Similarly, the absorption-type feature seen at 12.7 is compensated by a slightly increased intensity of Signal 2 at 12.7 $\mu$ m. In order to better understand the unmixing efficiency, two tests were conceived:"159both DE and DEDI,both DE and DFDI.160 Ins L.. we compare the RV uncertainties of DE aud DEDI under various conditious.," In \ref{sec:CompDeDFDI}, we compare the RV uncertainties of DE and DFDI under various conditions."161 In 5.. we predict the photou-Iimited performance ofa DEDI-based Doppler instrument iu the NIB aud discuss its potential coutributious to exoplauets search around. M cdewarfs.," In \ref{sec:Performance}, we predict the photon-limited performance of a DFDI-based Doppler instrument in the NIR and discuss its potential contributions to exoplanets search around M dwarfs."162 Iu 86... we discuss the iullueuce of tellurie lines on precision RV measurements aud differeut methods of removing telluric line effects.," In \ref{sec:Telluric}, we discuss the influence of telluric lines on precision RV measurements and different methods of removing telluric line effects."163 A stummary of the study is given iu 37.., A summary of the study is given in \ref{sec:Conclusion}.164 The theory of DEDI has been discussed by several papers (22?)..," The theory of DFDI has been discussed by several papers \citep{Ge2002, Erskine2003, VanEyken2010}."165 We briefly introduce the principle of DEDI in this section. readers may refer to previous references for more detailed discussion.," We briefly introduce the principle of DFDI in this section, readers may refer to previous references for more detailed discussion."166 DEDI is realized by coupling a fixed delayinterferometer with a post-disperser (Fig. 1))., DFDI is realized by coupling a fixed delayinterferometer with a post-disperser (Fig. \ref{fig:DFDI_setup}) ).167 The resulting [ringing spectrum is recorded ou a 2-D detector., The resulting fringing spectrum is recorded on a 2-D detector.168 The formation of the final (riugiug spectrum is illustrated in Fig. 2.., The formation of the final fringing spectrum is illustrated in Fig. \ref{fig:DFDI_illus}.169 Boy.y) is a mathematical representation of the final image formed at the 2-D detector aud it is described by the following equation: where So(7) is the intrinsic stellar spectrum aud 7 is optical frequency.," $B(\nu,y)$ is a mathematical representation of the final image formed at the 2-D detector and it is described by the following equation: where $S_0(\nu)$ is the intrinsic stellar spectrum and $\nu$ is optical frequency."170 Sp is divided by fv to convert energy flux into photon flux., $S_0$ is divided by $h\nu$ to convert energy flux into photon flux.171 JF is the intensity trausinissiou Luuction (Equation (2))). 9 is the coordinate aloug the slit direction which is trausverse to dispersion direction. ο) represents convolution and LSF is the line spread function of the post-disperser which is a funcetiou of 7 aud spectral resolution A.," $IT$ is the intensity transmission function (Equation \ref{eq:IT}) )), $y$ is the coordinate along the slit direction which is transverse to dispersion direction, $\otimes$ represents convolution and $LSF$ is the line spread function of the post-disperser which is a function of $\nu$ and spectral resolution $R$."172 In Equation (2)): 5 is visibility lor a given frequency chanuel. the ratio of half ol the peak-valley ziuplitude and the DC offset. which is determiued by stellar flux Sy): c is the speed of light: aud 7 is the optical path difference (OPD) of the interferometer which is designed to be tilled along the slit direction such that several [riuges are formed aloug each 7 channel (Middle. Fig. 2)).," In Equation \ref{eq:IT}) ): $\gamma$ is visibility for a given frequency channel, the ratio of half of the peak-valley amplitude and the DC offset, which is determined by stellar flux $S_0(\nu)$; $c$ is the speed of light; and $\tau$ is the optical path difference (OPD) of the interferometer which is designed to be tilted along the slit direction such that several fringes are formed along each $\nu$ channel (Middle, Fig. \ref{fig:DFDI_illus}) )."173 We assume the LSF is a gaussian function (Equation (3))). Av=v/R/2.35 because we asstuue that oue resolution element is equal to the FWHM of a spectral liue.," We assume the LSF is a gaussian function (Equation \ref{eq:LSF}) )), $\Delta\nu=\nu/R/2.35$ because we assume that one resolution element is equal to the FWHM of a spectral line."174 Fig., Fig.175 3. shows high-resolution (0.005 sspacing) svuthetic spectra of M. dwarfs with solar metallicity (22)...," \ref{fig:Wav_Flux} shows high-resolution (0.005 spacing) synthetic spectra of M dwarfs with solar metallicity \citep{Hauschildt1999,Allard2001}."176 Teg ranges from 21001. to 91001. aud logg is 1.5.," $T_{\rm{eff}}$ ranges from 2400K to 3100K, and $\log g$ is 4.5."177 No rotational broacdeniug is added in the spectrum., No rotational broadening is added in the spectrum.178 Most absorption lines are shallow with FWHAIs of several tenths of an A., Most absorption lines are shallow with FWHMs of several tenths of an .179. Since RV information is embecdecd in the slope, Since RV information is embedded in the slope180was detected on 2003 229 during a scan of the Galactic plane by the IBIS/ISGRI soft gamma-ray detector onboard the International Gamma Ray Laboratory2003).,was detected on 2003 29 during a scan of the Galactic plane by the IBIS/ISGRI soft gamma-ray detector onboard the International Gamma Ray Laboratory.181 The source was the first and most extreme example of a number of highly absorbed Galactic X-ray binaries discovered withINTEGRAL., The source was the first and most extreme example of a number of highly absorbed Galactic X-ray binaries discovered with.182. Due to the strong absorption. which can exceed an equivalent hydrogen column of 107em7*. these sources are extremely faint in the soft X-rays and had not been detected by earlier missions2005).," Due to the strong absorption, which can exceed an equivalent hydrogen column of $10^{24}\,\mathrm{cm}^{-2}$, these sources are extremely faint in the soft X-rays and had not been detected by earlier missions."183" Right after its discovery. a re-analysis of archival data by revealed a highly photoabsorbed source (Vy=4x107 em"") coincident with the position given byINTEGRAL."," Right after its discovery, a re-analysis of archival data by revealed a highly photoabsorbed source $N_\mathrm{H} = 4 \times 10^{23}\,\mathrm{cm}^{-2}$ ) coincident with the position given by."184. The data also suggested an iron emission line at kKKeV. These results were confirmed by various subsequent studies 2003)., The data also suggested an iron emission line at keV. These results were confirmed by various subsequent studies .185 detected intense Fe Κα. Fe Kf. and Ni Ke emission lines in the spectrum.," detected intense Fe $\alpha$ , Fe $\beta$, and Ni $\mathrm{K\alpha}$ emission lines in the spectrum."186 Based on the interstellar absorption toward the system. which is two orders of magnitude lower than the measured Ny.(2003)..(2004).. and also suggested that much of the X-ray absorption is intrinsic to the compact object.," Based on the interstellar absorption toward the system, which is two orders of magnitude lower than the measured $N_\mathrm{H}$, and also suggested that much of the X-ray absorption is intrinsic to the compact object."187 In an optical study of the system. proposed that IGR 116318—4848 is a High Mass X-ray Binary (HMXB) with an sgB[e] star as the mass donor surrounded by a dense and absorbing circumstellar material2007).," In an optical study of the system, proposed that IGR $-$ 4848 is a High Mass X-ray Binary (HMXB) with an sgB[e] star as the mass donor surrounded by a dense and absorbing circumstellar material."188. This dense stellar wind results in significant photoabsorption within the binary system., This dense stellar wind results in significant photoabsorption within the binary system.189 Based on the optical data. suggest a distance between 0.9 and kkpe for the system.," Based on the optical data, suggest a distance between 0.9 and kpc for the system."190 A likely location for the source is in the Norma-Cygnus arm2004).. which would place it at a distance of kkpe2004).," A likely location for the source is in the Norma-Cygnus arm, which would place it at a distance of kpc."191 In thisPaper. we describe the results of follow-up observations of IGR 116318—4848 obtained with the satellite. the instruments on which are uniquely suited to study Compton-thick absorption.," In this, we describe the results of follow-up observations of IGR $-$ 4848 obtained with the satellite, the instruments on which are uniquely suited to study Compton-thick absorption."192 In Sect., In Sect.193 ?? we describe the data reduction., \ref{sec:data} we describe the data reduction.194 Section ?? is devoted to a presentation of the results of the spectral and temporal analysis., Section \ref{sec:obs} is devoted to a presentation of the results of the spectral and temporal analysis.195 We discuss our results in Sect. ?2.., We discuss our results in Sect. \ref{sec:conclusions}.196 We observed IGR J16318—4848 with from 2006 August ]4 until 2006 August 17 for a total net exposure of 97kks sequence number 401094010)., We observed IGR $-$ 4848 with from 2006 August 14 until 2006 August 17 for a total net exposure of ks sequence number 401094010).197 We used the standard. procedures to reduce the data from the X-Ray Imaging Spectrometer and the Hard X-Ray Detector2007)., We used the standard procedures to reduce the data from the X-Ray Imaging Spectrometer and the Hard X-Ray Detector.198.. For the XIS in particular we barycentered the data with (version 2008-03-03) and then extracted source events. images. spectra. and lighteurves with XSELECT v2.4.," For the XIS in particular we barycentered the data with (version 2008-03-03) and then extracted source events, images, spectra, and lightcurves with XSELECT v2.4."199 A circular source extractior region of 3/223 radius was applied., A circular source extraction region of 23 radius was applied.200 The background spectrum was extracted from a circular region having the same area as the source extraction region., The background spectrum was extracted from a circular region having the same area as the source extraction region.201 This process was done for every XIS., This process was done for every XIS.202 Response matrices and ancillary response files were generated using XISRMFGEN (version 2009-02-28) and XISSIMARFGEN (version 2009-02-28). taking into account the hydrocarbon contamination on the optical blocking filter2007).," Response matrices and ancillary response files were generated using XISRMFGEN (version 2009-02-28) and XISSIMARFGEN (version 2009-02-28), taking into account the hydrocarbon contamination on the optical blocking filter."203. As recommended by the team. the spectra of the three front illuminated CCDs (XISO. XIS2. and XIS3) were then combined with (version 1.30).," As recommended by the team, the spectra of the three front illuminated CCDs (XIS0, XIS2, and XIS3) were then combined with (version 1.30)."204 Although the XIS1 was operational when the observation was made. it is not used in the present study due to cross calibration Issues.," Although the XIS1 was operational when the observation was made, it is not used in the present study due to cross calibration issues."205 To extract the HXD PINspectrum. weagain followed the standard procedure of barycentric correction. eti-filtered," To extract the HXD PINspectrum, weagain followed the standard procedure of barycentric correction, gti-filtered"206spectrum as [lat as the observed. one.,spectrum as flat as the observed one.207 Therefore. an cllicient particle acceleration. mechanism is requested: to boost electrons toward. higher energies and to flatten the emitted svichrotron spectrum., Therefore an efficient particle acceleration mechanism is requested to boost electrons toward higher energies and to flatten the emitted synchrotron spectrum.208 In order to avoid to exceed the observed. brightness. a relatively small injection rate of secondary electrons. anc positrons i8. required.," In order to avoid to exceed the observed brightness, a relatively small injection rate of secondary electrons and positrons is required."209" More quantitatively, we find that the parameter space with C,f/Eyye&10.7 is excluded for this strongly magnetized case."," More quantitatively, we find that the parameter space with ${\cal E}_p/{\cal E}_{th} > 10^{-3}$ is excluded for this strongly magnetized case."210 In this Section we illustrate our calculations of the volume integrated. fluxes of radiation generated by. reaccelerated electrons and. positrons through svynchrotron emission. ancl 1C., In this Section we illustrate our calculations of the volume integrated fluxes of radiation generated by reaccelerated electrons and positrons through synchrotron emission and IC.211 The central gas density. ΕΞ 0). the 7 parameter and the core radius r7 are chosen as the representative values of the Coma cluster (Briel et al.," The central gas density, $n_{th}(r=0)$ , the $\beta$ parameter and the core radius $r_c$ are chosen as the representative values of the Coma cluster (Briel et al."212 1992)., 1992).213 In Fig., In Fig.214 5 we plot our results for the svnchrotron spectra (left panel) and the IC spectra (right panel)., \ref{fig:broad} we plot our results for the synchrotron spectra (left panel) and the IC spectra (right panel).215 The data points refer to the radio. hard X-ray and. gamma ray bands.," The data points refer to the radio, hard X-ray and gamma ray bands."216 All curves are obtained in the assumption that the cosmic rav energy density at the beginning of the reacceleration stage is proportional o the thermal energy density at any point., All curves are obtained in the assumption that the cosmic ray energy density at the beginning of the reacceleration stage is proportional to the thermal energy density at any point.217" The values of Pi(rΞ0) and the ratio £,/£u,e are not chosen to obtain a best fit to the data. they are only fixed in order to provide a viable representation of the data."," The values of $P_A(r=0)$ and the ratio ${\cal E}_p/{\cal E}_{\rm th}$ are not chosen to obtain a best fit to the data, they are only fixed in order to provide a viable representation of the data."218 Some general remarks emerge [rom the inspection. of lig. 5 , Some general remarks emerge from the inspection of Fig. \ref{fig:broad} :219The very broad extension of the svachrotron emission from. giant radio halos is among the properties which are cillicult to be fitted. by secondary models (o... Brunetti 2004 ancl rof.," The very broad extension of the synchrotron emission from giant radio halos is among the properties which are difficult to be fitted by secondary models (e.g., Brunetti 2004 and ref."220 therein)., therein).221 Although this Section is not devoted. to a detailedcomparison between observed. svnchrotron profiles, Although this Section is not devoted to a detailedcomparison between observed synchrotron profiles222galaxies. so the simulated dispersion is likely overestimated by à [actor of ~5.,"galaxies, so the simulated dispersion is likely overestimated by a factor of $\sim5$."223 While the data show a slight trend of σ increasing with ορ. the observed relation is inconsistent with simulations.," While the data show a slight trend of $\sigma$ increasing with $\Sigma_{SFR}$, the observed relation is inconsistent with simulations."224 We therefore conclude that. supernova feedback is insullicient to explain. the observed: velocity dispersions., We therefore conclude that supernova feedback is insufficient to explain the observed velocity dispersions.225 Figure 7 shows the relation between Vm Mere. clearly demonstrating that Vf decreases with sry.," Figure \ref{fig:sfrsigma} shows the relation between $V/\sigma$ $\Sigma_{SFR}$ , clearly demonstrating that $V/\sigma$ decreases with $\Sigma_{SFR}$."226 Llowever. this trend is likely ultimately due to the velocity-size relation: larger galaxies tend to have larger rotation velocities (Figure 6)) and smaller κ (Figure 7)).," However, this trend is likely ultimately due to the velocity-size relation: larger galaxies tend to have larger rotation velocities (Figure \ref{fig:dynamics}) ) and smaller $\Sigma_{SFR}$ (Figure \ref{fig:sfrsigma}) )."227 This is explained by dilferent. sensitivities of the data. as deeper spectra (lower ορ) reveal more extended: structures at larger radius with larger rotation speed.," This is explained by different sensitivities of the data, as deeper spectra (lower $\Sigma_{SFR}$ ) reveal more extended structures at larger radius with larger rotation speed."228 The velocity-size correlation contributes much more to the observed. Vo Nerr relation than any correlation between ο and the velocity. dispersion., The velocity-size correlation contributes much more to the observed $V/\sigma$ $\Sigma_{SFR}$ relation than any correlation between $\Sigma_{SFR}$ and the velocity dispersion.229 Fhese data thus do not support. the hypothesis that Ve is strongly allected by the density of star formation: e increases by less than a factor of 2 over two orders of magnitude in spp., These data thus do not support the hypothesis that $V/\sigma$ is strongly affected by the density of star formation: $\sigma$ increases by less than a factor of 2 over two orders of magnitude in $\Sigma_{SFR}$.230" The small Vi,fomLs and clumpy morphology of all ealaxies suggest that the rotating disks are highly turbulent and mav be dynamically unstable.", The small $V_{max}/\sigma \leq 1.8$ and clumpy morphology of all galaxies suggest that the rotating disks are highly turbulent and may be dynamically unstable.231 We therefore explore the scale lengths for gravitational collapse within the high redshift disk galaxies., We therefore explore the scale lengths for gravitational collapse within the high redshift disk galaxies.232 Evidence is accumulating that the mode of. star formation may be very. different in early systems compared to that seen locally (22)..," Evidence is accumulating that the mode of star formation may be very different in early systems compared to that seen locally \citep{Bournaud08,Elmegreen05}."233 Rather than forming stars within elant molecular clouds which condense out of a stable ealaxy. star formation mav be triggered by fragmentation of a dynamically unstable system.," Rather than forming stars within giant molecular clouds which condense out of a stable galaxy, star formation may be triggered by fragmentation of a dynamically unstable system."234" Driellv. in a rotating disk of gas ancl stars. perturbations smaller than a critical wavelength: £,,,; are stabilized. against the inward pull of gravity by velocity dispersion while those larger than some £L, are stabilized. by centrifugal force."," Briefly, in a rotating disk of gas and stars, perturbations smaller than a critical wavelength $L_{max}$ are stabilized against the inward pull of gravity by velocity dispersion while those larger than some $L_{min}$ are stabilized by centrifugal force."235 1£ the dispersion. and. rotation velocity are too low. LivinL4; and perturbations of intermediate wavelength grow exponentially.," If the dispersion and rotation velocity are too low, $L_{min} > L_{max}$ and perturbations of intermediate wavelength grow exponentially."236 This interplay is summarized by the Toomre parameter Qo—Linesτων which is calculated from the velocity dispersion. rotation curve. ancl mass. distribution (?)..," This interplay is summarized by the Toomre parameter $Q=L_{max}/L_{min}$ which is calculated from the velocity dispersion, rotation curve, and mass distribution \citep{Toomre64}."237" Galaxies with Q«I are therefore unstable on scales between £,,4; and L,,;, and will fragment into giant dense clumps.", Galaxies with $Q < 1$ are therefore unstable on scales between $L_{max}$ and $L_{min}$ and will fragment into giant dense clumps.238 This could trigger star formation in clouds of much higher mass and radius than GMCSs in local spiral galaxies with Q71. and can explain the clump-cluster and chain morphologies observed in many high-redshift galaxies.," This could trigger star formation in clouds of much higher mass and radius than GMCs in local spiral galaxies with $Q > 1$, and can explain the clump-cluster and chain morphologies observed in many high-redshift galaxies."239 Dynamical friction. viscosity anc tidal interactions may cause these clumps to migrate toward the center of the galaxy potential. forming a bulge which stabilizes the svstem against further fragmentation.," Dynamical friction, viscosity and tidal interactions may cause these clumps to migrate toward the center of the galaxy potential, forming a bulge which stabilizes the system against further fragmentation."240 From the galaxies whose velocity fields. can be reasonably well described by rotating svstems. we calculate the Toomre parameter via: which describes the stability of a rotating disk of gas.," From the galaxies whose velocity fields can be reasonably well described by rotating systems, we calculate the Toomre parameter via: which describes the stability of a rotating disk of gas."241 IQ-1 the system. is unstable to localgravitational collapse and will fragment into overdense clumps., If $Q<1$ the system is unstable to localgravitational collapse and will fragment into overdense clumps.242" The value of & is somewhat uncertain as it depends on the unknown mass distribution: our observations are consistent with a range ντf» oh25 correspondingm: to constant V,t and V.txJi respectively.", The value of $\kappa$ is somewhat uncertain as it depends on the unknown mass distribution; our observations are consistent with a range $\sqrt{2}\frac{V_c}{R}$ $2\frac{V_c}{R}$ corresponding to constant $V_c$ and $V_c\propto R$ respectively.243 Adopting &=νο1 appropriate for a uniform clisk and using dynamical mass to estimate the surface mass density. X. we find an inclination-corrected €x;0.6 for all galaxies in our sample.," Adopting $\kappa=\sqrt{3}V_{max}/R$ appropriate for a uniform disk and using dynamical mass to estimate the surface mass density $\Sigma$ , we find an inclination-corrected $Q\lsim0.6$ for all galaxies in our sample."244 We estimate that the uncertainty in € is dominated by à factor of 2 error in the dynamical mass., We estimate that the uncertainty in $Q$ is dominated by a factor of $\simeq2$ error in the dynamical mass.245 Phe assumed & introduces a negligible uncertainty. with an additional random error of ~30% [from the input. parameters.," The assumed $\kappa$ introduces a negligible uncertainty, with an additional random error of $\sim30$ from the input parameters."246 Disk thickness and stellar abundance also alfect the value of Q., Disk thickness and stellar abundance also affect the value of $Q$.247 Combined. these elfects result in roughly a factor of 2 uncertainty.," Combined, these effects result in roughly a factor of 2 uncertainty."248 Even so. these galaxies all appear to be dynamically unstable since Q<I.," Even so, these galaxies all appear to be dynamically unstable since $Q<1$."249 Hence we expect them to fragment into massive clumps on scales of order the Jeans length for dispersion support., Hence we expect them to fragment into massive clumps on scales of order the Jeans length for dispersion support.250 In a uniform disk. the largest scale for whieh velocity dispersion stabilizes against gravitational collapse is which is readily estimated from. the dispersion. and dynamical mass density.," In a uniform disk, the largest scale for which velocity dispersion stabilizes against gravitational collapse is which is readily estimated from the dispersion and dynamical mass density."251 As with Q. the uncertainty in Lj is à factor of &2 dominatedby the dynamical mass with additional uncertainty from the unknown mass cistribution. disk height. stellar content. and directional dependence of m.," As with $Q$, the uncertainty in $L_J$ is a factor of $\simeq2$ dominatedby the dynamical mass with additional uncertainty from the unknown mass distribution, disk height, stellar content, and directional dependence of $\sigma$ ."252 The resulting instability scale is 13 kpefor CI00024|1709 and 0.1.1.5 kpe for all other objects. consistent with the observed. clump sizes.," The resulting instability scale is 1–3 kpcfor 0024+1709 and 0.1–1.5 kpc for all other objects, consistent with the observed clump sizes."253"in their targeted observations of eSZ clusters, which resulted in detections with peak S/Ns ranging from 6.3 to 13.8 (Storyetal.2011).","in their targeted observations of eSZ clusters, which resulted in detections with peak S/Ns ranging from 6.3 to 13.8 \citep{story11}."254" 'These data were reduced according to the procedures described in detail in Sayersetal.(2011), with only minor changes."," These data were reduced according to the procedures described in detail in \citet{sayers11}, with only minor changes."255 We briefly summarize the data reduction here., We briefly summarize the data reduction here.256" First, we used frequent observations of bright quasars to obtain pointing corrections accurate to 5 arcsec, and we used observations of Uranus and Neptune to obtain flux calibration accurate to596."," First, we used frequent observations of bright quasars to obtain pointing corrections accurate to 5 arcsec, and we used observations of Uranus and Neptune to obtain flux calibration accurate to."257". In particular, the flux calibration has been updated based on recent WMAP results as described in detail in Sayersetal. (2012)."," In particular, the flux calibration has been updated based on recent WMAP results as described in detail in \citet{sayers12}."258. The FOV-average signal is then subtracted at each time sample and the data timestreams are high-pass filtered at 250 mHz in order to remove atmospheric brightness fluctuations., The FOV-average signal is then subtracted at each time sample and the data timestreams are high-pass filtered at 250 mHz in order to remove atmospheric brightness fluctuations.259" Consequently, the cluster images are high-pass filtered in a way which we characterize via simulation to obtain a signal transfer function for each cluster."," Consequently, the cluster images are high-pass filtered in a way which we characterize via simulation to obtain a signal transfer function for each cluster."260 We searched for clusters in these images using a matched filter according to the formalism described in Vanderlindeetal.(2010) (see also Haehnelt&TegmarkMarriage(1996);etal. (2011))).," We searched for clusters in these images using a matched filter according to the formalism described in \citet{vanderlinde10}261 (see also \citet{haehnelt96, herranz02a, herranz02b,262melin06, marriage11}) )."263" We (2002a,b);approximate the cluster (2006);SZ surface brightness profile S(0) as where 0 is an angular distance and 0, is the core radius.", We approximate the cluster SZ surface brightness profile $S(\theta)$ as where $\theta$ is an angular distance and $\theta_c$ is the core radius.264" We then form a filter according to where Wu) is the signal transfer function in Fourier space, S(u) is the cluster profile in Fourier space, B(u) is the point-spread function in Fourier space, is the map-noise power spectrum, u is an angular N(u)frequency, and 77-! denotes the Fourier transform back to map space."," We then form a filter according to where $\tilde{W}(u)$ is the signal transfer function in Fourier space, $\tilde{S}(u)$ is the cluster profile in Fourier space, $\tilde{B}(u)$ is the point-spread function in Fourier space, $\tilde{N}(u)$ is the map-noise power spectrum, $u$ is an angular frequency, and $\mathcal{FT}^{-1}$ denotes the Fourier transform back to map space."265 We filter our images in map-space by convolving them with after truncating at a radius of 4 arcmin.," We filter our images in map-space by convolving them with $\psi(\theta)$, after truncating $\psi(\theta)$ at a radius of 4 arcmin."266" This Φ(θ),truncation is required to v(0)prevent the filter from introducing noise in the central region of the images from the low-coverage outer regions.", This truncation is required to prevent the filter from introducing noise in the central region of the images from the low-coverage outer regions.267" Analogous to Vanderlindeetal. each image is filtered using 12 different filters, with 0, (2010),,varied from 0.25 to 3.00 arcmin in 0.25 arcmin increments (note that our PSF has a FWHM of ~1 arcmin), and we define our detection significance ¢ as the peak found in any of these filtered images within an apertureS/N of 4 arcmin radius centered on the Planck eSZ coordinates."," Analogous to \citet{vanderlinde10}, each image is filtered using 12 different filters, with $\theta_c$ varied from 0.25 to 3.00 arcmin in 0.25 arcmin increments (note that our PSF has a FWHM of $\simeq 1$ arcmin), and we define our detection significance $\zeta$ as the peak S/N found in any of these filtered images within an aperture of 4 arcmin radius centered on the Planck eSZ coordinates."268 This search radius was chosen because it corresponds to the upper limit on the Planck astrometry for all but the lowest redshift clusters (PlanckCollaboration2011)., This search radius was chosen because it corresponds to the upper limit on the Planck astrometry for all but the lowest redshift clusters \citep{planck_esz}.269. We find ¢=5.7 for PLCKESZ G115.71 (with θ.=0.25) and ¢=3.8 for PLCKESZ G189.84 (with θ.=0.25)., We find $\zeta = 5.7$ for PLCKESZ G115.71 (with $\theta_c = 0.25$ ) and $\zeta = 3.8$ for PLCKESZ G189.84 (with $\theta_c = 0.25$ ).270" The centroids of these maxima are given in Table 1,, and each is within 1 arcmin of the coordinates given in the Planck eSZ."," The centroids of these maxima are given in Table \ref{tab:one}, and each is within 1 arcmin of the coordinates given in the Planck eSZ."271 Figure 1 shows thumbnails of each target filtered with the filter that produces the maximum S/N. We characterize our detection significance via simulation by generating noise maps from the combination of jackknife realizations of our data and a model for the astronomical fluctuations due to the cosmic microwave background and point sources based on SPT measurements of the mm-wave power spectrum (Sayersetal.2011;Reichardt2011).," Figure \ref{fig:one} shows thumbnails of each target filtered with the filter that produces the maximum S/N. We characterize our detection significance via simulation by generating noise maps from the combination of jackknife realizations of our data and a model for the astronomical fluctuations due to the cosmic microwave background and point sources based on SPT measurements of the mm-wave power spectrum \citep{sayers11, reichardt11}."272". We generated 1000 such realizations for each target, along with the 14 other targets observed with Bolocam in October 2011 to similar depths."," We generated 1000 such realizations for each target, along with the 14 other targets observed with Bolocam in October 2011 to similar depths."273" We then searched for the peak S/N in each of these noise realizations, the distributions of which were statistically identical for all 16 targets."," We then searched for the peak S/N in each of these noise realizations, the distributions of which were statistically identical for all 16 targets."274" We therefore used all 16000 measurements to characterize the probability of measuring a given peak S/N, with the results shown in Figure 2.."," We therefore used all 16000 measurements to characterize the probability of measuring a given peak S/N, with the results shown in Figure \ref{fig:two}. ."275" We find the probability of a false detection of PLCKESZ G115.71 is 5.3x107°, and we therefore confirm it as a cluster."," We find the probability of a false detection of PLCKESZ G115.71 is $5.3 \times 10^{-5}$, and we therefore confirm it as a cluster."276" Note that PLCKESZ G115.71 has ¢=5.7, which exceeds the value of ¢ obtained in all 16000 of our noise realizations, we have therefore extrapolated our simulation results using a parametric fit."," Note that PLCKESZ G115.71 has $\zeta = 5.7$, which exceeds the value of $\zeta$ obtained in all 16000 of our noise realizations, we have therefore extrapolated our simulation results using a parametric fit."277" The probability of a false detection of PLCKESZ G189.84 is 0.027, and we therefore do not claim a detection of this candidate."," The probability of a false detection of PLCKESZ G189.84 is 0.027, and we therefore do not claim a detection of this candidate."278" At a given value of C, our false detection rate per given map area is approximately three times higher than the SPT false detection rate described in Vanderlindeetal."," At a given value of $\zeta$, our false detection rate per given map area is approximately three times higher than the SPT false detection rate described in \citet{vanderlinde10}."279 The false detection probability is similar when ¢(Bolocam)(2010)..~¢(SPT)+0.3.," The false detection probability is similar when $\zeta(\textrm{Bolocam}) \simeq 280\zeta(\textrm{SPT}) + 0.3$."281" Although SPT survey data are similar to our Bolocam data in many respects, there are subtle differences that contribute to this increase in our false detection probability."," Although SPT survey data are similar to our Bolocam data in many respects, there are subtle differences that contribute to this increase in our false detection probability."282" In particular, the Bolocam images have tapered coverage and consequently non-uniform noise properties."," In particular, the Bolocam images have tapered coverage and consequently non-uniform noise properties."283" This means that for a given map pixel our filter will introduce noise from both lower- and higher-coverage regions of the map, and the filter is therefore not as optimal as the filter used by SPT."," This means that for a given map pixel our filter will introduce noise from both lower- and higher-coverage regions of the map, and the filter is therefore not as optimal as the filter used by SPT."284 We have also analyzed the Wide-field Infrared Survey Explorer (WISE) public-release data (Wrightetal.2010) at the location of each eSZ candidate., We have also analyzed the Wide-field Infrared Survey Explorer (WISE) public-release data \citep{wright10} at the location of each eSZ candidate.285" The central wavelengths of the WISE bands, which areat 3.4, 4.6, 12, and 22 um, are too long to search for these candidates using a red sequence technique (Gladders&Yee 2000),,"," The central wavelengths of the WISE bands, which areat 3.4, 4.6, 12, and 22 $\mu$ m, are too long to search for these candidates using a red sequence technique \citep{gladders00}, ,"28615cm Adelman-MeCarthiy et aL.,"0.15cm Adelman-McCarthy et al.,"287 900ίx. 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In Figures 5-—7,, we show the line intensity ratio maps between the CO isotopologues and the different rotational transitions."," In Figures \ref{ratio3}- \ref{ratio2}, we show the line intensity ratio maps between the CO isotopologues and the different rotational transitions."345 From the image of the tto J-6-5ratio(Fig., From the image of the to $J=6-5$ ratio (Fig.346"Supperpanel), wecanseethespatialdistributiono pidrreguopauedififletleelv6locities."," \ref{ratio3} upper panel), we can see the spatial distribution of high optical depth regions at different velocities."347T southdenseridge f romOrionBN/K LtoOrionS , The north-south dense ridge from Orion BN/KL to Orion South is clearly seen at 9.348"This high optical depth ridge is similar to the filamentary structures of the NH3 emission (Wiseman&Ho,1996,1998),, but has some morphological differences in the north of the Orion BN/KL region."," This high optical depth ridge is similar to the filamentary structures of the $_{3}$ emission \citep{Wiseman1996,Wiseman1998}, but has some morphological differences in the north of the Orion BN/KL region."349" Besides, the straight shape of the Orion Bar is pronounced at sgz110-11s!,, where three high optical depth regions are seen at the two ends and center of the Bar at Visp=110 and 11s!,, respectively."," Besides, the straight shape of the Orion Bar is pronounced at 10–11, where three high optical depth regions are seen at the two ends and center of the Bar at 10 and 11, respectively."350" In the lower panel of Figure 5,, the J=6-5toJ=3-2ratiosaround10——11km sshow a gradient in the Orion Bar which goes in the direction from the Trapezium stars."," In the lower panel of Figure \ref{ratio3}, the $J=6-5$ to $J=3-2$ ratios around 10–11 show a gradient in the Orion Bar which goes in the direction from the Trapezium stars."351 It indicates that J-6-5isstronglyexcitedattheedgeo ftheBarbyU V photons fromtheT rapez , It indicates that $J=6-5$ is strongly excited at the edge of the Bar by UV photons from the Trapezium stars.352"Figure 6 shows the ratio between J=7-6andJ=6-Satthreedif ferentradialvelocitieso f5, 10, andl5km |."," Figure \ref{ratio1} shows the ratio between $J=7-6$ and $J=6-5$ at three different radial velocities of 5, 10, and 15."353 The three panels show clear variations across the integrated line emission., The three panels show clear variations across the integrated line emission.354" It is interesting to note that at the cloud velocity of 10 km s, there are high 7—6/6—5 ratios located very close to the position of the Trapezium stars toward Orion BN/KL."," It is interesting to note that at the cloud velocity of 10 km $^{-1}$, there are high 7–6/6–5 ratios located very close to the position of the Trapezium stars toward Orion BN/KL."355" These gradients are likely produced by those massive stars that heat the molecular cloud, causing the stronger fleghobmeaide outhisclearlyseenaf$ine"," These gradients are likely produced by those massive stars that heat the molecular cloud, causing the stronger $J=7-6$ line emission compared with the $J=6-5$ line."356stbradientisalsoseenintheOrionBarwhichgoesintheperpendiculard henorth— s, A gradient is also seen in the Orion Bar which goes in the perpendicular direction to the Trapezium stars (Fig.357"~!)), and some patches with higher J-7-6brightnesstemperaturesareseeninsidetheBarorbehindtheionizatior"," \ref{ratio1} at $V_{\rm LSR}=10$ ), and some patches with higher $J=7-6$ brightness temperatures are seen inside the Bar or behind the ionization front."358 gi," Some horizontal and vertical strips, artifacts from the OTF mapping, arealso seen in the Orion Bar and South regions."359ven the calibration errors of 10% for both J=6-SandJ=7-6., These artifacts can affect the intensity ratio by $\sim 14 \%$ given the calibration errors of $10 \%$ for both $J=6-5$ and $J=7-6$.360"However, somestructuresseeninthe J=7-6toJ=6-5ratiomaps, e.g., thedashed linesinFigure6,, areunlikelyduetothecalibrationerroror scanning strip sdi "," However, some structures seen in the $J=7-6$ to $J=6-5$ ratio maps, e.g., the dashed-lines in Figure \ref{ratio1}, are unlikely due to the calibration error or scanning strips during theobservation, and seem to be footprints of filaments or outflows."361, Some similar filament structures have been noticed in the dust continuum emission observed by \citet{Johnstone1999}. .362"In the ratio map of J23-210CO J=3-2showninF igure7, , aclearelongatedanddenseridgeisseeninthenorth southdirection, wherethe"," In the ratio map of $J=3-2$ to $J=3-2$ shown in Figure \ref{ratio2}, , a clear elongated and dense ridge is seen in the north-south direction, where the"363"In the ratio map of J23-210CO J=3-2showninF igure7, , aclearelongatedanddenseridgeisseeninthenorth southdirection, wherethe'"," In the ratio map of $J=3-2$ to $J=3-2$ shown in Figure \ref{ratio2}, , a clear elongated and dense ridge is seen in the north-south direction, where the"364"In the ratio map of J23-210CO J=3-2showninF igure7, , aclearelongatedanddenseridgeisseeninthenorth southdirection, wherethe'-"," In the ratio map of $J=3-2$ to $J=3-2$ shown in Figure \ref{ratio2}, , a clear elongated and dense ridge is seen in the north-south direction, where the"365"In the ratio map of J23-210CO J=3-2showninF igure7, , aclearelongatedanddenseridgeisseeninthenorth southdirection, wherethe'-?"," In the ratio map of $J=3-2$ to $J=3-2$ shown in Figure \ref{ratio2}, , a clear elongated and dense ridge is seen in the north-south direction, where the"366"In the ratio map of J23-210CO J=3-2showninF igure7, , aclearelongatedanddenseridgeisseeninthenorth southdirection, wherethe'-?C"," In the ratio map of $J=3-2$ to $J=3-2$ shown in Figure \ref{ratio2}, , a clear elongated and dense ridge is seen in the north-south direction, where the"367"In the ratio map of J23-210CO J=3-2showninF igure7, , aclearelongatedanddenseridgeisseeninthenorth southdirection, wherethe'-?CO"," In the ratio map of $J=3-2$ to $J=3-2$ shown in Figure \ref{ratio2}, , a clear elongated and dense ridge is seen in the north-south direction, where the"368we use f=0 (i.e. no overshooting). whereas for niasses equal to or ligher than 2.0M... we set f=0.018.,"we use $f=0$ (i.e. no overshooting), whereas for masses equal to or higher than $2.0\, M_\odot$ we set $f= 0.018$."369 In the intermediate mass range the cfitcicucy of overshooting varies lhuearlv with mass The πια]. discoutinuitv iu the overshooting efficiency is of no consequence for our study., In the intermediate mass range the efficiency of overshooting varies linearly with mass The small discontinuity in the overshooting efficiency is of no consequence for our study.370 1.1M. models with f£=0.005. as would result frou application of the above equation to this mass. lead. eiven the low overshooting efficieucv. to the same evolutionary tracks as models without overshooting.," $1.1\, M_\odot$ models with $f=0.005$, as would result from application of the above equation to this mass, lead, given the low overshooting efficiency, to the same evolutionary tracks as models without overshooting."371 This prescription for the overshooting eficiency leads to evolutionary tracks that reproduce well those by Pietiuferuietal.(2001)., This prescription for the overshooting efficiency leads to evolutionary tracks that reproduce well those by \citet{pietr:04}.372. Atomic diffusion is treated within the same diffusive uunercal scheme., Atomic diffusion is treated within the same diffusive numerical scheme.373 In this paper. hydrogen. helium aud heavicr clemeuts (Gucliding won) are diffusing.," In this paper, hydrogen, helium and heavier elements (including iron) are diffusing."374 Radiative levitation is not taken iuto account., Radiative levitation is not taken into account.375 To agree with the physical assuuptious in VCO. the default set of nuclear reaction rates are those of the NACRE collaboration (Auguloetal.1999).," To agree with the physical assumptions in VG07, the default set of nuclear reaction rates are those of the NACRE collaboration \citep{ang:99}."376 To investigate their influence. for individual reactions alternative rates were used.," To investigate their influence, for individual reactions alternative rates were used."377" For the UNGp,3350 reaction. we also used the rate from Maurtaetal.(2008).. the newest result from the LUNA collaboration. which is lower bv about a factor of two with respect to the NACRE rate at the relevant temperatures."," For the $^{14} \mathrm378N(p,\gamma)^{15} \mathrm O$ reaction, we also used the rate from \citet{mfn14:2008}, the newest result from the LUNA collaboration, which is lower by about a factor of two with respect to the NACRE rate at the relevant temperatures."379 This has a considerable effect on the TO morphology., This has a considerable effect on the TO morphology.380" Another reaction that turned out to be of surprisinely strong influence is the ITO(p,oHN yeaction."," Another reaction that turned out to be of surprisingly strong influence is the $^{17} \mathrm O(p,\alpha)^{14} \mathrm N$ reaction."381 We tested this by cluploving either the recent nieasureimeuts by Moazeuetal. (2007). which for T>τς105 K is very similar to the NACRE vrecouunendation. or the one given bv Caughlan&Fowler(1988).," We tested this by employing either the recent measurements by \citet{moaz:07}, which for $T > 4\times 10^8$ K is very similar to the NACRE recommendation, or the one given by \citet{cf:1988}."382.. A detailed discussion ou tle reaction rates can be found in$ L.2.., A detailed discussion on the reaction rates can be found in \ref{s:nucleo}.383 For all solar composition choices (ACSOS. CSOs) consistent Rosselaud mean opacity tables were prepared following the procedure described in Weiss&Schlattl (2008).," For all solar composition choices (AGS05, GS98) consistent Rosseland mean opacity tables were prepared following the procedure described in \citet{wsch:2008}."384. The final step to compare isochroues with observed CNIDs is the transformation to colors., The final step to compare isochrones with observed CMDs is the transformation to colors.385 For this we used hat bv VandenBere&Clem(2003.Χο)— which. ogether with a choice for the distance modulus and reddening of MGT. results in satisfring CMD fits on the nai sequence and subeiant brauch.," For this we used that by \citet[VC03]{vc:03}386 which, together with a choice for the distance modulus and reddening of M67, results in satisfying CMD fits on the main sequence and subgiant branch."387" Alternatively. we used the transformations by Cassisietal.(2001)/ for esting purposes,"," Alternatively, we used the transformations by \citet{cas:04} for testing purposes."388 The initial stellaz parameters (Yi. Zi. mixing length xmanieter) are obtained from solar model calibrations.," The initial stellar parameters $Y_\mathrm{in}$, $Z_\mathrm{in}$, mixing length parameter) are obtained from solar model calibrations."389 This will be discussed. in more detail in 3.2.., This will be discussed in more detail in \ref{s:calib}.390 With hese. we computed the evolution from the zero-age uaiu-sequeuce (ZAMS) to the tip of the Red Ciaut Brauch (ROB) for mass values from 0.6 to 1.5AL. in steps of 0.1AL...," With these, we computed the evolution from the zero-age main-sequence (ZAMS) to the tip of the Red Giant Branch (RGB) for mass values from $0.6$ to $1.5\ M_\odot$ in steps of $0.1\ M_\odot$."391 We recall here that. as in VGUOT. we are not interested im considering the ROB of M67. where deficiencies in our treatment of the outer lavers of the star could have au inpact on the location of the moclels in the IIRD.," We recall here that, as in VG07, we are not interested in considering the RGB of M67, where deficiencies in our treatment of the outer layers of the star could have an impact on the location of the models in the HRD."392 We confirmed by tests starting from the pre-inain sequence that for stars with mass below the critical mass for the occurrence of a convective core. Meee. the trausieut convective core at the eud of the pre-nian sequence phase also appears here.," We confirmed by tests starting from the pre-main sequence that for stars with mass below the critical mass for the occurrence of a convective core, $M_\mathrm{ccc}$, the transient convective core at the end of the pre-main sequence phase also appears here."393 This couvective core is the result of the short phase of CN-couversion. but may be sustained if couvective overshooting is iucluded.," This convective core is the result of the short phase of CN-conversion, but may be sustained if convective overshooting is included."394 Finally. for coustructing isochrones. the tracks are normalized to the so-called equivalent poiuts (Berebuscli&Vaudeuberg1992:Pietriuferuietal.2001) aud the interpolation to an isochroue is done between— the normalized tracks.," Finally, for constructing isochrones, the tracks are normalized to the so-called equivalent points \citep{vb:92,pietr:04}395 and the interpolation to an isochrone is done between the normalized tracks."396 After an isochrone age was fixed. we calculated an additional model with the TO-nass and recaleulated the isochrouc to make sure that the 'TOAanorpholosv does not depend on the isochrone interpolation sclicie.," After an isochrone age was fixed, we calculated an additional model with the TO-mass and recalculated the isochrone to make sure that the TO-morphology does not depend on the isochrone interpolation scheme."397 To compare our inodels with M67 we used the photometric data by Saudquist(2001)., To compare our models with M67 we used the photometric data by \citet{esm67:2004}.398.. These are more accurate than the older data from Aloutgomeryctal.(1993).. which were used by ΧιθἘν aud coutain bona fide suele stars only.," These are more accurate than the older data from \citet{mmm67:93}, , which were used by VG07, and contain bona fide single stars only."399 Thus. this CAID has a narrower 1iain-sequence baud.," Thus, this CMD has a narrower main-sequence band."400 However. we also tested some of our isochrones with the data by Montgomeryetal.19900).," However, we also tested some of our isochrones with the data by \citet{mmm67:93}."401 We used both (BG.V) aud (V.P) colors., We used both $(B-V)$ and $(V-I)$ colors.402 The dereddened distance modulus to AIG? is (nAM)p=9.70 according to VGOT. and 9.72+0.05 (Saudquist2001) based on subdwuf fitting to the lower imain-sequence following Percivaletal.(2003).," The dereddened distance modulus to M67 is $(m-M)_V = 9.70$ according to VG07, and $9.72\pm 0.05$ \citep{esm67:2004} based on subdwarf fitting to the lower main-sequence following \citet{psk:03}."403. The reddeniug is £(2BVy)=Οδ (WCF) iu eood agreenient with Sarajedinictal.(1999).. who eave (0.01+0.02.," The reddening is $E(B-V)=0.038$ (VG07) in good agreement with \citet{shkd:99}, who gave $0.04\pm0.02$."404 Simular values have been recently obtained by Twarogetal.(2009)., Similar values have been recently obtained by \citet{twarog:2009}.405. For the metallicity we assumed a value of ΓοΠΠ=0.0. which is well witlin spectroscopically determined errors. for example by Catton (20003.. who gave [FeTT]=0.02+0.06.," For the metallicity we assumed a value of $\mathrm{[Fe/H]}=0.0$, which is well within spectroscopically determined errors, for example by \citet{gm67:2000}, , who gave $\mathrm{[Fe/H]}=0.02\pm0.06$."406 To be cousistent with VOOT. we used for the old respectively new solar abundances those by CSO8 aud ACSü5. although the former are simply au update of GN93 taking iuto account additional literature values. and ACSO9 would be the most recent aud complete re-analysis.," To be consistent with VG07, we used for the old respectively new solar abundances those by GS98 and AGS05, although the former are simply an update of GN93 taking into account additional literature values, and AGS09 would be the most recent and complete re-analysis."407 Since ACGS09 abundances are slightly higher than ACSOS. our choice is testing the more extreme case.," Since AGS09 abundances are slightly higher than AGS05, our choice is testing the more extreme case."408 The initial abuudances of the stellar models for the M67 isochrones are taken to be the same as those resulting from solar model calibrations., The initial abundances of the stellar models for the M67 isochrones are taken to be the same as those resulting from solar model calibrations.409 The idea of WOOT to use MT for testing the effect of the new solar abundances rests ou the fact that the turn-off mass of this open cluster is very close to the critical mass for the onset of core convection. A4. or “transition mass” (VandeuBerectal.2007).," The idea of VG07 to use M67 for testing the effect of the new solar abundances rests on the fact that the turn-off mass of this open cluster is very close to the critical mass for the onset of core convection, $M_\mathrm{ccc}$, or ”transition mass” \citep{vgeef:2007}."410.. This transition mass depends on the average exponeut of the euecrgev ecueration rate in the core (Kippeuhlahnu&Weigert1990.Chap. 22).. that increases with the contribution from. the CNO-evele. for which eaxg~ T. in contrast to €upwT for the pp-chaius at the relevaut temperatures.," This transition mass depends on the average exponent of the energy generation rate in the core \citep[Chap.~22]{kw:90}, that increases with the contribution from the CNO-cycle, for which $\epsilon_\mathrm{CNO} \sim T^{15}$ , in contrast to $\epsilon_\mathrm{pp} \sim T^5$ for the pp-chains at the relevant temperatures."411 The importance of the CNO-cvcle depends on the nuclear reaction rates (see L2)) as well as on the amount of “catalysts”. tthe suu of the CNQO-abuudauces.," The importance of the CNO-cycle depends on the nuclear reaction rates (see \ref{s:nucleo}) ) as well as on the amount of “catalysts”, the sum of the CNO-abundances."412" These are. incidentally, the clemeuts with the largest reduction in their abundance according to AGSOS,"," These are, incidentally, the elements with the largest reduction in their abundance according to AGS05."413 Therefore. the morphological chanec in the CMD. ddisplaving the characteristichook at the TO. ora gap instardensity. cau be used to determine whether the TO-iass is below or above AM.," Therefore, the morphological change in the CMD, displaying the characteristichook at the TO, or a gap in stardensity, can be used to determine whether the TO-mass is below or above $M_\mathrm{ccc}$ ."414de ., .415. Here is the mass e is the fluid velocity. B is the magneticp field. is the density.gravitational acceleration. and ~ is the adiabatic index.," Here $\rho$ is the massdensity, $\bb{v}$ is the fluid velocity, $\bb{B}$ is the magnetic field, $\bb{g}$ is the gravitational acceleration, and $\gamma$ is the adiabatic index."416 gThe Lagrangian andEulerian derivatives are related via d/dt=OfOf|aV.," The Lagrangian andEulerian derivatives are related via $d/dt \equiv \pa/\pa t + \bb{v}417\bcdot \nabla$."418 (2))-(23)) describe the dynamics of a binary mixture in Equationsthe low-collisionality regime and they differ from standard MHD in three important respects: (0) The pressure tensor P.—pil|(pjpajbb. is where the symbols L and refer to the directions anisotropic:perpendicular and parallel to the magnetic| field. whose direction ts given by the versor 6=B/D. (ii))," Equations \ref{rho}) \ref{c}) ) describe the dynamics of a binary mixture in the low-collisionality regime and they differ from standard MHD in three important respects: ) The pressure tensor $\mathsf{P} \equiv p_\bot \mathsf{I} +419(p_\parallel - p_\bot) \hat{\bb{b}} \hat{\bb{b}}$, is anisotropic; where the symbols $\bot$ and $\parallel$ refer to the directions perpendicular and parallel to the magnetic field, whose direction is given by the versor $\hat{\bb{b}}\equiv \bb{B}/B$. )"420 Heat flows field lines. because the electron mean free mainly is alonglarge magneticcompared to its Larmor radius.," Heat flows mainly along magnetic field lines, because the electron mean free path is large compared to its Larmor radius."421 This process is pathmodeled by the second term on the hand side of (20)) via Q..εδ). rightwhere T is the plasma Equationtemperature. assumed to be the same for ions and electrons. and y.z6«10‘T°’? eres em1 + Lis the thermal conductivity (Spitzer1962:Bragin-skit 19635).. (iii))," This process is modeled by the second term on the right hand side of Equation \ref{S}) ) via $\bb{Q}_{\rm s}422\equiv-\chi\b(\b\bcdot\na)T$, where $T$ is the plasma temperature, assumed to be the same for ions and electrons, and $\chi \approx 6423\times 10^{-7} T^{5/2}$ ergs $^{-1}$ $^{-1}$ $^{-1}$ is the thermal conductivity \citep{1962pfig.book.....S, 1965RvPP....1..205B}. . )"424 The composition of fluid elements can change due to particle fluxes., The composition of fluid elements can change due to particle fluxes.425" Q,= Db(b-W)c on the right hand side of Equation Considering (23)) ensures that the diffusion of ions is field lines.", Considering $\bb{Q}_{\rm c}\equiv-D\b(\b\bcdot\na)c$ on the right hand side of Equation \ref{c}) ) ensures that the diffusion of ions is mainly along magnetic field lines.426 This is à good approximation mainlywhen alongthe magneticis dilute for the ion meanfree path to be large plasmacompared to the ion enoughLarmor radius., This is a good approximation when the plasma is dilute enough for the ion meanfree path to be large compared to the ion Larmor radius.427" Note that the concentration c is related to the mean molecular weight vial/jg—(1.011Zu)fpr,|60 where and Z;. with ¢=1.2. are the molecular weightsZo) fpr.and the ii;atomic numbers for the two ton "," Note that the concentration $c$ is related to the mean molecular weight via $1/\mu \equiv (1-c)(1+Z_1)/\mu_1 + c(1+Z_2)/\mu_2$, where $\mu_i$ and $Z_i$ , with $i=1,2$, are the molecular weights and the atomic numbers for the two ion species."428The of the pressure tensor is thus P?=2p.species./3|p)/3isotropicphypartpm. where &p is the Boltzmann constant and 0 is the atomic mass unit.," The isotropic partof the pressure tensor is thus $P\equiv 2p_\bot/3 + p_\parallel/3 = \rho k_{\rm B}429T/\mu m_{\rm H}$, where $k_{\rm B}$ is the Boltzmann constant and $m_{\rm H}$ is the atomic mass unit."430 We assume a plane-parallel in a constant gravitational field g=—yz which is atmospherestratified in. both and the vertical direction., We assume a plane-parallel atmosphere in a constant gravitational field $\bb{g}\equiv-g\hat{\bb{z}}$ which is stratified in both temperature and composition along the vertical direction.431 We temperatureconsider a backgroundcompositionalong field which is weak that the mechanical magnetic of the atmosphere. with enough /7. is maintained via equilibriumοον=," We consider a backgroundmagnetic field which is weak enough that the mechanical equilibrium of the atmosphere, with scaleheight $H$, is maintained via $dP/dz=-g\rho$ ."432 In general. the scaleheightbackground heat and particle fluxes do not vanish.αρ. Le.. bVT=0 and &Ve=0. unless the magnetic field and the gradients are ," In general, the background heat and particle fluxes do not vanish, i.e., $\hat{\bb{b}}\bcdot \na T \ne 0$ and $\hat{\bb{b}}\bcdot \na c \ne 0$, unless the magnetic field and the background gradients are orthogonal."433"The existence of a well defined backgroundsteady state. Le. orthogonal.V«Q.=VQ,0. demands that the gradients should be linear functions of the distance the backgrounddirection of the field."," The existence of a well defined steady state, i.e., $\na\bcdot\bb{Q}_{\rm s}=\na\bcdot\bb{Q}_{\rm c}=0$, demands that the background gradients should be linear functions of the distance along the direction of the magnetic field."434 However. even If this alongcondition is not magneticsatisfied. the dynamics of the modes that we consider is strictlyunlikely to be significantly affected if the local dynamical timescale is short compared to the timescale in which the entire system evolves (see also Quataert2008)).," However, even if this condition is not strictly satisfied, the dynamics of the modes that we consider is unlikely to be significantly affected if the local dynamical timescale is short compared to the timescale in which the entire system evolves (see also \citealt{2008ApJ...673..758Q}) )."435 The modes of interest have associated timescales that are long compared to the sound crossing time and it thus suffices to work in the Boussinesg approximation., The modes of interest have associated timescales that are long compared to the sound crossing time and it thus suffices to work in the Boussinesq approximation.436 In this limit. the equations for the linear perturbations 6—cf!eX become .. Αιde. | ," In this limit, the equations for the linear perturbations $\delta \sim e^{\sigma t + i \bb{k}\bcdot\bb{x}}$ become ), v_z + ) ."437"In agreement with the Boussinesq approximation, the velocity perturbations satisfy μυ=0 and the fluctuations in density. temperature. and mean molecular weight are related via"," In agreement with the Boussinesq approximation, the velocity perturbations satisfy $\bb{k}\bcdot \delta \bb{v} = 0$ and the fluctuations in density, temperature, and mean molecular weight are related via."438" Here. we have introduced the Alfvénn speed. v4 B/\/Tzp. the thermal speed. ey,= \/2P/p. the plasma $= ο the viscosity i of the binary mixture. the thermal diffusion coefficient «=κ. ο. and the Váusállá frequencyN? ~= -- I"," Here, we have introduced the Alfvénn speed, $\bb{v}_{\rm A}\equiv \bb{B}/\sqrt{4\pi\rho}$ , the thermal speed, $v_{\rm th}\equiv \sqrt{2P/\rho}$ , the plasma $\beta\equiv v_{\rm th}^2/v_{\rm A}^2$ , the viscosity $\nu$ of the binary mixture, the thermal diffusion coefficient $\kappa\equiv \chi T/P$ , and the $-$ Väiisällä frequencyN^2 = g ."439O For we define here several that play an important completeness.role inthe stability analysis.," For completeness,we define here severalquantities that play an important role inthe stability analysis."440 We quantitiesdenote, We denote441IMF tend to have lower values.,IMF tend to have lower values.442 This difference is induced by the larger metal content associated to the top-heavy IMF. which makes cooling more efficient within halos near the resolution limit.," This difference is induced by the larger metal content associated to the top–heavy IMF, which makes cooling more efficient within halos near the resolution limit."443 Finally. we show in Figure 8 the effect of increasing the feedback efficiency on the LF.," Finally, we show in Figure \ref{fi:lf_sw} the effect of increasing the feedback efficiency on the LF."444 In this case. we use the same normalization for the two IMFs. in order to directly see the effect of changing the feedback strength.," In this case, we use the same normalization for the two IMFs, in order to directly see the effect of changing the feedback strength."445 Quite interestingly. the effect is that of suppressing the bright end of the LF. while leaving the faint end almost unaffected.," Quite interestingly, the effect is that of suppressing the bright end of the LF, while leaving the faint end almost unaffected."446 A number of observations have established that the galaxy population in clusters is characterized by the presence of color gradients. with bluer galaxies preferentially avoiding to reside in the innermost cluster regions (2)..," A number of observations have established that the galaxy population in clusters is characterized by the presence of color gradients, with bluer galaxies preferentially avoiding to reside in the innermost cluster regions \citep{1984ApJ...285..426B}."447 For instance. ?.— found a decreasingtrend ofthe ./? color with cluster-centric distance for the galaxies lying on the CMR of nearby optically selected clusters.," For instance, \cite{2006MNRAS.366..645P} found a decreasingtrend of the $B-R$ color with cluster-centric distance for the galaxies lying on the CMR of nearby optically selected clusters."448 Similar results have also been found by 2.. ? and ? for moderately distant X-ray selected clusters.," Similar results have also been found by \cite{1996ApJ...471..694A}, \cite{1997ApJ...478..462C} and \cite{2005ApJ...627..186W} for moderately distant X–ray selected clusters."449 Quite consistently. outer cluster regions are populated by a larger fraction of blue galaxies (e.g. ?).. thus confirming. that more external galaxies are generally," Quite consistently, outer cluster regions are populated by a larger fraction of blue galaxies \citep[e.g.,450][]{2004MNRAS.351..125D}, , thus confirming that more external galaxies are generally"451gas.,gas.452" Like the 8 o'clock arc, all three are relatively massive (M.~101 ΜΜΟ) and they also show dynamics that suggest rotational support rather than merger-driven star formation (which may be more dominant in lower-mass UV-luminous systems)."," Like the 8 o'clock arc, all three are relatively massive $_\ast\sim10^{11}$ $_\odot$ ) and they also show dynamics that suggest rotational support rather than merger-driven star formation (which may be more dominant in lower-mass UV-luminous systems)."453 A cold-accreting system of this kind is likely to display the same discrepancy between metallicities determined from the youngest stars and from other methods., A cold-accreting system of this kind is likely to display the same discrepancy between metallicities determined from the youngest stars and from other methods.454" Cold-mode accretion has been hypothesised as a dominant galaxy formation mechanism at the highest redshifts (Dekeletal. 2009),, although this hypothesis remains controversial (seee.g.Steideletal.2010).."," Cold-mode accretion has been hypothesised as a dominant galaxy formation mechanism at the highest redshifts \citep{2009Natur.457..451D}, , although this hypothesis remains controversial \citep[see e.g.][]{2010ApJ...717..289S}."455" While such a case has not been proven in the 8 o’clock arc, it may prove an interesting target for detailed analysis with integral field spectroscopy, to determine whether there is any evidence for this scenario."," While such a case has not been proven in the 8 o'clock arc, it may prove an interesting target for detailed analysis with integral field spectroscopy, to determine whether there is any evidence for this scenario."456" The remaining three galaxies differ to those already discussed in that they do not require the simultaneous invocation of low metallicity, reduced carbon abundance and QHE in their synthetic stellar population to explain the spectral features under consideration, but rather display some or none of these features."," The remaining three galaxies differ to those already discussed in that they do not require the simultaneous invocation of low metallicity, reduced carbon abundance and QHE in their synthetic stellar population to explain the spectral features under consideration, but rather display some or none of these features."457 The z=3.1 Cosmic Eye spectrum (Quideretal. is illustrated in Figure 9 and is notably devoid of strong emission., The $z=3.1$ Cosmic Eye spectrum \citep{quid1} is illustrated in Figure \ref{eye} and is notably devoid of strong emission.458 This can be explained if the galaxy lies above the metallicity limit at which QHE no longer occurs., This can be explained if the galaxy lies above the metallicity limit at which QHE no longer occurs.459" The absorption section of the P Cygni profile also implies a relatively strong metallicity somewhere between Z—0.004 and 0.008, with a reduced carbon abundance required at the higher metallicity mass fraction."," The absorption section of the P Cygni profile also implies a relatively strong metallicity somewhere between $Z=0.004$ and $0.008$, with a reduced carbon abundance required at the higher metallicity mass fraction."460 Higher metallicities are ruled out by the relatively shallow absorption., Higher metallicities are ruled out by the relatively shallow absorption.461" The remaining two examples, cB58 al.2002) and the Cosmic Horseshoe (z=2.4,Quider 2009),, in Figures 10 and 11 respectively, tell a similarstory."," The remaining two examples, cB58 \citep[$z=2.7$,][]{cb58paper} and the Cosmic Horseshoe \citep[$z=2.4$,][]{horse}, in Figures \ref{cb58} and \ref{horse} respectively, tell a similarstory."462" The lack of a strong line, yet apparent P-Cygni"," The lack of a strong line, yet apparent P-Cygni"463"large fraction of pathological objects and spectra of low SNR, have redshifts derived via manual inspection of the spectra.","large fraction of pathological objects and spectra of low SNR, have redshifts derived via manual inspection of the spectra."464" Independent spectrum classifications and redshift determinations, based on direct ?-fitting of template spectra to the data, have been made at Princeton using thecode?."," Independent spectrum classifications and redshift determinations, based on direct $\chi^2$ -fitting of template spectra to the data, have been made at Princeton using the."465". The redshift determination, essentially via cross-correlation, differs from the implementation employed in thespectrold pipeline but the same composite quasar template from was used."," The redshift determination, essentially via cross-correlation, differs from the implementation employed in the pipeline but the same composite quasar template from was used."466 Fig., Fig.467 1 shows a comparison of the SDSS final-redshifts and Princeton redshifts as a function of quasarredshift?., \ref{sdss_prince} shows a comparison of the SDSS final-redshifts and Princeton redshifts as a function of quasar.468". The selection of the sub-sample of more than 700000 spectra is conservative in that only spectra with high-confidence SDSS redshifts, where there is also no inconsistency between the cross-correlation and emission line redshift determinations, are used."," The selection of the sub-sample of more than 000 spectra is conservative in that only spectra with high-confidence SDSS redshifts, where there is also no inconsistency between the cross-correlation and emission line redshift determinations, are used."469 The data in Fig., The data in Fig.470" 1 should essentially represent an internal consistency check and the large differences between redshifts, extending to +5x10~°, or!,, are surprising."," \ref{sdss_prince} should essentially represent an internal consistency check and the large differences between redshifts, extending to $\pm$ $\times$ $^{-3}$, or, are surprising."471 Perhaps even more striking is the sequence of apparent discontinuities in the behaviour as a function of redshift., Perhaps even more striking is the sequence of apparent discontinuities in the behaviour as a function of redshift.472" A second illustration of the extent of redshift-dependent systematics comes from comparing the redshift derived from the location of the AA2796,2803 emission in each quasar spectrum with the SDSS redshift."," A second illustration of the extent of redshift-dependent systematics comes from comparing the redshift derived from the location of the $\lambda\lambda$ 2796,2803 emission in each quasar spectrum with the SDSS redshift."473 Fig., Fig.474 2 presents the data for more than 600000 spectra with SNR>10 emission line locations (from the SDSS spectroscopic pipeline’))., \ref{sdss_mgii} presents the data for more than 000 spectra with $\ge$ 10 emission line locations (from the SDSS spectroscopic ).475" The rest-frame location of the emission line has been shown by many studies over the decades to be well-behaved and there is no reason to expect 7-500 !shifts over small redshift intervals, or, indeed, an apparent systematic 2x 10? s!) change in the location of the emission with increasing redshift of the quasars."," The rest-frame location of the emission line has been shown by many studies over the decades to be well-behaved and there is no reason to expect $\simeq$ shifts over small redshift intervals, or, indeed, an apparent systematic $\times$ $^{-3}$ ) change in the location of the emission with increasing redshift of the quasars."476 The systematic redshift differences show similar patterns over the redshift range common to both Fig., The systematic redshift differences show similar patterns over the redshift range common to both Fig.477 1 and Fig. 2.., \ref{sdss_prince} and Fig. \ref{sdss_mgii}.478" Although somewhat more complex to interpret (Section ??)), the equivalent plot for the emission, Fig. 3,,"," Although somewhat more complex to interpret (Section \ref{sec:em_shifts}) ), the equivalent plot for the emission, Fig. \ref{sdss_ciii},"479 also shows strong systematic effects as a function of redshift., also shows strong systematic effects as a function of redshift.480 The form and substantial amplitude of the systematic and random differences in Figs. 1-, The form and substantial amplitude of the systematic and random differences in Figs. \ref{sdss_prince}-481-3 led to the initiation of the investigation presented here.," \ref{sdss_ciii}482 led to the initiation of the investigation presented here."483 The generation of the high-SNR quasar template to be used to calculate cross-correlation redshifts begins with a sample of quasars at low redshifts that possess emission line-determined redshifts., The generation of the high-SNR quasar template to be used to calculate cross-correlation redshifts begins with a sample of quasars at low redshifts that possess emission line-determined redshifts.484 A somewhat more involved procedure is then necessary to incorporate additional quasars at higher redshifts into the master template., A somewhat more involved procedure is then necessary to incorporate additional quasars at higher redshifts into the master template.485 In this section the recipe for each element of the master template construction are outlined., In this section the recipe for each element of the master template construction are outlined.486" The narrow forbidden emission lines of A44960,5008 are prominent in many quasar spectra with redshifts z<0.8 and a composite spectrum based on the combination of quasars with redshifts determined via the location of emission forms the starting point for the construction of the master quasar template."," The narrow forbidden emission lines of $\lambda\lambda$ 4960,5008 are prominent in many quasar spectra with redshifts $z$$<$ 0.8 and a composite spectrum based on the combination of quasars with redshifts determined via the location of emission forms the starting point for the construction of the master quasar template."487In simulations we follow the procedure used by. Bednarz Ostrowski (1996) with a hvbrid approach used in Dednarz Ostrowski (1908).,In simulations we follow the procedure used by Bednarz Ostrowski (1996) with a hybrid approach used in Bednarz Ostrowski (1998).488 Mlonoenergetic seed particles are injected at the shock and then their trajectories are derived in the perturbed magnetic field., Monoenergetic seed particles are injected at the shock and then their trajectories are derived in the perturbed magnetic field.489 Phe inhomogeneities are simulated bv small amplitude particle momentum scattering within a cone with angular opening AY less than the particle anisotropy L/5 (cL., The inhomogeneities are simulated by small amplitude particle momentum scattering within a cone with angular opening $\Delta \vartheta$ less than the particle anisotropy $\sim 1/\gamma$ (cf.490 Ostrowski 1991)., Ostrowski 1991).491 A particle is excluded: from. simulations if dt escapes through the frec-escape boundary. placed far olf the shock or reaches the energy larger than the assumed. upper limit., A particle is excluded from simulations if it escapes through the free-escape boundary placed far off the shock or reaches the energy larger than the assumed upper limit.492 These particles are replaced with the ones arising from splitting the remaining high-weight particles. preserving their physical parameters.," These particles are replaced with the ones arising from splitting the remaining high-weight particles, preserving their physical parameters."493 Particles that exist longer than the time upper limit for simulations are excluded: from. simulations without replacing., Particles that exist longer than the time upper limit for simulations are excluded from simulations without replacing.494 All computations are performed. in the respective upstream or downstream plasma rest frame., All computations are performed in the respective upstream or downstream plasma rest frame.495 When particles cross the shock their parameters are. transformed. to the current plasma rest frame and the weighted: contribution divided by the particle velocity component normal to the shock (= particle density) is. added: to the time anc momentum bin depending on particle parameters. as measured in the shock normal rest framoe.," When particles cross the shock their parameters are transformed to the current plasma rest frame and the weighted contribution divided by the particle velocity component normal to the shock $\equiv$ particle density) is added to the time and momentum bin depending on particle parameters, as measured in the shock normal rest frame."496 For the considered continuous injection after initial time. the energy. cut-olf of the formed spectrum shifts toward higher energies with time.," For the considered continuous injection after initial time, the energy cut-off of the formed spectrum shifts toward higher energies with time."497 The resulting spectra allows one to fit spectral indices aud derive acceleration time in the shock normal rest. frame in units of downstream ryfe (ry - particle gvroradius in the homogeneous magnetic field component. e - speed of light: for details see Bednarz Ostrowski 1996).," The resulting spectra allows one to fit spectral indices and derive acceleration time in the shock normal rest frame in units of downstream $r_{g}/c$ ( $r_{g}$ - particle gyroradius in the homogeneous magnetic field component, $c$ - speed of light; for details see Bednarz Ostrowski 1996)."498 We transform the acceleration. time foe to the downstream: plasma rest. frame., We transform the acceleration time $t_{acc}$ to the downstream plasma rest frame.499 Llerealter. subscripts U or D mean that a parameter is measured in the upstream or downstream plasma rest frame respectively.," Hereafter, subscripts U or D mean that a parameter is measured in the upstream or downstream plasma rest frame respectively."500" We will use downstream ry, as a distance and ryὁ as à time units.", We will use downstream $r_{g}$ as a distance and $r_{g}/c$ as a time units.501 The magnetic Ποιά inclination to the shock normal upstream of the shock. c. is measured. in the upstream plasma rest [rame.," The magnetic field inclination to the shock normal upstream of the shock, $\psi$, is measured in the upstream plasma rest frame."502 Let us denote the ratio of the cross-lield diffusion covllicient #y to the parallel. diffusion cocllicicnt &q as T (the value is measured in the plasma rest. frame)., Let us denote the ratio of the cross-field diffusion coefficient $\kappa_\perp$ to the parallel diffusion coefficient $\kappa_\|$ as $\tau$ (the value is measured in the plasma rest frame).503 Simulations prove that Uuctuations upstream of the shock (measured by 7!) and downstream of the shock (measured wor?) influence the acceleration process. independently., Simulations prove that fluctuations upstream of the shock (measured by $\tau^{U}$ ) and downstream of the shock (measured by $\tau^{D}$ ) influence the acceleration process independently.504 The minimum fluctuations upstream of the shock needed o run the acceleration process cllicienthy tend to zero when ~ox., The minimum fluctuations upstream of the shock needed to run the acceleration process efficiently tend to zero when $\gamma \rightarrow \infty$.505 We. checked by simulations. with. different- 7?) that its value does not influence the spectral index considerably Or à given Tp, We checked by simulations with different $\tau^{D}$ that its value does not influence the spectral index considerably for a given $\tau^{U}$.506 Our scattering model is very simple but also universal., Our scattering model is very simple but also universal.507 In the model we are not able to cliscuss gxroresonat scattering., In the model we are not able to discuss gyroresonat scattering.508 Upstream of the shock particles have not enough time to interact resonantly with low-frequeney waves and the rough relation 7(6B/B)! (ef., Upstream of the shock particles have not enough time to interact resonantly with low-frequency waves and the rough relation $\tau \sim (\delta B/B)^{4}$ (cf.509 Blandford Eichler 1987) cannot be deduce from the interaction there., Blandford Eichler 1987) cannot be deduce from the interaction there.510 However. for erowing τί and fixed AW the time between scattering acts decreases what is equivalent to increasing the magnetic field fluctuations.," However, for growing $\tau^{U}$ and fixed $\Delta \vartheta$ the time between scattering acts decreases what is equivalent to increasing the magnetic field fluctuations."511 In the [following simulations we consider shocks with ~= 20. 40. SO. 160. 320. magnetic field inclinations wos1ο.45°. 607.757.90 and downstream: values of magnetic field Uuctuations 7?=O.L0-107.1.1 0.11.0.69.," In the following simulations we consider shocks with $\gamma=$ 20, 40, 80, 160, 320, magnetic field inclinations $\psi=15^\circ, 30^\circ,51245^\circ$, $60^\circ, 75^\circ, 90^\circ$ and downstream values of magnetic field fluctuations $\tau^{D}=0, 1.0\cdot 10^{-3}, 1.1\cdot 10^{-2}, 0.11, 0.69$ ."513 ‘Thus. as a first case we consider downstream conditions without magnetic field fluctuations.," Thus, as a first case we consider downstream conditions without magnetic field fluctuations."514 By simple data inspection (cf., By simple data inspection (cf.515 Fig., Fig.516 2) we look for minimum 7 where the, 2) we look for minimum $\tau^{U}$ where the517Disks evolve on time-scales that are orders of magnitudes smaller than expected from microphysical transport processes. and various suggestions have been made over the vears to explain this discrepancy.,"Disks evolve on time-scales that are orders of magnitudes smaller than expected from microphysical transport processes, and various suggestions have been made over the years to explain this discrepancy."518 Turbulent transport. in particular. has figured among the leading candidates since the inception of the a-disk paradigm. and a number of hydrodynamic and MHD turbulent transport mechanisms have been proposed in the literature.," Turbulent transport, in particular, has figured among the leading candidates since the inception of the $\alpha$ -disk paradigm, and a number of hydrodynamic and MHD turbulent transport mechanisms have been proposed in the literature."519 On the hydrodynamic side. subcritical turbulence (? and references therein). if present. is apparently too inefficient (??)..," On the hydrodynamic side, subcritical turbulence \citealt{RZ99}520 and references therein), if present, is apparently too inefficient \citep{LL05,JBSG06}."521 Convection was up to now found too inetficient and to transport angular momentum inthe wrong direction (??).. but ἃ recent reinvestigation of the problem indicates that this might be an artifact of these simulations being performed too close to the stability threshold (2)..," Convection was up to now found too inefficient and to transport angular momentum inthe wrong direction \citep{C96,SB96}, but a recent reinvestigation of the problem indicates that this might be an artifact of these simulations being performed too close to the stability threshold \citep{LO10}."522 Two-dimensional weak turbulence driven by small-scale. incoherent gravitational instabilities (density waves) is an option (?)..," Two-dimensional weak turbulence driven by small-scale, incoherent gravitational instabilities (density waves) is an option \citep{G96}."523 Alternatively. the baroclinic instability (?) may generate vorticity. and transport through the coupling with density waves. but its conditions of existence are still controversial (??).. although ? have probably identified the root of this debate by pointing out the nonlinear nature of the instability: also the resulting vortices would be subject to 3D instabilities (?)..," Alternatively, the baroclinic instability \citep{KB03} may generate vorticity, and transport through the coupling with density waves, but its conditions of existence are still controversial \citep{JG06,PSJ07}, although \cite{LP10} have probably identified the root of this debate by pointing out the nonlinear nature of the instability; also the resulting vortices would be subject to 3D instabilities \citep{LP09}."524 ? have proposed that the magnetorotational instability (MRI) is a potentially efficient source of turbulent transport in the nonlinear regime. an expectation soon borne out in numerical simulations.," \cite{BH91a} have proposed that the magnetorotational instability (MRI) is a potentially efficient source of turbulent transport in the nonlinear regime, an expectation soon borne out in numerical simulations."525 This instability provides by now the most extensively studied transport mechanism. through local unstratified (?).. stratified (2).. and global (2?) 3D disk simulations.," This instability provides by now the most extensively studied transport mechanism, through local unstratified \citep{HGB95}, stratified \citep{SHGB96}, and global \citep{H00}526 3D disk simulations."527 These initial simulations as well as the numerous ones following them have shown that MRI turbulence is an efficient way to transport angular momentum. in the presence or absence of a mean vertical or toroidal field. with an overall transport efficiency depending on the field configuration and strength.," These initial simulations as well as the numerous ones following them have shown that MRI turbulence is an efficient way to transport angular momentum, in the presence or absence of a mean vertical or toroidal field, with an overall transport efficiency depending on the field configuration and strength."528 However. the significant role played by microphysical dissipation in the resolutions accessible to date had largely been underestimated (??)..," However, the significant role played by microphysical dissipation in the resolutions accessible to date had largely been underestimated \citep{LL07,FPLH07}."529 By now. both the field strength and dissipation dependence of the simulated turbulent transport have been studied to some extent (and only in unstratified local shearing box settings for the latter one).," By now, both the field strength and dissipation dependence of the simulated turbulent transport have been studied to some extent (and only in unstratified local shearing box settings for the latter one)."530" The dependence of the Shakura-Sunyaev « parameter has been characterized very early on by ?. who showed that momentum transport o:7!7 both fora net vertical or toroidal (albeit with very different efficiencies in the two configurations), a scaling further confirmed in later simulations. as summarized in ?.."," The dependence of the Shakura-Sunyaev $\alpha$ parameter has been characterized very early on by \cite{HGB95} who showed that momentum transport $\propto \beta^{-1/2}$ both for a net vertical or toroidal (albeit with very different efficiencies in the two configurations), a scaling further confirmed in later simulations, as summarized in \cite{PCP07}."531 Until recently. the effect of physical viscosity (v) and resistivity Gp on the transport had been neglected. under the implicit assumption that these should not matter too much once inertial turbulent scales are resolved in the simulations.," Until recently, the effect of physical viscosity $\nu$ ) and resistivity $\eta$ ) on the transport had been neglected, under the implicit assumption that these should not matter too much once inertial turbulent scales are resolved in the simulations."532 However. ? have shown that. in the presence of à mean vertical field. the MRI-driven turbulent transport did exhibit a substantial dependence on the magnetic Prandtl number Pri v/n. with no clear trends with respect to either viscosity of resistivityalone.," However, \cite{LL07} have shown that, in the presence of a mean vertical field, the MRI-driven turbulent transport did exhibit a substantial dependence on the magnetic Prandtl number $Pm=\nu/\eta$ , with no clear trends with respect to either viscosity of resistivity."533. Recently. ? found similar results in shearing boxes with a mean toroidal field instead of a mean vertical one.," Recently, \cite{SH09} found similar results in shearing boxes with a mean toroidal field instead of a mean vertical one."534 When the mean magnetic flux vanishes. the transport behavior is more complex.," When the mean magnetic flux vanishes, the transport behavior is more complex."535 The initial investigation by ? concluded that the transport was converging to a finite value. but ? found that the transport efficiency was dependent on the simulation. resolution.," The initial investigation by \cite{HGB96} concluded that the transport was converging to a finite value, but \cite{GS05} found that the transport efficiency was dependent on the simulation resolution."536 More recently. the role of the magnetic Prandtl number Pri has been identified in this setting (2): turbulence exists only for magnetic Prandtl numbers larger than about 2. which requires the explicit inclusion of viscous and resistive terms in the fluid equations for numerical simulations to correctly capture the physies of the problem.," More recently, the role of the magnetic Prandtl number $Pm$ has been identified in this setting \citep{FPLH07}: turbulence exists only for magnetic Prandtl numbers larger than about 2, which requires the explicit inclusion of viscous and resistive terms in the fluid equations for numerical simulations to correctly capture the physics of the problem."537 The disappearance of turbulence at low Pri. as well as the need of large enough amplitudes in the initial conditions at Par> 2. indicate that the zero net flux magnetized shearing box is a subcritical system rather than a linearly unstable one (??)..," The disappearance of turbulence at low $Pm$, as well as the need of large enough amplitudes in the initial conditions at $Pm > 2$ , indicate that the zero net flux magnetized shearing box is a subcritical system rather than a linearly unstable one \citep{LO08b,LO08a}. ."538observations is presented in Table 1..,observations is presented in Table \ref{tabobs}.539 Spectra of the stellar templates 61 Cvg X B (IN5V and INTV) were also observed during the 2008 run for the purpose of radial velocities and rotational broadening analysis., Spectra of the stellar templates 61 Cyg A B (K5V and K7V) were also observed during the 2008 run for the purpose of radial velocities and rotational broadening analysis.540 In addition. eight templates of spectral tvpes G6-MOV. were collected during the 2003 campaign and another KSVY in 1999.," In addition, eight templates of spectral types G6-M0V were collected during the 2003 campaign and another K5V in 1999."541 The images were bias corrected and Hat-fielded. and the spectra subsequently. extracted. using conventional optimal extraction techniques in order to optimize the signal-to-noise ratio of the output (Llorne1986).," The images were bias corrected and flat-fielded, and the spectra subsequently extracted using conventional optimal extraction techniques in order to optimize the signal-to-noise ratio of the output \citep{Horne86}."542. Every target was bracketed with observations of a comparison CuAdr|CuNe are lamp and the pixel-to-wavelongth scale was derived through polynomial fits to a large number οἱ identified reference lines., Every target was bracketed with observations of a comparison CuAr+CuNe arc lamp and the pixel-to-wavelength scale was derived through polynomial fits to a large number of identified reference lines.543 The final rms scatter of the fit was always «1/30 of the spectral dispersion., The final rms scatter of the fit was always $<$ 1/30 of the spectral dispersion.544 We rectified the 27 individual spectra by subtracting à low-order spline fit to the continuum. after masking out the main emission and atmospheric absorption lines.," We rectified the 27 individual spectra by subtracting a low-order spline fit to the continuum, after masking out the main emission and atmospheric absorption lines."545 Phe spectra were subsequently rebinned into a uniform velocity scale of 36 kin 5 pix.1., The spectra were subsequently rebinned into a uniform velocity scale of 36 km $^{-1}$ $^{-1}$.546 Phe IK5V template 61 Cve A was broadened to 78 uns+ to match the width of the donor photospheric lines (sce Sect., The K5V template 61 Cyg A was broadened to 78 km $^{-1}$ to match the width of the donor photospheric lines (see Sect.547 4)., 4).548 Every spectrum of SY Cne was then cross-correlated: against the broadened. template in the spectral regions free [rom emission and telluric absorption features., Every spectrum of SY Cnc was then cross-correlated against the broadened template in the spectral regions free from emission and telluric absorption features.549 tadial velocities. were extracted. following the method. of lTonry&Davis(1979).. where parabolic fitshi were performed o the peak of the cross-correlation functions. and the uncertainties are purely statistical.," Radial velocities were extracted following the method of \cite{ton79}, where parabolic fits were performed to the peak of the cross-correlation functions, and the uncertainties are purely statistical."550 Since the orbital period is poorly constrained to 0.380. +0.001 d. we. performed a power spectrum analysis on the radial velocities in the range V.1-2 davs. and the results are. clisplavec in Fig. l..," Since the orbital period is poorly constrained to 0.380 $\pm0.001$ d we performed a power spectrum analysis on the radial velocities in the range 0.1-2 days, and the results are displayed in Fig. \ref{figperiod}. ."551 Here we have rescaled the errorbars by a factor 1.3 so that. the minimum v; is 1.0., Here we have rescaled the errorbars by a factor 1.3 so that the minimum $\chi^{2}_{\nu}$ is 1.0.552 The periodogram is dominated by strong aliasing due to the sparse sampling of our observations., The periodogram is dominated by strong aliasing due to the sparse sampling of our observations.553 In order to test the significance of the cillerent peaks above the noise level we performed. a Monte Carlo simulation., In order to test the significance of the different peaks above the noise level we performed a Monte Carlo simulation.554 Synthetic 47. periodograms were computed. from. a large population (10°) of velocities randomly picked from a white-noise distribution ancl with identical time sampling as our data., Synthetic $\chi^{2}$ periodograms were computed from a large population $^5$ ) of velocities randomly picked from a white-noise distribution and with identical time sampling as our data.555 A te significance level is defined by the 99.99. per cent of the computed X7. values and this is indicated. in lig., A $\sigma$ significance level is defined by the 99.99 per cent of the computed $\chi^{2}_\nu$ values and this is indicated in Fig.556 1 bv a horizontal dashed. line., \ref{figperiod} by a horizontal dashed line.557 Most. of the peaks between. [requencies 2.5-2.7  are under the line and hence periods in the range 0.37-0.40 days are significantIv above noise at the 99.99. per cent level., Most of the peaks between frequencies 2.5-2.7 $^{-1}$ are under the line and hence periods in the range 0.37-0.40 days are significantly above noise at the 99.99 per cent level.558 The two deeper peaks correspond to 0.3824 cay ancl 0.3837. day and. have v»2—L0 and 2.3 respectively. forB 24 degrees of ⋅⋅freedom., The two deeper peaks correspond to 0.3824 day and 0.3837 day and have $\chi^{2}_{\nu}=1.0$ and 2.3 respectively for 24 degrees of freedom.559 X deo significance level around the minimm peak will exclude the second. peak (Lamptonetal.1976). and hence we can conclude that 0.3824 dav is by far the most significant period., A $\sigma$ significance level around the minimm peak will exclude the second peak \citep{lampton76} and hence we can conclude that 0.3824 day is by far the most significant period.560 A least-squares sinewave fit to the radial velocities. using 22=(0.3824 day as input parameter. vielcls the following parameters where 75 corresponds to the Heliocentrie Julian date of the inferior conjunction of the donor star.," A least-squares sine-wave fit to the radial velocities, using $P=0.3824$ day as input parameter, yields the following parameters where $T_{0}$ corresponds to the Heliocentric Julian date of the inferior conjunction of the donor star."561 ALL quoted. errors are 68 per cent confidence., All quoted errors are 68 per cent confidence.562 “Lhe svstemic velocity 5. has been corrected fromthe radial velocity of 61 €vg A. that we take as -64.3 20.9 kms. 3 (Wilson1953).," The systemic velocity $\gamma$ has been corrected fromthe radial velocity of 61 Cyg A, that we take as -64.3 $\pm$ 0.9 km $^{-1}$ \citep{wilson53}."563.. Note that a sinewave fit fixing P=(0.3837 clay also vields A»=ὅτιE33 km 1. an indication⋠⋠⋠ that our Av»⊳ value is. robust and its. error realistic. irrespectively of the true value of the orbital period.," Note that a sinewave fit fixing $P=0.3837$ day also yields $K_2=87.3\pm3.3$ km $^{-1}$, an indication that our $K_2$ value is robust and its error realistic, irrespectively of the true value of the orbital period."564 The same is found when other peaks around the minimum are taken., The same is found when other peaks around the minimum are taken.565 mEe., Fig.566 2 displays the radial velocity. points folded on our favoured orbital period. £2=0.3823753 clay together with the best sine fitsolution., \ref{figrv} displays the radial velocity points folded on our favoured orbital period $P=0.3823753$ day together with the best sine fitsolution.567 Our A» velocity disagrees with the one reported. by Smithetal.(2005). which was obtained using the Na doublet., Our $K_2$ velocity disagrees with the one reported by \cite{smith05} which was obtained using the Na doublet.568 We note that the Na doublet can be quenched— by heating elfects. as opposed. to the metallic lines usec by us (Alartinetal. 1989)..," We note that the Na doublet can be quenched by heating effects, as opposed to the metallic lines used by us \citep{martin89}. ."569 LIÉ this were the case. the light centre of the Na lines would be displaced towards the back side of the star.," If this were the case, the light centre of the Na lines would be displaced towards the back side of the star."570 The effects of irradiation can be estimated. using the Ix-correction approach of Wade&Lorne(1988). Advefive=οαλά|q). where Adv is the increment in A» velocity clue to irradiation. re the radius of the donor star. @ the binary separation anc f the fractional displacement of the absorption lines site with respect to the center of mass of the star.," The effects of irradiation can be estimated using the K-correction approach of \cite{wadehorne88} $\Delta571K_2/K_2= f{\bf (}r_2/a{\bf )} (1+q)$, where $\Delta K_2$ is the increment in $K_2$ velocity due to irradiation, $r_2$ the radius of the donor star, $a$ the binary separation and $f$ the fractional displacement of the absorption line's site with respect to the center of mass of the star."572 In the extreme case. when the Na absorption is completely supressed from the irracliatecl hemisphere. f.=4/(32).," In the extreme case, when the Na absorption is completely supressed from the irradiated hemisphere, $f=4/(3\pi)$."573 Thus. replacing τω by I5eeleton's equation (Eeeleton1983) and adopting q=1.18 (sec next section) we find NA»=32 kms 1.," Thus, replacing $r_2/a$ by Eggleton's equation \citep{eggleton83} and adopting $q=1.18$ (see next section) we find $\Delta 574K_2=32$ km $^{-1}$."575 This cüllerence is just enough to accommodate Smith ct als value with ours. for maxiniuun quenching of the Na1 lines.," This difference is just enough to accommodate Smith et al's value with ours, for maximum quenching of the Na lines."576 Pherefore. we conclude that Smith ct als A» is likely a significant overestimate due to irradiation while our value is much less allected by these ellects.," Therefore, we conclude that Smith et al's $K_2$ is likely a significant overestimate due to irradiation while our value is much less affected by these effects."577 In order to measure the rotational broadening of the donor's absorption features we have [focused on the 10 highest resolution spectra gathered during the 2003 campaign., In order to measure the rotational broadening of the donor's absorption features we have focused on the 10 highest resolution spectra gathered during the 2003 campaign.578 We broadenedthe G6-MÓ templates [roni 5 to 100 km + in μαeps of 5 km using a Gray profile (Gray1992)and continuum limb-darkening coellicients appropriate for every μα»ectral type ancl our wavelength range.," We broadenedthe G6-M0 templates from 5 to 100 km $^{-1}$ in steps of 5 km $^{-1}$ , using a Gray profile \citep{Gray92} and continuum limb-darkening coefficients appropriate for every spectral type and our wavelength range."579 The broadened templates were multiplied by factors f« 1. to account Lor 16 fractional contribution to the total light.," The broadened templates were multiplied by factors $f<1$ , to account for the fractional contribution to the total light."580 These were, These were581process that clears out the disk to produce laree planets.,process that clears out the disk to produce large planets.582" Three parameters — M;/X.. py. and p, — provide good measures of the transition from oligarchy to chaos."," Three parameters – $\Sigma_l / \Sigma_s$ , $p_H$ , and $p_o$ – provide good measures of the transition from oligarchy to chaos."583" The Hill parameter measures when the oligarchs have enough mass {ο interact dwnanucally,", The Hill parameter measures when the oligarchs have enough mass to interact dynamically.584" The ratio X;/X, isolates (he Gime when planetesimals cannot camp the oligarchs and thus prevent large-scale dvnamical interactions.", The ratio $\Sigma_l / \Sigma_s$ isolates the time when planetesimals cannot damp the oligarchs and thus prevent large-scale dynamical interactions.585 The orbit overlap parameter distinguishes times when orbit overlap is important., The orbit overlap parameter distinguishes times when orbit overlap is important.586 To understand the transition from oligarchy {ο chaos in less idealized situations. we now consider complete planet formation simulations using the full hybrid code.," To understand the transition from oligarchy to chaos in less idealized situations, we now consider complete planet formation simulations using the full hybrid code."587 The caleulations start wilh 110 km planetesimals and allow all objects to collide. merge. and interact gravitationallv.," The calculations start with 1–10 km planetesimals and allow all objects to collide, merge, and interact gravitationally."588 When objects in the coagulation code reach mzz2x107(“y/8gem7) g. we promote them into the v-body code and follow their individual trajectories.," When objects in the coagulation code reach $m \approx 2 \times 10^{25}~(\Sigma_0 / {\rm 8~g~cm^{-2}})$ g, we promote them into the $n$ -body code and follow their individual trajectories."589 We describe caleulations in a small (large) torus in 823.3 (833.4)., We describe calculations in a small (large) torus in 3.3 3.4).590 The calculations begin with ὁ km planetesimals in a torus extending from 0.86 AU to 1.14 AU., The calculations begin with 1–3 km planetesimals in a torus extending from 0.86 AU to 1.14 AU.591 We divide this region into 32 annuli ancl seed each annulus with planetesimals in nearly circular and coplanar orbits (ey=10? and 4j= e4/2)., We divide this region into 32 annuli and seed each annulus with planetesimals in nearly circular and coplanar orbits $e_0 = 10^{-5}$ and $i_0 = e_0/2$ ).592 The planetesimals have surface densitv X=μίαAU)τι with X; = 116 g 7 at 1 AU.," The planetesimals have surface density $\Sigma = \Sigma_0 (a / {\rm 1 ~ AU})^{-3/2}$, with $\Sigma_0$ = 1–16 g $^{-2}$ at 1 AU."593 In these caleulations. we do nol consider lragmentation. which generally speeds up Che growth of the largest objects αἱ (he expense of mass loss [rom disruptions and gas drag (Wetherill&Stewart1993:IXenvon&Luu 1993).," In these calculations, we do not consider fragmentation, which generally speeds up the growth of the largest objects at the expense of mass loss from disruptions and gas drag \citep{ws93,kl98}."594. Weidenschillingetal.(1997) consider a similar suite of calculations.," \citet{wei97}595 consider a similar suite of calculations."596 Where il is possible to compare. our results agree with these calculations 2002 )..," Where it is possible to compare, our results agree with these calculations \citep[see also][]{kom02}."597 For Xj — 8 g 7. growth at 1 AU follows a standard pattern (Wetherill&Stewartetal.1997:IXenvon&Luu 1998).," For $\Sigma_0$ = 8 g $^{-2}$, growth at 1 AU follows a standard pattern \citep{ws93, wei97, kl98}."598. After a few thousand vears. mergers produce a few large objects with radii of ~ 10 km.," After a few thousand years, mergers produce a few large objects with radii of $\sim$ 10 km."599 As dynamical frietion. circularizes the orbits of these objects. runaway growth beeins.," As dynamical friction circularizes the orbits of these objects, runaway growth begins."600 It takes only 104 vr to produce several dozen 100300 km objects., It takes only $10^4$ yr to produce several dozen 100–300 km objects.601 At ~2xI0! vr. the first object is promoted into the »-body code.," At $\sim 2 \times 10^4$ yr, the first object is promoted into the $n$ -body code."602 As larger5 objects form farther out in the disk. more promotions occur.," As larger objects form farther out in the disk, more promotions occur."603" These objects continue to 5grow rapidly until they reach isolation! masses of ~1079 5ο, when stirring 55begins to reduce eravitational focusing factors."," These objects continue to grow rapidly until they reach `isolation' masses of $\sim 10^{26}$ g, when stirring begins to reduce gravitational focusing factors."604 The transition to oligarchic growth: beeins at the inner edge of the erid and rapidly propagates outwards., The transition to oligarchic growth begins at the inner edge of the grid and rapidly propagates outwards.605" At ~3xLO?vr. the number of oligarchs with masses m.2 107 e peaks al Ni,e T."," At $\sim$$3 \times 10^5$yr, the number of oligarchs with masses $m \gtrsim$ $10^{26}$ g peaks at $N_o \sim$ 7."606 Soon after oligarchic growth begins at the outer edge of the grid. oligarchs," Soon after oligarchic growth begins at the outer edge of the grid, oligarchs"607Part of this increase is undoubtedly due to the increase in noise in measuring the surface brightness at the faint outer wings of the stars.,Part of this increase is undoubtedly due to the increase in noise in measuring the surface brightness at the faint outer wings of the stars.608 However. we assume conservatively that the increase is entirely due to PSF variability and represent it by a parabolic eXpression where csi) 1s the uncertainty in the PSF relative to the intensity at radius r (pixels) from the PSF center.," However, we assume conservatively that the increase is entirely due to PSF variability and represent it by a parabolic expression where $\sigma_{\rm PSF}(r)$ is the uncertainty in the PSF relative to the intensity at radius $r$ (pixels) from the PSF center."609 We then compute the expected variance of a pixel 7 with intensity / (ADU) and distance r from the center of from the expression where G is the effective gain and Ris the effective readout noise. and compute the y- from where M is the model intensity and the summation is over all unmasked pixels within the fitting radius.," We then compute the expected variance of a pixel $\sigma^2$ with intensity $I$ (ADU) and distance $r$ from the center of from the expression where $G$ is the effective gain and $R$ is the effective readout noise, and compute the $\chi^2$ from where $M$ is the model intensity and the summation is over all unmasked pixels within the fitting radius."610 In addition to the i-band images. two spectra with an exposure time of 900 s were obtained using grism #44 of ALFOSC. which covers the wavelength range 3200-9100A.," In addition to the i-band images, two spectra with an exposure time of 900 s were obtained using grism 4 of ALFOSC, which covers the wavelength range 3200-9100."611. The spectral resolution achieved using the 1733 slit wasÁ., The spectral resolution achieved using the 3 slit was.612. Due to the effect of the secondary spectrum and fringing longwards of 6000Á.. we studied only the wavelength range 4000-6000À.," Due to the effect of the secondary spectrum and fringing longwards of 6000, we studied only the wavelength range 4000-6000."613. The summed spectrum has a signal-to-noise ratio (S/N) of ~ 250. but the spectrum remains featureless.," The summed spectrum has a signal-to-noise ratio (S/N) of $\sim$ 250, but the spectrum remains featureless."614 Table | indicates the results of the model fits. and the upper panel of Fig.," Table \ref{tulokset} indicates the results of the model fits, and the upper panel of Fig."615 2. shows the one-dimensional surface brightness profile of and the model profiles., \ref{prof} shows the one-dimensional surface brightness profile of and the model profiles.616 The I-band magnitude of the nucleus translates into R ~ 14.2 using I) = 0.5(22).. so the nucleus had brightened by ~ 0.6 mag in the R-band from the deep minimum on Dec 17th.," The I-band magnitude of the nucleus translates into R $\sim$ 14.2 using (R-I) = 0.5, so the nucleus had brightened by $\sim$ 0.6 mag in the R-band from the deep minimum on Dec 17th."617 The host galaxy is faint (I = 17.5) compared to the nucleus and never exceeds the core brightness at any radius. but is visible as à small excess in the surface brightness profile of (see Fig. 2)).," The host galaxy is faint (I = 17.5) compared to the nucleus and never exceeds the core brightness at any radius, but is visible as a small excess in the surface brightness profile of (see Fig. \ref{prof}) )."618 Since PSFI was constructed from stars closer to than PSF2. it is unsurprising that PSFI provides a more accurate description of the data (smaller y7) than PSF2.," Since PSF1 was constructed from stars closer to than PSF2, it is unsurprising that PSF1 provides a more accurate description of the data (smaller $\chi^2$ ) than PSF2."619 The fit with core + galaxy reduces the y of the fit. but none of the fits provide formally satisfactory fits. most likely due to higher-order PSF variability unaccounted for in our radial PSF variability model.," The fit with core + galaxy reduces the $\chi^2$ of the fit, but none of the fits provide formally satisfactory fits, most likely due to higher-order PSF variability unaccounted for in our radial PSF variability model."620 We completed several tests to ensure that the observed excess Is real and not due to PSF variability over the field of view., We completed several tests to ensure that the observed excess is real and not due to PSF variability over the field of view.621 Firstly. we compared the sealed surface brightness profiles of stars 2. 3. 6. SI. and S2 and with the surface brightness profile of star 5 (see the lower panel of Fig.," Firstly, we compared the scaled surface brightness profiles of stars 2, 3, 6, S1, and S2 and with the surface brightness profile of star 5 (see the lower panel of Fig."622 2)., 2).623 There is a clear excess around that exceeds the rms scatter of stellar profiles by a factor of 3-6 at r>27, There is a clear excess around that exceeds the rms scatter of stellar profiles by a factor of 3-6 at $r >$.624"%, The excess is clearly above any PSF variability observed over the field of view.", The excess is clearly above any PSF variability observed over the field of view.625 Secondly. although the fits with PSF2 provide a slightly worse fit than with PSFI. the host galaxy component is still present with similar brightness and effective radius as with PSFI.," Secondly, although the fits with PSF2 provide a slightly worse fit than with PSF1, the host galaxy component is still present with similar brightness and effective radius as with PSF1."626 Also this test indicates that PSF variability does not affect the results significantly., Also this test indicates that PSF variability does not affect the results significantly.627 Finally. we fitted core + host galaxy models to stars 6. S2. and S4. which are similar in brightness to0716+714.," Finally, we fitted core + host galaxy models to stars 6, S2, and S4, which are similar in brightness to."628. Using PSFI. the fit converged towards a solution ry;—O in all three cases. 1.9. no host galaxy component was detected in targets known to be unresolved.," Using PSF1, the fit converged towards a solution $r_{\rm629 eff} \rightarrow 0$ in all three cases, i.e. no host galaxy component was detected in targets known to be unresolved."630 Based on the three test mentioned above. we conclude that the excess around is real and we have detected the host galaxy.," Based on the three test mentioned above, we conclude that the excess around is real and we have detected the host galaxy."631"the line-of-sight i.e., considering the imposing dimensions of the large region (e.g., Lagrois&Joncas 2009a,b)), the interface between compressive shocks and the surrounding ISM could be several times smaller than the size of the nebula itself.","the line-of-sight i.e., considering the imposing dimensions of the large region (e.g., \citealt{Lag2009a,Lag2009b}) ), the interface between compressive shocks and the surrounding ISM could be several times smaller than the size of the nebula itself."632" This said, the expected spectral signature of shock excitation could be strongly diluted by photoionized foreground/background material."," This said, the expected spectral signature of shock excitation could be strongly diluted by photoionized foreground/background material."633" A total of 23378 out of 30057 emission-line profiles retained for this study are directly associated to the bright, central structure clearly visible in Figure 8."," A total of 378 out of 057 emission-line profiles retained for this study are directly associated to the bright, central structure clearly visible in Figure 8."634" The strong emission of its ionized component (see peak intensities in Figures 3 to 7) and therefore the quality of the gathered signal make this structure, surrounded by the most massive stars of the Melotte 15 cluster, the ideal feature in our quest for shock excitation in central 11805."," The strong emission of its ionized component (see peak intensities in Figures 3 to 7) and therefore the quality of the gathered signal make this structure, surrounded by the most massive stars of the Melotte 15 cluster, the ideal feature in our quest for shock excitation in central 1805."635" First, a series of four weaker portions [in gas emission], specifically surrounding the central structure, were selected."," First, a series of four weaker portions [in gas emission], specifically surrounding the central structure, were selected."636 Each of these portions was spatially binned into a single 1x 11x 2249 x x cchannels)profile?.., Each of these portions was spatially binned into a single $\times$ $\times$ 249 $\times$ $\times$ channels).637" For each of the 23378 spectra selected and investigated in this subsection, the corresponding foreground/background emission was approximately recovered using a linear combination of these four 1x x 2249 profiles."," For each of the 378 spectra selected and investigated in this subsection, the corresponding foreground/background emission was approximately recovered using a linear combination of these four $\times$ $\times$ 249 profiles."638" Each of the four linear coefficients was weighted via the inverse of the distance separating the targeted pixel from the center of the corresponding weaker portion (e.g., the larger this distance is, the smaller is the corresponding linear coefficient and, therefore, the smaller is the statistical impact of this weaker zone on the computation of the foreground/background spectral signature at the position of this given pixel)."," Each of the four linear coefficients was weighted via the inverse of the distance separating the targeted pixel from the center of the corresponding weaker portion (e.g., the larger this distance is, the smaller is the corresponding linear coefficient and, therefore, the smaller is the statistical impact of this weaker zone on the computation of the foreground/background spectral signature at the position of this given pixel)."639" Hence, a unique foreground/background spectrum is constructed for each of the 23378 points (see below) although neighbor pixels have [as it should be] foreground/background material with very similar spectral signatures (i.e., roughly identical linear coefficients)."," Hence, a unique foreground/background spectrum is constructed for each of the 378 points (see below) although neighbor pixels have [as it should be] foreground/background material with very similar spectral signatures (i.e., roughly identical linear coefficients)."640" The subtraction of the foreground/background emission obviously had a certain incidence on the S/N of the resulting profiles, the peak intensity of all five lines being reduced in the subtracting process."," The subtraction of the foreground/background emission obviously had a certain incidence on the S/N of the resulting profiles, the peak intensity of all five lines being reduced in the subtracting process."641" Still following all conditions listed in 8 4.2.2, 22229 emission-line profiles out of 23378 were said to “survive” the procedure."," Still following all conditions listed in $\S$ 4.2.2, 229 emission-line profiles out of 378 were said to “survive” the procedure."642 Panels (a) and (b) of Figures, Panels (a) and (b) of Figures643Not all azimuthal components mm contribute al the same level.,Not all azimuthal components $m$ contribute at the same level.644" Figure 1. shows the amplitudes of the ;1,, as a function of m Dor two different values of the tube radius. &."," Figure \ref{fig.exact_and_born} shows the amplitudes of the $A_m$ as a function of $m$ for two different values of the tube radius, $R$ ."645 In this particular example. pj=5x10* ces. ec=11 km/s. and B=1 kG are fixed.," In this particular example, $\rho_0=5\times10^{-7}$ cgs, $c=11$ km/s, and $B=1$ kG are fixed."646 For IH—0.5 Mm. whieh is less than the wavelength (AJ?=0.36). only the m.—0.41 azimuthal components contribute.," For $R=0.5$ Mm, which is less than the wavelength $kR=0.86$ ), only the $m=0,\pm1$ azimuthal components contribute."647 For tubes with larger radii the higher order components have larger amplitudes. as can be seen in the case 22=2 Mm (hit=3.43).," For tubes with larger radii the higher order components have larger amplitudes, as can be seen in the case $R=2$ Mm $kR = 3.43$ )."648 Magnetic effects cause perturbations to both the steady. background state ancl the wavelfield., Magnetic effects cause perturbations to both the steady background state and the wavefield.649 In this section we use the Born approximation to derive an approximate solution {ο equations (11))-(15)) based on tlie assumption that magnetic effects are small 1995)., In this section we use the Born approximation to derive an approximate solution to equations \ref{cont}) \ref{temp}) ) based on the assumption that magnetic effects are small \citep[see e.g.][]{Rosenthal1995}.650. The Lorentz force is quadratic in the magnetic field., The Lorentz force is quadratic in the magnetic field.651 As à result we introduce a small parameter that is second order in (he magnetic field., As a result we introduce a small parameter that is second order in the magnetic field.652" We choose to expand all quantities in powers of the small dimensionless parameter In this expansion framework the magnetic field appears al order εντ,", We choose to expand all quantities in powers of the small dimensionless parameter In this expansion framework the magnetic field appears at order $\epsilon^{1/2}$.653 In particular. we write the steady background magnetic field as The magnetic field causes a shift. ey. in the steady component of the density inside the tube relative to the steady. component of the density outside the tube. py: Likewise. we write the steady. component of pressure as Thesechanges are related to (he magnetic field through equation (10)) aud (hie equationof state:," In particular, we write the steady background magnetic field as The magnetic field causes a shift, $\epsilon\rho_1$, in the steady component of the density inside the tube relative to the steady component of the density outside the tube, $\rho_0$ : Likewise, we write the steady component of pressure as Thesechanges are related to the magnetic field through equation \ref{eq.pressure_bal}) ) and the equationof state:"654"quadrant Q«c(«c 57. 5""«fOF. which comprises Daade's Window. is so far only partially released by 2\LASS.","quadrant $0^{\circ}<\ell<5^{\circ}$ , $-5^{\circ}<{\it b}<0^{\circ}$, which comprises Baade's Window, is so far only partially released by 2MASS."655 Fig., Fig.656" 4 shows a histogram of values for the cells in the 10"".10 extinction map.", 4 shows a histogram of values for the cells in the $^{\circ} \times 10^{\circ}$ extinction map.657 The mean extinction in the entire map ds <ly>=0.29 with a standard deviation o=0.12 from the mean., The mean extinction in the entire map is ${\it<A_K>} = 0.29$ with a standard deviation $\sigma = 0.12$ from the mean.658 63 of the cells fall within 2-0 of this mean value. ancl of them have τν1.0.," 63 of the cells fall within $\sigma$ of this mean value, and of them have ${\it A_K} < 1.0$."659 The upper panel of Fie., The upper panel of Fig.660 5 shows the histogram of internal crrors in extinction determination., 5 shows the histogram of internal errors in extinction determination.661 The mean internal error is «0;“=0.08. with a standard eviation of 0.02 around this mean.," The mean internal error is $<\sigma_i> = 0.08$, with a standard deviation of $0.02$ around this mean."662 of the cells have internal errors within 2 standard deviations from the mean value (0.04.<m; 0.12)., of the cells have internal errors within 2 standard deviations from the mean value $0.04 \leq \sigma_i \leq 0.12$ ).663 The lower panel shows the dependence of internal errors withely: we note that for Ay&1.5 the internal errors increase significantly., The lower panel shows the dependence of internal errors with; we note that for ${\it A_K} > 1.5$ the internal errors increase significantly.664 Since the present extinction map can be useful for a wide varicty of Galactic and extragalactic studies in such central directions. it will be provided in electronic form in the CDS. bv columns: (1) ancl (2) galactic longitude and latitucle of the cell centre. (3) the band. extinction and (4) he uncertainty in the determination στ.," Since the present extinction map can be useful for a wide variety of Galactic and extragalactic studies in such central directions, it will be provided in electronic form in the CDS, by columns: (1) and (2) galactic longitude and latitude of the cell centre, (3) the band extinction and (4) the uncertainty in the determination $\sigma_i$."665 Schultheis ct al. (, Schultheis et al. (6661999). provided. an extinction. map for he inner Galactic Bulge (covering [ff«8 and 1« 5°) obtained [rom heJ and DENIS CMDs. together with isochrones from Aertelli ct al. (,"1999) provided an extinction map for the inner Galactic Bulge (covering $|\ell|<8^{\circ}$ and $|{\it b}|<1.5^{\circ}$ ) obtained from the and DENIS CMDs, together with isochrones from Bertelli et al. ("6671994). hereafter called DISNIS extinction map.,"1994), hereafter called DENIS extinction map."668 The cdilferences tween the present extinction determinaion applied to 2NASS photometry and he procedure adopted: by Schultheis e al. (, The differences between the present extinction determination applied to 2MASS photometry and the procedure adopted by Schultheis et al. (6691999) are the ollowing: (1) the latter use an isochrone from Bertelli οἱ al. (,1999) are the following: (i) the latter use an isochrone from Bertelli et al. (6701994). with metallicity Z—0.02. age of LO Gyr and distance d=S Ipc. to represent the dereddened (Α.Ο ΔΕΗ of the Bulee fields: (ii) Schultheis ct al.,"1994), with metallicity =0.02, age of 10 Gyr and distance =8 Kpc, to represent the dereddened ) CMD of the Bulge fields; (ii) Schultheis et al."671" adopt a transformation romA to with an estimated error of 0.04 mag. in order to x able to use isochrone fitting: and (ii) the DENIS infrared ohotometry is limited to A,—11.0. with detection limits at J=160 and A.=13.0 (Schulthejs ct al."," adopt a transformation from to with an estimated error of 0.04 mag, in order to be able to use isochrone fitting; and (iii) the DENIS infrared photometry is limited to =11.0, with detection limits at $J = 16.0$ and $K_s = 13.0$ (Schultheis et al."672 1999)., 1999).673 Unavane et al. (, Unavane et al. (674"1998) estimaed a DENIS completeness imiting magnitude of A,—10.0 in the inner Bulec.",1998) estimated a DENIS completeness limiting magnitude of =10.0 in the inner Bulge.675 The postution of the DENTS extinction. map is also 4., The resolution of the DENIS extinction map is also $^{\prime}$.676 Lig., Fig.677" 6 shows the comparison of the extinction. values derived rom the 2ALASS photometry. lAoir ith those derived rom the DENIS photometry. .NODENIS- or the area in COoninioln between the two mapμα nos5"" and [0«1.5 )"," 6 shows the comparison of the extinction values derived from the 2MASS photometry, ${\it A_{K,2MASS}}$ , with those derived from the DENIS photometry, ${\it A_{K,DENIS}}$, for the area in common between the two maps $|\ell|<5^{\circ}$ and $|{\it b}|<1.5^{\circ}$ )."678 The extinction values derivec from he 2ALASS and DIELS photometric data presen ul CACOent agreement. especially αρ to =l.0.," The extinction values derived from the 2MASS and DENIS photometric data present an excellent agreement, especially up to =1.0."679 3evoned this imit dkpENIS valttes are higher than Ayospyss ones. bu if we consider ha the uncertainties in the extinction cleermination and ohotometric errors increase in these zones. he agreement is still significant.," Beyond this limit ${\it A_{K,DENIS}}$ values are higher than ${\it A_{K,2MASS}}$ ones, but if we consider that the uncertainties in the extinction determination and photometric errors increase in these zones, the agreement is still significant."680 The departure from identiv line in Fig., The departure from identity line in Fig.681 6 COUd be partially due to dilferences in the filter profiles and Zero-point calibrations adopted by the two surveys., 6 could be partially due to differences in the filter profiles and zero-point calibrations adopted by the two surveys.682 Schlegel et al. (, Schlegel et al. (6831998) (hereafter SEDOS) presented an all-sky reddening map basedon the 100 jm dust emission. modeling the emission by dust. grains with blackbocly radiation at a temperature 7—18.2 Wk. Temperature correctionswere,"1998) (hereafter SFD98) presented an all-sky reddening map basedon the 100 $\mu$ m dust emission, modeling the emission by dust grains with blackbody radiation at a temperature =18.2 K. Temperature correctionswere"684properties in molecular line observations despite their similar internal liminosities.,properties in molecular line observations despite their similar internal luminosities.685 LAA 04191 eet al., IRAM 04191 et al.686 1999: Belloche et al., 1999; Belloche et al.687 2002) n L152MEG Crapsi οἱ al., 2002) and L1521F (Crapsi et al.688associated 2004) show evidence for infall whereas L1014 does not (Crapsi et al., 2004) show evidence for infall whereas L1014 does not (Crapsi et al.689 2005)., 2005).6901 IRAM 04191 is with a well-collimated outflow eel al., IRAM 04191 is associated with a well-collimated outflow et al.691 1999): the other two are not. although al least LIOI4 and possibly L1521E feature weak. compact outflows (Bourke et al.," 1999); the other two are not, although at least L1014 and possibly L1521F feature weak, compact outflows (Bourke et al."692 2005: Bourke et al., 2005; Bourke et al.693 2006)., 2006).694" The discovery of VeLLOs with has put into question the picture of low-mass star lormation as a continuous process of constant mass accretion al the standard rate of —2x10"" vr| (Shu. Adams. Lizano 1987) through a single evolutionary sequence. (he well-established class svstem progressing from Class 0 to III (Myers Lada 1993. André et al."," The discovery of VeLLOs with has put into question the picture of low-mass star formation as a continuous process of constant mass accretion at the standard rate of $\sim 2\times 10^{-6}$ $yr^{-1}$ (Shu, Adams, Lizano 1987) through a single evolutionary sequence, the well-established class system progressing from Class 0 to III (Myers Lada 1993, André et al."695 1993)., 1993).696 This standard accretion rate predicts a much higher Iuminositv than observed for VeLLOs: VeLLOs must feature some combination of a very low central mass aud a very low accretion rate (e.g. Dunham et al., This standard accretion rate predicts a much higher luminosity than observed for VeLLOs; VeLLOs must feature some combination of a very low central mass and a very low accretion rate (e.g. Dunham et al.697 2006)., 2006).698 If the accretion continues at the current low rate to the very small central mass. it might not make a star.," If the accretion continues at the current low rate to the very small central mass, it might not make a star."699 ILowever. the accretion rate is not necessarily constant.," However, the accretion rate is not necessarily constant."700 For instance. FU Orionis (FU Ori) objects undergo outbursts (Bell et al.," For instance, FU Orionis (FU Ori) objects undergo outbursts (Bell et al."701 1995 and references therein)., 1995 and references therein).702 Studies (Vorobvoy Basu 2005 and references therein) lor the nature ol the FU Ori variables suggest. accretion bursts [rom the disk to the central star bv. the thermal instability of the disk., Studies (Vorobyov Basu 2005 and references therein) for the nature of the FU Ori variables suggest accretion bursts from the disk to the central star by the thermal instability of the disk.703 Therefore. (wo potential explanations for the verv low luminosities of VeLLOs are 1) proto-brown cdwarls. and 2) objects in a quiescent phase of the episoclic accretion process.," Therefore, two potential explanations for the very low luminosities of VeLLOs are 1) proto-brown dwarfs, and 2) objects in a quiescent phase of the episodic accretion process."704 The former can be discriminated [rom the latter with studies of the chemistry since they involve vastly different. thermal histories. which is crucial (o the chemical evolution.," The former can be discriminated from the latter with studies of the chemistry since they involve vastly different thermal histories, which is crucial to the chemical evolution."705 The thermal history is especially important in interactions between gas ancl ice: ice evaporation and eas [reeze-out [rom and onto grain surfaces. respectively. depend on the dust temperature (Lee et al.," The thermal history is especially important in interactions between gas and ice; ice evaporation and gas freeze-out from and onto grain surfaces, respectively, depend on the dust temperature (Lee et al."706 2004)., 2004).707 Proto-brown clwarls. with their very low masses. will never experience a hot phase. whereas the outbursts of a evele of episodic accretion. a short time period when (he majority of the mass is dumped onto the central protostar. involve significant. warming of the surrounding dust.," Proto-brown dwarfs, with their very low masses, will never experience a hot phase, whereas the outbursts of a cycle of episodic accretion, a short time period when the majority of the mass is dumped onto the central protostar, involve significant warming of the surrounding dust."708 The quiescent states between outbursts feature much colder dust temperatures., The quiescent states between outbursts feature much colder dust temperatures.709 As a result. envelopes of proto-brown dwarls will be similar (to starless cores in (heir chemical distributions. while objects in a quiescent state of episodic accretion will show different chemical distributions from starless cores or normal. embedded Class 0/1 objects.," As a result, envelopes of proto-brown dwarfs will be similar to starless cores in their chemical distributions, while objects in a quiescent state of episodic accretion will show different chemical distributions from starless cores or normal, embedded Class 0/I objects."710 IRAM 04191 may be undergoing episodie accretion since it features a strong outflow which predicts a higher acceretion rate by (wo orders of magnitude (han inferred. [rom the internal Iuminositv of the source, IRAM 04191 may be undergoing episodic accretion since it features a strong outflow which predicts a higher accretion rate by two orders of magnitude than inferred from the internal luminosity of the source711Aliminum size estimates can be obtained straight{οναον from lines whieh correspond to total coverage.,Miminum size estimates can be obtained straightforwardly from lines which correspond to total coverage.712 The proper separation at reshift z of the light. paths from the two images of a lensed QSO with emission redshift tem due to a lens at redshift z; is given by (Young et al., The proper separation at reshift $z$ of the light paths from the two images of a lensed QSO with emission redshift $z_{\rm em}$ due to a lens at redshift $z_{\rm l}$ is given by (Young et al.713 1981) where do is the observed angular separation of the images., 1981) where $\delta\phi$ is the observed angular separation of the images.714 Phe light paths converge at toon and the angular clameter distances. D. are given by where the comoving distance for a [lat universe (ο =0:Peebles 1993: Loge 2000).," The light paths converge at $z_{\rm con}=0$ and the angular diameter distances, $D$, are given by where is the comoving distance for a flat universe $\Omega_K=0$; Peebles 1993; Hogg 2000)."715 Equ., Equ.716 6 holds for 2. 27zas assumed. here., \ref{sep} holds for $z>z_{\rm l}$ as assumed here.717 Eeami ct al. (, Egami et al. (7182000) argue that the lensing ealaxy should be at ο~3 based on the Einstein ane core racii of their model.,2000) argue that the lensing galaxy should be at $z_{\rm l} \sim 3$ based on the Einstein and core radii of their model.719 The damped ssvsteni at 2~2.974 may |be compatible with this estimate., The damped system at $z\sim 2.974$ may be compatible with this estimate.720 Additionally. Petitjean et al. (," Additionally, Petitjean et al. ("7212000) suggest. that. strong ssvstenis are prime lense candidates because the roughly equal brightnesses of images A and D suggest the LOS are traversing the central regions of the lensing object.,2000) suggest that strong systems are prime lense candidates because the roughly equal brightnesses of images A and B suggest the LOS are traversing the central regions of the lensing object.722 We have thus calculated the separation for five values of 2; as shown in Tables 4. and 5..," We have thus calculated the separation for five values of $z_{\rm l}$ as shown in Tables \ref{tab:sep}723 and \ref{tab:sep2}."724 Phese values include an arbitrary value of 0.7. not corresponding to any known object. three values corresponding to observed. ssystenis and one value from the damped ssvstemi mentioned.," These values include an arbitrary value of 0.7, not corresponding to any known object, three values corresponding to observed systems and one value from the damped system mentioned."725 The observed. angular separation of image B from the combined A}€ image was taken to be 00=0.360 arcsec., The observed angular separation of image B from the combined A+C image was taken to be $\delta\phi=0.369$ arcsec.726 Phere is some ambiguity as to wha one means by the location of the AX|€ image. and we have simply chosen the location of the Uusx-weightecl centro of the A|C image.," There is some ambiguity as to what one means by the location of the A+C image, and we have simply chosen the location of the flux-weighted centroid of the A+C image."727 Size estimates scale with 3o (this stil holds. approximately. in the statistical approach of the nex section) and so the elfect is of the order of no more than a few percent.," Size estimates scale with $\delta\phi$ (this still holds, approximately, in the statistical approach of the next section) and so the effect is of the order of no more than a few percent."728 Thus the results remain qualitatively unallected., Thus the results remain qualitatively unaffected.729 We then applied à maximum likelihood method in order to estimate the most probable size of the absorbers. given the information that we have obtained through this work.," We then applied a maximum likelihood method in order to estimate the most probable size of the absorbers, given the information that we have obtained through this work."730 We assumed two simple gcomoetries for absorbers of uniform size., We assumed two simple geometries for absorbers of uniform size.731 The probability that asphericalcloud is intersected by both LOS. given that it is intersected by one is (MeGill 1990). for Yoo0. 1].and zero otherwise.," The probability that acloud is intersected by both LOS, given that it is intersected by one is (McGill 1990), for $X \in [0,1]$ ,and zero otherwise."732 Lore N(s)= S(MB. where A is the absorber radius.," Here $X(z)\equiv 733S(z)/2R$ , where $R$ is the absorber radius."734 bor, For735should be dominated by imerger-trieeered AGN. even at moderate Iuniünosities (L4~10 cre Ly),"should be dominated by merger-triggered AGN, even at moderate luminosities $L_{\rm x} \sim 10^{43}$ erg $^{-1}$ )."736 This is because increcr-driven accretion in this model is tied to the cosmological ealaxy merger rate. which increases rapidly with redshift (Cousclice ct al.," This is because merger-driven accretion in this model is tied to the cosmological galaxy merger rate, which increases rapidly with redshift (Conselice et al."737 2003: IKartaltepe et al., 2003; Kartaltepe et al.738 2007) whereas quiesceut accretion is related to the mass fiction aud eas fraction of late-type ealaxies. which evolve more slowly.," 2007) whereas quiescent accretion is related to the mass function and gas fraction of late-type galaxies, which evolve more slowly."739 The IIIIOG model predicts that at 2= the number density of quiesceutly accreting AGN will not equal that of mereer-fucled ACN until roughly bolow the kuee in the AGN huuinositv function., The HH06 model predicts that at $z=2$ the number density of quiescently accreting AGN will not equal that of merger-fueled AGN until roughly below the knee in the AGN luminosity function.740 Iu the hard N-rav baud this kuee occurs at a Iuuinositv of roughly Ly~10H erg s+ (Aird et al.," In the hard X-ray band this knee occurs at a luminosity of roughly $L_{\rm X} \sim74110^{44}$ erg $^{-1}$ (Aird et al."742 2010)., 2010).743 This mecaus the predicted X-ray Iuninositv at which au equal fraction of ACN are fueled by quiesceut aud. mierger-triggered accretion at 2= is roughly Lx~1072 cre Ἐν," This means the predicted X-ray luminosity at which an equal fraction of AGN are fueled by quiescent and merger-triggered accretion at $z=2$ is roughly $L_{\rm744 X} \sim 10^{42}$ erg $^{-1}$."745 TÉ we asstune that disk-like hosts are fucling their ACN via internal processes and have not experienced a major merecr in the recent past. then this prediction is at odds with the high disk fraction we observe at Lx~10% eve st. an order of maguitude above this uumositv.," If we assume that disk-like hosts are fueling their AGN via internal processes and have not experienced a major merger in the recent past, then this prediction is at odds with the high disk fraction we observe at $L_{\rm X} \sim74610^{43}$ erg $^{-1}$, an order of magnitude above this luminosity."747 We fiud that the Inuiimnositv at which au equal raction of ACN are losted by disk and splieroid galaxies is roughly Lx~10% eres+., We find that the luminosity at which an equal fraction of AGN are hosted by disk and spheroid galaxies is roughly $L_{\rm X} \sim 10^{43}$ erg $^{-1}$.748 This fiudiug suggests that he stochastic fuchue of SAIBUs is far more prevalent at moderate huuinosities than predicted by the Πο noclel., This finding suggests that the stochastic fueling of SMBHs is far more prevalent at moderate luminosities than predicted by the HH06 model.749 This appareut disagreenmient with the IIIIO6 ficling uodel was previously reported at lower redshifts o» Ceorgakakis et al. (, This apparent disagreement with the HH06 fueling model was previously reported at lower redshifts by Georgakakis et al. (7502009). who found that the contribution to the N-rav. Iuninositv function at τον1 roni ACN iu late-tvpe hosts exceeded the predicted Πο function for stochastically fueled ACN.,"2009), who found that the contribution to the X-ray luminosity function at $z\sim1$ from AGN in late-type hosts exceeded the predicted luminosity function for stochastically fueled AGN."751 It was also noted by Cisternas et al. (, It was also noted by Cisternas et al. (7522011). who found a large Yaction }) of huninous AGN (Ex>10H erg 1) at 2~L hosted by disk-dominated galaxies.,"2011), who found a large fraction ) of luminous AGN $L_{\rm X} > 10^{44}$ erg $^{-1}$ ) at $z\sim1$ hosted by disk-dominated galaxies."753 While the veh disk fraction we observe is similar to what has been weviously reported iu these studies. the disagreement οtween our Ποιος and the predictions of the IITIOG uodel is more acute eiven the higher redshift of our sample aud the strong redshift evolution predicted for nerecr-driven accretion.," While the high disk fraction we observe is similar to what has been previously reported in these studies, the disagreement between our findings and the predictions of the HH06 model is more acute given the higher redshift of our sample and the strong redshift evolution predicted for merger-driven accretion."754" Overall our findings generally agree with au ciereine consensus that inajor galaxy iereers likely plav a subdominant role in triggering mocderate-liuunosity AGN,", Overall our findings generally agree with an emerging consensus that major galaxy mergers likely play a subdominant role in triggering moderate-luminosity AGN.755 This has been asserted from a morphological standpoint by Cisternas et al. (, This has been asserted from a morphological standpoint by Cisternas et al. (7562011) aud Ceorgakalis et al. (,2011) and Georgakakis et al. (7572009) at 2~1. aud by Schawinski et al. (,"2009) at $z\sim1$, and by Schawinski et al. ("7582011) at zo2. based on the large disk fraction found. among ACN hosts.,"2011) at $z\sim2$, based on the large disk fraction found among AGN hosts."759 It has also been proposed by Miillaney et al. (, It has also been proposed by Mullaney et al. (7602011) based ou the average specific star formation rates (SSFR) of ACN hosts out to z~3.,2011) based on the average specific star formation rates (SSFR) of AGN hosts out to $z\sim3$.761 They fiud that a vast majority of hosts have SSERs consistent with the star foriing main sequence (Noeske et al., They find that a vast majority of hosts have SSFRs consistent with the star forming main sequence (Noeske et al.762 2007) and that less than appear to be undergoing a starburst phase., 2007) and that less than appear to be undergoing a starburst phase.763 From this they couclude that the muclear activity in these galaxies is being fucled by internal πουαπστις rather than violent mergers., From this they conclude that the nuclear activity in these galaxies is being fueled by internal mechanisms rather than violent mergers.764 A similar conclusion was also reached by Allevata et al. (, A similar conclusion was also reached by Allevato et al. (7652011) based on the projected clustering of AGN in the COSMOS field out to 123.,2011) based on the projected clustering of AGN in the COSMOS field out to $z\sim2.2$.766 There are several reasons why nonanerger related accretion inav contribute more to the onset of ACN activity at this redshift than previously expected., There are several reasons why non-merger related accretion may contribute more to the onset of AGN activity at this redshift than previously expected.767 This includes such thiugs as a shorter post-blowout quasar lhfetime. which would reduce the contribution frou moreci-trigecred ACN to the N-rav luminosity function. or a faster evolving gas fraction than that assumed bv IHIIO6.," This includes such things as a shorter post-blowout quasar lifetime, which would reduce the contribution from merger-triggered AGN to the X-ray luminosity function, or a faster evolving gas fraction than that assumed by HH06."768 It may also be due to the rise of violeut eravitational imstabilities iu disk ealaxics due to the effects of rapid cold flow accretion (Dekel. Sari. Coeoverino 2009).," It may also be due to the rise of violent gravitational instabilities in disk galaxies due to the effects of rapid cold flow accretion (Dekel, Sari, Ceverino 2009)."769 Such instabilities become iucreasiuelv cohbunon at z21 (Ehueercen et al., Such instabilities become increasingly common at $z>1$ (Elmegreen et al.770 05. Cenzel et al.," 05, Genzel et al."771 06) and are not accounted for in the IHHIOG model., 06) and are not accounted for in the HH06 model.772 Unlike the weaker disk iustabilities that are associated with secular evolution at low redshift (0.9.. bar iustabilities). these high redshift instabilities are highly cficicut at continuously fuuucliug seas aud stars to the centers of ealaxies on short timescales (a single disk rotation) aud at hieh inflow rates (~LOAD. ft: Cacciato Dekel 2011). potentially fueliug increased ACN activity in disk ealaxies without the need for ealaxv-ealaxy icrecrs (Bournaurd et al.," Unlike the weaker disk instabilities that are associated with secular evolution at low redshift (e.g., bar instabilities), these high redshift instabilities are highly efficient at continuously funneling gas and stars to the centers of galaxies on short timescales (a single disk rotation) and at high inflow rates $\sim10 M_{\odot}$ $^{-1}$; Cacciato Dekel 2011), potentially fueling increased AGN activity in disk galaxies without the need for galaxy-galaxy mergers (Bournaurd et al."773 2011. in prep).," 2011, in prep)."774 Of course. the disagreciuent between the high disk fraction we observe and the merger-doniüuated fueliug model is predicated on the assumption that disk-like hosts have not experienced a mereer iu the recent past.," Of course, the disagreement between the high disk fraction we observe and the merger-dominated fueling model is predicated on the assumption that disk-like hosts have not experienced a merger in the recent past."775 The two cau be reconciled if these disks lave instead survived or reformed following a merger event., The two can be reconciled if these disks have instead survived or reformed following a merger event.776 Munerical simulations have shown that disks cau reform after a auerecr if the iuteractiug systems are gas rich (Robertson et al., Numerical simulations have shown that disks can reform after a merger if the interacting systems are gas rich (Robertson et al.777 2006: Bundy et al., 2006; Bundy et al.778 2010). although it has been argued that such interactions are nof conducive to the fueling of SMDITs (Hopkius Ieruquist 20093.," 2010), although it has been argued that such interactions are not conducive to the fueling of SMBHs (Hopkins Hernquist 2009)."779 Alternatively. minor mereers provide a leans to trigger ACN-activity within galaxies without cutirely destroviug their pre-existing morphology.," Alternatively, minor mergers provide a means to trigger AGN-activity within galaxies without entirely destroying their pre-existing morphology."780 Seni-analvtic cosmological galaxy formation models in which all ACN activity is assumed to be triggered by imerecrs (Somerville ct al., Semi-analytic cosmological galaxy formation models in which all AGN activity is assumed to be triggered by mergers (Somerville et al.781 2008) do predict that the average lerecr event that trigecrs an AGN with Lx>10 eres + las a ass ratio of 115 as opposed to the more disruptive 1:1 or 1:2 mergers (Somerville ct al., 2008) do predict that the average merger event that triggers an AGN with $L_{\rm X} > 10^{42}$ erg $^{-1}$ has a mass ratio of 1:8 as opposed to the more disruptive 1:1 or 1:2 mergers (Somerville et al.782 2011)., 2011).783 Coupled with a tine delay between the merger aud the visibility of the ACN. the signatures of these mergers could prove difficult to detect.," Coupled with a time delay between the merger and the visibility of the AGN, the signatures of these mergers could prove difficult to detect."784 Therefore. since we caunot rule out such interactions. minor mergers would secun to be one of the remaining wavs to reconcile the merecr-dominated fueling mocel with the hieh disk fraction aud lack of disturbed morphologics that we observe.," Therefore, since we cannot rule out such interactions, minor mergers would seem to be one of the remaining ways to reconcile the merger-dominated fueling model with the high disk fraction and lack of disturbed morphologies that we observe."785 To explore if major galaxy mergers are the primary mechanisiu fucling AGN activity at i~2. we have used /WNTEC2 imaging to examine the rest-frame optical morphologies of ealaxics hosting nmodoerate-Iuninosity. X-ray selected ACN at 2=15weD.," To explore if major galaxy mergers are the primary mechanism fueling AGN activity at $z\sim2$, we have used /WFC3 imaging to examine the rest-frame optical morphologies of galaxies hosting moderate-luminosity, X-ray selected AGN at $z=1.5-2.5$."786 Eaploving visual classifications. we have determined both the predominant morphological type of these galaxies and the frequency at which they exhibit morphological disturbances indicative of recent interactions.," Employing visual classifications, we have determined both the predominant morphological type of these galaxies and the frequency at which they exhibit morphological disturbances indicative of recent interactions."787 To determine if the ACN hosts show ierecr or interaction signatures more often than simular non-active galaxies. we have also classified a saluple of mass-inatched coutrol galaxies at the same redshift.," To determine if the AGN hosts show merger or interaction signatures more often than similar non-active galaxies, we have also classified a sample of mass-matched control galaxies at the same redshift."788 First. we fined that just over half of the AGN reside in disk ealaxies (51.1 23%). while a smaller percentage," First, we find that just over half of the AGN reside in disk galaxies $51.4^{+5.8}_{-5.9}\%$ ), while a smaller percentage"789A reliable age for the local Galactic Dise places a valuable constraint on both elobular cluster ages ancl cosmological models.,A reliable age for the local Galactic Disc places a valuable constraint on both globular cluster ages and cosmological models.790 A number of independent methods of investigating this problem have been emploved in the past (eg., A number of independent methods of investigating this problem have been employed in the past (eg.791 Jimenez 998 and references therein). resulting in à broad consensus that the lower limit for the Disc age lies between 5 and 2 Gyr.," Jimenez 1998 and references therein), resulting in a broad consensus that the lower limit for the Disc age lies between 8 and 12 Gyr."792 Potentially one of the most. reliable means of estimating the Disc age is via cool white dwarl (CWD) stars., Potentially one of the most reliable means of estimating the Disc age is via cool white dwarf (CWD) stars.793 These estimates use the idea. first. proposed. by Schmidt (1050). that in a galaxy of finite age there will be a emperature bevond which the oldest. coolest white cars (WDs) have not had time to cool.," These estimates use the idea, first proposed by Schmidt (1959), that in a galaxy of finite age there will be a temperature beyond which the oldest, coolest white dwarfs (WDs) have not had time to cool."794 This predicted: eut-olf in the luminosity function. (LE) of Ws. if satisfactorily observed. can then be used in conjunction with WD cooling mocels to derive the Disc age.," This predicted cut-off in the luminosity function (LF) of WDs, if satisfactorily observed, can then be used in conjunction with WD cooling models to derive the Disc age."795 CWDs are difficult to finc. being both extremely faint and of similar colour to the numerous. [x and. Al-type cdwarfs: and are almost exclusively discovered. by means of their proper motion.," CWDs are difficult to find, being both extremely faint and of similar colour to the numerous K and M-type dwarfs; and are almost exclusively discovered by means of their proper motion."796 The cut-off. in the. WDLE was observed. (Liebert. Dahn Monet. LOSS. hereafter. LDAL) after thorough follow up observations of CWD candidates crawn from the Luyten Half Second. (LIIS). Catalogue (Luvten. 1979).," The cut-off in the WDLF was observed (Liebert, Dahn Monet 1988, hereafter LDM) after thorough follow up observations of CWD candidates drawn from the Luyten Half Second (LHS) Catalogue (Luyten 1979)."797 Although at that time a Disc. age of 9342 Gyr was derived from this sample (Winget et al., Although at that time a Disc age of $9.3\pm2$ Gyr was derived from this sample (Winget et al.798 987). further observations ancl improvements in moclel atmospheres (Bergeron. Ruiz Leggett 1997. hereafter BL) and theoretical LP's (Wood 1992. 1995) has prompted a recent redetermination of the Disc age for the same sample (Leggett. Ruiz Bergeron 1998. hereafter LRB). vielding a value of 8Sd1.5 Gyr.," 1987), further observations and improvements in model atmospheres (Bergeron, Ruiz Leggett 1997, hereafter BRL) and theoretical LFs (Wood 1992, 1995) has prompted a recent redetermination of the Disc age for the same sample (Leggett, Ruiz Bergeron 1998, hereafter LRB), yielding a value of $8\pm1.5$ Gyr."799 While the existence of the cut-olf in he LDM WDLE has not been challenged. by subsequent observational work. the details of its precise position and shape have.," While the existence of the cut-off in the LDM WDLF has not been challenged by subsequent observational work, the details of its precise position and shape have."800 A sample of CWDs found using conimon proper motion binaries (CPMDs). again cullecl from the Luvten surveys. suggest that there are ~5 times more very faint CWDs than found by ΕΟΝ (Oswalt et al.," A sample of CWDs found using common proper motion binaries (CPMBs), again culled from the Luyten surveys, suggest that there are $\sim5$ times more very faint CWDs than found by LDM (Oswalt et al."801 1996. hereafter ΟΝΕ).," 1996, hereafter OSWH)."802 A Disc age of 9.541 Gyr was found using this sample. and the factor of 5 increase in the faintest WDs has been confirmed by an independent search for CWDs in the south (Ruiz and Takamiva 1995).," A Disc age of $9.5\pm1$ Gyr was found using this sample, and the factor of $\sim5$ increase in the faintest WDs has been confirmed by an independent search for CWDs in the south (Ruiz and Takamiya 1995)."803 Until now. the proper motion catalogues usec to extract samples of C\WDs have been produced: by blink? comparison.," Until now, the proper motion catalogues used to extract samples of CWDs have been produced by `blink' comparison."804 While these surveys have clearly been successful in picking up individual stars of low luminosity and high, While these surveys have clearly been successful in picking up individual stars of low luminosity and high8051l min in QQ Vul (Osborne.Cropper&Christiani:1987).. and in AL Tr 6.5 7 min and 13.5. 14 min (Schwarz 1998).,"11 min in QQ Vul \cite{b24}, and in AI Tri 6.5– 7 min and 13.5 – 14 min \cite{b36}."806". We speculate that the QPOs in V1309 Ori are due to ""blobby. accretion’. already observed in X-ray data (Walter. Wolk Aclams 1995: cle Martino et al."," We speculate that the QPOs in V1309 Ori are due to 'blobby accretion', already observed in X-ray data (Walter, Wolk Adams 1995; de Martino et al."807 1998)., 1998).808 We compare these timescales with those derived: by Ixing (1989).. and King (1995). (see also Chanmugam 1995).," We compare these timescales with those derived by King \shortcite{b17}, and King \shortcite{b18} (see also Chanmugam 1995)."809" The irradiation of the accretion Dow may ionise the subsonic acecretion [low below the inner £4, point and modulate eas How through this point on the timescale of the dynamical time scale in the Roche potential near £4.", The irradiation of the accretion flow may ionise the subsonic accretion flow below the inner $L_{1}$ point and modulate gas flow through this point on the timescale of the dynamical time scale in the Roche potential near $L_{1}$ .810" The equation presented by Ixing (1989) where LL, is the scale height and c; is local sound speed near Ly. predicts the timescales for these oscillations."," The equation presented by King \shortcite{b17}811 where ${\rm H_{*}}$ is the scale height and ${\rm c_{*}}$ is local sound speed near ${\rm L_{1}}$, predicts the timescales for these oscillations."812 The orbital period of 479 minutes gives us a prediction of 26 minutes for V1309 Ori., The orbital period of 479 minutes gives us a prediction of 26 minutes for V1309 Ori.813 The observed. timescales of QPOs in V1309 Ori. LO and. 15 minutes. are approximately half of the predicted.," The observed timescales of QPOs in V1309 Ori, 10 and 15 minutes, are approximately half of the predicted."814 The QPOs are seen strongest in CDV. and are negligible in the longer wavelengths. which may due to reason that only a fraction of How. will undergo. these oscillations near Ly. as pointed out by Wing (1995).," The QPOs are seen strongest in $UBV$, and are negligible in the longer wavelengths, which may due to reason that only a fraction of flow will undergo these oscillations near ${\rm L_{1}}$, as pointed out by King \shortcite{b18}."815 several eclipsing polars have been observed with high signal to noise ancl high time resolution., Several eclipsing polars have been observed with high signal to noise and high time resolution.816 These include HU. αν (Llarrop-Allinetal.1999). and. UZ For (Perrymanctal. 2001)., These include HU Aqr \cite{b15} and UZ For \cite{b26}.817. Both of these systenis show a sharp eclipse ingress lasting several seconds., Both of these systems show a sharp eclipse ingress lasting several seconds.818 This sharp drop in intensity is associated with the eclipse of the bright accretion region on the white dwarf., This sharp drop in intensity is associated with the eclipse of the bright accretion region on the white dwarf.819 In the case of UZ For there are. two sharp intensity drops. indicating that there are two accretion regions visible during the eclipse.," In the case of UZ For there are two sharp intensity drops, indicating that there are two accretion regions visible during the eclipse."820 One of the most striking features about the eclipse profiles of V1309 Ori is the obvious lack of a sharp ingress or egress which indicate the (cisjappearance of the white dwarf and/or hot spots in the surface of the white chwarl behind the secondary., One of the most striking features about the eclipse profiles of V1309 Ori is the obvious lack of a sharp ingress or egress which indicate the (dis)appearance of the white dwarf and/or hot spots in the surface of the white dwarf behind the secondary.821 The relative faintness of the accretion region(s). compared to the bright accretion stream in VI309 Ori. may be the reason for this.," The relative faintness of the accretion region(s), compared to the bright accretion stream in V1309 Ori, may be the reason for this."822 After the eclipse of the white dwarf. the accretion stream is still visible for a length of time.," After the eclipse of the white dwarf, the accretion stream is still visible for a length of time."823 Observations of other polars such as HU Jer (Glenn et al., Observations of other polars such as HU Aqr (Glenn et al.824 1994. Dridge et al.," 1994, Bridge et al."825 2002) show that this length of time can vary [rom one cycle to the next., 2002) show that this length of time can vary from one cycle to the next.826 Phe fact that we observe a variable eclipse ingress of the accretion stream in V1309 Ori is therefore not un-typical of polars., The fact that we observe a variable eclipse ingress of the accretion stream in V1309 Ori is therefore not un-typical of polars.827 However. what does make V1309. Ori unique amongst polars is the fact that the eclipse egress is highly variable: all other polars show a rapid rise at the same phase coming out from eclipse.," However, what does make V1309 Ori unique amongst polars is the fact that the eclipse egress is highly variable: all other polars show a rapid rise at the same phase coming out from eclipse."828 Phe fact that V1309 Ori does not implies either that we can observe the stream above the orbital plane before the white dwarf is visible. or that the accretion stream travels far enough around the white dwacl so that it is visible before the white cwarl itself.," The fact that V1309 Ori does not implies either that we can observe the stream above the orbital plane before the white dwarf is visible, or that the accretion stream travels far enough around the white dwarf so that it is visible before the white dwarf itself."829 To investigate if this further. we shown in Ligure ll the view of the system. at two different phases (b= 0.96 and 1.04).," To investigate if this further, we shown in Figure \ref{system} the view of the system at two different phases $\Phi$ = 0.96 and 1.04)."830" We use the following svsten parameters in determining these: ;/=TS"". q=0.67. Alay=O.7 (Staude.Schwope&Schwarz2001) and a white dwarf - secondary star separation of 104+ em (determined using the above parameters. ancl standard. Roche lobe e&cometrv)."," We use the following system parameters in determining these: $i=78^{\circ}$, $q$ =0.67, $M_{wd}=0.7$ \cite{b42} and a white dwarf - secondary star separation of $\times10^{11}$ cm (determined using the above parameters and standard Roche lobe geometry)."831 We also show a single magnetic field. line originating from the negative circularly polarised accretion region (3=35 and lace onto the observer at 0.2. 87.3)).," We also show a single magnetic field line originating from the negative circularly polarised accretion region $\beta=35^{\circ}$ and face onto the observer at $\Phi$ =0.2, \ref{modelling}) )."832 In Figure 11.. the accretion streams leading to both poles are visible at &=0.96.," In Figure \ref{system}, the accretion streams leading to both poles are visible at $\rm \Phi=0.96$."833 At —0.04 only the stream leading to the negative pole is visible., At $\rm \Phi=0.04$ only the stream leading to the negative pole is visible.834 “Phe white dwarf. appears before the stream [leading to the positive pole is. visible., The white dwarf appears before the stream leading to the positive pole is visible.835 Even if the negative pole is not visible at 0.04. the emission from the stream leading to that pole is.," Even if the negative pole is not visible at 0.04, the emission from the stream leading to that pole is."836" We take £2),/a—0.2: thiss implies. 2,=.2.9.107Lu cm.", We take $R_{\mu}/a$ =0.2: this implies $R_{\mu}=2.9\times10^{10}$ cm.837 «prosThis is consistent.. with. our findings in ES.3.., This is consistent with our findings in \ref{mass}.838 This shows that for this accretion stream geometry the accretion stream. is. visible after the white dwarf has been eclipsed ancl also before the white cwarl comes out of eclipse., This shows that for this accretion stream geometry the accretion stream is visible after the white dwarf has been eclipsed and also before the white dwarf comes out of eclipse.839 I£ the stream emission was highly variable then this could explain the variable egress profile., If the stream emission was highly variable then this could explain the variable egress profile.840 CGarnavich et al., Garnavich et al.841 (1994) and Shafter et al., \shortcite{b12} and Shafter et al.842 (1995). noted that the secondary star in VI309. Ori is oversized. for its spectral type (MO - MI) and mass (0.4:0.6 AZ. )., \shortcite{b35} noted that the secondary star in V1309 Ori is oversized for its spectral type (M0 - M1) and mass (0.4–0.6 $M_{\odot}$ ).843 Indeed. recent binary evolution models (eg Smith Dhillon 1998 and Baralle Ixolb 2000) which assume an unevolved donor star and typical mass transfer rates. all predict either a much earlier or later spectral type for V1309 Ori than observed (cf Figure |. of Baralle Ixolb 2000).," Indeed, recent binary evolution models (eg Smith Dhillon 1998 and Baraffe Kolb 2000) which assume an unevolved donor star and typical mass transfer rates, all predict either a much earlier or later spectral type for V1309 Ori than observed (cf Figure 1 of Baraffe Kolb 2000)."844 Llowever. by assuming an evolved donor it is possible to match the observed spectral (ype to the predicted. value.," However, by assuming an evolved donor it is possible to match the observed spectral type to the predicted value."845 For instance. [rom Figure 3 of Baralle Ixolb (2000)... for an initial secondary star mass of Mo—1.2M... a central llvdrogen abundance at the start of mass transfer. of X005. and a mass transfer rate of M=15.1. 101) g 1) we fined we that a spectral type of ALL is predicted for an orbital period of S hrs.," For instance, from Figure 3 of Baraffe Kolb \shortcite{b1}, for an initial secondary star mass of $M_{2}$, a central Hydrogen abundance at the start of mass transfer of $X_{c}$ =0.05, and a mass transfer rate of $\dot{M} =1.5846\times 10^{-9} M_{\odot} (\sim1\times10^{17}$ ) g $^{-1}$ ) we find we that a spectral type of M1 is predicted for an orbital period of 8 hrs."847 This is within the estimated range of values required to satisfy. conditions for observed oversized secondary to fll its Roche lobe (the main uncertainties are the distance and the mass of the white dwarl. eg Llarrop-Allin ct al.," This is within the estimated range of values required to satisfy conditions for observed oversized secondary to fill its Roche lobe (the main uncertainties are the distance and the mass of the white dwarf, eg Harrop-Allin et al."848 1997. de Martino et al.," 1997, de Martino et al."849 1998)., 1998).850 As already noted by Ixing. Osborne Schenker (2002).. V1309 Ori is indeed. à good. possible candidate for a binarysystem which has gone through a supersoft: source. phase and contains a nuclear evolved donor star.," As already noted by King, Osborne Schenker \shortcite{b19}, V1309 Ori is indeed a good possible candidate for a binarysystem which has gone through a supersoft source phase and contains a nuclear evolved donor star."851 Szkocdy Silber (1996) ancl Schmidt Stockman (2001) have. noticed that V1309 Ori has extraordinary strong excitation lines of NVAI240 and OV AI370) which may support such an interpretation.," Szkody Silber \shortcite{b43} and Schmidt Stockman \shortcite{b33} have noticed that V1309 Ori has extraordinary strong excitation lines of ${852\rm N~V~\lambda 1240}$ and ${ \rm O~V~\lambda1370}$ ) which may support such an interpretation."853cni.,cm.854 The frequencies at which clectrous with energy Las cnt their peak power for cach cutoff mechanisin are then Of course. iu a given object. the lowest value of Eyes will be the operative value.," The frequencies at which electrons with energy $E_{\rm max}$ emit their peak power for each cutoff mechanism are then Of course, in a given object, the lowest value of $E_{\rm max}$ will be the operative value."855 Thus if one can determine the mechanism causing the spectral cutoff. its value constrains considerably more pliysical parameters than the simple observation of a radio power-law spectra.," Thus if one can determine the mechanism causing the spectral cutoff, its value constrains considerably more physical parameters than the simple observation of a radio power-law spectrum."856 Populations- of+ relativisticol- ious- aud clectrous can produci observable coutinmun radiation through four mechanisius. one hadronic aud three leptonic (reviewed iu Revuolds 20082).," Populations of relativistic ions and electrons can produce observable continuum radiation through four mechanisms, one hadronic and three leptonic (reviewed in Reynolds 2008a)."857 The hadronic mechanisi is the inelastic κοπομοβ of cosuiccray protons on thermal uncle. producing vious.," The hadronic mechanism is the inelastic scattering of cosmic-ray protons on thermal nuclei, producing pions."858 The charged pious decay to electrous aud yositrous. making a (probably) uceligible contribution o the relativistic lepton pool.but the zx decay o eununa rays of comparable cnerey E-(uin)=m2/2~70 MeV. The spectrum of emitted photons should be that of the ious that produce them.," The charged pions decay to electrons and positrons, making a (probably) negligible contribution to the relativistic lepton pool,but the $\pi^0$ 's decay to gamma rays of comparable energy $E_\gamma ({\rm min}) = m_\pi c^2/2 \sim 70$ MeV. The spectrum of emitted photons should be that of the ions that produce them."859 The three eptonie processes are svichrotron emission. described above. as well ax nouthermal brouisstralilung. with the same spectrum as that of the nonthermal electrons. (IC) upscatterine of photons from on observed any significant ambicut radiation.," The three leptonic processes are synchrotron emission, described above, as well as nonthermal bremsstrahlung, with the same spectrum as that of the nonthermal electrons, and inverse-Compton (IC) upscattering of photons from any significant ambient radiation."860" Tn practice. this is ikely to be primarily the cosmic microwave backerouud (CMB). though iu. some cases. IC. from"" UV-opticaTc-IR photons may be competitive."," In practice, this is likely to be primarily the cosmic microwave background (CMB), though in some cases, IC from UV-optical-IR photons may be competitive."861" The spectrum wil jio the same as that of the svuchrotron ciission from whatever population of particles is responsible. that ix. considerable harder iu the keV TeV range than hat of the other processes,"," The spectrum will be the same as that of the synchrotron emission from whatever population of particles is responsible, that is, considerably harder in the keV – TeV range than that of the other processes."862 Whilen. the synchrotron Xxocess is clearly operating. it is not clear which of he other processes unight be responsible for cussion roni any particular object.," While the synchrotron process is clearly operating, it is not clear which of the other processes might be responsible for emission from any particular object."863 The best evidence for ion acceleration is the spectral feature resulting from tlie photon2. οσον from a+ created pion nearly. at either rest. about 70 MeV. Detailed caleulatious (c.g.Dariugetal.1999) show that this feature may not be liehly distinct in a real object.," The best evidence for ion acceleration is the spectral feature resulting from the minimum photon energy from a created pion nearly at rest, about 70 MeV. Detailed calculations \citep[e.g.,][]{baring99} show that this feature may not be highly distinct in a real object."864 Several shell (ie. not containing a pulsar) SNR& have been detected in TeV sanuua rays. using air-Coereukoy detectors such as the IHigb-Euergy Stereoscopie System iu Namibia.," Several shell (i.e., not containing a pulsar) SNRs have been detected in TeV gamma rays, using air-\v{C}eerenkov detectors such as the High-Energy Stereoscopic System in Namibia."865 These include €0317.3-0.5. Vela Jr. ROW 86. and SN 1006sa).," These include G347.3-0.5, Vela Jr., RCW 86, and SN 1006."866 The spectra are steep. with photon indices PT~2 (FLx(hv)DP for G317.3-0.5.the spectrum. is observed to steepen above 1 TeV. Elaborate models for jese four cases have been constructed (e.g..Berezhko&VOIk2006).," The spectra are steep, with photon indices $\Gamma \sim 2$ $F_\gamma867\propto (h\nu)^-\Gamma$ ); for G347.3-0.5, the spectrum is observed to steepen above 1 TeV. Elaborate models for these four cases have been constructed \citep[e.g.,][]{berezhko06}."868. The TeV emission in these models can jo due either to IC from the CAMB. or to z? decay.," The TeV emission in these models can be due either to IC from the CMB, or to $\pi^0$ decay."869 Both classes of ΠοΟΙ have difficulty., Both classes of model have difficulty.870 The former require low chline factors of magnetic feld. aud imply ineficicut shock acceleration. while the latter sufferfrou severe imuits ou thermal gas fou X-rayobservations. implying insufiicicnt targets for the relativistic protons (Ellison(al.2010).," The former require low filling factors of magnetic field, and imply inefficient shock acceleration, while the latter sufferfrom severe limits on thermal gas from X-ray observations, implying insufficient targets for the relativistic protons \citep{ellison10}."871.. For complex objects such as C317.3- and Vela Jh. simple ouc-zone models nay be inadequate. though there is as vet no clear path to consistent models.," For complex objects such as G347.3-0.5 and Vela Jr., simple one-zone models may be inadequate, though there is as yet no clear path to consistent models."872 An iniportant result first suggested many years ago. but only recently put ou a firmer observational foundation. 18 the merease in magnetic-feld strength in SNRs over 2 ο factor of the compression ratio expected iu üghlv ionized gases.," An important result first suggested many years ago, but only recently put on a firmer observational foundation, is the increase in magnetic-field strength in SNRs over a simple factor of the compression ratio expected in highly ionized gases."873 The possibility of uch stronger Shock amplification of maguctic fields was first proposed or heliospherie shocks by Chevalier (1977). while the uodels of Revuolds&Chevalier(1981)— demanded Sthstantial amplification.," The possibility of much stronger shock amplification of magnetic fields was first proposed for heliospheric shocks by Chevalier (1977), while the models of \cite{reynolds81} demanded substantial amplification."874 Early gamma-ray upper Inti roni Cas A bounded the electron population from 2bove (from the inferred absence of brenisstralilung). vottnding the maguetic-field strength from below based radio svuchrotroutae] fluxes.," Early gamma-ray upper limits from Cas A bounded the electron population from above (from the inferred absence of bremsstrahlung), bounding the magnetic-field strength from below based on observed radio synchrotron fluxes."875"⋅ Cowsikware! &rate heSarkarSalesaudinverse-Compton(L980) used this argument to deduce a dium uagneticetic fieldFe streusthdvo of to.about 7L1 πλαν1 The""e slightele COLllCAN(.yo or]curvatiununD observedOTIO iuH radiom1 spectra:vetas of""CONDO. SNRs was explained by Revnolds&Ellison(1992). as due o cficicut shock acceleration modifying the shock structure, but values of maguotic field were also implied of 100 μέ and more — far higher than a few times the vpical ⋅interstellar∖⋅↴∖⊀⋅ maeuctic ⊀↜∖⋅⋡⋅∖field of ⊳∙≻3 54 ""es Ilish-resolution.[m] N-yav nuagesoO from show hat the “thin ritus"" present in most historical shell SNRs ave in fact very thin so thin that au unusual depletion (beyond. simple post-shock expansion) of relativisticàwe clectrousvolatixsetie orlest↴ magnetic⋅ field ⊀≼⊾∖⋅⊳∎∖is required ivonininm to explain the sudden disappearauce of svuchrotrou cuissivity downstream (Bambaetal,2003:Vink& 2003).."," \cite{cowsik80} used this argument to deduce a minimum magnetic field strength of about 1 mG. The slight concave curvature observed in radio spectra of SNRs was explained by \cite{reynolds92}876 as due to efficient shock acceleration modifying the shock structure, but values of magnetic field were also implied of 100 $\mu$ G and more – far higher than a few times the typical interstellar magnetic field of 3 – 5 $\mu$ G. High-resolution X-ray images from show that the “thin rims” present in most historical shell SNRs are in fact very thin – so thin that an unusual depletion (beyond simple post-shock expansion) of either relativistic electrons or magnetic field is required to explain the sudden disappearance of synchrotron emissivity downstream \citep{bamba03,vink03}. ."877 If synchrotron losses are depleting the Clectrons. we iufer (Parizotetal.2006) where the shock speed ay=«4/1000 kins 1 and the fibuneut width is e.," If synchrotron losses are depleting the electrons, we infer \citep{parizot06}878 where the shock speed $u_8 \equiv u/1000$ km $^{-1}$ and the filament width is $w$ ."879 However. if the amplified magnetic," However, if the amplified magnetic"880is also found as temperature dependence of Ale IIA.& emission in stars (both dwarls and ejants) of minimal activitv. a likely indicator of the overall chromospheric energv. density (Buchholz.Ulnschneider.&Cuntz1993.seetheirFig.15)..,"is also found as temperature dependence of Mg II, emission in stars (both dwarfs and giants) of minimal activity, a likely indicator of the overall chromospheric energy density \cite*[][see their Fig.~15]{buc98}."881" If the mechanical energy. [αν Fy, utilized [ου generating stellar mass loss is assumed as FNxLi. the surlace-integratecd mechanical energy. [lux Lay can now be expressed as Next we consider the characteristic chromospheric radius. Rey."," If the mechanical energy flux $F_{\rm M}$ utilized for generating stellar mass loss is assumed as $F_{\rm M} \propto T_{\rm eff}^{7.5}$, the surface-integrated mechanical energy flux $L_{\rm M}$ can now be expressed as Next we consider the characteristic chromospheric radius $R_{\rm Chr}$."882 For cool giants aud supereiants. no well-defined boundary between (he chromosphere and (he wind exists.," For cool giants and supergiants, no well-defined boundary between the chromosphere and the wind exists."883 Hence. we use (he sonic point of the average velocity fiekl as relerence.," Hence, we use the sonic point of the average velocity field as reference."884" For the well-stuclied Ix supergiant ¢ Aur (with logg,~ 0.8). Rey, is found to be close to 222, (Dadeοἱal.1996).. and for general giants and supergiants. (Rep,—1,)/R. is assumed (o varv as g,|. which elves With the above temperature dependence of the mechanical energy flux. (eq. ["," For the well-studied K supergiant $\zeta$ Aur (with $\log{g_*} \simeq 0.8$ ), $R_{\rm Chr}$ is found to be close to $2 R_*$ \citep{baa96}, and for general giants and supergiants, $(R_{\rm Chr}-R_*)/R_*$ is assumed to vary as $g_*^{-1}$, which gives With the above temperature dependence of the mechanical energy flux (eq. ["885"2]) and chromospheric radius Rey, (eq. [",2]) and chromospheric radius $R_{\rm Chr}$ (eq. [8863]). we finally obtain as mass loss rate JM. see eq. (,"3]), we finally obtain as mass loss rate $\dot{M}$, see eq. ("887"1). with f2,. M,. and L, as stellar raclius. mass. ancl luminosity given in solar units. aud gy, and g. as stellar ancl solar surface gravity. respectively.","1), with $R_*$ , $M_*$, and $L_*$ as stellar radius, mass, and luminosity given in solar units, and $g_*$ and $g_\odot$ as stellar and solar surface gravity, respectively."888 This is. apart from the two new factors. indeed the old Reimers law.," This is, apart from the two new factors, indeed the old Reimers law."889" To satisfy the well-constrained RGB mass-loss of globular cluster stars (see 3). the fitting parameter 7 will be set to S(E1)xLOM, fl"," To satisfy the well-constrained RGB mass-loss of globular cluster stars (see 3), the fitting parameter $\eta$ will be set to $8 (\pm1) \times 10^{-14} M_{\odot}$ $^{-1}$."890 For the newly developed mass loss formula various tests and applications have been devised., For the newly developed mass loss formula various tests and applications have been devised.891" In particular. we want to oblain insight into the importance of the new [actors eiven bv the stellar effective temperature Zur and eravily g,."," In particular, we want to obtain insight into the importance of the new factors given by the stellar effective temperature $T_{\rm eff}$ and gravity $g_*$."892 In fact. for ordinary giants the (vo new [actors do not make much difference. which explains (he long-lasting success of the Reimers relation.," In fact, for ordinary giants the two new factors do not make much difference, which explains the long-lasting success of the Reimers relation."893 In particular. the Z5. factor is. despite its high power. restricted in iis impact by the small band of relevant. effective temperatures (3000 (ο 4500 Ix). and the g-sensilive factor remains of the order of one for all but the smallest gravities.," In particular, the $T_{\rm eff}^{3.5}$ factor is, despite its high power, restricted in its impact by the small band of relevant effective temperatures (3000 to 4500 K), and the $g$ -sensitive factor remains of the order of one for all but the smallest gravities."894 In fact. as previously discussed. the Z;r exponentin eq. (," In fact, as previously discussed, the $T_{\rm eff}$ exponentin eq. ("8954) is somewhat uncertain.,4) is somewhat uncertain.896 However. due to the," However, due to the"897the wavelength.,the wavelength.898 If the grain size changes with cometocentric distance. the light scattered by the dust will be affected in a different manner at different wavelengths.," If the grain size changes with cometocentric distance, the light scattered by the dust will be affected in a different manner at different wavelengths."899 The images obtained with SUSI 2 on March 24. 2007 did not allow us to detect any cometary activity.," The images obtained with SUSI 2 on March 24, 2007 did not allow us to detect any cometary activity."900 Because no photometric standard star could be observed during the same night (nonphotometric night) we have used the predicted Echeclus average magnitude for calibrating the profile with absolute magnitudes., Because no photometric standard star could be observed during the same night (nonphotometric night) we have used the predicted Echeclus average magnitude for calibrating the profile with absolute magnitudes.901 We base this prediction on the phase curve published by ?.. and the heliocentric and geocentric distances. as well as the phase angle during the observations.," We base this prediction on the phase curve published by \cite{rousselot:2005a}, and the heliocentric and geocentric distances, as well as the phase angle during the observations."902 Figure 7. presents the surface brightness profile of Echeclus obtained when all the R-band images are co-added (after centering)., Figure \ref{f:sbp} presents the surface brightness profile of Echeclus obtained when all the R-band images are co-added (after centering).903 We compare this profile to the one of a star apprearingσι in the same field of view and adjusted in intensity., We compare this profile to the one of a star apprearing in the same field of view and adjusted in intensity.904 No differences can be detected up to the sky background. i.e. up to Rz27/arcsec.," No differences can be detected up to the sky background, i.e. up to $\simeq$ $^2$."905 We have used the method mentioned by ? to derive an order of magnitude of the maximum Afp parameter that can be derived from these data.," We have used the method mentioned by \cite{jewitt:1984}906 to derive an order of magnitude of the maximum $Af\rho$ parameter that can be derived from these data."907" We have used the R,,,, magnitude where the surface brightness profile reaches the sky background. i.e. about 27/aresec."," We have used the $R_{max}$ magnitude where the surface brightness profile reaches the sky background, i.e. about $^2$."908" From this magnitude we have derived a lower limit for the coma magnitude. if it exists. by using the formula: A,==?5Log(207)Ryu."," From this magnitude we have derived a lower limit for the coma magnitude, if it exists, by using the formula: $R_{coma}\simeq-2.5Log_{10}(2\pi r^2)+R_{max}$."909" 1n this formula. + represents the diameter corresponding to the A,,,, magnitude. ie. 5 arcsec."," In this formula, $r$ represents the diameter corresponding to the $R_{max}$ magnitude, i.e. 5 arcsec."910 These values lead to an upper limit for A£p equal to about 75 em., These values lead to an upper limit for $Af\rho$ equal to about 75 cm.911 This upper limit can be compared to the one measured one year before (10.000 cm for the R-band. see above).," This upper limit can be compared to the one measured one year before (10,000 cm for the R-band, see above)."912 The ratio is about 130., The ratio is about 130.913 By using similar parameters and formulae as the one mentionned in Sect., By using similar parameters and formulae as the one mentionned in Sect.914 3 we derive an upper dust production rate Qiu;=0.0 kes!., 3 we derive an upper dust production rate $Q_{max}\simeq 0.6$ $^{-1}$.915 In the range covered by our spectra different emission bands corresponding to different radicals could be observed., In the range covered by our spectra different emission bands corresponding to different radicals could be observed.916 Among these emission bands the more intense are CN (3880 A)) and C: , Among these emission bands the more intense are CN (3880 ) and $_2$ 917that. moclels he propagation of photons from the neutron star surface towards a distant observer.,that models the propagation of photons from the neutron star surface towards a distant observer.918 To generate ight) curves we use the Oblate Schwarzschile (OS) approximation οἱ Morsinkelal.(2007) to model reativistic light-bending. Doppler shifts ancl eravitational recshift.," To generate light curves we use the Oblate Schwarzschild (OS) approximation of \citet{MLCB} to model relativistic light-bending, Doppler shifts and gravitational redshift."919 Phe OS model. which takes into account rotation-incuced oblateness. is more appropriate for very rapidly rotating neutron stars than the more usual Schwarzschilel Doppler approximation (Poutanen&Cicrliiski20 3).," The OS model, which takes into account rotation-induced oblateness, is more appropriate for very rapidly rotating neutron stars than the more usual Schwarzschild + Doppler approximation \citep{PGie}."920. Assuming that burst oscillation [requenevy is à good measure of stellarspin.. 4U. 1636-536 rotates al zz580 112.," Assuming that burst oscillation frequency is a good measure of stellar, 4U 1636-536 rotates at $\approx 580$ Hz."921 The associated rotational cleformation is a [ow percent. depending on the assumed mass ancl nuclear equation of state. leading to a small but noticeable inlluence on the light curve (Morsinkctal.2007).," The associated rotational deformation is a few percent, depending on the assumed mass and nuclear equation of state, leading to a small but noticeable influence on the light curve \citep{MLCB}."922. We neglect both special relativistic time delay and the additional time delay experienced. by initially αναον wopagatingoὃν photons. since these delays are much smaller (~101 s. Poutanen&Beloborodoy(2006))) than the time bins we consider (~0.1 8).," We neglect both special relativistic time delay and the additional time delay experienced by initially inwardly propagating photons, since these delays are much smaller $\sim 10^{-4}$ s, \citet{PBel}) ) than the time bins we consider $\sim 0.1$ s)."923 We specify stellar mass AZ and equatorial radius Ro and then compute the deformed spherical surface using the OS mocel., We specify stellar mass $M$ and equatorial radius $R_\mathrm{eq}$ and then compute the deformed spherical surface using the OS model.924 To start the burst we specify an initial small burning area and then track the propagation of the burning front across the star., To start the burst we specify an initial small burning area and then track the propagation of the burning front across the star.925 The stellar surface is divided into a grid of xuches with area ~ 0.1 kim. and we consider a patch to be ienited as soon as the burning front reaches the centre point of the patch.," The stellar surface is divided into a grid of patches with area $\sim$ 0.1 $^2$, and we consider a patch to be ignited as soon as the burning front reaches the centre point of the patch."926 Once a patch has started burning. we need o specify how its emission. varies with tine.," Once a patch has started burning, we need to specify how its emission varies with time."927 As discussed in Section L.. there are various numoerically-generated single »oint emission models. but no simple analvtie models.," As discussed in Section \ref{intro}, there are various numerically-generated single point emission models, but no simple analytic models."928" In his stuely we follow Bhattacharvva&Strohmaver(2006a.b) and assume that the temperature. of the burning front ollows the following profile after ignition: where /,, is the time at which the temperature reaches HS maximum d,=dug0.99(173du)."," In this study we follow \citet{BSa, BSb} and assume that the temperature of the burning front follows the following profile after ignition: where $t_m$ is the time at which the temperature reaches its maximum $T_m = T_0 + 0.99(T_1-T_0)$."929" Vhe time scale fiy ses the time scale at whichthe temperature increases. while /,, sets the time scale on which it cecavs."," The time scale $t_\mathrm{lr}$ sets the time scale at whichthe temperature increases, while $t_\mathrm{ld}$ sets the time scale on which it decays."930 Unburnt patches are assumed to have a temperature Zi until ignition., Unburnt patches are assumed to have a temperature $T_0$ until ignition.931 The xwameters in this model depend. primarily on. the composition of the burning maerial. which will vary with on accretion rate (see Section 1)).," The parameters in this model depend primarily on the composition of the burning material, which will vary with on accretion rate (see Section \ref{intro}) )."932 Bursts which are helium-rich. or example. would be expected to have shorter timescales han those which contain a higher fraction of hvdrogen.," Bursts which are helium-rich, for example, would be expected to have shorter timescales than those which contain a higher fraction of hydrogen."933 Our »arameter space must tjerefore. be wide enough to ake into account the expected level of variation., Our parameter space must therefore be wide enough to take into account the expected level of variation.934 One ollow-on question is whether his exponential temperature model remains valid across all burning regimes., One follow-on question is whether this exponential temperature model remains valid across all burning regimes.935 lt has oen used successfully in. detailed: spectral modelling of yUPStS at dilferent accretion rates by Bhattacharyya&Strohmaver (2006a.b).. but ultimately one would. like to see this confirmed by detailed nuclear physics caleulations.," It has been used successfully in detailed spectral modelling of bursts at different accretion rates by \citet{BSa,BSb}, but ultimately one would like to see this confirmed by detailed nuclear physics calculations."936 We then assume black body. emission at the specified temperature from cach patch., We then assume black body emission at the specified temperature from each patch.937 In Figure 7 we show the tvpical single pateh light curve., In Figure \ref{singlepoint} we show the typical single patch light curve.938 The rise portion is similar in shape to the bursts shown in. Woosleyctal.(2004)., The rise portion is similar in shape to the bursts shown in \citet{W}.939. The decay portion does dilfer from that seen in some of the cases studied by Woosleyetal. (2004).. but because we are focusing on the rise we never reach the points late in the," The decay portion does differ from that seen in some of the cases studied by \citet{W}, , but because we are focusing on the rise we never reach the points late in the"940requency distributions of the relative 5;dv colours of the 69 quasars in our sample. and the relative ον colours of the LBQS quasars in Figure S... a Ixuiper test. shower he two cistributions to be different at the confidence evel.,"frequency distributions of the relative $b_J - K$ colours of the 69 quasars in our sample, and the relative $b_J - K$ colours of the LBQS quasars in Figure \ref{relbjMkCDFs}, a Kuiper test showed the two distributions to be different at the confidence level."941" Phe statistics of the two relative 6,AN distributions are consistent with our quasar sample having a broader anc rededer relative byA distribution than the LBQS quasars.", The statistics of the two relative $b_J - K$ distributions are consistent with our quasar sample having a broader and redder relative $b_J - K$ distribution than the LBQS quasars.942 Dased on the dillerences between Figures 4. and 7.. and our statistical analyses here and in Section 3.2... we determine hat whether we used observed or relative quasar colours. he results of comparinge our quasar sample to a sample of LBQS quasars is the same. that our sample has a broader. redder 6.)AN distribution than the LBOS quasars.," Based on the differences between Figures \ref{bjMKhistogram} and \ref{relbjMkHist}, and our statistical analyses here and in Section \ref{comparison}, we determined that whether we used observed or relative quasar colours, the results of comparing our quasar sample to a sample of LBQS quasars is the same, that our sample has a broader, redder $b_J - K$ distribution than the LBQS quasars."943 The acditional information gleaned from our comparison of the relative 5; ἰν colours is that the small excess of blue quasars in our sample. when compared to the LDOS. appears to be caused. by. Ix-correction. effects. and is not. actually. an intrinsic property of the 5;ἐν distribution.," The additional information gleaned from our comparison of the relative $b_J - K$ colours is that the small excess of blue quasars in our sample, when compared to the LBQS, appears to be caused by K-correction effects, and is not actually an intrinsic property of the $b_J - K$ distribution."944 Because the excess of blue. quasars in our quasar sample. when compared to the LBQS quasar sample. is probably caused by WKeeorrection ellects. the small excess of blue quasars is much less significant than the excess of τος quasars when Comparing our quasar sample to the LBOS sample.," Because the excess of blue quasars in our quasar sample, when compared to the LBQS quasar sample, is probably caused by K-correction effects, the small excess of blue quasars is much less significant than the excess of red quasars when comparing our quasar sample to the LBQS sample."945" To understand. the effects of cur sample sclection on the b, and IX magnitude parameter space. we plottec 5; and"," To understand the effects of our sample selection on the $b_J$ and K magnitude parameter space, we plotted $b_J$ and"946 software. oue having 30 slitets and he other 27 slilets on M31 RGB star candidates. with the targets distribued more-or-less uuiforuilv over he LRIS feld «of view.," software, one having 30 slitlets and the other 27 slitlets on M31 RGB star candidates, with the targets distributed more-or-less uniformly over the LRIS field of view."947 Multi-slit spectroscopic observations were carried. usdic Week/LRIS chiving a wo-nigh run on Septeuiber 28.29. 1998 (UT).," Multi-slit spectroscopic observations were carried using Keck/LRIS during a two-night run on September 28–29, 1998 (UT)."948 Each spectiuu covers the spectral rauee AATHHO ssh0A conainiue t16 near-nfrarec triplet: AAS198. 8512. audAA.," Each spectrum covers the spectral range $\lambda\lambda7550\>$ $\>8850\,\rm\AA$ containing the near-infrared triplet: $\lambda\lambda8498$, 8542, and."949. The instruneutal spectral/velocity resolutions AA//GS km (FWIIAD: see ROO2 or detais., The instrumental spectral/velocity resolution is /68 km $^{-1}$ (FWHM); see RG02 for details.950 The total exposure times for the two masks is 1.7 aud 2.0 hr., The total exposure times for the two masks is 1.7 and 2.0 hr.951 Individual exposures are typicallv 30 1 lone. althougLsome exposures were stopped short due to telescope. iustmeut. and weather preleis.," Individual exposures are typically 30 min long, although some exposures were stopped short due to telescope, instrument, and weather problems."952 Overscan correction. 2D bias structure sitraction. and cosmic rav removal are accomplished using standard tasks.," Overscan correction, 2D bias structure subtraction, and cosmic ray removal are accomplished using standard tasks."953 Cosmic ravs are remove’ ou the basis of object sharpness aud peal pixel brightuess., Cosmic rays are removed on the basis of object sharpness and peak pixel brightness.954 Thev are nasked from cach image aloug with :Q summrouncdiue l-pixel buffer to remove the low-level wines of each eveut., They are masked from each image along with a surrounding 1-pixel buffer to remove the low-level wings of each event.955 A flat-ficld correction or each cata frame is performed using a spectral dome flat that is wellanatched to the data frame in terms of LRIS flexure effects., A flat-field correction for each data frame is performed using a spectral dome flat that is well-matched to the data frame in terms of LRIS flexure effects.956 Data reduction issues/complicatious for LRIS specPa atὉ cdiseussed in sole dezül iu RC2: that study did not however use the reduction software that is used here., Data reduction issues/complications for LRIS spectra are discussed in some detail in RG02; that study did not however use the \citet{phi03} reduction software that is used here.957 Wavelenetli calibration. skv subraction and extraction are all accomplished using the LRIS data reduction pipeline developed by Phillipsctal.(2000).," Wavelength calibration, sky subtraction and extraction are all accomplished using the LRIS data reduction pipeline developed by \citet{phi03}."958.. The software uses an optical model for the various ements of the LRIS spectrograph (colnuator. erating. canuera. ete.)," The software uses an optical model for the various elements of the LRIS spectrograph (collimator, grating, camera, etc.)"959 to derive a mapping from the slitinask to ic CCD detector as a fiction of waveleneth., to derive a mapping from the slitmask to the CCD detector as a function of wavelength.960 This optical model is based on spectrograpl design daawines. id has been empiricallv refined usinο calibration spectra (arc lamp through a ericd-of-holes mask) taken ‘lose to the observing run to account or nusaligninent of auv of LRIS’ clemenuts.," This optical model is based on spectrograph design drawings, and has been empirically refined using calibration spectra (arc lamp through a grid-of-holes mask) taken close to the observing run to account for misalignment of any of LRIS' elements."961 Even so the model is oulv ood to about 0.3 pixels (0.06 in the spatial direction and ~0.2A 1 the dispersion direction)., Even so the model is only good to about 0.3 pixels $0.06''$ in the spatial direction and $\sim$ in the dispersion direction).962 Iu addition. one iust allow for small time-dependent aliguiment/focus errors. id variations from exposure to exposure because of instruneut flexure.," In addition, one must allow for small time-dependent alignment/focus errors, and variations from exposure to exposure because of instrument flexure."963 These errors are removed by corrections: a zeropoint correction iu waveleueth measured from a bright uieht-kv. emission line. aud a plate-scale and offset which are solved for using the measured locii of slitlet edges.," These errors are removed by low-order corrections: a zeropoint correction in wavelength measured from a bright night-sky emission line, and a plate-scale and offset which are solved for using the measured locii of slitlet edges."964 Iu order to determine the radial velocity of cach object. its final coadded προςτα is cross-correlated against a tempate spectimi (average spectrin of three control sample stars from ROO2. where the coadditiou is done after süfting each to zero velocity).," In order to determine the radial velocity of each object, its final coadded spectrum is cross-correlated against a template spectrum (average spectrum of three control sample stars from RG02, where the coaddition is done after shifting each to zero velocity)."965 The cross-correlation fiction (CCE) is computed from 1000 O |1000 Iau 1. covering a plausible range of radial velocities for stars associated with ΑΠ).," The cross-correlation function (CCF) is computed from $-1000$ to +1000 km $^{-1}$, covering a plausible range of radial velocities for stars associated with M31."966 The CCF echuique vieks an unanibieuous peak and a reliable radial velocity for 11 of the 57 objects coiuprising the uain sample o| potential M31 targets., The CCF technique yields an unambiguous peak and a reliable radial velocity for 41 of the 57 objects comprising the main sample of potential M31 targets.967 A complete description of this CCF procedure is given d1i RGO2., A complete description of this CCF procedure is given in RG02.968 The radia velocity determined from the location of the CCF peak. ei. is corrected to the heliocentric yale using he task iu IRAE.," The radial velocity determined from the location of the CCF peak, $v_{\rm969obs}$, is corrected to the heliocentric frame using the task in IRAF."970 We estimate the ris error in radial velocity from t16 degree of sienificance of the CCF peak: σι=clIP(1το).b (Toury&Davis1979)., We estimate the rms error in radial velocity from the degree of significance of the CCF peak: $\sigma_v=\sigma_v^{\rm TD}(1+r_{\rm TD})^{-1}$ \citep{ton79}.971". The value of σTD"" Is enipirically ound to be 7T damus+ for ow ustimuental set-up (RGO2).", The value of $\sigma_v^{\rm TD}$ is empirically found to be 77 km $^{-1}$ for our instrumental set-up (RG02).972 The mean lo error in velocity for lis Cl fold salple is 21 xls1, The mean $1\sigma$ error in velocity for this G1 field sample is 21 km $^{-1}$ .973out” due to the nulling condition.,out” due to the nulling condition.974 If only a limited number of redshift bins is available. (20)) holds only approximately. leading to a residual 1n (21)).," If only a limited number of redshift bins is available, \ref{eq:GGIsplit}) ) holds only approximately, leading to a residual in \ref{eq:tomonull}) )."975" Since the nulling condition i$ the only condition. that the weight 7? must satisfy in order to ""null"". there is much freedom in choosing the form of it."," Since the nulling condition is the only condition that the weight $T^{(ij)}$ must satisfy in order to “null”, there is much freedom in choosing the form of it."976 We would like to further specify its form such that it preserves as much Fisher information in Y? as possible., We would like to further specify its form such that it preserves as much Fisher information in $Y^{(ij)}$ as possible.977 The method we have adopted for the nulling weight construction will be detailed in 4..," The method we have adopted for the nulling weight construction will be detailed in $\,$ \ref{sec:weight}."978 Note that for each (7.{) combination. one can in principle apply more than one nulling weight to the original bispectrum. and obtain more nulled measures.," Note that for each $(i,j)$ combination, one can in principle apply more than one nulling weight to the original bispectrum, and obtain more nulled measures."979 If one retains the condition of maximizing the Fisher information and demands that all the weight functions built for one (./) combination are orthogonal to each other. one arrives at higher-order modes that have the second-most. third-most. ete..," If one retains the condition of maximizing the Fisher information and demands that all the weight functions built for one $(i,j)$ combination are orthogonal to each other, one arrives at higher-order modes that have the second-most, third-most, etc.,"980 information content (higher-order weights. see JSO8).," information content (higher-order weights, see JS08)."981 The total number of such linearly independent nulled measures for a certain (7./) equals the possible values ofk>i1.," The total number of such linearly independent nulled measures for a certain $(i,j)$ equals the possible values of $k \ge i+1$."982 In this schematic study we will only use the optimum. re. the first-order nulling weights.," In this schematic study we will only use the optimum, i.e. the first-order nulling weights."983 We will assess the information loss due to this limitation in 5.4..," We will assess the information loss due to this limitation in $\,$ \ref{sec:compression}. ."984 We set up a fictitious survey with a survey size of A = 4000 deg? which is similar to the survey size of DES., We set up a fictitious survey with a survey size of $A$ = 4000 $^2$ which is similar to the survey size of DES.985 This can be easily scaled to any survey size using the proportionality of statistical errors to A7!7., This can be easily scaled to any survey size using the proportionality of statistical errors to $A^{-1/2}$.986" We assume a galaxy intrinsic ellipticity dispersion σε=|"")0.35.", We assume a galaxy intrinsic ellipticity dispersion $\sigma_{\epsilon}=\sigma(\epsilon_{\rm I}^{\rm ran})=0.35$.987 As galaxy redshift probability distribution we adopt the frequently used parameterization (Smailetal.1994).. and use zy=0.64. a=2. =1.5.," As galaxy redshift probability distribution we adopt the frequently used parameterization \citep{smail94}, and use $z_0 = 0.64$, $\alpha = 2$, $\beta = 1.5$."988 The distribution is cut at tna=3 and normalized to 1., The distribution is cut at $z_{\textrm{max}} = 3$ and normalized to 1.989 The corresponding median redshift of this fictitious survey is zi=0.9. which is compatible to a survey like EUCLID.," The corresponding median redshift of this fictitious survey is $z_{\rm m}=0.9$, which is compatible to a survey like EUCLID."990 We adopt an average galaxy number density 5.=40aremin. which ts again EUCLID-like., We adopt an average galaxy number density $\bar{n}_{\textrm{g}}=40~ {\textrm{arcmin}}^{-2}$ which is again EUCLID-like.991" Disjunct redshift bins without photo-z error are assumed. which means that the galaxy redshift probability distribution in redshift bin / takes the form p(2)ep(x) if and only if the redshift that corresponds to comoving distance y, is within the boundaries of redshift bin ;."," Disjunct redshift bins without photo-z error are assumed, which means that the galaxy redshift probability distribution in redshift bin $i$ takes the form $p^{(i)}_{\textrm{s}}(z) \propto p_{\textrm{s}}(z)$ if and only if the redshift that corresponds to comoving distance $\chi_{\rm s}$ is within the boundaries of redshift bin $i$."992 A number of 10 redshift bins are used by default., A number of 10 redshift bins are used by default.993 The boundaries of the redshift bins are set such that each bin contains the same number of galaxies., The boundaries of the redshift bins are set such that each bin contains the same number of galaxies.994 We adopt 20 angular frequency bins spaced logarithmically between Gyin=50 and ἕμ=3000. and denote the characteristic angular frequency of a bin as £.," We adopt 20 angular frequency bins spaced logarithmically between $\ell_{\textrm{min}}=50$ and $\ell_{\textrm{max}}=3000$, and denote the characteristic angular frequency of a bin as $\bar{\ell}$."995 Within this range the noise properties of the cosmic shear field are still not too far in the non-Gaussian regime. allowing à more realistic theoretical estimation. of the bispectrum and its covariance.," Within this range the noise properties of the cosmic shear field are still not too far in the non-Gaussian regime, allowing a more realistic theoretical estimation of the bispectrum and its covariance."996 Whether this number of angular frequency bins can reconstruct the angular frequency dependence of the bispectrum is tested. and 20 bins are found to be sufficient for our requirements on precision.," Whether this number of angular frequency bins can reconstruct the angular frequency dependence of the bispectrum is tested, and 20 bins are found to be sufficient for our requirements on precision."997 This is also expected since thebispectrum ts rather featureless as a function of angular frequency., This is also expected since thebispectrum is rather featureless as a function of angular frequency.998 We show the modeling of Boog and its covariance in this section., We show the modeling of $B_{\textrm{GGG}}$ and its covariance in this section.999 We will only consider the tomographic bispectrum at redshift bins satisfying z;< and z;<z. which already ensures an elimination of By; and Bey systematics in our case.," We will only consider the tomographic bispectrum at redshift bins satisfying $z_i<z_j$ and $z_i<z_k$ , which already ensures an elimination of $B_{\textrm{III}}$ and $B_{\textrm{GII}}$ systematics in our case."1000" Applying Limber’s equation. it can be shown that the tomographic convergence bispectrum can be written as à projection of the three-dimensional matter bispectrum By(ki.koΚαὶy) (see e.g. TIOF): To compute B,. we employ the fitting formula by Scoceimarro&Couchman(2001)... which is based on hyper-extended perturbation theory (Scoccimarro&Frieman 1999)."," Applying Limber's equation, it can be shown that the tomographic convergence bispectrum can be written as a projection of the three-dimensional matter bispectrum $B_\delta\!\left({k_1},{k_2},{k_3}; \chi\right)$ (see e.g. TJ04): To compute $B_{\delta}$, we employ the fitting formula by \citet{sco01}, which is based on hyper-extended perturbation theory \citep{sco99}. ."1001 A comparison of this formula with the halo model results can be found in Takada&Jain(2003a.b).," A comparison of this formula with the halo model results can be found in \citet{TJ03b,TJ03c}."1002". Estimating the bispectrum covariance is often done within a flat-sky spherical harmonie. formalism (Hu2000.Hu00Ohereafter)... which suffers - at least formally - from drawbacks since its basis functions Yj, are only defined for discrete angular frequency values and full sky coverage."," Estimating the bispectrum covariance is often done within a flat-sky spherical harmonic formalism \citep[Hu00 hereafter]{hu00}, which suffers - at least formally - from drawbacks since its basis functions $Y_{lm}$ are only defined for discrete angular frequency values and full sky coverage."1003 In Joachimietal.(2009) another approach exclusively based on the two- Fourier formalism was constructed. which we use here.," In \citet{joachimi09b} another approach exclusively based on the two-dimensional Fourier formalism was constructed, which we use here."1004 The bispectrum covariance is à six-point correlation function which can be expanded into its connected parts as outlined in e.g. Bernardeauetal.(2002a)., The bispectrum covariance is a six-point correlation function which can be expanded into its connected parts as outlined in e.g. \citet{ber02a}.1005. As argued in TJOA. for angular scales £€3000. the term which is a triple of two-point functions still dominates.," As argued in TJ04, for angular scales $\ell \le 3000$, the term which is a triple of two-point functions still dominates."1006" Keepingonly this term. the bispectrum covariance readsin which AZ; is the bin width of the angular frequency bin with typical value £;. and P""(£) is theobserved powerspectrum which contains the intrinsic ellipticity noise (e.g.Kaiser 2008): where i; is the galaxy number density in redshift bin {."," Keepingonly this term, the bispectrum covariance readsin which $\Delta \bar{\ell}_i$ is the bin width of the angular frequency bin with typical value $\bar{\ell}_i$ , and $\bar{P}^{(ij)}(\bar{\ell})$ is theobserved powerspectrum which contains the intrinsic ellipticity noise \citep[e.g.][]{kaiser92,hu99,JS08a}: : where $\bar{n}_i$ is the galaxy number density in redshift bin $i$ ."1007 The term A(£j.£5.(3) 18 defined as," The term $\Lambda \br{\ell_1,\ell_2,\ell_3}$ is defined as \eqa{"1008 Anomalous Microwave Emission ((AME) is the name given to excess microwave emission. observed. at. frequencies in the range ~1060 CGllz. that is stronely correlated with fr infrared. (ELI) dust. emission2010).," Anomalous Microwave Emission (AME) is the name given to excess microwave emission, observed at frequencies in the range $\sim10-60$ GHz, that is strongly correlated with far infrared (FIR) dust emission."1009. This dust-correlatecd emission is known to be a significant source of contamination [or Cosmic Microwave jJackground (CMD). data. that must be separated: accurately from the CAIB signal (Bennett2008:Goldetal.2009:Dickinson 2009b).," This dust-correlated emission is known to be a significant source of contamination for Cosmic Microwave Background (CMB) data, that must be separated accurately from the CMB signal \citep{Bennett03,Bonaldi07,Miville-Deschenes08,Gold09,Dickinson09b}."1010. Although there is still some debate about the physical mechanism that is responsible for the emission. the most. favoured explanation is in terms of small. rapidly spinning cust grains (Draine&Lazarian1998a.b).," Although there is still some debate about the physical mechanism that is responsible for the emission, the most favoured explanation is in terms of small, rapidly spinning dust grains \citep{Draine98a,Draine98b}."1011. Assumine this is the case. microwave observations of spinning dust represent à new wav of studying the properties of interstellar dust. grains and its environment within the interstellar medium," Assuming this is the case, microwave observations of spinning dust represent a new way of studying the properties of interstellar dust grains and its environment within the interstellar medium"1012. Assumine this is the case. microwave observations of spinning dust represent à new wav of studying the properties of interstellar dust. grains and its environment within the interstellar medium.," Assuming this is the case, microwave observations of spinning dust represent a new way of studying the properties of interstellar dust grains and its environment within the interstellar medium"1013The A-values and Auger widths for the Ar isonuclear sequence previously computed by Diémontetal.(2000) with and the MCDE code have given us the opportunity {ο benchmark the accuracy of the present data sets.,The $A$ -values and Auger widths for the Ar isonuclear sequence previously computed by \citet{bie00} with and the MCDF code have given us the opportunity to benchmark the accuracy of the present data sets.1014 This has been useful to sort oul the large discrepancies reported by Palmerietal.(2008a) for Fe and Palmeretal.(2006). [or 5 with the MCDE data of Chenetal.(1997)., This has been useful to sort out the large discrepancies reported by \citet{pal03a} for Fe and \citet{pal06} for S with the MCDF data of \citet{che97}.1015. Similar discrepancies are found with (their data for Ar which. in the light of the good agreement of HERI with Diémmont et al..," Similar discrepancies are found with their data for Ar which, in the light of the good agreement of HFR1 with Biémmont et al.,"1016 are cerlainiv not due to the more formal relativistic representation of the MCDE method., are certainly not due to the more formal relativistic representation of the MCDF method.1017 Sienilieant cliscords of FRI with the Auger widths reported by Faenovetal.(1994) [or the Ale. Si. aud 5 isonuclear sequences and with those by Behar&Netzer(2002) [or levels in the D and C isoelectronic sequences are difficult to explain.," Significant discords of HFR1 with the Auger widths reported by \citet{fae94}1018 for the Mg, Si, and S isonuclear sequences and with those by \citet{beh02} for levels in the B and C isoelectronic sequences are difficult to explain."1019 Accuracy ratings of the present A-values and Auger widths greater than LOM ! are conticently assigned (to and20'4... respectively. except lor special cases: e.g. transitions involving Ix-vacancy levels in the carbon isoelectronic sequence where strong admixture causes severe departures.," Accuracy ratings of the present $A$ -values and Auger widths greater than $10^{13}$ $^{-1}$ are confidently assigned to and, respectively, except for special cases; e.g. transitions involving K-vacancy levels in the carbon isoelectronic sequence where strong admixture causes severe departures."1020 The present radiative and Auger widths will be used in the computations of the IX-shell photoionization cross sections of these medium-Z ions which are required in NSTAR for the modelling of interesting spectral features., The present radiative and Auger widths will be used in the computations of the K-shell photoionization cross sections of these $Z$ ions which are required in XSTAR for the modelling of interesting spectral features.1021 Future work will involve extension of the present approach to the Ni isonuclear sequence., Future work will involve extension of the present approach to the Ni isonuclear sequence.1022 ALIAD acknowledges partial support from FONACIT. Venezuela. under contract No. 20011000912.," MAB acknowledges partial support from FONACIT, Venezuela, under contract No. S1-20011000912."1023 This work was funded in part by the NASA Astronomy and Physics Research and Analysis Program., This work was funded in part by the NASA Astronomy and Physics Research and Analysis Program.1024 Partial support for CAL was provided by a travel grant. [rom IVIC and the FNRS of Belgium., Partial support for CM was provided by a travel grant from IVIC and the FNRS of Belgium.1025ADI.200L).. similar to the Large Magellanic Cloud.,"$_{\odot}$, similar to the Large Magellanic Cloud."1026 It is oue of the nearest. examples of a starburst. and was the host of a Type I supernova ancl recent nova2010).," It is one of the nearest examples of a starburst, and was the host of a Type I supernova and recent nova."1027. It therefore has been studied im detail. especially at UV and NIR waveleneths that probe the voune stellar populations.," It therefore has been studied in detail, especially at UV and NIR wavelengths that probe the young stellar populations."1028 For example. were able to make use of &£u-UV imagine from the Ultraviolet Imaging Telescope aud ground-based Ebaud to decompose the galaxy iuto a centrally concentrated intense star forming coniponent and an extended soothi disk.," For example, were able to make use of far-UV imaging from the Ultraviolet Imaging Telescope and ground-based I-band to decompose the galaxy into a centrally concentrated intense star forming component and an extended smooth disk."1029 They sugeest the two component structure is the result of a recent merger., They suggest the two component structure is the result of a recent merger.1030 The buelt resolved stellar populations lave also been characterized., The bright resolved stellar populations have also been characterized.1031 A dominant red giant brauch was detected. and a large metallicity spread was 1ieasured by using WEPC2 aud NICAIOS photometry.," A dominant red giant branch was detected, and a large metallicity spread was measured by using WFPC2 and NICMOS photometry."1032 used UST/WEPC2 and ΠοΤΙΣ Πασάς to sugeest that the stellar initial mass functiou appears to be steeper than that of at high masses (£720 ΔΕ.) even though the ealaxw’s metallicity is similar to that of the Simall Magellanic Cloud.," used HST/WFPC2 and HST/STIS imaging to suggest that the stellar initial mass function appears to be steeper than that of at high masses $>$ 20 $_{\odot}$ ), even though the galaxy's metallicity is similar to that of the Small Magellanic Cloud."1033 However. it is unclear how this slope is affected by fluctuations in the star formation rate.," However, it is unclear how this slope is affected by fluctuations in the star formation rate."1034 We Πάτμο examine the stellar populations of NGC 1211 using deeper data than previous studies., We further examine the stellar populations of NGC 4214 using deeper data than previous studies.1035 The jw data include two DUST WFPC2 fields of the outer disk aud one WECS3 field of the immer regions., The new data include two HST WFPC2 fields of the outer disk and one WFC3 field of the inner regions.1036 Through detailed. stellar evolution iuodel fitting. we measure he star formation history (SEII) of these regions ik ook for differences between quiesceut and intensely star ornüue regions.," Through detailed stellar evolution model fitting, we measure the star formation history (SFH) of these regions and look for differences between quiescent and intensely star forming regions."1037 Section 2 describes our data set am xiotonmetry., Section 2 describes our data set and photometry.1038 Section 3 prescuts the results of our mode chting procedure., Section 3 presents the results of our model fitting procedure.1039 Section [| discusses the results of the ucasureineuts m the context of galaxy morphology iik euvironment. aud Section 5 sumunarizes our conclusions.," Section 4 discusses the results of the measurements in the context of galaxy morphology and environment, and Section 5 summarizes our conclusions."1040 Weasstune (0)Mjoy= 3.03 Mpc Or conversions of angular measurements to plivsica distances and assume an inclination of 38° for surface density measurements., We assume $(m-M)_0 =$ 3.03 Mpc for conversions of angular measurements to physical distances and assume an inclination of $^{\circ}$ for surface density measurements.1041 We adopt five-vear WMAP cosiuologv. for ] conversions between time and redshift., We adopt a five-year WMAP cosmology for all conversions between time and redshift.1042 As part of the ANGST. program after the fülure of ACS. from 2007-Dec-0L1 to 2007-Dec-23. we performed deep WFPC? observations a field in the NGC 1211 disk located at R.À. (2000)—182.817375. (12:15:23.10). decl. (," As part of the ANGST program after the failure of ACS, from 2007-Dec-04 to 2007-Dec-23, we performed deep WFPC2 observations a field in the NGC 4214 disk located at R.A. (2000)=183.847375 (12:15:23.4), decl. ("10432000)=36.362333 (136:21: with a rotation angle PA_VV3=119.9 degrees (GO-10915).,2000)=36.362333 (+36:21:44) with a rotation angle V3=119.9 degrees (GO-10915).1044.L1) To. iniprove our radial coverage to be closer to the goal of the original ANGST program. from 2009-Feb-23 to 2009-Feb-26. we performed shallower supplemental observations for a field located at R.A. (2000)=183.878103 (12:15:30.7). decl. (," To improve our radial coverage to be closer to the goal of the original ANGST program, from 2009-Feb-23 to 2009-Feb-26, we performed shallower supplemental observations for a field located at R.A. (2000)=183.878103 (12:15:30.7), decl. ("10452000)236.356808 (1236:21:21.5). with a rotation anele PA_-VV3=51.0 (GO-11986).,2000)=36.356808 (+36:21:24.5) with a rotation angle V3=51.0 (GO-11986).1046 At the same time. WEC3/IR and WEC3/UVIS imaging of the central area of the ealaxy. proposed by the Scicutific Oversight Committee (SOC). were released.," At the same time, WFC3/IR and WFC3/UVIS imaging of the central area of the galaxy, proposed by the Scientific Oversight Committee (SOC), were released."1047 Both fields were observed from) 2009-Dec-22 to 2009-Dec-23 located. at R.A. (2000) =183.913333 (12:15:39.2). decl. (," Both fields were observed from 2009-Dec-22 to 2009-Dec-23 located at R.A. (2000) =183.913333 (12:15:39.2), decl. ("10482000) = 36.226911. (126:19:297.0). with a rotation anele VV3=120.0 (CGO-11360. PE: O'Connell).,"2000) = 36.326944 (+36:19:37.0) with a rotation angle V3=120.0 (GO-11360, PI: O'Connell)."1049 Figure 1 shows outlines of the fields’ locations.," Figure \ref{field_loc}1050 shows outlines of the fields' locations."1051 Our field locations were chosen to maximize the uuuber of disk stars aud avoid crowding., Our field locations were chosen to maximize the number of disk stars and avoid crowding.1052 Iu the deep field. we obtained 15 full-orbit exposures with the ΝΕΤΟΖ through the F606W (wide V) filter. aud 29 full-orbit exposures through the ESIWV (7 equivalent) filter.," In the deep field, we obtained 15 full-orbit exposures with the WFPC2 through the F606W (wide $V$ ) filter, and 29 full-orbit exposures through the F814W $I$ equivalent) filter."1053 These data totaled 39000 s and 75100 s of exposure time in F606W and FSIIWNV. respectively.," These data totaled 39000 s and 75400 s of exposure time in F606W and F814W, respectively."1054 In the other WFDPC? field. we obtained 2 orbits through FG6OGW. totaling [800 s. aud. { orbits through ESLIW. totaling 9600 s. The WEC3/TR data contained 1198 s aud 2308 s of exposure in FLIOW aud. F160W. respectively.," In the other WFPC2 field, we obtained 2 orbits through F606W, totaling 4800 s, and 4 orbits through F814W, totaling 9600 s. The WFC3/IR data contained 1198 s and 2398 s of exposure in F110W and F160W, respectively."1055" The WEC3/UVIS data contained 1683 s. 1510 s. aud 1339 « in F336W. EDW. and FaliW, respectively."," The WFC3/UVIS data contained 1683 s, 1540 s, and 1339 s in F336W, F438W, and F814W, respectively."1056 All WEPC2 taecs were calibrated in the IST pipeline ith CALWDP?2 using OPUS version 2006_66a for the 2007 data and 2008_55¢ for the 2009 data., All WFPC2 images were calibrated in the HST pipeline with CALWP2 using OPUS version 6a for the 2007 data and 5c for the 2009 data.1057 All WEC'3 images were calibrated in the IST pipeline with CALWE3 version 2.0., All WFC3 images were calibrated in the HST pipeline with CALWF3 version 2.0.1058 All of the data were processed through the ACS Nearby Calaxy Survey Treasury (ANGST) data analysis pipeline2009).. updated to include WEC3 UVIS and IR data2011).," All of the data were processed through the ACS Nearby Galaxy Survey Treasury (ANGST) data analysis pipeline, updated to include WFC3 UVIS and IR data."1059. As a brief sumunary. the photometry was measured sinultaueouslwv for all of the objects in the uncombiued inages using the software packages IISTPIIOT (for WFPC2) and DOLPIIOT 1.2 including the ΝΕΟ module.," As a brief summary, the photometry was measured simultaneously for all of the objects in the uncombined images using the software packages HSTPHOT (for WFPC2) and DOLPHOT 1.2 including the WFC3 module."1060 These packages are optimized for 1icasuriug photometry of stars on DIST tages using the well-characterizecd aud stable point spread function (PSF) calculated with The software fits the PSF to all of the stars in cach individual frame to fud PSF magnitudes., These packages are optimized for measuring photometry of stars on HST images using the well-characterized and stable point spread function (PSF) calculated with The software fits the PSF to all of the stars in each individual frame to find PSF magnitudes.1061 It then determines aud applies the aperture correction for cach iuase uxing the most isolated stars. corrects for the charec transfer efficiency of the WEPC?detector®.. conibines the results frou the individual exposures. aud converts the measured count rates to the VECAmae svsteni.," It then determines and applies the aperture correction for each image using the most isolated stars, corrects for the charge transfer efficiency of the WFPC2, combines the results from the individual exposures, and converts the measured count rates to the VEGAmag system."1062 Our photometric error aud completeness were then assessed. by running at least LO° artificial star tests for each field. in which a star of known color and magnitude was placed iuto the images aud the photometry rerun to determine if the star was recovered aud. if so. the difference between the iiput aud output magnitudo.," Our photometric error and completeness were then assessed by running at least $^6$ artificial star tests for each field, in which a star of known color and magnitude was placed into the images and the photometry rerun to determine if the star was recovered and, if so, the difference between the input and output magnitude."1063 The photometry output was then filtered to ouly allow objects classifies as stars with signal-to-noise > lain both filters., The photometry output was then filtered to only allow objects classified as stars with signal-to-noise $>$ 4 in both filters.1064" The list was further culled using sharpucss μαper,m1BSLUVspar)<<0.27 for WEPC2. [E336]aarp|BIBSως0.27 for UVIS. and [PILave,|F1601Tery|(0.35 for IR) anc crowding (F606ord|PSLi<0.7 for WEPC2. Puord|PIBoe0.7 for UVIS. anc PUNod|EIT601T.4<0.18 for IR)."," The list was further culled using sharpness $|F606W_{sharp} +1065F814W_{sharp}| < 0.27$ for WFPC2, $|F336W_{sharp} + F438W_{sharp}| <10660.27$ for UVIS, and $|F110W_{sharp} + F160W_{sharp}| < 0.35$ for IR) and crowding $F606W_{crowd} + F814W_{crowd} < 0.7$ for WFPC2, $F336W_{crowd} + F438W_{crowd} < 0.7$ for UVIS, and $F110W_{crowd} +1067F160W_{crowd} < 0.48$ for IR)."1068 The sharpuess xuwanmeter returus zero if a star is porfectlv fit. negative if it is broader. aud positive if it is sharper than a tvpica star2000).," The sharpness parameter returns zero if a star is perfectly fit, negative if it is broader, and positive if it is sharper than a typical star."1069. The crowding parameter gives the difference between the magnitude of a star measure: vefore and after subtracting the neieliboring stars in the nuaec., The crowding parameter gives the difference between the magnitude of a star measured before and after subtracting the neighboring stars in the image.1070 When this value is large. it sugeests that the stars photometry was siguificautly affected by crowding. auc," When this value is large, it suggests that the star's photometry was significantly affected by crowding, and"1071power spectrum.,power spectrum.1072 When (he covariance matrix is used. we have six parameters.," When the covariance matrix is used, we have six parameters."1073 We use (he Monte-Carlo Markov. Chain (MCMC) method to explore the parameter space., We use the Monte-Carlo Markov Chain (MCMC) method to explore the parameter space.1074 Our MCMC code is based on the publicly available package COSMOAIC (Lewis&Bridle2002)., Our MCMC code is based on the publicly available package COSMOMC \citep{cosmomc}.1075. The paper is organized as follows., The paper is organized as follows.1076" In section Il. we give all (he formulae and show the constraint on the cosmic curvature is much better by using the parameters A. /, and (heir covariance malrix (an (hat by using the parameter 7? only."," In section II, we give all the formulae and show the constraint on the cosmic curvature is much better by using the parameters $R$, $l_a$ and their covariance matrix than that by using the parameter $R$ only."1077" We also discuss the effect of the radiation component Q, on /,.", We also discuss the effect of the radiation component $\Omega_r$ on $l_a$.1078 In section III. we eive our results.," In section III, we give our results."1079" We discuss (he analvtical marginalization over //j in appendix A. For the SN Ia data.we caleulate where the extinction-corrected distance modulus (2)=5logy{dp(2)/Alpe}]+25. σι is the total uncertainty in the SN Ia data. and the luminosity distance is here and the dimensionless Hubble parameter is where Ὁ=8zCp/(3Iz). p,=oT}emb* oy is the Stelan-Doltzmann constant. the CMD temperature 7,,,)= 2.726). and Qp pis the DE density."," We discuss the analytical marginalization over $H_0$ in appendix A. For the SN Ia data,we calculate where the extinction-corrected distance modulus $\mu(z)=5\log_{10}[d_L(z)/{\rm Mpc}]+25$, $\sigma_i$ is the total uncertainty in the SN Ia data, and the luminosity distance is here and the dimensionless Hubble parameter is where $\Omega=8\pi G\rho/(3H^2_0)$, $\rho_r=\sigma_bT_{cmb}^4$, $\sigma_b$ is the Stefan-Boltzmann constant, the CMB temperature $T_{cmb}=2.726$ K, and $\Omega_{DE}$ is the DE density."1080" Note (hat the clistance normalization is arbitrary in the SN Ia data. the Hubble constant //, determined [rom the SN data is also an arbitrary number. not the observed IInbble constant."," Note that the distance normalization is arbitrary in the SN Ia data, the Hubble constant $H_0$ determined from the SN data is also an arbitrary number, not the observed Hubble constant."1081 Therefore we need to marginalize over (his nuisance parameter f/f)., Therefore we need to marginalize over this nuisance parameter $H_0$ .1082" The parameter Jf, is mareinalized over with flat prior. the"," The parameter $H_0$ is marginalized over with flat prior, the"1083planetesimals shape the protoplanetary disc.,planetesimals shape the protoplanetary disc.1084" Kokubo Ida (1998)) coined this growth regime ""oligarchie growth"". “in the sense that not only one but several protoplanets dominate the planetesimal system’."," Kokubo Ida \cite{kokubo1}) ) coined this growth regime “oligarchic growth”, `in the sense that not only one but several protoplanets dominate the planetesimal system'."1085 Kokubo Ida (2000)) investigated. through 3D N-body simulations. the growth from planetesimals to. protoplanets including the effect of the nebular gas drag.," Kokubo Ida \cite{kokubo2}) ) investigated, through 3D N–body simulations, the growth from planetesimals to protoplanets including the effect of the nebular gas drag."1086 They confirmed the existence of an initial runaway phase in protoplanetary growth and a second stage of oligarchic growth of protoplanets. in the same sense as in Kokubo Ida (1998)).," They confirmed the existence of an initial runaway phase in protoplanetary growth and a second stage of oligarchic growth of protoplanets, in the same sense as in Kokubo Ida \cite{kokubo1}) )."1087 Also. when analysing the evolution of the RMS eccentricity and inclination of the planetesimal system during the oligarchic growth stage they found that their results agree with those predicted by the semi- theory of Ida Makino (1993)) for their second stage.," Also, when analysing the evolution of the RMS eccentricity and inclination of the planetesimal system during the oligarchic growth stage they found that their results agree with those predicted by the semi--analytical theory of Ida Makino \cite{ida}) ) for their second stage."1088 In the present version of the code we have introduced a time-dependent planetesimal aecretion. rate., In the present version of the code we have introduced a time–dependent planetesimal accretion rate.1089 In this kind of calculation most authors (Pollack et al. 1996:;, In this kind of calculation most authors (Pollack et al. \cite{pollack};1090 Hubickyy et al. 2005::, Hubickyj et al. \cite{hubickyj};1091 Alibert et al. 2005)), Alibert et al. \cite{alibert}) )1092 usually prescribe that obtained by Greenzweig Lissauer (1992)) which assumes a rapid growth regime for the core., usually prescribe that obtained by Greenzweig Lissauer \cite{greenzweig}) ) which assumes a rapid growth regime for the core.1093 Instead. we adopt that corresponding to the oligarchie growth of Ida Makino (1993)): a slower aceretion rate that still has not been explored with a self-consistent code for giant planet formation.," Instead, we adopt that corresponding to the oligarchic growth of Ida Makino \cite{ida}) ); a slower accretion rate that still has not been explored with a self–consistent code for giant planet formation."1094 The condition for the dominance of the oligarchic growth over the (previous) runaway growth of a protoplanet. M/ii=50— 100. was derived semi-analytically by Ida Makino (1993)).," The condition for the dominance of the oligarchic growth over the (previous) runaway growth of a protoplanet, $M/m \simeq 50-100$ , was derived semi–analytically by Ida Makino \cite{ida}) )."1095 In all the cases of interest for this study. the cross-over mass Is very low — 1.8. some orders of magnitude below the Earth mass (Thommes et al. 2003)).," In all the cases of interest for this study, the cross–over mass is very low — i.e. some orders of magnitude below the Earth mass (Thommes et al. \cite{thommes}) )."1096 Due to the initial runaway regime. the cross-over mass is reached m a negligible time and thus. the formation time of a giant planet's core 15 almost entirely regulated by the oligarchic growth.," Due to the initial runaway regime, the cross–over mass is reached in a negligible time and thus, the formation time of a giant planet's core is almost entirely regulated by the oligarchic growth."1097 For this reason. we prescribe the oligarchic growth for the core since the very beginning of our simulations.," For this reason, we prescribe the oligarchic growth for the core since the very beginning of our simulations."1098" In the dispersion-dominated regime. a solid embryo growth rate 1s well described by the particle-in-a-box approximation (Safranov. 1969)). where M, is the mass of the solid protoplanet (in. our case. the core of the giant planet). / is the planetesimals? dise scale height. Rey is the effective capture radius and F is a factor mtroduced to compensate for the underestimation of the accretion rate by a two-body algorithm when considering the velocity dispersion of a population of planetesimals modelled by a single eccentricity and inclination equal to the RMS values."," In the dispersion–dominated regime, a solid embryo growth rate is well described by the particle–in–a–box approximation (Safranov, \cite{safranov}) ), where $M_\mathrm{c}$ is the mass of the solid protoplanet (in our case, the core of the giant planet), $h$ is the planetesimals' disc scale height, $R_\mathrm{eff}$ is the effective capture radius and $F$ is a factor introduced to compensate for the underestimation of the accretion rate by a two–body algorithm when considering the velocity dispersion of a population of planetesimals modelled by a single eccentricity and inclination equal to the RMS values."1099 F is estimated to be ~3 (Greenzweig Lissauer 1992))., $F$ is estimated to be $\sim 3$ (Greenzweig Lissauer \cite{greenzweig}) ).1100" Due to gravitational focusing. the effective capture radius of a protoplanet. Ray. is larger than its geometrical radius with A. the geometrical radius of the solid embryo. v4. the escape velocity from its surface and οι the relative velocity between the protoplanet and planetesimals. where. hereafter. ¢=(62)p αἱ=(i2374) is planetesimals RMS eccentricity (inclination) with respect to the dise (e. / << 1) and O, is the Keplerian angular velocity."," Due to gravitational focusing, the effective capture radius of a protoplanet, $R_\mathrm{eff}$, is larger than its geometrical radius with $R_\mathrm{c}$ the geometrical radius of the solid embryo, $v_\mathrm{esc}$ the escape velocity from its surface and $v_\mathrm{rel}$ the relative velocity between the protoplanet and planetesimals, where, hereafter, $e=\mean{e_m^2}^{1/2}$ $i= \mean{i_m^2}^{1/2}$) is planetesimals RMS eccentricity (inclination) with respect to the disc $e$, $i$ $<<$ 1) and $\Omega_\mathrm{k}$ is the Keplerian angular velocity."1101 We apply the approximations 7=e/2 and ἡ=ai., We apply the approximations $i \simeq e/2$ and $h \simeq ai$.1102 Following Thommes et al. (2003)).," Following Thommes et al. \cite{thommes}) ),"1103" we adopt for e the equilibrium expression that is deduced for the case when gravitational perturbations due to the protoplanet are balanced by dissipation due to gas drag. where M is the protoplanet mass (here we assume M to be the total mass of the proto-giant planet. meaning the core mass plus the envelope mass). oj is the planetesimal bulk density. p is the gas volume density of the protoplanetary disc. Cp is the drag coefficient (dimensionless and of the order of 1). M, is the mass of the central star and £ is the width of the “heated region"" in units of the Hill radius (considering that potentially other embryos are growing as well. 6 is of the order of 10)."," we adopt for $e$ the equilibrium expression that is deduced for the case when gravitational perturbations due to the protoplanet are balanced by dissipation due to gas drag, where $M$ is the protoplanet mass (here we assume $M$ to be the total mass of the proto–giant planet, meaning the core mass plus the envelope mass), $\rho_m$ is the planetesimal bulk density, $\rho$ is the gas volume density of the protoplanetary disc, $C_\mathrm{D}$ is the drag coefficient (dimensionless and of the order of 1), $M_{\star}$ is the mass of the central star and $\beta$ is the width of the “heated region” in units of the Hill radius (considering that potentially other embryos are growing as well, $\beta$ is of the order of 10)."1104 For calculations that do not assume equilibrium values for the eccentricity and the inclination. we refer the reader to Chambers (2006)).," For calculations that do not assume equilibrium values for the eccentricity and the inclination, we refer the reader to Chambers \cite{chambers}) )."1105 His results show that using equilibrium values for e and / is an acceptable approximation when considering embryos of a2107?M.. consistent with the initial core mass of all our simulations (see Sect. 3)).," His results show that using equilibrium values for $e$ and $i$ is an acceptable approximation when considering embryos of $m \ga 10^{-2} \; \mathrm{M_{\oplus}}$, consistent with the initial core mass of all our simulations (see Sect. \ref{sec:results}) )."1106 However. when the solid embryo is massive enough to gravitationally bind gas from the surrounding nebula. the presence of this envelope should be considered when calculating the effective capture radius. Ra.," However, when the solid embryo is massive enough to gravitationally bind gas from the surrounding nebula, the presence of this envelope should be considered when calculating the effective capture radius, $R_\mathrm{eff}$."1107 The gaseous envelope modifies the trajectory of incoming planetesimals. as they are affected by the gas drag that enlarges the capture radius of the protoplanet.," The gaseous envelope modifies the trajectory of incoming planetesimals, as they are affected by the gas drag that enlarges the capture radius of the protoplanet."1108" In addition to the gravitational focusing. a ""viscous focusing"" due to gas drag should be considered."," In addition to the gravitational focusing, a “viscous focusing” due to gas drag should be considered."1109 The effective radius Ryy. 1n. the form stated in Eq. (115) ," The effective radius $R_\mathrm{eff}$, in the form stated in Eq. \ref{eq:reff}) )"1110dominates when the mass of bound gas tis negligible., dominates when the mass of bound gas is negligible.1111 But when the embryo acquires enough gas to form a thir atmosphere. its effective radius becomes larger and it separates from that caleulated previously.," But when the embryo acquires enough gas to form a thin atmosphere, its effective radius becomes larger and it separates from that calculated previously."1112 To caleulate the effective radius of the protoplanet in the presence of gas around the solid embryo we take into account. the action of gravity and gas drag on. the incoming planetesimals., To calculate the effective radius of the protoplanet in the presence of gas around the solid embryo we take into account the action of gravity and gas drag on the incoming planetesimals.1113" Consider one planetesimal entering the protoplanet atmosphere with a velocity ve,(Eq. (12))).", Consider one planetesimal entering the protoplanet atmosphere with a velocity $v_\mathrm{rel}$(Eq. \ref{eq:vrel}) )).1114 Its equation of motion results from the action of gravity together with the action of gas drag., Its equation of motion results from the action of gravity together with the action of gas drag.1115 In Eq. (14)).," In Eq. \ref{eq:grav}) ),"1116" ¢ ts the radial coordinate from the centre of the protoplanet and M, is the mass contained within r.", $r$ is the radial coordinate from the centre of the protoplanet and $M_r$ is the mass contained within $r$ .1117" For the gas drag force acting on a spherical body of radius 7, travelling with velocity v. we adopt the Stokes law"," For the gas drag force acting on a spherical body of radius $r_m$ travelling with velocity $v$ , we adopt the Stokes law"1118The 30 Doradus nebula in the Large Alagellanie Cloucl (LAIC) is the closest example of a giant extragalactic rregion and the largest in the local group of galaxies.,The 30 Doradus nebula in the Large Magellanic Cloud (LMC) is the closest example of a giant extragalactic region and the largest in the local group of galaxies.1119" Lt is regarded as undergoing intense enough star formation to be referred to as a ""mini-starburst, by Leitherer(1998). ancl as such is an important nearby laboratory of both massive star formation and starburst. phenomena.", It is regarded as undergoing intense enough star formation to be referred to as a `mini-starburst' by \citet{leitherer98} and as such is an important nearby laboratory of both massive star formation and starburst phenomena.1120 The highly: dynamic nebulosity (e.g. Meaburn1981:Meaburn. 1987)) is powered by a super star cluster of LOO massive stars.," The highly dynamic nebulosity (e.g. \citealt{meaburn81,meaburn87}) ) is powered by a super star cluster of $\sim 100$ massive stars."1121 Remarkable UST imagery of the environment. of the central cluster ol massive stars has recently: been presented by Walbornetal. (2002)., Remarkable HST imagery of the environment of the central cluster of massive stars has recently been presented by \citet{walborn.et.al02}.1122.. Phe combined. winds. UW radiation and supernova explosions [roni so many massive stars ab a similar evolutionary epoch enables the generation. of the nested elant (20 300 pe diameter) shells that comprise the giant rregion (Aleaburn1980:Meaburn1990:Leitherer 1998)).," The combined winds, UV radiation and supernova explosions from so many massive stars at a similar evolutionary epoch enables the generation of the nested giant (20 – 300 pc diameter) shells that comprise the giant region \citealt{meaburn80,meaburn90,leitherer98}) )."1123 On the largest scales. surrounding 30 Dor are supergiant. (600 1400 pe diameter) interstellar shells such as LMC3.," On the largest scales, surrounding 30 Dor are supergiant (600 – 1400 pc diameter) interstellar shells such as LMC3."1124" The term ""shell will be used in this paper rather than the commonly. used term “bubble” since it is preferable to use a term that is civnamically neutral and constrained. to no specilie geometry. (c.g. spherical).", The term 'shell' will be used in this paper rather than the commonly used term `bubble' since it is preferable to use a term that is dynamically neutral and constrained to no specific geometry (e.g. spherical).1125 Phe term ‘bubble’. often erroneously presupposes a roughly spherical. pressuredriven. energv-conserving shell.," The term `bubble', often erroneously presupposes a roughly spherical, pressure--driven, energy-conserving shell."1126 Ες is certainlv not the case For the supergiant shells which are unlikely to be either spherical or energv-conserving., This is certainly not the case for the supergiant shells which are unlikely to be either spherical or energy-conserving.1127" The division between ‘giant’ and ""supergiant when applied to the LMC shells will be for the diameter ranges above and recently confirmed. by the LE observations of Iximetal.(1999).", The division between 'giant' and 'supergiant' when applied to the LMC shells will be for the diameter ranges above and recently confirmed by the H observations of \citet{kim.et.al99}.1128.. Dilferent. though related. mechanisms must be involved in the formation of LAIC shells in these distinctly. separate diameter ranges.," Different, though related, mechanisms must be involved in the formation of LMC shells in these distinctly separate diameter ranges."1129 The most important dillerence is that supergiant shells have diameters in excess of the neutral gas scale-height. of the LMC., The most important difference is that supergiant shells have diameters in excess of the neutral gas scale-height of the LMC.1130 The overlapping giant shells comprising the halo of 30 Doradus have been shown to be expanding at around. 50 ((c.@. Aleaburn1984:Chu&Ixennicutt. 1994)). whereas a multitude of 15pe diameter regions exhibit outllows of =200kms. .," The overlapping giant shells comprising the halo of 30 Doradus have been shown to be expanding at around 50 (e.g. \citealt{meaburn84,chu&kennicutt94}) ) whereas a multitude of $15~{\rm pc}$ diameter regions exhibit outflows of $\ga 200~{\rm1131km~s^{-1}}$ ."1132 Lhe latter were interpreted as voung supernova remnants in the perimeters of giant shells (Meaburn1988)., The latter were interpreted as young supernova remnants in the perimeters of giant shells \citep{meaburn88}.1133. lis a cartoon that illustrates the hierarchy. of scale sizes present in a giant rreeion like 30 Doradus., 1 is a cartoon that illustrates the hierarchy of scale sizes present in a giant region like 30 Doradus.1134 The brightest. dominant velocity. components of 30 Doradus are complex. but seem to be comprised. of three distinct velocity regimes corresponding to LL sheets along the sightline.," The brightest, dominant velocity components of 30 Doradus are complex but seem to be comprised of three distinct velocity regimes corresponding to H sheets along the sightline."1135 These are at. 250kms 270kms! and 300kms (AleGeeotal.1978:Chu&Wennicutt1994:timetal. 1999)..," These are at $250~{\rm km~s^{-1}}$, $270~{\rm km~s^{-1}}$ and $300~{\rm km~s^{-1}}$ \citep{mcgee.et.al78,chu&kennicutt94,kim.et.al99}. ."1136 In this paper. the systemic velocity. Voy. is taken to be the average heliocentric velocity (Viger) of these components. 270kms.l. in agreement with previous observations (see for example Peckctal.1997:1991:Garayetal.1993:Clayton 1987)).," In this paper, the systemic velocity, $V_{\rm sys}$ is taken to be the average heliocentric velocity $V_{\rm HEL}$ ) of these components, $270~{\rm km~s^{-1}}$, in agreement with previous observations (see for example \citealt{peck.et.al97short,meaburn91,garay.et.al93,clayton87}) )."1137 In this work. the aim is to investigate the faint. highest speed. phenomena in the halo of 30 Doradus in order to completethe kinematical characterisation of this important eu rregion.," In this work, the aim is to investigate the faint highest speed phenomena in the halo of 30 Doradus in order to completethe kinematical characterisation of this important giant region."1138 New echelle observations of the line profiles. of, New echelle observations of the line profiles of1139In order {ο evaluate equation AS we assume that both the point sources and the noise have zero-mean Gaussian distribution functions with the variances 97 and 07 and are not correlated. spatially.,In order to evaluate equation \ref{eq5} we assume that both the point sources and the noise have zero-mean Gaussian distribution functions with the variances $\sigma_x^2$ and $\sigma_n^2$ and are not correlated spatially.1140 We also assume that there is only one point source in the windowW., We also assume that there is only one point source in the window.1141 Under these assumptions the integration in À4 can be performed to vield: Ilere After substituting equation AG in equation AS we obtain the linal expression lor the point source probability: The original downhill simplex algorithm described in Nelder&Mead:(1965) ancl (1971) minimizes a [unetion of No variables by using the values of the function at several verlices and (irving to move away from the highest vertex.," Under these assumptions the integration in \ref{eq4} can be performed to yield: Here After substituting equation \ref{eq6} in equation \ref{eq5} we obtain the final expression for the point source probability: The original downhill simplex algorithm described in \citet{Nelder}1142 and \citet{O'Neill} minimizes a function of $N$ variables by using the values of the function at several vertices and trying to move away from the highest vertex."1143 In our paper the function being minimized is the goodness-ol-lit measure |? delined in equation 4.., In our paper the function being minimized is the goodness-of-fit measure $\chi^2$ defined in equation \ref{chi2}.1144 There are [our basic wavs lo move a vertex: reflection. expansion. contraction and shrinkage.," There are four basic ways to move a vertex: reflection, expansion, contraction and shrinkage."1145 We adopted the simplex algorithin with a number of improvements., We adopted the simplex algorithm with a number of improvements.1146 The changes areilustrated in Figure 13.., The changes areillustrated in Figure \ref{Simplex}.1147 First. we modified reflection.," First, we modified reflection."1148 If the change in \? is smaller than a user-specilied threshold. it is an indication that the reflection is done almost parallel to the iso-\7 lines.," If the change in $\chi^2$ is smaller than a user-specified threshold, it is an indication that the reflection is done almost parallel to the $\chi^2$ lines."1149 In (his case an attempt is made to replace the reflection with a move in a perpendicular direction., In this case an attempt is made to replace the reflection with a move in a perpendicular direction.1150 The number of perpendicular directions are equal to ΔΝ—1)., The number of perpendicular directions are equal to $2(N-1)$.1151 The move is performed. if it results in a A? lower than the one achieved by the reflection.," The move is performed, if it results in a $\chi^2$ lower than the one achieved by the reflection."1152 Another modification is that contraction and shrinkage have been replaced with the line minimization of 4? along the unsuccessful reflection direction., Another modification is that contraction and shrinkage have been replaced with the line minimization of $\chi^2$ along the unsuccessful reflection direction.1153 Le. if the reflection results in point with higher than the original V7. a point with the lowest 4? is found on the line of the unsuccessful reflection.," I.e. if the reflection results in point with higher than the original $\chi^2$ , a point with the lowest $\chi^2$ is found on the line of the unsuccessful reflection."1154outskirts.,outskirts.1155 On the largest scale the pressure as well as the image appears to be quite smooth., On the largest scale the pressure as well as the image appears to be quite smooth.1156 A weak lensing mass reconstruction of Clowe et al. (, A weak lensing mass reconstruction of Clowe et al. (11572003) shows that the cluster exhibits three dark matter peaks. with only the weakest of them corresponding to a X-ray peak. yet all of them are preceded by a shocked zone. seen in the entropy map.,"2003) shows that the cluster exhibits three dark matter peaks, with only the weakest of them corresponding to an X-ray peak, yet all of them are preceded by a shocked zone, seen in the entropy map."1158 The main pressure peak is approximately located at the position of the center of the mass distribution from the weak lensing reconstruction., The main pressure peak is approximately located at the position of the center of the mass distribution from the weak lensing reconstruction.1159 This center is adopted for the volume calculations and reported in Table .., This center is adopted for the volume calculations and reported in Table \ref{t:ol}.1160 The entropy dip of the bullet is offset from the potential minimum and there 15 no entropy dip associated with the potential minimum of the main cluster., The entropy dip of the bullet is offset from the potential minimum and there is no entropy dip associated with the potential minimum of the main cluster.1161 There are. however. entropy fluctuations in the pressure core. possibly associated with debris of the eitropy core of the main cluster.," There are, however, entropy fluctuations in the pressure core, possibly associated with debris of the entropy core of the main cluster."1162 The spectroscopic analysis is reported in Table 13. and Fig.13.., The spectroscopic analysis is reported in Table \ref{t:cl14:t} and \ref{f:cl14}.1163 It reveals temperature fluctuations by a factor of 1.5., It reveals temperature fluctuations by a factor of 1.5.1164 The temperature of the bullet is only slightly lower than the bulk of the cluster., The temperature of the bullet is only slightly lower than the bulk of the cluster.1165 However it exhibits a distinctly low entropy. which also allows us to trace the tail of the bullet.," However it exhibits a distinctly low entropy, which also allows us to trace the tail of the bullet."1166 The zone assigned to bullet can be seen as negative deviation in entropy profile in Fig.13.., The zone assigned to bullet can be seen as negative deviation in entropy profile in \ref{f:cl14}.1167 The bullet pressure peak is confirmed: it amounts to and is located behind the zone of lowest entropy in the bullet., The bullet pressure peak is confirmed; it amounts to and is located behind the zone of lowest entropy in the bullet.1168 By combining together all the high-entropy zones. associated with the shock heating. we have achieved significance in the temperature variation. from 10.," By combining together all the high-entropy zones, associated with the shock heating, we have achieved significance in the temperature variation, from 10."1169 to 1422 keV. This corresponds to à Mach number of 1.4+0.2., to $14\pm2$ keV. This corresponds to a Mach number of $1.4\pm0.2$.1170 This estimate is lower. compared to the shock parameters deduced from the image showing the Mach cone.," This estimate is lower, compared to the shock parameters deduced from the image showing the Mach cone."1171 A higher Mach number would be obtained from the entropy enhancement: 2.6+0.2., A higher Mach number would be obtained from the entropy enhancement: $2.6\pm0.2$.1172 It is plausible that the extraction region captures both shock and postshock gas., It is plausible that the extraction region captures both shock and postshock gas.1173 The later has lower pressure. but records its state in the entropy.," The later has lower pressure, but records its state in the entropy."1174 As was noted above. the observed shock is located in front of the outward moving dark matter potential.," As was noted above, the observed shock is located in front of the outward moving dark matter potential."1175 Since the potentials carry no longer any gas. they do not cause this shock. but just travel at the same speed.," Since the potentials carry no longer any gas, they do not cause this shock, but just travel at the same speed."1176 This implies that we observe the initial forward shock propagating through the cluster., This implies that we observe the initial forward shock propagating through the cluster.1177 The entropy ratio also shows that the eastern part of the cluster has lower entropy. as due to the stripping of the bulk of the bullet cluster.," The entropy ratio also shows that the eastern part of the cluster has lower entropy, as due to the stripping of the bulk of the bullet cluster."1178 An analysis of the two-dimensional structure 1n the REFLEX clusters. as seen in the images and spectral hardness ratio maps. reveals statistically significant substructure. probably originating from different stages of cluster merger.," An analysis of the two-dimensional structure in the REFLEX clusters, as seen in the images and spectral hardness ratio maps, reveals statistically significant substructure, probably originating from different stages of cluster merger."1179 We are able to see the substructure even at very late merger stages. where for example the X-ray image appears to be quite symmetric.," We are able to see the substructure even at very late merger stages, where for example the X-ray image appears to be quite symmetric."1180 We identify the entropy to be most sensitive to both late stage mergers with the associated slow buoyancy action of relaxation of the cluster and to strong shocks. which change the entropy.," We identify the entropy to be most sensitive to both late stage mergers with the associated slow buoyancy action of relaxation of the cluster and to strong shocks, which change the entropy."1181 Two mergers with large Mach numbers are found., Two mergers with large Mach numbers are found.1182 A statistical analysis of the substructure in the pressure and entropy maps. reveals significant fluctuations around the mean profile.," A statistical analysis of the substructure in the pressure and entropy maps, reveals significant fluctuations around the mean profile."1183 Typically. pressure fluctuations are found on the level. while the entropy fluctuations are at the level.," Typically, pressure fluctuations are found on the level, while the entropy fluctuations are at the level."1184 Apparently. smoother appearance of the pressure maps should be attribtted to the larger dynamical range of the map. covering typically two orders of magnitude.," Apparently, smoother appearance of the pressure maps should be attributed to the larger dynamical range of the map, covering typically two orders of magnitude."1185 A comparison of our sample with a similar analysis of hydro-dynamical simulations. by Finoguenov et al. (, A comparison of our sample with a similar analysis of hydro-dynamical simulations by Finoguenov et al. (11862005) reveals a similar distribution of clusters vs the level of the substructure in both entropy and pressure.,2005) reveals a similar distribution of clusters vs the level of the substructure in both entropy and pressure.1187 Anunber of clusters exhibit a presence of low entropy gas in the outskirts. deviating by at least an order of magnitude from the prescription of gravitational heating.," A number of clusters exhibit a presence of low entropy gas in the outskirts, deviating by at least an order of magnitude from the prescription of gravitational heating."1188 Surprisingly enough. these regions have gas pressures similar to that of," Surprisingly enough, these regions have gas pressures similar to that of"1189of perturbation wave-vector perpendicular to the magnetic Ποια.,of perturbation wave-vector perpendicular to the magnetic field.1190" Simplilving the linearized equations (8))-(13)) by repeated use of (he unperturbed background equations (15))-(13)). we obtain OD, The perturbed αν velocity due to the perturbed magnetic lied changes the ambipolar diffusion heating rate."," Simplifying the linearized equations \ref{drift}) \ref{ebstate}) ) by repeated use of the unperturbed background equations \ref{backgden}) \ref{st}) ), we obtain where The perturbed drift velocity due to the perturbed magnetic field changes the ambipolar diffusion heating rate."1191 In fact. the net cooling Function € in equation (21)) must contain also (he ambipolear heating due to perturbed magnetic field.," In fact, the net cooling function $\Omega$ in equation \ref{lineng}) ) must contain also the ambipolar heating due to perturbed magnetic field."1192 Iowever. because we have expressed (he ambipolar heating in equation (6)) bv parameters. in numerical calculations for drawing ligures. we can involve this effect by the amount of parameters.," However, because we have expressed the ambipolar heating in equation \ref{heatad}) ) by parameters, in numerical calculations for drawing figures, we can involve this effect by the amount of parameters."1193 Thus. for simplicitv. we neglect the explicit calculations of the changes of ambipolar heating due to perturbed crilt velociv.," Thus, for simplicity, we neglect the explicit calculations of the changes of ambipolar heating due to perturbed drift velocity."1194 since (he equilibrium is Gime dependent. (he normal modes of the svstem are time dependent too. (hus. we must apply some approximation techniques namely WID approximation (e.g.. Dora aud Daruah 2008) to gain valuable insight into the nature of problem: this analysis mav be a challenging task in a subsequent research.," Since the equilibrium is time dependent, the normal modes of the system are time dependent too, thus, we must apply some approximation techniques namely WKB approximation (e.g., Bora and Baruah 2008) to gain valuable insight into the nature of problem; this analysis may be a challenging task in a subsequent research."1195 Here. we consider the isobaric TI. which is more realistic phenomena in (he interstellar gases.," Here, we consider the isobaric TI, which is more realistic phenomena in the interstellar gases."1196 Gathering the equations (23)) and (21)) with equation (19)). in isobaric case (py= 0). leads to an exponential growth as follows," Gathering the equations \ref{linsta}) ) and \ref{lineng}) ) with equation \ref{linden}) ), in isobaric case $p_1=0$ ), leads to an exponential growth as follows"1197After optimizing the Πί for the autocorrelation measurements. we then looked at how conditioning the cross-ccorrelation covariance matrices affects the overall reconstruction ofο,"After optimizing the fits for the autocorrelation measurements, we then looked at how conditioning the correlation covariance matrices affects the overall reconstruction of."1198"ρ), Since the uncertainty in iis dominated by the uncertainty inz).. this conditioning should have the greatest impact onw,,(7. the reconstruction."," Since the uncertainty in is dominated by the uncertainty in, this conditioning should have the greatest impact on the reconstruction."1199" We generate 10 pick-4 measurements by averaging the correlation measurements from four randomly selected fields out of the 24. which we then use to calculate©,(<)."," We generate $10^4$ pick-4 measurements by averaging the correlation measurements from four randomly selected fields out of the 24, which we then use to calculate."1200. For calculating the risk. we know the true redshift distribution in each field perfectly from the simulation. so we do not need to rely on synthetic techniques as in refsec:optwpp..," For calculating the risk, we know the true redshift distribution in each field perfectly from the simulation, so we do not need to rely on synthetic techniques as in \\ref{sec:optwpp}."

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