ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 The present, The present3(Figure 2 of 2)) ane are therefore. extreme horizontal branch (LEB) stars.,(Figure 2 of \citealt{Maxted01}) ) and are therefore extreme horizontal branch (EHB) stars.4 The two exceptions are the two hottest stars. DO0934|ISG and PO1244|113. which are sulliciently displaced from the band to be considered. post-ELLB stars.," The two exceptions are the two hottest stars, PG0934+186 and PG1244+113, which are sufficiently displaced from the band to be considered post-EHB stars."5 The effective temperatewe and gravity of PCL244|113 were determined. by Saller (as reported. by 2)) with a method similar to ours but using a cilferent erid of svnthetic spectra o be Tr= 338001. and logg=5.67. which places it just outside of the ENB band. although the uncertainty on he measurement was such that it could not be positively identified as a post-I5l2 star.," The effective temperature and gravity of PG1244+113 were determined by Saffer (as reported by \citealt{Maxted01}) ) with a method similar to ours but using a different grid of synthetic spectra to be $_{\rm eff} = 33 800$ K and $\log g = 5.67$, which places it just outside of the EHB band, although the uncertainty on the measurement was such that it could not be positively identified as a post-EHB star."6 We determine a a somewhat igher Tr and lower gravitv. which places the star away rom the ELL.," We determine a a somewhat higher $_{\rm eff}$ and lower gravity, which places the star away from the EHB."7 We also note that we find EC221:wx4d6446 to be one of he rave helium-rich sdB stars., We also note that we find EC22133-6446 to be one of the rare helium-rich sdB stars.8 EC22LI:wx4d6446 is one of the objects in our survey in which we detect no significant radial velocity variations., EC22133-6446 is one of the objects in our survey in which we detect no significant radial velocity variations.9 ? took high-resolution spectra of 15 sdB binaries. ane for a hired of these found the orbits to be slightly eccentric with ο00.03 0.06.," \citet{Edelmann05} took high-resolution spectra of 15 sdB binaries, and for a third of these found the orbits to be slightly eccentric with $e \sim$$0.03$ – $0.06$."10 To investigate cllipticity in our binaries we itted cach of our data sets using the Levenbure-A\arquarelt method (2) with a model consisting of a sine Function and its irst harmonic. a reasonable approximation to an elliptical orbit for small values of e.," To investigate ellipticity in our binaries we fitted each of our data sets using the Levenburg-Marquardt method \citep{Press02} with a model consisting of a sine function and its first harmonic, a reasonable approximation to an elliptical orbit for small values of $e$."11 The cecentricity is determined rom the ratio of the amplitudes of the first harmonic to the 'undamental., The eccentricity is determined from the ratio of the amplitudes of the first harmonic to the fundamental.12 In Table 5 we list the best-fit value of e for cach target. and the improvement in X7 over a circular orbit.," In Table \ref{tab:eccentric} we list the best-fit value of $e$ for each target, and the improvement in $\chi^{2}$ over a circular orbit."13 The change in the orbital period determination compared Ot10 values reported in Table 2. is very small (less than one per cent in all cases. and much less than this in most).," The change in the orbital period determination compared to the values reported in Table \ref{tab:results} is very small (less than one per cent in all cases, and much less than this in most)."14 For each target. we computed the £ statistic comparing he elliptical model fit with the circular fit.," For each target, we computed the $F$ statistic comparing the elliptical model fit with the circular fit."15 In all cases. we ind the improvement is not significant at the 95% level.," In all cases, we find the improvement is not significant at the $95$ level."16 We, We17 , 18expected to be «quite sensitive to that of 7.,expected to be quite sensitive to that of $\tau_{\rm o}$.19" Furthermore. as the value of 7, increases. (hedecrease of 5, accelerates. due to the L/In5, factor in the exponent."," Furthermore, as the value of $\tau_{\rm o}$ increases, thedecrease of $\gamma_{\rm c}$ accelerates, due to the $1/\ln \gamma_{\rm c}$ factor in the exponent."20" Both of these properties derive from the fact that the elfective number of inverse Compton orders is proportional to Iny/5,.", Both of these properties derive from the fact that the effective number of inverse Compton orders is proportional to $\ln y/ \ln \gamma_{\rm c}$.21 In the external photon scenario. equations (14)) and (15)) completely describe the relation between the source properties and (he values of a and 5..," In the external photon scenario, equations \ref{eq:1.15}) ) and \ref{eq:1.16}) ) completely describe the relation between the source properties and the values of $\alpha$ and $\gamma_{\rm c}$."22" This is not quite the case [or the SSC-scenario. since il was tacitly assumed in equation (10)) that a.>san. where 54,4; is the Lorentz factor corresponding to the svnchrotron self-absorption frequency (Maps)."," This is not quite the case for the SSC-scenario, since it was tacitly assumed in equation \ref{eq:1.11}) ) that $\gamma_{\rm c} > \gamma_{\rm abs}$, where $\gamma_{\rm abs}$ is the Lorentz factor corresponding to the synchrotron self-absorption frequency $\nu_{\rm abs}$ )."23" When 5.€ 544. the energy densitv of svnehrotron photons peaks al 7j, rather than the cooling frequency (4%= 5275)."," When $\gamma_{\rm c} < \gamma_{\rm abs}$ , the energy density of synchrotron photons peaks at $\nu_{\rm abs}$ rather than the cooling frequency $\nu_{\rm c} = \gamma_{\rm c}^2 \nu_{\rm B}$ )."24" Hence. the same analvsis as above can be made except that (wo substitutions need to be made: UpL—pliμμ)abs, and vpL—Varn.abs=52,!absvp.""E Since where the last [actor on the RIIS accounts for the decreasingcolumn clensity of electrons wilh +=545, due to cooling. the expression corresponding to equation (15)) is When 7,=1 occurs [or +.<a. as IS the value of 544, al 7,=1."," Hence, the same analysis as above can be made except that two substitutions need to be made: $U_{\rm B} \rightarrow U_{\rm ph}(\nu_{\rm abs})$ and $\nu_{\rm B} \rightarrow \nu_{\rm abs} = \gamma_{\rm abs}^2 \nu_{\rm B}$ Since where the last factor on the RHS accounts for the decreasingcolumn density of electrons with $\gamma = \gamma_{\rm abs}$ due to cooling, the expression corresponding to equation \ref{eq:1.16}) ) is When $\tau_{\rm o} = 1$ occurs for $\gamma_{\rm c} < \gamma_{\rm abs}$, $\gamma_{\rm abso}$ is the value of $\gamma_{\rm abs}$ at $\tau_{\rm o} = 1$."25 In this case. separate values for ος and μυ cannot be obtained: however. their combination. which occurs in equation (17)). is given bv an expression similar (o that in equation (13)) The main difference between equation (15)) ancl equation (17)) is that (he exponent of the RIIS-side is roughly a [actor of (wo smaller lor the latter as compared to the former.," In this case, separate values for $\gamma_{\rm co}$ and $\gamma_{\rm abso}$ cannot be obtained; however, their combination, which occurs in equation \ref{eq:1.18}) ), is given by an expression similar to that in equation \ref{eq:1.14}) ) The main difference between equation \ref{eq:1.16}) ) and equation \ref{eq:1.18}) ) is that the exponent of the RHS-side is roughly a factor of two smaller for the latter as compared to the former."26" Formally the reason for this is that when 7,=1 occurs for 5c>Gabe. Gabo—w, and equation (151) becomes identical to equation (13))."," Formally the reason for this is that when $\tau_{\rm o} = 1$ occurs for $\gamma_{\rm c} > \gamma_{\rm abs}$, $\gamma_{\rm abso} \rightarrow \gamma_{\rm co}$ and equation \ref{eq:1.19}) ) becomes identical to equation \ref{eq:1.14}) )."27" Hence. the variation of +, with τι slows down considerablv for 5.<545."," Hence, the variation of $\gamma_{\rm c}$ with $\tau_{\rm o}$ slows down considerably for $\gamma_{\rm c} < \gamma_{\rm abs}$."28 Phe physical reason for (his is (hat the energy density. of svuchrotron seed photons varies much slower in (his regime., The physical reason for this is that the energy density of synchrotron seed photons varies much slower in this regime.29" This conclusion hinges on the assumption that the value of 5,4, varies more slowly than ο.", This conclusion hinges on the assumption that the value of $\gamma_{\rm abs}$ varies more slowly than $\gamma_{\rm c}$ .30 It is shown in the next section that this isindeed the case.o«(p— 1)/2:, It is shown in the next section that this isindeed the case.$\alpha<(p-1)/2$ :31 In this regime. a is obtained directly from equation (8)).," In this regime, $\alpha$ is obtained directly from equation \ref{eq:1.9}) )."32 The variation of . is quite similar to that for a>(p—1)/2 ancl expressions corresponding to equations (15)), The variation of $\gamma_{\rm c}$ is quite similar to that for $\alpha>(p-1)/2$ and expressions corresponding to equations \ref{eq:1.16}) )33Now if is convenient to introduce the normalised phase space distribution function of the beam particlesΕμ). where E=Vl|(p/ime)?. so that Eq. (21)),"Now it is convenient to introduce the normalised phase space distribution function of the beam particles, where $E=\sqrt {1+(p/mc)^2}$, so that Eq. \ref{alfpsi}) )"34 reduces to where {1μι= 1(0) for or(«)U is the step function., reduces to where $H[x]=1(0)$ for $x>(<)0$ is the step function.35 Summing over protons and electrons separately. and introducing the proton and electron Larmor radii. HnRQον 1/0). B.—evT?ΩΙ. respectively. Eq. 3p ," Summing over protons and electrons separately, and introducing the proton and electron Larmor radii, $R_{\rm p}= c\sqrt{\Gamma ^2-1}/\Omega_{\rm p}$ , $R_{\rm e}=c\sqrt{\Gamma ^2-1}/|\Omega_{\rm e}|$, respectively, Eq. \ref{22}) )"36becomes withPc According to Eqs. (13)), becomes with According to Eqs. \ref{15}) )37 and (20)) written in the form we derivet and andxX with which relates the wave intensities of forward (+) and backward (-) moving waves at any time £ to the initial wave intensities at time f=(., and \ref{20a}) ) written in the form we derive and and with which relates the wave intensities of forward (+) and backward (-) moving waves at any time $t$ to the initial wave intensities at time $t=0$.38 In terms of the normalised distribution functions (22)) the proton and electron distribution functions evolve according to Eqs. (17))-(18) ," In terms of the normalised distribution functions \ref{21}) ) the proton and electron distribution functions evolve according to Eqs. \ref{17}) \ref{Dmumu}) ),"39Integrating Eqs. (??)), = ] = ] with Integrating Eqs. \ref{28}) )40 and (??)) over Τ and µ gives because of αμ1)-0 respectively.," and \ref{29}) ) over $t$ and $\mu $ gives because of $a_{\rm p,e}(\mu =-1)=0$ respectively."41 Evaluating Eq. (36) , Evaluating Eq. \ref{31}) )42at j|=(Rk)+ for protons and at µ=(RÀ)! we obtain and Eqs. (379) , at $\mu =-(R_{\rm p}k)^{-1}$ for protons and at $\mu =(R_{\rm e}k)^{-1}$ we obtain and Eqs. \ref{32}) )43and (38)) can be inserted in Eq. (32)), and \ref{33}) ) can be inserted in Eq. \ref{27c}) )44" yielding The system of the coupled equations (30..31..32)) and (39)) describes the temporal developmentof the particle distribution functions Fi, und F. under the influence of self-excited Alfvénn waves propagating either forward (+) or backward (-)."," yielding The system of the coupled equations \ref{27a}, \ref{27b}, \ref{27c}) ) and \ref{34}) ) describes the temporal developmentof the particle distribution functions $F_{\rm p}$ und $F_{\rm e}$ under the influence of self-excited Alfvénn waves propagating either forward (+) or backward (-)."45 Here the boundary conditions are as follows: in the beginning (f= 0) there is the mono-energetic beam distribution (1). Le. in terms of the normalised distribution (22)) |1) The final state of the tsotropisation phase is reached at time 7;when both growth rate and temporal derivative of the distribution disappear. i.e. when 9F;/0j= 0.," Here the boundary conditions are as follows: in the beginning $t=0$ ) there is the mono-energetic beam distribution \ref{1})), i.e. in terms of the normalised distribution \ref{21}) ) +1) The final state of the isotropisation phase is reached at time $T_i$when both growth rate and temporal derivative of the distribution disappear, i.e. when $\partial F_i/\partial \mu =0$ ."46 Consequently Γιο. D AXrthis. time. the AlfvénnApoe waves. have. completely 2isotropised. the beam distrution.," Consequently , At this time the Alfvénn waves have completely isotropised the beam distrution."47 In order to estimate this time scale 7; or, In order to estimate this time scale $T_i$ or48"maps is now corresponding to the 4 charges for the extended-Yang monopole, in agreement with [9]..","maps is now corresponding to the 4 charges for the extended-Yang monopole, in agreement with \cite{DL}."49" As mentioned in the introduction, there is an apparent inconsistency in the system on K3 model we have just considered and which we claim as the Yang monopole."," As mentioned in the introduction, there is an apparent inconsistency in the D2-D4 system on K3 model we have just considered and which we claim as the Yang monopole."50 It precisely concerns its charges., It precisely concerns its charges.51 There is a simple mechanism which would allow in principle to add an infinite charge to the monopole without breaking the spherical symmetry., There is a simple mechanism which would allow in principle to add an infinite charge to the monopole without breaking the spherical symmetry.52" It would contradict the two charge nature of the Yang monopole and, consequently, the model would be incomplete."," It would contradict the two charge nature of the Yang monopole and, consequently, the model would be incomplete."53 This is not the case though., This is not the case though.54 We devote this section to this issue., We devote this section to this issue.55" The D4-D2 brane model proposed in [1] seemed to fit the Yang monopole gauge solution [2] nicely: the dimension was correct; the 5(/(2) gauge group was geometrically engineered by the D2-brane; the magnetic charge, carried by the D4-brane, had just two possible configurations in accordance with the the two charges the Yang solution permits; spherical symmetry was manifest by construction; the model happened to be dual to another [19] who claimed to have given a realization of the Yang monopole in M-theory... However, as compared to the well-studied gauge solutions, there was a crack in our brane model concerning the multiple charge configurations and the (apparently) unavoidable spherical symmetry the model showed."," The D4-D2 brane model proposed in \cite{BDS2} seemed to fit the Yang monopole gauge solution \cite{Y} nicely: the dimension was correct; the $SU(2)$ gauge group was geometrically engineered by the D2-brane; the magnetic charge, carried by the D4-brane, had just two possible configurations in accordance with the the two charges the Yang solution permits; spherical symmetry was manifest by construction; the model happened to be dual to another \cite{BGT}56 who claimed to have given a realization of the Yang monopole in M-theory... However, as compared to the well-studied gauge solutions, there was a crack in our brane model concerning the multiple charge configurations and the (apparently) unavoidable spherical symmetry the model showed."57 It has been objected that the model was not by itself capable to explain the two-charge quality of the Yang monopole as opposed to the Z-tower of charges that characterizes Diracmonopoles'., It has been objected that the model was not by itself capable to explain the two-charge quality of the Yang monopole as opposed to the Z-tower of charges that characterizes Dirac.58. The objection takes into account that there is a simple mechanism which would allow in principle to add an infinite charge to the monopole without breaking spherical symmetry., The objection takes into account that there is a simple mechanism which would allow in principle to add an infinite charge to the monopole without breaking spherical symmetry.59" It soon urged for a deeper study since it would contradict the two charge nature of the Yang monopole and, consequently, the model proposed in [1] would be incomplete."," It soon urged for a deeper study since it would contradict the two charge nature of the Yang monopole and, consequently, the model proposed in \cite{BDS2} would be incomplete."60 Let us go a little deeper in the problem and explain how the model cures itself., Let us go a little deeper in the problem and explain how the model cures itself.61 Consider a D4-brane wrapped on the K3 surface and located at r=0 in a polar, Consider a D4-brane wrapped on the K3 surface and located at $r=0$ in a polar62between GC luminosity and colour of the blue. metal-poor. sub-population (Strader 2005: Llarris 2005) requires significant spectroscopic follow-up. το be. both confirmed. απ üncerstood.,"between GC luminosity and colour of the blue, metal-poor, sub-population (Strader 2005; Harris 2005) requires significant spectroscopic follow-up to be both confirmed and understood."63 Another property of the blue sub-population to be studied is the correlation between host galaxy luminosity and mean blue GC sub-population colour (Strader. Broclic Forbes 2004b). which implies a correlation. between ealaxv mass aud blue GC metallicitv.," Another property of the blue sub-population to be studied is the correlation between host galaxy luminosity and mean blue GC sub-population colour (Strader, Brodie Forbes 2004b), which implies a correlation between galaxy mass and blue GC metallicity."64. his is another indication that the formation of blue GC's is allected by the mass of the host. halo., This is another indication that the formation of blue GCs is affected by the mass of the host halo.65 The majority of the most recent GC spectroscopy for large ellipticals has focused on group ellipticals (e.g. NGC 1052 Pierce 2005a: NGC 3379 Pierce 2005b: NGC 3610 Strader 2003.2004a: NGC 5128 Peng 2004: NGC 2434. NGC 3379. NGC 3585. NGC 5846 and. NGC 7192 Puzia 2004).," The majority of the most recent GC spectroscopy for large ellipticals has focused on group ellipticals (e.g. NGC 1052 Pierce 2005a; NGC 3379 Pierce 2005b; NGC 3610 Strader 2003,2004a; NGC 5128 Peng 2004; NGC 2434, NGC 3379, NGC 3585, NGC 5846 and NGC 7192 Puzia 2004)."66 From the literature there are several Large ellipticals in clusters for which GC spectra have been analysed to measure ages and metallicities., From the literature there are several large ellipticals in clusters for which GC spectra have been analysed to measure ages and metallicities.67 Cohen. Blakeslee ltvzhov. (1998) oesent spectral indices for 150 of MSY's GC's.," Cohen, Blakeslee Ryzhov (1998) present spectral indices for 150 of M87's GCs."68 These vary in S/N. with a sizeable fraction of high enough quality to »e useful.," These vary in S/N, with a sizeable fraction of high enough quality to be useful."69 Co-adding GCs of similar metallicitv. they find he GCs are generally. old. (210 Ces) with metallicities spanning from Fe/H]—2 to above solar.," Co-adding GCs of similar metallicity, they find the GCs are generally old $\geq$ 10 Gyrs) with metallicities spanning from [Fe/H]=–2 to above solar."70 Cohen. Blakeslec Cote (2003) measure metallicities for 47 GC's associated with GC 4472 (A149).," Cohen, Blakeslee Cote (2003) measure metallicities for 47 GCs associated with NGC 4472 (M49)."71 However the S/N is less than 30 for all of the spectra and therefore ages for individual GC's cannot » measured with any confidence., However the S/N is less than 30 for all of the spectra and therefore ages for individual GCs cannot be measured with any confidence.72 Beasley (2000) actelecL spectra for NGC 4472 GCs finding both the rich and metal-poor sub-populations to be old., Beasley (2000) co-added spectra for NGC 4472 GCs finding both the metal-rich and metal-poor sub-populations to be old.73 For the Fornax cluster. IWissler-Patie (1998) measured metallicities for LS GC's around NCC 1399.," For the Fornax cluster, Kissler-Patig (1998) measured metallicities for 18 GCs around NGC 1399."74 Forbes (2001) presented higher S/N spectra for LO CC's and found. two to be young (1-2 Cvrs)., Forbes (2001) presented higher S/N spectra for 10 GCs and found two to be young (1-2 Gyrs).75 From the CGoucdfrooij (2001) spectroscopic sample of NGC 1316. only the spectra of 3 exceptionally bright GC's have high enough S/N to measure ages.," From the Goudfrooij (2001) spectroscopic sample of NGC 1316, only the spectra of 3 exceptionally bright GCs have high enough S/N to measure ages."76 The Lick indices of all 3 bright GC's indicate a voung age (3 Cives) corresponding to the host galaxys recent merger event., The Lick indices of all 3 bright GCs indicate a young age $\sim$ 3 Gyrs) corresponding to the host galaxy's recent merger event.77 The GC colour-magnitude: plot. for NGC 1316 is atypical in that there is a significant population of bright. intermecdiate-colour GC's.," The GC colour-magnitude plot for NGC 1316 is atypical in that there is a significant population of bright, intermediate-colour GCs."78 One galaxy with what appears to be conflicting results is NGC 4365 in the Vireo cluster., One galaxy with what appears to be conflicting results is NGC 4365 in the Virgo cluster.79 Broclie (2005) present spectroscopic results for NGC 4365 GCs and. find some CC's previously thought to belong to an intermediate age sub-population (Larsen 2003: Puzia 2002). are in fact an intermediate metallicity sub-population with old ages.," Brodie (2005) present spectroscopic results for NGC 4365 GCs and find some GCs previously thought to belong to an intermediate age sub-population (Larsen 2003; Puzia 2002), are in fact an intermediate metallicity sub-population with old ages."80 Kundu (2005) present HIST. NICS H-band data and find that these agree with earlier. claims of a GC sub-population with intermediate ages 2-8 Cars., Kundu (2005) present HST NIC3 H-band data and find that these agree with earlier claims of a GC sub-population with intermediate ages 2-8 Gyrs.81 There appears to be no consensus vet. for the GC€ population of this galaxy. unlike other svstenms.," There appears to be no consensus yet for the GC population of this galaxy, unlike other systems."82 While possessing a larger. GC) population. cD and brightest cluster galaxies have the additional complication of GCs potentially associated. with the cluster potential.," While possessing a larger GC population, cD and brightest cluster galaxies have the additional complication of GCs potentially associated with the cluster potential."83 The Virgo cluster elliptical NGC 4649 (M60) is a worthy target for GC spectroscopy as a non-central. giant. cluster elliptical.," The Virgo cluster elliptical NGC 4649 (M60) is a worthy target for GC spectroscopy as a non-central, giant, cluster elliptical."84 NGC 4649. (M60). is. luminous. Mi 22.38. and relatively nearby at D=16.8 Alpe.," NGC 4649 (M60) is luminous, $_V$ =–22.38, and relatively nearby at D=16.8 Mpc."85 UV data for the galaxy ight) suggests a major old. population. plus minor on-&oing star-formation (Magris Bruzual 1993).," UV data for the galaxy light suggests a major old population, plus minor on-going star-formation (Magris Bruzual 1993)."86 However. rom optical spectra. Verlevich Forbes (2002) measure Lick indices and obtain an age of Ll Gyr. metallicity of Fe/l=10.3 and. Mg/Ec]-10.3 for the central regions of he galaxy.," However, from optical spectra, Terlevich Forbes (2002) measure Lick indices and obtain an age of 11 Gyr, metallicity of [Fe/H]=+0.3 and [Mg/Fe]=+0.3 for the central regions of the galaxy."87 Phe Chandra X-ray observations of Rancall (2004) find some structure in the diffuse gas., The Chandra X-ray observations of Randall (2004) find some structure in the diffuse gas.88 The GC imaging study of Forbes (2004) found he standard colour bimodality and. Sy—4.1., The GC imaging study of Forbes (2004) found the standard colour bimodality and $_N$ =4.1.89. Assuming he two sub-populations have similar mass functions. this sugeests a similar formation age.," Assuming the two sub-populations have similar mass functions, this suggests a similar formation age."90" NGC 4649 is one of the ealaxies with the observed. ""bluc-tilt (Strader 2005).", NGC 4649 is one of the galaxies with the observed “blue-tilt” (Strader 2005).91" tecenthy Spitler (2006) have shown that the ""hlue-it is present amonest the GC population of a nearby spiral galaxy. the Sombrero."," Recently Spitler (2006) have shown that the ``blue-tilt'' is present amongst the GC population of a nearby spiral galaxy, the Sombrero."92" Unfortunately our spectroscopic sample does not sample far enough. down the luminosity tunction to adequately test hypotheses regarding the 7blue-it""", Unfortunately our spectroscopic sample does not sample far enough down the luminosity function to adequately test hypotheses regarding the ``blue-tilt''.93 The observations described below are. part of Cremini »ogram GN-2002A-O-13., The observations described below are part of Gemini program GN-2002A-Q-13.94 GC candidates were selected from. Gemini North Multi-Object Spectrograph (GMOS: Hook 2002) imaging. obtained curing 2002 April. for. three i¢lds around NGC. 4649.," GC candidates were selected from Gemini North Multi-Object Spectrograph (GMOS; Hook 2002) imaging, obtained during 2002 April, for three fields around NGC 4649."95 Phe data reduction. and. CC candidate selection process is described in Forbes (2004) and. Bridges (2006)., The data reduction and GC candidate selection process is described in Forbes (2004) and Bridges (2006).96 GAIOS masks for three fields were designed. but only he central field was observed. within the time allocated.," GMOS masks for three fields were designed, but only the central field was observed within the time allocated."97 Spectra of NGC 4649 globular clusters were obtained with GAIOS on the Gemini North telescope during. 2003 on May 31. June 1l. June 4 and June 27.," Spectra of NGC 4649 globular clusters were obtained with GMOS on the Gemini North telescope during 2003 on May 31, June 1, June 4 and June 27."98 Seeing ranged from 0.650.9 arc-seconds overthe four nights., Seeing ranged from 0.65–0.9 arc-seconds overthe four nights.99 Exposures of Ls00s were taken. vielding a total of S hours on-source integration time.," Exposures of $\times$ 1800s were taken, yielding a total of 8 hours on-source integration time."100 Bias frames. dome Llat-ficlels aud CopperArgon. (CuAr) are exposures were taken as part of the Gemini baseline calibrations.," Bias frames, dome flat-fields and Copper-Argon (CuAr) arc exposures were taken as part of the Gemini baseline calibrations."101 From the CuAr ares. wavelength solutions with typical residuals of wavere achieved.," From the CuAr arcs, wavelength solutions with typical residuals of were achieved."102 These cata were reduced using the Gemini/€MOS packages in DRAB and a number of custom mace scripts (see Bridges 2006 for details)., These data were reduced using the Gemini/GMOS packages in IRAF and a number of custom made scripts (see Bridges 2006 for details).103 After some experimentation. optimal (variance) extraction was found to vield the best results since our data are over-sampled on the detector.," After some experimentation, optimal (variance) extraction was found to yield the best results since our data are over-sampled on the detector."104 In some cases. objects were too faint to trace individually and we therefore. co-added: several 2-d images. taken adjacent in time. to act as a reference for the cxtractions.," In some cases, objects were too faint to trace individually and we therefore co-added several 2-d images, taken adjacent in time, to act as a reference for the extractions."105 We verified. beforehand. that Ucxure was minimal between the reference images., We verified beforehand that flexure was minimal between the reference images.106 Finally. the extracted spectra were median combined and weighted. by their κος with cosmic rav rejection.," Finally, the extracted spectra were median combined and weighted by their fluxes with cosmic ray rejection."107 1n the absence of any velocity standard: stars. the recession velocities were measured by using six Bruzual Charlot (2003) model stellar οποίον distributions (SEDs) for 14 and 5 Gyr ages with metallicities Fe/ll] = 1.64. 0.33 anc 10.1.," In the absence of any velocity standard stars, the recession velocities were measured by using six Bruzual Charlot (2003) model stellar energy distributions (SEDs) for 14 and 5 Gyr ages with metallicities [Fe/H] = –1.64, --0.33 and +0.1."108 The task PXNCOR in LRA was used. and the average was taken., The task FXCOR in IRAF was used and the average was taken.109 Objects with recession velocities in the range 100-000 km/s are potentially associated with NGC 4649., Objects with recession velocities in the range $\pm$ 600 km/s are potentially associated with NGC 4649.110 These are presented in Table 1.., These are presented in Table \ref{tabobs}. .111 Phere was one, There was one112 Sd0? S ο.,"Up to now, we have taken $\lambda$ to be a constant, i.e., $d\lambda=0$ in \ref{drho}) )."113 (1)where ⋅ τα ⋅ ⋅ ⋅ ⋅ = and ο we Ανν ," But we achieve the same effect (i.e., \ref{drho}) ) still reduces to \ref{drb}) ) ) even when $d\lambda \neq 0$ provided we require that $F=0$."114"note the PP Aa?sin? 0, (3) D0 oot oi 0. (D mThe =?|Y /A a"," In other words: the function $\rb(r,\theta)$, given by \ref{rho}) ) with $\lambda$ now a $\lambda(r,\theta)$ ,remains a solution of \ref{pde}) ) provided its extra dependence on $r,\theta$ through $\lambda$ does not change the algebraic form of the differential \ref{drb}) )."115?sin? 0. (6) Itis casyto obtain a particular," This will indeed be so if we impose the constraint This condition fixes the dependence of $\lambda$ on $r,\theta$ for any given choice of $f(\lambda)$."116 (separable) solution of (6))depending on two arbitrary ," Thus we now have a general solution, depending upon an arbitrary $f[\lambda(r,\theta)]$."117"coustauts (a ""conuplete iutegral-E) bv addi", The explicit form of the general solution \ref{rho}) ) is then where the radial dependence has been arranged to ensure convergence of the definite integral at its upper limit.118ng.audsubtracting au arbitraryB separatiouB constant«À DontherightH -haud side.," When performing the integrations in \ref{F2}) ) and \ref{solution}) ), we are allowed to treat $\lambda$ as merely a passive constant parameter – it is in fact a function of the limits of integration $r$ $\theta$, not of the integration variables – with the constraint \ref{constraint}) ) imposed."119Let us define QO?| AP?= SR. (8) complete integral which," It is possible, though not especially illuminating or useful, to express each of these integrals in terms of standard elliptic integrals."120 followsfrom (3)).)A of (6))is then obta," As a simple illustrative example (and because we shall need some of the results later), we specialize in this section to the case $m=0$ ."121ined by iutegratiugthe exact ditfereutial dr. (QUA) denoteWe asnexta? fCA)/2. proceedwhereinthe," The Kerr line-element reduces to the metric of flat spacetime expressed in terms of oblate spheroidal coordinates $r,\theta$ – related to Cartesians by The second integral in \ref{F2}) ) can be reduced to the same general form as the first integral when $m=0$."122fusualis complet," Assume that we are in a domain where $\lambda(r,\theta)<1$."123eexpression where Fis thepartial derivative," Setting and making the substution we find Thus the two integrals in \ref{F2}) ) can be combined into a single integral, togive"124We already saw [rom Figure 4 that imposing a z-dependent cilferential rotation on the boundary has rather little effect on (he positions of nodes in (he streamfunction.,We already saw from Figure 4 that imposing a $z$ -dependent differential rotation on the boundary has rather little effect on the positions of nodes in the streamfunction.125 In Figure 11 we see (hal the perturbation in differential rotation does not extend (hat far into the polar cap domain., In Figure 11 we see that the perturbation in differential rotation does not extend that far into the polar cap domain.126 When no differential rotation is imposed (blue curve) a drop in linear rotation is produced (hat is confined to the fist 107 of the forcing boundary., When no differential rotation is imposed (blue curve) a drop in linear rotation is produced that is confined to the first $10^{\circ}$ of the forcing boundary.127 This arises due to the Coriolis force [rom the meridional flow. which itself is declining in amplitude with distance polarward from the forcing boundary.," This arises due to the Coriolis force from the meridional flow, which itself is declining in amplitude with distance polarward from the forcing boundary."128 The amplitude of this differential rotation is about (hat of the observed torsional oscillations., The amplitude of this differential rotation is about that of the observed torsional oscillations.129 For much higher [forcing bv differential rotation at the boundary. this structure is overwhelmed by the simple viscous clamping of the rotational flow: with poleward distance from the boundary.," For much higher forcing by differential rotation at the boundary, this structure is overwhelmed by the simple viscous damping of the rotational flow with poleward distance from the boundary."130 Coriolis forces from (he meridional flow can not maintain these higher values. ancl (he Coriolis force from the imposed differential rotation has only a minor effect on ihe meridional flow.," Coriolis forces from the meridional flow can not maintain these higher values, and the Coriolis force from the imposed differential rotation has only a minor effect on the meridional flow."131 As a point of comparison. the observed z-independent linear differential rotation at high latitudes is given by a straight diagonal line (in black) from the lower right corner of Fieure 11. up to the zero point on the left axis. in accordance with the solutions that contain only differential rotation discussed in section 3.6.1.," As a point of comparison, the observed $z$ -independent linear differential rotation at high latitudes is given by a straight diagonal line (in black) from the lower right corner of Figure 11, up to the zero point on the left axis, in accordance with the solutions that contain only differential rotation discussed in section 3.6.1."132 The large difference between (his amplitude and that of the four colored curves shown shows how small the differential rotalion in our m=I solutions is. except verv close (o the boundary. where the forcing is applied.," The large difference between this amplitude and that of the four colored curves shown shows how small the differential rotation in our $n=1$ solutions is, except very close to the boundary where the forcing is applied."133 We have developed a relatively simple hvdrodisnamical model of the circulation. ad hieh latitudes in the solar convection zone aud photosphere that contains only three forces: pressure gradients. viscous and Coriolis forces.," We have developed a relatively simple hydrodynamical model of the circulation at high latitudes in the solar convection zone and photosphere that contains only three forces: pressure gradients, viscous and Coriolis forces."134 The model equations are solved in a cartesian analog of a spherical polar cap that leaves out. curvature effects as well as the large density increase with depth., The model equations are solved in a cartesian 'analog' of a spherical polar cap that leaves out curvature effects as well as the large density increase with depth.135 This svstem is assumed to be stress-Iree al the top and bottom. corresponding to the top and bottom of the solar convection zone.," This system is assumed to be stress-free at the top and bottom, corresponding to the top and bottom of the solar convection zone."136 It is forced with meridional flow and differential rotation. guided by observations. imposed at the low latitude boundary of the cap. placed at latitudes between 60° and 70* latitude.," It is forced with meridional flow and differential rotation, guided by observations, imposed at the low latitude boundary of the cap, placed at latitudes between $60^{\circ}$ and $70^{\circ}$ latitude."137 While the inclusion of such a boundary is artificial. it is intended (o separate the physics of low and midlatitudes. responsible for the primary meridional circulation cell (hat has polewarcl flow at the top. from the physics active al high latitudes. which should be (he primary determinant of the circulation found there.," While the inclusion of such a boundary is artificial, it is intended to separate the physics of low and mid-latitudes, responsible for the primary meridional circulation cell that has poleward flow at the top, from the physics active at high latitudes, which should be the primary determinant of the circulation found there."138 Our general results are that. as the turbulent viscosity is increased. the imumnber of nodes decreases.," Our general results are that, as the turbulent viscosity is increased, the number of nodes decreases."139 As the meridional flow is increased [or a given turbulent. viscosity. the latitude of," As the meridional flow is increased for a given turbulent viscosity, the latitude of"140ie efficicney of the prompt eutrainnient mechanisni as a 1uneans of trausforriug momentum to ambient molecular eas without causing dissociation.,the efficiency of the prompt entrainment mechanism as a means of transferring momentum to ambient molecular gas without causing dissociation.141 It is found. as oue would expect. that the fraction of jet momentum transferred o the ambient enviroment depends ¢1 the jet/unbieut density ratio.," It is found, as one would expect, that the fraction of jet momentum transferred to the ambient environment depends on the jet/ambient density ratio."142 More importantly. we see that cooling. which is particularly iuportant at higher densities. decreases the ractionaljet momentum that goes iutom," More importantly, we see that cooling, which is particularly important at higher densities, decreases the fractional jet momentum that goes into."143"olecules, Tt would seem on the basis of the simulations preseuted rere that both heavy aud equal density (with respect o the enviroument) jets with radiative cooling have very low cffiicicucies at accelerating abicut molecules without causing dissociation.", It would seem on the basis of the simulations presented here that both heavy and equal density (with respect to the environment) jets with radiative cooling have very low efficiencies at accelerating ambient molecules without causing dissociation.144 In part this is because cooled jets have more aerodyiiunie bow shocks than the corresponding adiabatic ones tthey present a sialler cross sectional area to the ambicut medium)., In part this is because cooled jets have more aerodynamic bow shocks than the corresponding adiabatic ones they present a smaller cross sectional area to the ambient medium).145 The actua shape. however. of the bow shock also seems to to be iuportaut as the decrease in momentum transferred to he ambient medium seenis to affect the acceleration of uolecules more so than atomsious.," The actual shape, however, of the bow shock also seems to to be important as the decrease in momentum transferred to the ambient medium seems to affect the acceleration of molecules more so than atoms/ions."146 We have also tested whether pulsed jets are more cfüicieut at tranusferriug nmoinentuni to the zaüubien uediuu than the correspondingo steady jet with the sams. average velocity., We have also tested whether pulsed jets are more efficient at transferring momentum to the ambient medium than the corresponding steady jet with the same average velocity.147 Somewhat surprisingly we found tha even relatively large velocity variations do not eive rise o sjenificaut changes in the amount of momentum beime deposited in ambient gas., Somewhat surprisingly we found that even relatively large velocity variations do not give rise to significant changes in the amount of momentum being deposited in ambient gas.148 Funcamentally this is because in high Mach mmmber jets. even with cooling. there is very Little coupling between the jet’s cocoon anc the “sheath” tthe post-shiock ambicut eas).," Fundamentally this is because in high Mach number jets, even with cooling, there is very little coupling between the jet's cocoon and the “sheath” the post-shock ambient gas)."149 This lack of, This lack of150are inevitable.,are inevitable.151" To assess (his. we took some individual high resolution spectra from the COND models ancl smoothed them with the 241ASS and bandpasses and found that {νο[4.5] was accurately reproduced (to within 0.1 mag or better) but that A,—[3.6] was less so. particularly at the lowest temperatures."," To assess this, we took some individual high resolution spectra from the COND models and smoothed them with the 2MASS and bandpasses and found that $K_s\!-\![4.5]$ was accurately reproduced (to within 0.1 mag or better) but that $K_s\!-\![3.6]$ was less so, particularly at the lowest temperatures."152 Nevertheless. given the other errors involved in the temperature estimation procedure. we have found that this interpolation error is a relatively minor contributor.," Nevertheless, given the other errors involved in the temperature estimation procedure, we have found that this interpolation error is a relatively minor contributor."153 For a given model. Zi; was restricted (o the nominal range of physical validity. corresponding to Leg«2000 IK (COND). 13800<Zar3000 (DUSTY). or Tuyz2200 Ix (NextGen).," For a given model, $T_{\rm eff}$ was restricted to the nominal range of physical validity, corresponding to $T_{\rm eff}<2000$ K (COND), $1800<T_{\rm eff}<3000$ (DUSTY), or $T_{\rm eff}>2200$ K (NextGen)."154 For each extracted source. the estimates of Toy. a. and Ay were then based on ihe model which gave the minimum value of ©.," For each extracted source, the estimates of $T_{\rm eff}$, $\alpha$, and $A_V$ were then based on the model which gave the minimum value of $\phi$."155 Such estimates were mace for all sources detected in at least 4 of the 5 bands., Such estimates were made for all sources detected in at least 4 of the 5 bands.156 Solutions which gave a poor fit. as indicated by a large value of reduced chi squared (42> 20). were excluded.," Solutions which gave a poor fit, as indicated by a large value of reduced chi squared $\chi_\nu^2>20$ ), were excluded."157" A total of 1022 successful fits was thereby obtained for the ""cloud"" region. representing of the extracted sources."," A total of 1022 successful fits was thereby obtained for the “cloud"" region, representing of the extracted sources."158 In parüceular it was found that the predicted spectral peculiarities of low temperature brown cdwarfs (Teg~1000 IX) were well fit bv the observations., In particular it was found that the predicted spectral peculiarities of low temperature brown dwarfs $T_{\rm eff}\sim1000$ K) were well fit by the observations.159 Figure 3. shows some sample model fils to the deredcdened fluxes. with estimated τομ values as indicated.," Figure \ref{fig3} shows some sample model fits to the dereddened fluxes, with estimated $T_{\rm eff}$ values as indicated."160" The temperature filling procedure was repeated for the ""exterior region."," The temperature fitting procedure was repeated for the “exterior"" region."161 This region was not covered by the 3.6 ji observations and was incomplete at 4.5 jim. as can be seen from Figure 1..," This region was not covered by the 3.6 $\mu$ m observations and was incomplete at 4.5 $\mu$ m, as can be seen from Figure \ref{fig1}."162 Nevertheless. temperature fitting was still possible with relatively little loss of aceuracy.," Nevertheless, temperature fitting was still possible with relatively little loss of accuracy."163 A total of 684 successful fits was thereby obtained. representing of the extracted sources.," A total of 684 successful fits was thereby obtained, representing of the extracted sources."164 This is comparable to the number of fits obtained for the “cloud” region even though the area of skv was substantially smaller.," This is comparable to the number of fits obtained for the “cloud"" region even though the area of sky was substantially smaller."165 We verified that the lack of 3.5 jm data did not cause any systematic effects bv repeating the “cloud” analvsis without the 3.5 jan. data.," We verified that the lack of 3.5 $\mu$ m data did not cause any systematic effects by repeating the “cloud"" analysis without the 3.5 $\mu$ m data."166" Figure 4. shows plots of dereddened A, (Iux as a Function of estimated temperature for", Figure \ref{fig4} shows plots of dereddened $K_s$ flux as a function of estimated temperature for167rotation of the secondary. spreacing the heated atmosphere into a nonspherical shape (tezu-drop mocel).,rotation of the secondary spreading the heated atmosphere into a nonspherical shape (tear-drop model).168 Xn eclipse can be ruled. out because the modulation amplitude would. be larger in time as observed [or some other novae (e.g... VS3S Ler: Leibowitz et al.," An eclipse can be ruled out because the modulation amplitude would be larger in time as observed for some other novae (e.g., V838 Her: Leibowitz et al."169 1992. V1494 Acl: Ixato et al.," 1992, V1494 Aql: Kato et al."170 2004)., 2004).171 A recent search for. variations/periodicities in the light. curve of faint CVs (including old novae) reveals that irracldiation vields larger amplitude for modulations (Woudt & Warner 2003a.b) as detected in our study.," A recent search for variations/periodicities in the light curve of faint CVs (including old novae) reveals that irradiation yields larger amplitude for modulations (Woudt $\&$ Warner 2003a,b) as detected in our study."172 After a nova explosion. the hot WDs are candidates or heating their cooler companion.," After a nova explosion, the hot WDs are candidates for heating their cooler companion."173 Some classical nova systems were recovered to show this irradiation elfect. Like: (1) V1500 Cve (N νο 1975) which showed an unperturbed emperature of 3000 Ix for the secondary and SOOO WK for the 10ated side (Schmidt et al., Some classical nova systems were recovered to show this irradiation effect like: (1) V1500 Cyg (N Cyg 1975) which showed an unperturbed temperature of 3000 K for the secondary and 8000 K for the heated side (Schmidt et al.174 1995: Somers & Navlor 1999): (2) DN Gem (N Gem 1912) (Better. Leibowitz & Navlor 1999): (3) WY See (N See 1783) which indicated that the accretion uminosity [rom the disk could even be responsible for the irradiation of the secondary (Somers. Büngwald & Navlor 1997).," 1995; Somers $\&$ Naylor 1999); (2) DN Gem (N Gem 1912) (Retter, Leibowitz $\&$ Naylor 1999); (3) WY Sge (N Sge 1783) which indicated that the accretion luminosity from the disk could even be responsible for the irradiation of the secondary (Somers, Ringwald $\&$ Naylor 1997)."175 Hlowever. only one of such svstems resemble V2275 Cve closely: orbital modulations due to aspect. variations of the heated face of the secondary. was detected for Nova νο 1992 (V1974 Cvg) at the outburst stage (about a vear and a half after outburst) by DeYoung & Schmidt. (1994) before the WD cooled to a point where it was no longer a strong X-rav source.," However, only one of such systems resemble V2275 Cyg closely: orbital modulations due to aspect variations of the heated face of the secondary was detected for Nova Cygni 1992 (V1974 Cyg) at the outburst stage (about a year and a half after outburst) by DeYoung $\&$ Schmidt (1994) before the WD cooled to a point where it was no longer a strong X-ray source."176" The orbital variations in. V1974 (νο were —0.1 in the J band and «0.05 in the VY band. when the H-burning had. just. turnec-oll (the WD. temperature was about 10"" Ix: Dalman et al.", The orbital variations in V1974 Cyg were $\sim$ 0.1 in the $I$ band and $<$ 0.05 in the $V$ band when the H-burning had just turned-off (the WD temperature was about $\times$ $^5$ K; Balman et al.177 1998)., 1998).178 V1974 Cvg was discovered: as a Super Soft. X-ray source (SSS) while burning the hydrogen over its surface (Balman ct al., V1974 Cyg was discovered as a Super Soft X-ray source (SSS) while burning the hydrogen over its surface (Balman et al.179 1998 and references therein) consistent with the facet that most novae are expected to be a SSS at a certain point. during their outburst stage (see Ixrautter 2002 for a review)., 1998 and references therein) consistent with the fact that most novae are expected to be a SSS at a certain point during their outburst stage (see Krautter 2002 for a review).180 A hot WD at a temperature above 10 Ix (Le.. emits mostly in the soft N-ray wavelengths) with a radiative wind can be the source of an ionization front irraciating the secondary star.," A hot WD at a temperature above $\times$ $^5$ K (i.e., emits mostly in the soft X-ray wavelengths) with a radiative wind can be the source of an ionization front irradiating the secondary star."181 Therefore. we suggest that V2275 (νο was also a SSS during 2002-2003. and the radiative winds/ionization [ront of à SSS reaching out well into the piotosphere of the secondary. can explain the observations of V2275 Cvg in 2002.," Therefore, we suggest that V2275 Cyg was also a SSS during 2002-2003, and the radiative winds/ionization front of a SSS reaching out well into the photosphere of the secondary, can explain the observations of V2275 Cyg in 2002."182 The decrease of 50% in the moulation depth. from. 2002 to 2003 is another indication of the changing conclitions in the ionization front., The decrease of $\%$ in the modulation depth from 2002 to 2003 is another indication of the changing conditions in the ionization front.183" The strong tird harmonic of P, detected in 2003 could support the exisence of several hot zones over he total surface of the secondarv along with the significantly vealed inner face resulting in t1e higher harmonics becoming »ominent.", The strong third harmonic of $_1$ detected in 2003 could support the existence of several hot zones over the total surface of the secondary along with the significantly heated inner face resulting in the higher harmonics becoming prominent.184 We also detected another periodicity. D220.017079(17) d in the light. curve of 2003., We also detected another periodicity $_2$ =0.017079(17) d in the light curve of 2003.1852 We suggest that this is a ughly coherent QPO from tlre system., We suggest that this is a highly coherent QPO from the system.186 The power of the signal varies on different nights (independent. of length of he observation togethere with the small changes of the »eriodicitv which diller accorcling to the color (νο. filter)," The power of the signal varies on different nights (independent of length of the observation together with the small changes of the periodicity which differ according to the color (i.e., filter)."187 Vhe characteristics of the oscillations revealed in 20039 does not strongly support a VVD-spin period as the origin., The characteristics of the oscillations revealed in 2003 does not strongly support a WD-spin period as the origin.188 The timescale and. characteristics of the QPOs (~1475 s) resemble Uiekering. or reprocessing from. blobs orbiting within the inner regions/magnetosphere of the accretion disk," The timescale and characteristics of the QPOs $\sim$ 1475 s) resemble flickering, or reprocessing from blobs orbiting within the inner regions/magnetosphere of the accretion disk"1890.1zEO--IoO.5kms LI. (Xeysony) = 1640241.5kins band (Nei) = -O14L1405kms ,"$0.1 \pm1900.2\pm0.5\,\mbox{km\,s$ $}$ $\langle\Delta191v_\mathrm{(890)}\rangle$ = $1.6 \pm1920.2\pm1.5\,\mbox{km\,s$ $}$, and $\langle\Delta193v_\mathrm{(910)}\rangle$ = $-0.1 \pm1941.1\pm0.5\,\mbox{km\,s$ $}$."195In comparing (he velocity shifts of the OL and water lines in the 300—822cm1 region (which has most measured values). we note that (he svstematic. instrumental shifts will be the same for both species.," In comparing the velocity shifts of the OH and water lines in the $800-822\cm1$ region (which has most measured values), we note that the systematic, instrumental shifts will be the same for both species."196 Thus. there might be a small red-shift of the IIO lines relative to the OII lines of 0.52:0.3kms.!.," Thus, there might be a small red-shift of the $_2$ O lines relative to the OH lines of $0.5\pm0.3\kms$."197 A velocity shift of this order is indeed expected between lines formed at different depths in the photosphere in a star such as Arcturus. see for example (2002)..," A velocity shift of this order is indeed expected between lines formed at different depths in the photosphere in a star such as Arcturus, see for example \cite{allende}."198 The FWIIM of the water-vapor lines is measured to be 1. ," The FWHM of the water-vapor lines is measured to be $\langle\mathrm{FWHM}\rangle= 8.2 \pm 0.3\,\mbox{km\,s$ $}$."199Correcting for the intrinsic line width. we find (FWIIM)=7.340.4kans which is slightly lower than the line widths found for the OIL lines.," Correcting for the intrinsic line width, we find $\langle\mathrm{FWHM}\rangle= 7.3 \pm 0.4\,\mbox{km\,s$ $}$, which is slightly lower than the line widths found for the OH lines."200 Thus. the water-vapor lines.by their line width aud velocity. appear to be formed in (the photosphere Gustafssonetal.(1975). Plezetal.(1992)..," Thus, the water-vapor lines,by their line width and velocity, appear to be formed in the photosphere \citet{marcs:75} \citet{plez:92}, \citet{jorg:92}, \citet{BDP:93}."201 Jorgensenοἱal.(1992).. Edvardssonetal.(1993). (Pisku," \citep{VALD} \citet{griffin} \citet{peterson} \citet{leen_aBoo} \citet{leen_aBoo} \citet{leen_aBoo}. \citep{arcturusatlas,arcturusatlas_II}, \ref{fig4}."202novetal. , \ref{fig4} 203"magnitude. and on colour in the ""cool blackbody. regime where the colours approach the bulk of the main sequence at 2zz TOmmin.","magnitude, and on colour in the `cool' blackbody regime where the colours approach the bulk of the main sequence at $P\approx 70$ min."204 We construct a two-dimensional grid. [or the completeness €! in intervals of 0.5 magnitude in g and 5 minutes in orbital period. P? from which we againget Coat arbitrary 2 ancl g via bilinear interpolation., We construct a two-dimensional grid for the completeness $C$ in intervals of 0.5 magnitude in $g$ and 5 minutes in orbital period $P$ from which we againget $C$ at arbitrary $P$ and $g$ via bilinear interpolation.205 Since the SDSS has five colour bands. vgrit. the completeness of spectroscopic follow-up is not uniquely defined for each point in (ag.g—r) space. but may in principle depend on the ὃς colours.," Since the SDSS has five colour bands, $ugriz$, the completeness of spectroscopic follow-up is not uniquely defined for each point in $(u-g,g-r)$ space, but may in principle depend on the $iz$ colours."206 In the hot blackbody regime where the AM CVn stars are. however. it is unlikely that the ἐς colours ave of much influence.," In the hot blackbody regime where the AM CVn stars are, however, it is unlikely that the $iz$ colours are of much influence."207 We verify this by determining the completeness as a function of rf anc? z for the objects in a strip along the modelled cooling track from about IXIx. which includes the 6 AM. CVn stars found in the SDSS.," We verify this by determining the completeness as a function of $r-i$ and $i-z$ for the objects in a strip along the modelled cooling track from about K, which includes the 6 AM CVn stars found in the SDSS."208 I turns out to be a very Llat distribution: in other words the completeness along the cooling track in (#αςor) is only weakly dependent on the (p7.72) colours of the corresponding objects.," It turns out to be a very flat distribution; in other words the completeness along the cooling track in $(u-g,g-r)$ is only weakly dependent on the $(r-i,i-z)$ colours of the corresponding objects."209 Finally. we need to determine a suitable value gins to delimit a well-defined. sample of AAL οVn stars.," Finally, we need to determine a suitable value $g_\mathrm{max}$ to delimit a well-defined sample of AM CVn stars."210 We choose Guns=21 for two reasons: first. the completeness of spectroscopic follow-up in the SDSS plummets between g=20.5 and g=21 (see also figure 3)). and second. up to this brightness limit we can still be confident. that our efficiency. [or identifving emission-lino AM CVn stars in the SDSS spectroscopic database is (nearly)10054.," We choose $g_\mathrm{max}=21$ for two reasons: first, the completeness of spectroscopic follow-up in the SDSS plummets between $g=20.5$ and $g=21$ (see also figure \ref{completeness_P}) ), and second, up to this brightness limit we can still be confident that our efficiency for identifying emission-line AM CVn stars in the SDSS spectroscopic database is (nearly)."211.. ALL six AM CVn stars identified in the spectroscopic database have g«21., All six AM CVn stars identified in the spectroscopic database have $g<21$.212 Table 1. shows the expected number of emission-line AAL CVn stars in the SDSS spectroscopic database based on the different population svnthesis models., Table \ref{densities} shows the expected number of emission-line AM CVn stars in the SDSS spectroscopic database based on the different population synthesis models.213 From this we obtain the observed? local space density. po by multiplving the modelled pt with MaoLINT reftransform)). where Noyce=6.," From this we obtain the `observed' local space density $\rho_0$ by multiplying the modelled $\rho'_0$ with $N_\mathrm{spec}/N'_\mathrm{spec}$ \\ref{transform}) ), where $N_\mathrm{spec}=6$."214 We see that all models predict more systems than are observed. except. for. the pessimistic model in which additionally there are no AM CVns from the Lle-star channel.," We see that all models predict more systems than are observed, except for the pessimistic model in which additionally there are no AM CVns from the He-star channel."215" Although the space densities in the cdillerent. models. vary by more than two orders of magnitude. the observed. space density based on these input populations varies only by a factor of 3. lom po=l310""ppe ."," Although the space densities in the different models vary by more than two orders of magnitude, the observed space density based on these input populations varies only by a factor of 3, from $\rho_0=1-3\times 10^{-6}$ $^{-3}$."216 As mentioned in section 2.2.. this is because the variation in the total number of systems produced. in the clilferent models is large whereas he variation in the orbital period distribution is quite small. and the latter is what causes a variation in the calibrated (observed) space density.," As mentioned in section \ref{recent}, this is because the variation in the total number of systems produced in the different models is large whereas the variation in the orbital period distribution is quite small, and the latter is what causes a variation in the calibrated (observed) space density."217 The uncertainties in the values in table 1 are dominated by the Poisson statistics of the observed sample (Nopee= 6) and the uncertainties in the parametrization of the temperature ancl absolute magnitude with orbital »eriod. rol leand5)) LE, The uncertainties in the values in table \ref{densities} are dominated by the Poisson statistics of the observed sample $N_\mathrm{spec}=6$ ) and the uncertainties in the parametrization of the temperature and absolute magnitude with orbital period \\ref{T_P} and \ref{Mg_P}) ).218 hesmeallsampleof6systemscontiribulesanintrinsicuncerlaint to the measured values in table 1.., The small sample of 6 systems contributes an intrinsic uncertainty of order $6^{-1/2}\approx 40\%$ to the measured values in table \ref{densities}.219 We shift. the xwametrization of absolute magnitude with orbital period ret Megp)Dupanddouwnbyü.3megniludesasanestimateduncerlaintig, We shift the parametrization of absolute magnitude with orbital period \\ref{Mg_P}) ) up and down by 0.3 magnitudes as an estimated uncertainty; this yields a variation of in the observed space densities.220 thisgiclds and find a variation of in the resulting space densities., Similarly we vary the effective temperature as a function of orbital period with $\pm 20\%$ and find a variation of in the resulting space densities.221 Adding up all the numbers. we thus estimate a total uncertainty in the derived space densities that is elose to a factor of 2 for each of the model populations.," Adding up all the numbers, we thus estimate a total uncertainty in the derived space densities that is close to a factor of 2 for each of the model populations."222" Note that the pessimistic model from. Nelemansctal. (2001).. when calibrated. with the observed. systems. [rom the SD!ο, actually vields a space density than the optimistic mocoel."," Note that the pessimistic model from \citet{nelemans}, , when calibrated with the observed systems from the SDSS, actually yields a space density than the optimistic model."223 This is due to the fact that the pessimistic model is dominated by AM CVns from the Lle-star channel.," This is due to the fact that the pessimistic model is dominated by AM CVns from the He-star channel,"224but indicates that the Na line profiles may not be Lorentzian on wide scales.,but indicates that the Na line profiles may not be Lorentzian on wide scales.225 Instead they present narrow cores extending over a broader plateau., Instead they present narrow cores extending over a broader plateau.226 The observations presented here are not sensitive to absorption on these large spectral scales., The observations presented here are not sensitive to absorption on these large spectral scales.227 Recently. Redfield et al. (," Recently, Redfield et al. ("2282008) measured DD absorption in the transmission spectrum of the other known bright transiting hot Jupiter HD189733b. at a level of 0.06740.021% in a passband of12A.,"2008) measured D absorption in the transmission spectrum of the other known bright transiting hot Jupiter HD189733b, at a level of $\pm0.021$ in a passband of."229. Note that their in-transit data originate from short observations of eleven different transit events. but in total reach a similar SNR as the data presented in this paper.," Note that their in-transit data originate from short observations of eleven different transit events, but in total reach a similar SNR as the data presented in this paper."230 The detection of Redfield et al., The detection of Redfield et al.231 is about a factor of 3 higher than that measured for HD209458b., is about a factor of 3 higher than that measured for HD209458b.232" From their figure | we conclude that they have derived the strength of the DD feature by integrating INFi/F,, mstead of integrating INFi/Foy.", From their figure 1 we conclude that they have derived the strength of the D feature by integrating $\int_{\Delta \lambda}F_{in}/F_{out}$ instead of integrating $\int_{\Delta \lambda}F_{in}/\int_{\Delta \lambda}F_{out}$.233 This means that their result cannot be directly comparedIN to the results of HD209458b. since it puts much higher weights (210) on the pixels in the center of the stellar absorption lines where most planetary absorption is seen.," This means that their result cannot be directly compared to the results of HD209458b, since it puts much higher weights $>$ $\times$ ) on the pixels in the center of the stellar absorption lines where most planetary absorption is seen."234 The number of absorbed photons for a ~ planetary absorption at the stellar line center would be equal to the number of absorbed photons for a ~0.1% planetary absorption at the stellar continuum., The number of absorbed photons for a $\sim$ planetary absorption at the stellar line center would be equal to the number of absorbed photons for a $\sim$ planetary absorption at the stellar continuum.235 By multiplying the data points from their figure 1 by the stellar flux at each wavelength. we estimate that the measured DD absorption from HD189733b is only a factor ~2 above that measured for HD209458b.," By multiplying the data points from their figure 1 by the stellar flux at each wavelength, we estimate that the measured D absorption from HD189733b is only a factor $\sim$ 2 above that measured for HD209458b."236 This remaining difference however does not mean that the planets have a different Na atmosphere., This remaining difference however does not mean that the planets have a different Na atmosphere.237 Physically. these levels of absorption correspond to a variation in the apparent planetary radius of (~750 km) for HD209458b. and (~780 km) for HD189733b.," Physically, these levels of absorption correspond to a variation in the apparent planetary radius of $\sim$ 750 km) for HD209458b, and $\sim$ 780 km) for HD189733b."238 Hence the results for both planets are actually very similar., Hence the results for both planets are actually very similar.239 Remarkably. Redfield et al. (," Remarkably, Redfield et al. ("2402008) find à significant blueshift of their planetary absorption signal. of the order of ~38 km 7! (corresponding to ~0.75A)).,"2008) find a significant blueshift of their planetary absorption signal, of the order of $\sim$ 38 km $^{-1}$ (corresponding to $\sim$ )."241 No such shift of the planetary absorption ts present in the transmission spectrum of HD209458b., No such shift of the planetary absorption is present in the transmission spectrum of HD209458b.242 If this velocity shift is real. it is rather puzzling how it could be produced. since it is about an order of magnitude higher than the expected sound speed in the upper layer of the planet’s atmosphere (Brown 2001).," If this velocity shift is real, it is rather puzzling how it could be produced, since it is about an order of magnitude higher than the expected sound speed in the upper layer of the planet's atmosphere (Brown 2001)."243 We note that the data analysis of Redfield et al., We note that the data analysis of Redfield et al.244" is affected by the intrinsic variations in stellar line shapes due to the Rossiter-MeLaughlin effect. due to the use of the fy,Fin/Foy integral. which does not have to integrate down to zero. even if there is no additional planetary absorption. (see section 2)."," is affected by the intrinsic variations in stellar line shapes due to the Rossiter-McLaughlin effect, due to the use of the $\int_{\Delta \lambda}F_{in}/F_{out}$ integral, which does not have to integrate down to zero, even if there is no additional planetary absorption (see section 2)."245 If the spectra are not evenly distributed over the transit. this can also lead to spurious velocity offsets. although it is difficult to see how these could become larger than the vsini of the star.," If the spectra are not evenly distributed over the transit, this can also lead to spurious velocity offsets, although it is difficult to see how these could become larger than the $v$ $i$ of the star."246 We present the first ground-based detection of the NaDD absorption feature in. the transmission. spectrum of the extrasolar planet HD209458b. fully consistent with the HST measurements by Charbonneau et al. (," We present the first ground-based detection of the D absorption feature in the transmission spectrum of the extrasolar planet HD209458b, fully consistent with the HST measurements by Charbonneau et al. ("2472002).,2002).248 The absorption is) measured. at. à level of 0.13540.017%.. 0.07040.011%.. and 0.0562z0.0076c in three passbands of 2x0.75AÀ.. 2x1.5À.. and 2x3.0À wide. indicatingthattheabsorptionispartiallvresolvedoutinthetwosmalles ," The absorption is measured at a level of $\pm$, $\pm$, and $\pm$ in three passbands of $\times$, $\times$, and $\times$ $ $ wide, indicating that the absorption is partially resolved out in the two smallest bands."249linearitvxoftheCCD.," Crucial in our analysis was the removal of an empirical correlation between line depth and the continuum count level in the spectra, likely to be caused by non-linearity of the CCD."250Weshowthatduetoeitherchangesinthespectralresoltti MeLaughlineffect.itiscrucialtointegratetheatinosphericabsorptionovet passbandtoavoids puriouse ffects.," We show that due to either changes in the spectral resolution, or intrinsic changes in the stellar line profiles during the transit due to the Rossiter-McLaughlin effect, it is crucial to integrate the atmospheric absorption over a wide-enough passband to avoid spurious effects."251"of 1+z=1.26, as assumed by Heger et al. (","of $1+z=1.26$, as assumed by Heger et al. ("2522007).,2007).253" We see that while the redshift is sensitive to the details of the fitting, the normalization Fops/Fmodel is well-determined."," We see that while the redshift is sensitive to the details of the fitting, the normalization $F_{\rm obs}/F_{\rm model}$ is well-determined."254" Therefore, here we use the normalization, but leave fits to the shape of the entire lightcurve to future work when a greater number of simulations are available."," Therefore, here we use the normalization, but leave fits to the shape of the entire lightcurve to future work when a greater number of simulations are available."255 A second constraint comes from spectral fitting., A second constraint comes from spectral fitting.256" Fitting the Observed burst spectrum with a blackbody gives the total flux F5, color temperature Τζος. and the blackbody normalization The color correction factor f.=T./Ter takes into account the hardening of the burst spectrum compared to a blackbody at the same effective temperature Tz."," Fitting the observed burst spectrum with a blackbody gives the total flux $F_{\infty}$ , color temperature $T_{c,\infty}$, and the blackbody normalization The color correction factor $f_c=T_c/T_{\rm eff}$ takes into account the hardening of the burst spectrum compared to a blackbody at the same effective temperature $T_{\rm eff}$."257" We plot K as a function of time in 2 for two average burst profiles, for recurrence times Figure5.74 and 4.07hr respectively."," We plot $K$ as a function of time in Figure \ref{fig:Knorm} for two average burst profiles, for recurrence times $5.74$ and $4.07\ {\rm hr}$ respectively."258" Following the burst rise, which lasts for approximately 5 seconds, the normalization levels off until ~60 seconds into the burst, when the normalization drops dramatically over 100 seconds to only about of its original value."," Following the burst rise, which lasts for approximately 5 seconds, the normalization levels off until $\approx 60$ seconds into the burst, when the normalization drops dramatically over 100 seconds to only about of its original value."259" We discuss the variation of K in the tail, and the difference in K for the two different recurrence times in the next section."," We discuss the variation of $K$ in the tail, and the difference in $K$ for the two different recurrence times in the next section."260" For our purposes here we find the mean value of K forthe frecur=4.07 hr profile during the period following the peak where it is constant, giving K=1103-2(km/10kpc)’."," For our purposes here we find the mean value of $K$ forthe $t_{\rm recur}=4.07$ hr profile during the period following the peak where it is constant, giving $K=110\pm 2\ ({\rm km}/10\ {\rm kpc})^2$."261" If we take into account the deadtime correction near the burst peak (5: 6%), the value we find is consistent with the more detailed analysis ofblackbody normalization in these bursts carried out by Galloway Lampe (2011)."," If we take into account the deadtime correction near the burst peak $\approx6\%$ ), the value we find is consistent with the more detailed analysis ofblackbody normalization in these bursts carried out by Galloway Lampe (2011)."262" Dividing equations (2)) and (4)), R/d and ἐν drop out, giving We show model calculations of f. from Suleimanov et al. ("," Dividing equations \ref{eq:Fratio}) ) and \ref{eq:K}) ), $R/d$ and $\xi_b$ drop out, giving We show model calculations of $f_c$ from Suleimanov et al. ("2632011b) in the next section which typically have f;2:1.4— 1.5 during the phase where K is relatively constant.,2011b) in the next section which typically have $f_c\approx 1.4$ $1.5$ during the phase where $K$ is relatively constant.264" For fc=1.4,1.5 we get 1+z= 1.19,1.28."," For $f_c=1.4,1.5$ we get $1+z=1.19,1.28$ ."265" Note that as well as being independent of d and £j, the value of 1+z determined in this is not very sensitive to the values of K and Fyodei/ way(proportional to the 1/4 power of each)."," Note that as well as being independent of $d$ and $\xi_b$, the value of $1+z$ determined in this way is not very sensitive to the values of $K$ and $F_{\rm model}/F_{\rm obs}$ (proportional to the 1/4 power of each)."266" For example, ουςintroducing an uncertainty in Finodei/Fors of +10%gives a prefactor in equation (9)) of 1.173:0.03 or 14-z21.28+0.03 "," For example, introducing an uncertainty in $F_{\rm model}/F_{\rm obs}$ of $\pm10$gives a prefactor in equation \ref{eq:z}) ) of $1.17\pm 0.03$ or $1+z=1.28\pm 0.03\ (f_c/1.5)$."267"There is one more (f./1.5).constraint which comes from the agreement between the measured and model recurrence times, which effectively measures the local mass accretion rate m onto the star."," There is one more constraint which comes from the agreement between the measured and model recurrence times, which effectively measures the local mass accretion rate $\dot m$ onto the star."268 We define m to be the rest mass accretion rate at the stellar surface., We define $\dot m$ to be the rest mass accretion rate at the stellar surface.269" Then the accretion flux as observed at infinity is Dividing equations (2)) and (7)) gives the observed quantity a direct measure of redshift, independent of distance, but dependent on the anisotropy parameter ratio €,/€,."," Then the accretion flux as observed at infinity is Dividing equations \ref{eq:Fratio}) ) and \ref{eq:FX}) ) gives the observed quantity a direct measure of redshift, independent of distance, but dependent on the anisotropy parameter ratio $\xi_p/\xi_b$."270 The accretion rate in model A3 of Heger et al. (, The accretion rate in model A3 of Heger et al. (271"2007) was m=7980gcm?s!, and the measured persistent flux in 2000 was Fy=2.91+0.03x10?ergcm?s“, givingAn alternative way to derive this result is to match the theoretical o value, the ratio of persistent fluence between bursts to burst fluence, to the observed value.","2007) was $\dot m=7980\ {\rm g\ cm^{-2}\ s^{-1}}$, and the measured persistent flux in 2000 was $F_X=2.91\pm0.03\times 10^{-9}\ {\rm erg\ cm^{-2}\ s^{-1}}$, givingAn alternative way to derive this result is to match the theoretical $\alpha$ value, the ratio of persistent fluence between bursts to burst fluence, to the observed value."272 The models of Heger et al. (, The models of Heger et al. (273"2007) with recurrence time of 4 hours have a theoretical value Omodel=AM-55(&»/ £5), where Emc is the burstC Zmodet/Epurst(Eb/€p)energy, AM the ignition mass, and a redshift Zmode}=0.26.","2007) with recurrence time of 4 hours have a theoretical value $\alpha_{\rm model} = \Delta M c^2z_{\rm model}/E_{\rm burst}(\xi_b/\xi_p)=55\ (\xi_b/\xi_p)$ , where $E_{\rm nuc}$ is the burst energy, $\Delta M$ the ignition mass, and a redshift $z_{\rm model}=0.26$."274 The observed o at the same recurrence time is αους©37 (Fig., The observed $\alpha$ at the same recurrence time is $\alpha_{\rm obs}\approx 37$ (Fig.275 2 of Heger et al., 2 of Heger et al.276" 2007), giving ζ-Zmodel(obs/=0.17(€)/€5), in agreement with the value in equation Amodel)(9))."," 2007), giving $z=z_{\rm model}(\alpha_{\rm obs}/\alpha_{\rm model})=0.17 (\xi_p/\xi_b)$, in agreement with the value in equation \ref{eq:z}) )."277" If the anisotropy parameters were known, equations (9)), (2)) and (4)) uniquely determine the three quantities 1+z, f; and "," If the anisotropy parameters were known, equations \ref{eq:z}) ), \ref{eq:Fratio}) ) and \ref{eq:K}) ) uniquely determine the three quantities $1+z$, $f_c$ and $R/d$."278"However, as noted in $2, the anisotropy are not R/d.well-constrained."," However, as noted in 2, the anisotropy parameters are not well-constrained."279" In particular, equation (9))parameters for the redshift is not constraining once the large uncertainty in €,/& is taken into account."," In particular, equation \ref{eq:z}) ) for the redshift is not constraining once the large uncertainty in $\xi_p/\xi_b$ is taken into account."280" The main result of this section is therefore the relation between 1+z and f. in equation (5)), since it is independent of d and £;."," The main result of this section is therefore the relation between $1+z$ and $f_c$ in equation \ref{eq:fczcorr}) ), since it is independent of $d$ and $\xi_b$."281" In the next section, we constrain the Eddington flux by fiting the burst cooling tracks to spectral models."," In the next section, we constrain the Eddington flux by fitting the burst cooling tracks to spectral models."282" We can use the model lightcurve to say something about the expected value of Fgaa, the observed flux which corresponds to the Eddington flux at the surface of the star."," We can use the model lightcurve to say something about the expected value of $F_{\rm Edd}$, the observed flux which corresponds to the Eddington flux at the surface of the star."283" In the model theEddington flux locally is Fea—cg/&=0.882x102g14 erg cm? s! for X= 0.7, giving Frodel,pk/FmodelEdd- 1.46/g14."," In the model theEddington flux locally is $F_{\rm Edd}=cg/\kappa=0.882\times 10^{25} g_{14}$ erg $^{-2}$ $^{-1}$ for $X=0.7$ , giving $F_{\rm model,pk}/F_{\rm model,Edd}=1.46/g_{14}$ ."284" Scaling the observed peak flux, the Eddington flux as observed atinfinity should be 1.95x108g,4(1.7/1+X) sl, or Fig/(1075 s!)=1.95,3.89,7.79 for log;o2= 14.0,14.3,14.6."," Scaling the observed peak flux, the Eddington flux as observed atinfinity should be $1.95\times 10^{-8} g_{14}(1.7/1+X)$ , or $F_{\rm Edd}/(10^{-8}$ $)\,=1.95,3.89,7.79$ for $\log_{10} g=14.0,14.3,14.6$ ."285 We now turn to fitting theoretical calculations of the color- factor f. to the data., We now turn to fitting theoretical calculations of the color-correction factor $f_c$ to the data.286" First we describe the fitting procedure and results ($5.1) and then the constraints on neutron star parameters, in particularan upper limit on Ry "," First we describe the fitting procedure and results 5.1) and then the constraints on neutron star parameters, in particularan upper limit on $R_\infty$ "287and cach sample has a cillerent uncertainty.,and each sample has a different uncertainty.288 In section d we describe our procedure for estimating the covariance matrix of the residuals by spectrum. analysis and. demonstrate it on two pulsars with different tvpes of timing noise., In section 4 we describe our procedure for estimating the covariance matrix of the residuals by spectrum analysis and demonstrate it on two pulsars with different types of timing noise.289 In section 5 we show that the Cholesky method is consistently superior to the WLS. polvnomial. and. Fourier. methods. using simulations to make the comparisons more precise.," In section 5 we show that the Cholesky method is consistently superior to the WLS, polynomial, and Fourier methods, using simulations to make the comparisons more precise."290 Finally in section 6 we use simulations to establish the sensitivity of the Cholesky method to errors in estimating the covariance matrix., Finally in section 6 we use simulations to establish the sensitivity of the Cholesky method to errors in estimating the covariance matrix.291 “Phe tools that we discuss have been incorporated into the timing analysis package and are available for the community., The tools that we discuss have been incorporated into the timing analysis package and are available for the community.292 A step-by-step tutorial on using the Cholesky method is also available on the web site., A step-by-step tutorial on using the Cholesky method is also available on the web site.293 The least-squares formalism separates the observations into a deterministic component. the timing mocel. ancl a (zero mean) random component.," The least-squares formalism separates the observations into a deterministic component, the timing model, and a (zero mean) random component."294" The random component is referred. to in the statistical literature as the ""error"". and in the pulsar community as “post-Lit timing residuals.", The random component is referred to in the statistical literature as the “error” and in the pulsar community as “post-fit timing residuals”.295 The least-squares is linear if the timing model is a linear function of the parameters which must be estimated., The least-squares is linear if the timing model is a linear function of the parameters which must be estimated.296 Phe formalism can be compactly described using matrix algebra as follows., The formalism can be compactly described using matrix algebra as follows.297 Llere » timing residuals are modelled using a system of linear equations in me«cm parameters. where £ is an n-point column vector representing the pre-it timing residuals. Mois an àoom matrix describing the pulsar timing model. P is an m-point column vector containing the fitted parameters and Éisan n-point column vector representing the post-fit. residuals.," Here $n$ timing residuals are modelled using a system of linear equations in $m < n$ parameters, where $\vec{R}$ is an $n$ -point column vector representing the pre-fit timing residuals, ${\bf M}$ is an $n \times m$ matrix describing the pulsar timing model, $\vec{P}$ is an $m$ -point column vector containing the fitted parameters and $\vec{E}$ is an $n$ -point column vector representing the post-fit residuals."298 Lf the post-fit residuals are independent with equal variance (067) for all observations (homoscedastic). then one minimises the squared. error.," If the post-fit residuals are independent with equal variance $\sigma^2$ ) for all observations (homoscedastic), then one minimises the squared error."299 In vector notation the squared error is and the solution. which is called ordinary least. squares (OLS). ts If the residuals have a gaussian clistribution this is also “maximum likelihood. solution”.," In vector notation the squared error is and the solution, which is called ordinary least squares (OLS), is If the residuals have a gaussian distribution this is also “maximum likelihood solution”."300 The covariance matrix of the parameters is given by Ilere the angle brackets denote a statistical expectation., The covariance matrix of the parameters is given by Here the angle brackets denote a statistical expectation.301 The normalised squared error EUEIG isa chi-squared random variable with »om degrees of freedom., The normalised squared error $\vec{E}^T \vec{E} / \sigma^2$ is a chi-squared random variable with $n-m$ degrees of freedom.302" Lt is often referred to as 47 and used as part ofa ""goodness-o[-lit test."""," It is often referred to as $\chi^2$ and used as part of a “goodness-of-fit test."""303 ]t is the normal practice to scale cortD.) bv ATf(rm) at least when X7c(nm)., It is the normal practice to scale $cov(\vec{P}_{\rm est})$ by $\chi^2/(n-m)$ at least when $\chi^2 > (n-m)$.304 lt us«(nm) there may be a problem., If $\chi^2 < (n-m)$ there may be a problem.305" Either the data may have been ""overfit or a? may have been underestimated.", Either the data may have been “overfit” or $\sigma^2$ may have been underestimated.306H ΗΕ 07 Do.is unknown a priori.H then one estimates it using If the residuals are white. but cach To has a different variance (heteroscedastic). then one minimises the weighted squared error (the WLS solution).," If $\sigma^2$ is unknown a priori, then one estimates it using If the residuals are white, but each ToA has a different variance (heteroscedastic), then one minimises the weighted squared error (the WLS solution)."307 Fhis approach is widely used in pulsar timing analysis., This approach is widely used in pulsar timing analysis.308 For white residuals. the covariance matrix of the residuals is V. à diagonal matrix with the variance of the samples on the main diagonal.," For white residuals, the covariance matrix of the residuals is ${\bf V}$ a diagonal matrix with the variance of the samples on the main diagonal."309" In this form the weighted. squared: error is EUNVE and the solution is The same result can be obtained by normalizing both the data and the model bv multiplving each bv Wo"".", In this form the weighted squared error is $\vec{E}^T {\bf V}^{-1} \vec{E}$ and the solution is The same result can be obtained by normalizing both the data and the model by multiplying each by ${\bf V}^{-0.5}$.310" That is Ry=VUf and IN—V""M.", That is $\vec{R_N} = {\bf V}^{-0.5} \vec{R}$ and ${\bf M_N} = {\bf V}^{-0.5}{\bf M}$.311 Then the errors will all have unit variance and the solution is Thus the WLS solution becomes an OLS problem in the normalized variables., Then the errors will all have unit variance and the solution is Thus the WLS solution becomes an OLS problem in the normalized variables.312 If {he normalization is correct the münimum squared error EN will have a us clistribution with nm. degrees of freedom., If the normalization is correct the minimum squared error $\vec{E_N}^T \vec{E_N}$ will have a $\chi^2$ distribution with $n-m$ degrees of freedom.313 The covariance matrix of the parameters 1s (C(n.om))(MniMn)5., The covariance matrix of the parameters is $(\chi^2/(n-m))({\bf M_N}^T{\bf M_N})^{-1}$.314 H must be scaled by the measured X7 to allow for errors in the normalization., It must be scaled by the measured $\chi^2$ to allow for errors in the normalization.315 The OLS and. WLS solutions have been known since the work of Gauss and Legendre at the beginning of the 19th century., The OLS and WLS solutions have been known since the work of Gauss and Legendre at the beginning of the 19th century.316 Phe WLS analysis can be extended to the case of correlated residuals if the covariance matrix of the residuals C=ET» js known., The WLS analysis can be extended to the case of correlated residuals if the covariance matrix of the residuals ${\bf C} = \langle \vec{E} \vec{E}^T\rangle$ is known.317 In this case one minimises E'CE and the solution (Aitken. is often referred to as generalised least squares (GLS).," In this case one minimises $\vec{E}^T {\bf C}^{-1}\vec{E}$ and the solution (Aitken, is often referred to as generalised least squares (GLS)."318 The GLS solution was derived. and is best. described. as a normalizing and whitening process.," The GLS solution was derived, and is best described, as a normalizing and whitening process."319 C is Llerniitian »ositive semi-cdelinite and so can be factored into C.=UU! using a Cholesky lower triangle [actorisation., ${\bf C}$ is Hermitian positive semi-definite and so can be factored into ${\bf C} = {\bf U}{\bf U}^T$ using a Cholesky lower triangle factorisation.320 The matrix U|! can be used as a normalizing and. whitening ransformation ( is not unique. the Alahalanobis ransformation can also be used).," The matrix ${\bf U^{-1}}$ can be used as a normalizing and whitening transformation (but is not unique, the Mahalanobis transformation can also be used)."321 Defining E.—-U!fk Ro=UiH and M.=UIM. we find that cov(E)= I the identity matrix.," Defining $\vec{E}_{\rm w} = {\bf U}^{-1}\vec{E}$, $\vec{R}_{\rm w} = {\bf U}^{-1}\vec{R}$ and ${\bf M}_{\rm w} = {\bf U}^{-1}{\bf M}$, we find that $\rm{cov}(\vec{E}_{\rm w}) = {\bf I}$ , the identity matrix."322 Phe transformed. resicuals £y are herefore both white anc normalized to unit variance., The transformed residuals $\vec{E}_{\rm w}$ are therefore both white and normalized to unit variance.323 The GLS solution is now an OLS problem in the transformed variables. and Equation (8) can be rewritten as Again. iflp the normalization. is. correct x7>=Leviousον is à X73 random variable with om degrees of freedom and the covariance matrix of the parameters is (x/(nm))(MeiMe) +.," The GLS solution is now an OLS problem in the transformed variables, and Equation (8) can be rewritten as Again if the normalization is correct $\chi^2 = \vec{E_{\rm w}}^T \vec{E_{\rm w}}$ is a $\chi^2$ random variable with $n-m$ degrees of freedom and the covariance matrix of the parameters is $(\chi^2/(n-m))({\bf M_{\rm w}}^T{\bf M_{\rm w}})^{-1}$ ."324 In summary. alb linear least-squares problems can »* reduced. {ο ordinary least-squares by a suitable ransformation.," In summary, all linear least-squares problems can be reduced to ordinary least-squares by a suitable transformation."325 However. to find this transformation we must know the covariance matrix of the residuals at. least within a constant multiplier.," However, to find this transformation we must know the covariance matrix of the residuals at least within a constant multiplier."326 We will defer until section 4 he discussion of how to estimate the covariance matrix [rom he observations., We will defer until section 4 the discussion of how to estimate the covariance matrix from the observations.327 Ehe least squares solution. when properly ransformed.. provides minimum. variance. linear unbiased estimators of the model parameters and their uncertainties.," The least squares solution, when properly transformed, provides minimum variance, linear unbiased estimators of the model parameters and their uncertainties."328 lt should. be noted that inverting matrices of theform (MM) directly is not computationally cllicient and other, It should be noted that inverting matrices of theform $({\bf M}^T {\bf M})$ directly is not computationally efficient and other32931933|503 is the most complex aresec-scale gravitational ens system known and the most noteworthy λα discovered. in the Cosmic Lens Al-Sky Survey (CLASS: Browne et al.,B1933+503 is the most complex arcsec-scale gravitational lens system known and the most noteworthy system discovered in the Cosmic Lens All-Sky Survey (CLASS; Browne et al.330 1998). a survey of approximately 15.000 Llat-spectrum radio sources observed with the VLA at S44 Gz with a resolution of 200 milliaresec (mas).," 1998), a survey of approximately 15,000 flat-spectrum radio sources observed with the VLA at 8.4 GHz with a resolution of 200 milliarcsec (mas)."331 Sykes ct al. (, Sykes et al. (3321998) report the discovery of this lens and. present VLA and ALERLIN maps that reveal up to ten components. our of which are compact and have [lat spectra while the pest are more extended: and have steep. spectra.,"1998) report the discovery of this lens and present VLA and MERLIN maps that reveal up to ten components, four of which are compact and have flat spectra while the rest are more extended and have steep spectra."333 The ten components are. believed to be the multiple images of a vackerouncl source that consists of a [lat-spectrum: core (quacruply imaged) and two compact lobes svmmoetrically situated on opposite sides of the core (one quadruply imaged and the other cloubly imaged)., The ten components are believed to be the multiple images of a background source that consists of a flat-spectrum core (quadruply imaged) and two compact lobes symmetrically situated on opposite sides of the core (one quadruply imaged and the other doubly imaged).334). A (ΣΙΛΕΡΟΣ image (f-band) of B1933|503 (Sykes ct al., A /WFPC2 image $I$ -band) of B1933+503 (Sykes et al.335 1998) shows a faint galaxy with a compact core (the lensing galaxy) but none of the images of the background object are detected., 1998) shows a faint galaxy with a compact core (the lensing galaxy) but none of the images of the background object are detected.336 Spectra taken with the Weck telescope have eiven a redshift for the lensing galaxy of 0.755 (Sykes et al., Spectra taken with the Keck telescope have given a redshift for the lensing galaxy of 0.755 (Sykes et al.337 1998)., 1998).338 Sub-num observations of B1933|503 (Chapman ct al., Sub-mm observations of B1933+503 (Chapman et al.339" 1998) pointed to the fact that the source ofthe lens system should be Iving above a redshift of 2 and that has been confirmed. recently by observations mace with the United Ixingdom LInfra-red ""Telescope (UINIICE) that have vielded a redshift of 2.62 for the background source (Norbury et al."," 1998) pointed to the fact that the source of the lens system should be lying above a redshift of 2 and that has been confirmed recently by observations made with the United Kingdom Infra-red Telescope (UKIRT) that have yielded a redshift of 2.62 for the background source (Norbury et al.,"340 in preparation)., in preparation).341ST NICMOS E160-band: observations (Marlow e al., NICMOS F160W-band observations (Marlow et al.342 1998) of D1933|508 have uncovered. the infra-rec counterparts to two of the four compact components., 1998) of B1933+503 have uncovered the infra-red counterparts to two of the four compact components.343 These same two Components were also detected in a VLBA Cllz map with a resolution of 6 mas., These same two components were also detected in a VLBA 1.7-GHz map with a resolution of 6 mas.344 Marlow et al., Marlow et al.345 sugecs that the. failure. to detect the other two. [lat-spectrum components in the infra-red. can be due to either. rapic variability on a time-scale less than the time delay or due to extinction in the interstellar medium. (ISM) of the lensing galaxy., suggest that the failure to detect the other two flat-spectrum components in the infra-red can be due to either rapid variability on a time-scale less than the time delay or due to extinction in the interstellar medium (ISM) of the lensing galaxy.346 The absence of these same two components in the radio could arise due to scatter-broadening of the images, The absence of these same two components in the radio could arise due to scatter-broadening of the images347Due to tle projection of Weywot’s orbit ou the sky. two equally satisfactory fits to the observations cau be fouucl.,"Due to the projection of Weywot's orbit on the sky, two equally satisfactory fits to the observations can be found."348 This degeueracy does not affect the system inass determination liowever. as both orbits |ave virtually identical periods aud semi-major axes.," This degeneracy does not affect the system mass determination however, as both orbits have virtually identical periods and semi-major axes."349 The best-fit orbits a'e preseutecd in Figure L. with parameters presented tn Table L.," The best-fit orbits are presented in Figure \ref{fig:orbit}, with parameters presented in Table \ref{tab:orbits}."350 The orbits have a period of 12.13820.005 days ancl a seini-major axis c£1.15 40.08x107 kin and imply that the Quaoar-Wevwot sysel nass ls 1.650.3x10? ke. or roughly that of Eris (Brown&Schaller2007)..," The orbits have a period of $12.438\pm0.005$ days and a semi-major axis of $1.45 \pm 0.08 \times 10^4$ km and imply that the Quaoar-Weywot system mass is $1.6\pm0.3 \times 10^{21}$ kg, or roughly that of Eris \citep{Brown2007b}."351 Quaoar's size lias been measured by two different methods., Quaoar's size has been measured by two different methods.352 Partially resolved inages of Quaoar from the Hubble Space Telescope suggest a diameter. D=1260c190kin 200 L).. while two tndepenuclent size determinatious from its thermal eimision observed by he Spizer telescope give diameters D=Stl207156 (Stausberryetal.οίJOS) auc D—908I>lan 2009).," Partially resolved images of Quaoar from the Hubble Space Telescope suggest a diameter, $D=1260\pm190 \mbox{ km}$ \citep{Brown2004b}, while two independent size determinations from its thermal emission observed by the Spitzer telescope give diameters $D=844_{-190}^{+207}$ \citep{Stansberry2008} and $D=908_{-118}^{+112} \mbox{ km}$ \citep{Brucker2009}."353". h the case of the HST measurement. the inferred size cepeids on Quaoar's unknown fueion aud depends roughly linearly ou he hal(-liel diameter of this function - the diaeer of an aperture wlich contaius half of the liglt reflected f'om Quaoar towards tle obse""ver (Brow1&TrujiΠο2001).."," In the case of the HST measurement, the inferred size depends on Quaoar's unknown limb-darkening function and depends roughly linearly on the half-light diameter of this function - the diameter of an aperture which contains half of the light reflected from Quaoar towards the observer \citep{Brown2004b}."354 At the time of the HST measurenent. litle was known about the surace properties of Ixuper belt ojects. and a Lambert sple'e was acloped for the limb darkeniug prolile. with uncertainies reflecting the lack of kuowledge of Qiaoa5 true limb darkeniug p‘ofile.," At the time of the HST measurement, little was known about the surface properties of Kuiper belt objects, and a Lambert sphere was adopted for the limb darkening profile, with uncertainties reflecting the lack of knowledge of Quaoar's true limb darkening profile."355 The uucertaluties in the HST measurement are cdomiuated by this uukuowu., The uncertainties in the HST measurement are dominated by this unknown.356 We now kiow that the surface of Quaoar appears ii any ways similar to those of the icy satellies of Uranus aud Neptuue., We now know that the surface of Quaoar appears in many ways similar to those of the icy satellites of Uranus and Neptune.357 Tvey exhibit similar ice-absorption features (C'‘uikshank&Brown1956:Schaller&Brown 2007).. have high albedos (Ixarkoschka2001:Brown&Trujillo2001).. aud have siuitlar optical colours.," They exhibit similar ice-absorption features \citep{Cruikshank1986,Schaller2007}, have high albedos \citep{Karkoschka2001,Brown2004b}, and have similar optical colours."358" Quaoa""s opposition surge. with slope 2(V)=0.16£0.03magdeg is also sinlar to that of the Uranian satellites. with slopes i the range (V)0.07—0.18magdeg (hark»chka2001:Rabilowilyetal.2007:Belskaya2005)."," Quaoar's opposition surge, with slope $\beta(V)=0.16\pm0.03 \mbox{ mag deg$ $}$ is also similar to that of the Uranian satellites, with slopes in the range $\beta(V)=0.07-0.18 \mbox{ mag deg$ $}$ \citep{Karkoschka2001, Rabinowitz2007,Belskaya2008}."359.. Adopting a Uraniau-satellite limb darkeningist profile ratlerthan a Laubert profile appears o be a better approach., Adopting a Uranian-satellite limb darkening profile ratherthan a Lambert profile appears to be a better approach.360 From the fits of the Hapse surface relleeauce model (Hapke2002) tothe icy satellite phase Functions 2001). we have calculaed the imb-darkeiing profiles o ‘the satellites aud found their hall-light cliamete ‘sto be betweet 0.834 (1hat of Triton) and 0.58d (that of Vimbriel). where d is the diameter oL the object in questior.," From the fits of the Hapke surface reflectance model \citep{Hapke2002} to the icy satellite phase functions \citep{Karkoschka2001}, we have calculated the limb-darkening profiles of the satellites and found their half-light diameters to be between $ 0.82 d$ (that of Triton) and $0.88 d$ (that of Umbriel), where $d$ is the diameter of the object in question."361 The acopted hall-ight diameter - that of a Lambert sphere - is 0.6d., The adopted half-light diameter - that of a Lambert sphere - is $0.6 d$.362 This suggests that the size eslinate o[ Quaoar iuerred [rom the HST data is ~105€ too aree., This suggests that the size estimate of Quaoar inferred from the HST data is $\sim 40\%$ too large.363 Adopting the average limb-carkering prolile of the satellites. the Hubble observatious sugges that Qua0nbs diameter is D=900 kin.," Adopting the average limb-darkening profile of the satellites, the Hubble observations suggest that Quaoar's diameter is $D=900$ km."364 While he icy satelites exhibit a wide diversity of surface properties. tley ouly exhibit a small rauge in balllieht diaueters. 0.82-0.38d. or of their mean value.," While the icy satellites exhibit a wide diversity of surface properties, they only exhibit a small range in half-light diameters, $0.82 \mbox{-} 0.88 d$, or of their mean value."365 Licleed. icy bodies throughout the Solar system for which stullicieut data are available - Euceladus. Το. Europa. Ganuyimece. Callisto. aud the Urauian aud Neptuniau satellites discussed here - span ouly a range (Verbisceretal.2005:Dominere&Verbiscer1997:Dominete 1998)..," Indeed, icy bodies throughout the Solar system for which sufficient data are available - Enceladus, Io, Europa, Ganymede, Callisto, and the Uranian and Neptunian satellites discussed here - span only a range \citep{Verbiscer2005, Domingue1997, Domingue1998}. ."366 The'efore.," Therefore,"367show that an S/N of 5 gives a detection probability of 95 per cent (see Fig. ,show that an S/N of 5 gives a detection probability of 95 per cent (see Fig. \ref{fig:deteff}) )368which we will use as our required value for confident detectionB» in the subsequent sections., which we will use as our required value for confident detection in the subsequent sections.369" Real data is generally non-stationary and may contain interference, so this idealised detection statistic may be slightly optimistic, but should be close to reality, given well understood and cleaned data."," Real data is generally non-stationary and may contain interference, so this idealised detection statistic may be slightly optimistic, but should be close to reality, given well understood and cleaned data."370 For aLIGO we assume two kkm interferometers based at the Hanford site and one 4kkm interferometer at the Livingston site all with equivalent sensitivity and operating at the designed value (LIGOScientificCollaboration|2009)., For aLIGO we assume two km interferometers based at the Hanford site and one km interferometer at the Livingston site all with equivalent sensitivity and operating at the designed value \citep{LSC:2009}.371. For AdvVirgo we use one kkm interferometer at its design sensitivity (see Fig. gi, For AdvVirgo we use one km interferometer at its design sensitivity (see Fig. \ref{fig:strains}) ).372, Fig.373"ves the angle averaged S/N for 1 year of observationsΠ)).Fig. with all these detectors (3 aLIGO and 1 AdvVirgo, or ALV from now on) and shows that potentially 58 pulsars could be observed with an S/N greater than 5 (best case orientation gives 74 with S/N above 5 and the worst case orientation gives 47 with S/N above 5)."," \ref{fig:AL_ET_SNRs} gives the angle averaged S/N for 1 year of observations with all these detectors (3 aLIGO and 1 AdvVirgo, or ALV from now on) and shows that potentially 58 pulsars could be observed with an S/N greater than 5 (best case orientation gives 74 with S/N above 5 and the worst case orientation gives 47 with S/N above 5)."374" Some similar, but unpublished work,has been presented by (2006)."," Some similar, but unpublished work,has been presented by \citet{Santostasi:2006}. ."375formula then the observed polarization can be well fitted.,formula then the observed polarization can be well fitted.376 The same model can explain the observed polarization [rom 2MAÀSS J2158-15 (L4). 2\TASS JOILI+18 (L4.5) and 2MASS 101110 CL:5) if their rotational velocities are about 45. 25. 25 KR respectively.," The same model can explain the observed polarization from 2MASS J2158-15 (L4), 2MASS J0141+18 (L4.5) and 2MASS J0144-07 (L5) if their rotational velocities are about 45, 25, 25 $^{-1}$ respectively."377 However. this model fails to fit the data [rom Ixelu 1. (L2.5) unless its actual rotational velocity is between 25 to 330 B," However, this model fails to fit the data from Kelu 1 (L2.5) unless its actual rotational velocity is between 25 to 30 $^{-1}$."378 Figure 6 presents the degree of polarization wilh the same model but with larger mean particle diameter., Figure 6 presents the degree of polarization with the same model but with larger mean particle diameter.379 It is found that the observed degree of polarization [rom 2MAÀSS 17074-43 (L0.5) can also be explained if its rotational velocity is 20 | but the atmosphere contains erains with mean diameter 3.0 som., It is found that the observed degree of polarization from 2MASS 1707+43 (L0.5) can also be explained if its rotational velocity is 20 $^{-1}$ but the atmosphere contains grains with mean diameter 3.0 $\mu m$.380 However. the mean grain size of objects with the same spectral tvpe should not differ much and therefore we predict the rotational velocity of this object is about 5-10 ! with mean particle diameter 1.1 ji as presented in figure 5.," However, the mean grain size of objects with the same spectral type should not differ much and therefore we predict the rotational velocity of this object is about 5-10 $^{-1}$ with mean particle diameter 1.4 $\mu m$ as presented in figure 5."381 Figure 6 shows that the observed polarization of Ixelu 1 (L2.5) can be explained if (he mean particle diameter is 3.0 jon., Figure 6 shows that the observed polarization of Kelu 1 (L2.5) can be explained if the mean particle diameter is 3.0 $\mu m$.382 However. it is worth mentioing here that the actual rotational velocity of L clwarls can not be determined from their projected rotational velocity unless the inclination angle is known.," However, it is worth mentioning here that the actual rotational velocity of L dwarfs can not be determined from their projected rotational velocity unless the inclination angle is known."383 Figure 6 shows that the mode with mean particle size 3.0 µη} and polviropic index n—1.5- ( non-reladivistic completely degenerate polvtropic distribution) can explain the observed polarization of 2MIASS JOL414+18 (L4.5) and 24MAÀSS JO144-07 (L5.0) if their rotational velocities ave the same of Ixelu 1 (60 1)., Figure 6 shows that the model with mean particle size 3.0 $\mu m$ and polytropic index n=1.5 ( non-relativistic completely degenerate polytropic distribution) can explain the observed polarization of 2MASS J0141+18 (L4.5) and 2MASS J0144-07 (L5.0) if their rotational velocities are the same of Kelu 1 (60 $^{-1}$ ).384 As mentioned earlier. the object 2ALASS J0036--1821 (L3.5) is observed in (ree different wavelength regions and the degree of polarization is found to decrease substantially with the increase in wavelength.," As mentioned earlier, the object 2MASS J0036+1821 (L3.5) is observed in three different wavelength regions and the degree of polarization is found to decrease substantially with the increase in wavelength."385 This trends strongly supports the presence of dust in the atmosphere ol L dwarls as it is very much unikelv (hat anv other mechanisms such as (he presence of magnetic fielcl can explain this., This trends strongly supports the presence of dust in the atmosphere of L dwarfs as it is very much unlikely that any other mechanisms such as the presence of magnetic field can explain this.386 Figure T presents the degree of polarization as a function ol wavelength for L3.5 object wit1 (he polviropie index n=1.5 and the rotational velocity v—15 |., Figure 7 presents the degree of polarization as a function of wavelength for L3.5 object with the polytropic index n=1.5 and the rotational velocity v=15 $^{-1}$.387 It is obvious [rom 11ο Observed data at three different. wavelengths that the atmosphere of 2\TASS J00364-1321 should have grains of sub-micron size., It is obvious from the observed data at three different wavelengths that the atmosphere of 2MASS J0036+1821 should have grains of sub-micron size.388 We find the best fit of the three observed data with the mean particle diameter dj —0.43 jun., We find the best fit of the three observed data with the mean particle diameter $d_0=$ 0.43 $\mu m$.389 Larger grain size would have made (he polarization to peak at longer wavelength., Larger grain size would have made the polarization to peak at longer wavelength.390 The degree of polarization increases wilh the decrease in the polviropic index because with »=1.0. the oblateness of the object is higher than that with »=1.5 for the same rotational velocity and surface gravitv.," The degree of polarization increases with the decrease in the polytropic index because with $n=1.0$, the oblateness of the object is higher than that with $n=1.5$ for the same rotational velocity and surface gravity."391 On the other hand Seneupta (2003) showed that the oblateness decreases with the increase in surface gravity vielding into less amount of polarization., On the other hand Sengupta (2003) showed that the oblateness decreases with the increase in surface gravity yielding into less amount of polarization.392 As mentioned before. we have considered only forsterite in our models as il is very common in the atinosphere of L (tvpe dwarls wilh solar metalicitv.," As mentioned before, we have considered only forsterite in our models as it is very common in the atmosphere of L type dwarfs with solar metalicity."393 This is because of large abundances of Mg. Si ancl O. However. eehlenite. enstatite etc.," This is because of large abundances of Mg, Si and O. However, gehlenite, enstatite etc."394 should also be present in, should also be present in395the GC extinetion law.,the GC extinction law.396 However. a major uncertainty in these extinction measurements is the intrinsic spectrum of the background stars. specilically (he amount of excess photospheric IR emission. which may be variable.," However, a major uncertainty in these extinction measurements is the intrinsic spectrum of the background stars, specifically the amount of excess photospheric IR emission, which may be variable."397 Near-IR (3. 8 jam) extinction derived from the measurements ol line ratios may therefore be more reliable (han those derived [rom stellar continua. an issue that can only be resolved by more observations of background sources with well understood stellar spectrum.," Near-IR (3 – 8 $\mu$ m) extinction derived from the measurements of line ratios may therefore be more reliable than those derived from stellar continua, an issue that can only be resolved by more observations of background sources with well understood stellar spectrum."398 Alter the initial submission of this paper for publication. Inclebetomw et al. (," After the initial submission of this paper for publication, Indebetouw et al. ("3992004) presented the 1.25 to 8.0 jm extinction derived from data obtained by (heSpitzer along the two £6 = 42 and 284 lines of sight in the Galactic plane.,2004) presented the 1.25 to 8.0 $\mu$ m extinction derived from data obtained by the along the two $\ell$ = $\arcdeg$ and $\arcdeg$ lines of sight in the Galactic plane.400 The two extinction laws were found to be consistent with the Lutz (1999) measurements towards the GC. strengthening the case for the universality of this law in our Galaxy.," The two extinction laws were found to be consistent with the Lutz (1999) measurements towards the GC, strengthening the case for the universality of this law in our Galaxy."401 Whether (he needles are uniformly or inhomogeneously distributed in the ISM. the upper limit to the total mass of needles in the Galaxy is about 3x 10 \L.. assuming an ISM mass of 5x10? AL. (Sodroskiet al.," Whether the needles are uniformly or inhomogeneously distributed in the ISM, the upper limit to the total mass of needles in the Galaxy is about $\times$ $^4$ $_{\odot}$, assuming an ISM mass of $\times$ $^9$ $_{\odot}$ (Sodroskiet al."402 1997)., 1997).403 The average lifetime of interstellar dust is about LOS vr (Dwek 1998. Jones 2001). requiring a needle production rate of 6x10.  M. vet.," The average lifetime of interstellar dust is about $\times$ $^{8}$ yr (Dwek 1998, Jones 2001), requiring a needle production rate of $\sim$ $\times$ $^{-4}$ $_{\odot}$ $^{-1}$."404" The SCUBA observations of Cas A suggest that about 7 M, of metallic needles formed in the SN ejecta.", The SCUBA observations of Cas A suggest that about $^{-3}$ $_{\odot}$ of metallic needles formed in the SN ejecta.405 IL the Cas A vield is typical. and if à comparable production rate takes also place in quiescent O-rich stellar outflows. then a Galactic SN rate of about 0.03 ! will be sufficient to account for the mass of ISM needles.," If the Cas A yield is typical, and if a comparable production rate takes also place in quiescent O-rich stellar outflows, then a Galactic SN rate of about 0.03 $^{-1}$ will be sufficient to account for the mass of ISM needles."406 It is interesting (o examine whether (he needles can provide any signilicant extinction (o cosmological sources., It is interesting to examine whether the needles can provide any significant extinction to cosmological sources.407" The optical depth to redshift z is given by: where o(r7) is the needles’ cross section [assumed to be flat in the m to vo/(1+z) frequency range]. n,(2)x(1+z)*ni is their number density in the intergalactic medium. αν is their mass absorption coelficient. p, 1s their present mass density. and fy,οfly is the Hubble radius."," The optical depth to redshift $z$ is given by: where $\sigma(\nu)$ is the needles' cross section [assumed to be flat in the $\nu_0$ to $\nu_0/(1+z)$ frequency range], $n_n(z) \propto (1+z)^3$ is their number density in the intergalactic medium, $\kappa_n$ is their mass absorption coefficient, $\rho_n$ is their present mass density, and $R_H\equiv c/H_0$ is the Hubble radius."408" The function E(z)=[C1+z)(Q,z1)2z(29z)Q4]!2. where O,, and O4 are. respectively. the matter density aud the the cosmological constant. normalized to (heir critical values."," The function $E(z) = [(1+z)^2(\Omega_m z+1) - z (2+z)\Omega_{\Lambda}]^{1/2}$, where $\Omega_m$ and $\Omega_{\Lambda}$ are, respectively, the matter density and the the cosmological constant, normalized to their critical values."409" Using standard ΛΟΡΝΤ cosmology with O,, = 0.27 and O4 = 0.73. the optical depth to a hypothetical source at redshift z = 2 is given bv 7=4.5&,p,Ry."," Using standard $\Lambda$ CDM cosmology with $\Omega_m$ = 0.27 and $\Omega_{\Lambda}$ = 0.73, the optical depth to a hypothetical source at redshift $z$ = 2 is given by $\tau = 4.5\ \kappa_n \rho_nR_H$."410 The dusi-to-gas nass ralioof needles in the Milky Way ISAT sets an upper limit on their abundance in the intergalactic medium., The dust-to-gas mass ratioof needles in the Milky Way ISM sets an upper limit on their abundance in the intergalactic medium.411" The barvonic mass density for Jf, = 70 km ! ! is 42x10 e . giving an intergalactic needle mass density of p, = 2.9x107 e ."," The baryonic mass density for $H_0$ = 70 km $^{-1}$ $^{-1}$ is $\times 10^{-31}$ g $^{-3}$, giving an intergalactic needle mass density of $\rho_n$ = $\times 10^{-36}$ g $^{-3}$ ."412" The Hubble radius 2, = 4290 Mpc. giving a mass column density of ~ 2x10* g 7 out to z = 2."," The Hubble radius $R_H$ = 4290 Mpc, giving a mass column density of $\sim$ $\times 10^{-7}$ g $^{-2}$ out to $z$ = 2."413 For a value of &(V) &10? em? !. the visual optical depth to that distance will be about," For a value of $\kappa$ (V) $\approx 10^5$ $^2$ $^{-1}$ , the visual optical depth to that distance will be about"414Ou the nights of February 1718 and 1819. we used the Acquisition Camera (AcqCam) ou CeminiSoutl to obtain fast V. band optical photometry (sec Table 1 for details).,"On the nights of February 17–18 and 18–19, we used the Acquisition Camera (AcqCam) on Gemini-South to obtain fast $V$ band optical photometry (see Table \ref{OpticalTable} for details)."415 Conditions were photometric. with realized nuage quality on target mostly ~0.9 aarcesec. although this degraded to ~1.2aarcesec in the latter part of the second. nieht.," Conditions were photometric, with realized image quality on target mostly $\sim0.9$ arcsec, although this degraded to $\sim1.2$ arcsec in the latter part of the second night."416 For practical data acquisition it was necessary to break each night iuto series of (usually) Oinmages at a time., For practical data acquisition it was necessary to break each night into series of (usually) images at a time.417 The series obtained. totaling το images. are listed in Table 1..," The series obtained, totaling 000 images, are listed in Table \ref{OpticalTable}."418 One of the great strengths of this instrament for fast rotometry is the fast readout., One of the great strengths of this instrument for fast photometry is the fast readout.419 We usedthe camera windowed and binned (2«2 eivine 256 Laarcsec jnned pixels)., We usedthe camera windowed and binned $2\times2$ giving $256\times256$ arcsec binned pixels).420 Other data acquisition modifications were uade to further minimize the dead-time between images., Other data acquisition modifications were made to further minimize the dead-time between images.421 This dead-time was not absolutely coustaut. but was usually O.310ss. with occasional (less than one per ew hundred) elitches to as high as LIS. The precise Hue-stamps were taken from when the image completed writing to disk. so the start time of the subsequent mage (relative to the first in a series) was known.," This dead-time was not absolutely constant, but was usually s, with occasional (less than one per few hundred) glitches to as high as s. The precise time-stamps were taken from when the image completed writing to disk, so the start time of the subsequent image (relative to the first in a series) was known."422 The start iue of the first imaee is taken from a GPS based clock., The start time of the first image is taken from a GPS based clock.423 Basic reductions including bias removal. subtraction of the significant dark current. and flat-fieldinge were done usne the script withinmaris.," Basic reductions including bias removal, subtraction of the significant dark current, and flat-fielding were done using the script within."424 The windowed field includes one star much brighter thanVoL. which provided a high fidelity reference star and two other comparisons (one brighter. one fainter) which were used to verify the accuracy of the results.," The windowed field includes one star much brighter than, which provided a high fidelity reference star and two other comparisons (one brighter, one fainter) which were used to verify the accuracy of the results."425 We experimented with both simall aperture photometry musing aud optimal photometry as implemented iu the Starlink package (see Navlor1998 for the algoritlin this is based on)., We experimented with both small aperture photometry using and optimal photometry as implemented in the Starlink package (see \citealt{Naylor:1998a} for the algorithm this is based on).426 We found uceligible— difference between the two methods proviced the aperture (for munveighted photometry) was optimized., We found negligible difference between the two methods provided the aperture (for unweighted photometry) was optimized.427 We opted to use the results from the optimal aleorithiu as this explicitly adjusts the weighting per image aud so should be more robust against changes iu seeing., We opted to use the results from the optimal algorithm as this explicitly adjusts the weighting per image and so should be more robust against changes in seeing.428 We used the comparison stars to verify that the standard deviations of the resulting lighteurves are dominated by the formal errors in the photometry., We used the comparison stars to verify that the standard deviations of the resulting lightcurves are dominated by the formal errors in the photometry.429 The formal errors for wwere typically ~2.5 pperceut per sec exposure., The formal errors for were typically $\sim2.5$ percent per sec exposure.430 Absolute calibration was done with respect to two stars from 1101 (Landolt 1992) on the first night., Absolute calibration was done with respect to two stars from 104 (Landolt 1992) on the first night.431 We derive magnitudes of V—13.63 for the reference star aud 17.115.0 for (Cexcluding bursts)., We derive magnitudes of $V=13.63$ for the reference star and 17.4--18.0 for (excluding bursts).432 The magnitude range derived for Hs within the range observed bv earlier studies 1lr.l18.1: wanParadij.vander[Elis&Pedersen 1988))., The magnitude range derived for is within the range observed by earlier studies 17.1–18.1; \citealt{vanParadijs:1988a}) ).433 The orbital lighteurves will be considered in a subsequent paper., The orbital lightcurves will be considered in a subsequent paper.434 Finally. we corrected the observed iuaguitudes for interstellar extinction (αππιο LBV)=0.06 based on the ffeature in our ddataj anc converted to fluxes with the couversion constant of Fukueita.Shinasaku.&Ichikawa(1995)..," Finally, we corrected the observed magnitudes for interstellar extinction (assuming $E(B-V)=0.06$ based on the feature in our data) and converted to fluxes with the conversion constant of \citet{Fukugita:1995a}."435 N-rav observations were obtained with the Rossi X-rav Tinune Explorer (JXTE)) mu two blocks timed to coincide with optical spectroscopy (Paper II). aud the optical and UV observations described above.," X-ray observations were obtained with the Rossi X-ray Timing Explorer ) in two blocks timed to coincide with optical spectroscopy (Paper II), and the optical and UV observations described above."436 A log is preseuted in Table 1.., A log is presented in Table \ref{OpticalTable}.437 A-av lightcurves of the bursts were recovered from a Glechanuecl event mode of the Proportional Counter Array (PCA)., X-ray lightcurves of the bursts were recovered from a channel event mode of the Proportional Counter Array (PCA).438 See Jaliodaetal.(2006). for discussion of the current status of the PCA., See \citet{Jahoda:2005a} for discussion of the current status of the PCA.439 Since the source counts are hieh during a burst. and the timescale is short. we used all PCUs which were switched on. iucludiug PCUO.," Since the source counts are high during a burst, and the timescale is short, we used all PCUs which were switched on, including PCU0."440 We initially processed lightcirves frou cach PCT separately. however. to check that no background fares were preseut in PCUO. before combining them.," We initially processed lightcurves from each PCU separately, however, to check that no background flares were present in PCU0, before combining them."441" Backeround lightcurves (with 16ss time-resolution) were constructed frou, the LT/210 faint source combined uodels dated 2002 Feb 1.", Background lightcurves (with s time-resolution) were constructed from the L7/240 faint source combined models dated 2002 Feb 1.442 This should allow| the most reliable background subtraction frou the pre-and post-must Leltcurves., This should allow the most reliable background subtraction from the pre-and post-burst lightcurves.443 Since the L7 rate is modified for bright sources. however. this model lighteurve is contaminated diving the burst.," Since the L7 rate is modified for bright sources, however, this model lightcurve is contaminated during the burst."444 We therefore interpolated between he pre- aud post-burst modeled background rates to define the burst backeround and subtracted this., We therefore interpolated between the pre- and post-burst modeled background rates to define the burst background and subtracted this.445 We note hat in practice the background subtraction has little iupact on the results described here as we perform au additional enipirical subtraction of the persistent (pre- and post-burst) fux., We note that in practice the background subtraction has little impact on the results described here as we perform an additional empirical subtraction of the persistent (pre- and post-burst) flux.446 Hence more refined backerounel models would not significantly affect our results., Hence more refined background models would not significantly affect our results.447 Liehteurves were initially extracted for kkeV. 12kkeV aud 60XkeV bandpasses.," Lightcurves were initially extracted for keV, keV and keV bandpasses."448 The burst profiles varied siguificautly with energev. so it ds important to be careful in choosing au appropriate dliehteurve for a deconvolution.," The burst profiles varied significantly with energy, so it is important to be careful in choosing an appropriate lightcurve for a deconvolution."449 We therefore also constructed a 20kkeV integrated flux liehteurve., We therefore also constructed a keV integrated flux lightcurve.450 To do this. we estimated approximate per-clhaunel couversions fron count rates to fluxes using and appropriate response matrices.," To do this, we estimated approximate per-channel conversions from count rates to fluxes using and appropriate response matrices."451 We used a black body fit to the average burst spectrum ) efiue these conversious to eusure that the relative weighting within cach chanucl was approximately correct., We used a black body fit to the average burst spectrum to define these conversions to ensure that the relative weighting within each channel was approximately correct.452 We then applied these conversions to cach channel aud Μπο the fluxes., We then applied these conversions to each channel and summed the fluxes.453" This will be somewhat uoisicr than a straight suia of couut rates, but represcuts our best estimate of the evolution of the flux iradiatiug the disk aud the companion star."," This will be somewhat noisier than a straight sum of count rates, but represents our best estimate of the evolution of the flux irradiating the disk and the companion star."454 Based ou the black body fits to the spectra. the 20kkeV bandpass accounts for most of the burst flux (90 bolometric corrections are ignored.," Based on the black body fits to the spectra, the keV bandpass accounts for most of the burst flux $\ga90$ bolometric corrections are ignored."455 Auv attempt to quantitatively model observations of rrequires syste parameters., Any attempt to quantitatively model observations of requires system parameters.456 ddoes not vet benefit from dyvuanical estimates. so we must use more indirect constraints.," does not yet benefit from dynamical estimates, so we must use more indirect constraints."457 Fortunately it is eclipsing. aud precisely defined. X-ray eclipses provide exquisitely detailed measurements of the orbital period aud duration of the neutron star eclipse (Wolffetal. 2002)..," Fortunately it is eclipsing, and precisely defined X-ray eclipses provide exquisitely detailed measurements of the orbital period and duration of the neutron star eclipse \citep{Wolff:2002a}. ."458 Through these eclipses. we know that the inclination must be high. aud the relationship between mass ratio and inclination is well definect.," Through these eclipses, we know that the inclination must be high, and the relationship between mass ratio and inclination is well defined."459"skip annulus cross-correlation (by cross-correlating signals at the center with signals averaged from an annulus around that center but with two acoustic skips), rather than the scheme of annulus- cross-correlation employed by Braun(1997),, although both schemes measure second-skip acoustic travel times.","skip annulus cross-correlation (by cross-correlating signals at the center with signals averaged from an annulus around that center but with two acoustic skips), rather than the scheme of annulus-annulus cross-correlation employed by \citet{bra97}, although both schemes measure second-skip acoustic travel times."460" We employ a similar scheme of annulus-annulus cross-correlation as used by by dividing one circular annulus into two semi-annuli and cross-correlating acoustic signals inside these two semi-annuli, as illustrated in Figure 6.."," We employ a similar scheme of annulus-annulus cross-correlation as used by \citet{bra97} by dividing one circular annulus into two semi-annuli and cross-correlating acoustic signals inside these two semi-annuli, as illustrated in Figure \ref{fg6}."461" After applying the phase-speed filtering, commonly used in time-distance measurements, to the data of AR8243 (same Dopplergram dataset as used in Section 2.2)), we have measured the second-skip travel times for an annulus with the inner radius of 32.2 Mm and the outer radius of 41.3 Mm, both of which are larger than the distance from the sunspot umbra center to the boundary of sunspot penumbra."," After applying the phase-speed filtering, commonly used in time-distance measurements, to the data of AR8243 (same Dopplergram dataset as used in Section \ref{sec2p2}) ), we have measured the second-skip travel times for an annulus with the inner radius of 32.2 Mm and the outer radius of 41.3 Mm, both of which are larger than the distance from the sunspot umbra center to the boundary of sunspot penumbra."462" It is worthwhile pointing out here, that the oscillation power reduction (“masking’’) effect has been corrected based on the acoustic power map of the studied region (Rajaguru,Zhao,&Duvall2005) before measuring the acoustic travel times."," It is worthwhile pointing out here, that the oscillation power reduction (“masking”) effect has been corrected based on the acoustic power map of the studied region \citep{raj05} before measuring the acoustic travel times."463" In addition to this second-skip experiment, another useful experiment is to compute acoustic travel times through the annulus-annulus cross-correlations, but without using oscillation signals inside the entire sunspot region."," In addition to this second-skip experiment, another useful experiment is to compute acoustic travel times through the annulus-annulus cross-correlations, but without using oscillation signals inside the entire sunspot region."464 This experiment is feasible because the, This experiment is feasible because the465distinguished from the signal [rom the surrounding dust.,distinguished from the signal from the surrounding dust.466 Some of these objects could even be nothing more than unusually dense clouds of dust. alübough others do appear to have sufficient mass to perturb nearby ring material (Beurleetaf2010).," Some of these objects could even be nothing more than unusually dense clouds of dust, although others do appear to have sufficient mass to perturb nearby ring material \citep{Beurle10}."467. The distinctive transmission spectra of these objects in VIMS occultations may (therefore provide useful new insights into these structures., The distinctive transmission spectra of these objects in VIMS occultations may therefore provide useful new insights into these structures.468" In order to better quantify the distinctive characteristics of (he narrow peak in Figure 12.. consider (he following (wo-component ansatz for (he particle size distribution in (he F ring: On the one had. there is the ""dust component"" of the ring. consisting of particles smaller than ~30 jam. and on the other hand. there is a “hig particle component” Consisting exclusively of particles larger (han ~30 jan. For this simple model. we will ignore the variations in the cust size distribution within the F ring discussed above and assume that the ratio of optical depths for the dust component is à constant. p,=0.9 throughout the ring. where the specific value is chosen to be close to the peak of the distribution shown in Figure 7.."," In order to better quantify the distinctive characteristics of the narrow peak in Figure \ref{alpscoplot}, consider the following two-component ansatz for the particle size distribution in the F ring: On the one hand, there is the “dust component"" of the ring, consisting of particles smaller than $\sim30$ $\mu$ m, and on the other hand, there is a “big particle component” consisting exclusively of particles larger than $\sim30$ $\mu$ m. For this simple model, we will ignore the variations in the dust size distribution within the F ring discussed above and assume that the ratio of optical depths for the dust component is a constant $\rho_d=0.9$ throughout the ring, where the specific value is chosen to be close to the peak of the distribution shown in Figure \ref{rhodist}."469 Similarly. we will assume the big particle component of the ring has an optical depth ratio ον=1.0.," Similarly, we will assume the big particle component of the ring has an optical depth ratio $\rho_b=1.0$."470 In this model. radial variations in the optical depth ratio p are interpreted as variations in (he relative amounts of 7dust and “big particles” in different parts of the rings.," In this model, radial variations in the optical depth ratio $\rho$ are interpreted as variations in the relative amounts of “dust” and “big particles” in different parts of the rings."471" More specifically, a sharp increase in p indicates an excess of particles larger than tens of microns across in that particular region of the ring."," More specifically, a sharp increase in $\rho$ indicates an excess of particles larger than tens of microns across in that particular region of the ring."472" Let us denote (he continuum (i.e. 3.2 yan) optical depths of these two components as 7, and τι, respectively."," Let us denote the continuum (i.e., 3.2 $\mu$ m) optical depths of these two components as $\tau_d$ and $\tau_b$, respectively."473 Then the slant optical depths al our two standard wavelenetls are given. by: ancl solving these equations for ty and τε. we find: Figure 12. shows profiles of τι and τι derived Irom the Rev 13 egress a Scorpii occultation using this method.," Then the slant optical depths at our two standard wavelengths are given by: and Solving these equations for $\tau_d$ and $\tau_b$, we find: Figure \ref{alpscoplot} shows profiles of $\tau_d$ and $\tau_b$ derived from the Rev 13 egress $\alpha$ Scorpii occultation using this method."474 Note that since 1—py=0.1. the noise levels in these profiles are roughly 10 (mes larger than those of the individual spectral channels.," Note that since $1-\rho_d=0.1$, the noise levels in these profiles are roughly 10 times larger than those of the individual spectral channels."475 Nevertheless. (his decomposition clearly isolates (he narrow spike Irom the rest of the F ring.," Nevertheless, this decomposition clearly isolates the narrow spike from the rest of the F ring."476 Hence. even if the above model is a gross oversimplilication of (he real particle size distribution in the F ring. it provides a useful method of identibving (hese highly," Hence, even if the above model is a gross oversimplification of the real particle size distribution in the F ring, it provides a useful method of identifying these highly"477due to electrons wilh the lowest energies (i.e. sin).,"due to electrons with the lowest energies (i.e., $\gamma_{\rm min}$ )."478 Two breaks are expected for 5444<te. which would result in a rather flat peak in vf(v).," Two breaks are expected for $\gamma_{\rm min} < \gamma_{\rm c}$, which would result in a rather flat peak in $\nu f(\nu)$."479 The gamma-ray emission from LSPs is usually interpreted as first order Compton scattering., The gamma-ray emission from HSPs is usually interpreted as first order Compton scattering.480 Although the number of HSPs in the 509 sample is low. their mean value of ag (20.8) is consistent with the same value of p as for the LSPs and negligible cooling.," Although the number of HSPs in the S09 sample is low, their mean value of $\alpha_{\rm G}$ $\approx 0.8$ ) is consistent with the same value of $p$ as for the LSPs and negligible cooling."481 Furthermore. (he spectral properties of the ISPs. which fall in between those of LSPs and HSPs. are consistent with being transition cases for which the eanmmnma-ravy enussion is produced in the Ixlein-Nishina limit but with the cooling frequency in or somewhat above the LAT οποιον range.," Furthermore, the spectral properties of the ISPs, which fall in between those of LSPs and HSPs, are consistent with being transition cases for which the gamma-ray emission is produced in the Klein-Nishina limit but with the cooling frequency in or somewhat above the LAT energy range."482 It is well known that in general the peak Ireeuency of the IC-component shifts to lower yequencies lor higher luminosities1998)., It is well known that in general the peak frequency of the IC-component shifts to lower frequencies for higher luminosities.483. S09 show (hat on a more detailed level (his is due to more luminous sources having spectra with smaller values of ay as well as larger values of ac., S09 show that on a more detailed level this is due to more luminous sources having spectra with smaller values of $\alpha_{\rm X}$ as well as larger values of $\alpha_{\rm G}$.484 Furthermore. this correlation seems to be valid also within the eroup of the most luminous sources. which have their peak frequencies in between the DAT and LAT frequeney ranges.," Furthermore, this correlation seems to be valid also within the group of the most luminous sources, which have their peak frequencies in between the BAT and LAT frequency ranges."485 As can be seen [rom relligl.. this is consistent with a MIC-scenario.," As can be seen from \\ref{fig1}, this is consistent with a MIC-scenario."486 llence. (he varving spectral properties along (he blazar sequence can be interpreted as a continuous variation of the cooling frequency.," Hence, the varying spectral properties along the blazar sequence can be interpreted as a continuous variation of the cooling frequency."487 Although this agrees with the suggestion originally put forward by(1993).. the implications of this in the MIC-scenario are quite different.," Although this agrees with the suggestion originally put forward by, the implications of this in the MIC-scenario are quite different."488 The blazar sequence is normally thought to be governed by the energy density of external photons so that a hieher density would correspond to a lower cooling frequency and. hence. a higher total huminositv.," The blazar sequence is normally thought to be governed by the energy density of external photons so that a higher density would correspond to a lower cooling frequency and, hence, a higher total luminosity."489 At some luminosity. the enerey density of external photons have decreased to the extent that internally produced svuchrotron photons would take over as seed photons2007).," At some luminosity, the energy density of external photons have decreased to the extent that internally produced synchrotron photons would take over as seed photons."490. The former group corresponds {ο LSPs and the latter to HSPs., The former group corresponds to LSPs and the latter to HSPs.491 LAT observations show that LSPs tend to have ας>1 and ISPs/HSPs ocS1. with most of the objects with ας21 being classified as ISPs2010a).," LAT observations show that LSPs tend to have $\alpha_{\rm G} > 1$ and ISPs/HSPs $\alpha_{\rm G} \lesssim 1$, with most of the objects with $\alpha_{\rm G} \approx 1$ being classified as ISPs."492. This indicates that the transition from external photons to internal svnchrotron photons as the dominant source of seed photons corresponds (o a cooling Irequency. line in or close to the LAT frequeney. range., This indicates that the transition from external photons to internal synchrotron photons as the dominant source of seed photons corresponds to a cooling frequency lying in or close to the LAT frequency range.493 Such a coincidence remains to be explained in the standard interpretation of the blazar sequence but is expected in (he MIC-scenario., Such a coincidence remains to be explained in the standard interpretation of the blazar sequence but is expected in the MIC-scenario.494 With a bulk Lorentz factor P~LO and emission in the Ixlein-Nishina limit. the LAT spectral range corresponds. roughly. to electrons with Lorentz factors >~107.," With a bulk Lorentz factor $\Gamma \sim 10$ and emission in the Klein-Nishina limit, the LAT spectral range corresponds, roughly, to electrons with Lorentz factors $\gamma \sim 10^3$."495 Standard svuchrotron theory implies (hat svnchrotron self-absorption sets in for electrons will 10°., Standard synchrotron theory implies that synchrotron self-absorption sets in for electrons with $\gamma_{\rm abs} \sim 10^2$ .496 In the MIC-scenario. the peak of the svnchrotron component in LSPs corresponds. roughly. to the sell-absorption frequeney.," In the MIC-scenario, the peak of the synchrotron component in LSPs corresponds, roughly, to the self-absorption frequency."497 Hence. electrons radiating in the LAT-frequeney range have energies similar {ο those producing the optical svnclirotron radiation.," Hence, electrons radiating in the LAT-frequency range have energies similar to those producing the optical synchrotron radiation."498 The ISPs were originally identified as those blazars having their svnchrotron peak frequency in between, The ISPs were originally identified as those blazars having their synchrotron peak frequency in between499"that the low-enerey portion oftheir spectra are extremely uncderpopulated with respect to higher euergles is consistent with the hypothesis of higli extiuction: ou average. ""uou-ID"" harduess ratios suggest optical extinction Z»30 iuaguitudes.","that the low-energy portion of their spectra are extremely underpopulated with respect to higher energies is consistent with the hypothesis of high extinction: on average, “non-ID” hardness ratios suggest optical extinction $\gtrsim 30$ magnitudes."500 Having established that a majority of our unidentified sources are associated with lighly torbed objects. we next cousiler whether or not t[une hypothesis that they are higb-intrinsic uiinosity. embedded. cluster members is compatible with the observational coustraint that they t'e uot detected in the deep A-bau survey.," Having established that a majority of our unidentified sources are associated with highly absorbed objects, we next consider whether or not the hypothesis that they are high-intrinsic luminosity, embedded cluster members is compatible with the observational constraint that they are not detected in the deep $K$ -band survey."501" We can derive an empirical relationship between stellar uass and intrinsic: non absorbed. A-baud yy considering the two quantities for ONC uembers with low measured optical extinction G4,< 1.0)."," We can derive an empirical relationship between stellar mass and intrinsic, non absorbed, $K$ -band by considering the two quantities for ONC members with low measured optical extinction $A_V < 1.0$ )."502 We then derive. as a Duuction of mass. he miuinum {να extiuctiou needed to make these sources fall below the A-band seusitivity hreshold of. dy-=απ 17.5.," We then derive, as a function of mass, the minimum $K$ -band extinction needed to make these sources fall below the $K$ -band sensitivity threshold of $K= 17.5$ ."503 1Converting⋅ this⋅ minimum⋅⋅ Ay to a minimun⋅⋅ VjH=9.344-2-.i3602107!e2? and, Converting this minimum $A_K$ to a minimum $N_H = 9.3 A_K \cdot 2\cdot~10^{21} \ cm^{-2}$ and504We are thus left with a single complex equation for g. which contains the observable brighltucss moments of the nuage. as well as the unobservable brightuess momeuts of the source.,"We are thus left with a single complex equation for $g$, which contains the observable brightness moments of the image, as well as the unobservable brightness moments of the source."505 This equation can be used to estimate the reduced shear if we male assumptions concerning the properties of the source brightness moments., This equation can be used to estimate the reduced shear if we make assumptions concerning the properties of the source brightness moments.506 We assume that the sources are oriented randomly. which iunplies that all quautitics with spin unequal zero have a vanishing expectation value.," We assume that the sources are oriented randomly, which implies that all quantities with spin unequal zero have a vanishing expectation value."507 That is. we set Q5=0. T=0. to arrive at Qi where we have indicated⋅⋅ that the right-hand⋅ side.. depends ou the reduced shear Gu ⋅fact it⋅ does so in↕∐∶↴∙⊾↸∖∐↸∖↥⋅⋜↧↕∙⋎↴∖↴∐⊔↻↕↸∖↥⋅↸∖↴∖↴↑∐⊔⋜↧↑↸∖↕↴∖↴∪↴⋝↑⋜⊔∐↸∖≼↧↕↕↖↖⇁↸∖⋜↧↴∖∷∖↴⋯⊔↸∖ a very coniplex manner).," That is, we set $Q_2^{\rm s}=0$, ${\cal T}^{\rm s}=0$, to arrive at Q_2 - 2g Q_0 + g^2 Q_2^* = + ^2 =:, where we have indicated that the right-hand side depends on the reduced shear (in fact it does so in a very complex manner)."508 However. since. we have argued above that the terms on the left-hand. are much lareer than those on the right-hand. side.. au iterative. solution. ↑∐↕↴∖↴↸∖≺∣∏⋜↧⊓∪∐↕↴∖↴↴∖↴∏∶↴∙⊾∶↴∙⊾↸∖↴∖↴↑↸∖≼↧∙⊀≚↴∖↴↴∖↴∏⋯↸∖↑↕∐∖↥⋅↕∶↴∙⊾∐↑≓∐⋜↧∐≺↧↴∖↴↕≼↧↸∖↕↴∖↴of. ⋅⋅ ⋅ ⋅ ⋅⋅∪↕↴∖↴↻∐↕↕∩⋜⋯∖↕⊔⋯⊳∐," However, since we have argued above that the terms on the left-hand are much larger than those on the right-hand side, an iterative solution of this equation is suggested."509↴∖↴⋯⋜↧∐↸∖↥⋅↑∐⋜⋯↑∐↸∖↸⊳∪↥⋅↥⋅↸∖↴∖↴↻∪⋯∐∐∶↴⋁∪∐↸∖↴∖↴ then⋅ we ect the solutions with is the complex cllipticity of the image.," Assume the right-hand side is given, then we get the solutions, is the complex ellipticity of the image."510 Obviously. there are two solutions gy for a eiven value of Y.," Obviously, there are two solutions $g$ for a given value of $Y$."511" This situation is shudlar to that of ""ordinary. weak leusine. where this aiubiguitv also occurs: as shown bv Schueider aud Seitz (1995). from shape measurements of backeround ealaxies. ⋅⋅⋅ ⋜⋯≼↧⋯∐∐∪↑≼∐↴∖↴⊓↕∶↴∙⊾⋯↴∖↴↕↓↕∪↸⊳⋜↧∐⋅↖↽↴⋝↸∖↑↖↖↽↸∖↸∖∐⋜⋯↸∖↴∖↴↑∐⊔⋜↧↑↸∖∙↙∕ ⋅ aud .l/g=ο”."," This situation is similar to that of `ordinary' weak lensing, where this ambiguity also occurs: as shown by Schneider and Seitz (1995), from shape measurements of background galaxies, and cannot distinguish locally between an estimate $g$ and $1/g^*=g/|g|^2$."512 3nThe same occurs here: we therefore. asstuue that we pick one of the two solutions. sav the one corresponding to the  sien: this then vields for sinall shear gzc2.," The same occurs here; we therefore assume that we pick one of the two solutions, say the one corresponding to the $-$ ' sign; this then yields for small shear $g\approx \chi/2$."513 It should be stressed that flexion nupacts the determination of shear from the second-order brightness moments. due to its impact on higher-order brightuess moments: hence. iun eeueral the determination of. shear and flexion. are coupled.," It should be stressed that flexion impacts the determination of shear from the second-order brightness moments, due to its impact on higher-order brightness moments; hence, in general the determination of shear and flexion are coupled."514 We start the iteration by setting Jy=0., We start the iteration by setting $Y_0=0$.515 This vields a first-order solution for the estimate of g.," This yields a first-order solution for the estimate of $g$,."516 We then use the iteration equations 1):E, We then use the iteration equations );.517E This procedure converges quickly to one of the two solutions (g.G4.G3): the other solution is obtained bv taking the | sign in the above equations.," This procedure converges quickly to one of the two solutions $(g,G_1,G_3)$; the other solution is obtained by taking the `+' sign in the above equations."518 Of course. our approach of setting (Q5=0 viclds a biased. estimator for g: this is true even iu the absence of flexion (c.g. Schucider Seitz 1995).," Of course, our approach of setting $Q_2^{\rm s}=0$ yields a biased estimator for $g$; this is true even in the absence of flexion (e.g., Schneider Seitz 1995)."519 The reason is that. although the expectation value of Q5 vanishes. the resulting estimator for g is à uou-linear function of q=Q3/Q aud thus biased.," The reason is that, although the expectation value of $Q_2^{\rm s}$ vanishes, the resulting estimator for $g$ is a non-linear function of $\chi^{\rm s}=Q_2^{\rm s}/Q_0^{\rm s}$ and thus biased."520 The bias depends ou the ellipticity distribution of the sources., The bias depends on the ellipticity distribution of the sources.521 It should be stressed. however. that a modified definition of image ellipticity exist such that its expectation value is an unbiased estimate of the reduced shear (Seitz Schucider 1997).," It should be stressed, however, that a modified definition of image ellipticity exist such that its expectation value is an unbiased estimate of the reduced shear (Seitz Schneider 1997)."522 The flexion estimator is eiveu by (57))., The flexion estimator is given by \ref{eq:g13}) ).523 Since the matrix C contaius many ternis.this is a fairly complicated equation . .," Since the matrix $\tens{C}$ contains many terms,this is a fairly complicated equation in general."524 . . » that the reduced shear is. sinall. |g|«EEαν in which. case the matrix. C simplifies.⋅⋅ considerablv⋅ see Apponudix.," A simpler estimate is obtained if we assume that the reduced shear is small, $|g|\ll 1$, in which case the matrix $\tens{C}$ simplifies considerably – see Appendix."525⋅ Furtheruore. if» we assume that the brightuess. moments ⋅ ⋅ spin⋅ 0.⋅ then we find the⋅ simple relatious⋅ eiven.⋅ne (VeeEO STs ABCs.," Furthermore, if we assume that the brightness moments of spin $\ne 0$ are much smaller than the corresponding ones with spin 0, then we find the simple relations G_1 T_3- G_3."526" If we then set the 77=0. as would be true for the expectation value. then we obtain as estimates for the reduced fiexiou Cam: Ca2 LTT,U"," If we then set the $T_n^{\rm s}=0$, as would be true for the expectation value, then we obtain as estimates for the reduced flexion G_1; G_3 T_3."527t Thus. the flexion. is. then given. by the third-order. . ↴⋝↥⋅↕∶↴∙⊾∐↑∐↸∖↴∖∷∖↴↕⊔∪⋯↸∖∐↑↴∖↴∪↕↑↕∐∖∐⊔⋜↧∶↴∙⊾↸∖∙≼∐↖↽↕≼∐∖≼∏⋝∙↖⇁⋜↧≺∣∏⋜⋯⊓↑⋅↖⇁ . . ⋅⋅ ⋅ that just. depends on the size. of. the nuage.," Thus, the flexion is then given by the third-order brightness moments of the image, divided by a quantity that just depends on the size of the image."528". Similar""M . ↥⋅↸∖↕⋜↧↑↕∪∐↴∖↴↑∪⊓⊳↓⊔∐⋜↧↖↽↸∖↴⋝↸∖↸∖∐∶↴∙⊾↕↖⇁↸∖∐∐↕≼∣∪↕≺∏⋝↸∖↥⋅∶↴⋁∙∖↽∫⇀↸∖∪∐⋜⋯↧. . ⋅⊲ ⋖⊇∪∩∏∙↖↖↽∐↸∖↥⋅↸∖⋜↧↴∖↴≼↙∐∏∐⋅⋜⊔∖↑⋜↧↕∙⊓⊇∩∩∏∪↴⋝↑⋜↕↕∐⋜↧≺∐↕−∐∖↥⋅↸∖∐↑ expression for G4."," Similar relations to \ref{eq:eg13}) ) have been given in Goldberg Leonard (2007), whereas Okura et (2007) obtain a different expression for $G_1$."529 We will check the accuracy of (61)) in below., We will check the accuracy of \ref{eq:eg13}) ) in \\ref{Sc:6} below.530 A more accurato estimate is obtained if we cousider the reduced shear as well as the ratios⋅ of non-zero spin brightness moments to zero spin monieuts (such as (Qo/Qu| or |Fa. Εν} to be of order 9. and then expand the flexion to first order in the (simdl) parameter à to Ghtain no τῃ," A more accurate estimate is obtained if we consider the reduced shear as well as the ratios of non-zero spin brightness moments to zero spin moments (such as $|Q_2/Q_0|$ or $|F_{2,4}/F_0|$ ) to be of order $\delta$ and then expand the flexion to first order in the (small) parameter $\delta$ to obtain T_3 T_1^*"531black in the plot) and to develop a high tail.,black in the plot) and to develop a high $\delta$ tail.532" This trend continues at z—1, with increased scatter6 in both the logarithmic and linear relations, and with the linear relation deviating from slope of -1."," This trend continues at $z=1$, with increased scatter in both the logarithmic and linear relations, and with the linear relation deviating from a slope of -1."533" Finally, by z=0 the linear relation deviatesa drastically from slope of -1 while the logarithmic relation does very well,a though with much scatter."," Finally, by $z=0$ the linear relation deviates drastically from a slope of -1 while the logarithmic relation does very well, though with much scatter."534" It is not unexpected that the linear relation does not hold, since 1.6 h-! Mpc is by no means in the linear regime, but the fact that the logarithmic relation holds so well echoes the results of Neyrincketal.(2009) and others that the logarithmic transform of the density field increases the information content of the matter power spectrum in the weakly nonlinear regime."," It is not unexpected that the linear relation does not hold, since 1.6 $^{-1}$ Mpc is by no means in the linear regime, but the fact that the logarithmic relation holds so well echoes the results of \citet{ney09} and others that the logarithmic transform of the density field increases the information content of the matter power spectrum in the weakly nonlinear regime."535" When the CIC cell size is increased to 12.5 h-!Mpc, both the linear and logarithmic relations become very tight, though the logarithmic approximation continues to do slightly better."," When the CIC cell size is increased to 12.5 $^{-1}$ Mpc, both the linear and logarithmic relations become very tight, though the logarithmic approximation continues to do slightly better."536" Figure 2 is the same as Figure 1 but at z=0, showing the CIC method for cell sizes of 1.6 h~'Mpc and 12.5 h-!Mpc, along with the two other methods discussedin the next sections."," Figure \ref{fig:divz0} is the same as Figure \ref{fig:divcic4z} but at $z=0$, showing the CIC method for cell sizes of 1.6 $^{-1}$ Mpc and 12.5 $^{-1}$ Mpc, along with the two other methods discussedin the next sections."537" We also try an adaptive smoothing technique, described by Colombietal. (2007),, on both the density and the displacement fields."," We also try an adaptive smoothing technique, described by \citet{col07}, , on both the density and the displacement fields."538" We assume that each particle p traces some physical quantity A,.", We assume that each particle $p$ traces some physical quantity $A_p$.539" For the purpose of this paper, will be either a particle count or the displacement Αρvector VW between the final and initial particle positions."," For the purpose of this paper, $A_p$ will be either a particle count or the displacement vector $\mathbf{\Psi}$ between the final and initial particle positions."540" We sample the adaptively-smoothed field onto a three-dimensional grid, with grid sites denoted by the integers (4,j,k)."," We sample the adaptively-smoothed field onto a three-dimensional grid, with grid sites denoted by the integers $(i,j,k)$."541" At eachgrid site we define the smoothing radius R(i,j,k) which corresponds to half the distance from the gridsite to the M-th particle, where M is defined as: and Mbinnea(t,j,k) is the number of particles binnedon the grid site (i, j,k)."," At eachgrid site we define the smoothing radius $R(i,j,k)$ which corresponds to half the distance from the gridsite to the $M$ -th particle, where $M$ is defined as: and $M_\mathrm{binned}(i,j,k)$ is the number of particles binnedon the grid site $(i,j,k)$ ."542" Following Colombietal. (2007),, we conservatively set Mj,= 32, corresponding to the"," Following \citet{col07}, , we conservatively set $M_\text{min}=32$ , corresponding to the"543increasing photometric scatter wilh increasing M; magnitude. (his spread is also consistent wilh the range of modeled effective temperatures.,"increasing photometric scatter with increasing $_{3.6}$ magnitude, this spread is also consistent with the range of modeled effective temperatures."544 For the oxvgen-rich. AGBs at a given elfective temperature. varving the composition of the wind from AIOx. to Si and AIOx. and to Si vield tracks roughly (he same shape.," For the oxygen-rich AGBs at a given effective temperature, varying the composition of the wind from AlOx, to Si and AlOx, and to Si yield tracks roughly the same shape."545 However. increasing the Si fraction shifts the tracks redward.," However, increasing the Si fraction shifts the tracks redward."546 Changing the spectral (wpe for a given wind composition from ALO to M6 to MIO produces brighter M magnitudes and redder [3.6]— [4.5] colors., Changing the spectral type for a given wind composition from M0 to M6 to M10 produces brighter $_{3.6}$ magnitudes and redder $-$ [4.5] colors.547 Because of the similarities between the tracks of oxvgen- and carbon-rich AGBs. we cannot distinguish between them in our CMD.," Because of the similarities between the tracks of oxygen- and carbon-rich AGBs, we cannot distinguish between them in our CMD."548 However. we can still investigate (he MLRs of AGB stars by comparing the distribution of our sources to the various models.," However, we can still investigate the MLRs of AGB stars by comparing the distribution of our sources to the various models."549 The [3.6]— 4.5] color of AGB stars corresponds (o a unique 7. which in turn corresponds to à MLB. scaled by (he square root of (he stellar huminosity and by the inverse of the dust-to-gas ratio (ο) Lor a given stellar/wind composition. as prescribed by Groenewegen(2006).," The $-$ [4.5] color of AGB stars corresponds to a unique $\tau$, which in turn corresponds to a MLR, scaled by the square root of the stellar luminosity and by the inverse of the dust-to-gas ratio $\psi$ ) for a given stellar/wind composition, as prescribed by \citet{gro06}."550. We calculated the total MLBs by binning the AGDs according to the modeled optical depths and applying the appropriately scaled MLB. given (he stellar color aud luminosity.," We calculated the total MLRs by binning the AGBs according to the modeled optical depths and applying the appropriately scaled MLR, given the stellar color and luminosity."551 Dolphin(2000). estimates the metallicity of WLM 1-2.5 Gyr ago (an appropriate timescale for (he formation of the current AGB population) to be [Fe/II|] = —1.13. while the current. metallicity of WEM. as measured by both the nebular oxvgen abundance (Leeetal.2006) ancl blue supereiants (Dresolinetal.2006) is Ο/Η) = —0.8.," \citet{dol00} estimates the metallicity of WLM 1-2.5 Gyr ago (an appropriate timescale for the formation of the current AGB population) to be [Fe/H] = $-$ 1.13, while the current metallicity of WLM, as measured by both the nebular oxygen abundance \citep{lee06} and blue supergiants \citep{bre06} is [O/H] = $-$ 0.8."552 These upper and lower limits give us a reasonable range of values for the expected metallicities of the AGB population. and also allow us to estimate an uncertaintv in the calculated. MLBs.," These upper and lower limits give us a reasonable range of values for the expected metallicities of the AGB population, and also allow us to estimate an uncertainty in the calculated MLRs."553" Assuming the dust-to-gas ratio scales as eee. EM asd ο, — 0.005 (vanLoonetal.2005)... we adopt cita; = x101,"," Assuming the dust-to-gas ratio scales as $\psi$ = $\psi_{\sun}$ $^{-[Fe/H]}$ and $\psi_{\sun}$ = 0.005 \citep{van05}, we adopt $\psi_{WLM}$ = $\times10^{-4}$."554" If the entire AGB population is composed of carbon-rich AGDs with T,;; = 3600 Ix and wind composition of AMC and SiC we derive a total MLR of = L.1-2.4x10 3[f", If the entire AGB population is composed of carbon-rich AGBs with $_{eff}$ = 3600 K and wind composition of AMC and SiC we derive a total MLR of = $\times$ $^{-3}$.555" If instead we assume a population with the same properties except T,ει = 2650 I. we find a similar total MLR of = 0.9-1.9x 7?vr!"," If instead we assume a population with the same properties except $_{eff}$ = 2650 K, we find a similar total MLR of = $\times$ $^{-3}$."556 In both of these cases we are not including the contribution from sources bluer than the model colors: however. these objects contribute a negligible amount to the total. MLB.," In both of these cases we are not including the contribution from sources bluer than the model colors; however, these objects contribute a negligible amount to the total MLR."557 Ninety percent of the total MLR from both models are from sources with — [3.6]4.5] > 0.5. and over of the mass-loss is from sources with — [3.6]4.5] > 1.0.," Ninety percent of the total MLR from both models are from sources with $-$ [4.5] $>$ 0.5, and over of the mass-loss is from sources with $-$ [4.5] $>$ 1.0."558 The total MLRs are a factor of 3.3 higher if the population is composed of oxvgen-rich. AGDs with Silicate and AIOx winds. and a [actor of 2.9 higher for oxvgen-rich. AGBs with silicate winds.," The total MLRs are a factor of 3.3 higher if the population is composed of oxygen-rich AGBs with Silicate and AlOx winds, and a factor of 2.9 higher for oxygen-rich AGBs with silicate winds."559 We are particularly interested in the sources recdwrd of the main stellar distribution (shown in the box in the right panel of Figure 11))., We are particularly interested in the sources redward of the main stellar distribution (shown in the box in the right panel of Figure \ref{groen}) ).560 These sources are well modeled bv both oxygen-rich AGBs with Tissjn = 3-0 and carbon-rich. AGBs with 715275pm = 0.54., These sources are well modeled by both oxygen-rich AGBs with $\tau_{\mbox{\scriptsize{11.75 \micron}}}$ = 3.0 and carbon-rich AGBs with $\tau_{\mbox{\scriptsize{11.75 \micron}}}$ = 0.54.561 The only models ruled out bv these data are an entire population of oxveen-rich AGDs, The only models ruled out by these data are an entire population of oxygen-rich AGBs562Debris disks older than ~10 Myr coutainine dust at temperatures 100 IE are extremely rare (Amman&Probst1991:Silverstoneetal. 2006).,"Debris disks older than $\sim$ 10 Myr containing dust at temperatures $>$ 100 K are extremely rare \citep{Aumann1991,Silverstone06}."563". When warn dust does appear. it is likely to be from a stochastic event. perhaps akin to our own solar svstenis ""Late Ποανν Boubarcdinent.” at about 600 AIvr after formation."," When warm dust does appear, it is likely to be from a stochastic event, perhaps akin to our own solar system's “Late Heavy Bombardment,” at about 600 Myr after formation."564 Late episodes of dust production may signal the presence of a planctary syste undergoing architectural reconfiguration (Comesetal.2005)., Late episodes of dust production may signal the presence of a planetary system undergoing architectural reconfiguration \citep{Gomes2005}.565. BD|20 307 is one of the few examples of a non-vouus star with hot debris (Songetal.2005)., BD+20 307 is one of the few examples of a non-young star with hot debris \citep{Song2005}.566. Tt has a ring of dust at ~0.5 AU (Weinbergeretal.2008)., It has a ring of dust at $\sim$ 0.5 AU \citep{Weinberger08}.567. Tn order to nuderstaud the duplications of the large amount of in dust. it would help ercatly to kuow the age of the star.," In order to understand the implications of the large amount of close-in dust, it would help greatly to know the age of the star."568 Songetal.(2005) used the Li eequivaleut width aud chromospheric activity to sugecst an age of ~300 Myr., \citet{Song2005} used the Li equivalent width and chromospheric activity to suggest an age of $\sim$ 300 Myr.569 New observatious reported here show that DD |20 307 is actually a spectroscopic binary., New observations reported here show that BD +20 307 is actually a spectroscopic binary.570 I reexamine the evidence for the age of the star., I reexamine the evidence for the age of the star.571 The Magellan Tnamori Kyocera Echelle (MIKE) spectrograph on the Clav (Magellan II). telescope was used to observe BD |20 307 on three cousecutive nights 2007 October 21-26 (UT)., The Magellan Inamori Kyocera Echelle (MIKE) spectrograph on the Clay (Magellan II) telescope was used to observe BD +20 307 on three consecutive nights – 2007 October 24-26 (UT).572" The 0.357 wide « 5"" lone slit provided a resolution of about 55.000 at waveleneths 3100. 7250A."," The 0.35” wide $\times$ 5” long slit provided a resolution of about 55,000 at wavelengths 3400 – 7250."573". Secing was 0.5"" on the first two nights and 0.51.27 on the third.", Seeing was $\sim$ 0.5” on the first two nights and 0.8–1.2” on the third.574 Ou all three nights. data were obtained with au iodine cell iu place to facilitate looking for planets around the star. and on the first night an observation without the iodine cell was also obtained.," On all three nights, data were obtained with an iodine cell in place to facilitate looking for planets around the star, and on the first night an observation without the iodine cell was also obtained."575 I do not use the iodine lines for the racial velocity analyses that follow., I do not use the iodine lines for the radial velocity analyses that follow.576 An observing log is given in Table 1.., An observing log is given in Table \ref{tab_observlog}.577 The spectra were flattened. extracted and wavelength calibrated using the MIKE pipeline written by D. helson with methods described in EKelsouctal.(2000):I&elsou(2003):Iselsonctal. (2006)...," The spectra were flattened, extracted and wavelength calibrated using the MIKE pipeline written by D. Kelson with methods described in \citet{Kelson2000,Kelson2003,Kelson2006}. ."578 The two observatious from the first nieht were averaged., The two observations from the first night were averaged.579 The sigual-to-noise ratio (S/N) per pixel was 2100 for wavelengths > 000 oon the first two nights. except in the region of maximal jodine absorption around50004À.," The signal-to-noise ratio (S/N) per pixel was $>$ 100 for wavelengths $>$ 4000 on the first two nights, except in the region of maximal iodine absorption around."580. The S/N was abou worse ou the third night due to the worse secing., The S/N was about worse on the third night due to the worse seeing.581 BD |20 307 was also observed on 2001 August 2 with the echelle spectrograph ou the 2.5 im du Pow Telescope at Las Campanas Observatory., BD +20 307 was also observed on 2004 August 24 with the echelle spectrograph on the 2.5 m du Pont Telescope at Las Campanas Observatory.582 These data cover wavelengths ~ aand have a resolution of about 25.000 and S/N of 30100.," These data cover wavelengths $\sim$ and have a resolution of about 25,000 and S/N of 30–100."583 The data were extracted and calibrated using standard IRAF tasks., The data were extracted and calibrated using standard IRAF tasks.584 TWehoceutric aud barvceeutrie velocities were calculate with the RVSAO package iu IRAF., Heliocentric and barycentric velocities were calculated with the RVSAO package in IRAF.585 Two sets of lines are clearly visible in adl που welts of MIKE data., Two sets of lines are clearly visible in all three nights of MIKE data.586 To obtain the velocities of the double-Iued spectroscopic biuary. cross-correlatious with a svuthetic spectrum with effective temperature 6000 Is. aud log(g)j-5.0 were performed.," To obtain the velocities of the double-lined spectroscopic binary, cross-correlations with a synthetic spectrum with effective temperature 6000 K and log(g)=5.0 were performed."587 This spectrum was ecucrated using R. O. (σαν SPECTRUM code aud line aud shown in Figure L.., This spectrum was generated using R. O. Gray's SPECTRUM code and line and shown in Figure \ref{fig_binaryvel}.588 On all three nights. the ΠΑΝ star produced a higher cross correlation peak.," On all three nights, the primary star produced a higher cross correlation peak."589 The same cross-correlation was done for the lower resolution du Pout spectrum., The same cross-correlation was done for the lower resolution du Pont spectrum.590 A double-peaked appearsonly for the lowest two orders 11504A))., A double-peaked cross-correlation appearsonly for the lowest two orders ).591 I do not consider this detection of the binary, I do not consider this detection of the binary592Early-type galaxies are often regarded as the objects at the final stage of galaxy evolution.,Early-type galaxies are often regarded as the objects at the final stage of galaxy evolution.593 Throughout niu observations. it has been revealed that most nearby carly-type galaxies have red colors and very poor contents of cold eas (e.g.etal. 2006).," Throughout many observations, it has been revealed that most nearby early-type galaxies have red colors and very poor contents of cold gas \citep[e.g.][]{fab76,tra00,tre06}."594. Such observational evidence indicates that earbv-tvpe galaxies are composed of old stars and that they probably will not have additional star formation in the future., Such observational evidence indicates that early-type galaxies are composed of old stars and that they probably will not have additional star formation in the future.595 That is. most cartype galaxies seei to evolvepassiccly.. πα]κο latype galaxies with active star formation.," That is, most early-type galaxies seem to evolve, unlike late-type galaxies with active star formation."596 Ilowever. since Abrahametal.(1999) and Menafeatetal.(1999) found a considerale fracticπι of early-type galaxies with blue cokDES and evidence of current star-forination in he IIlubble Deep Field (Willamsctal.1996).. he existence of (lereatCY. BEGs) has become a new nmuportaut factor to be coidered iu the formation scenario of," However, since \citet{abr99} and \citet{men99} found a considerable fraction of early-type galaxies with blue colors and evidence of current star-formation in the Hubble Deep Field \citep{wil96}, the existence of (hereafter, BEGs) has become a new important factor to be considered in the formation scenario of"5973efore discussing the results of the global. turbulent disc simulations. we present the results of some simulations designed to calibrate the code.,"Before discussing the results of the global turbulent disc simulations, we present the results of some simulations designed to calibrate the code."598 In particular. we will examine the role that gravitational softening of the. protoplanet eravitational potential has on the migration time in laminar disce simulations.," In particular, we will examine the role that gravitational softening of the protoplanet gravitational potential has on the migration time in laminar disc simulations."599 The migration time of à non gap forming protoplanet embedded in a three dimensional cise has been calculated using a linear analysis by Tanaka. Takeuchi. Ward (2002).," The migration time of a non gap forming protoplanet embedded in a three dimensional disc has been calculated using a linear analysis by Tanaka, Takeuchi, Ward (2002)."600" ""They derive the following expression for the migration time ofa protoplanet embedded in a locally isothermal disc with a power law surface density. profile: llere. M, is the surface density at the. position of the protoplanet. , is the Ixeplerian. angular velocity of the protoplanet. ce is the sound speed in the disc at the protoplanet position. ancl > is the power law index for the racial surface density. distribution."," They derive the following expression for the migration time of a protoplanet embedded in a locally isothermal disc with a power law surface density profile: Here $\Sigma_p$ is the surface density at the position of the protoplanet, $\Omega_p$ is the Keplerian angular velocity of the protoplanet, $c$ is the sound speed in the disc at the protoplanet position, and $- \gamma$ is the power law index for the radial surface density distribution."601 These authors comment that in general this expression gives a migration time that is a [actor of between 2 3λ times slower than similar expressions derived for flat. twodimensional clises (e.g. Ware 1997).," These authors comment that in general this expression gives a migration time that is a factor of between 2 – 3 times slower than similar expressions derived for flat, two–dimensional discs (e.g. Ward 1997)."602 The finite clise thickness thus acts to soften the disc.planet. gravitational interaction., The finite disc thickness thus acts to soften the disc–planet gravitational interaction.603 The global turbulent disc simulations presented: here use evlindrical disc models in which the vertical component of gravity is neglected. and thus the full three dimensional structure of the disc is not. modeled.," The global turbulent disc simulations presented here use cylindrical disc models in which the vertical component of gravity is neglected, and thus the full three dimensional structure of the disc is not modeled."604 In the limit of a laminar disc. the cvlindrical cise can be viewed as a series of two dimensional disces stacked. on top of one another. providing the protoplanet. gravitational potential is also cvlindrical. (ie. no vertical component).," In the limit of a laminar disc, the cylindrical disc can be viewed as a series of two dimensional discs stacked on top of one another, providing the protoplanet gravitational potential is also cylindrical (i.e. no vertical component)."605 Civen hat gravitational softening of the protoplanet potential is emploved. we are interested in (7) How Large a gravitational softening is required in a two dimensional disc simulation o obtain agreement with equation 1: (4) What is the deviation from equation 1. obtained for dillering softening xwameters.," Given that gravitational softening of the protoplanet potential is employed, we are interested in ) How large a gravitational softening is required in a two dimensional disc simulation to obtain agreement with equation \ref{ward-tmig}; ) What is the deviation from equation \ref{ward-tmig} obtained for differing softening parameters."606 In order to address these points a number of wo dimensional simulations using laminar. viscous a disces ve been performed with varving physical ancl softening XUOelers.," In order to address these points a number of two dimensional simulations using laminar, viscous $\alpha$ –discs have been performed with varying physical and softening parameters."607 Figure 1 shows the migration time for a series of models in which protoplanets of dillering masses were placed in a ootostellar dise model and. the torque of the disc acting on the protoplanet was calculated., Figure \ref{fig1} shows the migration time for a series of models in which protoplanets of differing masses were placed in a protostellar disc model and the torque of the disc acting on the protoplanet was calculated.608" These torques were then used to caleulate a migration time using the expression where j, is the specific angular momentum of the", These torques were then used to calculate a migration time using the expression where $j_p$ is the specific angular momentum of the6092011).,.610. The star V311 Lvr (KIC 7659570) is a SU UMA star that lies iu the field., The star V344 Lyr (KIC 7659570) is a SU UMa star that lies in the field.611 ato(1995). observed. the star during a superoutburst (V—L1). and reported the detection of superhunips with a period 7=2.191840.0005 hr.," \citet{kato93} observed the star during a superoutburst $V\sim14$ ), and reported the detection of superhumps with a period $P = 2.1948\pm 0.0005$ hr."612 Iu a later study Natoetal.(2002). reported that the DN outbursts have a recurrence timescale of 1643 d. and that the superoutbursts have a recuenuce timescale of ~110 d. Aketal.(2008)/— estimated a distance of 619 pe for the star using a period-Inuinosity relatiouship.," In a later study \citet{kato02} reported that the DN outbursts have a recurrence timescale of $16\pm3$ d, and that the superoutbursts have a recurrence timescale of $\sim$ 110 d. \citet{ak08} estimated a distance of 619 pc for the star using a period-luminosity relationship."613 Tn Paper I we reported prelaminary findings for Χο Lyr based on the second-quarter (Q2) observations. during which observed the star with a —1-1n cadence. obtaining over 123.000 photometric measurements.," In Paper I we reported preliminary findings for V344 Lyr based on the second-quarter (Q2) observations, during which observed the star with a $\sim$ 1-min cadence, obtaining over 123,000 photometric measurements."614 In that paper we reported on a periodic signal at quiescence that was either the orbital or negative superhunp period. aud the fact that the positive πρη signal persisted iuto quiescence aud through the following dwarf nova outburst.," In that paper we reported on a periodic signal at quiescence that was either the orbital or negative superhump period, and the fact that the positive superhump signal persisted into quiescence and through the following dwarf nova outburst."615 Tn Cannizzootal.(2010.hereafterPaperID we preseuted time-dependent modelius based on the accretion disk limit cvele model for the 270 d (Q2OI) light curve of V311. Lyr., In \citet[hereafter Paper II]{cannizzo10} we presented time-dependent modeling based on the accretion disk limit cycle model for the 270 d (Q2--Q4) light curve of V344 Lyr.616.. We reported that. the nain decay of the superoutbursts is ucarly perfectly exponeutial decaving at a rate of —12 d 5|. aud hat the normal outbursts displav a decay. rate that is aster-than-exponcutial.," We reported that the main decay of the superoutbursts is nearly perfectly exponential, decaying at a rate of $\sim$ 12 d $^{-1}$, and that the normal outbursts display a decay rate that is faster-than-exponential."617 In addition. we noted that the wo superoutbursts are initiated by a normal outburst.," In addition, we noted that the two superoutbursts are initiated by a normal outburst."618 Using the standard accretion disk ludit evele model. we were able to reproduce the main features of the outburst ight curve of V311I Lyr.," Using the standard accretion disk limit cycle model, we were able to reproduce the main features of the outburst light curve of V344 Lyr."619 We significantly: expand on this in Caunizzoctal(2011) where we preseut the l-vear outburst properties of both οι Lar aud V1501L Cre (Canuizzo et 22011)., We significantly expand on this in \citet{cannizzo11} where we present the 1-year outburst properties of both V344 Lyr and V1504 Cyg (Cannizzo et 2011).620 Iu this work. we report in detail ou the results obtained by studviue the Q2Ql data. which comprise without question the sinele-best data set obtained to-date from a cataclysmic variable star.," In this work, we report in detail on the results obtained by studying the Q2–Q4 data, which comprise without question the single-best data set obtained to-date from a cataclysmic variable star."621 The data set reveals signals from the orbital period as well as frou positive aud negative superlumps., The data set reveals signals from the orbital period as well as from positive and negative superhumps.622 Before digging into the data. we brefle review the physical processes that lead to the photometric modulations termed superlinnups.," Before digging into the data, we briefly review the physical processes that lead to the photometric modulations termed superhumps."623 The accretion disk of a typical dwarf nova CV that is in quiescence has a low disk viscosity and so inefficient exchange of angular momentum., The accretion disk of a typical dwarf nova CV that is in quiescence has a low disk viscosity and so inefficient exchange of angular momentum.624 As a result. the mass transfer rate η through the inner Lagrange poiut L1 is lugher than the mass transfer rate M4 oute the primary.," As a result, the mass transfer rate $\dot M_{\rm L1}$ through the inner Lagrange point L1 is higher than the mass transfer rate $\dot M_1$ onto the primary."625" ""Thus. mass acciunimlates iu the disk wutil a critical surface density is reached at some anuulus. aud the fluicl im that anuulus transitions to a high-viscosity state (C'anuizzo1998:Canuizzoctal. 2010)."," Thus, mass accumulates in the disk until a critical surface density is reached at some annulus, and the fluid in that annulus transitions to a high-viscosity state \citep{cannizzo98,cannizzo10}."626. This hieh-viscositv state propagates inward and/or outward in radius until the entire disk is iu a high-viscosity state characterized by very officicut angular momenta and mass trausport he standard DN outburst (see.ce.CanuizzoL993a:Lasota2001.for reviews)..," This high-viscosity state propagates inward and/or outward in radius until the entire disk is in a high-viscosity state characterized by very efficient angular momentum and mass transport -- the standard DN outburst \citep[see, e.g.,][for627reviews]{cannizzo93,lasota01}."628 In this state. M4>AL aud the disk draius mass outo the primary white chart.," In this state, $\dot M_1 > \dot M_{\rm629L1}$ and the disk drains mass onto the primary white dwarf."630 During cach DN outburst. however. the aneular momentum transport acts to expand the outer disk radius slightly. aud after a few to several of these. au otherwise normal DN outburst can expaud the outer radius of the disk to the inner Lindblad resonance (near the 3:1 corotation resonance).," During each DN outburst, however, the angular momentum transport acts to expand the outer disk radius slightly, and after a few to several of these, an otherwise normal DN outburst can expand the outer radius of the disk to the inner Lindblad resonance (near the 3:1 corotation resonance)."631 This can oulv occur for systems with mass ratios g=Ah/Ay&0.35 (Woodctal.2009)., This can only occur for systems with mass ratios $q=M_2/M_1 \lesssim 0.35$ \citep{wts09}.632. Ouce sufficient mass is present at the resonance radius. the conunon superlinup oscillation mode can be driven to amplitudes that vield photometric oscillations.," Once sufficient mass is present at the resonance radius, the common superhump oscillation mode can be driven to amplitudes that yield photometric oscillations."633" The superliunp oscillation has a period P, which is a few percent longer than the orbital period. where the ει is defined as These are the are the so-called or superhunips. where the latter term reflects the sien of the period excess ει."," The superhump oscillation has a period $P_+$ which is a few percent longer than the orbital period, where the $\epsilon_+$ is defined as These are the are the so-called or superhumps, where the latter term reflects the sign of the period excess $\epsilon_+$."634 Iu addition to the SU UMua stars. positive superhuunips have also been observed in uovalike CVs (Pattersonetal.1993:Retter1997:Skilhnanetal.1997:Patterson2005:Iia 2009).. the interacting binary white dwart AM CV stars (Pattersonal.2007:Fontaineet 2011).. aud iu low-1ass binaries (Charlesetal.1991:Mineshige1992:etal.2006).," In addition to the SU UMa stars, positive superhumps have also been observed in novalike CVs \citep{pattersonea93b,retterea97,skillmanea97,patterson05,kim09}, the interacting binary white dwarf AM CVn stars \citep{pattersonea93a,warner95amcvn,nelemans05,roelofs07,fontaine11}, and in low-mass X-ray binaries \citep{charlesea91,mho92,oc96,retterea02,hynesea06}."635. Figure 1 shows snapshots from one full orbit of a xmoothed. particle bydrodvuamics (SPIT) simulation (q=0.25. 100.000 particles) as well as the associated simulation light curve (secSimpson&Wood1998:&Burke2007:Woodetal. 2009).," Figure \ref{fig: sph+} shows snapshots from one full orbit of a smoothed particle hydrodynamics (SPH) simulation $q=0.25$, 100,000 particles) as well as the associated simulation light curve \citep[see][]{sw98,wb07,wts09}."636. The disk particles are color-coded by the chauge in internal cucrey over the previous timestep. and the Roche lobes auc positions of M1 are also shown.," The disk particles are color-coded by the change in internal energy over the previous timestep, and the Roche lobes and positions of $M_1$ are also shown."637 Panels 1 aud 6 of Figure 1. shows the econmietry of the disk at πηρα maxinuun., Panels 1 and 6 of Figure \ref{fig: sph+} shows the geometry of the disk at superhump maximum.638 Note that here the ΕΕΠΕ lieht source is viscous dissipation resulting from the compression of the disk opposite the secondary star., Note that here the superhump light source is viscous dissipation resulting from the compression of the disk opposite the secondary star.639 The local ceusity aud shear in this region are both high. leading to cuhanced viscous dissipation in the stronglv couvergcut flows.," The local density and shear in this region are both high, leading to enhanced viscous dissipation in the strongly convergent flows."640 The orbit sampled iu he Figure is characteristic of carly superlauups where he disk oscillation mode is saturated. aud the resulting wuplitude significantly higher (—0.15 mae) than the uodels produce when dynamical equilibrium (~0.03 nag) due to the lower mean euecrgv production iu the nodels at «ΙΙπα ouset.," The orbit sampled in the Figure is characteristic of early superhumps where the disk oscillation mode is saturated, and the resulting amplitude significantly higher $\sim$ 0.15 mag) than the models produce when dynamical equilibrium $\sim$ 0.03 mag) due to the lower mean energy production in the models at superhump onset."641" As a further detail we uote that whereas the 2 spiral dissipation waves are stationary in the co-rotating rane before the onset of the superlaunp oscillation. ouce the oscillation begins. the spiral armis advance in the prograde direction by —180"" in the co-rotating rene during cach superhuup cycle."," As a further detail, we note that whereas the 2 spiral dissipation waves are stationary in the co-rotating frame before the onset of the superhump oscillation, once the oscillation begins, the spiral arms advance in the prograde direction by $\sim$ $^\circ$ in the co-rotating frame during each superhump cycle."642 This progracde advancement cau be seen by careful inspection of the xuiels in Figure 1.., This prograde advancement can be seen by careful inspection of the panels in Figure \ref{fig: sph+}.643 Indeed. this motion of the spiral dissipation waves is central to the superliuup oscillation a spiral arin is “cast” outward as it rotates through he tidal field of the secondary. and then brighteus shortly afterward as it compresses back iuto the disk iu a converging flow (Siuithetal.2007:Wood 2009)..," Indeed, this motion of the spiral dissipation waves is central to the superhump oscillation – a spiral arm is “cast” outward as it rotates through the tidal field of the secondary, and then brightens shortly afterward as it compresses back into the disk in a converging flow \citep{smith07,wts09}. ."644 While viscous dissipation within the periodically- disk provides the dominant source of the, While viscous dissipation within the periodically-flexing disk provides the dominant source of the645when (he ionized regions of the intergalactic medium become multiply connected provides a robust criterion for assessing (he progress οἱ reionization.,when the ionized regions of the intergalactic medium become multiply connected provides a robust criterion for assessing the progress of reionization.646 Clustering of galaxies can resull in bubbles containing multiple ionizing sources even al verv early (mes. and recent work ias highlighted the importance of such effects on ionized bubble sizes (Wyithe Loeb 2005: Furlanetto. Zaldarriaga. ILernequist 2004: Furlanetto Oh 2005).," Clustering of galaxies can result in bubbles containing multiple ionizing sources even at very early times, and recent work has highlighted the importance of such effects on ionized bubble sizes (Wyithe Loeb 2005; Furlanetto, Zaldarriaga, Hernquist 2004; Furlanetto Oh 2005)."647 SUH. many bubbles nist om independently in (he early phases of reionization. ancl must merge before the universe achieves the high level of ionization seen al all redshifts 2«6.," Still, many bubbles must form independently in the early phases of reionization, and must merge before the universe achieves the high level of ionization seen at all redshifts $z < 6$."648 Thus. an overlap pliase is an inevitable part of the reionizalion process.," Thus, an overlap phase is an inevitable part of the reionization process."649 The spatial distribution of neutral and ionized regions during reionization can be studied witli a wide range of statistics., The spatial distribution of neutral and ionized regions during reionization can be studied with a wide range of statistics.650 Considerable attention has been given already to quantitatively characterizing the size distribution of ionized bubbles (Furlanetto et al 2004: Furlanetto Oh 2005) and the power spectrum of the neutral hyedrogen distribution. as traced by 2lem enission (see early work by Macau. Meiksin. Rees 1997; Gnedin Ostriker 1997: Shaver et al 1999: Tozzi et al 2000: and the recent review by Furlanetto. Oh. Briges 2006).," Considerable attention has been given already to quantitatively characterizing the size distribution of ionized bubbles (Furlanetto et al 2004; Furlanetto Oh 2005) and the power spectrum of the neutral hydrogen distribution, as traced by 21cm emission (see early work by Madau, Meiksin, Rees 1997; Gnedin Ostriker 1997; Shaver et al 1999; Tozzi et al 2000; and the recent review by Furlanetto, Oh, Briggs 2006)."651 Here. we sueeest (he application of a quantitative topological statistic. (he genus number. to the ionized / neutral interlace during reionization.," Here, we suggest the application of a quantitative topological statistic, the genus number, to the ionized / neutral interface during reionization."652 This will allow us to study properties of the distribution that are not retained by the other statistics., This will allow us to study properties of the distribution that are not retained by the other statistics.653 Testing topology depends on the dimensionalitv of the data available., Testing topology depends on the dimensionality of the data available.654" Given a (wo pliase medium in (του dimensions. il is possible for either one of the (wo phases to percolate: this is (he ""spongelike"" topology that Gott. Melott. Dickinson (1986) predicted for (he cosmic density field."," Given a two phase medium in three dimensions, it is possible for either one of the two phases to percolate; this is the “spongelike” topology that Gott, Melott, Dickinson (1986) predicted for the cosmic density field."655 In a Gwo-dimensional space. al most one phase can percolate. while in one dimension. both phases are necessarily broken into a set of disjoint regions.," In a two-dimensional space, at most one phase can percolate, while in one dimension, both phases are necessarily broken into a set of disjoint regions."656 Large scale structures have been studied with the three-climensional genus curve statistic (Gott. Melott. Dickinson 1986 [GMD]: Hamilton. Gott. Weinberg 1986 ΠΟΝΤ) and its (two-dimensional analog (Melott et al L989 [M89]).," Large scale structures have been studied with the three-dimensional genus curve statistic (Gott, Melott, Dickinson 1986 [GMD]; Hamilton, Gott, Weinberg 1986 [HGW]) and its two-dimensional analog (Melott et al 1989 [M89])."657 The conventional Gunn-Peterson test. provides a one dimensional section through the IGM along the line of sight to a bright quasar., The conventional Gunn-Peterson test provides a one dimensional section through the IGM along the line of sight to a bright quasar.658 Ionized cavities of size ZIpMpce in the IGM will produce sections of spectrum will ooptical depths ΤιZ1. which can be easily identified. (," Ionized cavities of size $\ga 1 \pMpc$ in the IGM will produce sections of spectrum with optical depths $\tlya \la 1$, which can be easily identified. ("659Throughout the paper we denote a physical MIpe by pMpe and comoving megaparsec by eMpe: IpMpe(1+ z)eMpe.),Throughout the paper we denote a physical Mpc by $\pMpc$ and comoving megaparsec by $\cMpc$; $1 \pMpc = (1+z) \cMpc$ .)660" Given enough continu, sources al 2>z,. we could determine the volume traction of ionized gas as a function of redshift."," Given enough continuum sources at $z > \zre$, we could determine the volume fraction of ionized gas as a function of redshift."661 However. the surface densitv of suitably bright continuum sources is much (oo low to expect information on multiple sight lines through anv single ionized bubble.," However, the surface density of suitably bright continuum sources is much too low to expect information on multiple sight lines through any single ionized bubble."662 Fortunately. other probes of reionization exist and can more naturally provide (wo- and," Fortunately, other probes of reionization exist and can more naturally provide two- and"663validity of using the strength of the 10 jum silicate feature to trace the sizes of grains in the surfaces of disks.,validity of using the strength of the 10 $\mu$ m silicate feature to trace the sizes of grains in the surfaces of disks.664 The left panel of Figure 10 shows the correlation between (dwarm) and S for all 4 samples.," The left panel of Figure \ref{f_s10_2} shows the correlation between $\langle a_{\rm warm} \rangle$ and $S^{10\mu{\rm665 m}}_{{\rm peak}}$ for all 4 samples."666" The Kendall 7 coefficient of -0.29, P — 0.01 supports the effectiveness of S as a proxy for grain ""Msizes, with. smaller values of S1 implying larger grain sizes."," The Kendall $\tau$ coefficient of -0.29, $P$ = 0.01 supports the effectiveness of $S^{10\mu{\rm m}}_{{\rm peak}}$ as a proxy for grain sizes, with smaller values of $S^{10\mu{\rm m}}_{{\rm peak}}$ implying larger grain sizes."667" On the other hand, it is also possible to test how the degree of crystallinity can influence the strength of the 10 jm silicate feature."," On the other hand, it is also possible to test how the degree of crystallinity can influence the strength of the 10 $\mu$ m silicate feature."668" The lack of correlation between Cwarm and S (r — -0.07, P — 0.14), shown in the right panel of Figure 10 for all samples, supports that the degree of crystallinity is not the dominant parameter setting the strength of the 10 jm silicate feature."," The lack of correlation between $C_{\rm warm}$ and $S^{10\mu{\rm m}}_{{\rm peak}}$ $\tau$ = -0.07, $P$ = 0.14), shown in the right panel of Figure \ref{f_s10_2} for all samples, supports that the degree of crystallinity is not the dominant parameter setting the strength of the 10 $\mu$ m silicate feature."669 These results argue against the results of Sargentetal.(2009) that find a high crystallinity fraction and small grains fitting low strengths of the 10 jum silicate feature., These results argue against the results of \citet{ST09} that find a high crystallinity fraction and small grains fitting low strengths of the 10 $\mu$ m silicate feature.670" Although it may be possible to fit a few spectra with a certain prescription, a good model should be able to explain the robust relationship between the strength and shape of the 10 ym silicate feature observed for large numbers of disks."," Although it may be possible to fit a few spectra with a certain prescription, a good model should be able to explain the robust relationship between the strength and shape of the 10 $\mu$ m silicate feature observed for large numbers of disks."671" Despite the many processes able to change the shape or the strength of this feature, only grain size has so far demonstrated capability to explain the observed trend."," Despite the many processes able to change the shape or the strength of this feature, only grain size has so far demonstrated capability to explain the observed trend."672 Our conclusion is that S and dust sizes are appropriately correlated.," Our conclusion is that $S^{10\mu{\rm m}}_{{\rm673 peak}}$ and dust sizes are appropriately correlated."674 Dust composition results are available in the literature for the disks in Taurus and η Cha (see Table 4 for an overview)., Dust composition results are available in the literature for the disks in Taurus and $\eta$ Cha (see Table \ref{t_lit} for an overview).675" Sicilia-Aguilaretal.(2009) present their analysis in η Cha considering the same 5 dust species and three grain sizes (enstatite in their model is the only species for which only the 2 smaller grain sizes are but for a distribution of temperatures derivedconsidered), using the Two Layer Temperature Distribution (TLTD, Juhászetal.2009)) decomposition procedure."," \citet{SI09} present their analysis in $\eta$ Cha considering the same 5 dust species and three grain sizes (enstatite in their model is the only species for which only the 2 smaller grain sizes are considered), but for a distribution of temperatures derived using the Two Layer Temperature Distribution (TLTD, \citealt{JU09}) ) decomposition procedure."676" For the same 4 objects, their mean amorphous fraction is 80.1 + 9.3 %."," For the same 4 objects, their mean amorphous fraction is 80.1 $\pm$ 9.3 ."677. This result is consistent with the 82.8 + 12.9 mean amorphous fraction found here., This result is consistent with the 82.8 $\pm$ 12.9 mean amorphous fraction found here.678 The mean crystalline fractions derived are 18.4 + 10.7 with TLTD and 17.1 + 12.8 derived here., The mean crystalline fractions derived are 18.4 $\pm$ 10.7 with TLTD and 17.1 $\pm$ 12.8 derived here.679 Sargentetal.(2009) present their decomposition procedure for 65 YSOs in Taurus., \citet{ST09} present their decomposition procedure for 65 YSOs in Taurus.680" This method also takes into consideration a warm and a cold temperature, and makes use of two amorphous species (olivine and pyroxene) with two grain sizes (small and large), and 3 crystalline species (enstatite, forsterite and crystalline silica) of a single size."," This method also takes into consideration a warm and a cold temperature, and makes use of two amorphous species (olivine and pyroxene) with two grain sizes (small and large), and 3 crystalline species (enstatite, forsterite and crystalline silica) of a single size."681" Their mean warm amorphous fraction is 82.9 + 19.3 and warm crystalline fraction is 17.1+19.3 96, while here the derived fractions are 89.0 + 6.6 and 10.9 + 6.6 for the warm amorphous and crystalline fractions, respectively."," Their mean warm amorphous fraction is 82.9 $\pm$ 19.3 and warm crystalline fraction is $17.1 \pm 19.3$ , while here the derived fractions are 89.0 $\pm$ 6.6 and 10.9 $\pm$ 6.6 for the warm amorphous and crystalline fractions, respectively."682" For the cold component, Sargentetal.(2009) derive à mean cold amorphous fraction of 77.3 - 19.9 and cold crystalline fraction of 22.6 + 19.9%,, while here the values are 85.9 + 10.6 and 13.9 + 10.5%,, respectively."," For the cold component, \citet{ST09} derive a mean cold amorphous fraction of 77.3 $\pm$ 19.9 and cold crystalline fraction of 22.6 $\pm$ 19.9, while here the values are 85.9 $\pm$ 10.6 and 13.9 $\pm$ 10.5, respectively."683 The consistently lower amorphous (higher crystalline) fractions found by Sargentetal.(2009) could be a result of their choice to use silica in crystalline rather than amorphous form (as used here)., The consistently lower amorphous (higher crystalline) fractions found by \citet{ST09} could be a result of their choice to use silica in crystalline rather than amorphous form (as used here).684" Section 4 has shown that the disk populations in the four regions presented here, young and older, have very similar distributions in the two main dust parameters: grain size and composition."," Section \ref{sres} has shown that the disk populations in the four regions presented here, young and older, have very similar distributions in the two main dust parameters: grain size and composition."685 The large number of objects in the two young regions studied occupy a region in parameter space of either grain size or crystallinity fraction that is also populated by the small number of older disks., The large number of objects in the two young regions studied occupy a region in parameter space of either grain size or crystallinity fraction that is also populated by the small number of older disks.686" The grain sizes derived for the cold component never reach the biggest grain size modeled (6 ym), different from the warm component results that span the entire range in sizes."," The grain sizes derived for the cold component never reach the biggest grain size modeled (6 $\mu$ m), different from the warm component results that span the entire range in sizes."687" The crystallinity fraction does not seem to be correlatedwith mean grain size, warmor cold."," The crystallinity fraction does not seem to be correlatedwith mean grain size, warmor cold."688" Whatever processes are responsible for the crystallization of the initially amorphous grains, they"," Whatever processes are responsible for the crystallization of the initially amorphous grains, they"689models 1n a future study.,models in a future study.690 In the LIS model the mechanism responsible for the flare emission is the synchrotron radiation from relativistic electrons accelerated in the shocks., In the LIS model the mechanism responsible for the flare emission is the synchrotron radiation from relativistic electrons accelerated in the shocks.691 An additional radiation mechanism that may also play an important role is the synchrotron self Compton (SSC) emission. Le. the up-scattering of the synchrotron photons by the same relativistic electrons to much higher energies.," An additional radiation mechanism that may also play an important role is the synchrotron self Compton (SSC) emission, i.e. the up-scattering of the synchrotron photons by the same relativistic electrons to much higher energies."692 The synchrotron and SSC components from IS have been considered in the context of the prompt emission by Guetta&Granot(2003)., The synchrotron and SSC components from IS have been considered in the context of the prompt emission by \citet{guetta03}.693 Following Guetta&Granot(2003).. we estimate in this work the high energy emission produced by SSC of the X-ray flare photons.," Following \citet{guetta03}, we estimate in this work the high energy emission produced by SSC of the X-ray flare photons."694 As noted by several authors. e.g. Wangetal.(2000... Fanetal.(2007) and Galli&Piro(2007). the detection of the predicted high energy (MeV to GeV) flare emission by observations with AGILE and GLAST combined with the X-ray flares detection by would enable us to check the validity of different models proposed to explain the afterglow phenomenology of GRBs.," As noted by several authors, e.g. \citet{wang06}, \citet{fan07} and \citet{galli07}, the detection of the predicted high energy (MeV to GeV) flare emission by observations with AGILE and GLAST combined with the X-ray flares detection by would enable us to check the validity of different models proposed to explain the afterglow phenomenology of GRBs."695 The paper is organized as follows., The paper is organized as follows.696 In Sect., In Sect.697 2 we report the AGILE and GLAST sensitivities., 2 we report the AGILE and GLAST sensitivities.698 In Sect., In Sect.699 3 we summarize the calculations of the synchrotron and SSC spectra in Guetta&Granot(2003) for the prompt emission and provide the expression for the peak energy and the flux normalization., 3 we summarize the calculations of the synchrotron and SSC spectra in \citet{guetta03} for the prompt emission and provide the expression for the peak energy and the flux normalization.700 In Sect., In Sect.701 4 we show how the peak energies and flux normalization change for X-ray flares and estimate the high energy flare fluxes., 4 we show how the peak energies and flux normalization change for X-ray flares and estimate the high energy flare fluxes.702 Finally in Sect., Finally in Sect.703 5 we give our summary and conclusions., 5 we give our summary and conclusions.704 In this section we present an estimate of the sensitivity of the high energy detectors aboard the AGILE and GLAST satellites., In this section we present an estimate of the sensitivity of the high energy detectors aboard the AGILE and GLAST satellites.705 This is necessary to assess the detectability of high energy emission during the prompt and flare phases of GRB we calculate in the following sections., This is necessary to assess the detectability of high energy emission during the prompt and flare phases of GRB we calculate in the following sections.706 The AGILE satellite is equipped with the GRID (Gamma-Ray Imaging Detector) instrument operating between 30MeV and 50GeV., The AGILE satellite is equipped with the GRID (Gamma-Ray Imaging Detector) instrument operating between $30~MeV$ and $50~GeV$.707 We estimate the GRID sensitivity by adopting the criterion that a detection is made when at least 5 photons are collected by the detector (Zhang&Meszaros2001)., We estimate the GRID sensitivity by adopting the criterion that a detection is made when at least 5 photons are collected by the detector \citep{zhang01}.708 According to Galli&Piro(2007) when the detector is source dominated. the detection threshold ts given by: where E is the photon energy. Αν 1s the effective area of the detector at this energy. and Τη 1s the detector integration time.," According to \citet{galli07} when the detector is source dominated, the detection threshold is given by: where $E$ is the photon energy, $A_{eff}$ is the effective area of the detector at this energy, and $T_{int}$ is the detector integration time."709" For 75,250 s the GRID is source dominated. thus we estimate the GRID sensitivity using the equation above."," For $T_{int}$ =50 s the GRID is source dominated, thus we estimate the GRID sensitivity using the equation above."710" In calculating the GRID sensitivity we assume its effective area to be A,;;=550eni throughout the energy range.", In calculating the GRID sensitivity we assume its effective area to be $A_{eff}=550~cm^{2}$ throughout the energy range.711 The Large Area Telescope (LAT) aboard GLAST (Gamma-ray Large Area Telescope) observes between 30 MeV and 300 GeV. The LAT effective wea varies with energy in all the band: we take the value of the effective area at different energies from the LAT web page. glast.slac.stanford.edu/software/IS/glast.pperformance.htm.," The Large Area Telescope (LAT) aboard GLAST (Gamma-ray Large Area Telescope) observes between 30 MeV and 300 GeV. The LAT effective area varies with energy in all the band; we take the value of the effective area at different energies from the LAT web page, performance.htm."712" As shown by Galli&Piro(2007) for an integration time Tin,=50 s. the LAT is source dominated at all energies. thus we can estimate its sensitivity using Eq. 1."," As shown by \citet{galli07} for an integration time $T_{int}=50$ s, the LAT is source dominated at all energies, thus we can estimate its sensitivity using Eq. \ref{soglia}."713 In this section we estimate the synchrotron and SSCemission in the framework of the IS model. following the prescriptions presented in Guetta&Granot(2003).," In this section we estimate the synchrotron and SSCemission in the framework of the IS model, following the prescriptions presented in \citet{guetta03}."714". In this model the flow Lorentz factor E is assumed to vary on a typical time scale 4, and with an amplitude oP~Γ.", In this model the flow Lorentz factor $\Gamma$ is assumed to vary on a typical time scale $t_v$ and with an amplitude $\delta \Gamma \sim \Gamma$.715" The shells collide at a radius 6x10T3ον. em. where P25=Γ/{10- and t,=(./(107s)."," The shells collide at a radius $R \approx 2\Gamma^2ct_v=6 \times 10^{13} \Gamma^2_{2.5}t_{v,-2}$ cm, where $\Gamma_{2.5}=\Gamma/10^{2.5}$ and $t_{v,-2}=t_v/(10^{-2}s)$ ."716 The internal energy released in each collision is distributed among electrons. magnetic field and protons with fractions &. eg and (1—€) respectively.," The internal energy released in each collision is distributed among electrons, magnetic field and protons with fractions $\epsilon_e$, $\epsilon_B$ and $(1-\epsilon_e)$ respectively."717" The electrons are accelerated in the shocks to a power law distribution of energy N(y)«y. and radiatively cool by the combination of synchrotron and SSC processes. the timescales of which are ESποσιBry and tssc=fa4/Y. the combined cooling time being ο V/tsscY tss/(E+Y). where B is the magnetic field. and Y is the Compton y-parameter (Sarietal.1996). Y=€,/ep for e,<<eg and Y=(eeg)7 for e&>>ep «Της synchrotron spectrum ts where vy. v,. and va; are defined in Guetta&(2003) and the synchrotron peak energy is given by: for p2 2.5."," The electrons are accelerated in the shocks to a power law distribution of energy $N(\gamma) \propto \gamma^{-p}$, and radiatively cool by the combination of synchrotron and SSC processes, the timescales of which are $t_{syn} \sim 6 \pi m_ec/\sigma_T B^{2}\gamma$ and $t_{SSC}=t_{syn}/Y$, the combined cooling time being $t_c=(1/t_{syn}+1/t_{SSC})^{-1}$ $t_{syn}/(1+Y)$, where $B$ is the magnetic field, and $Y$ is the Compton y-parameter \citep{sari96}$ $, Y \approx \epsilon_e/\epsilon_B$ for $\epsilon_e << \epsilon_B$ and $Y \approx (\epsilon_e/\epsilon_B)^{1/2}$ for $\epsilon_e >> \epsilon_B$ .The synchrotron spectrum is where $\nu_{sa}$ , $\nu_{ac}$ and $\nu_M$ are defined in \citet{guetta03} and the synchrotron peak energy is given by: for $p=2.5$ ."718 From the normalization condition we find the flux at the peak of the spectrum to be: where Day is the burst distance in unityof 1075 em., From the normalization condition we find the flux at the peak of the spectrum to be: where $D_{28}$ is the burst distance in unityof $10^{28}$ cm.719 The SSC spectrum is given by where νο. 3f. and vj. are defined in and the SSC peak energy ts:," The SSC spectrum is given by where $\nu_{sa}^{SC}$ , $\nu_M^{SC}$ and $\nu_{KN}^{SC}$ are defined in \citet{guetta03} and the SSC peak energy is:"720"does not allow to account for this configuration, and we need an external asymmetry.","does not allow to account for this configuration, and we need an external asymmetry."721" There is, in fact, a nearby group at about 38” South-West, and at redshift zgroup=0.7+0.1 that can be the origin of this external perturbation."," There is, in fact, a nearby group at about $38''$ South-West, and at redshift $z_{group}=0.7{\pm} 0.1$ that can be the origin of this external perturbation."722" (Hjortetal.2002) measured the time delay obtaining the results Atga,=—143+6days, Atga,=—149+6days and Atga,=—154+16days."," \cite{Hjorth02} measured the time delay obtaining the results $\Delta t_{BA_{1}}=-143 {\pm} 6 \hspace{0.1 cm}723\textrm{days}$, $\Delta t_{BA_{2}}=-149 {\pm} 6 \hspace{0.1 cm}724\textrm{days}$ and $\Delta t_{BA_{3}}=-154 {\pm} 16 \hspace{0.1725cm} \textrm{days}$."726" It is also possible to observe a second galaxy near the main one, that can affect the modelling."," It is also possible to observe a second galaxy near the main one, that can affect the modelling."727 In the following we present the main results of the application of our codes:, In the following we present the main results of the application of our codes:728al..,"al.,"729 along with the maximum likelihood solution by Fan ct al., along with the maximum likelihood solution by Fan et al.730 For z=4.0 Fan et al., For $z=4.0$ Fan et al.731 give pMap(1450)€56.60]=S.044.6 7. compared to 12.5€5.6 ?5 in this work.," give $\rho [M_{\rm AB} (1450) \le -26.6] = 8.0 \pm 4.6$ $^{-3}$ , compared to $12.5 \pm 5.6$ $^{-3}$ in this work."732 These two values are consistent. within the errors.," These two values are consistent, within the errors."733 A sample of 94 radio-emitting OQSO candidates has been derived by cross-correlating the FIRST survey. APM POSS-] and the SDSS photometric survey. selecting objects with Ec 19.1. οEc2. and starlike in SDSS.," A sample of 94 radio-emitting QSO candidates has been derived by cross-correlating the FIRST survey, APM POSS-I and the SDSS photometric survey, selecting objects with $E \le$ 19.1, $O-E \ge7342$, and starlike in SDSS."735 78 of the 94 sources (83 per cent) are spectroscopically classified. mainly from SDSS. but also from the literature and. from PNG spectroscopy. presented. here (13. sources).," 78 of the 94 sources (83 per cent) are spectroscopically classified, mainly from SDSS, but also from the literature and from TNG spectroscopy presented here (13 sources)."736 The. classified sources include 51 QSOs. with redshifts 0.27 <2« 4.31.," The classified sources include 51 QSOs, with redshifts 0.27 $< z737<$ 4.31."738 Our main results are as follows: ) The eflicicney of selection of high-redshift QSOs is 23/78 = 29 per cent for zc3. and 10/78 = 13 per cent for 2z3.7. comparable to that for previous searches. for high-redshift QSOs at much radio Lux densities. ," Our main results are as follows: (i) The efficiency of selection of high-redshift QSOs is 23/78 = 29 per cent for $z \ge 3$, and 10/78 = 13 per cent for $z \ge 3.7$, comparable to that for previous searches for high-redshift QSOs at much radio flux densities. ("739ii) We found no 3.7 «z 4.4 QSOs wilh2«O0.E« 3. supporting our assumption that no z23.7 QSOs are missed by selecting OLfc 2. (,"ii) We found no 3.7 $< z <$ 4.4 QSOs with 2 $< O-E <$ 3, supporting our assumption that no $z > 3.7$ QSOs are missed by selecting $O-E \ge$ 2. ("740ii) Lhe BAL fraction for the QSOs with 2<x44 in our sample is ~27+10 per cent (7/26). larger than ound for FBOS-2 (Becker et al.,"iii) The BAL fraction for the QSOs with $2 \le z \le 4.4$ in our sample is $\sim 27 \pm 10$ per cent (7/26), larger than found for FBQS-2 (Becker et al."741 2000) and for the optically-selected SDSS samples in Reichard ct al. (, 2000) and for the optically-selected SDSS samples in Reichard et al. (7422003) and Trump et al. (,2003) and Trump et al. (7432006). despite these three works being more complete or lower balnicity index.,"2006), despite these three works being more complete for lower balnicity index."744 Our sample also has an unusually igh fraction of LoBALs. four to five out of seven. compared o the above samples.," Our sample also has an unusually high fraction of LoBALs, four to five out of seven, compared to the above samples."745 Ehe most likely explanation for the jigh frequency. of BALs and LoBALs in our sample is the red colour selection. O—1>2," The most likely explanation for the high frequency of BALs and LoBALs in our sample is the red colour selection, $O-E \ge 2$."746 A comparison of the three studies suggests that the BAL fraction in radio-selected QSO samples is at least as high as in opticallv-selected. ones. , A comparison of the three studies suggests that the BAL fraction in radio-selected QSO samples is at least as high as in optically-selected ones. (747iv) We note the unusual QSO FIRST 1413|4505 (2=3.11). whose optical spectrum reveals à strong associated Lya absorber (clamped orBAL-like) that completely removes the Lya emission.,"iv) We note the unusual QSO FIRST 1413+4505 $z=3.11$ ), whose optical spectrum reveals a strong associated $\alpha$ absorber (damped orBAL-like) that completely removes the $\alpha$ emission."748 Lhe source is highlv luminous in the radio. has a Hat radio spectral index. ancl is detected in JRAS 12 and 25 pom. vielding a bolometric Luminosity in the range from SDSS 2 band to 25 pim L—LS107L.. which places it amonest the most luminous objects known. (," The source is highly luminous in the radio, has a flat radio spectral index, and is detected in $IRAS$ 12 and 25 $\mu$ m, yielding a bolometric luminosity in the range from SDSS $z$ band to 25 $\mu$ m $L \sim 1.8 \times 10^{15} L_\odot$, which places it amongst the most luminous objects known. ("749"v) Using a sub-sample of seven QSOs with 3.7<0x44 and foxo19.1. we derive a space density of radio loud. QSOs. pMap(1450).x26.6.P4.cH,5 ","v) Using a sub-sample of seven QSOs with $3.7 \le z \le 4.4$ and $E750\le 19.1$, we derive a space density of radio loud QSOs, $\rho [M_{\rm AB}751(1450) \le -26.6 , P_{\rm 1.4 \ GHz} \ge 10^{25.7} ({\rm W \752Hz^{-1}})] = 1.7 \pm 0.6$ $^{-3}$."753Assuming aradio-loud fraction 13.4d:3 per cent. - μαKenace density for all QSOs is pMan(450)<26.6]=12.545.6 ° ," Assuming aradio-loud fraction $13.4 \pm 3$ per cent, the space density for all QSOs is $\rho [M_{\rm AB} (1450) \le -26.6] = 12.5 \pm 5.6$ $^{-3}$ ."754This result is in good agreement with the best-fitting mocel in Fan et al. (, This result is in good agreement with the best-fitting model in Fan et al. (7552001a.b). considering the statistical errors.,"2001a,b), considering the statistical errors."756Is nueasured for al events. aix sampled bw (at least) three filters: this xcπιο] corresponds to measuring the D.V aud R (vest frane) standard bauds.,"is measured for all events, and sampled by (at least) three filters: this roughly corresponds to measuring the B,V and R (rest frame) standard bands."757 Current distance estimators only τοςnie two baids (they can of course accommodate nore bands)., Current distance estimators only require two bands (they can of course accommodate more bands).758 Recmurine three bands will either allow o1ο fo USC LLOLE οaXyate distance estimators. or to use the buil-in reduudaicv to compare derived distances.," Requiring three bands will either allow one to use more elaborate distance estimators, or to use the built-in redundancy to compare derived distances."759 Requiring that the sae rest frame wavelengths are lueasured at all redshifts make the comparison of superuovae briehtnesses as diniovudeut as possible from a supernova node1., Requiring that the same rest frame wavelengths are measured at all redshifts make the comparison of supernovae brightnesses as independent as possible from a supernova model.760 Although we require three bands to nuüeasure a disance. the observi1g strategy proposed beQW provides us with more than three bands at all redshifts.," Although we require three bands to measure a distance, the observing strategy proposed below provides us with more than three bands at all redshifts."761 The duratiou of the survey is arbitrarily chosen as 1.5 year. Le. abott one third of a five-vear mussion.," The duration of the survey is arbitrarily chosen as 1.5 year, i.e. about one third of a five-year mission."762 This raige of survey time provides O(LO4) events. ie. an order of magnitude over current cosmological samples (e.g. ? ," This range of survey time provides $\mathrm{10^4}$ ) events, i.e. an order of magnitude over current cosmological samples (e.g. \citealt{Amanullah10}) )."763Alterations o| fhe survey duration will be cousiderec 85.1., Alterations of the survey duration will be considered in \ref{sec:variations}.764" The depth of the observations is driven by the maximal tarect redsuft. and considering three requirements: (1) the lueasureneuts should be accurate chough so that the distance esnuate has a ieasurement uncertaintv that relmaius significantly smaller than the observe scatter of the Hubble «lagraim (namely around 0.15 mae ‘or modcru νους, SOC CLLe 777735 (2) the sanie superuova parameter space shoulc be observable at all redshifts i order to woicd the shexteominugs of Malmiquist bias corrections: (3)H 1C auplitude of he three bands roughly maching rest rae D.V.R bauds should 1ο nieasured at an acctiracv setter or coniparae to the iuieasured ""colour suearimg. iunuelv about 0.025 imag. see ??.."," The depth of the observations is driven by the maximum target redshift, and considering three requirements: (1) the measurements should be accurate enough so that the distance estimate has a measurement uncertainty that remains significantly smaller than the observed scatter of the Hubble diagram (namely around 0.15 mag for modern surveys, see e.g. \citealt{Guy07,Kessler09,Guy10,Conley10}) ); (2) the same supernova parameter space should be observable at all redshifts in order to avoid the shortcomings of Malmquist bias corrections; (3) the amplitude of the three bands roughly matching rest frame B,V,R bands should be measured at an accuracy better or comparable to the measured “colour smearing”, namely about 0.025 mag, see \cite{Guy07,Guy10}."765" Colour refers o the spread of «'olour-colour relations of SNe Ta: it is he scatter of sinee-band light curve amplitudes oue has Q aCd to measurenent uncertainties in order to properly describe the observed spread. of colour-colow relations of SNe Ta. One cau for example model the rest frame V-R cok1v from D-V. The scatter of this colour-colour relation Is properlv. descrilved by assunune that the D.V aud R reals magnitudes scatter dependently by o,2 0.025 mae aroulvl a two-paraucter model."," Colour refers to the spread of colour-colour relations of SNe Ia: it is the scatter of single-band light curve amplitudes one has to add to measurement uncertainties in order to properly describe the observed spread of colour-colour relations of SNe Ia. One can for example model the rest frame V-R colour from B-V. The scatter of this colour-colour relation is properly described by assuming that the B,V and R peak magnitudes scatter independently by $\sigma_c \simeq$ 0.025 mag around a two-parameter model."766 One can estimate the cok1r wuenarius as a function of wavceleusth (?)). aud find that the B.V.R τοσο is less scattered than bluer 2cs.," One can estimate the colour smearing as a function of wavelength \citealt{Guy10}) ), and find that the B,V,R region is less scattered than bluer bands."767 The colour simearing contrimites to the Dubble diagram scatter. but docs not accotut for the eutiretv of he nieasured ~0.15 mae ranis.," The colour smearing contributes to the Hubble diagram scatter, but does not account for the entirety of the measured $\sim$ 0.15 mag r.m.s."768 Iu practice. the requirement (2) about Maliiquist bias indicates that events one imaenitide füuter than the averwoe at the highest redshift shoud be easily detected.," In practice, the requirement (2) about Malmquist bias indicates that events one magnitude fainter than the average at the highest redshift should be easily detected."769 We find that requirement (5) 1 t1 most demanding. and the survey setup we present later fulfils these three requirements.," We find that requirement (3) is the most demanding, and the survey setup we present later fulfils these three requirements."770 Superuiova redshifts are obviously needed to assenible a Hubble diagraun, Supernova redshifts are obviously needed to assemble a Hubble diagram.771i Obtaining SNe Ia spectra from the eroulLas technically feasije up to :~L., Obtaining SNe Ia spectra from the ground is technically feasible up to $z\sim 1$.772 At higher redslits. the required exposure times 1dwerease Vverv rapidly with reshift becase the SNe Ia fux decreases rapidly in the near UV (buer than ~ 236004). and the atiuospliere glow increases rapidly towards the red.," At higher redshifts, the required exposure times increase very rapidly with redshift because the SNe Ia flux decreases rapidly in the near UV (bluer than $\sim$ ), and the atmosphere glow increases rapidly towards the red."773 A large spectroscopic followup of supernovae at 2Lis hence out of reach of current erouud-based iustrunienuts; and even if adaptive optics. OIL suppression and larecr telescopes will certainly help very significanth. massive statistics will likely remain out of reach during at least the next decade.," A large spectroscopic followup of supernovae at $z>1$ is hence out of reach of current ground-based instruments, and even if adaptive optics, OH suppression and larger telescopes will certainly help very significantly, massive statistics will likely remain out of reach during at least the next decade."774 Since acquindug a sICCrun for each SHpOOrLnoVva Was à core goal of the xoposed SNAPconcept}... its baseliue design iucπάσα a Bieb-througlipit low-resolution spectrograph.," Since acquiring a spectrum for each supernova was a core goal of the proposed SNAP, its baseline design included a high-throughput low-resolution spectrograph."775 Iu this concet. the supernova spectroscoDy requirements. drove the ο size axd Πίος tie statistics to. O(2000) πιpernovae. becarse of the lo18o exposures required for sλοςroscopy of distaut superiovac.," In this concept, the supernova spectroscopy requirements drove the mirror size and limited the statistics to O(2000) supernovae, because of the long exposures required for spectroscopy of distant supernovae."776 We believe that obtaining supernova spectra one at a time with a small field lustrmment is nof a realislc eoal for O(10) eveuts. exoeciallv if sdnünug at redshits bevoud 1ity.," We believe that obtaining supernova spectra one at a time with a small field instrument is not a realistic goal for $\mathrm{10^4}$ ) events, especially if aiming at redshifts beyond unity."777 Wide field space-based slitless spectrosco lav be ¢Onskdered. but he S/N ratio of slitless spectra Is naturalv myor. because every pixel integrates the s backerotxd 5]λοςruni iu the whole bandwidth: spectra at a 06est magnitude JF~21 secur out of reach EUCLID slit-less spectrograph.," Wide field space-based slitless spectroscopy may be considered, but the S/N ratio of slitless spectra is naturally poor, because every pixel integrates the sky background spectrum in the whole bandwidth: spectra at a modest magnitude $H \sim 24$ seem out of reach of EUCLID slit-less spectrograph."778 Space-based specTOSCO with svuthetic slits (as originally proposed for the SPACE project. ater anereed with DUNE into EUCLID) ls sjenificaurlv more scusitive. and for a superuova VOLTA OU a jolu -uaelre-spectroscopy-witl-slits mission (such as the origiwl EUCLID concept). oue should οwiously consider obalnig supernovae spectra in paralcl with repeated inivine.," Space-based spectroscopy with synthetic slits (as originally proposed for the SPACE project, later merged with DUNE into EUCLID) is significantly more sensitive, and for a supernova program on a joint imaging-spectroscopy-with-slits mission (such as the original EUCLID concept), one should obviously consider obtaining supernovae spectra in parallel with repeated imaging."779" So. for (104) supernovac. we should consider he case where ""uperj0va spectra cannot be acquired for al events,"," So, for $\mathrm{10^4}$ ) supernovae, we should consider the case where supernova spectra cannot be acquired for all events."780 Since the Ihbhble diagram obviously requires redshifts. we consider the following alternatives:," Since the Hubble diagram obviously requires redshifts, we consider the following alternatives:"781One of the interesting problems in cosmology is the evolution of the large-scale peculiar velocity field in the Universe.,One of the interesting problems in cosmology is the evolution of the large-scale peculiar velocity field in the Universe.782 The evolution of the large-scale velocity field has been studied in a number of papers (see. e.g.. Davis ct al.," The evolution of the large-scale velocity field has been studied in a number of papers (see, e.g., Davis et al."783 1985: IXofman ct al., 1985; Kofman et al.784 1994: Drainerd Villumsen 1994: CGramann et al., 1994; Brainerd Villumsen 1994; Gramann et al.785 1995: Jenkins et al., 1995; Jenkins et al.786 1998: Juszkiewicz. Springe Durrer 1999: Colin. IXIvpin Wravtsoy 2000: CGramann Suhhonenko 2002: Ciecielag et al.," 1998; Juszkiewicz, Springel Durrer 1999; Colin, Klypin Kravtsov 2000; Gramann Suhhonenko 2002; Ciecielag et al."787 2003)., 2003).788 The linear rms peculiar velocity on a given scale 77 can be expressed as where fy ids the Llubble constant anc f is the dimensionless growth rate. which is related to the cosmological matter density parameter. ©). and the cosmological constant. O4. by (Lahav et al.," The linear rms peculiar velocity on a given scale $R$ can be expressed as where $H_0$ is the Hubble constant and $f$ is the dimensionless growth rate, which is related to the cosmological matter density parameter, $\Omega_m$, and the cosmological constant, $\Omega_{\Lambda}$, by (Lahav et al."789 1991)., 1991).790 The spectral moments m;(, The spectral moments $\sigma_j(R)$ are defined for any integer $j$ by where $P(k)$ is the power spectrum of density fluctuations and $W(kR)$ is a Fourier transform of the smoothing window.791/7) ," For the top-hat window in real space that we will use in this paper, $W(x)=(3/x^3)[\sin(x)-x\cos(x)]$ ."792are def, Notice that the predicted rms peculiar velocity depends both on cosmology and on the shape of the power spectrum.793ine, Jenkins et al. (794d fo,1998) used a N-body simulation to investigate the rms peculiar velocity of the dark matter smoothed on the scales $R=10-80h^{-1}$ Mpc.795r any inte," They compared the results with the linear approximation (1) and found that on scales above $20h^{-1}$ Mpc, the linear theory prediction agrees very well with the simulation."796, Kofman et al. (797g,1994) and Ciecielag et al. (798er j b,"2003) studied the evolution of the peculiar velocity one-point distribution function, beginning with Gaussian initial fluctuations."799y smoothing) the distribution of the Cartesian components of the peculiar. velocity. field is well approximated. by a Gaussian.," They showed that on mildly non-linear scales $4-10h^{-1}$ Mpc, Gaussian smoothing) the distribution of the Cartesian components of the peculiar velocity field is well approximated by a Gaussian."800 On smaller scales the velocity distribution of dark matter becomes non-Gaussian due to the motions of matter within dense svstems (see e.g. Sheth Dialerio (2001) for the discussion of the velocity. cistribution of clark matter particles in different. cosmological models)., On smaller scales the velocity distribution of dark matter becomes non-Gaussian due to the motions of matter within dense systems (see e.g. Sheth Diaferio (2001) for the discussion of the velocity distribution of dark matter particles in different cosmological models).801 Important information for the large-scale velocity field is provided by peculiar. velocities of galaxy clusters., Important information for the large-scale velocity field is provided by peculiar velocities of galaxy clusters.802 The evolution of peculiar velocities. of clusters in. dilferent cosmological models has been examined. in several papers (c.g. Baheall. Ciràmann Cen 1994: Croft Efstathiou 1994: Moscarcini et al.," The evolution of peculiar velocities of clusters in different cosmological models has been examined in several papers (e.g. Bahcall, Gramann Cen 1994; Croft Efstathiou 1994; Moscardini et al."803 1996: Suhhonenko Ciramann 1999: Colbere ct al., 1996; Suhhonenko Gramann 1999; Colberg et al.804 2000: Sheth Dialerio 2001: Suhhonenko Gramann 2003: Llamana ct al., 2000; Sheth Diaferio 2001; Suhhonenko Gramann 2003; Hamana et al.805 2003)., 2003).806 Clusters represent high-density maxima in the dark matter density field., Clusters represent high-density maxima in the dark matter density field.807 Bardeen ct αἱ. (, Bardeen et al. (8081986) studied. the peculiar velocity distribution for peaks of a Caussian densitv field.,1986) studied the peculiar velocity distribution for peaks of a Gaussian density field.809 They showed that the velocity distribution function for peaks 1s also Gaussian. with the rms peculiar velocity Peaks have lower peculiar velocities than field. points.," They showed that the velocity distribution function for peaks is also Gaussian, with the rms peculiar velocity Peaks have lower peculiar velocities than field points."810 The reason for this dillerence is the fact that the velocity, The reason for this difference is the fact that the velocity811amount of stripped-off material might has been dramatically overestimated as discussed above.,amount of stripped-off material might has been dramatically overestimated as discussed above.812 Based on the discussions above. further attempts to observe hydrogen lines in nebular spectra of SNe la are encouraged to check our suggestion.," Based on the discussions above, further attempts to observe hydrogen lines in nebular spectra of SNe Ia are encouraged to check our suggestion."813 The WD + RG system may also be an origin of single low-mass white dwarfs., The WD + RG system may also be an origin of single low-mass white dwarfs.814The development over the last two decades of efficient and reltable wide-field multi-objeet spectrograσας has resulted in enormous advances in the ability to compile large samples of high-quality astronomical spectra.,The development over the last two decades of efficient and reliable wide-field multi-object spectrographs has resulted in enormous advances in the ability to compile large samples of high-quality astronomical spectra.815 The Sloan Digital Sky Survey (SDSS:Yorketal.2000) represents the most imoressive application vet of such an instrument to provide spectroscovic samples of quasars. galaxies and stars of unprecedented size.," The Sloan Digital Sky Survey \citep[SDSS;][]{2000AJ....120.1579Y} represents the most impressive application yet of such an instrument to provide spectroscopic samples of quasars, galaxies and stars of unprecedented size."816 The third- data release (DR3: Abazajian et al., The third data release (DR3; Abazajian et al.817 provides the astronomical community with nearly 500.000. object spectra and further releases will take the number to 750.000 within eighteen months.," \nocite{astro-ph/0410239} provides the astronomical community with nearly 500,000 object spectra and further releases will take the number to 750,000 within eighteen months."818 The SDSS spectra present a dramatic improvement in quality over data from previous surveys: extended wavelength coverage. 38009200 intermediate resolution. AfAA—2500: quality relative and absolute flux-calibration: typical signal-to-noise ratios (S/N) of LO30: availability of accurate noise and mask arrays.," The SDSS spectra present a dramatic improvement in quality over data from previous surveys: extended wavelength coverage, $3800-9200\,$ ; intermediate resolution, $\lambda/\Delta\lambda \simeq 2500$; high-quality relative and absolute flux-calibration; typical signal-to-noise ratios (S/N) of $10-30$; availability of accurate noise and mask arrays."819 Coupled with the overall homogeneity of the dataset this makes them suitable for an almost limitless number of quantitative investigations., Coupled with the overall homogeneity of the dataset this makes them suitable for an almost limitless number of quantitative investigations.820 A particularly impressive aspect of the instrumental design. observing strategy and data reduction pipeline (Newmanetal.2004) has been the quality of the sky-subtraction achieved considering the relatively large. 3 aresecond diameter fibres and fully automated reduction.," A particularly impressive aspect of the instrumental design, observing strategy and data reduction pipeline \citep{astro-ph/0408167} has been the quality of the sky-subtraction achieved considering the relatively large, 3 arcsecond diameter fibres and fully automated reduction."821 Subsets of the SDSS spectra. such as the fainter quasars. include objects with magnitudes in red passbands equivalent to the skv-brightness per square arcsecond.," Subsets of the SDSS spectra, such as the fainter quasars, include objects with magnitudes in red passbands equivalent to the sky-brightness per square arcsecond."822 Despite the demonstrable quality of the SDSS spectra. visual inspection reveals significant systematic sky-subtraction residuals longward of 6700 iin manyspectra.," Despite the demonstrable quality of the SDSS spectra, visual inspection reveals significant systematic sky-subtraction residuals longward of $6700\,$ in manyspectra."823 For fainter objects in particular. the," For fainter objects in particular, the"824"pointed out that the measured CDS 301 intensity in Wangctal.(2010) was underestimated by a factor of 2 due to a bug found in the calibration routine.nis_calib, Which was fixed as of 2011 Mas.","pointed out that the measured CDS 304 intensity in \citet{wan10} was underestimated by a factor of 2 due to a bug found in the calibration routine, which was fixed as of 2011 May."825 In the following we present the CDS underfight calibration update with EUNIS-07 mcasurements., In the following we present the CDS underflight calibration update with EUNIS-07 measurements.826 Fieure L shows the common FOVs between EUNIS-07 TW aud CDS NIS as illustrated by the rastered images in 301 aand 368À.. indicating that a quiet region was observed.," Figure \ref{fgcdsmap} shows the common FOVs between EUNIS-07 LW and CDS NIS as illustrated by the rastered images in 304 and 368, indicating that a quiet region was observed."827 Figure 6 slows their cospatial average spectra. where 202 exposure frames were averaged for EUNIS-07.," Figure \ref{fgcdsspc} shows their cospatial average spectra, where 202 exposure frames were averaged for EUNIS-07."828 Note that the two regions around the 335 and 360 ]lines of CDS NIS 1 spectrum are suffering from depression due to wide-slit burn-in effects from the lines. where the loug-terii correction is more uncertain (DelZauuaetal. 2010)..," Note that the two regions around the 335 and 360 lines of CDS NIS 1 spectrum are suffering from depression due to wide-slit burn-in effects from the lines, where the long-term correction is more uncertain \citep{del10}. ."829 Both the calibrated EUNIS-Or LAV and CDS NIS spectra (as well as the calibrate EUNIS-07 SW and EIS spectra shown in Figure 11 aac Figure 13)) exhibit a significant backerouud particularly in the low-respousivitv waveleneth ranec., Both the calibrated EUNIS-07 LW and CDS NIS spectra (as well as the calibrated EUNIS-07 SW and EIS spectra shown in Figure \ref{fgsws} and Figure \ref{fglws}) ) exhibit a significant background particularly in the low-responsivity wavelength range.830" This mainly resulted frou, a combined effect of the instrumenta roise and scattered Leht with the special shape of their response curves.", This mainly resulted from a combined effect of the instrumental noise and scattered light with the special shape of their response curves.831" For the EUNIS spectra. we first divxος he full spectral window iuto several siuall sectiols. and then fitted spectral lines by a unultiple Ciaussiau ""unctiou witha linear background using the staudard line fitting routine (rccfit.pre) im SSW."," For the EUNIS spectra, we first divided the full spectral window into several small sections, and then fitted spectral lines by a multiple Gaussian function with a linear background using the standard line fitting routine ) in SSW."832 Iu this way the slowly. smoothly varvine Gvith wavelength) “backeround” level ily shiehtly affects the iuteerated intensities of the fitted ine profiles.," In this way the slowly, smoothly varying (with wavelength) “background” level only slightly affects the integrated intensities of the fitted line profiles."833 Moeasurenmenuts of the Lue iutensities from EUNIS-07SW aud EIS SW/IAV spectra in Sections 5 and 6 were made using the same technique., Measurements of the line intensities from EUNIS-07SW and EIS SW/LW spectra in Sections \ref{sctswc} and \ref{scteis} were made using the same technique.834 The CDS line iuteusities were obtained by fitting multiple broadened Gaussian functious to the full spectrum., The CDS line intensities were obtained by fitting multiple broadened Gaussian functions to the full spectrum.835 The broadened Gaussian function is a combination of a Caussian tena plus a terii describing the wings (Thompson1999)., The broadened Gaussian function is a combination of a Gaussian term plus a term describing the wings \citep{thomp99}.836. We chose the broadening with uno asvnunetry aud kept the relative amplitude of the wines equal to a value of 0.8. but allowed the width of the Gaussian term for the line to vary (within 0.29 aud 0.1 in FWIDIMD. as well as its ceutroid aud peak values.," We chose the broadening with no asymmetry and kept the relative amplitude of the wings equal to a value of 0.8, but allowed the width of the Gaussian term for the line to vary (within 0.29 and 0.4 in FWHM), as well as its centroid and peak values."837 All lines were fitted at once. with the backeround fitted with a polvnonual curve.," All lines were fitted at once, with the background fitted with a polynomial curve."838 Fieure 7 shows the fitted CDS line profiles in two selected wavelength ranges., Figure \ref{fgnisft} shows the fitted CDS line profiles in two selected wavelength ranges.839 Even with its moderate spectral resolution. CDS cau resolve the lines that we used for calibration.," Even with its moderate spectral resolution, CDS can resolve the lines that we used for calibration."840 The nucertaity caused by the moderate spectral resolution of CDS is relatively simall compared to that in the backeround when assuming the common backeround fit for all spectral lines., The uncertainty caused by the moderate spectral resolution of CDS is relatively small compared to that in the background when assuming the common background fit for all spectral lines.841 Table 1. lists 12 strong enuüssion lines observed ly both EUNIS LW and CDS (NIS 1 in first order aud NIS 2 in secoud order), Table \ref{tabcds} lists 12 strong emission lines observed by both EUNIS LW and CDS (NIS 1 in first order and NIS 2 in second order).842 To examine the eurreut CDS respousivitics and long-terii corrections. we measured the line intensities with three kinds of calibration as used in DelZaunactal.(2010).," To examine the current CDS responsivities and long-term corrections, we measured the line intensities with three kinds of calibration as used in \citet{del10}."843. The fourth column ERAN shows the iuteusities obtained with the current standard CDS respousivities aud the new long-term corrections derived by DelZauuaetal.(2010)... which has been nuplemented with the kevword «ltslit6 in the SSW routineedscalib.," The fourth column $I_{CDS}^{SN}$ ) shows the intensities obtained with the current standard CDS responsivities and the new long-term corrections derived by \citet{del10}, which has been implemented with the keyword in the SSW routine."844 The fifth cohuun (IE 4) shows the intensities obtained with the DelZauuaetal.(2001) scaled responsivities (ising2010 i SSW) and the new loue-term corrections., The fifth column $I_{CDS}^{GZ}$ ) shows the intensities obtained with the \citet{del01} scaled responsivities (using in SSW) and the new long-term corrections.845 Note that differences between the standard CDS respousivities auc the DelZamnaetal.(2001) sealed ones are sinall. overall of the order of or so.," Note that differences between the standard CDS responsivities and the \citet{del01} scaled ones are small, overall of the order of or so."846 The sixth cohuun UA ps) shows the iuteusities obtaired with the current standard CDS responsivitioes (version 1L. 2002) aud the standard long-term corrections (usiiccalib with the kevword slit6 |default] ).," The sixth column $I_{CDS}^{S}$ ) shows the intensities obtained with the current standard CDS responsivities (version 4, 2002) and the standard long-term corrections (using with the keyword [default] )."847 Cousideriic long-term corrections have the relative uucertüntv of204.. combined with the uncertainties i the back:oOround aud the responsivities (20%to30%sceDelZainaetal.POOL)... it means a typical uncertainty of dn micasturcments of CDS line iuteusities.," Considering long-term corrections have the relative uncertainty of, combined with the uncertainties in the background and the responsivities \citep[20\% to 30\% see][]{del01}, it means a typical uncertainty of in measurements of CDS line intensities."848" Ratic5 of the EUNIS-07 to various CDS liue iuteusities are Iz ediucohuuus 9 aud shown in Figure δν, where errors of the ratios were calculated Dy assuninemeerainty(as alower lunt) iu"," Ratios of the EUNIS-07 to various CDS line intensities are listed in columns $-$ 9 and shown in Figure \ref{fgcdscal}, , where errors of the ratios were calculated by assuminguncertainty(as alower limit) in"849the cüllerence between the (LID. LL) and (LID. Ho) interaction potentials (Wright Morton 1979).,"the difference between the (HD, H) and (HD, He) interaction potentials (Wright Morton 1979)."850 In Fig., In Fig.851 A2 we summarize the dillerent. contributions to the cooling of a gas of primordial composition., A2 we summarize the different contributions to the cooling of a gas of primordial composition.852 Although the curves have been obtained in the limits ΕΙ)20. they are valid for nl)=107 .," Although the curves have been obtained in the limits $n({\rm H})\rightarrow 0$, they are valid for $n({\rm853H})\la 10^2$ $^{-3}$."854 At larger densities. the cooling functions rapidly approach the corresponding LLL values: at intermediate densities. the formula (A5)) represents a very good approximation.," At larger densities, the cooling functions rapidly approach the corresponding LTE values; at intermediate densities, the formula \ref{holl}) ) represents a very good approximation."855" The cooling functions for Πο and L-LID are obtained as described in this work. the LH-Lill cooling function is computed IL, cooling function for collisions with LL and / was computed by Suchkov Shchekinoy. (1978)."," The cooling functions for $_2$ and H-HD are obtained as described in this work, the H-LiH cooling function is computed $_2^+$ cooling function for collisions with H and $^-$ was computed by Suchkov Shchekinov (1978)."856" The cooling function of LID in the low-density limit [or TiS10? W is accurately reproduced by the expression where £j)=128k. fe,=255k. and the 5,; are given in Table X3."," The cooling function of HD in the low-density limit for $\tg\la 10^3$ K is accurately reproduced by the expression where $E_{10}=128 k$, $E_{21}=255 k$, and the $\gamma_{JJ^\prime}$ are given in Table A3."857" As for Lill. the cooling function in the low-density Limit is well approximated. by the polynomial expression logAvin(ill)-O)Sey|ο(log7.)cs(log2;)? in the temperature range 107 Ix. With Avin in erg em? +. the fit coellicients are cy=31.4. cy,—δι ον=41d. ὃν=028292. 6,=0.04996."," As for LiH, the cooling function in the low-density limit is well approximated by the polynomial expression $\log\Lambda_{\rm LiH}(n{\rm H})\rightarrow8580)=c_0+c_1(\log\tg)+c_2(\log\tg)^2 +c_3(\log\tg)^3+c_4(\log\tg)^4$ in the temperature range $^3$ K. With $\Lambda_{\rm LiH}$ in erg $^3$ $^{-1}$, the fit coefficients are $c_0=-31.47$, $c_1=8.817$, $c_2=-4.144$, $c_3=0.8292$, $c_4=-0.04996$."859 In the standard model. the radiation temperature is higher than the matter temperature and molecules are a net heating source for the gas.," In the standard model, the radiation temperature is higher than the matter temperature and molecules are a net heating source for the gas."860 Molecular hydrogen dominates the heating of the gas at. temperatures higher than 150 Ix. whereas LID dominates at. lower temperatures.," Molecular hydrogen dominates the heating of the gas at temperatures higher than $\sim 150$ K, whereas HD dominates at lower temperatures."861 The ability of LID to heat/cool a gas when Ilo molecules become uncllicient is a remarkable property of a gas of primordial composition. and has been verified in a number of studies (Varshalovich Ixhersonskiü 1977. Shehekinoy 1986. Bougleux Galli 1997. Puy Signore 1991).," The ability of HD to heat/cool a gas when $_2$ molecules become unefficient is a remarkable property of a gas of primordial composition, and has been verified in a number of studies (Varshalovich Khersonskii 1977, Shchekinov 1986, Bougleux Galli 1997, Puy Signore 1997)."862was observed at the Very Large Telescope Interferometer (VLTI:?).. using the AMBER instrument that allows the simultaneous combination of three beams | the near-infrared (?)..,"was observed at the Very Large Telescope Interferometer \citep[VLTI;][]{vlti1}, using the AMBER instrument that allows the simultaneous combination of three beams in the near-infrared \citep{petrov07}."863 The instrument delivers spectrally ooispersed interferometric observables (visibilities. closure phases. differential phases) at spectral resolutions up to 12 000.," The instrument delivers spectrally dispersed interferometric observables (visibilities, closure phases, differential phases) at spectral resolutions up to 12 000."864 In the following. we present K-band observations take n the medium spectral resolution mode (MR: R~ 1500) with the 8.2 m Unit Telescopes (UTs) as well as with the 1.5 m Auxiliary Telescopes (ATs). and in the high spectral resolutior mode (HR: R~12 000) with the ATs.," In the following, we present K-band observations taken in the medium spectral resolution mode (MR; $\sim$ 1500) with the 8.2 m Unit Telescopes (UTs) as well as with the 1.8 m Auxiliary Telescopes (ATs), and in the high spectral resolution mode (HR; $\sim$ 12 000) with the ATs."865 The data were obtained within programs of Guaranteed Time. Director’s Discretionary Time. and Open Time observations.," The data were obtained within programs of Guaranteed Time, Director's Discretionary Time, and Open Time observations."866 was observed with 11. different baselines of 4 VLTI configurations. during 5 nights in December 2008 and one night in January 2010.," was observed with 11 different baselines of 4 VLTI configurations, during 5 nights in December 2008 and one night in January 2010."867 The longest baseline is ~ 120 m corresponding to à maximum angular resolution of 3.7 mas., The longest baseline is $\sim$ 120 m corresponding to a maximum angular resolution of 3.7 mas.868 A summary of the observations presented in this paper is given in Table {.., A summary of the observations presented in this paper is given in Table \ref{tab:obs}.869 With the UTs. the observations are coupled with the use of adaptive optics and the resulting field of view ranges from 50 to 60 mas.," With the UTs, the observations are coupled with the use of adaptive optics and the resulting field of view ranges from 50 to 60 mas."870 This allowed us to spatially resolve the binary and obtain measurements of the FU Or and the Herbig Be., This allowed us to spatially resolve the binary and obtain measurements of the FU Or and the Herbig Be.871 In contrast. the ATs field-of-view. ranging from 230 to 280 mas. includes both stars and the interferometric signal results from both emissions.," In contrast, the ATs field-of-view, ranging from 230 to 280 mas, includes both stars and the interferometric signal results from both emissions."872 In addition to Z CMa. calibrators (HD45420. HD00742. HD55137. HD55832) were observed to correct for instrumental effects.," In addition to Z CMa, calibrators (HD45420, HD60742, HD55137, HD55832) were observed to correct for instrumental effects."873 All observations were performed using the fringe-tracker FINITO (?).., All observations were performed using the fringe-tracker FINITO \citep{lebouquin08}.874" The data reduction was performed following standard procedures described in ?. and ?.. using the package. release 2.99, and the interface provided by the Jean-Marie Mariottifootnotetexthttp://www."," The data reduction was performed following standard procedures described in \citet{tatulli07} and \citet{chelli09}, using the package, release 2.99, and the interface provided by the Jean-Marie Mariotti."875jmme.fr... Raw spectral visibilities. differential phases. and closure phases were extracted for all the frames of each observing file.," Raw spectral visibilities, differential phases, and closure phases were extracted for all the frames of each observing file."876 A selection of of the highest quality frames was made and consecutive observations were merged to enhance the signal-to-noise ratio., A selection of of the highest quality frames was made and consecutive observations were merged to enhance the signal-to-noise ratio.877 The accuracy of the wavelength/velocity calibration is ~50 km/s. Because the K-band continuum measured by the ATs (due to both stars) is very resolved on long baselines (V~O). the observations obtained on the GI-AO and KO-AO baselines could not be exploited.," The accuracy of the wavelength/velocity calibration is $\sim$ 50 km/s. Because the K-band continuum measured by the ATs (due to both stars) is very resolved on long baselines $\sim$ 0), the observations obtained on the G1-A0 and K0-A0 baselines could not be exploited."878 The absolute value of the visibilities obtained with the UT baselines could not be determined due to random vibrations of the telescopes., The absolute value of the visibilities obtained with the UT baselines could not be determined due to random vibrations of the telescopes.879 However. this issue affects all spectral channels in the same way. and does not modify our conclusions.," However, this issue affects all spectral channels in the same way, and does not modify our conclusions."880 We recall that the visibilities provide information about the spatial extent of the emission. and decrease as the extension increases.," We recall that the visibilities provide information about the spatial extent of the emission, and decrease as the extension increases."881 Differential phases provide a measurement of the photocenter displacements across the sky. projected along the baseline direction.," Differential phases provide a measurement of the photocenter displacements across the sky, projected along the baseline direction."882 They can therefore be converted into differential spectro-astrometric shifts., They can therefore be converted into differential spectro-astrometric shifts.883 They are measured relative to the continuum. for which we assume a zero phase.," They are measured relative to the continuum, for which we assume a zero phase."884 Finally. the closure phases are related to the asymmetry of the brightness distribution(e.g... they are null for a symmetric object).," Finally, the closure phases are related to the asymmetry of the brightness distribution, they are null for a point-symmetric object)."885 We show in Figs., We show in Figs.886 | and 2 a subsample of the observations that illustrate the main characteristics of the data., \ref{fig:all} and \ref{fig:all2} a subsample of the observations that illustrate the main characteristics of the data.887 Since the absolute values of the visibilities measured with the UTs are unknown. we normalized the continuum values to ] — even though the emission is resolved.," Since the absolute values of the visibilities measured with the UTs are unknown, we normalized the continuum values to 1 -- even though the emission is resolved."888 The left and middle columns of Fig., The left and middle columns of Fig.889 1. present examples of the MR observations obtained with the UTs for each star during the outburst., \ref{fig:all} present examples of the MR observations obtained with the UTs for each star during the outburst.890 Each column includes a spectrum (normalized to the continuum). squared visibilities. differential phases. and closure phases.," Each column includes a spectrum (normalized to the continuum), squared visibilities, differential phases, and closure phases."891 For the FU Or (left panels). within the error bars. the spectrum shows in neither emission nor absorption.," For the FU Or (left panels), within the error bars, the spectrum shows in neither emission nor absorption."892 Consequently. no change in the visibilities or phases across the line ts expected/seen.," Consequently, no change in the visibilities or phases across the line is expected/seen."893 In contrast. the Herbig Be star exhibits a clear line in emission (middle panels). although at this spectral resolution (Av.— 200 km/s). the line is not spectrally resolved.," In contrast, the Herbig Be star exhibits a clear line in emission (middle panels), although at this spectral resolution $\Delta v\sim$ 200 km/s), the line is not spectrally resolved."894 The visibility increases through the line and the differential phases produce an S-shape variation., The visibility increases through the line and the differential phases produce an S-shape variation.895 The closure phases differ from zero. with values of 25°412°.," The closure phases differ from zero, with values of $^\circ 896\pm$ $^\circ$."897 The phase. line. anc visibility signals are present from ~-600 to 500 km/s. although because of the low line-to-continuum ratio in the extended wings. the flux and visibilities appear narrower.," The phase, line, and visibility signals are present from $\sim$ -600 to 500 km/s, although because of the low line-to-continuum ratio in the extended wings, the flux and visibilities appear narrower."898 Within the large errors. no variation in the closure phases is detected across the line.," Within the large errors, no variation in the closure phases is detected across the line."899 The right part of the figure shows measurements obtained with the ATs.Le... with both stars in the field of view.," The right part of the figure shows measurements obtained with the ATs, with both stars in the field of view."900 lt this case. the level of continuum is determined by both stellar components.," In this case, the level of continuum is determined by both stellar components."901 These panels present observations obtained iu HR., These panels present observations obtained in HR.902 In this case. the line is spatially and spectrally resolved (Av ~25 km/s). and the spectra exhibit a clear double-peaked and asymmetric profiles. with less emission at blueshiftec velocities.," In this case, the line is spatially and spectrally resolved $\Delta903v\sim$ 25 km/s), and the spectra exhibit a clear double-peaked and asymmetric profiles, with less emission at blueshifted velocities."904 The spectral visibilities present a similar profile., The spectral visibilities present a similar profile.905 Finally. Fig.," Finally, Fig."906 2) compares the spectra and the visibilities obtained during and after the outburst: the emission line. anc the signature in the visibilities. disappear after the outburst.," \ref{fig:all2} compares the spectra and the visibilities obtained during and after the outburst: the emission line, and the signature in the visibilities, disappear after the outburst."907 Plotted within a large velocity range. the visibilities show a," Plotted within a large velocity range, the visibilities show a"908We have studied the productivity aud impact of the CEHT over its twenty-vear history by ooking at the number of papers in refereed journals aud the number of citatious to these papers.,We have studied the productivity and impact of the CFHT over its twenty-year history by looking at the number of papers in refereed journals and the number of citations to these papers.909 It took teu years for CFHT to achieve aud maintain a high level of paper production., It took ten years for CFHT to achieve and maintain a high level of paper production.910 We attribute his to a fairly long cotunissioniug period [or the telescope aud the time to develop a competitive suite of instrunentatlo1, We attribute this to a fairly long commissioning period for the telescope and the time to develop a competitive suite of instrumentation.911 Direct imagers (photographie plates. CCD tnagers) have been. CEHTs nost productive instruments. both iu the uumnber of papers and the number of papers per night ol selieduled elescope ime.," Direct imagers (photographic plates, CCD imagers) have been CFHT's most productive instruments, both in the number of papers and the number of papers per night of scheduled telescope time."912 The excellent image αιality at. CFHT is a sienilicaut [actor in direct imagines lie1 productivity., The excellent image quality at CFHT is a significant factor in direct imaging's high productivity.913 We retrieved citatiol counts and tie years of the citiug papers [roiitihe ADS for all CFHT yapers in our database., We retrieved citation counts and the years of the citing papers from the ADS for all CFHT papers in our database.914 Using this daa. we developed a procedure lor esllinatine the uumber of citations tlal a yaper cau be expeced to receive alter a period of alios twenty vears.," Using this data, we developed a procedure for estimating the number of citations that a paper can be expected to receive after a period of almost twenty years."915 This estimation alowed us to compare the citation nuu-—ers for papers [ron diferent vears aud to compare the impact of different lustruijents., This estimation allowed us to compare the citation numbers for papers from different years and to compare the impact of different instruments.916 The instrument that. prodcec the papers with the hieheste impact (averagee citatious/pape‘) was the Milti-Object Spectrograpl (NOS). which was uxed in the highly cited CERS aud CNOC studies.," The instrument that produced the papers with the highest impact (average citations/paper) was the Multi-Object Spectrograph (MOS), which was used in the highly cited CFRS and CNOC studies."917 Direct imagiug had the secord highest impact., Direct imaging had the second highest impact.918 Iu looking a the number of citations/uigh ol allocated time. direct imaging had the highest impact. followed by MOS aud the two Coucdé spectrographls.," In looking at the number of citations/night of allocated time, direct imaging had the highest impact, followed by MOS and the two Coudé spectrographs."919 The elicieucy of converting observiug nights into papers or citations varies considerably betweeu iustrments., The efficiency of converting observing nights into papers or citations varies considerably between instruments.920" For example. there is a factor of five difference iu he average final citation count per ulelit between ""Direc hnuaging"" and the FTS."," For example, there is a factor of five difference in the average final citation count per night between “Direct Imaging” and the FTS."921" In order to naxluize a telescope's impact. one might cousider offering ouly the ""high-efliciency instruments."," In order to maximize a telescope's impact, one might consider offering only the “high-efficiency” instruments."922 Finally. a look at the correlation betwee1 the predicted. final citation count and the TAC ranking of the observing proposal. showed a weak negative correlation. Le. lower-ranked proposals eud up with a higher number of ciallons.," Finally, a look at the correlation between the predicted final citation count and the TAC ranking of the observing proposal, showed a weak negative correlation, i.e. lower-ranked proposals end up with a higher number of citations."923 Analernative interpretation has bigher-raukecl proposals with a lower nuuumber of citations with a πι scatter., An alternative interpretation has higher-ranked proposals with a lower number of citations with a small scatter.924 Lower-rauked proposals have more scatter in the number of citations aid sone of these eid up with significantly more citations than most of the higher ranked proposals., Lower-ranked proposals have more scatter in the number of citations and some of these end up with significantly more citations than most of the higher ranked proposals.925 We acknowledge the Canacla-Frauce-Hawaii Telescope aud the Herzberg blustitute of Ástropliysic for their support of this project., We acknowledge the Canada-France-Hawaii Telescope and the Herzberg Institute of Astrophysics for their support of this project.926 We thank Pierre Couturier for hiis impetus in initiating the analysis ol CFHT publications., We thank Pierre Couturier for his impetus in initiating the analysis of CFHT publications.927 We also thank Cordon W. Brysou for his editing aud Virgiuia Sinith for her assistance curiug her mentorship at CEHT., We also thank Gordon W. Bryson for his editing and Virginia Smith for her assistance during her mentorship at CFHT.928 This research has inade use of NASAs Astrophysics Data System Bibliographic Services., This research has made use of NASA's Astrophysics Data System Bibliographic Services.929Vaisala Irecuency Nia“2poy) “ath which can be made positive. negative or zero by varying 5—I.,"$\ddot{\rm{a}}$ $\ddot{\rm{a}}$ $\ddot{\rm{a}}$ frequency N_x^2(x) = which can be made positive, negative or zero by varying $\gamma-\Gamma$."930 We fix some of the model parameters to vield an eequilibrium profile that is appropriate for a thin disk., We fix some of the model parameters to yield an equilibrium profile that is appropriate for a thin disk.931 In particular. we want νοIH«1 in order to be consistent with our use of a razor-thin. (6wo-dimensional) disk model.," In particular, we want $H/L_P \sim H/R \ll9321$ in order to be consistent with our use of a razor-thin (two-dimensional) disk model."933 In. addition. we want (he equilibrium values for each fluid variable to. be of (he same order to ensure the applicability of our linear analvsis.," In addition, we want the equilibrium values for each fluid variable to be of the same order to ensure the applicability of our linear analysis."934" These requirements can be met by choosing A=1. e=0.1. L,=12 and h,=&GF/(O—1). where ο=v(,/X8) Lis (to within a factor of J/5) the 7 average of the sound speed."," These requirements can be met by choosing $K = 1$, $\epsilon =9350.1$, $L_x = 12$ and $h_a = \bar{c}_s^2 \Gamma/(\Gamma-1)$, where $\bar{c}_s \equiv \sqrt{\< P_0/\Sigma_0 \>} \equiv 1$ is (to within a factor of $\sqrt{\gamma}$ ) the $x$ average of the sound speed."936 Since the equilibrium profile changes with D. we choose a fixed value of D— 4/3. which lor 5=E corresponds to athiree-dimensional adiabatic index of 7/5.," Since the equilibrium profile changes with $\Gamma$, we choose a fixed value of $\Gamma = 4/3$ , which for $\gamma = \Gamma$ corresponds to athree-dimensional adiabatic index of $7/5$."937 These numbers vield |/7/Lp|<0.2., These numbers yield $|H/L_P| \leq 0.2$.938" Our unfixed model parameters are thus L,. q and 5."," Our unfixed model parameters are thus $L_y$, $q$ and $\gamma$."939 The sinusoidal equilibrium profile we are using generates radial oscillations in the shearing sheet. since the analvtie equilibrium dilfers from the numerical equlibrium because of truncation error.," The sinusoidal equilibrium profile we are using generates radial oscillations in the shearing sheet, since the analytic equilibrium differs from the numerical equlibrium because of truncation error."940 We apply an exponential-damping term (o the governing equations in order to reduce the spurious oscillations and therefore get cleaner growtli-rate measurements., We apply an exponential-damping term to the governing equations in order to reduce the spurious oscillations and therefore get cleaner growth-rate measurements.941 We clamp the oscillations until their amplitude is equal to that of machine-level noise. and subsequently apply low-level random. perturbations to trigger anv imstabilities (hat may be present.," We damp the oscillations until their amplitude is equal to that of machine-level noise, and subsequently apply low-level random perturbations to trigger any instabilities that may be present."942 As a dest for our code. we evolve a particular solution for the incompressive shwaves in the radially-stratified shearing sheet (equations [??]] and [??]|-[2??]]).," As a test for our code, we evolve a particular solution for the incompressive shwaves in the radially-stratified shearing sheet (equations \ref{BOUSSVX2D}] ] and \ref{XIY}] \ref{SOLDH}] ])."943" The initial conditions are δα=0N/My)—1x10! and hy=—128z/L,.", The initial conditions are $\delta v_x/\bar{c}_s = \delta \Sigma/\Sigma_0 = 1 \times 10^{-4}$ and $k_{x0} = -128\pi/L_x$.944" We sel L,—0.315 and hk,=2x/L, in order to operate in the short-wavelength regime. ancl the other model parameters are q=1.5 and ;—I=—0.3102."," We set $L_y = 0.375$ and $k_y = 2\pi/L_y$ in order to operate in the short-wavelength regime, and the other model parameters are $q = 1.5$ and $\gamma - \Gamma = -0.3102$."945 The latter value vields a mininimum. value for Απ) of —0.01., The latter value yields a minimum value for $N_x^2(x)$ of $-0.01$.946 The results of the linear theory test are shown in Figure I.., The results of the linear theory test are shown in Figure \ref{f1}.947 Table 1 gives a summary of the runs that we have performed., Table 1 gives a summary of the runs that we have performed.948 A detailed description of the setup and results for each is eiven in the following subsections., A detailed description of the setup and results for each is given in the following subsections.949" Our primary. diagnostic is a measurement of erowth rates. aud (he probe (hat we use for these measurements is an average over azimuth of the absolute value of e,=dr, at the minimum in NT."," Our primary diagnostic is a measurement of growth rates, and the probe that we use for these measurements is an average over azimuth of the absolute value of $v_x = \delta v_x$ at the minimum in $N_x^2$."950" Measuring v, allows us to demonstrate the damping of the initial radial oscillations. aud (he average over"," Measuring $v_x$ allows us to demonstrate the damping of the initial radial oscillations, and the average over"951S(y.5) mav not be evaluated: analytically. but it is garaightforward to compute numerically for fixed. value of 16 slope parameter 5.,"${\cal{S}}(y, \gamma)$ may not be evaluated analytically, but it is straightforward to compute numerically for fixed value of the slope parameter $\gamma$."952 The result is shown in reffig:surf. where we use a logarithmic scale to make easier 16 visualization., The result is shown in \\ref{fig: surf} where we use a logarithmic scale to make easier the visualization.953 Ht is worth noting that the slope parameter > plavs a key role in determining the behaviour of X in the inner regions. while has a still significant but less clramatic ellect for large values of y.," It is worth noting that the slope parameter $\gamma$ plays a key role in determining the behaviour of $\Sigma$ in the inner regions, while has a still significant but less dramatic effect for large values of $y$."954 In particular. we find that the higher is 5. the lower is the surface density for a given vr.," In particular, we find that the higher is $\gamma$, the lower is the surface density for a given $x$."955 This is particularly evident in the very inner regions às it is seen comparing the [lat part of the curves in reffig: surL., This is particularly evident in the very inner regions as it is seen comparing the flat part of the curves in \\ref{fig: surf}.956 Ht is worth stressing that the surface density may not mimic neither the usual £F! law nor its generalization pU., It is worth stressing that the surface density may not mimic neither the usual $r^{1/4}$ law nor its generalization $r^{1/n}$.957 phis is not a serious. drawback. of POLLS models. however. since they were introduced to describe clark haloes rather than luminous components.," This is not a serious drawback of PoLLS models, however, since they were introduced to describe dark haloes rather than luminous components."958 I is nonetheless interesting to compute also the integrated. surface density that is givenas: that is shown in reffig: surfint.., It is nonetheless interesting to compute also the integrated surface density that is given: that is shown in \\ref{fig: surfint}. .959 The dependence on 5 is further weakened bv the integration process with the result. that (y) is almost independent on the slope parameter up toy2., The dependence on $\gamma$ is further weakened by the integration process with the result that $S(y)$ is almost independent on the slope parameter up to $y \sim 2$.960" Note. however. that both X, and S,=S/(2xXsr5)5 are increasing function of > as it is expected since models with smaller values of = are more concentrated. Le. the projected mass within a given distance from the centre is larger."," Note, however, that both $\Sigma_n$ and $S_n = S/(2 \pi \Sigma_{-2} r_{-2}^2)$ are increasing function of $\gamma$ as it is expected since models with smaller values of $\gamma$ are more concentrated, i.e. the projected mass within a given distance from the centre is larger."961 In 33. we have evaluated the velocity dispersion. but indeed it is not this quantity that is measured.," In 3, we have evaluated the velocity dispersion, but indeed it is not this quantity that is measured."962 Actually. [rom the observations it is possible to estimate the velocity dispersion projected. along the line of sight. and. weighted with the surface Iuminosity density.," Actually, from the observations it is possible to estimate the velocity dispersion projected along the line of sight and weighted with the surface luminosity density."963 This is given where Z(H) is the total surface luminosity density. panis the mass density of the stellar component and Afy the total (stellar plus clark matter) mass profile.," This is given: where $I(R)$ is the total surface luminosity density, $\rho_{stars}$ the mass density of the stellar component and $M_{T}$ the total (stellar plus dark matter) mass profile."964 Fo be more realistic. we average over a finite racial bin (22).H2) as follows (see. e.g.. the appendix in Dalal Ixeeton::with: A caveat is in order here.," To be more realistic, we average over a finite radial bin $(R_1, R_2)$ as follows (see, e.g., the appendix in Dalal Keeton: A caveat is in order here."965 In. principle. £(/2) is not equal to SQA).," In principle, $I(R)$ is not equal to $\Sigma(R)$."966 Actually. we have to distinguish among three possibilities.," Actually, we have to distinguish among three possibilities."967 First. let us suppose that we use a PoLLS model for the dark halo of a galaxy in which case X(41) does not enter in £02). while the mass profile of the mocel still enters in determining the velocity dispersion. through Aly in Eqs.(32)) and (33)).," First, let us suppose that we use a PoLLS model for the dark halo of a galaxy in which case $\Sigma(R)$ does not enter in $I(R)$, while the mass profile of the model still enters in determining the velocity dispersion through $M_T$ in \ref{eq: sigmalos}) ) and \ref{eq: sigmabin}) )."968 On the other hand. a PoLLS model may also be used to fit the surface brightness profile of an elliptical galaxy so that we need both X. p and Al to evaluate σας ancl 05; ancl also choose a model for the dark halo.," On the other hand, a PoLLS model may also be used to fit the surface brightness profile of an elliptical galaxy so that we need both $\Sigma$, $\rho$ and $M$ to evaluate $\sigma_{los}$ and $\sigma_{bin}$ and also choose a model for the dark halo."969 Finally. if the galaxy is a spiral one. we have a three component system. thus complicating a lot describing the whole system: and computing the velocity dispersion.," Finally, if the galaxy is a spiral one, we have a three component system thus complicating a lot describing the whole system and computing the velocity dispersion."970 In order to not introduce clegencracy among the model parameters and to better investigate the properties of the PoLLS models. we restrict our attention to elliptical ealaxies and assume that it is possible to use a PoLLS model to[it the surface brightness.," In order to not introduce degeneracy among the model parameters and to better investigate the properties of the PoLLS models, we restrict our attention to elliptical galaxies and assume that it is possible to use a PoLLS model tofit the surface brightness."971" Moreover. we arbitrarily set Ro=LAR, which implies that the larger is the distance from the centre. the larger is the bin width thus allowing"," Moreover, we arbitrarily set $R_2 = 1.1 R_1$ which implies that the larger is the distance from the centre, the larger is the bin width thus allowing"9722009).,.973". At large r, the dependence on o?(r) of the relation between the eccentricities in the halo and the seed becomes important."," At large $r$, the dependence on $\sigma^2(r)$ of the relation between the eccentricities in the halo and the seed becomes important."974" Yet, we can still determine the expected outer asymptotic behaviour of the eccentricities in the halo, taking only into account that, as mentioned, the object becomes more spherical at very large r."," Yet, we can still determine the expected outer asymptotic behaviour of the eccentricities in the halo, taking only into account that, as mentioned, the object becomes more spherical at very large $r$."975" In that asymptotic regime, the power indexes of the mean squared density, squared potential and crossed density-potential fluctuation profiles coincide (see Sec. ??))"," In that asymptotic regime, the power indexes of the mean squared density, squared potential and crossed density–potential fluctuation profiles coincide (see Sec. \ref{eccentricity}) )"976" and the more or less marked departure of isodensity and isopotential contours from spheres, given by the ratio Q/P, depends on the index « and the asymptotic logarithmic slope —a of the density profile (eq. [44]])."," and the more or less marked departure of isodensity and isopotential contours from spheres, given by the ratio $Q/P$, depends on the index $\kappa$ and the asymptotic logarithmic slope $-\alpha$ of the density profile (eq. \ref{QP}] ])."977" For values of a approaching 3 as near the outer asymptotic regime of virialised haloes, the only possible negative values of κ. leading to outward-decreasing eccentricitieswith isopotential contours moderately more spherical than the isodensity contours (Q/P not much greater than one) as found in the literature (Springeletal.2004;Kasun&Evrard2005;Hayashi2007) are in the range —0.2<&«0 (see the regions in dark blue, or quite strong grey if black and white, in Fig. 3))."," For values of $\alpha$ approaching 3 as near the outer asymptotic regime of virialised haloes, the only possible negative values of $\kappa$ leading to outward-decreasing eccentricitieswith isopotential contours moderately more spherical than the isodensity contours $Q/P$ not much greater than one) as found in the literature \citep{Sp04,KE05,Ha07} are in the range $-0.2\la \kappa< 0$ (see the regions in dark blue, or quite strong grey if black and white, in Fig. \ref{f3}) )."978" Thus, the outer asymptotic logarithmic slope, &, is also severely constrained in this approximate treatment."," Thus, the outer asymptotic logarithmic slope, $\kappa$, is also severely constrained in this approximate treatment."979 And what about the typical halo kinematics?, And what about the typical halo kinematics?980" The typical mean squared potential fluctuation profile for CDM haloes in log-log should be approximately given by the natural spline between a uniform value of ~0.11, as implied by the above mentioned typical eccentricities, below about one hundredth the virial radius and a straight line with logarithmic slope & beyond about one tenth the virial radius."," The typical mean squared potential fluctuation profile for CDM haloes in log-log should be approximately given by the natural spline between a uniform value of $\sim 0.11$, as implied by the above mentioned typical eccentricities, below about one hundredth the virial radius and a straight line with logarithmic slope $\kappa$ beyond about one tenth the virial radius."981" We will consider two values of &, —0.175 and —0.1, in order to better sample the allowed range —0.2S&«0 and to see how robust the theoretical typical halo kinematics are against variations in the individual shapes of haloes. ("," We will consider two values of $\kappa$, $-0.175$ and $-0.1$, in order to better sample the allowed range $-0.2\la \kappa< 0$ and to see how robust the theoretical typical halo kinematics are against variations in the individual shapes of haloes. ("982Different triaxial shapes must give rise to different mean squared potential fluctuation profiles.),Different triaxial shapes must give rise to different mean squared potential fluctuation profiles.)983 'The two squared potential fluctuation profiles so built are shown in Figure 4.., The two squared potential fluctuation profiles so built are shown in Figure \ref{fIII2}.984" Once the form of the squared potential fluctuation profile has been fixed, we can calculate the ratio o?(r)/c?(r) (eq. [74]])"," Once the form of the squared potential fluctuation profile has been fixed, we can calculate the ratio $\sigma\tang^2(r)/\sigma^2(r)$ (eq. \ref{00th}] ])"985" and, from it, the anisotropy profile (eq. [75]])."," and, from it, the anisotropy profile (eq. \ref{beta}] ])."986 Figure 5 shows the velocity anisotropy profiles inferred from the two different squared potential fluctuation profiles., Figure \ref{fIII5} shows the velocity anisotropy profiles inferred from the two different squared potential fluctuation profiles.987" As can be seen, they are both in good agreement with the results of numerical simulations."," As can be seen, they are both in good agreement with the results of numerical simulations."988" Specifically, for «=—0.1, we find an anisotropy profile that closely follows the typical ‘universal’ law proposed by Hansen&Stadel(2006) (the red line in the right panel)."," Specifically, for $\kappa=-0.1$, we find an anisotropy profile that closely follows the typical `universal' law proposed by \citet{HS06} (the red line in the right panel)."989" While, for «=—0.175, we find it closer to the anisotropy profile found by Navarroetal(2010) in a realisation of a Milky Way mass halo (the red line in the left panel)."," While, for $\kappa=-0.175$, we find it closer to the anisotropy profile found by \citet{Navea10} in a realisation of a Milky Way mass halo (the red line in the left panel)."990 The only noticeable disagreement in this latter case is that the theoretical profiles show no cutoff near the halo edge as found by Navarroetal But this is a very unusual feature (it does not follow the ‘universal’ trend) and likely reflects an incomplete relaxation of this particular simulated halo at those large radii., The only noticeable disagreement in this latter case is that the theoretical profiles show no cutoff near the halo edge as found by \citeauthor{Navea10} But this is a very unusual feature (it does not follow the `universal' trend) and likely reflects an incomplete relaxation of this particular simulated halo at those large radii.991" Using the previous theoretical velocity anisotropy profiles, we can solve the generalised Jeans equation (86)) to find the corresponding velocity dispersion profiles and, using the typical spherically averaged halo density profile derived in SVMS, the corresponding pseudo phase-space density profiles, (p)(r)/o? (r).In Figure 6,, we show the results obtained from the two mean squared potential fluctuation profiles above."," Using the previous theoretical velocity anisotropy profiles, we can solve the generalised Jeans equation \ref{exJeq2}) ) to find the corresponding velocity dispersion profiles and, using the typical spherically averaged halo density profile derived in SVMS, the corresponding pseudo phase-space density profiles, $\srho(r)/\sigma^3(r)$ .In Figure \ref{f6}, , we show the results obtained from the two mean squared potential fluctuation profiles above."992" In both cases, the theoretical pseudo phase-space density profile is very"," In both cases, the theoretical pseudo phase-space density profile is very"993"relationship. since Eq.(16)) is only a statistical mocel aud does not cousider the ""clouddu-cloud problem).","relationship, since \ref{Deltax-def}) ) is only a statistical model and does not consider the “cloud-in-cloud” problem)."994 Thus. sinall-scale structures ave no longer erased. since we keep a trace of planar features.," Thus, small-scale structures are no longer erased, since we keep a trace of planar features."995 This is expressed by the factor (Lo?)+P inH the exponentialH aregmiueut inB expressionB (76)).μον which suppresses the Gaussian decaving term of the form c 2.for poc. d.," This is expressed by the factor $(1-\mu^2)$ in the exponential argument in expression \ref{Psc-def1}) ), which suppresses the Gaussian decaying term of the form $e^{-k^2}$ for $\mu \simeq 1$ ."996 Thisqc vives. a width. Ay~Kk27. hence Pooth)~kD> at highBoO &. as would be the case for+ a density+ field where planar objects are the relevant noulinear structures (1.0. biccimensional structures. as opposed to oolutlike iuasses or lines for instance).," This gives a width $\Delta \mu \sim k^{-2}$, hence $\Psc(k) \sim k^{-2}$ at high $k$, as would be the case for a density field where planar objects are the relevant nonlinear structures (i.e. bi-dimensional structures, as opposed to pointlike masses or lines for instance)."997 Coutrary to the Zeldovich power spectrum there is uo dependence on à or the hielh-& slope. for poweraw linear power Spectra thy)xKI with 30xld.," Contrary to the Zeldovich power spectrum there is no dependence on $n$ for the $k$ slope, for power-law linear power spectra $P_L(k) \propto k^n$ with $-3<n<-1$."998 This gives the universal asviuptote ADsticky(k)xKk for the nonlinear logarithiuic oower of the “sticky model at high &., This gives the universal asymptote $\Delta^2_{\rm sticky}(k) \propto k$ for the nonlinear logarithmic power of the “sticky model” at high $k$.999 To clearly see the range of scales where perturbative schemes are relevant. we plot in Fig.," To clearly see the range of scales where perturbative schemes are relevant, we plot in Fig."1000" 2 the ratios of the successive termi of the ""renormalized perturbative expansion (031) with respect to the nonlinear power spectrum of the ""sticky iode. ¢WotPUpy?ricky(A). for Ξ1 to 5S. as well as (à=10.15.20.30.50. and 70."," \ref{fig_lrDk} the ratios of the successive terms of the “renormalized” perturbative expansion \ref{Psigv}) ) with respect to the nonlinear power spectrum of the “sticky model”, $e^{-k^2\sigma_v^2} P_{\sigma_v}^{(n)}(k)/P_{\rm sticky}(k)$, for $n=1$ to $5$, as well as $n=10, 15, 20, 30, 50$, and $70$."1001 We also ot the ratio Poh)/Pauast&). to compare with the auplitude of the nouperturbative correction associated with shell-crossiug effects;," We also plot the ratio $\Psc(k)/P_{\rm sticky}(k)$, to compare with the amplitude of the nonperturbative correction associated with shell-crossing effects."1002 We consider the four redshifts D-01.2. and 3.," We consider the four redshifts $z=0,1,2$, and $3$."1003 Here we focus ou the “renormalized” perturbative expansion (32)). rather than on the standard expansion (21)). to avoid the iutertercuces brought by the chanecs in sign aud the cancellations between various ternis.," Here we focus on the “renormalized” perturbative expansion \ref{Psigv}) ), rather than on the standard expansion \ref{Pstd}) ), to avoid the interferences brought by the changes in sign and the cancellations between various terms."1004 We can see that the potential of perturbative ONpaIS]OUS SLOWS a higher redshift for a ACDAL power spectrum. because of the change iu slope of Prth).," We can see that the potential of perturbative expansions grows at higher redshift for a $\Lambda$ CDM power spectrum, because of the change in slope of $P_L(k)$."1005 Thus. at +=3 we can go up to the order p»=66 oofore the perturbative termi becomes subdonunant with respect to the nouperturbative correction. while at 2=) the crossover takes place a no=€. as the term (WotpU(y is the lowest order one that is fully below he nouperturbative correction P(AK).," Thus, at $z=3$ we can go up to the order $n=66$ before the perturbative term becomes subdominant with respect to the nonperturbative correction, while at $z=0$ the crossover takes place at $n=9$, as the term $e^{-k^2\sigma_v^2} P_{\sigma_v}^{(10)}(k)$ is the lowest order one that is fully below the nonperturbative correction $\Psc(k)$."1006 This agrees with he observation that in the C»eravitational case perturbative schemes (and resuninatioun approaches) secur to fare etter at higher : (?).., This agrees with the observation that in the gravitational case perturbative schemes (and resummation approaches) seem to fare better at higher $z$ \citep{Carlson2009}.1007 We can see that perturbative schemes are relevant over roughly one decade over &., We can see that perturbative schemes are relevant over roughly one decade over $k$.1008" Thus. if we require an accuracy of L4 at 2=0. linear theory is sufficient up to Aj,~0.0337 lowhile ligher order perturbative terms allow reaching A...~0.234 |."," Thus, if we require an accuracy of $1\%$ at $z=0$, linear theory is sufficient up to $k_{1\rm loop} \sim 0.033 h$ $^{-1}$ , while higher order perturbative terms allow reaching $k_{\rm s.c.} \sim 0.23 h$ $^{-1}$."1009 At hieher À one must take the nouperturbative correction associated with shell-crossiug; effects iuto account. which iuplies eoiug bevoud the fluid approximation and requires new approaches.," At higher $k$ one must take the nonperturbative correction associated with shell-crossing effects into account, which implies going beyond the fluid approximation and requires new approaches."1010 To help the reader. we eive in Table 1 the waveummber Ausg. below which the linear terii is enough to reach a or LOY accuracy. for the four redshifts show iu Fig. 2..," To help the reader, we give in Table \ref{Table_range}1011 the wavenumber $k_{1\rm loop}$ , below which the linear term is enough to reach a $1\%$ or $10\%$ accuracy, for the four redshifts shown in Fig. \ref{fig_lrDk}."1012 We also give the wavemmuiber Aye. bevoud which the nonperturbative correction is required to reach an accuracy of 1!τον or 5O% (in uuits of Pu).," We also give the wavenumber $k_{\rm s.c.}$ beyond which the nonperturbative correction is required to reach an accuracy of $1\%, 10\%$, or $50\%$ (in units of $P_{\rm sticky}(k)$ )."1013 Thus. the interval [Adiccy.Ase.) gives the range where perturbation theories based on the fluid description aro relevant.," Thus, the interval $[k_{1\rm loop},k_{\rm s.c.}]$ gives the range where perturbation theories based on the fluid description are relevant."1014 Of course. this rause shifts to higher & at higher redshift.," Of course, this range shifts to higher $k$ at higher redshift."1015" It is interesting to uote that this range is also broader at higher redshift. as the slope of the CDAL linear power spectiun on the relevant scales changes slowly,"," It is interesting to note that this range is also broader at higher redshift, as the slope of the CDM linear power spectrum on the relevant scales changes slowly."1016 The last column gives the last order. noe. of the “renormalized” perturbative expansion that is not fully below the nonperturbative term.," The last column gives the last order, $n_{\rm s.c.}$, of the “renormalized” perturbative expansion that is not fully below the nonperturbative term."1017 As noticed above in Fie. 2.. ," As noticed above in Fig. \ref{fig_lrDk}, ,"1018this expansion order is significantly üeher at higher redshift., this expansion order is significantly higher at higher redshift.1019 This corresponds to a ereater voteutial for perturbative schemes., This corresponds to a greater potential for perturbative schemes.1020 However. nog. grows aster than the logarithmic width of the perturbative range. [hi4IAs].," However, $n_{\rm s.c.}$ grows faster than the logarithmic width of the perturbative range, $[\ln k_{1\rm loop},\ln k_{\rm s.c.}]$."1021 Tudeed. as shown in Fie. 2..," Indeed, as shown in Fig. \ref{fig_lrDk},"1022 oeaks associated with ligher order perturbative ternis are jucreasingly narrow on the lif axis., peaks associated with higher order perturbative terms are increasingly narrow on the $\ln k$ axis.1023 This nuplies hat to uultiplv the upper wavenumber À. defined bv a fixed accuracy. by a giveu amount. oue needs to add au increasinely ereater ΠΡΟ of new perturbative terms.," This implies that to multiply the upper wavenumber $k$, defined by a fixed accuracy, by a given amount, one needs to add an increasingly greater number of new perturbative terms."1024 Iu practice. we do not expect that perturbative terms will becomputed up to such high orders. since in the case of the eravitational dynamics this would involve multidineusioual integrals that are bevoud the reach of current numerical possibilities.," In practice, we do not expect that perturbative terms will becomputed up to such high orders, since in the case of the gravitational dynamics this would involve multidimensional integrals that are beyond the reach of current numerical possibilities."1025" Towever. resuuunatiou schemes allow one to consider parts of such higher orderterms (actually, an iufuite nuuber ofdiagrams that contribute to ternis of allorders)."," However, resummation schemes allow one to consider parts of such higher orderterms (actually, an infinite number ofdiagrams that contribute to terms of allorders)."1026 Then. the hope is that," Then, the hope is that"1027independent of the translating distance and direction.,independent of the translating distance and direction.1028 Note that &=(Εν.εν.&-) here is different from e in the first filter.," Note that $\vec \varepsilon=(\varepsilon _x, \varepsilon_y, \varepsilon _z)$ here is different from $\varepsilon$ in the first filter."1029 This filter is for constraining half-turn corkserew motion. eg. yi=TALOTL.) ΤΟ(απ). and glide reflection. eg. ys=TALΤΙ Α..," This filter is for constraining half-turn corkscrew motion, e.g. $\gamma _1=T_x(L_1)T_y(L_2)$ $T_z(L_3)O_z(\pi)$, and glide reflection, e.g. $\gamma_2=T_x(L_1)T_y(L_2)T_z(L_3)R_z$ ."1030" For a given. quadruplet [QjXj.QU.XD] to. be a y,-quadruplet. there are two possibilities such that γα2(V.X) or (XX)."," For a given quadruplet $[(\vec x_i, \vec x_j),(\vec x_k, \vec x_l)]$ to be a $\gamma _{n}$ -quadruplet, there are two possibilities such that $\gamma_n (\vec x_i , \vec x _j)=(\vec x_k, \vec x_l)$ or $\gamma_n (\vec x_i , \vec x _j)=(\vec x_l, \vec x_k)$ ."1031" In the former case. we ideally have a relation for n=1 and for Ξ2 In the latter case. on the other hand. we ideally have a relation for =| and for Ξ2 We consider these possibilities together to construct a filter: Here the rotation and reflection are based on the ""global directions of the universe about which we primarily have no idea. so m practice we have to find them by changing our choices of coordinate axes (see section 5.2.1 for details)."," In the former case, we ideally have a relation for $n=1$ and for $n=2$ In the latter case, on the other hand, we ideally have a relation for $n=1$ and for $n=2$ We consider these possibilities together to construct a filter: Here the rotation and reflection are based on the “global"" directions of the universe about which we primarily have no idea, so in practice we have to find them by changing our choices of coordinate axes (see section 5.2.1 for details)."1032 These filters are for constraining v-th turn. corkscrew motion for 1=4.3. and 6.," These filters are for constraining $n$ -th turn corkscrew motion for $n=4,3,$ and 6."1033 It is. for example. a holonomy y= T4LUOTALOTL3)0-422/n).," It is, for example, a holonomy $\gamma=T_x(L_1)T_y(L_2)T_z(L_3)O_z(2\pi/n)$ ."1034 As in the previous filters. there are two ways to pass through this filter for a given quadruplet.," As in the previous filters, there are two ways to pass through this filter for a given quadruplet."1035 We construct the filters by considering the two possibilities together. say. Corkserew motion meludes rotation based on the global directions. so we have to change our choices of coordinate axes to find it. as already mentioned.," We construct the filters by considering the two possibilities together, say, Corkscrew motion includes rotation based on the global directions, so we have to change our choices of coordinate axes to find it, as already mentioned."1036 An additional notice here is. that. in our caleulations we do not distinguish two. quadruplets [C.Vj).CU.ο] and [GGD.CV.Vj]. so the above filters will| ignore y'!- quadruplets.," An additional notice here is that in our calculations we do not distinguish two quadruplets $[(\vec x_i, \vec x_j),(\vec x_k, \vec x_l)]$ and $[(\vec x_k, \vec x_l),(\vec x_i, \vec x_j)]$, so the above filters will ignore $\gamma^{-1}$ -quadruplets."1037 For this we also use the filters which are unnecessary for the previous two cases since y! quadruplets can also be constrained by the same filters., For this we also use the filters which are unnecessary for the previous two cases since $\gamma^{-1}$ -quadruplets can also be constrained by the same filters.1038 Astronomical objects have finite lifetimes fj., Astronomical objects have finite lifetimes $t_{\mathrm{life}}$.1039 Suppose two objects X; and Y; whose cosmic times are r; and r;. respectively.," Suppose two objects $\vec x_i$ and $\vec x_j$ whose cosmic times are $t_i$ and $t_j$, respectively."1040 In order that they are ghost images of each other. is à necessary condition. so a quadruplet [0ο X] should be dropped unless Arg.Ary«fire Or Any.Ας<Nite.," In order that they are ghost images of each other, is a necessary condition, so a quadruplet $(\vec x_i,\vec x_j)$ $(\vec x_k, \vec x_l)$ ] should be dropped unless $\Delta t_{ik}, \Delta t_{jl}<t_{\mathrm{life}}$ or $\Delta t_{il}, \Delta t_{jk}<t_{\mathrm{life}}$."1041 This very closely corresponds to the redshift filter in Marecki et al. (, This very closely corresponds to the redshift filter in Marecki et al. (10422005). and the difference is only an expression.,"2005), and the difference is only an expression."1043 Some preceding studies ignore this effect and use all pairs despite their cosmic times., Some preceding studies ignore this effect and use all pairs despite their cosmic times.1044 This is a crucial fault unless L<=chiro. where L 1s a characteristic size of the universe.," This is a crucial fault unless $L \ll ct_{\mathrm{life}}$, where $L$ is a characteristic size of the universe."1045 Though the above three filters can drop false stochastic quadruplets while keeping real topological ones. it is possible that the false signal is still strong enough to hide the real signal.," Though the above three filters can drop false stochastic quadruplets while keeping real topological ones, it is possible that the false signal is still strong enough to hide the real signal."1046 For this situation. we introduce an additional technique to contrast real signals.," For this situation, we introduce an additional technique to contrast real signals."1047 Each object X;6=I.---.N) Is assigned an integer Hs;. the number of final candidate quadruplets that have passed through all filters and include X; as their members.," Each object $\vec x_i \ (i=1,\cdots,N)$ is assigned an integer $s_i$, the number of final candidate quadruplets that have passed through all filters and include $\vec x_i$ as their members."1048 False signals are stochastic. so the nembers of false quadruplets are randomly distributed.," False signals are stochastic, so the members of false quadruplets are randomly distributed."1049 As a result. the possibility that many final candidates share a single. common object is small. so s; takes a high value.," As a result, the possibility that many final candidates share a single, common object is small, so $s_i$ takes a high value."1050 Real signals. on the other hand. all come from ghostpairs.," Real signals, on the other hand, all come from ghostpairs."1051 If there are à y-pairs GG.YN.ss:(VjYN) where y is not a parallel translation. s;=2—| for each Xp. whereas s;>26:—1) if y is a parallel translation.," If there are $n \ \gamma$ -pairs $(\vec x_i, \gamma \vec x_i), \cdots, (\vec x_j, \gamma \vec x_j)$ where $\gamma$ is not a parallel translation, $s_k \ge n-1$ for each $\vec x_k$, whereas $s_k \ge2(n-1)$ if $\gamma$ is a parallel translation."1052 As a result the histogram of s; willcontrast real topological signals from false stochastic ones., As a result the histogram of $s_i$ willcontrast real topological signals from false stochastic ones.1053Do9d400H aud tre second oue corresponds to the tine when 5~(6j|0.)+. althouch hese transitions are very snuootlihy.,"$\gamma\sim1054(\theta_j-\theta_v)^{-1}$, and the second one corresponds to the time when $\gamma\sim (\theta_j+\theta_v)^{-1}$, although these transitions are very smoothly."1055 If the jet is 1xot ouform. within which the energy distribution is given by eq.(10). theji the calculation is nore coniplicated.," If the jet is not uniform, within which the energy distribution is given by eq.(10), then the calculation is more complicated."1056" Iu the case of 0,0. we can eive an analytical result. for kδρl)where p is the spectral index of electroLrenerey distriition) there should © two breaks in the light curve correspond to 5—0,! and 5—0lovespectivelv. while for komδέν|1) there should be oulv one break COLTCSPOlestor ~0,1. after hat the flux decays as Fy,κΤBEL "," In the case of $\theta_v =0$, we can give an analytical result, for $k<8/(p+4)$ (where $p$ is the spectral index of electron energy distribution) there should be two breaks in the light curve correspond to $\gamma\sim\theta_c^{-1}$ and $\gamma\sim\theta_j^{-1}$ respectively, while for $k>8/(p+4)$ there should be only one break corresponds to $\gamma\sim\theta_c^{-1}$, after that the flux decays as $F_\nu\propto T^{-3p/4}$."1057"Woe arene that this av exain some rapidly fading afterglows whose digit curves have no breass. Stace the tine T1. at which ~6,i is usualv carer than our first observation time."," We argue that this may explain some rapidly fading afterglows whose light curves have no breaks, since the time $T_1$, at which $\gamma\sim\theta_c^{-1}$, is usually earlier than our first observation time."1058" If the jet is non-uniforii aud the viewing angle 6,=0. ouly ποΊσα. restIts can be given."," If the jet is non-uniform and the viewing angle $\theta_v\neq 0$, only numerical results can be given."1059 We have shown that in this case the shape of afterglow licebit curve is dependeit ou the values of O.. 0. aid &.," We have shown that in this case the shape of afterglow light curve is dependent on the values of $\theta_v$, $\theta_c$ and $k$."1060" When 0, is near 0, aud & Is «αλα, then the lel curve is sinilar to the case of 0,=0. except the flux is somewhat lower."," When $\theta_v$ is near $\theta_c$ and $k$ is small, then the light curve is similar to the case of $\theta_v=0$, except the flux is somewhat lower."1061" IkNever. if t1ο VIEW]18o auele 0, is larger than 0, aud Kk isi rot stall. hen there will be a prominecut fattening in the afterglow liebit curve. which is quite different roni the case of uniforu jet. :uid after the fattening a verv sharp break will be occurred ALOTid the time 57(0,|0.)L"," However, if the viewing angle $\theta_v$ is larger than $\theta_c$ and $k$ is not small, then there will be a prominent flattening in the afterglow light curve, which is quite different from the case of uniform jet, and after the flattening a very sharp break will be occurred around the time $\gamma\sim (\theta_v + \theta_c)^{-1}$."1062OW think this is a main difference between the 1nifori aud 101n-unifornmi jet. :ud we cau identity whether the jet is wuform or not bv lis cature.," We think this is a main difference between the uniform and non-uniform jet, and we can identify whether the jet is uniform or not by this feature."1063 It is not very difficult to uudersand why sometiLLCs here is a flattening 1i the light curve., It is not very difficult to understand why sometimes there is a flattening in the light curve.1064 It is we] kiWAL hat. for a relativistic blast wave wit1 Lorentz factor Dm l. the observer can oulv observe asolid angle aroun f. with a half opeuiug arele of order D. 31. the couribulon roni other components can be neeleced. so when the bast wave decelerates. the observer cal see larecr componeits.," It is well known that, for a relativistic blast wave with Lorentz factor $\Gamma\gg 1$ , the observer can only observe a solid angle around $\theta_v$ with a half opening angle of order $\Gamma ^{-1}$ , the contribution from other components can be neglected, so when the blast wave decelerates, the observer can see larger components."1065" For the case of non-uniforni jet aud ο>0... the enerSv at 0—0, is winch staller than that of snaller 0. sow 1011 D decreases. the owervor can observe nore region with arecr enerev (snaler 0). so there will ο a flattening πι he Πο curve."," For the case of non-uniform jet and $\theta_v1066>\theta_c$, the energy at $\theta=\theta_v$ is much smaller than that of smaller $\theta$, so when $\Gamma$ decreases, the observer can observe more region with larger energy (smaller $\theta$ ), so there will be a flattening in the light curve."1067 We would poin out that. iu our caculation we have rwelected the sideways expansion of fje jet since this Xxocess is too complicated.," We would point out that, in our calculation we have neglected the sideways expansion of the jet since this process is too complicated."1068 However. we snow that. in fact his process is an iniportaut issue in determining the shape of a liebt. curve. since it will likely sigenificautly change he shape of the light curve for both he uniforii aud 1on-unifornmi jets.," However, we know that, in fact this process is an important issue in determining the shape of a light curve, since it will likely significantly change the shape of the light curve for both the uniform and non-uniform jets."1069 So we sugeestOO that for a nmnore realistic calculation the sideways expansion slotId be taken iuto account., So we suggest that for a more realistic calculation the sideways expansion should be taken into account.1070 Ne are very. grateful to J.D. Salmonson [or several important comments that improved this paper., We are very grateful to J.D. Salmonson for several important comments that improved this paper.1071 This work is supported by the National Natural Science Foundation (grants 10073022 and 10225314) and the National 073 Project onFundamental Researches of China (NIXDBRSE €19990754)., This work is supported by the National Natural Science Foundation (grants 10073022 and 10225314) and the National 973 Project onFundamental Researches of China (NKBRSF G19990754).1072The primary and secondary eclipses are apparent in the light curve as well as sinusoidal out-of-eclipse variability which is particularly evident in the 2006 data.,The primary and secondary eclipses are apparent in the light curve as well as sinusoidal out-of-eclipse variability which is particularly evident in the 2006 data.1073 Brightness variations due to photospheric star spots are often present on young and/or active stars and can be used to measure stellar rotation periods., Brightness variations due to photospheric star spots are often present on young and/or active stars and can be used to measure stellar rotation periods.1074" Thus, we investigated the presence of rotational variability on MML 53 to determine if the system is tidally synchronized."," Thus, we investigated the presence of rotational variability on MML 53 to determine if the system is tidally synchronized."1075" We measured the period of theout-of-eclipse variability by applying the Lomb-Scargle algorithm (Scargleetal.,1982;Horne&Baliunas,1986) to each season's light curve independently after removing all the in-eclipse data."," We measured the period of theout-of-eclipse variability by applying the Lomb-Scargle algorithm \citep{scargle,horne} to each season's light curve independently after removing all the in-eclipse data."1076 We searched periods between 0.2-30 days., We searched periods between 0.2-30 days.1077" In the 2006 data, there is a highly signficant sinusoidal signal with a period, P=2.09 days (see Fig. 2))."," In the 2006 data, there is a highly signficant sinusoidal signal with a period, $P=2.09$ days (see Fig. \ref{fig:pdgram}) )."1078 Aliased peaks due to the window function are also present at a reduced amplitude., Aliased peaks due to the window function are also present at a reduced amplitude.1079" In the 2007 and 2008 data sets, the signal is weaker, but still present."," In the 2007 and 2008 data sets, the signal is weaker, but still present."1080 This period is matched to the orbital period of the binary suggesting the out-of-eclipse variability is due to starspots on the surface of one or both of the binary components and that the component stars are rotating synchronously with the orbit., This period is matched to the orbital period of the binary suggesting the out-of-eclipse variability is due to starspots on the surface of one or both of the binary components and that the component stars are rotating synchronously with the orbit.1081 The sinusoidal variability is changing phase and amplitude on the timescale of months which manifests as visible scatter in the light curve (see Fig. 1)), The sinusoidal variability is changing phase and amplitude on the timescale of months which manifests as visible scatter in the light curve (see Fig. \ref{fig:swasplc}) )1082" indicating a slow drift in the starspot pattern, but the measured rotation period is consistent in all the seasons of data."," indicating a slow drift in the starspot pattern, but the measured rotation period is consistent in all the seasons of data."1083" For a short period binary like MML 53, we expect the components to berotating synchronously despite their young age (Zahn&Bouchet,1989;Mathieu,1994,andreferences therein).."," For a short period binary like MML 53, we expect the components to berotating synchronously despite their young age \citep[][and references therein]{zahn,mathieu}."1084" After determining the system was an eclipsing binary, we searched for existing archival spectroscopic data on the object and found one high resolution (R~ 50 000) spectrum located in the European Southern Observatory (ESO) archive."," After determining the system was an eclipsing binary, we searched for existing archival spectroscopic data on the object and found one high resolution $R\sim$ 50 000) spectrum located in the European Southern Observatory (ESO) archive."1085" The spectrum was obtained at heliocentric Julian date, HJD=2453909.622300 with the FEROS spectrograph on the 2.2m ESO telescope at La Silla (observing program 077.C-0138(A), which forms the basis of the SACY survey, see Torreset (2006)))."," The spectrum was obtained at heliocentric Julian date, $HJD=2453909.622300$ with the FEROS spectrograph on the 2.2m ESO telescope at La Silla (observing program 077.C-0138(A), which forms the basis of the SACY survey, see \citet{Torres}) )."1086" We reduced this spectrum with the echelle data reduction package (Piskunov&Valenti,2002),, using calibration data obtained on the same night."," We reduced this spectrum with the echelle data reduction package \citep{piskunov02}, using calibration data obtained on the same night."1087" We also downloaded and reduced the spectrum of a radial velocity standard, HD 10700."," We also downloaded and reduced the spectrum of a radial velocity standard, HD 10700."1088 Our final reduced spectrum covers the wavelength range of aand has a signal-to-noise of ~30 per pixel at6000A., Our final reduced spectrum covers the wavelength range of and has a signal-to-noise of $\sim 30$ per pixel at.1089". When the spectrum was examined by eye, multiple stellar components were clearly present as previously reported (Torresetal,2006;White2007) and as expected for an eclipsing binary where both the primary and secondary eclipses are visible."," When the spectrum was examined by eye, multiple stellar components were clearly present as previously reported \citep{Torres,White} and as expected for an eclipsing binary where both the primary and secondary eclipses are visible."1090" However, Whiteetal.(2007) report the system as a double-lined spectroscopic binary (SB2) while Torresetal.(2006) suggest the possibility of a third component (SB3)."," However, \citet{White} report the system as a double-lined spectroscopic binary (SB2) while \citet{Torres} suggest the possibility of a third component (SB3)."1091" To determine whether the system contains a third star and to measure the radial velocities of the components, we perform a standard cross-correlation (Fig. 3))"," To determine whether the system contains a third star and to measure the radial velocities of the components, we perform a standard cross-correlation (Fig. \ref{fig:ccf}) )"1092 and also apply our implementation of the least-squares deconvolution (LSD) algorithm to the MML 53 spectrum., and also apply our implementation of the least-squares deconvolution (LSD) algorithm to the MML 53 spectrum.1093" Least-squares deconvolution allows for deriving a very high signal-to-noise average absorption line profile of the system by properly combining the many individual lines throughout the entire spectrum (Donatietal.,1997).", Least-squares deconvolution allows for deriving a very high signal-to-noise average absorption line profile of the system by properly combining the many individual lines throughout the entire spectrum \citep{donati_lsd}.1094. This technique can be used in spectroscopic binary work to identify faint unresolved companions., This technique can be used in spectroscopic binary work to identify faint unresolved companions.1095 Both the cross-correlation function (CCF) and the result of the LSD analysis clearly show three stellar components present in the spectrum., Both the cross-correlation function (CCF) and the result of the LSD analysis clearly show three stellar components present in the spectrum.1096" We measure their radial velocities to be —85.8, 111.1 and —3.5 s, for the primary, secondary and tertiary, respectively."," We measure their radial velocities to be $-85.8$ , $111.1$ and $-3.5$ , for the primary, secondary and tertiary, respectively."1097 , 1098 et 22010) on the is a powerful new tool to study galaxy formation in both the redshift and local regimes., et 2010) on the is a powerful new tool to study galaxy formation in both the high-redshift and local regimes.1099 We know little about the formation of galaxy bulges. due in part to conflicting evidence regarding our own bulge (see Zoccah 2010).," We know little about the formation of galaxy bulges, due in part to conflicting evidence regarding our own bulge (see Zoccali 2010)."1100 From à populations perspective. our bulge looks like a “classical” bulge — similar to an old. nearly coeval elliptical galaxy.," From a populations perspective, our bulge looks like a “classical” bulge – similar to an old, nearly coeval elliptical galaxy."1101 From a morphological perspective. our bulge looks like a “pseudo-bulge.” with a peanut shape apparently arising from bar-driven secular processes.," From a morphological perspective, our bulge looks like a “pseudo-bulge,” with a peanut shape apparently arising from bar-driven secular processes."1102 As summarized by Kormendy Kennicutt (2004). a range of mechanisms may contribute to bulge formation. with rapid processes in discrete events (e.g.. dissipative collapse. mergers of clouds and proto-galaxies) dominating in the early universe. and secular processes (interactions between stars. gas clouds. bars. spiral structure. triaxial halos. ete.)," As summarized by Kormendy Kennicutt (2004), a range of mechanisms may contribute to bulge formation, with rapid processes in discrete events (e.g., dissipative collapse, mergers of clouds and proto-galaxies) dominating in the early universe, and secular processes (interactions between stars, gas clouds, bars, spiral structure, triaxial halos, etc.)"1103 dominating at later times., dominating at later times.1104 In broad terms. we see classical bulges if the earlier rapid processes are dominant. and pseudo-bulges if the later slower processes are dominant.," In broad terms, we see classical bulges if the earlier rapid processes are dominant, and pseudo-bulges if the later slower processes are dominant."1105 However. à new paradigm has recently emerged. driven by observations at z~2. that reveal the widespread existence of large. rotating. disk galaxies with much higher gas fractions compared to local spirals (Genzel et 22008: Fórrster Schreiber et 22009).," However, a new paradigm has recently emerged, driven by observations at $z \sim 2$, that reveal the widespread existence of large, rotating, disk galaxies with much higher gas fractions compared to local spirals (Genzel et 2008; Förrster Schreiber et 2009)."1106 Such gas-rich. clumpy disks are prone to instabilities that can lead to bulge formation at early cosmic epochs and over timescales much shorter than those traditionally associated with secular instabilities in local spirals (e.g.. Immeli et 22004: Elmegreen et 22009).," Such gas-rich, clumpy disks are prone to instabilities that can lead to bulge formation at early cosmic epochs and over timescales much shorter than those traditionally associated with secular instabilities in local spirals (e.g., Immeli et 2004; Elmegreen et 2009)."1107 These processes should imprint distinet age and metallicity gradients upon the bulge, These processes should imprint distinct age and metallicity gradients upon the bulge1108median host magnitude. with LEG ~ 0.3 mae brighter.,"median host magnitude, with LEG $\sim$ 0.3 mag brighter."1109 As originally sueeested by Cuiscllind&Celotti(2001.here-afterCCOL) the radio - host galaxy luuinosity plane can be translated into a jet-power vs black hole mass diagram.," As originally suggested by \citet[ hereafter GC01]{ghisellini01b}1110 the radio - host galaxy luminosity plane can be translated into a jet-power vs black hole mass diagram."1111 The substantial superposition between HEC aud LEG indicates that also the distribution of the estimated black hole masses aud jet power for the two classes are sinilar., The substantial superposition between HEG and LEG indicates that also the distribution of the estimated black hole masses and jet power for the two classes are similar.1112 CGCOL also note that the line huuinosity ciui be used as dudicator of the ionizing lhuuinositv. Li. that thev estimated. from the radio power (seee.g.Willottetal. 1999).," \citetalias{ghisellini01b} also noted that the line luminosity can be used as indicator of the ionizing luminosity, $L_{\rm ion}$, that they estimated from the radio power \citep[see e.g.][]{willott99}."1113. We can now derive this quantity directly from the [O III] huiuiuosity We also derived the black hole mass from the host Iuuinositv using the correlation of Marconi&Iuut(2003) In Fig., We can now derive this quantity directly from the [O III] luminosity We also derived the black hole mass from the host luminosity using the correlation of \citet{marconi03} In Fig.1114 Hd. we show the Lygp—My plane that. as explained above. cau be translated iuto a Lion—Mp aue.," \ref{ledlow3} we show the $L_{\rm [O~III]}-M_{\rm H}$ plane that, as explained above, can be translated into a $L_{\rm ion}-M_{\rm BH}$ plane."1115 With respect to Fig. 10..," With respect to Fig. \ref{ledlow},"1116 the location of LEC aud WEG ire substantially offset., the location of LEG and HEG are substantially offset.1117" LEG/ER I are located at he bottom of the diagram aud all have Zia πα<1043 where Lag=1:310Mp /M erg Lis the Eddinetou u""numositv."," LEG/FR I are located at the bottom of the diagram and all have $L_{\rm1118 ion}$ $L_{\rm Edd}\lesssim10^{-4}$, where $L_{\rm Edd}= 1.3 \cdot 10^{38}1119M_{\rm BH}$ $M_{\odot}$ erg $^{-1}$ is the Eddington luminosity."1120 LEG/ER II (aud also LEC of uncertain FR ype) lie in an intermediate area. while TEC cover the top region.," LEG/FR II (and also LEG of uncertain FR type) lie in an intermediate area, while HEG cover the top region."1121 Iu geuecral LEG (reeardless of the FR type) and WTEC are rather well separated. but they coexist over the range ἐν10|XLian πια<2107.," In general LEG (regardless of the FR type) and HEG are rather well separated, but they coexist over the range $4 \times 10^{-4}1122\lesssim L_{\rm ion}$ $L_{\rm Edd} \lesssim 2 \times 10^{-3}$."1123 The dividing line has apparently a positive slope. in the seuse that LEG can be found at high values of Zio only in the brightest ealaxies.," The dividing line has apparently a positive slope, in the sense that LEG can be found at high values of $L_{\rm[O III]}$ only in the brightest galaxies."1124 Marchesinietal.(2001). found that the bolometric Iuiuiuositv for racio-loud ACN has a bimodal distribution.," \citet{marchesini04} found that the bolometric luminosity for radio-loud AGN has a bimodal distribution,"1125of the spectral energy distribution of the discs very well.,of the spectral energy distribution of the discs very well.1126 Phe computational cheapness of the analytic approach makes the CG97 model very useful to compare with a Large sample of the dises observed., The computational cheapness of the analytic approach makes the CG97 model very useful to compare with a large sample of the discs observed.1127 Therefore. some attempts to refine the simple model of CXGO7 were performed (Chiangetal.2001:2003a:Rafikov&DeColle2006:GaraudLin 2007).," Therefore, some attempts to refine the simple model of CG97 were performed \citep{chi01,dul01,dul03a,raf06,gar07}."1128. Despite a great success of the CCG97 model. numerical simulations of the radiation transfer in the cdises showed a significant decrement of the equatorial temperature relative to the prediction bx the CG97 model (Dullemond&Natta2003a)," Despite a great success of the CG97 model, numerical simulations of the radiation transfer in the discs showed a significant decrement of the equatorial temperature relative to the prediction by the CG97 model \citep{dul03a}."1129 The internal energy. loss by the radiation at a long wavelength. where the optical depth of the disc. is relatively small is suggested. as a cause of the decrement (Dullemondetal.2002:Dullemond&Natta2003a).," The internal energy loss by the radiation at a long wavelength where the optical depth of the disc is relatively small is suggested as a cause of the decrement \citep{dul02,dul03a}."1130. In the CCG97 model and refined. ones. the wavelength dependence of dust opacity was taken into account in terms of mean opacity.," In the CG97 model and refined ones, the wavelength dependence of dust opacity was taken into account in terms of mean opacity."1131 Dullemoncctal.(2002) argued. the importance ( using full wavelength. dependent. opacity., \cite{dul02} argued the importance of using full wavelength dependent opacity.1132 However. we propose an alternative approach in this paper: a three-layer model with mean opacity which reproduces the temperature reduction quite well.," However, we propose an alternative approach in this paper: a three-layer model with mean opacity which reproduces the temperature reduction quite well."1133 In addition. we show that the two-layer approximation in the CG9O7 model is valid. only when the dust Opacity is teres” which is expected if the size of dust erains is larger than about 10pum.," In addition, we show that the two-layer approximation in the CG97 model is valid only when the dust opacity is “grey” which is expected if the size of dust grains is larger than about 10."1134. Elect of seattering on the vertical temperature structure was not considered in the literature very much., Effect of scattering on the vertical temperature structure was not considered in the literature very much.1135 Scattering of the stellar radiation was taken into account analvtically bv Calvetctal.(1991) and numerically bv Dullemoned&Natta(2003) who showed that. the temperature of the dise interior is slightly. reduced. by the scattering., Scattering of the stellar radiation was taken into account analytically by \cite{cal91} and numerically by \cite{dul03} who showed that the temperature of the disc interior is slightly reduced by the scattering.1136 Llow about scattering. of the cilluse clisc radiation?, How about scattering of the diffuse disc radiation?1137 As the size of grains increases. the scattering albedo increases.," As the size of grains increases, the scattering albedo increases."1138 In particular. the albedo of large icy. grains is close to unity even for the infrared wavelength.," In particular, the albedo of large icy grains is close to unity even for the infrared wavelength."1139 This may allect the disc structure significantly., This may affect the disc structure significantly.1140 Nevertheless. it. has not been examined. so far.," Nevertheless, it has not been examined so far."1141 This paper discusses the effect. of scattering of the diffuse radiation. as well as that of the stellar. radiation on the vertical temperature structure of protoplanctary disces., This paper discusses the effect of scattering of the diffuse radiation as well as that of the stellar radiation on the vertical temperature structure of protoplanetary discs.1142 Since the albedo. depends on the grain size. we examine the scattering cllect as a function of the grain size.," Since the albedo depends on the grain size, we examine the scattering effect as a function of the grain size."1143 Although there are. 2-D/3-D numerical radiation transfer codes available publicly. most. of them have ao serious dillieultv in solving the radiation equilibrium in very high optical depth (r~ 10°) found in protoplanetary discs (Dascuccictal.2004:Steinacker.Dacmann. 2006).," Although there are 2-D/3-D numerical radiation transfer codes available publicly, most of them have a serious difficulty in solving the radiation equilibrium in very high optical depth $\tau\sim10^6$ ) found in protoplanetary discs \citep{pas04,ste06}."1144". The RADICAL developed by Dullemond.&""Tur-olla(2000) can solve such a problem without any dilliculty manks to à variable Ecldineton tensor method.", The RADICAL developed by \cite{dul00} can solve such a problem without any difficulty thanks to a variable Eddington tensor method.1145 However. it reats scattering of only the stellar radiation.," However, it treats scattering of only the stellar radiation."1146 We present v variable. Eddington factor code with both scatterings of re stellar. radiation and of the cdilfuse radiation. but. in a LD ecometry., We present a variable Eddington factor code with both scatterings of the stellar radiation and of the diffuse radiation but in a 1-D geometry.1147 We also present an analytic model to interpret the numerical results., We also present an analytic model to interpret the numerical results.1148 This simple model would oe very useful to understand. the physics determining the emperature structure of protoplanetary clises., This simple model would be very useful to understand the physics determining the temperature structure of protoplanetary discs.1149 The rest of this paper consists of three sections: in section 2. we develop à numerical radiation transfer code aking into account both of the scatterings but. only for isotropic case and show the obtained numerical solutions.," The rest of this paper consists of three sections; in section 2, we develop a numerical radiation transfer code taking into account both of the scatterings but only for isotropic case and show the obtained numerical solutions."1150 In section 3. we construct an analytic model to interpret the numerical solutions and discuss the physical mechanism determining the temperature structure in protoplanetary discs.," In section 3, we construct an analytic model to interpret the numerical solutions and discuss the physical mechanism determining the temperature structure in protoplanetary discs."1151 In the final section. we summarise our findings.," In the final section, we summarise our findings."1152 Our method is an extension of the variable IEddington factor method developed by Dullemondctal.(2002): we include isotropic scattering of the diffuse radiation as well as that of the stellar raciiation., Our method is an extension of the variable Eddington factor method developed by \cite{dul02}; we include isotropic scattering of the diffuse radiation as well as that of the stellar radiation.1153 A disc is divided into many annuli in which the transfer of the diffuse radiation is treated one-dimensionally along the normal axis of cach annulus with neglecting the radiation energv iransport among annuli., A disc is divided into many annuli in which the transfer of the diffuse radiation is treated one-dimensionally along the normal axis of each annulus with neglecting the radiation energy transport among annuli.1154 This approximation. so-called. 1]1D approximation. would »* reasonable in an optically thick disc. but not at. the near of the disc inner edge nor in a ποπαονας region (c.g..Dullemond.Dominik.&Natta2001).," This approximation, so-called 1+1D approximation, would be reasonable in an optically thick disc, but not at the near of the disc inner edge nor in a self-shadowing region \citep[e.g.,][]{dul01}."1155. Phe radiation rom the central star is separated from the diluse radiation and is treated with the so-called grazing angle recipe., The radiation from the central star is separated from the diffuse radiation and is treated with the so-called grazing angle recipe.1156 In his paper. we onlv consider some single annulus cases in order to feature the effect. of the scattering on. the emperature structure along the normal axis of the annulus.," In this paper, we only consider some single annulus cases in order to feature the effect of the scattering on the temperature structure along the normal axis of the annulus."1157 Therefore. we assume a grazing angle a=0.05 radian hroughout of the paper.," Therefore, we assume a grazing angle $\alpha=0.05$ radian throughout of the paper."1158 The density structure along the normal axis of the annulus is solved to be consistent with the obtained. temperature structure assuming the hyvdrostatic equilibrium., The density structure along the normal axis of the annulus is solved to be consistent with the obtained temperature structure assuming the hydrostatic equilibrium.1159 In. Appendix A. we describe how to obtain the numerical solution of the dilfuse radiation transfer with isotropic scattering in each annulus in detail.," In Appendix A, we describe how to obtain the numerical solution of the diffuse radiation transfer with isotropic scattering in each annulus in detail."1160 We adopt a very simple cust model in. order to feature the cllect of scattering on the temperature structure., We adopt a very simple dust model in order to feature the effect of scattering on the temperature structure.1161 The absorption and scattering cross sections per unit gas mass at the wavelength A are assumed to be and respectively., The absorption and scattering cross sections per unit gas mass at the wavelength $\lambda$ are assumed to be and respectively.1162 The single scattering. albedo αἲ the wavelength A is The critical wavelength A. may be related to a typical erain racius e as A.=2re., The single scattering albedo at the wavelength $\lambda$ is The critical wavelength $\lambda_{\rm c}$ may be related to a typical grain radius $a$ as $\lambda_{\rm c} = 2\pi a$.1163" M we consider a spherical grain composed of uniform material. the absorption cross section is expressed as pil=(3DQYV"")(Ape). where QU is the absorption cross section normalised by the geometrical cross section mar. pa is the grain material density. and D is the cdlust-Lo-gas niass ratio."," If we consider a spherical grain composed of uniform material, the absorption cross section is expressed as $\kappa_\lambda^{\rm abs}=(3{\cal D}Q_\lambda^{\rm abs})/(4\rho_{\rm d}a)$, where $Q_\lambda^{\rm abs}$ is the absorption cross section normalised by the geometrical cross section $\pi a^2$, $\rho_{\rm d}$ is the grain material density, and $\cal D$ is the dust-to-gas mass ratio."1164 With the values of D=10> (Solar svstem nebula). ρα=3 ο em? (silicate). and QU.1 (À5» 0). we obtain the absorption cross section for small wavelengths as," With the values of ${\cal D}=10^{-2}$ (Solar system nebula), $\rho_{\rm d}=3$ g $^{-3}$ (silicate), and $Q_\lambda^{\rm abs} \to 1$ $\lambda \to 0$ ), we obtain the absorption cross section for small wavelengths as"1165The foregoing formula ts only true for an equatorial transit of a main-sequence star in a band which is not limb-darkened.,The foregoing formula is only true for an equatorial transit of a main-sequence star in a band which is not limb-darkened.1166 Including limb-darkening and a non-equatorial transit. one finds where v=V/1—52. b is the minimum impact parameter of the lens with respect to the center of the source star in units of R.. Dying is the mean surface brightness of the source along the path of the lens. and (74/4 1s the mean surface brightness of the source.," Including limb-darkening and a non-equatorial transit, one finds where $x=\sqrt{1-b^2}$ , $b$ is the minimum impact parameter of the lens with respect to the center of the source star in units of $R_*$, $\langle1167I \rangle_{line}$ is the mean surface brightness of the source along the path of the lens, and $\langle I \rangle_{disk}$ is the mean surface brightness of the source."1168 For quadratic limb-darkening. we find ΗΠΑ. and σι.το are known from. say. modeling of the spectrum of the main-sequence star. then equation has two unknowns. b (or x) and Meo.," For quadratic limb-darkening, we find If $R_*$ and $\gamma_1,\gamma_2$ are known from, say, modeling of the spectrum of the main-sequence star, then equation has two unknowns, $b$ (or $x$ ) and $M_{CO}$."1169 Another equation can be obtained from the ratio of the duration of the transit. fans; to the period of the orbit. P.," Another equation can be obtained from the ratio of the duration of the transit, $t_{transit}$, to the period of the orbit, $P$."1170 Since P depends on the semi-major axis. which depends on the masses of both stars. one finds which constitutes another equation for b and Mc assuming that Mays is known.," Since $P$ depends on the semi-major axis, which depends on the masses of both stars, one finds which constitutes another equation for $b$ and $M_{CO}$ assuming that $M_{MS}$ is known."1171 The mass of the compact object may be found by eliminating Moo in equations and21. which yields a 6th order equation for x which can be solved numerically for x which may then be used in equation to find Meo.," The mass of the compact object may be found by eliminating $M_{CO}$ in equations and, which yields a 6th order equation for $x$ which can be solved numerically for $x$ which may then be used in equation to find $M_{CO}$."1172" If the data are of sufficient quality then 5 may be found by fitting the shape of the transit and then Mc, may be found directly from equation (this is described in for the occultation case).", If the data are of sufficient quality then $b$ may be found by fitting the shape of the transit and then $M_{CO}$ may be found directly from equation (this is described in for the occultation case).1173" Uncertainties in M...R..>,. and 5» will contribute to uncertainty in Moo and b."," Uncertainties in $M_*, R_*, \gamma_1,$ and $\gamma_2$ will contribute to uncertainty in $M_{CO}$ and $b$."1174 Another technique for finding 5 relies on measuring the difference of the transit depth in different bands., Another technique for finding $b$ relies on measuring the difference of the transit depth in different bands.1175 Figure 7 shows the ratio of H(5) for the V and I bands as a function of impact parameter for a solar-type star., Figure 7 shows the ratio of $H(b)$ for the V and I bands as a function of impact parameter for a solar-type star.1176 The variation is nearly a factor of 3 for 5 ranging between 0 and 1., The variation is nearly a factor of 3 for $b$ ranging between 0 and 1.1177 Given this ratio. x may be solved for using the quadratic equation in x determined by equating the functions for V and I with the observed value.," Given this ratio, $x$ may be solved for using the quadratic equation in $x$ determined by equating the functions for V and I with the observed value."1178" The value of 5b measured from this relation can then be used to estimate H(b5) and determine R,/R..Fi", The value of $b$ measured from this relation can then be used to estimate $H(b)$ and determine $R_g/R_*$.1179c; The transit detection probability is ΑΔ.α. from which we can estimate the fraction of binaries for which transits can be detected assuming the the required fluence sensitivity can be achieved.," The transit detection probability is $R_*/a$, from which we can estimate the fraction of binaries for which transits can be detected assuming the the required fluence sensitivity can be achieved."1180 This is considered in detail for WD-MS binaries by who find that >10° such systems might be found with theKepler and missions. and for WD-WD. WD-NS. binaries by(2002).," This is considered in detail for WD-MS binaries by who find that $>10^2$ such systems might be found with the and missions, and for WD-WD, WD-NS, WD-BH binaries by."1181 Here we make some general considerations for the detection of NS-MS and BH-MS binaries., Here we make some general considerations for the detection of NS-MS and BH-MS binaries.1182 For the binary to not acerete. the main-sequence star must have a size smaller than the Roche-lobe size. Κι. by some factor fgSR.f Ry.," For the binary to not accrete, the main-sequence star must have a size smaller than the Roche-lobe size, $R_L$, by some factor $f_R=R_*/R_L$ ."1183" Toa good approximation. the Roche-lobe is given by Αι=O.Safy ""where fiy2MastMas-McoY| and the CO subscript stands for compact object1985)."," To a good approximation, the Roche-lobe is given by $R_L=0.5 a f_M^{1/3}$ where $f_M=M_{MS}(M_{MS}+M_{CO})^{-1}$ and the $CO$ subscript stands for compact object."1184" Typically. binaries show a distribution of semi-major axes which ts constant in Ina. which we assume to be the case from «5, to ρω for BH-MS and NS-MS binaries (clearly. reality is likelyto be more complicated due to the effectsof kick-velocities during the formation of the compact object. e.g. in à supernova collapse). common-envelope evolution of the massive star. and tidal evolution due to distortion of the main-sequence star)."," Typically, binaries show a distribution of semi-major axes which is constant in $\ln{a}$, which we assume to be the case from $a_{min}$ to $a_{max}$ for BH-MS and NS-MS binaries (clearly, reality is likelyto be more complicated due to the effectsof kick-velocities during the formation of the compact object, e.g. in a supernova collapse), common-envelope evolution of the massive star, and tidal evolution due to distortion of the main-sequence star)."1185 Since αμ isset by the Roche-lobe, Since $a_{min}$ isset by the Roche-lobe1186where J; changes linearly over à 5 Myr. period at the beginning and end of each burst [rom J;=96.15 (eres sb's bem 3? ! !) at the low level continuous star formation rate to J;=96.63 (eres s bem ? ! svt) during a burst.,where $J_{i}$ changes linearly over a $5$ Myr period at the beginning and end of each burst from $J_{i}=96.15$ (ergs $s^{-1}$ $^{-1}$ $^{-2}$ $^{-1}$ $^{-1}$ ) at the low level continuous star formation rate to $J_{i}=96.63$ (ergs $s^{-1}$ $^{-1}$ $^{-2}$ $^{-1}$ $^{-1}$ ) during a burst.1187 The addition of star formation will also result in supernova superheating the eas well above the temperature of the warm phase Any power from the supernova is assumed to go into heating gas into a hot (10° IX) phase., The addition of star formation will also result in supernova superheating the gas well above the temperature of the warm phase Any power from the supernova is assumed to go into heating gas into a hot $10^6$ K) phase.1188 In realitv. the enerey from the supernova will also eo into expanding the cold and warm phases. making them more susceptible (ο stripping. but due to the limitations of a smooth density profile we assume (liis energy is instead used to heat the gas.," In reality, the energy from the supernova will also go into expanding the cold and warm phases, making them more susceptible to stripping, but due to the limitations of a smooth density profile we assume this energy is instead used to heat the gas."1189 We find the power output of a supernova for continuous. non-bursty star formation is given by After à burst has commenced. the power output bv the supernovae increases over 38 Myr. with the power over this period of increasing output given by where / is the time in Myr since the burst commenced.," We find the power output of a supernova for continuous, non-bursty star formation is given by After a burst has commenced, the power output by the supernovae increases over $38$ Myr, with the power over this period of increasing output given by where $t$ is the time in Myr since the burst commenced."1190 During the increased star formation associated with the bursty period Sharp&Bland-Lawthorn2010). the power output is After the burst has ended and star formation drops back down to the continuous star formation rate. the power output subsides as massive stars die off.," During the increased star formation associated with the bursty period \citep[lasting $\le10^7$~yr][]{Sharp2010} the power output is After the burst has ended and star formation drops back down to the continuous star formation rate, the power output subsides as massive stars die off."1191 Over a period of 40 Myr. the power output declines according to where /' is the time since the starburst has ended in Mv.," Over a period of $40$ Myr, the power output declines according to where $t'$ is the time since the starburst has ended in Myr."1192 In (his simplified model. we assume that anv power from (he supernova is dissipated in (he gas and goes into heating the cold and warm gas al 1004. efficiency and split between the cold ancl warm phase in proportion to their mass.," In this simplified model, we assume that any power from the supernova is dissipated in the gas and goes into heating the cold and warm gas at $100\%$ efficiency and split between the cold and warm phase in proportion to their mass."1193 The mass loss rate will then be the, The mass loss rate will then be the1194anv time. for anv given mass.,"any time, for any given mass."1195 Also. the effect of the photospheric models on Tog was shown to be no larger than about IXIx. 22 of Chabrier οἱ al.," Also, the effect of the photospheric models on $T_{\rm eff}$ was shown to be no larger than about K 2 of Chabrier et al."1196 2000)., 2000).1197 With these reservations in mind. we conclude Chat the general trend of the observed. CM diagram can be reasonably well fitted with the predicted ones based on the evolutionary. models and (he photospheric models (and lla Ib can also be applied to any other evolutionary (track).," With these reservations in mind, we conclude that the general trend of the observed CM diagram can be reasonably well fitted with the predicted ones based on the evolutionary models and the photospheric models (and 1a 1b can also be applied to any other evolutionary track)."1198 It is to be noted that the “brightening” of the J flux in the early To cwarls is an artifact of observing objects with different masses and/or ages. and it should not imply. that a single cooling track of a given mass shows the “brightening”.," It is to be noted that the “brightening” of the $J$ flux in the early T dwarfs is an artifact of observing objects with different masses and/or ages, and it should not imply that a single cooling track of a given mass shows the “brightening”."1199 Nevertheless (he rather high Ihuninositv at the band reflects (he re-increase of BC) at the L/T transition noted before and (his is a natural consequence of the migration of the dust cloud from the optically thin region (7<1) in L dwarls to the optically thick region (721) in T dwarfs., Nevertheless the rather high luminosity at the $J$ band reflects the re-increase of $BC_{\rm J}$ at the L/T transition noted before and this is a natural consequence of the migration of the dust cloud from the optically thin region $(\tau < 1)$ in L dwarfs to the optically thick region $(\tau \ga 1)$ in T dwarfs.1200 This migration ol the dust cloud recovers the gaseous opacities including Il CLA at the A band region and makes the J flux large enough to compensate lor the decreasing bolometric [lux in the earlv T dwarls., This migration of the dust cloud recovers the gaseous opacities including $_2$ CIA at the $K$ band region and makes the $J$ flux large enough to compensate for the decreasing bolometric flux in the early T dwarfs.

Showing the first 1,200 of 10329 lines. Download the file for the rest.