ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 Despite much effort. little is presently known about the nature of these sources. particularly since the counterparts at. other wavelengths are difficult to find.," Despite much effort, little is presently known about the nature of these sources, particularly since the counterparts at other wavelengths are difficult to find."3 Indeed. these sources are often superposed against regions of high surface brightness in their host galaxy.," Indeed, these sources are often superposed against regions of high surface brightness in their host galaxy."4 Thus. most of the optical identifications are obtained by spatial coincidence of the counterparts and comparison with broadband spectral characteristics of known stars in the host (Liu et al.," Thus, most of the optical identifications are obtained by spatial coincidence of the counterparts and comparison with broadband spectral characteristics of known stars in the host (Liu et al."5 2002; Wu et al., 2002; Wu et al.6 2002: Zezas et al., 2002; Zezas et al.7 2002: Zampieri et al., 2002; Zampieri et al.8 2003)., 2003).9 In other cases. it has been possible to study only the nearby environment in the ULX host (Pakull Mirtont 2002: Wang 2002: Roberts et al.," In other cases, it has been possible to study only the nearby environment in the ULX host (Pakull Mirioni 2002; Wang 2002; Roberts et al."10 2003)., 2003).11 In one case (NGC4698-ULX1) the optical spectral features allowed a clear dentification as a background BL Lae object (Foschini et al., In one case (NGC4698-ULX1) the optical spectral features allowed a clear identification as a background BL Lac object (Foschini et al.12 20022)., 2002a).13 Here we report the identification of the nature of another ULX., Here we report the identification of the nature of another ULX.14 The counterparts in the infrared and optical bands were found. and spectroscopy revealed clear Balmer and forbidden transition emission lines.," The counterparts in the infrared and optical bands were found, and spectroscopy revealed clear Balmer and forbidden transition emission lines."15 The derived redshift of =0.217 indicates a background galaxy in this case also., The derived redshift of $z=0.217$ indicates a background galaxy in this case also.16 GC 4168 ts an E2 elliptical galaxy located in the Virgo cluster (d=16.8 Mpc)., NGC 4168 is an E2 elliptical galaxy located in the Virgo cluster $d=16.8$ Mpc).17 It hosts an active galactic nucleus (AGN). classified as a Seyfert 1.9 by Ho et al. (," It hosts an active galactic nucleus (AGN), classified as a Seyfert 1.9 by Ho et al. ("181997).,1997).19 The galaxy was observed on 4 December 2001 using the European Photon Imaging Camera (EPIC) on board the satellite (see Foschini et al., The galaxy was observed on 4 December 2001 using the European Photon Imaging Camera (EPIC) on board the satellite (see Foschini et al.20 20020: for the X-ray part. we refer in the following to the results obtained in this paper. unless explicitly stated).," 2002b; for the X-ray part, we refer in the following to the results obtained in this paper, unless explicitly stated)."21 EPIC is composed of two instruments: the PN-CCD camera (Strüdder et al., EPIC is composed of two instruments: the PN-CCD camera (Strüdder et al.22 2001) and two MOS-CCD detectors (Turner et al., 2001) and two MOS-CCD detectors (Turner et al.23 2001)., 2001).24 The effective exposure time was 17.4 ks., The effective exposure time was $17.4$ ks.25 One ULX was found apparently associated with NGC 4168. being inside the galaxy’s Dos ellipse. at 45” from the optical centre of the galaxy.," One ULX was found apparently associated with NGC 4168, being inside the galaxy's $D_{25}$ ellipse, at $45''$ from the optical centre of the galaxy."26" The ULX has coordinates (2000) à=12h|]2""[5 and 6=+13°12/48”. with an uncertainty radius of 4."," The ULX has coordinates (J2000) $\alpha = 12^{\rm h} 12^{\rm m}2714\fs5$ and $\delta = +13^{\circ} 12\arcmin 48\arcsec$, with an uncertainty radius of $4''$."28 The counts were not sufficient to extract à spectrum. so we could only convert to physical units using the count rates derived from the task of the XMM-SAS software (v. 5.2).," The counts were not sufficient to extract a spectrum, so we could only convert to physical units using the count rates derived from the task of the XMM-SAS software (v. 5.2)."29" We found a count rate of 4.0+0.7 counts s! in the 0.5-10 keV band. which corresponds to a flux of (1.8+0.3)x107 ere em7 s! adopting a conversion factor of 3x10"" counts env erg!. which in tum was derived by using a power-law model with [=2.0 and an average Galactic column density of Ny=3x10-° em7?."," We found a count rate of $4.0 \pm 0.7$ counts $^{-1}$ in the 0.5–10 keV band, which corresponds to a flux of $(1.8\pm 0.3)\times3010^{-14}$ erg $^{-2}$ $^{-1}$ adopting a conversion factor of $3\times 10^{11}$ counts $^2$ $^{-1}$, which in turn was derived by using a power-law model with $\Gamma=2.0$ and an average Galactic column density of $N_{\rm H} = 3\times 10^{20}$ $^{-2}$."31 This value for Tis common among the ULXs found withXMM-Newton., This value for $\Gamma$ is common among the ULXs found with.32. This flux value was corrected according to the energy encircled fraction (Ghizzardi 2001)., This flux value was corrected according to the energy encircled fraction (Ghizzardi 2001).33 Correction for vignetting (Lumb 2002) was not applied becausethe source is close to the center of the field of view (<2’)., Correction for vignetting (Lumb 2002) was not applied becausethe source is close to the center of the field of view $<$$2\arcmin$ ).34 At the distance of NGC 4168 the resulting 0.5—10 keV luminosity is 6»1075 erg s! (for a discussion on the luminosity threshold of ULXs. see Foschini et al.," At the distance of NGC 4168 the resulting $0.5-10$ keV luminosity is $6\times 10^{38}$ erg $^{-1}$ (for a discussion on the luminosity threshold of ULXs, see Foschini et al."35 2002c)., 2002c).36 A single optical object with coordinates. (J2000) 12{2111460 and 6=137 1247/8 (i.e.. [4 from the position. thus well within the X-ray error box) is clearly visible on the Digitized Sky Survey observation of NGC 4168. originally made with the 48-inch Schmidt telescope at Palomar Observatory on 14 April 1955.," A single optical object with coordinates (J2000) $\alpha = 12^{\rm h}3712^{\rm m} 14\fs60$ and $\delta = +13^{\circ} 12\arcmin 47\farcs$ 8 (i.e., $\farcs$ 4 from the position, thus well within the X-ray error box) is clearly visible on the Digitized Sky Survey observation of NGC 4168, originally made with the 48-inch Schmidt telescope at Palomar Observatory on 14 April 1955."38 We thus consider it as the optical counterpart of NGC4168-ULX1., We thus consider it as the optical counterpart of NGC4168-ULX1.39 The source is also present in the US Naval Observatory (USNO) BI.O Catalog (Monet et al., The source is also present in the US Naval Observatory (USNO) B1.0 Catalog (Monet et al.40 2003) with the identification number 1032—0222128., 2003) with the identification number $1032-0222128$.41 The magnitudes in the different bands are BI=19.1. B2=17.8. RI=18.1. R2=18.2. and J=17.8.," The magnitudes in the different bands are $B1=19.1$, $B2=17.8$, $R1=18.1$, $R2=18.2$, and $I=17.8$."42 The BI and RI magnitudes refer to the Palomar Observatory Sky Survey I (POSSI). performed between 1949 and 1965.," The $B1$ and $R1$ magnitudes refer to the Palomar Observatory Sky Survey I (POSSI), performed between 1949 and 1965."43 The B2. R2 and / magnitudes are measured from the Palomar Observatory Sky Survey II (POSSID. performed from 1985 to 2000.," The $B2$ , $R2$ and $I$ magnitudes are measured from the Palomar Observatory Sky Survey II (POSSII), performed from 1985 to 2000."44"timescale near the WD photosphlere. aud the Iuuinosity ofthe svstei is dominateds by the WD's quiesceut surface Iuniuositv. L,. which originates froii deep boucath the photosphere (Piroetal.2005).","timescale near the WD's photosphere, and the luminosity of the system is dominated by the WD's quiescent surface luminosity, $L_q$, which originates from deep beneath the photosphere \citep{piro05}."45. Ever since Sion(1990) diseussed the value of Tig measurements of dwarf novae iu quiescence. observers and theorists have vigorously pursued this important diagnostic.," Ever since \cite{sion99} discussed the value of $T_{\rm46eff}$ measurements of dwarf novae in quiescence, observers and theorists have vigorously pursued this important diagnostic."47 Most receutlv. Townsley&Gausicke(2009) sunuuarized the observations aud improved the earlier theoretical work (Townsley&Bildsten2002: 2005)..," Most recently, \cite{tg09} summarized the observations and improved the earlier theoretical work \citep{tb02,godon02,tb03,tb05,piro05}. ."48 In Figure 8.. we have added the Tuy evolutions for our two scenarios to the original figure from Townsley&Cansicke (2009).," In Figure \ref{fig:teffevol}, we have added the $T_{\rm eff}$ evolutions for our two scenarios to the original figure from \cite{tg09}."49. Some data are marginally cousisteut with the solid line (scenario A). whereas no observed WDs are as cold as predicted from our scenario D: however. it is unclear if the abseuce of these cold systems is physical or due to selection effects;," Some data are marginally consistent with the solid line (scenario A), whereas no observed WDs are as cold as predicted from our scenario B; however, it is unclear if the absence of these cold systems is physical or due to selection effects."50 It would be of iuterest to learn whether those cold svstenis near the solid line have anv other evidence for having low-1ass accretors., It would be of interest to learn whether those cold systems near the solid line have any other evidence for having low-mass accretors.51 The coutinnal discoveries of CVs in quiescence by the Sloan Digital Sky Survev (e.g. Szkodvetal.20001: Gansickeetal. 20093) and. im the near future. bv SkvMapper (Murphyctal.2008) will certainly provide new opportunitics to reveal acercting Πο WDs.," The continual discoveries of CVs in quiescence by the Sloan Digital Sky Survey (e.g., \citealt{szkody09}; \citealt{gaen09}) ) and, in the near future, by SkyMapper \citep{skymapper} will certainly provide new opportunities to reveal accreting He WDs."52 Iu particular. Causickeetal. (200937s recent discovery of the expected “pile-up” of CVs at the SOδ min orbital period miumnmn has alleviated long-standing— coucerus reearding binary evolution.," In particular, \cite{gaen09}' 's recent discovery of the expected “pile-up” of CVs at the $80-86$ min orbital period minimum has alleviated long-standing concerns regarding binary evolution."53 Heuce. as we noted iu the introduction. z20% of the CVs in Cansickeetal. (2009) compilation should harbor a Πο WD.," Hence, as we noted in the introduction, $\approx 20\%$ of the CVs in \cite{gaen09}' 's compilation should harbor a He WD."54 The discoverys and study of accreting WD. pulsators (see Mikadaimetal.2007 for an updated list) may well be our best hope. as Arrasetal.(2006) noted that low-1ass WDs have colder effective teirperatures for pulsation than higher mass WDs. aud our Z;4 calculations shown in Fieure δ are sliehtlv colder than the blue edge calculated by Arrasetal.(2006) for low eravity (6.9. low-uass WDz).," The discovery and study of accreting WD pulsators (see \citealt{muka07} for an updated list) may well be our best hope, as \cite{arras06} noted that low-mass WDs have colder effective temperatures for pulsation than higher mass WDs, and our $T_{\rm eff}$ calculations shown in Figure \ref{fig:teffevol} are slightly colder than the blue edge calculated by \cite{arras06} for low gravity (e.g., low-mass WDs)."55 Thus. a prevalence of pulsators at low Tig may be an iudicator of Te WDs.," Thus, a prevalence of pulsators at low $T_{\rm eff}$ may be an indicator of He WDs."56 Certainly more work. is needed to make this connection clear. but the rapid increase in the discovery of such pulsators is bound to reveal a few new systems wortliv of iuteusive study.," Certainly more work is needed to make this connection clear, but the rapid increase in the discovery of such pulsators is bound to reveal a few new systems worthy of intensive study."57 Iu the previous sections. we studied the secular evolution of the WD.," In the previous sections, we studied the secular evolution of the WD."58 We now turn our attention to details of the individual nova outbursts. focusing onu the evolution of the convective burning phase. the composition of the nova ejecta. aud the WD's post-nova appearance as a supersoft X-ray source.," We now turn our attention to details of the individual nova outbursts, focusing on the evolution of the convective burning phase, the composition of the nova ejecta, and the WD's post-nova appearance as a supersoft x-ray source."59 For most of the accretion phase of the nova cycle. he thermal profile is set by “compressional” heating (seo §3.2)).," For most of the accretion phase of the nova cycle, the thermal profile is set by “compressional” heating (see \ref{sec:constMdot}) )."60 Ποπονα. ouce the base of the envelope vecolmcs dense aud hot enoush. the energy generation rate from nuclear burning becomes large enough that radiative diffusion cau uo longer effectively transport the uumositv.," However, once the base of the envelope becomes dense and hot enough, the energy generation rate from nuclear burning becomes large enough that radiative diffusion can no longer effectively transport the luminosity."61 The radiative cuvelope is then transformed into a convective zone whose cutropy is increased * continued nuclear burning until mass is lost via a radiativelv-diiveu wind. aud the nova outburst is observed.," The radiative envelope is then transformed into a convective zone whose entropy is increased by continued nuclear burning until mass is lost via a radiatively-driven wind, and the nova outburst is observed."62 We now give a brief overview of the rolevaut physics cing this stage of the CN evolution: for a more coniplete explanation of simular physics iu IHe-burniug convective envelopes. see 83 of Shen&Bildsten(200900).," We now give a brief overview of the relevant physics during this stage of the CN evolution; for a more complete explanation of similar physics in He-burning convective envelopes, see 3 of \cite{sb09b}."63 Figure 9 shows au example of the evolution of a convective euvelope as it is heatedby nuclear burning. nunmercallv calculated for à 0.4AL. WD that accreted mass at a rate of 10t+AL.wv+ after it has reached its equilibrium core temperature of 5.5.10° K. Dotted," Figure \ref{fig:rhotzone} shows an example of the evolution of a convective envelope as it is heatedby nuclear burning, numerically calculated for a $0.4 \msol$ WD that accreted mass at a rate of $10^{-11} \smpy$ after it has reached its equilibrium core temperature of $5.5\E{6}$ K. Dotted"64The infrared radiation fro1l ΠΙΟΣ star-forming galaxies is dominated by eiission YOM ¢ust erains heated by absorbed stellay enerev.,The infrared radiation from most star-forming galaxies is dominated by emission from dust grains heated by absorbed stellar energy.65 Dust enüssion is powered by absorption of radiation frou loniziug and non-ioniziug stars., Dust emission is powered by absorption of radiation from ionizing and non-ionizing stars.66 Dust is nost efficient at absorbing photons in the ultraviolet. (UV) as the reative optical depth of dust is the highest in the UV (Cordonetal.2003)., Dust is most efficient at absorbing photons in the ultraviolet (UV) as the relative optical depth of dust is the highest in the UV \citep{Gordon2003}.67.. Oulv carly type CO and D) stars produce sienificaut amounts of UV photons: however. frese hot massive stars have short lifetimes (less than 100 nüllion vears) ancl are formed in relatively small uunbers compared to less massive. less luminous. auxL cooler stars that produce very few UV photons.," Only early type (O and B) stars produce significant amounts of UV photons; however, these hot massive stars have short lifetimes (less than 100 million years) and are formed in relatively small numbers compared to less massive, less luminous, and cooler stars that produce very few UV photons."68 Caven the initial mass ftnction and evolutionary history. this implies that star-forming ealaxies have a sinal lass fraction of UW bright. vouug stars as compared o UV faint. old stars.," Given the initial mass function and evolutionary history, this implies that star-forming galaxies have a small mass fraction of UV bright, young stars as compared to UV faint, old stars."69 Thus. the question arises: whic1 population of stars coluinates the dust heating in star-forming clouds?," Thus, the question arises: which population of stars dominates the dust heating in star-forming clouds?"70 The less numerous but much brighter iu the UN “young stars («100 Myr) or the unuuerous but uich faiuter iu the UV od stars?," The less numerous but much brighter in the UV young stars $<71100$ Myr) or the numerous but much fainter in the UV old stars?"72 Tow does this answer change when we consider the ciission at specific IR wavelengths?, How does this answer change when we consider the emission at specific IR wavelengths?73 The majority of the IR energv from star-forming ealaxies is endtted at £u-IR 100 μπι) wavelengths., The majority of the IR energy from star-forming galaxies is emitted at far-IR 100 ) wavelengths.74 Tistorically. this fav-IR cuuission has been identified as intrared crus emission from dust heated by nou-donizig populations (IIelou199L).. which ave older than 10 My.," Historically, this far-IR emission has been identified as infrared cirrus emission from dust heated by non-ionizing populations \citep{Helou1994}, which are older than 10 Myr."75 LousdalePersson&IIlou(1987) interpreted the far-IR cussion from spiral disks iu terms of two thermal COMPOleits with different temperatures and found tha the cirus componcut contributes amore than half of the total far-IR fiux., \citet{Cirrus1987} interpreted the far-IR emission from spiral disks in terms of two thermal components with different temperatures and found that the cirrus component contributes more than half of the total far-IR flux.76 However. as old stars cuit very few of the UV. photons hat power dust enüssion. 1 is possibe that UV-brigh voung stars could dominate cirus eniüsson.," However, as old stars emit very few of the UV photons that power dust emission, it is possible that UV-bright young stars could dominate cirrus emission."77 For exame. a stnall uuuber of vouug stars embedded ina larexορ optically thin cloud cau resul in a dihte radiation field. cold dust temperature and therefore cold cirrus emission.," For example, a small number of young stars embedded in a large optically thin cloud can result in a dilute radiation field, cold dust temperature and therefore cold cirrus emission."78 Star formation rate (SER) indicators are im)ortiui observational probes of the star formation histories of ealaxies., Star formation rate (SFR) indicators are important observational probes of the star formation histories of galaxies.79 They are ustally sinele-band or waveleugsth-integrated. quantities hat are presumed to trace a specific reguue of recaut star formation du a region or galaxv (Ixeunicutt1998)., They are usually single-band or wavelength-integrated quantities that are presumed to trace a specific regime of recent star formation in a region or galaxy \citep{Kennicutt1998}.80 The most conunon SER indicators include the Πα fiux (tracing unocured loniziug stars. <LO Aba) UV (tracing unocured joniziug aud UV-brigif. non-onizins stars. 100 Abvr). and total iufrared (TIR. tracing obscured star formation).," The most common SFR indicators include the $\alpha$ flux (tracing unobscured ionizing stars, $< 10$ Myr), UV (tracing unobscured ionizing and UV-bright, non-ionizing stars, $< 100$ Myr), and total infrared (TIR, tracing obscured star formation)."81" The UV aud Ho fiux are heavily attenuated by cist. with a typical extinction of 0-1 imag and 0-2 imag respectively (IKennicuttetal.2000),"," The UV and $\alpha$ flux are heavily attenuated by dust, with a typical extinction of 0-4 mag and 0-2 mag respectively \citep{Kennicutt2009}."82 Since the UV and IIo flux only trace the stellar light unabsorbed by dust. an accurate estimation ¢of star formation activity requires a correction factor to account for the effect of dust.," Since the UV and $\alpha$ flux only trace the stellar light unabsorbed by dust, an accurate estimation of star formation activity requires a correction factor to account for the effect of dust."83 For starburst galaxies. cquissiou-line diagnostics aud UV colors may be used to such purpose. but they are ofen difficult to obtain or liehly uncertain (Ikennicutt 2009).," For starburst galaxies, emission-line diagnostics and UV colors may be used to such purpose, but they are often difficult to obtain or highly uncertain \citep{Kennicutt2009}."84. An alternative wav is to look at the IR flux. wich accounts for the energy missing in the UV and the optical," An alternative way is to look at the IR flux, which accounts for the energy missing in the UV and the optical"85in Section 3. aud used to identify flares i our optical data to search for couteniporaneous flares in our full set. of IR data.,in Section \ref{results} and used to identify flares in our optical data to search for contemporaneous flares in our full set of IR data.86 We detected no statistically significant ceviatious in our IR photometry at the epochs of the four major. optically detected fares.," We detected no statistically significant deviations in our IR photometry at the epochs of the four major, optically detected flares."87 We quautify the 1-0 upper linits of these four eveuts by computing the staudard deviation of all data ina LO nàünute time window before cach event. and sununarize these hints iu Table 1..," We quantify the $\sigma$ upper limits of these four events by computing the standard deviation of all data in a 40 minute time window before each event, and summarize these limits in Table \ref{flarenergy}."88 Ow C-band photometry provides us with information about the starting time of cach flare event., Our -band photometry provides us with information about the starting time of each flare event.89 As secu in Figure 1l. and demonstrated by mauy others (see e.g. Hawley&Pettersen1991:Tiltonetal. 20113). the total duratiou of flares in the optical is color dependent.," As seen in Figure \ref{adleoall} and demonstrated by many others (see e.g. \citealt{haw91,hil11}) ), the total duration of flares in the optical is color dependent."90 Flare #11 in our survev. for example. was visible iu the filter for 10x longer than it was iu the filter (Table 1)).," Flare 1 in our survey, for example, was visible in the filter for 10x longer than it was in the filter (Table \ref{flarenergy}) )."91 We therefore estimated wpper limits to the duration which each fare event would be visible iu theJJ.IL. aud filters by adoptinge the duration of each event in the reddest optical filter iu which it was detected (c.g. the -hand for event #11).," We therefore estimated upper limits to the duration which each flare event would be visible in the, and filters by adopting the duration of each event in the reddest optical filter in which it was detected (e.g. the -band for event 1)."92 Our observing cadence (Table 1)) constrains the uncertainty in the duratious we quote., Our observing cadence (Table \ref{obssum}) ) constrains the uncertainty in the durations we quote.93" This information enabled us to time bin our data. as shown in Fieures 3.. L. aud Ὁ for theJ.JL. aud filters respectively, to intervals which would create two data poiuts (ic. —2 nmnünuute biunuiung) and 1 data point (i.c. | munute binuiung) across the upper lait duration of each eveut."," This information enabled us to time bin our data, as shown in Figures \ref{event1J}, \ref{event1H}, and \ref{event1K} for the, and filters respectively, to intervals which would create two data points (i.e. $\sim$ 2 minute binning) and 1 data point (i.e. $\sim$ 4 minute binning) across the upper limit duration of each event."94 As flare light curves can exhibit siguificaut changes over 2-l minute intervals (see e.g. Figure 1)). biuuiug our data to these longer cadences could cause flare signatures to be diminished.," As flare light curves can exhibit significant changes over 2-4 minute intervals (see e.g. Figure \ref{adleoall}) ), binning our data to these longer cadences could cause flare signatures to be diminished."95 Conversely. biunius will help to reduce the dispersion of quiesceut-phase data. and therefore could help elucidate the preseuce of low-auplitude slowly varving events. such as the long-duration flare shape of Hawleyctal.(1995).," Conversely, binning will help to reduce the dispersion of quiescent-phase data, and therefore could help elucidate the presence of low-amplitude slowly varying events, such as the long-duration flare shape of \citet{haw95}."96.. However. even the binned data did not reveal a statistically significant eveut iu the IR.," However, even the binned data did not reveal a statistically significant event in the IR."97 Following practices described in Iowalslsàetal.(2009). we also computed a Welch aud Stetson variability iudex (Welch&Stetson1993).. Ῥμν. for cach epoch of our data.," Following practices described in \citet{kow09}, we also computed a Welch and Stetson variability index \citep{wel93}, $\Phi_{JHK}$ , for each epoch of our data."98 This type of variability iudex builds on the principle that the photometric variations we are scarclineg for should appear at simular tine epochs across iiultiple filters: hence. it serves as away to identify füut signals conunon to cach of ourJ..IL. aud filter data.," This type of variability index builds on the principle that the photometric variations we are searching for should appear at similar time epochs across multiple filters; hence, it serves as a way to identify faint signals common to each of our, and filter data."99 In practice. the index is computed simply by: where the flux in cach ultiplicative terii is determined from cach filter’s differcutial photometry light curve.," In practice, the index is computed simply by: where the flux in each multiplicative term is determined from each filter's differential photometry light curve."100 The resultant τμ udex for our ποιος. ~2 minute binned. and —1 unimute binned data exhibited. no statistically significant change during the time of each fare event. as shown in Figure 6 for event 11. as compared to the value of the index preceeding aud following each eveut.," The resultant $\Phi_{JHK}$ index for our unbinned, $\sim$ 2 minute binned, and $\sim$ 4 minute binned data exhibited no statistically significant change during the time of each flare event, as shown in Figure \ref{phi1} for event 1, as compared to the value of the index preceeding and following each event."101 We can not exclude the possibility that our IR observing cadence (Table 1)) of one (0.87| second) integration every 60. seconds does not iuflueuce our ability to detect the optically observed flare events., We can not exclude the possibility that our IR observing cadence (Table \ref{obssum}) ) of one (0.874 second) integration every $\sim$ 60 seconds does not influence our ability to detect the optically observed flare events.102 To help better quantity whether our observations could iiss TR responses to flares which begin and eud on time-scales faster than the relative observing cadence we achieved. we identified the time of the peals flare cussion during each event. as listed in Table 5..," To help better quantify whether our observations could miss IR responses to flares which begin and end on time-scales faster than the relative observing cadence we achieved, we identified the time of the peak flare emission during each event, as listed in Table \ref{flaretime}."103 The quoted error bars ou these times correspond to the epoch of the prior aud subsequent inteeration in cach filter., The quoted error bars on these times correspond to the epoch of the prior and subsequent integration in each filter.104 We also list the epochs of the nearest 1-2 IR observations in Table 5 relative to the observed epoch of the peak AU- -baud flux., We also list the epochs of the nearest 1-2 IR observations in Table \ref{flaretime} relative to the observed epoch of the peak $\Delta$ -band flux.105 The epochs of our IR obscrvatious csscutially overlap with the epochs of the observed peak A C--baud flux for flare eveuts #11.5.and [| to within the timing uncertainties.," The epochs of our IR observations essentially overlap with the epochs of the observed peak $\Delta$ -band flux for flare events 1,3,and 4 to within the timing uncertainties."106 Our closest IR inteeration for flare eveut #22 was 18.5 seconds after the oberved AU-baud peak. which is huger than the £13 second uncertaüutv in the epoch of the peak A C-baud flux.," Our closest IR integration for flare event 2 was 18.5 seconds after the oberved $\Delta$ U-band peak, which is larger than the $\pm$ 13 second uncertainty in the epoch of the peak $\Delta$ -band flux."107 These data quantity the μες at which our different optical versus IR. observing cadences could have resulted in the uou-doetectiou of flare events., These data quantify the limits at which our different optical versus IR observing cadences could have resulted in the non-detection of flare events.108" We conclude that. at the Iit of our observational data. we find no compelling evidence of flare cuhancemenuts iu ourJ.IL. or filter data dung the ~7.8 x 10?"" to ~1.3 x LO? ere U-—baud fares we detected."," We conclude that, at the limit of our observational data, we find no compelling evidence of flare enhancements in our, or filter data during the $\sim$ 7.8 x $^{30}$ to $\sim$ 1.3 x $^{32}$ erg -band flares we detected."109 We have preseuted the results of ~ 17 hours of high cadence. high precision. sinultaueous optical and IR photometric monitoring of 3 active AL dwarfs.," We have presented the results of $\sim$ 47 hours of high cadence, high precision, simultaneous optical and IR photometric monitoring of 3 active M dwarfs."110 We now discuss the interpretation of these results in the context of the effects that stellar fares could have on a variety of AL dwarf exoplanet studies., We now discuss the interpretation of these results in the context of the effects that stellar flares could have on a variety of M dwarf exoplanet studies.111 For reference. we remind the reader that a Super-Earth (2 Ry.) residiug in the habitable zone around a (AIS stay (0.074 AU separation: see c.e. Nutziman&Charbonneau 2008)) would have an orbital period of 11.5 davs aud a transit duration of ~2 hours.," For reference, we remind the reader that a Super-Earth (2 $_{\earth}$ ) residing in the habitable zone around a dM5 star $\sim$ 0.074 AU separation; see e.g. \citealt{nut08}) ) would have an orbital period of 14.5 days and a transit duration of $\sim$ 2 hours."112 Tn Section 3.2. we demonstrated that during four sienificant optical flare eveuts. having C-banud euergies ranging frou ~7.8 x 1079 to —1.3 x 107 eres; we observed uo statistically significant evidence of corresponding broad-band enhancements in theJL.Mh. aud filters at the 5.1-11.7 nmüllinias level.," In Section \ref{irflares} we demonstrated that during four significant optical flare events, having -band energies ranging from $\sim$ 7.8 x $^{30}$ to $\sim$ 1.3 x $^{32}$ ergs, we observed no statistically significant evidence of corresponding broad-band enhancements in the, and filters at the 5.1-11.7 milli-mag level."113 These upper linits were computed from the standard deviation of all data ina LO minute time window before cach flare., These upper limits were computed from the standard deviation of all data in a 40 minute time window before each flare.114 We quautified the relative frequency that one woul expect for flares with cuereics similar to events ¥11-l in Section 3.1.. using flare frequency distributions observe for our specific dMoe stars in Wilton(2011) and IHiltonetal. (2011).," We quantified the relative frequency that one would expect for flares with energies similar to events 1-4 in Section \ref{opticalflares}, using flare frequency distributions observed for our specific dMe stars in \citet{hi11a} and \citet{hil11}."115 By conibiniug these two observationa properties. we can place upper lanits on the effects of stellar flaves on future continuuu-based observations of AMI dwart exoplanctary systems.," By combining these two observational properties, we can place upper limits on the effects of stellar flares on future continuum-based observations of M dwarf exoplanetary systems."116 For active M3Vo stars. we fud that a ~1.3 x 10°? ere U--land flare will induce «8.3. «B5. and «11.7 müilliauags of au effect iu theJ.7L. iux filters respectively.," For active M3Ve stars, we find that a $\sim$ 1.3 x $^{32}$ erg -band flare will induce $<$ 8.3, $<$ 8.5, and $<$ 11.7 milli-mags of an effect in the, and filters respectively."117 A flare of this cucrev or greater should occur less than once per 15 hours., A flare of this energy or greater should occur less than once per 18 hours.118 For active ML.5e stuw we find that a ~5.1 x 10° ere Ü-—-band flare wil induce <7.8. NG and «5.1 ndlliauaes of au effect in the J. IL. and Ws filters respectively.," For active M4.5e stars, we find that a $\sim$ 5.1 x $^{31}$ erg -band flare will induce $<$ 7.8, $<$ 8.8, and $<$ 5.1 milli-mags of an effect in the J, H, and Ks filters respectively."119 A fare of this energy or ereater should occur less than ounce per LO hours., A flare of this energy or greater should occur less than once per 10 hours.120 Moreover. we observe no evidence of stellar variability uot associated with discrete flare events at the level of 23.9 (J)). 28 (1110) aud 2.9 CA8S)) 1illiauags over 1 hour time-scales," Moreover, we observe no evidence of stellar variability not associated with discrete flare events at the level of $>$ 3.9 ), $>$ 3.8 ), and $>$ 3.9 ) milli-mags over 1 hour time-scales"121(centred at 23.75 Watt/I1z) containing only a single source (BOS830|5813) is omitted clue to its large uncertainty.,(centred at 23.75 Watt/Hz) containing only a single source (B0830+5813) is omitted due to its large uncertainty.122" We compared the resulting LLE with an LLP of a simulated: radio source population of 10"" objects. with random ages. and a jet-power distribution defined as in equation LO."," We compared the resulting LLF with an LLF of a simulated radio source population of $10^6$ objects, with random ages, and a jet-power distribution defined as in equation 10."123" The ""observed? Luminosity of à source was calculated assuming that it hack evolved. over its lifetime according to the luminosity evolution derived in section 4.1. out to a maximum size. r ."," The `observed' luminosity of a source was calculated assuming that it had evolved over its lifetime according to the luminosity evolution derived in section 4.1, out to a maximum size, $r_+$ ."124" Mr«ors. the size of the source evolves as r=(£2PET,"," At $r<r_*$, the size of the source evolves as $r=t^{1/2}P_J^{1/4}$."125 Lo avoid à. discontinuity in propagation velocity at ry. the source evolves from Εν as. withs=(403)/2.," To avoid a discontinuity in propagation velocity at $r_*$ , the source evolves from $r_*$ as, with $\gamma=(4-\beta)/2$."126 The luminosity ofa source increases abr rasL—PyTEN(rfr)2i τνb=PyTé(rfr)?20749 aborL9ry.," The luminosity of a source increases at $r<r_*$ as $L=P_J^{7/8}(r/r_*)^{2/3}$, and as $L=P_J^{7/8}(r/r_*)^{\frac{2}{3}-\frac{7}{6}\beta}$ at $r>r_*$."127 This results in a similar evolution for large size radio sources as derived in section 4.1. with the luminosity aber=gu only dependent on £27.," This results in a similar evolution for large size radio sources as derived in section 4.1, with the luminosity at $r=r_*$ only dependent on $P_J$."128 Lo was not our aim to determine absolute values for number densities ancl racio powers with these simulations., It was not our aim to determine absolute values for number densities and radio powers with these simulations.129 The results of the simulation were scaled in such way. that the LLE obtained for large size radio sources. matched the LLP of steep spectrum. sources as derived by Dunlop peacock (1990).," The results of the simulation were scaled in such way, that the LLF obtained for large size radio sources, matched the LLF of steep spectrum sources as derived by Dunlop peacock (1990)."130 ‘Table 4 lists the important characteristics of the simulated LLE of large size and GPS sources. and their dependence on the free model parameters.," Table \ref{param} lists the important characteristics of the simulated LLF of large size and GPS sources, and their dependence on the free model parameters."131 The parameters ó and 2. as defined in equations LO and 3. determine the slope of the low ancl high luminosity part of the LLP of aree size radio sources.," The parameters $\delta$ and $\beta$, as defined in equations 10 and 3, determine the slope of the low and high luminosity part of the LLF of large size radio sources."132 These were chosen to be similar to he parameters @1l and ὁ1 as derived by Dunlop Peacock (1990). with &=1.10 and 3=1.16.," These were chosen to be similar to the parameters $a-1$ and $b-1$ as derived by Dunlop Peacock (1990), with $\delta=-1.10$ and $\beta=1.16$."133 This value of ds slightly lower than derived (rom X-ray observations of nearby ellipticals (3=1.52. Trinchieri et al.," This value of $\beta$ is slightly lower than derived from X-ray observations of nearby ellipticals $\beta=1.5-2$, Trinchieri et al."134 1986)., 1986).135 ote however. that the radio source population is dominated » objects with size z20 kpe. for which the surrounding medium is dominated by intra-cluster gas. which is expected o have a [Blatter density. gradient.," Note however, that the radio source population is dominated by objects with size $>20$ kpc, for which the surrounding medium is dominated by intra-cluster gas, which is expected to have a flatter density gradient."136 With the parameters ó and 3 and the slopes of the LLP of large size. radio sources fixed. the relative positions of the break luminosities could. be determined.," With the parameters $\delta$ and $\beta$ and the slopes of the LLF of large size radio sources fixed, the relative positions of the break luminosities could be determined."137" A sharp cut-olf will occur near the highest luminosity. L,,,,."," A sharp cut-off will occur near the highest luminosity, $L_{max}$."138 Phe number of GPS galaxies in the highest luminosity bin. as shown in figure SN.. is lower han expected from the extrapolation of the LLE at lower uminosities.," The number of GPS galaxies in the highest luminosity bin, as shown in figure \ref{llf}, , is lower than expected from the extrapolation of the LLF at lower luminosities."139 Εις can be explained if this luminosity bin is near the cut-oll. luminosity Lue., This can be explained if this luminosity bin is near the cut-off luminosity $L_{max}$ .140 We therefore. chose og Linas to be 27.1 (W 1)., We therefore chose log $L_{max}$ to be 27.1 (W $^-1$ ).141 Phe break luminosity of arge size radio sources. is also determined by Dunlop Peacock (1990) to be log Lys. = 25.79 (corrected. to 5 (01414).," The break luminosity of large size radio sources, is also determined by Dunlop Peacock (1990) to be log $L_{LS*}$ = 25.79 (corrected to 5 GHz)."142 As can be seen from table 4.. the luminosity ratio LancefLis determines the value of &fry.," As can be seen from table \ref{param}, the luminosity ratio $L_{max}/L_{ls*}$ determines the value of $r_{+}/r_{*}$."143 Fhis corresponds o à maximum size for a radio source of LOO kpe. assuming ry=| kpc.," This corresponds to a maximum size for a radio source of 100 kpc, assuming $r_*=1$ kpc."144 This value is quite near the turnover seen in the linear size distribution of 3€1t. galaxies. as shown w O'Dea Baum (1997).," This value is quite near the turnover seen in the linear size distribution of 3CR galaxies, as shown by O'Dea Baum (1997)."145 The break luminosity of GPS sources. Lypss. relative to Line. is dependent on the range of jet-powers CP/P.).," The break luminosity of GPS sources, $L_{gps*}$, relative to $L_{max}$, is dependent on the range of jet-powers $(P_+/P_-)$."146 To let Lypss coincide with the peak in the observed. GPS LLE. a value of (2οJ=200 was used.," To let $L_{gps*}$ coincide with the peak in the observed GPS LLF, a value of $(P_+/P_-)$ =200 was used."147 Although the uncertainties on the datapoints are large ancl several free. parameters enter the simulation. figure shows that the shape of the LLE of GPS sources is as expected.," Although the uncertainties on the datapoints are large and several free parameters enter the simulation, figure \ref{llf} shows that the shape of the LLF of GPS sources is as expected."148 Note that most free parameters are determined by fitting the LLE of large size radio sources to that of Dunlop Peacock (1990). except rand (P./P.2.," Note that most free parameters are determined by fitting the LLF of large size radio sources to that of Dunlop Peacock (1990), except $r_{+}$ and $(P_+/P_-)$."149 This analysis should. be regarded as an example of how future. large ancl homogeneously defined: samples of GPS sources can constrain the luminosity evolution. of extragalactic racio SOULCCS., This analysis should be regarded as an example of how future large and homogeneously defined samples of GPS sources can constrain the luminosity evolution of extragalactic radio sources.150 The proposed. increase in luminosity for voung racio sources seems to be in contradiction to the high number counts ofGPS sources with respect to large size racio sources suggesting that they should. decrease in radio Luminosity. o» a factor 10 during their. lifetime (Fanti ct al., The proposed increase in luminosity for young radio sources seems to be in contradiction to the high number counts of GPS sources with respect to large size radio sources suggesting that they should decrease in radio luminosity by a factor $~10$ during their lifetime (Fanti et al.151 1995. veadhbead ct al.," 1995, Readhead et al."152 1996. οDea Daum 1997).," 1996, O'Dea Baum 1997)."153 Lowever. this is not the case.," However, this is not the case."154 Flux density. limited samples. as used. for hese analyses. only. probe the most luminous objects at any redshift.," Flux density limited samples, as used for these analyses, only probe the most luminous objects at any redshift."155 As can be seen from figure S.. at high luminosities. he two luminosity function approach each other. due to the latter slope of the Iuminosity function of GPS sources.," As can be seen from figure \ref{llf}, at high luminosities, the two luminosity function approach each other, due to the flatter slope of the luminosity function of GPS sources."156 This results in a relatively high number density of GPS sources in flux density limited samples., This results in a relatively high number density of GPS sources in flux density limited samples.157 In this paper we show that in addition to the well known correlation between spectral peak frequeney. and angular size (eg., In this paper we show that in addition to the well known correlation between spectral peak frequency and angular size (eg.158 Fanti ct al., Fanti et al.159 1990). a correlation exists between the peak flux density and angular size of GPS CSS sources.," 1990), a correlation exists between the peak flux density and angular size of GPS CSS sources."160 The strength. anc sign of these correlations are exactly as expected from SSA theory. assuming equipartition. and are therefore a strong indication that SSA is indeed the cause of the spectral turnovers in these objects.," The strength and sign of these correlations are exactly as expected from SSA theory, assuming equipartition, and are therefore a strong indication that SSA is indeed the cause of the spectral turnovers in these objects."161 Furthermore. these correlations are consistent with GPSCSS sources evolvingin a self-similar way.," Furthermore, these correlations are consistent with GPSCSS sources evolvingin a self-similar way."162 Interestingly. the scll-similar evolution scenario is better fitted by assuming an equipartition than a constant magneticfield.," Interestingly, the self-similar evolution scenario is better fitted by assuming an equipartition than a constant magneticfield."163 In Duxdensity limited samples. GPS galaxies are found at higher redshifts than large size radio sources.," In fluxdensity limited samples, GPS galaxies are found at higher redshifts than large size radio sources."164 Since the, Since the165GRBO70616 is intriguing in that the emission rises relatively slowly over 100 seconds to a peak. then persists at a fairly constant level before showing a very rapid decline.,"GRB070616 is intriguing in that the emission rises relatively slowly over 100 seconds to a peak, then persists at a fairly constant level before showing a very rapid decline."166 GRB 070129 is similar to GRB 070721B in that it has a possible internal plateau that is interrupted by a flare followed by a steep decline., GRB 070129 is similar to GRB 070721B in that it has a possible internal plateau that is interrupted by a flare followed by a steep decline.167 GRB 070110 displays a canonical early light curve with an initial steep decline. but then exhibits a period of relatively constant emission.," GRB 070110 displays a canonical early light curve with an initial steep decline, but then exhibits a period of relatively constant emission."168 Following this plateau the decay is surprisingly steep a~ 7) decay (Troja 22007)., Following this plateau the decay is surprisingly steep $\alpha \sim 7$ ) decay (Troja 2007).169 Thus in this case the proto-magnetar survived for much longer than in most of the other GRBs., Thus in this case the proto-magnetar survived for much longer than in most of the other GRBs.170 GRB 060607A appears to follow the canonical lighteurve with a “normal” X-ray plateau with multiple flares preventing a good fit with the two component model.," GRB 060607A appears to follow the canonical lightcurve with a ""normal"" X-ray plateau with multiple flares preventing a good fit with the two component model."171 However at late times the decay following the plateau is too steep for an afterglow and is consistient with a ~4.," However at late times the decay following the plateau is too steep for an afterglow and is consistient with $\alpha$ $\sim1724$."173 This is unlikely to be explained by anvthing other than central engine activity and thus has been included in the internal plateau sample., This is unlikely to be explained by anything other than central engine activity and thus has been included in the internal plateau sample.174 As in GRB 070110. the internal plateau seen in GRB 060607A dominates the burst emission unusually late starting at about 900 seconds when (from Table 1) most of the other internal plateaus have ended.," As in GRB 070110, the internal plateau seen in GRB 060607A dominates the burst emission unusually late starting at about 900 seconds when (from Table 1) most of the other internal plateaus have ended."175 GRB 060510B (also shown in Fig. Lis , GRB 060510B (also shown in Fig. \ref{fitexamples}) )176very similar to GRB 070616., is very similar to GRB 070616.177 In both cases the proposed internal plateau dominates the emission from the burst very early on., In both cases the proposed internal plateau dominates the emission from the burst very early on.178 GRB 060202 displays unusual emission attributed to an internal plateau between 325 and 766 seconds., GRB 060202 displays unusual emission attributed to an internal plateau between 325 and 766 seconds.179 The fluctuations during this plateau are unusually regular., The fluctuations during this plateau are unusually regular.180 GRB 050904 has multiple flares at early and late times. but at about 230 seconds there is a period where the emission appears relatively constant followed by a steep decay. leading it to be included in the sample as a possible internal plateau.," GRB 050904 has multiple flares at early and late times, but at about 230 seconds there is a period where the emission appears relatively constant followed by a steep decay, leading it to be included in the sample as a possible internal plateau."181 To further investigate the nature of the internal plateau we compared the X-ray data to optical/UV data from the UVOT., To further investigate the nature of the internal plateau we compared the X-ray data to optical/UV data from the UVOT.182 The GRBs within the sample with near-simultaneous optical/UV and X-ray light curves are shown in Fig. 3.., The GRBs within the sample with near-simultaneous optical/UV and X-ray light curves are shown in Fig. \ref{optical2}.183 While an early rise in the optical can be seen in some cases. the optical emission does not show the same behaviour as the X-ray.," While an early rise in the optical can be seen in some cases, the optical emission does not show the same behaviour as the X-ray."184 The internal plateau and following steep decay are significantly more prominent in X-rays., The internal plateau and following steep decay are significantly more prominent in X-rays.185 For example in GRB 070616. the optical is constant from before the plateau in the X-ray and until after the steep decline.," For example in GRB 070616, the optical is constant from before the plateau in the X-ray and until after the steep decline."186 In Fig., In Fig.187 2 if the plateau seen in each of the X-ray lightcurves is of an external origin. then the X-ray and optical lighteurve should be related to each other in a manner consistent with the external shock model. i.e. the breaks should be achromatic.," \ref{sample} if the plateau seen in each of the X-ray lightcurves is of an external origin, then the X-ray and optical lightcurve should be related to each other in a manner consistent with the external shock model, i.e. the breaks should be achromatic."188 However. if the X-ray and optical emission components are not related to each other. e.g. a sharp decay in X-ray but no break in optical. this strongly suggests that the X-ray emission is not external or a jet-break but rather is of internal origin.," However, if the X-ray and optical emission components are not related to each other, e.g. a sharp decay in X-ray but no break in optical, this strongly suggests that the X-ray emission is not external or a jet-break but rather is of internal origin."189 In Troja (2007) for GRB 0701[0 four spectral energy distributions (SEDs) were examined during the initial decay. the beginning and end of the plateau and during the shallow decay after the steep decline.," In Troja (2007) for GRB 070110 four spectral energy distributions (SEDs) were examined during the initial decay, the beginning and end of the plateau and during the shallow decay after the steep decline."190 These SEDs were constructed by extrapolating the X-ray spectrum to the lower energies., These SEDs were constructed by extrapolating the X-ray spectrum to the lower energies.191 During the initial decay the optical data are not consistent with the extrapolation of the X-ray spectrum to low energies., During the initial decay the optical data are not consistent with the extrapolation of the X-ray spectrum to low energies.192 During the internal plateau. the optical and X-ray spectral distributions are also completely inconsistent with one another. implying different origins for the optical and X-ray photons.," During the internal plateau, the optical and X-ray spectral distributions are also completely inconsistent with one another, implying different origins for the optical and X-ray photons."193 For GRB 080310 and GRB 070616 the extrapolation of the X-ray spectrum is also inconsistient with the optical during the internal plateau (Beardmore iin preparation. Starling 22008).," For GRB 080310 and GRB 070616 the extrapolation of the X-ray spectrum is also inconsistient with the optical during the internal plateau (Beardmore in preparation, Starling 2008)."194 Likewise. for GRBO60607A extrapolating the X-ray spectum to the optical in a similar way to Troja," Likewise, for GRB060607A extrapolating the X-ray spectum to the optical in a similar way to Troja"195The same-polarity encountering results in a merging of those elements to the flux related to sunspols.,The same-polarity encountering results in a merging of those elements to the flux related to sunspots.196" Whereas. (he opposite polarity encountering causes [Iux cancelations with the net results of lost smaller elements anc a diffusion of sunspot Πας,"," Whereas, the opposite polarity encountering causes flux cancelations with the net results of lost smaller elements and a diffusion of sunspot flux."197 What accompanied the sunspol flux diffusion is the reduced smaller elements with the turbulent origin., What accompanied the sunspot flux diffusion is the reduced smaller elements with the turbulent origin.198 This accounts [or the anti-correlated magnetic component possibly., This accounts for the anti-correlated magnetic component possibly.199 By this kind of interaction magnetic flux from turbulent dvnamo actively takes part in the operation of the solar cvele. helping with more ellicient magnetic diffusion.," By this kind of interaction magnetic flux from turbulent dynamo actively takes part in the operation of the solar cycle, helping with more efficient magnetic diffusion."200 To quantify Chis mechanism. studies of dynamic interaction between small-scale magnetic elements ancl active regions fields are crucially required.," To quantify this mechanism, studies of dynamic interaction between small-scale magnetic elements and active regions fields are crucially required."201 secondly. itis also possible that at the solar maximum. the stronger magnetic field from sunspots tends to suppress the Sun'ss global convection in some measure.," Secondly, it is also possible that at the solar maximum, the stronger magnetic field from sunspots tends to suppress the s global convection in some measure."202 As a result. the local dvnamo has been abated somehow. and the network elements created by turbulence are reduced in number and total Πας.," As a result, the local dynamo has been abated somehow, and the network elements created by turbulence are reduced in number and total flux."203 This seems to suggest that the (turbulent dynamo is. in fact. global but not local.," This seems to suggest that the turbulent dynamo is, in fact, global but not local."204 Unfortunately. so far there have been no definite observations about the changes in the global solar convection during the suuspot cycle.," Unfortunately, so far there have been no definite observations about the changes in the global solar convection during the sunspot cycle."205 Another possibility is that the anti-correlated component represents the recveling of parts of the previously diffused or submerged magnetic flux from the mean-field dvnamo (Parker 1937)., Another possibility is that the anti-correlated component represents the recycling of parts of the previously diffused or submerged magnetic flux from the mean-field dynamo (Parker 1987).206 The diffusion of magnetic flux [rom sunspots to the deep convection zone requires 5-7 vears (Jiang οἱ al., The diffusion of magnetic flux from sunspots to the deep convection zone requires 5-7 years (Jiang et al.207 2007)., 2007).208 Parts of the cdiffised or submerged flux serves as the seed field [ον the elobally turbulent. dvuamo., Parts of the diffused or submerged flux serves as the seed field for the globally turbulent dynamo.209 Its production is naturally out of phase with sunspols in the solar cvcle. and brings up the magnetic elements (hat. anti-phased. with sunspots.," Its production is naturally out of phase with sunspots in the solar cycle, and brings up the magnetic elements that anti-phased with sunspots."210 In a recent literature. Thomas and Weiss (2008) proposed a picture of the solar Dynamo on three seales (one large and two small). which. according to the above authors. were only loosely coupled to each other.," In a recent literature, Thomas and Weiss (2008) proposed a picture of the solar Dynamo on three scales (one large and two small), which, according to the above authors, were only loosely coupled to each other."211 Ht is not clear if some unknown interplay of different. scale dvnamos may result in the complicated behavior of the Sun's small-scale fields., It is not clear if some unknown interplay of different scale dynamos may result in the complicated behavior of the Sun's small-scale fields.212 If we adopt ihe common vision that the smaller magnetic elements are created bv a local turbulent dvnamo. then the local turbulent dvnamo on a certain scale must have closely correlated to the elobal mean-fiekd dynamo.," If we adopt the common vision that the smaller magnetic elements are created by a local turbulent dynamo, then the local turbulent dynamo on a certain scale must have closely correlated to the global mean-field dynamo."213 The global dvnaimo either provides seed Παν or moclilies the condition for this turbulent dvnamo., The global dynamo either provides seed flux or modifies the condition for this turbulent dynamo.214 At the smallest end. the dynamo is likely to be more'llocal'.," At the smallest end, the dynamo is likely to be more."215. The turbulent. dvnamo. either global or purely local. brings a tremendous amount of turbulent flux to the Sun that continuously interacts with the productis of the mean-field diamo.," The turbulent dynamo, either global or purely local, brings a tremendous amount of turbulent flux to the Sun that continuously interacts with the products of the mean-field dynamo."216 The interaction seems to not only help with the operation of the global denamo. but also power the ceaseless siall-scale magnetic activity. aud maintain the Sun'ss Povnting flux to Earth ancl interplanetary space.," The interaction seems to not only help with the operation of the global dynamo, but also power the ceaseless small-scale magnetic activity and maintain the s Poynting flux to Earth and interplanetary space."217"flows the eas is near LOK and the cooling timescale is of order the recombination timescale, zi10fn vr. where s is the hydrogen deusitv (cu?)","flows the gas is near $10^4$ K and the cooling timescale is of order the recombination timescale, $\tau_{\rm rec} \sim 10^5/n$ yr, where $n$ is the hydrogen density $^{-3}$ )."218 Since he free-fall timescale is of order 105 vr. the gas loses wdrostatic support aud frec-falls wherever the density exceedsLOn 7," Since the free-fall timescale is of order $10^8$ yr, the gas loses hydrostatic support and free-falls wherever the density $\sim 10^{-3}$ $^{-3}$."219" In the halos we are to consider, his occurs at about 6 scale radii or 50 kpc."," In the halos we are to consider, this occurs at about 6 scale radii or 50 kpc."220" Within his radius, the eas is effectively pressure-free and in yee-fall. achieving velocities of several hundred kn s1 w the time it reaches the halo core."," Within this radius, the gas is effectively pressure-free and in free-fall, achieving velocities of several hundred km $^{-1}$ by the time it reaches the halo core."221" Iu this picture of rapid accretion onto a dense ouwvonie core im the dark matter halo. the production of ionizing photons, Vy is given by: where M ds the mass accretion rate. ipods the mean atomic weight of the infalling gas. gp is the mass of a hydrogen atom."," In this picture of rapid accretion onto a dense baryonic core in the dark matter halo, the production of ionizing photons, $\dot{N}$, is given by: where $\dot{\cal M}$ is the mass accretion rate, $\mu$ is the mean atomic weight of the infalling gas, $m_{\rm H}$ is the mass of a hydrogen atom."222" For cach halo, we therefore need to compute both AM and the velocity of accretion onto the barvouic core, Which by use of equation 1. will then give us οην."," For each halo, we therefore need to compute both $\dot{\cal M}$ and the velocity of accretion onto the baryonic core, which by use of equation \ref{phi} will then give us $ \phi(v)_{\rm up}$."223" For the halos. we use the Einusato density profile (Navarroetal.200:Springel2008) for tle DAL density. in ternis of a scaled radius «6—rfr Iu this equation. the logarithinic derivative is taken tobeequalto 2 at the scale radius, so that p(1)=p»."," For the halos, we use the Einsato density profile \citep{Navarro04,Springel08} for the DM density, in terms of a scaled radius $x = r/r_s$: In this equation, the logarithmic derivative is taken to be equal to $-2$ at the scale radius, so that $\rho(1) = \rho_{-2}$."224" The parameter a has a sinall variation about à=0.15. which is the value adopted here; and p2 is chosen to eive the halo mean density insice the virial radius, pu. once the physical virial radius and halo overdeusitv are known."," The parameter $\alpha$ has a small variation about $\alpha = 0.18$, which is the value adopted here, and $\rho_{-2}$ is chosen to give the halo mean density inside the virial radius, $\rho_{\rm halo}$, once the physical virial radius and halo over–density are known."225" The overall scaling is obtained by requiring pua to be related to the critical density of the Universe at the redshift considered, Assuniug the collapse ofa spherical top hat perturbation the ratio of the mean halo deusity to the critical density of the Universe, A.=Prats/p.. is given by Norman LOO8):: where We take Qa,=0.2715 and O4=0.728 from the fy maxima likelihood value in the WALIAP seven vear analysis (I&omiatsuetal2011)."," The overall scaling is obtained by requiring $\rho_{\rm halo}$ to be related to the critical density of the Universe at the redshift considered, Assuming the collapse of a spherical top hat perturbation, the ratio of the mean halo density to the critical density of the Universe, $\Delta_c = \rho_{\rm halo}/\rho_{c}$, is given by \citep{Bryan98}; where We take $ \Omega_M = 0.2715$ and $ \Omega_\Lambda = 0.728$ from the $H_0$ maximum likelihood value in the WMAP seven year analysis \citep{Komatsu11}."226". The value of the virial radius ayy. iu units of the scale radius is obtained usine a fit bv Dutyetal.(2005). (termed as concentration in that worl) with the desired virial mass for the appropriate redshift +, and cosinoloey (here /—0.701) 1 Once the virial radius is known in terms of the scale radius, the plysical scale is chosen so that the mass of the halo averaged over the virial volume gives the desired mean halo deusitv."," The value of the virial radius $x_{\rm vir}$ in units of the scale radius is obtained using a fit by \citet{Duffy08}, (termed as concentration in that work) with the desired virial mass for the appropriate redshift $z$, and cosmology (here $h = 0.704$ ): Once the virial radius is known in terms of the scale radius, the physical scale is chosen so that the mass of the halo averaged over the virial volume gives the desired mean halo density."227 The gravitational potential is then calculated integrating (7)=GAI(r)/r., The gravitational potential is then calculated integrating $\Phi(r) = GM(r)/r$.228 An analytical form for this potential can be readily derived., An analytical form for this potential can be readily derived.229" As an approximation of the complex plivsics involved in the collapse process, we assunie that the barvonic uatter follows the dark matter until virialization of the dark matter halo, at which point the barvonic matter »eeius to fall freely towards the ceutre of the halo."," As an approximation of the complex physics involved in the collapse process, we assume that the baryonic matter follows the dark matter until virialization of the dark matter halo, at which point the baryonic matter begins to fall freely towards the centre of the halo."230" Thus, in our initial configuration, the barvonic nass starts off roni rest and with the same radial density profile as he dark matter halo."," Thus, in our initial configuration, the baryonic mass starts off from rest and with the same radial density profile as the dark matter halo."231" The barvonic matter is therefore already. bound within the potential of the dark matter malo, and therefore auv kinetic energy of iufall to the initial radius dunrug the assembly of the halo is effective asstuned to have been already dissipated - presumably hroughthe low velocity shocks associated with the halo asseimiblv in the cold accretion scenario."," The baryonic matter is therefore already bound within the potential of the dark matter halo, and therefore any kinetic energy of infall to the initial radius during the assembly of the halo is effective assumed to have been already dissipated - presumably through the low velocity shocks associated with the halo assembly in the cold accretion scenario."232" From this (somewhat uncertain) approximation to he initial state, we have followed the subsequent accretion in 1-D spherical coordinates using the Lagerangiauli warodvuamic code. (Sutherland.2010"," From this (somewhat uncertain) approximation to the initial state, we have followed the subsequent accretion in 1-D spherical coordinates using the Lagrangian hydrodynamic code, \citep{Sutherland10}."233) This code includes all relevant gas plivsics aud eravitaional fields., This code includes all relevant gas physics and gravitational fields.234 By using 5 nested comaius. a final resolution of 43 pc is achieved in this simulation.," By using 5 nested domains, a final resolution of 0.3 pc is achieved in this simulation."235 This should be compared with the ~0.5 kpe spatial resolution achieved in the best smoothed particle bydrodvuamics (SPIT) cosinological codes., This should be compared with the $\sim 0.5$ kpc spatial resolution achieved in the best smoothed particle hydrodynamics (SPH) cosmological codes.236 As expected. within the critical radius at which ff)essure support is lost due to fast cooling (within about Ro~50 kpe as estimated above) the barvonic latter effectively free-fall towards the centre. since it has no thermal pressure support. am very little rotation.," As expected, within the critical radius at which pressure support is lost due to fast cooling (within about $R \sim 50$ kpc as estimated above) the baryonic matter effectively free-falls towards the centre, since it has no thermal pressure support, and very little rotation."237" In the vicinity of the nucleus, the infalline gas is shocked. and collects into a s11all. dense. rotationallv-supported disk whose size is determined by the torquing of the parent halo."," In the vicinity of the nucleus, the infalling gas is shocked, and collects into a small, dense, rotationally-supported disk whose size is determined by the torquing of the parent halo."238 The vertical scale height of this disk is determined by thermal and turbulent support., The vertical scale height of this disk is determined by thermal and turbulent support.239" Its pressure ids given by the ram pressure of the accretion flow, since the radiative shocks can be treated"," Its pressure is given by the ram pressure of the accretion flow, since the radiative shocks can be treated"240twelve dises.,twelve discs.241 He finds ωςρω~ GBELO per cent. below maximal according to the definition of Sackett (1997).," He finds $v_{stars}/v_{total} \sim$ $\pm$ 10 per cent, below maximal according to the definition of Sackett (1997)."242 The small variation in. disc contribution to. the 2237|0305 rotation curve. as demonstrated in Figure 2.. provides a &ood determination of the degree of maximality in this galaxy.," The small variation in disc contribution to the 2237+0305 rotation curve, as demonstrated in Figure \ref{rot_curve}, provides a good determination of the degree of maximality in this galaxy."243 The overall rotation curve. although not constrained: observationally in the region. where this calculation is made (the disc maximum at à  2.2r4). is also reasonably tight given the HE constraints and the profiles we have used.," The overall rotation curve, although not constrained observationally in the region where this calculation is made (the disc maximum at $r$ $\sim$ $r_d$ ), is also reasonably tight given the HI constraints and the profiles we have used."244 ‘The contribution of the disc to the rotation has already been determined. by its mean central surface mass density (de = 506430 M. 7j., The contribution of the disc to the rotation has already been determined by its mean central surface mass density (dc = $\pm$ 30 $_\odot$ $^{-2}$ ).245" ""This corresponds to a maximum rotation of Paps,(2. = 168+5 ", This corresponds to a maximum rotation of $v_{disc}(2.2r_d)$ = $\pm$ 5 $^{-1}$.246The maximum rotation is calculated to be (iint: = 2ss+5 , The maximum rotation is calculated to be $v_{total}(2.2r_d)$ = $\pm$ 5 $^{-1}$.247"The percentage contribution of the dise to the rotation. the degree. is therefore. ""his value fits well with that found by Bottema (1993). and is well defined for the potential solutions presented in this work."," The percentage contribution of the disc to the rotation, the degree, is therefore, This value fits well with that found by Bottema (1993), and is well defined for the potential solutions presented in this work."248 The disc is clearly sub-maximal., The disc is clearly sub-maximal.249 The ιν observed from cach image in a gravitationallv lensecL system. is a direct measure of the magnification in that region of the lens plane.," The flux observed from each image in a gravitationally lensed system, is a direct measure of the magnification in that region of the lens plane."250 A comparison between the ας ratios of the images observed in 2237|0305 ancl those predicted by the solutions can further act as a check on the results., A comparison between the flux ratios of the images observed in 2237+0305 and those predicted by the solutions can further act as a check on the results.251 Observed fluxes in individual images are a combination of magnification due to microlensing. macrolensing ancl intrinsic. variability. coupled: with time delavs.," Observed fluxes in individual images are a combination of magnification due to microlensing, macrolensing and intrinsic variability coupled with time delays."252 Agol. Jones Blaes (2000). however. have measured LB. tluxes (5.9 11.) for the four components and from these the ratio of Ηχος can be calculated.," Agol, Jones Blaes (2000), however, have measured IR fluxes (8.9 $\mu$ m) for the four components and from these the ratio of fluxes can be calculated."253 In this region of the spectrum. nmücrolensing events are not observed and it is therefore »ostulated. that these observations sample an extended region of the source.," In this region of the spectrum, microlensing events are not observed and it is therefore postulated that these observations sample an extended region of the source."254 In addition. the infrared fluxes are not sensitive to the dust reddening cllects of optical light ravelling through the galaxy.," In addition, the infrared fluxes are not sensitive to the dust reddening effects of optical light travelling through the galaxy."255 Thus the LR fluxes should measure the macro-maegnification., Thus the IR fluxes should measure the macro-magnification.256 These Luxes. relative to he DB image. are displaved in Table 7..," These fluxes, relative to the B image, are displayed in Table \ref{flux}."257 The [lux ratios were calculated. from our results. by aking the ratio of the magnification for cach of the images relative to the D image., The flux ratios were calculated from our results by taking the ratio of the magnification for each of the images relative to the B image.258 The magnification is calculated. by aking the ratio of areas of triangles around the images mapped. from the image to the source. plane., The magnification is calculated by taking the ratio of areas of triangles around the images mapped from the image to the source plane.259 ον were calculated from the best-fit solution of Table 2 ancl are clisplaved in Table 7.., They were calculated from the best-fit solution of Table \ref{param_dev} and are displayed in Table \ref{flux}.260 Our results are consistent with the observations., Our results are consistent with the observations.261 The halo model used is a generic profile that is analytically. simple but has little physical motivation., The halo model used is a generic profile that is analytically simple but has little physical motivation.262 It does. however provide a mass profile with varving slope. and this is a useful attribute if one wishes to study the gradient. of the mass distribution.," It does, however provide a mass profile with varying slope, and this is a useful attribute if one wishes to study the gradient of the mass distribution."263 The best-fit solution for the mass distribution of this galaxy is not an adequate fit., The best-fit solution for the mass distribution of this galaxy is not an adequate fit.264 The rotation curve is rising ab the outer regions studied: instead. of falling. and the images are not close enough to their measured. points.," The rotation curve is rising at the outer regions studied instead of falling, and the images are not close enough to their measured points."265 A halo with a smaller core would alleviate the former problem but require a change of the other mass distributions to address the latter., A halo with a smaller core would alleviate the former problem but require a change of the other mass distributions to address the latter.266 The miass-to-light profile of the. disc suggests an increase in the cise scale length., The mass-to-light profile of the disc suggests an increase in the disc scale length.267 Such a move would change the shear introduced by the disc., Such a move would change the shear introduced by the disc.268 In any case. he core radii found as the best solutions in this study jiwe large core radii r. 13-I16kpc.," In any case, the core radii found as the best solutions in this study have large core radii, $r_c \sim$ 13-16kpc."269 These values are not consistent with the cuspy central regions of the CDM woliles., These values are not consistent with the cuspy central regions of the CDM profiles.270 In. order to reduce the 47 and [find an adequate solution. we firstly require further rotation data.," In order to reduce the $\chi^2$ and find an adequate solution, we firstly require further rotation data."271 Phe more volts we have with good accuracy. the more likely we are o be able to eliminate profiles and find the best. solution.," The more points we have with good accuracy, the more likely we are to be able to eliminate profiles and find the best solution."272 Until more data is obtained. it is not worth trving to twist 1f halo profile to fit the parameters better.," Until more data is obtained, it is not worth trying to twist the halo profile to fit the parameters better."273 I£ the error vars on the HIE rotation points were doubled. the fit would come quite consistent with the observations.," If the error bars on the HI rotation points were doubled, the fit would become quite consistent with the observations."274 The Barnes et al. (, The Barnes et al. (2751999) observations were undertaken with the VLA C array. a compact configuration with low angular resolution.,"1999) observations were undertaken with the VLA C array, a compact configuration with low angular resolution."276 More informative data is attainable with higher resolution observations., More informative data is attainable with higher resolution observations.277 The surface mass distribution of the four components combined can be represented on a log-log plot to study the slope as a function of radius., The surface mass distribution of the four components combined can be represented on a log-log plot to study the slope as a function of radius.278 This information is clisplaved in Figure 6.., This information is displayed in Figure \ref{slope}.279 The dashed lines are. normalised fits to Xxor? (short-dashed) and Xxr (long-dashed)., The dashed lines are normalised fits to $\Sigma \propto r^{-0.3}$ (short-dashed) and $\Sigma \propto r^{-1}$ (long-dashed).280 The central slope overall is reasonably steep given the [aree inlluence of the bulge., The central slope overall is reasonably steep given the large influence of the bulge.281 The dark matter halo has zero slope in the inner regions given its large core radius., The dark matter halo has zero slope in the inner regions given its large core radius.282 The transition to isothermal is expected. given the dominance of the halo in the outer regions., The transition to isothermal is expected given the dominance of the halo in the outer regions.283 We have undertaken a study of the structure of galaxy 2237)0305 using cynamical anc gravitational lensing constraints., We have undertaken a study of the structure of galaxy 2237+0305 using dynamical and gravitational lensing constraints.284 Phe combination of these techniques allows, The combination of these techniques allows285One wav in which barred spiral galaxies are commonly divided into subclasses is by takine note of where (he large scale spiral starts wilh relation to the bar 1994).,"One way in which barred spiral galaxies are commonly divided into subclasses is by taking note of where the large scale spiral starts with relation to the bar \citep[e.g.,][]{sandage94}."286. In 5D(s) galaxies. the spiral arms begin at the ends of the bar. whereas in SB) galaxies. (he spiral armis beein on a ring connecting the ends of the bar.," In SB(s) galaxies, the spiral arms begin at the ends of the bar, whereas in SB(r) galaxies, the spiral arms begin on a ring connecting the ends of the bar."287 10(19) ealaxies are a transition group., SB(rs) galaxies are a transition group.288 SD(s) structures are (thought (to be preferentially found in less strongly barred. galaxies than their 5D(r) counterparts (e.g..Sanders&Tubbs1980:Simkinetal. 1930).," SB(s) structures are thought to be preferentially found in less strongly barred galaxies than their SB(r) counterparts \citep[e.g.,][]{sanders80, simkin80}."289. Furthermore. SD(s) galaxies typically show large-scale dust lanes that are nol present in 5D(r) galaxies. ancl SD(r) galaxies are observed (o have less dust in (heir central regions (han SB(s) galaxies (Ixormendy.&Ixennieutt.2004).," Furthermore, SB(s) galaxies typically show large-scale dust lanes that are not present in SB(r) galaxies, and SB(r) galaxies are observed to have less dust in their central regions than SB(s) galaxies \citep{kormendy04}."290.. This is an apparent inconsistenev with the generic bar-[ueling picture: 5D(r) galaxies are thought to have less dustbut be more strongly barreclwhile more strongly barred galaxies should have a higher central dust content., This is an apparent inconsistency with the generic bar-fueling picture: SB(r) galaxies are thought to have less dust—but be more strongly barred—while more strongly barred galaxies should have a higher central dust content.291 As these conclusions have been based on measuring the barstrength as an axis ralio (e.g..Sanders&Tubbs1980).. rather than as a force ratio. this discrepancy might be because SD(r) galaxies are actually more weakly barred than SD(s) galaxies.," As these conclusions have been based on measuring the barstrength as an axis ratio \citep[e.g.,][]{sanders80}, rather than as a force ratio, this discrepancy might be because SB(r) galaxies are actually more weakly barred than SB(s) galaxies."292 We reinvestigate the relation between these bar sub-tvpes and barstrength., We reinvestigate the relation between these bar sub-types and barstrength.293 The breakdown by nuclear class. including LGD. of the 21 RC3-classified SB galaxies in our sample is given in Table 2..," The breakdown by nuclear class, including LGD, of the 21 RC3-classified SB galaxies in our sample is given in Table \ref{tbl:SB}."294 A small increase in ιν is seen from SBir) to 9105)., A small increase in $Q_b$ is seen from SB(r) to SB(s).295 Visually. the SD(r) galaxies have much less dust structure than the SD(rs) and SB(s) galaxies.," Visually, the SB(r) galaxies have much less dust structure than the SB(rs) and SB(s) galaxies."296 According to the Wilcoxon test. the SD(r) sample has a smaller Qy than the SB(s) galaxies ab a confidence level of," According to the Wilcoxon test, the SB(r) sample has a smaller $Q_b$ than the SB(s) galaxies at a confidence level of."29794%... Sanders&Tubbs(1980). suggest bar pattern speed as an alternative origin to the differences in SD(r) and SD(s) structure: a slowly rotating bar should give rise to 5D(r) structure. while a rapidly rotating bar should vield SB(s) structure.," \citet{sanders80} suggest bar pattern speed as an alternative origin to the differences in SB(r) and SB(s) structure: a slowly rotating bar should give rise to SB(r) structure, while a rapidly rotating bar should yield SB(s) structure."298 As the differences in barstrength are reversed from what was expected. rotation marx be more important in determining the large-scale morphology.," As the differences in barstrength are reversed from what was expected, rotation may be more important in determining the large-scale morphology."299" With respect to the amount of dust structure. we find with >99%. confidence that the SBfr) galaxies have less dust structure (smaller 0,4) than the SB(s) sample: similarly. we find with confidence that the SD(r) saniple has less dust than the 9D(1s) galaxies."," With respect to the amount of dust structure, we find with $\ge 99$ confidence that the SB(r) galaxies have less dust structure (smaller $\sigma_{\mbox{\scriptsize sm}}$ ) than the SB(s) sample; similarly, we find with confidence that the SB(r) sample has less dust than the SB(rs) galaxies."300We vow present the proof of Theorem 1.2 that involve finer estimates on the Hólkler For the sake of simplifying the ideas of the proof. we only couskler 1- dimensious «=;04.,"We now present the proof of Theorem \ref{theo2} that involve finer estimates on the Höllder For the sake of simplifying the ideas of the proof, we only consider $1$ -spatial dimensions $x=x_{1}$."301 The general n-dimensional case cau be easily deduced., The general $n$ -dimensional case can be easily deduced.302" Following the samenotations of [5].. we let OQ=(—1.2)x(CT.2T). 2,€Z3COy such that and We also take the cut-olf function W€CO(E?) 0€Wx1 satis[ving: The main idea of the proof consists in exteudiug the Muection / to a suitable function of the form Wf wheref is clelined on £24."," Following the samenotations of \cite{Ibrahim09}, we let $\widetilde{\O}_{T} = (-1,2) \times (-T,2T)$, $\mathcal{Z}_{1}303\subseteq \mathcal{Z}_{2} \subseteq \widetilde{\O}_{T}$ such that and We also take the cut-off function $\Psi\in C^{\infty}_{0}(\R^{2})$, $0\leq\Psi\leq 1$ satisfying: The main idea of the proof consists in extending the function $f$ to a suitable function of the form $ \Psi\tilde{f}$ where$\tilde{f}$ is defined on $\widetilde{\O}_{T}$."304 We then apply inequality (1.1)) (the scalar-valued. version. with ΗΞ 1) ιο Wf aud we estimate the different norms iu order to get the result.," We then apply inequality \ref{Ib:eq4}) ) (the scalar-valued version with $n=1$ ) to $305\Psi\tilde{f}$ and we estimate the different norms in order to get the result."306 However. away from the complicated extension (Sobolev extension) of the function f that was done in [5].. we here consider a sliupler sviunetric exteusion.," However, away from the complicated extension (Sobolev extension) of the function $\tilde{f}$ that was done in \cite{Ibrahim09}, we here consider a simpler symmetric extension."307 Lucleecd. we first take the spatial syiumetry of the function f: aud then the sviminetry. with respect to /: claim that Wf €C7(8?) withΠλ In this case. we apply the scalar-valued version of inequality (1.1)) (see Remark 1.3)) to the function Wf with ;—1 and gGr./)=INWy.fly.Ody.," Indeed, we first take the spatial symmetry of the function $f$: and then the symmetry with respect to $t$ : We claim that $\Psi \tilde{f} \in C^{\g,\g/2}(\R^{2})$ with In this case, we apply the scalar-valued version of inequality \ref{Ib:eq4}) ) (see Remark \ref{rem1}) ) to the function $\Psi308\tilde{f}$ with $i=1$ and $g(x,t) =309\int_{0}^{x} \Psi(y,t) \tilde{f}(y,t) dy$."310 This. together with the fact that Y=1 on ο). lead to the following estimate: ]t is worth noticing that choosing 7=1 above is somehow restrictive.," This, together with the fact that $\Psi = 1$ on $\O_T$, lead to the following estimate: It is worth noticing that choosing $i=1$ above is somehow restrictive."311 Iu fact. we could also have used the inequality with /—2 and gGr./)—fiWGr.s)fGr. s)ds.," In fact, we could also have used the inequality with $i=2$ and $g(x,t) = \int_{0}^{t} \Psi(x,s) \tilde{f}(x,s) ds$ ."312" In [7]. it was shown that |W||paoce,€CULLBALO(Oy}+ μμ... while it is clear that ΠρCWlexοιSOWPee onu "," In \cite{IM09} it was shown that $\|\Psi \tilde{f}\|_{BMO(\R^{2})}313\leq C (\|f\|_{BMO(\O_{T})} + \|f\|_{L^{1}(\O_{T})})$ , while it is clear that $\|g\|_{L^{\infty}(\R^{2})} \leq C314\|\tilde{f}\|_{L^{\infty}(\widetilde{\O}_T)}\leq C315\|f\|_{C^{\g,\g/2}(\O_{T})}$ ."316These arguments. along with (3.8))and (3.9)). directly terminate the proof.," These arguments, along with \ref{h}) )and \ref{estimate1}) ), directly terminate the proof."317 The ouly point left is to show the claim (3.8))., The only point left is to show the claim\ref{h}) ).318 Recall the norm, Recall the norm319which is not surprising given the increased resolution.,which is not surprising given the increased resolution.320" Observations indicate that the binary period distribution is extremely broad, covering separations from only a few stellar radii to >104 AU (?).."," Observations indicate that the binary period distribution is extremely broad, covering separations from only a few stellar radii to $\ga 10^4$ AU \citep{duquennoy91a}."321" It is therefore not surprising that some binaries that might be resolved into two separate stars in run HR instead appear as a single star in run LR - indeed, we would expect this result in essentially any simulation that did not resolve the radii of individual stars."," It is therefore not surprising that some binaries that might be resolved into two separate stars in run HR instead appear as a single star in run LR – indeed, we would expect this result in essentially any simulation that did not resolve the radii of individual stars."322" Nonetheless, notice that, if we normalize to the number of stars present at equal times and fractions of mass accreted, then the difference between the two runs disappears."," Nonetheless, notice that, if we normalize to the number of stars present at equal times and fractions of mass accreted, then the difference between the two runs disappears."323 The number of stars present at any given time in run HR is roughly 1.6 times the number present at the same time in run LR., The number of stars present at any given time in run HR is roughly $1.6$ times the number present at the same time in run LR.324" Thus the trend in terms of when the stars are formed in the simulations is nearly identical in the two cases, and we can regard as well-resolved the distribution in time of when stars form."," Thus the trend in terms of when the stars are formed in the simulations is nearly identical in the two cases, and we can regard as well-resolved the distribution in time of when stars form."325 The trend of number of stars versus mass shown in Figure 5 is interesting., The trend of number of stars versus mass shown in Figure \ref{starhist2} is interesting.326" In the radiative runs, when M.ox/ΜεS;0.1, the number of stars increases roughly linearly with the total stellar mass, as we might expect if the mass per star were constant."," In the radiative runs, when $M_{*,\rm tot}/M_c \la 0.1$, the number of stars increases roughly linearly with the total stellar mass, as we might expect if the mass per star were constant."327" However, the rate at which new stars appears drops sharply once M, 0.2."," However, the rate at which new stars appears drops sharply once $M_{*,\rm tot}/M_c \ga 0.2$ ."328" Indeed, we see that 60—7096 of all stars have totformed/Me at a time when only ~10% of the cloud mass has been incorporated into stars, By the time of the cloud mass has gone into stars, nearly of all the stars are in place."," Indeed, we see that $60-70\%$ of all stars have formed at a time when only $\sim 10\%$ of the cloud mass has been incorporated into stars, By the time of the cloud mass has gone into stars, nearly of all the stars are in place."329" In effect, the fragmentation of the gas into new stars has completely shut down."," In effect, the fragmentation of the gas into new stars has completely shut down."330" Given that this effect occurs nearly identically in runs LR and HR, this cannot be a resolution effect."," Given that this effect occurs nearly identically in runs LR and HR, this cannot be a resolution effect."331" In contrast, run ISO shows very different behavior."," In contrast, run ISO shows very different behavior."332" The number of stars as a function of total stellar mass is almost the same as in run HR up to the point where ~15% of the mass has been incorporated into stars, but the two runs diverge after that."," The number of stars as a function of total stellar mass is almost the same as in run HR up to the point where $\sim 15\%$ of the mass has been incorporated into stars, but the two runs diverge after that."333" New stars continue forming all the way through run ISO, at a rate that is only slightly less after M,tor/M_.20.2 than it was earlier in the simulation."," New stars continue forming all the way through run ISO, at a rate that is only slightly less after $M_{*,\rm tot}/M_c \ga 0.2$ than it was earlier in the simulation."334" This strongly suggests that the shutdown in new star formation we observe in runs LR and HR is a radiative effect, a topic to which we will return in Section 3.3.."," This strongly suggests that the shutdown in new star formation we observe in runs LR and HR is a radiative effect, a topic to which we will return in Section \ref{sec:thermo}."335" As one might expect, this shutoff of fragmentation into new stars in runs LR and HR even as the total stellar mass continues to increase produces a dramatic effect on the stellar mass distribution."," As one might expect, this shutoff of fragmentation into new stars in runs LR and HR even as the total stellar mass continues to increase produces a dramatic effect on the stellar mass distribution."336 Figures 6 and 7 show the cumulative and differential mass distributions of the stars formed in our simulations at the times when the total mass in stars is 10—5096 of the initial cluster mass., Figures \ref{imfplot1} and \ref{imfplot2} show the cumulative and differential mass distributions of the stars formed in our simulations at the times when the total mass in stars is $10-50\%$ of the initial cluster mass.337 All these plots show that the stellar mass distribution in the radiative runs moves continuously to higher masses as the simulation proceeds., All these plots show that the stellar mass distribution in the radiative runs moves continuously to higher masses as the simulation proceeds.338" This is because mass is accreting onto existing stars, which rise in mass, but very few new, lower-mass stars are forming."," This is because mass is accreting onto existing stars, which rise in mass, but very few new, lower-mass stars are forming."339" Note that, while the mean stellar masses are slightly different in runs LR and HR, the systematic drift of these mean to higher masses as the total stellar mass rises appears to about occur equally in"," Note that, while the mean stellar masses are slightly different in runs LR and HR, the systematic drift of these mean to higher masses as the total stellar mass rises appears to about occur equally in"340"The best-fit solutions of the Monte Carlo samples (dots in panels c to h, Fig. 9))","The best-fit solutions of the Monte Carlo samples (dots in panels c to h, Fig. \ref{fig:fit_sn5}) )"341" are of course centered around the true solution, which explains the small relative shift of the x-contours, which indicate the best-fit solutions for the simulated data."," are of course centered around the true solution, which explains the small relative shift of the $\chi^2$ -contours, which indicate the best-fit solutions for the simulated data."342 As statistically expected this shift is smaller than the lo error., As statistically expected this shift is smaller than the $\sigma$ error.343 In the second test case (Fig. 10)), In the second test case (Fig. \ref{fig:fit_sn1.5}) )344" we considered only 50, hhalf as many, data points and we considerably reduced the signal-to-noise ratio down to 1.5, which is more representative of the data by ?.."," we considered only 50, half as many, data points and we considerably reduced the signal-to-noise ratio down to 1.5, which is more representative of the data by \citet{berdyuginaetal2008a}."345 Here we assumed a circular orbit so that the longitude of the periastron becomes undefined., Here we assumed a circular orbit so that the longitude of the periastron becomes undefined.346" For the x?-minimization we nonetheless kept the eccentricity e as a free parameter, but we fixed w to90°.."," For the $\chi^2$ -minimization we nonetheless kept the eccentricity $e$ as a free parameter, but we fixed $\omega$ to."347 For very small eccentricities ω is not well constrained by the data but has also negligible influence on the polarization curves., For very small eccentricities $\omega$ is not well constrained by the data but has also negligible influence on the polarization curves.348" Therefore, we are left with six free parameters."," Therefore, we are left with six free parameters."349 Even under these more difficult circumstances the fitting procedure proved to be very robust., Even under these more difficult circumstances the fitting procedure proved to be very robust.350 The original curves are again quite well reproduced (Fig., The original curves are again quite well reproduced (Fig.351 10aa&bb) and the input parameters well identified (Table 1))., \ref{fig:fit_sn1.5}a b) and the input parameters well identified (Table \ref{table:parameters}) ).352 The y?-minimum, The $\chi^2$ -minimum353the cross power spectra from the overlapping portion of resicuals of cach pulsar pair with no further. processing.,the cross power spectra from the overlapping portion of residuals of each pulsar pair with no further processing.354 Llowever. upon simulating this procedure. we found that the lowest frequencies in the cross power spectra were biasec whenever diiJdosgsnp.," However, upon simulating this procedure, we found that the lowest frequencies in the cross power spectra were biased whenever $\tobs > \tol$."355 This bias took the form of a significantly. non-zero imaginary part in the cross power spectrum., This bias took the form of a significantly non-zero imaginary part in the cross power spectrum.356 Also. we found that much of the correlated signa at low frequencies was removed. as shown in Figure 7..," Also, we found that much of the correlated signal at low frequencies was removed, as shown in Figure \ref{fig:fit}."357 We were unable to eliminate these cllects unless we performer a WLSO fit of a quadratic function for each time series over the overlapping time range., We were unable to eliminate these effects unless we performed a WLSQ fit of a quadratic function for each time series over the overlapping time range.358 Γι restores the correlation in the GWD signal between dillerent pulsars (right panels of Figure 7))., This restores the correlation in the GWB signal between different pulsars (right panels of Figure \ref{fig:fit}) ).359 This additional WLSQ fit will introduce a new bias because of removing some of the GWD signal at fMua. but this new bias is easily corrected with the calibration factors 5;;Cf£).," This additional WLSQ fit will introduce a new bias because of removing some of the GWB signal at $f=1/\tol$, but this new bias is easily corrected with the calibration factors $\gamma_{ij}(f)$."360 However. there is an additional loss of 10 per cent of the GWD signal in the Verbiest ct al. (," However, there is an additional loss of 10 per cent of the GWB signal in the Verbiest et al. ("3612005. 2009) observations because ofthis extra WLSQ fit.,"2008, 2009) observations because of this extra WLSQ fit."362 The CAVB analysis is complicated by the unknown cllects of other correlated signals in the timing residuals., The GWB analysis is complicated by the unknown effects of other correlated signals in the timing residuals.363 Instabilities in TPP and errors in the Solar-Systemi ephemeris both produce signals which are correlated between: dillerent pulsars., Instabilities in TT and errors in the Solar-System ephemeris both produce signals which are correlated between different pulsars.364 We estimated the effect. of these uncertainties by using an updated: timescale anc the most recent Solar-System ephemeris., We estimated the effect of these uncertainties by using an updated timescale and the most recent Solar-System ephemeris.365 Instabilities in PP produce a positive cross correlation independent of angular separation., Instabilities in TT produce a positive cross correlation independent of angular separation.366 Any estimate of the clock error will thus be correlated with the estimate of the GWB amplitude., Any estimate of the clock error will thus be correlated with the estimate of the GWB amplitude.367 Lad. we made a significant detection of the GWD. this would. have to be accounted for.," Had we made a significant detection of the GWB, this would have to be accounted for."368 ‘To estimate the importance of possible clock instabilities. we processed the Verbiest et al. (," To estimate the importance of possible clock instabilities, we processed the Verbiest et al. ("3692008. 2009) observations using the version of TE. released by DIPM. in 2010 (sec.e.g. 7)..,"2008, 2009) observations using the version of TT released by BIPM in 2010 \citep[see, e.g.,][]{2003Petit}."370 his post-corrected timescale has revealed. statistically in T, This post-corrected timescale has revealed statistically significant inaccuracies in TT(TAI).371able 6.., The results are shown in Table \ref{tbl:ttephem}.372 While the change of clock reference only changes our estimated GAB level by nine per cent of the uncertainty. the absolute change (0.810 77) is at a significant level for some predictions of the GAVB (??)..," While the change of clock reference only changes our estimated GWB level by nine per cent of the uncertainty, the absolute change $0.8\e{-30}$ ) is at a significant level for some predictions of the GWB \citep{jb03,svc08}."373 This implies that such instabilities in LE must be accounted for when analysing future data sets., This implies that such instabilities in TT must be accounted for when analysing future data sets.374 The results. from using. the newest Solar-Svsteni ephemeris DE421 (2). are given in Table 6.., The results from using the newest Solar-System ephemeris DE421 \citep{2009DE421} are given in Table \ref{tbl:ttephem}.375 While there have been some improvements in this ephemeris version compared to DEL05. most of the changes are absorbed by the pulsar parameter fit.," While there have been some improvements in this ephemeris version compared to DE405, most of the changes are absorbed by the pulsar parameter fit."376 The estimated GWD level has changed by 24 per cent of the uncertainty., The estimated GWB level has changed by 24 per cent of the uncertainty.377 Lowe assume DIZ421 is correct. then the use of DIZ405 is similar to introducing a spurious CAB signal with 44—L5.10C. a signal which is undetectable in most time series from the Verbiest ct al. (," If we assume DE421 is correct, then the use of DE405 is similar to introducing a spurious GWB signal with $A=1.5\e{-15}$, a signal which is undetectable in most time series from the Verbiest et al. ("3782008. 2009) observations.,"2008, 2009) observations."379 However. future observations will need to account [or the cllects of inaccuracies in the Solar-System ephemoris.," However, future observations will need to account for the effects of inaccuracies in the Solar-System ephemeris."380 ]t is dillicult to. determine. the exact. contributions to the weighting of cach pulsar pair when using error. bars derived from Monte Carlo simulations., It is difficult to determine the exact contributions to the weighting of each pulsar pair when using error bars derived from Monte Carlo simulations.381 Phe dominant cllect is the size of Docertap., The dominant effect is the size of $\tol$.382 For a GWB caused. by SMDILDDs. the weighting factor increases approximately as TAS.," For a GWB caused by SMBHBs, the weighting factor increases approximately as $\tol^{4.3}$."383 A higher noise level in the residuals of cach pulsar in the pair will decrease the weight of that pair approximately linearly., A higher noise level in the residuals of each pulsar in the pair will decrease the weight of that pair approximately linearly.384" The angle subtended at the observer by the pair of pulsars 4), can be important 1£8;; is near the zeroes ofthe function plotted in Figure 1..", The angle subtended at the observer by the pair of pulsars $\theta_{ij}$ can be important if $\theta_{ij}$ is near the zeroes of the function plotted in Figure \ref{fig:HD}. .385 ‘To determine which pulsars contribute the most to our estimate of the GCWD. we perform the WLSQ fit described by Equations (10)) and (11)) to only 189 of the possible 190 (6;;) estimates.," To determine which pulsars contribute the most to our estimate of the GWB, we perform the WLSQ fit described by Equations \ref{eq:a2est}) ) and \ref{eq:a2esterr}) ) to only 189 of the possible 190 $\asqzeta$ estimates."386 By varving which estimate of Anc(6;;) is Anremoved. we can find the pulsar pairs which have the ereatest influence over the measurement. of 217. in these residuals.," By varying which estimate of $\asqzeta$ is removed, we can find the pulsar pairs which have the greatest influence over the measurement of $\hat{A^2}$ in these residuals."387 This is performed by finding Ald? for cach pair of pulsars. whichis the measured? from all pulsar pairs minus the value of AP when including the given pulsar pair.," This is performed by finding $\Delta\hat{A^2}$ for each pair of pulsars, which is the measured $\hat{A^2}$ from all pulsar pairs minus the value of $\hat{A^2}$ when including the given pulsar pair."388 Those pairs with the lareest contribution to this measure are given in Table 7.. and a histogram of the absolute value AL for all pulsar pairs is provided in Figure &..," Those pairs with the largest contribution to this measure are given in Table \ref{tbl:psrpairs}, and a histogram of the absolute value $\left|\Delta\hat{A^2}\right|$ for all pulsar pairs is provided in Figure \ref{fig:histdelA2}."389 This analvsis shows that the measurement of 20. is determined by only ai few pulsar pairs., This analysis shows that the measurement of $\hat{A^2}$ is determined by only a few pulsar pairs.390 This. severely reduces the number of degrees of freedom. when detecting the GAB. and thus decreases the maximum. attainable detection confidence (see?) because it reduces our ability to average out the sell-noise in the residuals caused by the CAB signal at each. pulsar.," This severely reduces the number of degrees of freedom when detecting the GWB, and thus decreases the maximum attainable detection confidence \citep[see][]{jhlm05} because it reduces our ability to average out the self-noise in the residuals caused by the GWB signal at each pulsar."391 Observing morestrong pulsars is essential to increasing the number of degrees of freedom, Observing morestrong pulsars is essential to increasing the number of degrees of freedom392Stars of low and intermediate mass with initial masses between 0.8. —SAL. evolve to the asymptotic giant branch (AGB).,Stars of low and intermediate mass with initial masses between $M_\odot$ – $M_\odot$ evolve to the asymptotic giant branch (AGB).393 Then. thanks to severe mass loss. the AGB star evolves rapidly at nearly constant luminosity to higher effective temperatures to the white dwarf cooling track.," Then, thanks to severe mass loss, the AGB star evolves rapidly at nearly constant luminosity to higher effective temperatures to the white dwarf cooling track."394 Typical stellar lifetimes of post-AGB stars are expected to be of the order of 10! years (Schónberner 1983)., Typical stellar lifetimes of post-AGB stars are expected to be of the order of $^{\rm 4}$ years nberner 1983).395 The gas lost by the AGB star forms a circumstellar shell., The gas lost by the AGB star forms a circumstellar shell.396 When ye post-AGB star is cool. the dust in the shell heated by stellar A4o4radiation provides an infrared excess.," When the post-AGB star is cool, the dust in the shell heated by stellar radiation provides an infrared excess."397 When the star has traversed the top of the H-R diagram to higher effective temperatures. the circumstellar gas is ionized.," When the star has traversed the top of the H-R diagram to higher effective temperatures, the circumstellar gas is ionized."398 Then. the star is said to have evolved to reached the proto-planetary nebula stage.," Then, the star is said to have evolved to reached the proto-planetary nebula stage."399 Shortly after this. the post-AGB star has evolved to become a planetary nebula with a hot white dwarf as the central star.," Shortly after this, the post-AGB star has evolved to become a planetary nebula with a hot white dwarf as the central star."400 Determinations of the chemical composition for post-AGB star hold the potential of yielding insights into the chemical history of the AGB star and its conversion by mass loss to its slimmer post-AGB form., Determinations of the chemical composition for post-AGB star hold the potential of yielding insights into the chemical history of the AGB star and its conversion by mass loss to its slimmer post-AGB form.401 In this paper we present a determination of the chemical composition of IRAS [8095+2704. a post-AGB star with a substantial dusty circumstellar shell.," In this paper, we present a determination of the chemical composition of IRAS 18095+2704, a post-AGB star with a substantial dusty circumstellar shell."402 The discovery of the optical counterpart TIRAS 1809542704. was made by Hrivnak. Kwok. Volk (1987. 1988).," The discovery of the optical counterpart IRAS 18095+2704 was made by Hrivnak, Kwok, Volk (1987, 1988)."403 This V = 10.4 mag star is a high-latitude F supergiant with a large far-IR excess., This $V$ = 10.4 mag star is a high-latitude F supergiant with a large far-IR excess.404 In the assembled by Hrivnak. Kwok. Volk (1988). the star has a peculiar TR continuum slope at wavelengths shortward of the 10 Silicate emission feature.," In the assembled by Hrivnak, Kwok, Volk (1988), the star has a peculiar IR continuum slope at wavelengths shortward of the 10 silicate emission feature."405 According to Volk Kwok (1987). this peculiar continuum shape is a result of a detached dust shell.," According to Volk Kwok (1987), this peculiar continuum shape is a result of a detached dust shell."406 Observational evidence for an expanding shell came from Lewis. Eder. Terzian (1985) and Eder. Lewis. Terzian (1988) via detection of OH maser emission at [612 and 1665/67 MHz from the Arecibo telescope.," Observational evidence for an expanding shell came from Lewis, Eder, Terzian (1985) and Eder, Lewis, Terzian (1988) via detection of OH maser emission at 1612 and 1665/67 MHz from the Arecibo telescope."407 Gledhill et al. (, Gledhill et al. (4082001) from imaging polarimetry report an extended envelope or a reflection nebula around the star.,2001) from imaging polarimetry report an extended envelope or a reflection nebula around the star.409 (0.2 em The pioneering study of TRAS 18095427048 composition was reported by Klochkova (1995) from echelle spectra (2?=24 000)," 0.2 cm The pioneering study of IRAS 18095+2704's composition was reported by Klochkova (1995) from echelle spectra $R410= 24\,000$ )"411The Ixuiper Belt is a vast swarm of iev bodies bevond the orbit of Neptune in our solar svstem.,The Kuiper Belt is a vast swarm of icy bodies beyond the orbit of Neptune in our solar system.412 Following the discovery of the first INuiper Belt objects (IXDOs) in 1930 (Pluto: and 1992 (1992OD:Jewitt&Luu1993).. several groups began survevs to characterize the limits of the Kuiper Belt," Following the discovery of the first Kuiper Belt objects (KBOs) in 1930 \citep[Pluto;][]{tom46}413 and 1992 \citep[1992 QB$_1$;][]{jew93}, several groups began large-scale surveys to characterize the limits of the Kuiper Belt"4145truciu BStrueiu Cnr Cnr Cnr Cnr σα1) clussilü ον CLUSSS ciusshbxlO 1102 ciutir clurd cutis clures 12pt,"5truein 8truein cmr8 cmr8 cmr8 cmr8 cmr10 cmssi10 cmss10 cmss8 cmssbx10 2 cmti7 cmr6 cmti8 cmr8 \def\ref{\par\noindent\hangindent 15pt}415 = 12pt"4165truciu BStrueiu Cnr Cnr Cnr Cnr σα1) clussilü ον CLUSSS ciusshbxlO 1102 ciutir clurd cutis clures 12pt-,"5truein 8truein cmr8 cmr8 cmr8 cmr8 cmr10 cmssi10 cmss10 cmss8 cmssbx10 2 cmti7 cmr6 cmti8 cmr8 \def\ref{\par\noindent\hangindent 15pt}417 = 12pt"418weights due to having cmereccd roni differeut depths iu the nebula.,weights due to having emerged from different depths in the nebula.419 We have ested this method of calculating uncertaimtiCR by running the same model multiple times. but with a different. random uunber seed each time the model was run.," We have tested this method of calculating uncertainties by running the same model multiple times, but with a different random number seed each time the model was run."420 This allowed us to compue the true uncertaiutv lu au outpit quantity directly from the variation of the quantity between imodel rus., This allowed us to compute the true uncertainty in an output quantity directly from the variation of the quantity between model runs.421 By comparing the truc value of the uncertainty with the values computed usii18o eqs., By comparing the true value of the uncertainty with the values computed using eqs.422 25 and 27.. we were able to evaluate the accuracy of our smnple method of estimating uucertainties m output quautitics.," \ref{eq_unc} and \ref{eq_unc_image}, we were able to evaluate the accuracy of our simple method of estimating uncertainties in output quantities."423 For this testing. we chose to use a sphere with a homogeneous dust distribution. a 7:=1l. V baud Milky Wav dust erai properties. and a central ilbhuuinatii18o star (sec Fie.," For this testing, we chose to use a sphere with a homogeneous dust distribution, a $\tau_V = 1$, V band Milky Way dust grain properties, and a central illuminating star (see Fig."424 2aa)., \ref{fig_exam}a a).425 Other optical depths eive similar results., Other optical depths give similar results.426 We rau the model 100 times and varied the total munhber of photous between 107 and 107., We ran the model 100 times and varied the total number of photons between $10^2$ and $10^5$.427 Figure 1 cisplavs the uncertainties in the scattered flux and Q component of the polarized flux as a fiction of the nunber of photous run., Figure \ref{fig_test_unc} displays the uncertainties in the scattered flux and Q component of the polarized flux as a function of the number of photons run.428 The general trend is for the muacertaity calculated using eq., The general trend is for the uncertainty calculated using eq.429 25 or eq., \ref{eq_unc} or eq.430 27. to uuderestinate he actual uncertantv by smaller amounts as the uuuer of photons run increases., \ref{eq_unc_image} to underestimate the actual uncertainty by smaller amounts as the number of photons run increases.431 This is due to small umuber statistics. especially when the uncertaiutyv was calculatexl using eq. 27..," This is due to small number statistics, especially when the uncertainty was calculated using eq. \ref{eq_unc_image}."432 For à large πα: of photous (e.g... 107). he uncertainty calculated using eq.," For a large number of photons (e.g., $10^5$ ), the uncertainty calculated using eq."433 25. or 27 Is a τον eood estimate of the actual uncertainty., \ref{eq_unc} or \ref{eq_unc_image} is a very good estimate of the actual uncertainty.434 The reason is tlat he majority of the scattered flax aud Q component of 1C xlarized flux comes from the ceutral region of the nella (sce Fig., The reason is that the majority of the scattered flux and Q component of the polarized flux comes from the central region of the nebula (see Fig.435 2aa) aud the intrinsic variation of the scatter Hux in the ceutral region is small., \ref{fig_exam}a a) and the intrinsic variation of the scattered flux in the central region is small.436 This implies that nucertaity calculated frou eq., This implies that the uncertainty calculated from eq.437 25 or 27 is domina o» Monte Carlo noise for this model., \ref{eq_unc} or \ref{eq_unc_image} is dominated by Monte Carlo noise for this model.438 There are mo systems where this will not be the case and. as a resu care mnust be taken calculating the uncertainty using uecthod outlined above.," There are model systems where this will not be the case and, as a result, care must be taken calculating the uncertainty using the method outlined above."439 We ested the results of the DIRTY model against those produced by Moute Carlo radiative trauster models which do not weight photous aud models which use the Witt(1977) photon weightine., We tested the results of the DIRTY model against those produced by Monte Carlo radiative transfer models which do not weight photons and models which use the \citet{wit77} photon weighting.440 These models include ones which we have code as well oues others have coded BBjorkinan 1999. 4mivate commuiuication: WWood 1999. private communication).," These models include ones which we have coded as well ones others have coded Bjorkman 1999, private communication; Wood 1999, private communication)."441 For computational reasons. these iiodels are usually resvicted to spherically svuuuetrie systems with smoothly varving radial dust distributions.," For computational reasons, these models are usually restricted to spherically symmetric systems with smoothly varying radial dust distributions."442 Our two main test cases were for 7=1 and T== LO.," Our two main test cases were for $\tau =4431$ and $\tau = 10$ ."444 We adopted an albedo of 1.6 and a scattering phase fiction asviunetrv of (1.6., We adopted an albedo of 0.6 and a scattering phase function asymmetry of 0.6.445 Tn all cases. he YusefZadeh.Morris.&White{1981) photon weighting method produced statistically simula results to the other two weighting methods.," In all cases, the \citet{yus84}446 photon weighting method produced statistically similar results to the other two weighting methods."447 Tn adeditiou. we computed the wavelength depeudence of the polarization for active ealactic imcleus models simular to those used by. Manzi&diSerego.Alighieri—(199(i) aud found qualitative agreement with their results.," In addition, we computed the wavelength dependence of the polarization for active galactic nucleus models similar to those used by \citet{man96} and found qualitative agreement with their results."448 Quantitative agreement is more difficult to test as we used a different «ust era mode than Manzini&diSerego, Quantitative agreement is more difficult to test as we used a different dust grain model than \citet{man96}.449Alighieri)(1996). Figure 2 illustrates the mages produced bx the DIRTY model., Figure \ref{fig_exam} illustrates the images produced by the DIRTY model.450 Figure 2aa shows how a spherical ucmula with a central ilhuuimatius star would look iu the V bond assunune Milky Way type ¢lust with a homogeneous distribution and a radial τι=l., Figure \ref{fig_exam}a a shows how a spherical nebula with a central illuminating star would look in the V band assuming Milky Way type dust with a homogeneous distribution and a radial $\tau_V = 1$.451 Figure 2bb shows how a biconical nebula or active galactic nucleus inclined by an anele of 30° would look in the V band assuming Milky Way type dust with a homogeneous cüstribution and a τι=1., Figure \ref{fig_exam}b b shows how a biconical nebula or active galactic nucleus inclined by an angle of $\degr$ would look in the V band assuming Milky Way type dust with a homogeneous distribution and a $\tau_V = 1$.452 Figure 3. displays the spectra enerev distribution before and after the inclusion of dust i 1a sinple starburst svsten., Figure \ref{fig_exam_sed} displays the spectral energy distribution before and after the inclusion of dust in a simple starburst system.453 This is a good illustration of how the dust redistributes energev froii the ultraviolet to the infrared., This is a good illustration of how the dust redistributes energy from the ultraviolet to the infrared.454 Iu. addition. the three components (thera equilibrium. thermal nou- aud aromatic feature emissions) of the dust Cluission spectrum are shown.," In addition, the three components (thermal equilibrium, thermal non-equilibrium, and aromatic feature emissions) of the dust emission spectrum are shown."455 Starburst svstenis are iu investigateddetail i Misseltetal. (2000a)., Starburst systems are investigated in detail in \citet{mis00}. .456. We have preseuted theDIRTY radiative trauster, We have presented theDIRTY radiative transfer457elescopes detailed analysis of the shape of the line profile is not possible.,telescopes detailed analysis of the shape of the line profile is not possible.458 It is possible to provide an improved fit to the data but this requires the power law of the X-ray source to rave a photon index that is significantly lower than 2., It is possible to provide an improved fit to the data but this requires the power law of the X-ray source to have a photon index that is significantly lower than 2.459 We conclude that the data favour a Ixerr over a Schwarzschild Mack hole model., We conclude that the data favour a Kerr over a Schwarzschild black hole model.460 Nevertheless. the work of Itevnolds Degelman (1997) ias highlighted the potential importance of [lows within the mareinally stable orbit.," Nevertheless, the work of Reynolds Begelman (1997) has highlighted the potential importance of flows within the marginally stable orbit."461 Lo the irraciiating X-ray source is at some clistance above the disc. particularly in a central ocation. then fluorescent iron line [features [rom such inllowing material should be observable.," If the irradiating X-ray source is at some distance above the disc, particularly in a central location, then fluorescent iron line features from such inflowing material should be observable."462 That the predicted deep absorption edge is not seen in the case of ALCG6-30-15 supports a Ixerr model and. since most of the time the line is not so broad. argues that the irradiating source lies close to the disc and. at times. changes in radius.," That the predicted deep absorption edge is not seen in the case of MCG–6-30-15 supports a Kerr model and, since most of the time the line is not so broad, argues that the irradiating source lies close to the disc and, at times, changes in radius."463 The edge in the predicted spectrum of the RBOT mocel is particularly large because the material is ionized. so enhancing the contrast at the edge.," The edge in the predicted spectrum of the RB97 model is particularly large because the material is ionized, so enhancing the contrast at the edge."464 lt may. be possible to have less highly ionized material within 6m if the accretion clisc were gas pressure rather than radiation pressure dominated all the way down to 67 since then the density of the disc would be many times larger., It may be possible to have less highly ionized material within $6m$ if the accretion disc were gas pressure rather than radiation pressure dominated all the way down to $6m$ since then the density of the disc would be many times larger.465 Phere is also a small edge to the cold disc rellection expected in the standard model., There is also a small edge to the cold disc reflection expected in the standard model.466 Lt is unlikely that such a small edge would be detectable with current X-ray telescopes. however.," It is unlikely that such a small edge would be detectable with current X-ray telescopes, however."467 ]t is also useful to consider other methods of probing the innermost regions of the accretion disc., It is also useful to consider other methods of probing the innermost regions of the accretion disc.468 Lf we assume rapid large variations in the continuum. are due to [Lares over the disc. then the time delay between the continuum variation and the [üorescent line response from the disc may o used to estimate the height of the Dare above the disc.," If we assume rapid large variations in the continuum are due to flares over the disc, then the time delay between the continuum variation and the fluorescent line response from the disc may be used to estimate the height of the flare above the disc."469 In the case of the 14297 model this would need to be larger han that for a coronal model in order to provide sullicient illumination of the material within Gre., In the case of the RB97 model this would need to be larger than that for a coronal model in order to provide sufficient illumination of the material within $6m$.470 As well as the time delay between the continuum. change ancl the response of he disc. the evolution of the iron line profile with time can ell us about the geometry of both the source and the disc.," As well as the time delay between the continuum change and the response of the disc, the evolution of the iron line profile with time can tell us about the geometry of both the source and the disc."471 Unfortunately with present X-ray telescopes the photon lux in the iron line is only a few hundred counts per day. and integration times are necessarily so large that observations of short term variability are unfeasible.," Unfortunately with present X-ray telescopes the photon flux in the iron line is only a few hundred counts per day, and integration times are necessarily so large that observations of short term variability are unfeasible."472 lt is exciting that we are now debating and able to distinguish. gross details of the accretion low of matter at radii less than 6m., It is exciting that we are now debating and able to distinguish gross details of the accretion flow of matter at radii less than $6m$.473 Future observations with ASCA. ANAL. XMM. ASTRO-E and Constellation-N. will continue. this exploration of the very near environment of black holes.," Future observations with ASCA, AXAF, XMM, ASTRO-E and Constellation-X will continue this exploration of the very near environment of black holes."474 AJY and ACE thank PPARC ancl the Roval Society. [or support. respectively.," AJY and ACF thank PPARC and the Royal Society for support, respectively."475Alore interesting is the scatter in the data.,More interesting is the scatter in the data.476 For a photon counting instrument such asGALEN.. (he instrumental scatter will be either due to photon noise or to errors in (he flat fielding (calibration) of the instrument.," For a photon counting instrument such as, the instrumental scatter will be either due to photon noise or to errors in the flat fielding (calibration) of the instrument."477 We have empirically derived the instrumental scatter by dividing each observation into (wo sets of visits. which may well be separated by several months.," We have empirically derived the instrumental scatter by dividing each observation into two sets of visits, which may well be separated by several months."478 There is excellent agreement between this aud the intrinsic photon noise (Fig. 4)).," There is excellent agreement between this and the intrinsic photon noise (Fig. \ref{scat_plot}) ),"479 confirming (hat the errors are dominated by poissonian rather than instrumental effects., confirming that the errors are dominated by poissonian rather than instrumental effects.480 As an independent test. we also took the overlap regions between clillerent observations and ealeulated the scatter between them.," As an independent test, we also took the overlap regions between different observations and calculated the scatter between them."481 Although the seatter for the overlap regions is somewhat higher than the caleulated: values. (his is due to the many fewer points in the overlap regions and (heir location near the edge of the detector.," Although the scatter for the overlap regions is somewhat higher than the calculated values, this is due to the many fewer points in the overlap regions and their location near the edge of the detector."482 We note here that all our comparisons are in skv coordinates because (here are arbitrary roll angle differences between different. visits. which do not allow a comparison between physical detector pixels.," We note here that all our comparisons are in sky coordinates because there are arbitrary roll angle differences between different visits, which do not allow a comparison between physical detector pixels."483" The FUV and NUV images of theSpitzer ""First Look” field obtained after subtraction ol the foreground emission are shown in Fig.", The FUV and NUV images of the “First Look” field obtained after subtraction of the foreground emission are shown in Fig.484" 5 at a spatial resolution of2"".", \ref{diffuse_image} at a spatial resolution of.485. The UV images of Fig., The UV images of Fig.486 5 max be compared with the IR. 100 mmap (Fie. 1))., \ref{diffuse_image} may be compared with the IR 100 map (Fig. \ref{IR_img}) ).487 There are several possible contributors to the astrophysical UV. emission. a significant one being. dust-scattered starlight which contributes to both the FUV and the NUV bands.," There are several possible contributors to the astrophysical UV emission, a significant one being, dust-scattered starlight which contributes to both the FUV and the NUV bands."488 This is reflected in the good correlation between the FUV and NUV bands (Fig. 6)), This is reflected in the good correlation between the FUV and NUV bands (Fig. \ref{fuv_nuv}) )489 and between the two UV bands and the IR. 100 [fluxes (Fig. 7))., and between the two UV bands and the IR 100 fluxes (Fig. \ref{UV_IR}) ).490 This is in contrast with the essentially flat UW-IR curves obtained by in Region Il. The UR emission is due to thermal radiation from an optically {hin laver of dust. as the cross-section of the grains is low in the IR.," This is in contrast with the essentially flat UV-IR curves obtained by \citet{SNV09} in Region I. The IR emission is due to thermal radiation from an optically thin layer of dust, as the cross-section of the grains is low in the IR."491 On the other hand. the cross-section of the grains is much higher in the UV and the optical depth transitions from being opticallv thin in these Draco observations to being optically thick in Region I. In Fig. 8..," On the other hand, the cross-section of the grains is much higher in the UV and the optical depth transitions from being optically thin in these Draco observations to being optically thick in Region I. In Fig. \ref{UV_IR_ratio},"492 we have plotted the ratio between the UV bands and the IR to understaud the nature of diffuse UV emission with optical depth., we have plotted the ratio between the UV bands and the IR to understand the nature of diffuse UV emission with optical depth.493 There is a clear trend. visible from the low optical depth Draco region to the hieh optical depth (in the UV) Reeion I with an empirical formula of It is interesüng to note that the ο ratio in our data follows a continuous curve verv similar to that found by Murthyetal.(2001) in Orion, There is a clear trend visible from the low optical depth Draco region to the high optical depth (in the UV) Region I with an empirical formula of It is interesting to note that the $F_{UV}/F_{IR}$ ratio in our data follows a continuous curve very similar to that found by \citet{JM01} in Orion494it has been cleared by an orbiüng giant planet. (Calvet οἱ 22002). it is tempting to inler that TW Iva shows weak molecular emission in (he mid-inliared because the planet has created a gap in thegaseous disk as well.,"it has been cleared by an orbiting giant planet (Calvet et 2002), it is tempting to infer that TW Hya shows weak molecular emission in the mid-infrared because the planet has created a gap in the disk as well."495 We discussed in section 4 some of the issues (hat need to be investigated in order to determine whether the difference we observe is the result of giant planet formation or other processes., We discussed in section 4 some of the issues that need to be investigated in order to determine whether the difference we observe is the result of giant planet formation or other processes.496 Given our limited understanding of the factors that govern the emission spectra of T Tauri disks. if may be useful to (take an empirical approach in exploring whether (he lack of molecular emission seen from TW Iva is a consequence of the physical evolution of the disk. its chemical evolution. or an excitation effect.," Given our limited understanding of the factors that govern the emission spectra of T Tauri disks, it may be useful to take an empirical approach in exploring whether the lack of molecular emission seen from TW Hya is a consequence of the physical evolution of the disk, its chemical evolution, or an excitation effect."497 For example. to explore the possibility of an excitation effect. we can compare theSpitzer spectyum of TW Iva with those of other non-lransition objects wilh comparable accretion rates.," For example, to explore the possibility of an excitation effect, we can compare the spectrum of TW Hya with those of other non-transition objects with comparable accretion rates."498 If non-(ransiGion objects with low accretion rates also lack strong molecular emission. the spectzum of TW Iva would not be unusual for its accretion rate and the lack of molecular emission max be the result of poor excitation.," If non-transition objects with low accretion rates also lack strong molecular emission, the spectrum of TW Hya would not be unusual for its accretion rate and the lack of molecular emission may be the result of poor excitation."499 However. if strong molecular emission is observed in other low accretion rate svslenms. (he absence of such emission in TW Iva would suggest a gap in ils gaseous clisk or a possible chemical effect.," However, if strong molecular emission is observed in other low accretion rate systems, the absence of such emission in TW Hya would suggest a gap in its gaseous disk or a possible chemical effect."500 We will take Chis approach in a future study., We will take this approach in a future study.501 Sinularly. it would be interesting to explore whether other transition objects also show weak molecular emission compared (o classical T Tauri stars.," Similarly, it would be interesting to explore whether other transition objects also show weak molecular emission compared to classical T Tauri stars."502" Lf transition objects with much weaker UV fluxes than that of TW Ilva (e.g.. DM Tan. GAL Aur) also show a clelicil ol molecular emission. that would suggest a more dominant role lor SED evolution (a deficit of grains: possible clearing by a eiut planet). rather than photochemistry. in accounting for the dilference in (he spectra,"," If transition objects with much weaker UV fluxes than that of TW Hya (e.g., DM Tau, GM Aur) also show a deficit of molecular emission, that would suggest a more dominant role for SED evolution (a deficit of grains; possible clearing by a giant planet), rather than photochemistry, in accounting for the difference in the spectra."503 We will report on Chis in future publications., We will report on this in future publications.504 While strong molecular emüssion is not detected [rom TW Ilva. we do detect a rich spectrum of emission lines of atoms (LU. [Nel]. and [NelH]) and molecules (II5. ΟΠ. CO». HCO. and possibly ClI4).," While strong molecular emission is not detected from TW Hya, we do detect a rich spectrum of emission lines of atoms (HI, [NeII], and [NeIII]) and molecules $\Htwo,$ OH, $\COtwo,$ $\HCOp,$ and possibly $\CHthree$ )."505 One of the most intriguing is (he OIL emission. which is hot and may result [rom the UV photodissociation of water.," One of the most intriguing is the OH emission, which is hot and may result from the UV photodissociation of water."506 A more detailed analvsis of the OIL enission spectrum may be able to determine whether it is produced by photodissociation., A more detailed analysis of the OH emission spectrum may be able to determine whether it is produced by photodissociation.507 The properties of the molecular emission Irom TW Iva. both the ΟΠΗ and other molecules. will be analvzed in greater detail in a future study.," The properties of the molecular emission from TW Hya, both the OH and other molecules, will be analyzed in greater detail in a future study."508 Because we detect multiple ILE lines. we can show Chat the IHE emission from TW Iva has a recombination spectrum.," Because we detect multiple HI lines, we can show that the HI emission from TW Hya has a recombination spectrum."509 In contrast to the neon emission from TW Iva. which can be well accounted for by (primarily) stellar X-ray irradiation of the disk. the physical origin of the IHE emission is difficult to identify.," In contrast to the neon emission from TW Hya, which can be well accounted for by (primarily) stellar X-ray irradiation of the disk, the physical origin of the HI emission is difficult to identify."510 As discussed in section 4. magnetospheres. disk abmospheres aud/or photoevaporative Lows could plausibly contribute to the emission ancl multiple components max play a role.," As discussed in section 4, magnetospheres, disk atmospheres and/or photoevaporative flows could plausibly contribute to the emission and multiple components may play a role."511 High resolution spectroscopy of the brightest ILE lines (III 7-6 and ILE 9-7) would likely provide valuable insights into the origin of the emission., High resolution spectroscopy of the brightest HI lines (HI 7-6 and HI 9-7) would likely provide valuable insights into the origin of the emission.512Modern estimates of the mean metallicity eracient in the TOO1000 pe closest to the Galactic plane (Llartkopl Yoss 1982: Yoshii et al.,Modern estimates of the mean metallicity gradient in the $\sim 700 - 1000$ pc closest to the Galactic plane (Hartkopf Yoss 1982; Yoshii et al.513 LOST: Yoss et al., 1987; Yoss et al.514 LOST: Sorensen Ixnude 1994: Buser Rone 1995: Trefzeer et al., 1987; rensen Knude 1994; Buser Rong 1995; Trefzger et al.515 1995: see also Robin et al., 1995; see also Robin et al.516 1996: Buser et al., 1996; Buser et al.517 1998) are in the range 0.6xdFe/H]/dz<0.3 dex *.," 1998) are in the range $-0.6 \le \hbox{\rm518d[Fe/H]/d{\it z}} \le -0.3$ dex $^{-1}$."519 ME of these results have been obtained from samples. along sight lines closely perpendicular to the Galactic plane ancl centered on the position of the Sun. thereby ignoring possible radial metallicity eracients.," All of these results have been obtained from samples, along sight lines closely perpendicular to the Galactic plane and centered on the position of the Sun, thereby ignoring possible radial metallicity gradients."520 Jonch-Sorensen (1995) observed FE and carly C-type (main sequence) stars in six selected directions of the Galaxy and. tried. to solve for radial and vertical eracients simultaneously., rensen (1995) observed F and early G-type (main sequence) stars in six selected directions of the Galaxy and tried to solve for radial and vertical gradients simultaneously.521 His best results for z«TOO pc are 0.2E0.3 dex + and 0.01£0.08 dex + for the vertical ancl racial gradients. respectively.," His best results for $z <522700$ pc are $-0.2 \pm 0.3$ dex $^{-1}$ and $-0.01 \pm 0.03$ dex $^{-1}$ for the vertical and radial gradients, respectively."523 This may indicate that the elects of such a small radial metallicity e&racient on the expected. vertical abundance gradients are small or negligible. in particular if the origin of either. eradient is clilferent.," This may indicate that the effects of such a small radial metallicity gradient on the expected vertical abundance gradients are small or negligible, in particular if the origin of either gradient is different."524 Colour distributions and colour. gradients are sensitive to the metal abundances and their gradients of the integrated stellar populations in galaxies., Colour distributions and colour gradients are sensitive to the metal abundances and their gradients of the integrated stellar populations in galaxies.525 Althoughradial colour gradients in moderately inclined and. face-on galaxies have been studied extensively. in general indicating blucr colours with increasing ealactocentric distance (e.g.. de Jong 1996. and references therein). only for a few relatively large. ancl well-resolvec edge-on galaxiesvertical colour gradients have been measurecl.," Although colour gradients in moderately inclined and face-on galaxies have been studied extensively, in general indicating bluer colours with increasing galactocentric distance (e.g., de Jong 1996, and references therein), only for a few relatively large and well-resolved edge-on galaxies colour gradients have been measured."526 In highly inclined galaxies. the interpretation of intrinsic colours ancl colour gradients is severely. hamperec by the presence of dust in the ealactic planes.," In highly inclined galaxies, the interpretation of intrinsic colours and colour gradients is severely hampered by the presence of dust in the galactic planes."527" However. from. a comparison with published colours of moderately inclines Se galaxies. Ixuchinski ""JTerndrup (1996) have shown tha for these [ate-tvpe galaxies there is little or no reddening away [rom the cust lane."," However, from a comparison with published colours of moderately inclined Sc galaxies, Kuchinski Terndrup (1996) have shown that for these late-type galaxies there is little or no reddening away from the dust lane."528 Since statistical studies have shown that the dust content of Sc galaxies is large compared. to other clise-clominatecl galaxy types (e.g. de Crijs ct al.," Since statistical studies have shown that the dust content of Sc galaxies is large compared to other disc-dominated galaxy types (e.g., de Grijs et al."529 1997). we may assume that the elfects of reddening on the intrinsic galaxy colours away from the dust lane are largest for these galaxy types.," 1997), we may assume that the effects of reddening on the intrinsic galaxy colours away from the dust lane are largest for these galaxy types."530 Thus. colours ancl colour graclients measured at those distances from the galactic planes where the influence of the dust lane is negligible likely rellect theinfrinsic galactic properties.," Thus, colours and colour gradients measured at those distances from the galactic planes where the influence of the dust lane is negligible likely reflect the galactic properties."531 Detailed studies of the intrinsic colours of galactic discs perpendicular to their planes (e.g.. llamabe et al.," Detailed studies of the intrinsic colours of galactic discs perpendicular to their planes (e.g., Hamabe et al."532 1979: Leevi Gerber 1979: van der Ixruit Searle 1981: Jensen Thuan 1982) are consistent with a small or no vertical colour gradient outside the cust [ane region (see also de Cirijs ct al., 1979; Hegyi Gerber 1979; van der Kruit Searle 1981; Jensen Thuan 1982) are consistent with a small or no vertical colour gradient outside the dust lane region (see also de Grijs et al.533 1997)., 1997).534 Although colour gradients along the minor axis may be due to some intrinsic buleeproperty’... van der. Ixruit Searle (1981). observed. that. at. various. galactocentric distances. the vertical colours of NGC SOL are. getting systematically bluer with greater height above the plane.," Although colour gradients along the minor axis may be due to some intrinsic bulge, van der Kruit Searle (1981) observed that, at various galactocentric distances, the vertical colours of NGC 891 are getting systematically bluer with greater height above the plane."535 On the other hand. Jensen Thuan (1982) did not find any evidence for a similar vertical colour eraclient in NGC 4565 in the region where the old thin disc dominates.," On the other hand, Jensen Thuan (1982) did not find any evidence for a similar vertical colour gradient in NGC 4565 in the region where the old thin disc dominates."536 However. as soon as the light of the thick cise starts to dominate a small perpendicular colour gradient is present in their data. in the sense that the dise colours become redder with increasing clistance from the galactic plane.," However, as soon as the light of the thick disc starts to dominate a small perpendicular colour gradient is present in their data, in the sense that the disc colours become redder with increasing distance from the galactic plane."537 A similar result has recently. been obtained. for NCC 5907 (Lequeux ct al., A similar result has recently been obtained for NGC 5907 (Lequeux et al.538 1996. 1998: Ruely et al.," 1996, 1998; Rudy et al."539 1997). which was interpreted as an extended stellar halo redder than the galactic disc or a very thick cise component.," 1997), which was interpreted as an extended stellar halo redder than the galactic disc or a very thick disc component."540 The conversion of broad-banc colour gradients. to abundance ancl population gradients in external galaxies is controversial. unfortunately.," The conversion of broad-band colour gradients to abundance and population gradients in external galaxies is controversial, unfortunately."541 For the cetailed analysis of the uminosity and colour profiles of edge-on galaxies one needs o adopt assumptions concerning the evolutionary stellar population svnthesis. the initial mass function. the metallicity and the star formation history. as well as about 1ο dust geometry and its eharacteristies.," For the detailed analysis of the luminosity and colour profiles of edge-on galaxies one needs to adopt assumptions concerning the evolutionary stellar population synthesis, the initial mass function, the metallicity and the star formation history, as well as about the dust geometry and its characteristics."542 Due to the relative insensitivity of broad-band colours to these characteristics. in particular because of the age/metallicity degeneracy in 10 colours. of an integrated stellar population (Worthey 1994). spectral line studies seem to be a more cllective tool to isentangle metallicity and age effects. as well as population eracicnts.," Due to the relative insensitivity of broad-band colours to these characteristics, in particular because of the age/metallicity degeneracy in the colours of an integrated stellar population (Worthey 1994), spectral line studies seem to be a more effective tool to disentangle metallicity and age effects, as well as population gradients."543 llowever. spectral line strength indices are relatively wud to measure. anc are also degenerate to age and metallicity. although to a lesser extent iun broad-band colours.," However, spectral line strength indices are relatively hard to measure, and are also degenerate to age and metallicity, although to a lesser extent than broad-band colours."544 Sincelocal colours correlate strongly with each other (cde Jong 1996. Peleticr Balceells 1996. 1997) they can be used. as indicators of the gross properties of galaxies. in the absence of dust. where the various wavelength. ranges can oe used as diagnosties for dillerent overall galaxy properties.," Since colours correlate strongly with each other (de Jong 1996, Peletier Balcells 1996, 1997) they can be used as indicators of the gross properties of galaxies, in the absence of dust, where the various wavelength ranges can be used as diagnostics for different overall galaxy properties."545 In this respect. de Jong's (1996) statistical studs is one of 1e first large surveys of spiral galaxy properties based on =uultiple passband optical ancl near-infrared observations.," In this respect, de Jong's (1996) statistical study is one of the first large surveys of spiral galaxy properties based on multiple passband optical and near-infrared observations."546 Fisher. Franx Ulineworth (1996) published. one. of we very few studies dealing. with abundance gradients »pendicular to the galactic planes in. highly-inclined galaxies other than our own.," Fisher, Franx Illingworth (1996) published one of the very few studies dealing with abundance gradients perpendicular to the galactic planes in highly-inclined galaxies other than our own."547 Basecl on Mg» spectral line observations of 20 S0 galaxies. they conclude that the minor axis behaviour of the 9 galaxies in their ccdge-on subsample is noticeably cillerent from that found along the major axis.," Based on $_2$ spectral line observations of 20 S0 galaxies, they conclude that the minor axis behaviour of the 9 galaxies in their edge-on subsample is noticeably different from that found along the major axis."548 Whereas the major axis Meg». profiles decrease with raclius and Hatten as the bulge light contribution decreases and the disc starts to dominate. the minor axis graclicnts display a uniformly decreasing Mg» strength. with distance from the," Whereas the major axis $_2$ profiles decrease with radius and flatten as the bulge light contribution decreases and the disc starts to dominate, the minor axis gradients display a uniformly decreasing $_2$ strength with distance from the"549characterising the transition of LBVs from quiescence to outburst phases and vice-versa. in a close match to evidence gathered at more conventional (blue) optical wavelengths: (v) offered the opportunity to test quantitatively the soundness of photoronisation modelling of the rich emission line spectrum observable over the RAVE range: (vii) discovered in R 127 the presence. and quantified the physical properties of. a massive detached tontsed shell which was ejected during the 1982-2000 outburst.,"characterising the transition of LBVs from quiescence to outburst phases and vice-versa, in a close match to evidence gathered at more conventional (blue) optical wavelengths; $v$ ) offered the opportunity to test quantitatively the soundness of photoionisation modelling of the rich emission line spectrum observable over the RAVE range; $vii$ ) discovered in R 127 the presence, and quantified the physical properties of, a massive detached ionised shell which was ejected during the 1982-2000 outburst."550deposition ean be seen by all three LCs diverging at ~ 40 clavs.,deposition can be seen by all three LC's diverging at $\sim$ 40 days.551 As the Ni mass is increased the secondary peak increases in both absolute magnitude and width., As the Ni mass is increased the secondary peak increases in both absolute magnitude and width.552 In fact when the Ni mass is 0.14 M. (he secondary peak is brighter than the plateau. and in the V light curve the secondary peak is even brighter (han the initial peak (fig.," In fact when the Ni mass is 0.14 $_\odot$ the secondary peak is brighter than the plateau, and in the V light curve the secondary peak is even brighter than the initial peak (fig."553 106)., 10c).554 At late times the V light curve have similar (ail slopes but scaled to lower Iuminositv (equation 3)., At late times the V light curve have similar tail slopes but scaled to lower luminosity (equation 3).555 For comparison a moclel is shown that contains no Ni mass and abrutlv falls after the plateau., For comparison a model is shown that contains no Ni mass and abrutly falls after the plateau.556 Since having no Ni mass eliminates (he secondary peak it is reasonable (o assume that Ni heating plavs a role in producing the secondary peak Cig The plateau is actually lengthened by increased amount of Ni as seen in all eraphis to the point where it is almost doubled for 0.14 M. Ni., Since having no Ni mass eliminates the secondary peak it is reasonable to assume that Ni heating plays a role in producing the secondary peak (fig The plateau is actually lengthened by increased amount of Ni as seen in all graphs to the point where it is almost doubled for 0.14 $_\odot$ Ni.557 The time of the secondary. peak maximum increases with increasine Ni mass., The time of the secondary peak maximum increases with increasing Ni mass.558 This can be explainecl bv the Ni-Co clecay keeping the malerial hotter for a longer time. (hus slowing the RW.," This can be explained by the Ni-Co decay keeping the material hotter for a longer time, thus slowing the RW."559 Figure 10b shows the photospheric temperature for the 0.14 AL. Ni model stays hot for greater than 115 days. indicating that (he gamma rays participate in the heating of the material below the photosphere.," Figure 10b shows the photospheric temperature for the 0.14 $_\odot$ Ni model stays hot for greater than 115 days, indicating that the gamma rays participate in the heating of the material below the photosphere."560 There is little change in the photopspheric velocity (fie., There is little change in the photopspheric velocity (fig.561 10d) which shows no difference until about 55 davs., 10d) which shows no difference until about 55 days.562 The slieht difference in velocity. after 55 days is due to an increase in the opacity. causing the photosphere to move into faster moving material.," The slight difference in velocity after 55 days is due to an increase in the opacity, causing the photosphere to move into faster moving material."563 The slopes of all the (ails (figs., The slopes of all the tails (figs.564 10a. 10c) are similar since there is no variation in mass. energy. or Ni mixing.," 10a, 10c) are similar since there is no variation in mass, energy, or Ni mixing."565 This can be easily explained since all models have almost identical density. velocity. and temperature profiles fies.," This can be easily explained since all models have almost identical density, velocity, and temperature profiles figs."566 11a. Lib. lle.," 11a, 11b, 11c."567 In figure Hc the heating due to Ni can be seen to slightly affect the temperature profile at day 47 in the region < 6 M..., In figure 11c the heating due to Ni can be seen to slightly affect the temperature profile at day 47 in the region $<$ 6 $_\odot$.568 Figure 1d shows (he most predominate allect of Ni mass., Figure 11d shows the most predominate affect of Ni mass.569 The Iuminosityv. profile directly reflects the amount of enerey supplied by racdioactivitv. similar profiles but. different. absolute Iuninosiües.," The luminosity profile directly reflects the amount of energy supplied by radioactivity, similar profiles but different absolute luminosities."570 In general since the only source of energv at lates times is the decay of Co it is possible to estimate (ae Ni mass based on the absolute magnitude of the tail., In general since the only source of energy at lates times is the decay of Co it is possible to estimate the Ni mass based on the absolute magnitude of the tail.571 However. a LC tail wilh a steeper slope than the decay rate of Co indicates (hal gamma ravs are escaping the ejecta and (hus an under-estimate of ihe Ni mass would be Figure 12a shows that lowering the II envelope mass enables Ni to power the full plateau.," However, a LC tail with a steeper slope than the decay rate of Co indicates that gamma rays are escaping the ejecta and thus an under-estimate of the Ni mass would be Figure 12a shows that lowering the H envelope mass enables Ni to power the full plateau."572 The affects of Ni appear at day. 20 due to the recombination wave moving quickly through the low mass Il envelope and uncover the regions heated by gamma. ravs faster., The affects of Ni appear at day 20 due to the recombination wave moving quickly through the low mass H envelope and uncover the regions heated by gamma rays faster.573 As the Ni mass is increased the Ie core is kept hot enough to allow the RW to move more slowly., As the Ni mass is increased the He core is kept hot enough to allow the RW to move more slowly.574 At later times the tails fall faster. when compared to figure I0a. due to the faster velocity. low density and (hus less (rapping of gammia Figure 12b shows that confining the Ni to < 0.3 M. delays the affects of the Ni energy source and consequently the LC continues to [all 15 days longer than the other models in," At later times the tails fall faster, when compared to figure 10a, due to the faster velocity, low density and thus less trapping of gamma Figure 12b shows that confining the Ni to $<$ 0.3 $_\odot$ delays the affects of the Ni energy source and consequently the LC continues to fall 15 days longer than the other models in"575during outburst.,during outburst.576 For the purpose of determining an upper limit to the optical Inmiinosity of the outburst. we assume (hat the counterpart candidate with 5=24.7050.08 was the counterpart.," For the purpose of determining an upper limit to the optical luminosity of the outburst, we assume that the counterpart candidate with $B=24.70\pm0.08$ was the counterpart."577 With Ny=5x107 7 (see Table 4)). applving the relation of Predehl&Schmitt(1995) and a standard extinction law. we find τν=0.4.," With $_H =5785\times10^{20}$ $^{-2}$ (see Table \ref{spectab1}) ), applying the relation of \citet{predehl1995} and a standard extinction law, we find $A_B = 0.4$."579 Assiuning m-M-—2447. the absolute 2 magnitude was B=—0.1740.08.," Assuming $m$ -M=24.47, the absolute $B$ magnitude was $B=-0.17\pm0.08$."580 Assuming an intrinsic D—V. color of —0.09=0.14 [the mean of the Galactic LMXD catalog of Liuetal.(2001)]]. we find A=—0.08£0.16. or an upper-Hmit of Af2—0.24.," Assuming an intrinsic $B-V$ color of $-0.09\pm0.14$ [the mean of the Galactic LMXB catalog of \citet{liu2001}] ], we find $M_V=-0.08\pm0.16$, or an upper-limit of $M_V\geq-0.24$."581 Our measurements allow us to provide a rough prediction of the orbital period of r1-36 using (he empirical relation between X-ray. Iuminosity. optical Iuminosityv. and orbital period for Galactie LAINBs determined by vanParadijs&MeClintoek.(1994).," Our measurements allow us to provide a rough prediction of the orbital period of r1-36 using the empirical relation between X-ray luminosity, optical luminosity, and orbital period for Galactic LMXBs determined by \citet{vanparadijs1994}."582.. This relation has been tested for more recent iransient events and lor observations separated by up (o 3 weeks bv Williamsοἱal.(2005a.d).. showing that it provides reliable orbital period predictions even for events with complex mulliwaveleneth lishteurves.," This relation has been tested for more recent transient events and for observations separated by up to 3 weeks by \citet{williams2005bh1,williams2005bh4}, showing that it provides reliable orbital period predictions even for events with complex multiwavelength lightcurves."583 In addition. since r1-36 shows a decay curve reminiscent of the second-half of the 1998-1999 outburst of NTE J1550-564. we tested the relation lor this ease.," In addition, since r1-36 shows a decay curve reminiscent of the second-half of the 1998-1999 outburst of XTE J1550-564, we tested the relation for this case."584 The second half of that outburst had an X-ray luminosity of ~2x105 erg ! (for a distance of 5.342.3 kpe: Oroszetal. 2002)). and the optical counterpart showed Wo~16.3.," The second half of that outburst had an X-ray luminosity of $\sim2\times 10^{38}$ erg $^{-1}$ (for a distance of $\pm$ 2.3 kpc; \citealp{orosz2002j1550}) ), and the optical counterpart showed $V\sim16.3$."585" Applving the extinction of ly=4.75 (Oroszetal.2002) gives My=—2.d""d", Applying the extinction of $A_V=4.75$ \citep{orosz2002j1550} gives $_V = -2.1^{+1.2}_{-0.8}$.586 These numbers would vield a period prediction of 2 1 dax., These numbers would yield a period prediction of $\gap$ 1 day.587 This limit is correct. as (the (rue period is 1.55 days.," This limit is correct, as the true period is 1.55 days."588 In the case of r1-36. if we insert the optical Iuminositv of Ady=—0.08zc0.16 and the unabsorbed 0.3.7 keV X-ray luminosity of 5x LO ere ! into the van relation. we obtain a prediction for the orbital period of 1.77) davs.," In the case of r1-36, if we insert the optical luminosity of $M_V=-0.08\pm0.16$ and the unabsorbed 0.3–7 keV X-ray luminosity of $\times$ $^{37}$ erg $^{-1}$ into the \citet{vanparadijs1994}589 relation, we obtain a prediction for the orbital period of $^{+3.5}_{-1.0}$ days."590 Therefore. assuming r1-36 is an LMXD similar to those in our own Galaxy and that the true counterpart was no brighter (han the only star detected within the 3e error ellipse during the outburst. the predicted upper-Iimit for the period of the svstem is Z 5.2 days.," Therefore, assuming r1-36 is an LMXB similar to those in our own Galaxy and that the true counterpart was no brighter than the only star detected within the $\sigma$ error ellipse during the outburst, the predicted upper-limit for the period of the system is $\lap$ 5.2 days."591 Ideally we would like to fully elassify the transient N-ravy source r1-36., Ideally we would like to fully classify the transient X-ray source r1-36.592 While its observed properties show that it is an LMXD in MBI. the current. observations do not allow a final conclusion to be drawn as to whether the primary member of (he binary is a neutron star or black hole.," While its observed properties show that it is an LMXB in M31, the current observations do not allow a final conclusion to be drawn as to whether the primary member of the binary is a neutron star or black hole."593 Nevertheless. the similarities between r1-36 and X-ray binaries known (o contain black holes make it a good black hole candidate.," Nevertheless, the similarities between r1-36 and X-ray binaries known to contain black holes make it a good black hole candidate."594(Goldreich&Lynden-Dell1965).,\citep{GoldreichLyndenBell65}.595. The source terms in (his approximation can be dropped to study other problems., The source terms in this approximation can be dropped to study other problems.596 We choose a local reference frame located at a fiducial radius. corotating at the orbital angular velocity Q.," We choose a local reference frame located at a fiducial radius, corotating at the orbital angular velocity $\Omega$."597 The clvnamical equations are written using the Carlesian coordinate. wilh ag.z denoting unit vectors pointing to the radial. azimuthal and vertical direction.," The dynamical equations are written using the Cartesian coordinate, with $\hat{\mb{x}},\hat{\mb{y}},\hat{\mb{z}}$ denoting unit vectors pointing to the radial, azimuthal and vertical direction."598" In (his non-inertial lraune. the coupled equations of particles and gas read In the above equations. py. 2, denote the mass density anc pressure of the gas. dlnO/dlnris the backerounc shear parameter. wilh q=3/2 lor Ixeplerian flow. ancl a. v denote velocities of the gas and particles in this reference Tame."," In this non-inertial frame, the coupled equations of particles and gas read In the above equations, $\rho_g$, $P_g$ denote the mass density and pressure of the gas, $q\equiv d\ln\Omega/d\ln r$ is the background shear parameter, with $q=3/2$ for Keplerian flow, and $\mb{u}$, $\mb{v}$ denote velocities of the gas and particles in this reference frame."599 The subseript πο in equation (1)) represents the 7th particle.," The subscript $i$ "" in equation \ref{eq:dustmotion}) ) represents the $i$ th particle."600 The particle stopping (ime due to gas drag. lop: depends on particle size aud gas [low properties (Weidenschiliing1977).," The particle stopping time due to gas drag, $t_{\rm stop}$, depends on particle size and gas flow properties \citep{Weidenschilling77}."601. Our code is capable of dealing with an arbitrary number of different particle species (each particle species has a different stopping time). but unless otherwise stated. we assume single particle species with constant stopping time throughout this paper for simplicitv.," Our code is capable of dealing with an arbitrary number of different particle species (each particle species has a different stopping time), but unless otherwise stated, we assume single particle species with constant stopping time throughout this paper for simplicity."602" ln equation (3)). v stands for averaged particle velocity in (he ""Iud element” (weiehted by mass). and e denotes the local nass density ratio between particle and gas €=pyj/p,."," In equation \ref{eq:gasmotion}) ), $\overline{\mb{v}}$ stands for averaged particle velocity in the “fluid element"" (weighted by mass), and $\epsilon$ denotes the local mass density ratio between particle and gas $\epsilon=\rho_p/\rho_g$."603 This term represents momentum feedback from the particles to (he gas. written in the form of treating particles as a fluid.," This term represents momentum feedback from the particles to the gas, written in the form of treating particles as a fluid."604 The particle treatinent of feedback term is described in relssec:scheme.. and conservation of total momentum is guaranteed.," The particle treatment of feedback term is described in \\ref{ssec:scheme}, and conservation of total momentum is guaranteed."605 In tliis paper. we consider non-stratified disks bv neglecting vertical gravity terms in the equations above (i.e.. the 07: terms).," In this paper, we consider non-stratified disks by neglecting vertical gravity terms in the equations above (i.e., the $\Omega^2z$ terms)."606 We also neglect terms associated with the magnetic field in this paper., We also neglect terms associated with the magnetic field in this paper.607 Thev are handled bv the underlying MIID integrators in Athena (Stoneetal.2008).., They are handled by the underlying MHD integrators in Athena \citep{AthenaTech}.608 An isothermal equation. of. state for. the gas is. used throughout this. paper. withB P—>pc2.," An isothermal equation of state for the gas is used throughout this paper, with $P=\rho_gc_s^2$."609 Our goal is to perform the local shearing box simulations (Llawlevetal.1995).. where the radial boundary. condition is periodic with additional shear to account [or differential rotation.," Our goal is to perform the local shearing box simulations \citep{HGB95}, where the radial boundary condition is periodic with additional shear to account for differential rotation."610 Therefore. it is not appropriate to include radial pressure gradient directly. which is inconsistent with the periodie boundary conditions.," Therefore, it is not appropriate to include radial pressure gradient directly, which is inconsistent with the periodic boundary conditions."611 Alternativelv. one can replace the pressure gradient by à constant radial force acting on the gas E—2eyGa. poimüngoulware.," Alternatively, one can replace the pressure gradient by a constant radial force acting on the gas ${\mb F}=2\eta v_K\Omega\hat{\mb x}$, pointing."612 The quantity egy measures the amount by which the gas (azimuthal) velocity is reduced from (he Keplerian value due to (he radial pressure gradient., The quantity $\eta v_K$ measures the amount by which the gas (azimuthal) velocity is reduced from the Keplerian value due to the radial pressure gradient.613 In our code. instead. we find it more," In our code, instead, we find it more"614which gave the shock properties such as the shock stanclolf distance A. the Mach number AS. and (he radius of curvature at the nose of the obstacle Ao.,"which gave the shock properties such as the shock standoff distance $\Delta$, the Mach number $M$, and the radius of curvature at the nose of the obstacle $R_{O}$."615 Figure 3((a) shows data and the initial fit. Figure 3((b) shows the shifted data and the shock fit using Equation (5)).," Figure \ref{f3}( (a) shows data and the initial fit, Figure \ref{f3}( (b) shows the shifted data and the shock fit using Equation \ref{Eq6}) )."616" The fast maegnetosonic Mach number was calculated using Mj,=(6,4,—Ose)μι. where v4, is the CME velocity. c4, is the solar wind velocity and 0,,, is the fast magnetosonic speed."," The fast magnetosonic Mach number was calculated using $M_{ms} = ({v_{cme}-v_{sw}})/{v_{ms}}$, where $v_{cme}$ is the CME velocity, $v_{sw}$ is the solar wind velocity and $v_{ms}$ is the fast magnetosonic speed."617" Since Cae and 04,; were not known at the position of the CALE. a model corona was used to evaluate them."," Since $v_{sw}$ and $v_{ms}$ were not known at the position of the CME, a model corona was used to evaluate them."618 This was based on the Parker solar wind solution with a simple dipolar magnetic field of the form Bir)=By(R./r)*. where was GG at the solar surface (Mannetal.2003)..," This was based on the Parker solar wind solution with a simple dipolar magnetic field of the form $B(r)=B_{0}(R_{\odot}/r)^{3}$, where was G at the solar surface \citep{Mann:2003p9016}."619" For each of the paired CME and shock observations the standoll distances A (=D,—Do) were obtained by three dillerent means: (1) using the 3D coordinates of the furthest point (max(/). where fh=y?+i? 27) on the shock and the CME as fy, and hi, respectively. Gi) the previous method can be applied but to the data in the common coordinate svstem which gave De and Dy. ancl (11) the Iront fitting procedure also produced stancoll distauces."," For each of the paired CME and shock observations the standoff distances $\Delta$ $D_{S}-D_{O}$ ) were obtained by three different means: (i) using the 3D coordinates of the furthest point $\textrm{max}(h)$, where $h=\sqrt{x^2+y^2+z^2}$ ) on the shock and the CME as $h_{shk}$ and $h_{cme}$ respectively, (ii) the previous method can be applied but to the data in the common coordinate system which gave $D_{O}$ and $D_{S}$, and (iii) the front fitting procedure also produced standoff distances."620 llowever the results of method (1) cannot be used with the relations from Section 1. as they are not ina CME/obstacle centred coordinate svstem. but (the results [rom method (ii) and ii) can be compared to Equations (2)). (2)) and (4)).," However the results of method (i) cannot be used with the relations from Section \ref{s_intro} as they are not in a CME/obstacle centred coordinate system, but the results from method (ii) and (iii) can be compared to Equations \ref{Eq2}) ), \ref{Eq4}) ) and \ref{Eq5}) )."621 A summary of the shock properties derived [rom the observations is shown in Figure 4((aj-() as a function of me., A summary of the shock properties derived from the observations is shown in Figure \ref{f4}( (a)-(f) as a function of time.622" With the exception of the CME (/,,,) and shock heights (Pha). All Che properties have been derived [rom the data collapsed on to a common coordinate svslem wilh respect to the CME."," With the exception of the CME $h_{cme}$ ) and shock heights $h_{shk}$ ), all the properties have been derived from the data collapsed on to a common coordinate system with respect to the CME."623 The gap between the first three data points and others is a result of both the CME and shock leaving the COR?2 [ield-of-view and entering the III field-ol-view., The gap between the first three data points and others is a result of both the CME and shock leaving the COR2 field-of-view and entering the HI1 field-of-view.624 The contrast between shock and background in the first three and last three observation is extremely low. making identification of the shock difficult.," The contrast between shock and background in the first three and last three observation is extremely low, making identification of the shock difficult."625 As a result. these points are not reliable. aud shoulel be neglected.," As a result, these points are not reliable, and should be neglected."626 Figure 4((a) shows (he derived heights of the CMEancl shock as they were tracked from SRR. to RIL. AAU)., Figure \ref{f4}( (a) shows the derived heights of the CMEand shock as they were tracked from $_{\odot}$ to $_{\odot}$ AU).627 Using a linear fil 10 hag—hus (=A) versus hi. (not shown). the extrapolated stancolf distance at Earth was Iound to be ~4O RI...," Using a linear fit to $h_{shk}-h_{cme}$ $\Delta$ ) versus $h_{cme}$ (not shown), the extrapolated standoff distance at Earth was found to be $\sim$ $_{\odot}$."628 Figure 4((b) shows the distance to nose of the CME (De) and shock (Ds) front by (filled svanbols). also shown are the values derived [rom fits to the shock aud CME front (hollow symbols).," Figure \ref{f4}( (b) shows the distance to nose of the CME $D_{O}$ ) and shock $D_{S}$ ) front by (filled symbols), also shown are the values derived from fits to the shock and CME front (hollow symbols)."629 The increasing offset between the (wo is due to their differing centres of the coordinate svstems. as one is elliptic and the other is parabolic.," The increasing offset between the two is due to their differing centres of the coordinate systems, as one is elliptic and the other is parabolic."630 Figure 4((¢) shows the stanclolf distance A derived using Do and Dy (fillel symbols) and from the fits to the fronts (hollow svimbols)., Figure \ref{f4}( (c) shows the standoff distance $\Delta$ derived using $D_{O}$ and $D_{S}$ (filled symbols) and from the fits to the fronts (hollow symbols).631 Both are in general agreement and show an increase with time., Both are in general agreement and show an increase with time.632 The standolf distance normalised using De is shown in Figure ία}., The standoff distance normalised using $D_{O}$ is shown in Figure \ref{f4}( (d).633 The normalised stancloll distance is roughly constant with à mean value of 0.37 £0.09., The normalised standoff distance is roughly constant with a mean value of $0.37\pm0.09$ .634 The stancloll distance, The standoff distance635 ~300 2=1 ;~2 ;~0. o CA) , $\sim 300$ $z > 1$ $z \sim 2$ $z \sim 0$ $\sigma$ $A$ 636Weak lensing provides a unique method to directly measure the mass lluctuations on large scales in the universe (see Alellier 1999: Ixaiser 1999: Dartelmann Schneider 1999 [or recent reviews).,Weak lensing provides a unique method to directly measure the mass fluctuations on large scales in the universe (see Mellier 1999; Kaiser 1999; Bartelmann Schneider 1999 for recent reviews).637" ""This method relies on the measurement of small. coherent. distortions produced. by lensing upon the shapes of background galaxies."," This method relies on the measurement of small, coherent distortions produced by lensing upon the shapes of background galaxies."638 This elect is now routinely used to map the mass of clusters of galaxies (see reviews by Fort Alellier 1994. Schneider 1996).," This effect is now routinely used to map the mass of clusters of galaxies (see reviews by Fort Mellier 1994, Schneider 1996)."639 ltecently. the technique was extended to the field by several groups who reported the statistical detection of weak lensing by large-scale structure (Wittman et al.," Recently, the technique was extended to the field by several groups who reported the statistical detection of weak lensing by large-scale structure (Wittman et al."640 2000: van Waerbeke ot al., 2000; van Waerbeke et al.641 2000: )acon. Itefregier Elis 2000 (BRE): Ixaiser. Wilson Luppino 2000).," 2000; Bacon, Refregier Ellis 2000 (BRE); Kaiser, Wilson Luppino 2000)."642" More precise measurements of this ""cosmic shear” from upcoming observations will provide invaluable cosmological information (eg.", More precise measurements of this “cosmic shear” from upcoming observations will provide invaluable cosmological information (eg.643 Ixaiser 1992: Jain Seljak 1997: Ixamionkowski et al., Kaiser 1992; Jain Seljak 1997; Kamionkowski et al.644 LOOT: Ixaiser 1998: Hu Tegmark 1998: van Waerbeke et al., 1997; Kaiser 1998; Hu Tegmark 1998; van Waerbeke et al.645 1998)., 1998).646 Because the distortions induced by lensing are only of the order of114.. these measurements are very challenging.," Because the distortions induced by lensing are only of the order of, these measurements are very challenging."647 In particular. they require tight control of systematic effects and a precise method for the measurement of the shear.," In particular, they require tight control of systematic effects and a precise method for the measurement of the shear."648 One of the potential weaknesses of the cosmic shear programme, One of the potential weaknesses of the cosmic shear programme649svslenmatic errors actually dominate in all emission models. which is tvpical for modeling of astrophysical observations of relatively complex phenomena.,"systematic errors actually dominate in all emission models, which is typical for modeling of astrophysical observations of relatively complex phenomena."650 The X-ray and TeV 5-rav data contribute the most to the overall 47., The X-ray and TeV $\gamma$ -ray data contribute the most to the overall $\chi^2$.651 Especially for the TeV 5-ray. data. the 4? value is 149 for 27 data points. corresponding to an average residuals about. 2.30.," Especially for the TeV $\gamma$ -ray data, the $\chi^2$ value is $149$ for $27$ data points, corresponding to an average residuals about $2.3\sigma$."652 That is to sav this simple leptonic model actually can not fit the £55 data well., That is to say this simple leptonic model actually can not fit the $HESS$ data well.653 This is a well-known result in previous studies (e.g..Aharonianetal.2006;Tanaka2008:Morlino20092:Fangetal. 2009)..," This is a well-known result in previous studies \citep[e.g.,][]654{2006A&A...449..223A,2008ApJ...685..988T,2009MNRAS.392..240M,6552009MNRAS.392..925F}."656" In Linetal.(2008) the authors proposed a stochastic acceleration model io generate (he electron spectrum. with sub-exponential eutoll (0,—0.5) to better fit the ILESS data.", In \cite{2008ApJ...683L.163L} the authors proposed a stochastic acceleration model to generate the electron spectrum with sub-exponential cutoff $\delta_e=0.5$ ) to better fit the $HESS$ data.657 ILowever. in such a case the fit to N-rav data becomes worse.," However, in such a case the fit to X-ray data becomes worse."658" The X-ray data actually favors super-exponential cutoff instead (with 9,=1.2 in this purely leptonic Lit).", The X-ray data actually favors super-exponential cutoff instead (with $\delta_e=1.2$ in this purely leptonic fit).659 The fit max be improved in some detailed leptonic models. as shown in Fanetal.(2010b).. though svstematic errors still dominate.," The fit may be improved in some detailed leptonic models, as shown in \cite{2010A&A...517L...4F}, though systematic errors still dominate."660 In (his subsection we discuss the model with a predominantly hadronie origin of the 5-, In this subsection we discuss the model with a predominantly hadronic origin of the $\gamma$ -rays.661" The spectrum of the accelerated protons is assunied to be F,U7)xE""rexp|l-(E/E?y] wilh 9,=1. which gives acceptable fit to the TeV data."," The spectrum of the accelerated protons is assumed to be $F_p(E)\propto E^{-\alpha_p}\exp[-(E/E_c^p)^{\delta_p}]$ with $\delta_p=1$, which gives acceptable fit to the TeV data."662 The normalization is fixed using the total. kinetic energv of protons with the enerey E>1 GeV. For the hadronic οτανproduction we adopt the parameterization of Kamaeetal. (2006)..., The normalization is fixed using the total kinetic energy of protons with the energy $E>1$ GeV. For the hadronic $\gamma$ -rayproduction we adopt the parameterization of \cite{2006ApJ...647..692K}. .663 With the additional, With the additional664lio various masses.,to various masses.665 Figure 3 gives the number of black holes as a [function of time for various choices of the initial black hole mass. μμ. wilh other parameters held constant.," Figure 3 gives the number of black holes as a function of time for various choices of the initial black hole mass, $M_{BH,0}$, with other parameters held constant."666 We can now use the same framework to estimate the huminositv of the ensemble of accreting stellar-mass black holes at the epoch. (.. We will adopt the parameterization of Park&RicotGi(2011) with the assumption that there is sufficient angular momentum {ο form a disk near the black hole. so that clisk-like efficiencies lor turning mass accretion rates into radiated energy are applicable.," We can now use the same framework to estimate the luminosity of the ensemble of accreting stellar-mass black holes at the epoch, t. We will adopt the parameterization of \citet{PR11} with the assumption that there is sufficient angular momentum to form a disk near the black hole, so that disk-like efficiencies for turning mass accretion rates into radiated energy are applicable."667 For critiques of Chis assumption. see Iuulfert&Arnett(1994):Beskin&Ixarpov (2005).," For critiques of this assumption, see \citet{RA94,BK05}."668. We write for the luminosity of a single accreting black hole: with 5~Q.1., We write for the luminosity of a single accreting black hole: with $\eta \sim 0.1$.669 If a disk does not form. or forms only sporaclically. the radiation efficiency would be correspondinglv less than the fiducial value we assume here.," If a disk does not form, or forms only sporadically, the radiation efficiency would be correspondingly less than the fiducial value we assume here."670" The luminosity per unit galaxv mass radiated by all black holes with mass between May aud Mp+dMg; al epoch. t. is given by: Using Equation 29.. (his can be written as: The total luminosity from all the accreting black holes born since /, can then be obtained bv integratingexe over all the current masses al epoch. t. to obtain: Once again. we can approximate the complex variation of the rate of production of black holes with a constant to obtain: Neglecting {η and /4,,4. taking /<<F4. and using VayoRyyl gives a simple estimate of the luminosity of Li;7Neu(yeMoή."," The luminosity per unit galaxy mass radiated by all black holes with mass between $M_{BH}$ and $M_{BH} + dM_{BH}$ at epoch, t, is given by: Using Equation \ref{diffnumber}, this can be written as: The total luminosity from all the accreting black holes born since $t_o$ can then be obtained by integrating over all the current masses at epoch, t, to obtain: Once again, we can approximate the complex variation of the rate of production of black holes with a constant to obtain: Neglecting $t_0$ and $t_{delay}$, taking $t << t_\infty$, and using $N_{BH} \sim R_{BH}t$ gives a simple estimate of the luminosity of $L_{tot} \sim N_{BH}(t) \eta c^2 M_{BH,0}/t_\infty$."671 Neglecting {η and {ων we have for the total luminosity of a galaxy of constant star formation rate:, Neglecting $t_0$ and $t_{delay}$ we have for the total luminosity of a galaxy of constant star formation rate:672calculate the mass within in5ükpe to he 5.4752«10AJ.. and the total mass to be 1.9.T25107A7..,"calculate the mass within $50\,$ kpc to be $5.4^{+0.2}_{-3.6} \times 10^{11} M_{\odot}$, and the total mass to be $1.9^{+3.6}_{-1.7} \times 10^{12} M_{\odot}$."673 Phe quoted uncertainties are larger than in earlier studies (c.g. Little Tremaine. LOST. Zaritsky et al.," The quoted uncertainties are larger than in earlier studies (e.g. Little Tremaine, 1987, Zaritsky et al."674 1989. Ixochanek.. 1996) and were determined by Monte Carlo simulation of artificial data sets.," 1989, Kochanek, 1996) and were determined by Monte Carlo simulation of artificial data sets."675 Phe two principal sources of error are i) the large uncertainties in the proper motions for the six satellites for which measures exist. and ii) the small size of the dataset tthere are currently only 27 known satellites at CGalactocentrie distances 20 kpe.," The two principal sources of error are i) the large uncertainties in the proper motions for the six satellites for which measures exist, and ii) the small size of the dataset there are currently only 27 known satellites at Galactocentric distances $> 20\,$ kpc."676 Therefore. we are in the »eculiar situation where the mass profile of the Galaxy. is ess well determined than for some nearby. spiral galaxies.," Therefore, we are in the peculiar situation where the mass profile of the Galaxy is less well determined than for some nearby spiral galaxies."677 There is no possibility of substantially increasing the number of known satellite galaxies and globular clusters ancl the »st prospect for improving the measurement of the mass is through isolating large numbers of another distant. haloracer., There is no possibility of substantially increasing the number of known satellite galaxies and globular clusters and the best prospect for improving the measurement of the mass is through isolating large numbers of another distant halo--tracer.678 Fielel blue horizontal branch. (BLIB) stars. should »ovide just such a tracer and WISZ99 ealeulate that to reduce he uncertainty on the total mass to 20% requires a sample of 200 distant. BILD stars., Field blue horizontal branch (BHB) stars should provide just such a tracer and WE99 calculate that to reduce the uncertainty on the total mass to $20\%$ requires a sample of 200 distant BHB stars.679 This is the first in a series of three papers presenting a new calculation of the mass of the Galaxy using racial velocities of DIID. stars., This is the first in a series of three papers presenting a new calculation of the mass of the Galaxy using radial velocities of BHB stars.680 Field BIB stars are. luminous standard candles that are abundant in the Galactic halo (c.g. Yanny et al., Field BHB stars are luminous standard candles that are abundant in the Galactic halo (e.g. Yanny et al.681 2000). and for nearly twenty vears. since the studs of Pier (1983). have presented an uncerexploited resource with which to measure the density profile and phase space structure of the Galaxy halo out to large distances. 100 kpe.," 2000), and for nearly twenty years, since the study of Pier (1983), have presented an under–exploited resource with which to measure the density profile and phase space structure of the Galaxy halo out to large distances, $\sim 100\,$ kpc."682 A number of dynamical analyses of rather small samples of DIID. stars have been published (e.g. SommerLarsen. Christensen Carter. 1950. Norris Llawkins. 1991. Arnold Gilmore. 1992).," A number of dynamical analyses of rather small samples of BHB stars have been published (e.g. Sommer--Larsen, Christensen Carter, 1989, Norris Hawkins, 1991, Arnold Gilmore, 1992)."683 Unfortunately. samples of field Aotype stars in the halo include not only DIID stars but also stars of main sequence surface gravity. field blue stragelers. tha are some 2 magnitudes less luminous.," Unfortunately, samples of field A–type stars in the halo include not only BHB stars but also stars of main sequence surface gravity, field blue stragglers, that are some 2 magnitudes less luminous."684 Progress towards the goal of acquiring a large sample of distant. DII. stars has been slow because of the dilliculty of separating ou the BIB stars without the investment of large amounts of telescope time., Progress towards the goal of acquiring a large sample of distant BHB stars has been slow because of the difficulty of separating out the BHB stars without the investment of large amounts of telescope time.685 In this first paper we describe our procedures [or classifving samples of halo Atype stars. and. presen a new efficient. method. that requires. only. spectroscopic observations of intermediate signaltonoise ratio.," In this first paper we describe our procedures for classifying samples of halo A–type stars, and present a new efficient method that requires only spectroscopic observations of intermediate signal–to–noise ratio."686 In Paper Η we will present. photometry ancl spectroscopy of. fain 16«D20 candidate BIB stars in two northern high Galactic latitude fields and four southern fields., In Paper II we will present photometry and spectroscopy of faint $16<B<20$ candidate BHB stars in two northern high Galactic latitude fields and four southern fields.687 Paper UL will contain the dvnamical analysis of the new sample of confirmed. DII stars and à new estimate of the mass of the Galaxy., Paper III will contain the dynamical analysis of the new sample of confirmed BHB stars and a new estimate of the mass of the Galaxy.688 The structure of this paper is as follows., The structure of this paper is as follows.689 In. 822 we provide a brief outline of the basic parameters of our new survey for distant field DIID2 stars in the halo., In 2 we provide a brief outline of the basic parameters of our new survey for distant field BHB stars in the halo.690 833 contains a summary of previous methods emploved to sieve out. BILB stars [rom samples of halo Atype stars., 3 contains a summary of previous methods employed to sieve out BHB stars from samples of halo A–type stars.691 In E44 we present the details of the two classification methods we employ. called theColour method. and the method.," In 4 we present the details of the two classification methods we employ, called the method, and the method."692 We describe the procedures used to measure the Balmer line profiles ancl the equivalent width of the Ca LL Ix line. ancl quantify the random and svstematic errors.," We describe the procedures used to measure the Balmer line profiles and the equivalent width of the Ca II K line, and quantify the random and systematic errors."693 In $55 we use the high signaltonoise ratio (S/N) spectra of Winman. Suntzell Ixraft. (1994: hereafter. WSIS) and their spectrophotomoetric classifications to quantify the S/N requirements for applving these methods to samples of faint halo stars.," In 5 we use the high signal–to–noise ratio (S/N) spectra of Kinman, Suntzeff Kraft (1994; hereafter KSK) and their spectrophotometric classifications to quantify the S/N requirements for applying these methods to samples of faint halo stars."694 In 866 we discuss the use of the Ca LL Ix line as a metallicity indicator., In 6 we discuss the use of the Ca II K line as a metallicity indicator.695 Finally. 877 provides à summary of the main conclusions of the paper.," Finally, 7 provides a summary of the main conclusions of the paper."696 Ina CDV. twocolour plot (or its equivalent such às ur or CB4) of a high Galactic latitude field. halo Atvpe stars are identifiable as à faint continuation of the spectral sequence to hotter types. beyond the main sequence turnoll at spectral type FE. with colours 0.0<(2Vo«0.2 (see c.g. Yanny et al.," In a $UBV$ two–colour plot (or its equivalent such as $ugr$ or $UB_JR$ ) of a high Galactic latitude field, halo A–type stars are identifiable as a faint continuation of the spectral sequence to hotter types, beyond the main sequence turnoff at spectral type F, with colours $0.0<(B-V)_0 <0.2$ (see e.g. Yanny et al."697 2000: Fig., 2000; Fig.698 B)., 1).699 As illustrated in striking fashion by Yanny et al., As illustrated in striking fashion by Yanny et al.700 using Sloan Digital Sky Survey (SDSS) data. these Atype stars include not only luminous ficld BILD stars. of absolute magnitude Ady~0.7. but also stars of mainsequence surface gravity that are some two magnitudes less luminous.," using Sloan Digital Sky Survey (SDSS) data, these A–type stars include not only luminous field BHB stars, of absolute magnitude $M_V\sim 0.7$, but also stars of main–sequence surface gravity that are some two magnitudes less luminous."701 The nature of these stars is not entirely. clear but recent work supports the notion that the majority are. blue stragelers in binary systems. created. by mass transfer when the companion star overfills its Roche lobe (Preston Sneden 2000)., The nature of these stars is not entirely clear but recent work supports the notion that the majority are blue stragglers in binary systems created by mass transfer when the companion star overfills its Roche lobe (Preston Sneden 2000).702 As noted by Preston. Beers Shectman (1994) this means that in the field blue stragelers are much more common than BIB stars. whereas in globular clusters they are usually rarer.," As noted by Preston, Beers Shectman (1994) this means that in the field blue stragglers are much more common than BHB stars, whereas in globular clusters they are usually rarer."703 Vhis difference could be explained by the destruction of wide binaries in. globular clusters., This difference could be explained by the destruction of wide binaries in globular clusters.704 This picture is supported by Carrera ct al. (, This picture is supported by Carrera et al. (7052002) who find an intermediate value of the ratio of the numbers of mainsequencegravity A stars and BIIB stars for the Ursa Minor cdwarl galaxy. which has a stellar density intermediate between that of the field and that of a globular cluster.,"2002) who find an intermediate value of the ratio of the numbers of main–sequence–gravity A stars and BHB stars for the Ursa Minor dwarf galaxy, which has a stellar density intermediate between that of the field and that of a globular cluster."706 For these reasons in the remainder of this paper we refer to these distant halo Atvpe stars with mainsequence surface eravitics as field blue stragelers., For these reasons in the remainder of this paper we refer to these distant halo A–type stars with main–sequence surface gravities as field blue stragglers.707 The combination of their. substantial luminosity. ensuring they can be detected to larec distances. and heir very small spread: in. absolute magnitude. making hem ellective standard candles. means BILB stars are ideal dynamical tracers.," The combination of their substantial luminosity, ensuring they can be detected to large distances, and their very small spread in absolute magnitude, making them effective standard candles, means BHB stars are ideal dynamical tracers."708 For the same apparent magnitude the ield. blue stragelers are a [actor 2.5 less distant and it is herefore crucial to separate the (wo populations., For the same apparent magnitude the field blue stragglers are a factor 2.5 less distant and it is therefore crucial to separate the two populations.709 Our survey employs APAL scans of Ulx Schmidt Telescope photographic dates., Our survey employs APM scans of UK Schmidt Telescope photographic plates.710 We use pairs of plates in cach of the C. D;. and 2 mands. in six fields.," We use pairs of plates in each of the $U$, $B_J$, and $R$ bands, in six fields."711 The coordinates of the six survey fields are provided in Table 1., The coordinates of the six survey fields are provided in Table 1.712 The fields were selected to give good coverage in opposing directions above and. below the Galactic plane. with a range of Galactic longitudes. subject to the availability of suitable plate material in the Ulx Schmidt Telescope archive wwhich cllectively restricts the search to negative declinations.," The fields were selected to give good coverage in opposing directions above and below the Galactic plane, with a range of Galactic longitudes, subject to the availability of suitable plate material in the UK Schmidt Telescope archive which effectively restricts the search to negative declinations."713 Phere was a preference for high Galactic latitudes to minimize extinction., There was a preference for high Galactic latitudes to minimize extinction.714 Phe cdilferent, The different715The more powerful component. responsible for of the infrared luminosity (L4.4000505). 18 a model of a dusty starburst of age MMwvr. with optical opacities of the GMCs in (he range τι—3200.,"The more powerful component, responsible for of the infrared luminosity $L_{1-1000\,\mu m}$ ), is a model of a dusty starburst of age Myr, with optical opacities of the GMCs in the range $\tau_{\rm v} =3-200$."716 The properties of this component are determined primarily by (he constraints imposed by the FUR and optical emission., The properties of this component are determined primarily by the constraints imposed by the FIR and optical emission.717 The starburst component alone is. however. unable to fit the mid-IR data.," The starburst component alone is, however, unable to fit the mid-IR data."718 Therefore. an extra contribution in (he form of emission from hot dust (I ~160—1600 ΝΑ) heated by a putative AGN is required.," Therefore, an extra contribution in the form of emission from hot dust (T $\sim 160 - 1600$ K) heated by a putative AGN is required."719 This component represents of the total infrared luminosity., This component represents of the total infrared luminosity.720 Acceptable fits could also be obtained using other AGN models. for example by allowing for emission from a dusty torus surrounding the central (black hole) source (Elstathiou. 1995).," Acceptable fits could also be obtained using other AGN models, for example by allowing for emission from a dusty torus surrounding the central (black hole) source \citep{Efs95}."721. Both classes of models lead to similar descriptions of the object in the CÀtext of this paper., Both classes of models lead to similar descriptions of the object in the context of this paper.722 The best fitted model SED in Figure 2. predicts an infrared Iuninosity of Ly LL... which classifies PDFJO11423 as an ultra-Iuminous infrared galaxy (ULIBG).," The best fitted model SED in Figure \ref{fig:sed} predicts an infrared luminosity of $_{1-1000\,\mu\rm{m}} = 7.1 \times 10^{12}~h_{65}^{-2}$ $_{\sun}$, which classifies PDFJ011423 as an ultra-luminous infrared galaxy (ULIRG)."723 The possibility that the high Iuminositv is due to gravitational lensing is unlikely. given the relatively low redshift of the object.," The possibility that the high luminosity is due to gravitational lensing is unlikely, given the relatively low redshift of the object."724 The existence of only one data point in the FIR/sub-mm part of the SED makes an estimate of the dust mass lor PDFJO11423 highly uncertain., The existence of only one data point in the FIR/sub-mm part of the SED makes an estimate of the dust mass for PDFJ011423 highly uncertain.725" However. the fitted SED in (his wavelength range is compatible with an optically thin thermal dust emission spectrum (emissivitv index of 1.5) with a temperature of Tyo=3323 NIN. which corresponds to a dust mass of Ming8—30x10*5,2 MM. (Hildebrand1983)."," However, the fitted SED in this wavelength range is compatible with an optically thin thermal dust emission spectrum (emissivity index of 1.5) with a temperature of $_{\rm dust}= 33 \pm 3$ K, which corresponds to a dust mass of $_{dust} 726\sim 8-30 \times\ 10^{8}~h_{65}^{-2}$ $_{\sun}$ \citep{Hil83}."727. Consistent with the extreme reddening of the galaxy. this value is an order of magnitude higher than the dust mass of 10*—10hz MAL. found for local ULIBGs (Sanders&Mirabel1996). and comparable to the hieher values found in the sample of PG quasars of Haasοἱa£.(2000).. for example.," Consistent with the extreme reddening of the galaxy, this value is an order of magnitude higher than the dust mass of $10^7-10^8~h_{65}^{-2}$ $_{\sun}$ found for local ULIRGs \citep{San96} and comparable to the higher values found in the sample of PG quasars of \citet{Haa00}, for example."728 The (wo models used to fit the observed SED do not predict the radio continuum luminosity or spectral index., The two models used to fit the observed SED do not predict the radio continuum luminosity or spectral index.729 To interpret (he radio data. we appeal to the remarkably light empirical correlation between the FIR and radio continuum. huminositv. observed in star-forming galaxies (Ilelou.Soifer&Rowan-Robinson1985:Condon1972).," To interpret the radio data, we appeal to the remarkably tight empirical correlation between the FIR and radio continuum luminosity observed in star-forming galaxies \citep{Hel85,Con92}."730. The favorecl explanation of the correlation holds Chat the same massive stars warm (he FUR-emittine cust ancl energise. through supernova explosions. the relativistie electrons responsible [or the radio continuum.," The favored explanation of the correlation holds that the same massive stars warm the FIR-emitting dust and energise, through supernova explosions, the relativistic electrons responsible for the radio continuum."731 Given the FUR luminosity of PDFJO11423. this correlation predicts a l4GGllz flux in the range 1.3 3.31inJy. compared wilh the measured value of 1.67 mJv.," Given the FIR luminosity of PDFJ011423, this correlation predicts a GHz flux in the range 1.3 – mJy compared with the measured value of 1.67 mJy."732 This agreement supports the possibility that most of the radio emission comes from star formation processes., This agreement supports the possibility that most of the radio emission comes from star formation processes.733 It should however be noted (hat a similar racio/FIR correlation holds for samples of racdio-quiel quasars. perhaps as a consequence of links between star formation and black hole feeding rates.," It should however be noted that a similar radio/FIR correlation holds for samples of radio-quiet quasars, perhaps as a consequence of links between star formation and black hole feeding rates."734" The relatively flat. racio spectralindex observed here. aj}—0.16 (S,xv ""). while being frequently linked to quasar emission"," The relatively flat radio spectralindex observed here, $\alpha_{1.4}^{2.4} = 0.16$ $_{\nu} \propto \nu^{-\alpha})$ , while being frequently linked to quasar emission"735A point mass. M. at a distance. Dj. will deflect a ight beam coming from a source at distance. Di.,"A point mass, $M$, at a distance, $D_l$, will deflect a light beam coming from a source at distance, $D_s$."736" In particular. if the source is observed at a 2-d angle 0 from the lens. then the beam would be deflected by an angle. a: More generally. if the lens is an extended object. with a surface mass deusitv. X(0). then a dimensionless mass. the convergence, nav be defined. as: The convergence may be thought of as a source terii for a potential. (0). and related via a Poissou-like equation: where all eradicuts and divergences are calculated in the two-dimensional 0-3pace."," In particular, if the source is observed at a 2-d angle $\vec{\theta}$ from the lens, then the beam would be deflected by an angle, $\vec\alpha$: More generally, if the lens is an extended object, with a surface mass density, $ \Sigma ( \vec{\theta})$, then a dimensionless mass, the convergence, may be defined as: The convergence may be thought of as a source term for a potential, $\psi(\vec{\theta})$, and related via a Poisson-like equation: where all gradients and divergences are calculated in the two-dimensional $\theta$ -space."737 Extension of equation (1)) to the coutinmous case. and combination with equation (2)) vields a deflection angle. A beam observed at angle 0 iust therefore have originated in the source plane at uder the thin lens approximation.," Extension of equation \ref{eq:ptmass}) ) to the continuous case, and combination with equation \ref{eq:kappa_def}) ) yields a deflection angle, A beam observed at angle $\vec\theta$ must therefore have originated in the source plane at under the thin lens approximation."738 Suppose we observe a galaxy with its ceuter of helt at the position oy)plane., Suppose we observe a galaxy with its center of light at the position $\vec\beta_0$.739 Throughout this paper. we will define a local set of coordinates such that oy. and correspoudinegly. Jy (the position of the source in the lens plane) are at the origin.," Throughout this paper, we will define a local set of coordinates such that $\vec\beta_0$, and correspondingly, $\vec\theta_0$ (the position of the source in the lens plane) are at the origin."740 This assumed convention does not change the final results. but merely makes the equations more compact.," This assumed convention does not change the final results, but merely makes the equations more compact."741 Solving the lensing equation to linear order. oue finds that both 9j aud (y correspond to the ceuter of mapping (i.e. the first order leus mapping from source plane to image plane preserves the position of the ceuter of light).," Solving the lensing equation to linear order, one finds that both $\vec{\beta}_0$ and $\vec{\theta}_0$ correspond to the center of mapping (i.e. the first order lens mapping from source plane to image plane preserves the position of the center of light)."742 Iu linear analysis both ου aud (y coirespoud to the ceuter of light., In linear analysis both $\vec\beta_0$ and $\vec\theta_0$ correspond to the center of light.743 Towever. in the higher order analysis. discussed low. if the position. Jy. in the source plane is leased to the foreground. the corresponding lensed position will uo longer recessarily be the center of light.," However, in the higher order analysis, discussed below, if the position, $\vec\beta_0$, in the source plane is lensed to the foreground, the corresponding lensed position will no longer necessarily be the center of light."744 Cnhinine equations (2)) (3)). the deflection angle. 6(0) can be written explicitly as the gradient of the scalar potential. 600)=Vac.," Combining equations \ref{eq:kappa_def}) ) \ref{eq:psi_def}) ), the deflection angle, $\vec{\alpha}(\vec{\theta})$ can be written explicitly as the gradient of the scalar potential, $\vec\alpha(\vec\theta)\equiv\nabla_{\vec\theta} \psi$."745 Since leusimg conserves surface brightness. a mapping from foreground to background coordinates is sufficient to determine a background brightuess map from a foreground one (or vice-versa) provided a full knowledge of he geometry of the syste (cosmology plus the redshifts of the source aud les) aud mass distribution of the lens.," Since lensing conserves surface brightness, a mapping from foreground to background coordinates is sufficient to determine a background brightness map from a foreground one (or vice-versa) provided a full knowledge of the geometry of the system (cosmology plus the redshifts of the source and lens) and mass distribution of the lens."746 Thus. we nav expand around the origin to determine a deprojection operator on a foreground lieht distribution. which viclds he amplification matrix. Rigorously speakiug. this expression is the first term: im a Taylor series expansion of the distortion operator.," Thus, we may expand around the origin to determine a deprojection operator on a foreground light distribution, which yields the amplification matrix, Rigorously speaking, this expression is the first term in a Taylor series expansion of the distortion operator."747" The ter > is a complex shear term. represeuting the anisotropic part of the distortion. with 5=τσ]τι aud the real and imaginary parts beiug denoted with the subscripts. ""1 and 727 respectively. as per convention."," The term $\gamma$ is a complex shear term, representing the anisotropic part of the distortion, with $\gamma=|\gamma|e^{2i\phi}$, and the real and imaginary parts being denoted with the subscripts, “1” and “2” respectively, as per convention."748 Using our locally defined coordinate svsteni we have: Likewise. asstuning the absence of a caustic crossing (Low[x] <0). this can be inverted uniquely to give a projection fiction. Iu this analvsis. we focus ou expanding this projection operator to the next higher order to derive the octopole moment rather than restricting ourselves to the quadrupole moment alone.," Using our locally defined coordinate system, we have: Likewise, assuming the absence of a caustic crossing $1-\kappa-|\gamma| < 0$ ), this can be inverted uniquely to give a projection function, In this analysis, we focus on expanding this projection operator to the next higher order to derive the octopole moment rather than restricting ourselves to the quadrupole moment alone."749 Iu general. researchers have treated weak lensing fields iu the manner described by NSB or its variants (Bacon. Refreeier Ellis. 2000: van Waerbeke et al.," In general, researchers have treated weak lensing fields in the manner described by KSB or its variants (Bacon, Refregier Ellis, 2000; van Waerbeke et al."750 2001)., 2001).751 These tecliniques describe the mapping of source-plane quadrupole light distributions to leus-plaue distributions. aud thus use the observed ellipticity aud an assumption of random oricutation to invert the shear field.," These techniques describe the mapping of source-plane quadrupole light distributions to lens-plane distributions, and thus use the observed ellipticity and an assumption of random orientation to invert the shear field."752 Du this work. we aim to generalize these transformations to the next higher order.," In this work, we aim to generalize these transformations to the next higher order."753 Our notation for the n-th order moments of a galaxy is:, Our notation for the $n$ -th order moments of a galaxy is:754mediuu has been speculated to be responsible for a number of other peculiar star-forming svstenus (6.9. Beaulieu et al.,"medium has been speculated to be responsible for a number of other peculiar star-forming systems (e.g., Beaulieu et al."755 2010)., 2010).756 Alternatively. the eas reservoir could have deen built slowly through multiple accretions of simaller eas clouds or streams. which could be either neutral or ionized.," Alternatively, the gas reservoir could have been built slowly through multiple accretions of smaller gas clouds or streams, which could be either neutral or ionized."757 Under this scenario. star formation would need to be suppressed somehow caring the buildup of the reservoir.," Under this scenario, star formation would need to be suppressed somehow during the buildup of the reservoir."758 The galaxy. formation models of Birnboim et al. (, The galaxy formation models of Birnboim et al. (7592007) exhibit quiescent. reservoir building periods simular to what would be needed here. but in general they apply to somewhat higher mass galaxies than GASS35981. aud also may not be valid at 2~0.,"2007) exhibit quiescent, reservoir building periods similar to what would be needed here, but in general they apply to somewhat higher mass galaxies than GASS35981, and also may not be valid at $z\sim0$."760 Multiple ninor mergers with sasadch dwarfs could also supplv the eas. but it becomes even harder in this case to imagine how the IIT could build up over time rather than form stars with each new accretion event.," Multiple minor mergers with gas-rich dwarfs could also supply the gas, but it becomes even harder in this case to imagine how the HI could build up over time rather than form stars with each new accretion event."761" We have reported ou the remarkable galaxy CASS35981. a disk galaxw with stellar ass =2«104) AL, which coutains an additional 2.1].«1019 MAL. of ΤΠ eas."," We have reported on the remarkable galaxy GASS35981, a disk galaxy with stellar mass $_*=2\times10^{10}$ $_\odot$ which contains an additional $2.1\times10^{10}$ $_\odot$ of HI gas."762 Millimeter observations indicate a molecular eas mass only a teuth this high., Millimeter observations indicate a molecular gas mass only a tenth this high.763 Through follow-up loue-slit spectroscopy. plus SED fitting using our UV through optical photometry we have shown that: The main conclusion from our observations ids that CASS35981 appears to he in the carly stages of formation ofits outer stellar disk.," Through follow-up long-slit spectroscopy, plus SED fitting using our UV through optical photometry we have shown that: The main conclusion from our observations is that GASS35981 appears to be in the early stages of formation of its outer stellar disk."764 We are not able to provide conclusive answers to questions portainiug to the origin aud fate of the eas in this galaxw with this data set alone., We are not able to provide conclusive answers to questions pertaining to the origin and fate of the gas in this galaxy with this data set alone.765 Scenarios iu which the eas was acquired iu a recent mereing event are cisfavoured because of the extremely regular kiuneuiatics of the disk., Scenarios in which the gas was acquired in a recent merging event are disfavoured because of the extremely regular kinematics of the disk.766 The ΤΗ mass of GÀSS35981 is too huge to be casily explained by gas transfer frou a passiug ealaxy., The HI mass of GASS35981 is too large to be easily explained by gas transfer from a passing galaxy.767 We therefore speculate that CCASS35981 acquired its eas directly from the interealactie medimn., We therefore speculate that GASS35981 acquired its gas directly from the intergalactic medium.768 Although our observations show that the stars in the outer disk formed within the last Cir. this does mot mean that the gas was also acquired less than 1 Gyr ago.," Although our observations show that the stars in the outer disk formed within the last Gyr, this does not mean that the gas was also acquired less than 1 Gyr ago."769 It is also nuclear whether CASS35981 will continue forming stars in its current low-cfhiciency state. or whether the eas will flow inwards towards the bulge. aud GASS35981 will eventually develop ito a more normal massive spiral ealaxy with a star formation surface deusity that decreases as a function of radius.," It is also unclear whether GASS35981 will continue forming stars in its current low-efficiency state, or whether the gas will flow inwards towards the bulge, and GASS35981 will eventually develop into a more normal massive spiral galaxy with a star formation surface density that decreases as a function of radius."770 Questions concerning the eventual fate of the σας can be addressed using the larger samples that will be provided by the full CASS aud COLD GÀSS surveys in the future., Questions concerning the eventual fate of the gas can be addressed using the larger samples that will be provided by the full GASS and COLD GASS surveys in the future.771 By studyiug trends iu SFR surface deusity. mean stellar age. metalliitv. aud stellar mass profiles as a function of atomic and molecular eas content for complete samples of galaxies. we hope to map out evolutionary sequences in disk galaxy. formation.," By studying trends in SFR surface density, mean stellar age, metallicity, and stellar mass profiles as a function of atomic and molecular gas content for complete samples of galaxies, we hope to map out evolutionary sequences in disk galaxy formation."772 Answers to questions concerning the origin of the eas will likely require a different approach., Answers to questions concerning the origin of the gas will likely require a different approach.773 Our comparison of the TT linescidth of CASS35981 with its CO line width and Wa rotation curve vield tantalizing hints that the atomic gas may not be iu equilixium with the rest of the ealaxy., Our comparison of the HI linewidth of GASS35981 with its CO line width and $\alpha$ rotation curve yield tantalizing hints that the atomic gas may not be in equilibrium with the rest of the galaxy.774 In addition. the ΤΗ spectiuui in Figure 1 is clearly asvuunetric about the line center.," In addition, the HI spectrum in Figure \ref{gas_prof} is clearly asymmetric about the line center."775 Hieh resolution III mapping of CASS35981 will be needed to uuderstiuid the dvnaiical state of the eas in more detail., High resolution HI mapping of GASS35981 will be needed to understand the dynamical state of the gas in more detail.776 Even so. such observations are uulikelv to prove that the III originated ποια a inore diffuse (and unuseen) reservolr of IGAL eas.," Even so, such observations are unlikely to prove that the HI originated from a more diffuse (and unseen) reservoir of IGM gas."777 This can only be doue if we are able to find tracers of this eas. for example absorption lines in the spectra of background quasars that arise when the quasar light passes through the circuimealactic medi of the ealaxy (Cou Ostriker 1999).," This can only be done if we are able to find tracers of this gas, for example absorption lines in the spectra of background quasars that arise when the quasar light passes through the circumgalactic medium of the galaxy (Cen Ostriker 1999)."778 These tracers must then be linked with galaxies like GASS35981., These tracers must then be linked with galaxies like GASS35981.779 The authors thauk J. Brinchinanu and €. Tremonti for making available their code for analysis of spectra., The authors thank J. Brinchmann and C. Tremonti for making available their code for analysis of spectra.780 Based ou observations carried out with the IRAM 30m. telescope., Based on observations carried out with the IRAM 30m telescope.781 IRAALD is supported by INSU/CNRS (France). MPG. (Cermany) and IGN (Spain).," IRAM is supported by INSU/CNRS (France), MPG (Germany) and IGN (Spain)."782 The Arecibo Observatory is part of the National Astronomy and Touosphere Center. which is operated by Cornell University under a cooperative aerecient with the National Scicuce Foundation.," The Arecibo Observatory is part of the National Astronomy and Ionosphere Center, which is operated by Cornell University under a cooperative agreement with the National Science Foundation."783 Observations reported here were obtained iu part at the AIMIT Observatory. a facility operated jointly by the Siuithsonian Iustitution aud the University of Arizona.," Observations reported here were obtained in part at the MMT Observatory, a facility operated jointly by the Smithsonian Institution and the University of Arizona."784 MAIT telescope time was eranted by NOAQO. through the Telescope System Tustrmuentation Program (TSIP).," MMT telescope time was granted by NOAO, through the Telescope System Instrumentation Program (TSIP)."785 TSIP is funded by NSF., TSIP is funded by NSF.786 Funding for the SDSS has been provided bx the Alfred P. Sloan Foundation. the Participating Tustitutions. the National Science Foundation. the U.S. Department of Enerev. the National Acronautics aud Space Acuninistration. the Japanese \loubukagalasho. the Max Planck Society. and the IHigher. Education Funding Council for Euglaud.," Funding for the SDSS has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England."787"Table 7. shows the median. fifth. and 95!"" percentiles for the expected TTV signal aud SNR for each of the candidate planets.","Table \ref{ttvtable} shows the median, fifth, and $^{\text{th}}$ percentiles for the expected TTV signal and SNR for each of the candidate planets."788 [istoerams sinular to figures 9 and 10 for cach svsteni are found in the Appendix., Histograms similar to figures \ref{ttv896} and \ref{ecc896} for each system are found in the Appendix.789 With the possible exception of KOI 191. each of the planets in these five svstenis will likely have observable transit inning variations by the eud of au extended missiou.," With the possible exception of KOI 191, each of the planets in these five systems will likely have observable transit timing variations by the end of an extended mission."790 For IKOI 191. even if the TTV signal is πα it may vet be detectable simply because here will be a laree number of transits Cuore han 1000) over the duration of au extended wission Which may compensate for the low sigual-o-hnoise ratio of the TTY signal to the transit nue uncertainties.," For KOI 191, even if the TTV signal is small it may yet be detectable simply because there will be a large number of transits (more than 1000) over the duration of an extended mission which may compensate for the low signal-to-noise ratio of the TTV signal to the transit time uncertainties."791 The primary reason for the small signal iu KOI 191 is the large ratio of orbital periods. exceeding 6:1.," The primary reason for the small signal in KOI 191 is the large ratio of orbital periods, exceeding 6:1."792 Thus. the TTV signal is weakened sieuificautlv.," Thus, the TTV signal is weakened significantly."793 If the outermost plauct in IKOI 191 were to have an eccentric orbit then it would eive a periodic TTY signal with a period equal to that of the outer planet as described iu Section | of Agoletal.(2005). (seealsoDorkovitsetal.2003)., If the outermost planet in KOI 191 were to have an eccentric orbit then it would give a periodic TTV signal with a period equal to that of the outer planet as described in Section 4 of \citet{agol2005} \citep[see also][]{bork2003}.794. For KOI 209. the expected TTV sigual for the inner planet shows au abrupt cutoff aud is expected to be larger than a few hundred seconds.," For KOI 209, the expected TTV signal for the inner planet shows an abrupt cutoff and is expected to be larger than a few hundred seconds."795 This is because WOT 209.02 has the lougest period of all of the iuner plaucts., This is because KOI 209.02 has the longest period of all of the inner planets.796 Caven the time bascline of the extended mission. planets with periods of a few teus of davs will likely prove to be among the most interesting for TTV studies as they siunultaneouslv/ have ongcr periods (the TTY signal is linear in the period) aud will have a sufücieut muuber of transits for a complete analysis.," Given the time baseline of the extended mission, planets with periods of a few tens of days will likely prove to be among the most interesting for TTV studies as they simultaneously have longer periods (the TTV signal is linear in the period) and will have a sufficient number of transits for a complete analysis."797 The proximity of IKOI 877 to the 2:1 MMRB lucicates tha this system is likely to have very laree variations., The proximity of KOI 877 to the 2:1 MMR indicates that this system is likely to have very large variations.798 However. a steep drop in the expected signal occurs when the orbits are nearly circular.," However, a steep drop in the expected signal occurs when the orbits are nearly circular."799 Figure ΤΕ shows an expanded view of the T'TV signal for the inner planet in NOT STI as a function of the iuuer and outer plauct eccentrieities., Figure \ref{877contours} shows an expanded view of the TTV signal for the inner planet in KOI 877 as a function of the inner and outer planet eccentricities.800" From this figure one cau see that. while the zero ecceutricitv case exlibits a relatively αιμα TTV signal. eccentricities nich larger than 0,01 cause the signal to increase bevoud an SNR of unity near LO? seconds (~15 1uuutes)."," From this figure one can see that, while the zero eccentricity case exhibits a relatively small TTV signal, eccentricities much larger than 0.01 cause the signal to increase beyond an SNR of unity near $10^3$ seconds $\sim 15$ minutes)."801 Should the TTY sienal © this size or smaller. it should stringently constrain the eccentricities of both planets in the abseuce of auv other data.," Should the TTV signal be this size or smaller, it should stringently constrain the eccentricities of both planets in the absence of any other data."802 We note that all of these results for the expected TTV signal have significant depeudence on the eccentrieities of the planets., We note that all of these results for the expected TTV signal have significant dependence on the eccentricities of the planets.803 Oue COlisequence of this fact is that. if a large fraction of these or other imultiple svstenms do not show a TTV sienal. then low eccentricity orbits are much more ΟΠΛΟ in unilti-planet systems than iu sinele planet svstenis.," One consequence of this fact is that, if a large fraction of these or other multiple systems do not show a TTV signal, then low eccentricity orbits are much more common in multi-planet systems than in single planet systems."804 The threc-plaue system of NOT 152 porteuds the exciting ar challenging studies of svstenis where there are more than two planets aud where multiple planets transit the star., The three-planet system of KOI 152 portends the exciting and challenging studies of systems where there are more than two planets and where multiple planets transit the star.805 This svstei js particularly interesting given the relatively close proximity to the [:2:1 uniltibody resonance., This system is particularly interesting given the relatively close proximity to the 4:2:1 multibody resonance.806 However. it is unlikely that this svsteu occupies this resonance eiven the estimated orbital periods of the planetsone being estimated from a sinele transit.," However, it is unlikely that this system occupies this resonance given the estimated orbital periods of the planets—one being estimated from a single transit."807 For KOT 152. the middle planet is likely to exhibit the largest TTV signalbeing just outside the 2:1 MMRB with an interior plauet aud perhaps just interior to the 2:1 MMRB ofthe exterior One challenge that theee-planet svstenis; such ax WOT 152. pose js the confusion that cal arise from uultiple. competing perturbers in the TTV signa for a particular planet.," For KOI 152, the middle planet is likely to exhibit the largest TTV signal—being just outside the 2:1 MMR with an interior planet and perhaps just interior to the 2:1 MMR of the exterior One challenge that three-planet systems, such as KOI 152, pose is the confusion that can arise from multiple, competing perturbers in the TTV signal for a particular planet."808 We present three broad scenarios for consideration in future studies; although other reeimics may exist: 1) nonresonaut/uonresonaut where there is uo 116211 motion conuuensurability between any pair of planets; 2) resonant/nouresonant where oue pair of plauets has a ΠΟΣΤ motion conunuensurability while the other does not. aud 3) resonant/resonaut where anv pair of planets lies near a mca motion conmieusurability.," We present three broad scenarios for consideration in future studies, although other regimes may exist: 1) nonresonant/nonresonant where there is no mean motion commensurability between any pair of planets, 2) resonant/nonresonant where one pair of planets has a mean motion commensurability while the other does not, and 3) resonant/resonant where any pair of planets lies near a mean motion commensurability."809 For the first scenario. the TTV signal due to one perturber should be lavegely independent of he TTY signal due to the second perturber.," For the first scenario, the TTV signal due to one perturber should be largely independent of the TTV signal due to the second perturber."810 The effect from both perturbers will be of order the yerturber to stellar ass ratio. and therefore nav be comparable.," The effect from both perturbers will be of order the perturber to stellar mass ratio, and therefore may be comparable."811 But their coutributions will contribute linearly. to the overall= signal aud he periodicities in the TTY signal due to one erturber will be independent of the periodicities induced by the other., But their contributions will contribute linearly to the overall signal and the periodicities in the TTV signal due to one perturber will be independent of the periodicities induced by the other.812 In other words. a Fourier raustorm of the TTV sienal would likely show wo sets of independent reals (seeSteffen2006) hat can be distinenishedOo provided the data have," In other words, a Fourier transform of the TTV signal would likely show two sets of independent peaks \citep[see][]{stef2006} that can be distinguished provided the data have"813using the SFR derived from the SED fitting we notice that NE and C2 are not strongly deviant anymore compared to the other regions.,using the SFR derived from the SED fitting we notice that NE and C2 are not strongly deviant anymore compared to the other regions.814" This shows that great caution must be employed to estimate the SFR as it can influence the results significantly, especially in the case of interacting systems in which the actual SFR can vary rapidly."," This shows that great caution must be employed to estimate the SFR as it can influence the results significantly, especially in the case of interacting systems in which the actual SFR can vary rapidly."815" As mentioned earlier, ? found that starburst galaxies follow a different Schmidt-Kennicutt law than more quiescent galaxies."," As mentioned earlier, \cite{daddi2010a} found that starburst galaxies follow a different Schmidt–Kennicutt law than more quiescent galaxies."816 The interaction in Arp 158 increases the turbulence in the system., The interaction in Arp 158 increases the turbulence in the system.817 The question is whether different regions in the system also follow different relations., The question is whether different regions in the system also follow different relations.818" In Fig. 6,,"," In Fig. \ref{fig:KS-plot-D10},"819 we compare the regions in Arp 158 with the relations found by ?.., we compare the regions in Arp 158 with the relations found by \cite{daddi2010a}.820" We see that similarly to what ? found, we are seeing 2 different regimes of star formation in Arp 158, provided the SFR estimator is accurate."," We see that similarly to what \cite{daddi2010a} found, we are seeing 2 different regimes of star formation in Arp 158, provided the SFR estimator is accurate."821" The first one regroups all regions, except for NE, which are well fitted by a power law with a slope of 1.42."," The first one regroups all regions, except for NE, which are well fitted by a power law with a slope of 1.42."822" Conversely NE presents a much higher SFR surface density for a similar surface density, with an offset which is qualitatively similar to the one found by ? for starburst galaxies."," Conversely NE presents a much higher SFR surface density for a similar surface density, with an offset which is qualitatively similar to the one found by \cite{daddi2010a} for starburst galaxies."823" The offset is slightly larger in the case of ?,, probably as the objects they studied are more extreme than ours."," The offset is slightly larger in the case of \cite{daddi2010a}, probably as the objects they studied are more extreme than ours."824 Another important point is that contrary to ? we find this offset while keeping the Xco conversion factor constant., Another important point is that contrary to \cite{daddi2010a} we find this offset while keeping the $_\mathrm{CO}$ conversion factor constant.825 Using a smaller conversion factor similar to that used for LIRGs and ULIRGs would only increase the discrepancy., Using a smaller conversion factor similar to that used for LIRGs and ULIRGs would only increase the discrepancy.826 What really sets NE apart is not the gas surface density but the high SFR surface density., What really sets NE apart is not the gas surface density but the high SFR surface density.827 A possible explanation is that this region is not simply an inflow-driven starburst but that the increased turbulence and a fragmentation into dense clouds strongly increase the SFR surface density for the same gas surface density (???)..," A possible explanation is that this region is not simply an inflow–driven starburst but that the increased turbulence and a fragmentation into dense clouds strongly increase the SFR surface density for the same gas surface density \citep{teyssier2010a,bournaud2010b,bournaud2011a}."828 An observational signature of this would be an an excess of the dense gas fraction as observed by ?.., An observational signature of this would be an an excess of the dense gas fraction as observed by \cite{juneau2009a}.829" In order to determine whether the dense gas fraction is higher, some HCN observations are required."," In order to determine whether the dense gas fraction is higher, some HCN observations are required."830" We stress that the use of a lower Xco factor, as is used for ULIRGs for instance, for the NE region would only exacerbate the discrepancy."," We stress that the use of a lower $_\mathrm{CO}$ factor, as is used for ULIRGs for instance, for the NE region would only exacerbate the discrepancy."831 The presence of these 2 modes seen in a resolved way in an interacting system shows that its origin does not depend on the global mass or size of the system but that it is rather linked to the physics of the ISM at scales no larger than 1 kpc., The presence of these 2 modes seen in a resolved way in an interacting system shows that its origin does not depend on the global mass or size of the system but that it is rather linked to the physics of the ISM at scales no larger than 1 kpc.832" Indeed, this scale corresponds to the largest gravitational instabilities in the ISM."," Indeed, this scale corresponds to the largest gravitational instabilities in the ISM."833 The Jeans length which is of the order of 100—200 pc in nearby spirals increases up to 500--1000 pc in mergers because of higher densities and velocity dispersions., The Jeans length which is of the order of 100–200 pc in nearby spirals increases up to 500–1000 pc in mergers because of higher densities and velocity dispersions.834 In addition this scale also corresponds to the injection scale of turbulence in the ISM (??)..," In addition this scale also corresponds to the injection scale of turbulence in the ISM \citep{elmegreen2003a,bournaud2010a}."835 In this paper we have studied how properties of star-forming regions vary across an interacting system., In this paper we have studied how properties of star–forming regions vary across an interacting system.836" To do so we have combined an extensive set of archival and proprietary data tracing the molecular gas (CO), the atomic gas (HD, star formation (FUV and 24 ym), and the stellar populations."," To do so we have combined an extensive set of archival and proprietary data tracing the molecular gas (CO), the atomic gas (HI), star formation (FUV and 24 $\mu$ m), and the stellar populations."837" The interacting system shows a complex morphology, the disks of the 2 colliding galaxies having already interpenetrated."," The interacting system shows a complex morphology, the disks of the 2 colliding galaxies having already interpenetrated."838 To ascertain the exact nature of the different regions in the interacting system we have also obtained optical spectra., To ascertain the exact nature of the different regions in the interacting system we have also obtained optical spectra.839" In particular we have obtained a firm identification of the nuclei of the merging galaxies, which was still under debate."," In particular we have obtained a firm identification of the nuclei of the merging galaxies, which was still under debate."840" One, to the East, exhibits a starburst, the other one hosts an AGN."," One, to the East, exhibits a starburst, the other one hosts an AGN."841" A third nucleus, to the West, turns out to be a foreground star."," A third nucleus, to the West, turns out to be a foreground star."842 A brief description of the regions of interest in Arp 158 is provided hereafter., A brief description of the regions of interest in Arp 158 is provided hereafter.843ONeMg-He bbs at the present.,ONeMg+He DDs at the present.844 During the same period. there are no new-born CO+CO DDs.," During the same period, there are no new-born CO+CO DDs."845 reftigdol showsthalthecontribulionofstar formaliontolhepresentnumbers(toppancls)andtotalimergedniumbers(boltompancis)ofalliypesof DL , \\ref{fig_cdot} shows that the of star formation to the present numbers (top panels) and total merged numbers (bottom panels) of all types of DDs decreases monotonically as a function of $t_{\rm sf}$.846This is because most DDs from all epochs survive to the present time due to their wide orbital separations., This is because most DDs from all epochs survive to the present time due to their wide orbital separations.847 The number of He+He DDs from each epoch decreases with /.; more sharply than for CO+CO DDs. although early star formation provides more He+He DDs than CO+CO DDs.," The number of He+He DDs from each epoch decreases with $t_{\rm sf}$ more sharply than for CO+CO DDs, although early star formation provides more He+He DDs than CO+CO DDs."848 A similar situation arises for CO+He and ONeMeg+He- DDs., A similar situation arises for CO+He and ONeMg+He DDs.849 This. result .is consistent. with. stellar evolution. and the assumed7 SF prate., This result is consistent with stellar evolution and the assumed SF rate.850" The significanceEN of. computing. the present number of. DDs using; 9,98refeq, umberl.; whichrepresentsthesumof DDsarisingfromdif ferentstar9.975 formalioncpochs. islhalitdemonslralesthelinkbebwecnthes FhistókyMFElyegalaa (9 ΑΣΕ ΠΛ ΜΜion)andt hec, deyDDs.whicheanbededuced from. forcrample. theirgravitationalwavesigneal,"," The significance of computing the present number of DDs using \\ref{eq_number1}, which represents the sum of DDs arising from different star-formation epochs, is that it demonstrates the link between the SF history of the galaxy (or, at least, the thin disc in the present investigation) and the distribution of the properties of present-day DDs, which can be deduced from, for example, their gravitational wave signal."851 rnmishowsthevariationof ς and M nmberly)ofdif ferenttgpesof v. ο Μα.," \\ref{fig_birnum} shows the variation of $\nu$, $\zeta$ and $n_{\rm dd}$ \\ref{eq_number1}) ) of different types of DD with age $t_{\rm disc}$."852 The individual properties of the current rad DDs will be used to calculate*aleul the gravitationalepavitatii wave“ave signalspon ?(2).., The individual properties of the current $n_{\rm dd}$ DDs will be used to calculate the gravitational wave signal \citep{Yu11}.853 The use of a realistic dise model is important in order to describe the distance distribution of white dwarf binary systems from the Sun., The use of a realistic disc model is important in order to describe the distance distribution of white dwarf binary systems from the Sun.854 ? proposed a double exponential distribution., \citet{Sackett97} proposed a double exponential distribution.855 ? derived three functions for the star density distribution in their model of a thin disc plus thick disc (exponential | exponential. hyperbolic secant | exponential. and squared hyperbolic secant || exponential. respectively) from fits to deep star counts carried out in the Calar Alto Deep Imaging Survey.," \citet{Phleps00} derived three functions for the star density distribution in their model of a thin disc plus thick disc (exponential $+$ exponential, hyperbolic secant $+$ exponential, and squared hyperbolic secant $+$ exponential, respectively) from fits to deep star counts carried out in the Calar Alto Deep Imaging Survey."856 We here model the thin dise in the Galaxy using a squared hyperbolic secant plus exponential distribution expressed as: where // and z are the natural eylindrical coordinates of the axisymmetric dise. j;=2.5 Kkpe is the scale length of the disc. and fy.=0.352 kkpe is the scale height of the thin dise.," We here model the thin disc in the Galaxy using a squared hyperbolic secant plus exponential distribution expressed as: where $R$ and $z$ are the natural cylindrical coordinates of the axisymmetric disc, $h_{R}=2.5$ kpc is the scale length of the disc, and $h_{z}=0.352$ kpc is the scale height of the thin disc."857" AZ, is the mass of the thin disc. which is determined by the star formation rate."," $M_{\rm tn}$ is the mass of the thin disc, which is determined by the star formation rate."858 We adopt the position of the Sun to be Rau=S. KKkpe. zou = 16.5 Προ (2)..," We adopt the position of the Sun to be $R_{\rm sun} = 8.5$ kpc, $z_{\rm sun}$ = $16.5$ pc \citep{Freudenreich98}."859 We neglect the age and mass dependence of the scale height., We neglect the age and mass dependence of the scale height.860 This thin-dise model is consistent with the model of ? and ?.. and also in agreement with Hipparcos results and the observed rotation curve.," This thin-disc model is consistent with the model of \citet{Klypin02} and \citet{Robin03}, and also in agreement with Hipparcos results and the observed rotation curve."861" From the SF rate. the total mass of stars in the thin dise at age 10 Gyr is Afi,z 107AL.."," From the SF rate, the total mass of stars in the thin disc at age 10 Gyr is $M_{\rm tn}\approx$ $\times10^{10}~M_{\odot}$."862 Combining the thin disc model and the mass of stars in the thin disc. the stellar density in the solar neighbourhood is 6.27107M.pe? for the thin disc. These values are consistent with the Hipparcos result. (7.6d1.5)/107?M.pe 72(2) and the dynamical structure of the thin disc (2?)..," Combining the thin disc model and the mass of stars in the thin disc, the stellar density in the solar neighbourhood is $6.27\times10^{-2}{\rm M_{\odot}pc^{-3}}$ for the thin disc, These values are consistent with the Hipparcos result, $7.6\pm1.5)\times10^{-2}~863{\rm M_{\odot}pc^{-3}}$ \citep{Creze98} and the dynamical structure of the thin disc \citep{Klypin02,Robin03}."864 The local density of DDs in the model is L98«1074 pe., The local density of DDs in the model is $1.98\times10^{-4}$ $\rm pc^{-3}$.865 The presence of unevolved DDs in facrilicallime when the rogeniorindicalestheeristenceof puxeceitgted cthe, The presence of unevolved DDs in \\ref{fig_progenitor} indicates the existence of a critical time when the first DD of each type was just born.866" reftig,πας| CO.CO|He andtLe UeDDsrespeelively. thetimesare25 Alyy. DOAL gr. SOOAL gr. and650AL yr."," For ONeMg+X, CO+CO, CO+He, and DDs respectively, the times are 25 Myr, 50 Myr, 560 Myr, and 650 Myr."867 Figipillustralesthecontribulionofdi fferentepochsof star formeationtoli dagdistribulionoflolalmassandorbilalperiodsofthe DDs, \\ref{fig_mp} illustrates the contribution of different epochs of star formation to the present-day distribution of total mass and orbital periods of the DDs.868 Meheredistinguis 6.026 ⋅<LafGyrD«SG) SXFa/Gvr‘«9. («D 9xfafvr<9.4. (e) 9.4mfyfOr«9.95. and (D 0.95xfafCivr<9.175. with the current dise age assumed to be 10 Gyr.," We here distinguish the star formation for the current thin disc in six stages, which are (a) $0 \leqslant t_{\rm sf}/\rm Gyr < 6$ , (b) $6 \leqslant t_{\rm sf}/\rm Gyr < 8$, (c) $8 \leqslant t_{\rm sf}/\rm Gyr < 9$, (d) $9 \leqslant t_{\rm sf}/\rm Gyr < 9.4$, (e) $9.4 \leqslant t_{\rm sf}/\rm Gyr < 9.95$, and (f) $9.95 \leqslant t_{\rm sf}/\rm Gyr < 9.75$, with the current disc age assumed to be 10 Gyr."869. We. do not obtain: any DD for- star formation-) taking. place after 9.975 Gyr., We do not obtain any DD for star formation taking place after 9.975 Gyr.870 pshousthatthe formationof veryclosecompactbinaries(los 2.5) is sensitive to star formation between 8 and 9.95 Gyr after the thin disc formed. which means that these DDs are most likely to be young.," \\ref{fig_mp} shows that the formation of very close compact binaries $\log f>-2.5$ ) is sensitive to star formation between 8 and 9.95 Gyr after the thin disc formed, which means that these DDs are most likely to be young."871 Their MS+MS progenitors formed between 50 Myr and 2000 Myr ago., Their MS+MS progenitors formed between 50 Myr and 2000 Myr ago.872" The total stellar mass formed during the time represented by each panel of reftig,,, p/83.62. 0.85. 0.38. 0.15.0.19. @7d0.0087- 102 AL. ta to T."," The total stellar mass formed during the time represented by each panel of \\ref{fig_mp} is $3.62$, $0.85$, $0.38$, $0.15$, $0.19$, and $0.0087\times10^{10}$ $M_{\odot}$ (a to f)."873 The current number of DDs in the thin disc derived from euch star formation in the figure is given in table 2.., The current number of DDs in the thin disc derived from each star formation epoch in the figure is given in table \ref{tab_DDsf}.874 These numbers indicate that. for epochcurrent He+He and CO+He DDs. a large number and 87.856)) have ages greater than + Gyr. while only and of CO+CO and ONeMg+X have ages in the same range.," These numbers indicate that, for current He+He and CO+He DDs, a large number and ) have ages greater than 4 Gyr, while only and of CO+CO and ONeMg+X have ages in the same range."875 A significant number and 6.7569) of CO+CO and ONeMg+X DDs have been produced by the last | Gyr of star formation., A significant number and ) of CO+CO and ONeMg+X DDs have been produced by the last 1 Gyr of star formation.876 The number of He+tHe and CO+He DDs from this period is negligible., The number of He+He and CO+He DDs from this period is negligible.877 However. ?. show that DDs with ages less than 2 Gyr would contribute substantially to the amplitude of the gravitational wave signal in several frequeney bands.," However, \citet{Yu11} show that DDs with ages less than 2 Gyr would contribute substantially to the amplitude of the gravitational wave signal in several frequency bands."878 According to the classification of the star formation stages and the eritical time for the birth of DDs. we can see from plhaltheALS| AlSprogenitorsofCO | CODDsare formedbe forety=9.95 Gyr.," According to the classification of the star formation stages and the critical time for the birth of DDs, we can see from \\ref{fig_mp} that the MS+MS progenitors of CO+CO DDs are formed before $t_{\rm sf}\approx9.95$ Gyr."879 The youngest CO+He DD has an age of about 560 Myr. but the majority of their MS progenitors formed 7600 Myr ago.," The youngest CO+He DD has an age of about 560 Myr, but the majority of their MS progenitors formed $>$ 600 Myr ago."880 These results are consistent with stellar evolution calculations., These results are consistent with stellar evolution calculations.881 Note that in the stellar evolution model a fraction of ONeM;z white dwarfs become neutron stars and. stellar-mass black holes due to accretion-induced collapse., Note that in the stellar evolution model a fraction of ONeMg white dwarfs become neutron stars and stellar-mass black holes due to accretion-induced collapse.882 These do not form type Ia supernovae and are not otherwise considered in our results., These do not form type Ia supernovae and are not otherwise considered in our results.883 with a. quasi- declining SF rate., We have simulated the present DD population with a quasi-exponential declining SF rate.884 In presentorder to see the /IDDChiNpuldtidninfluence on the, In order to see the influence on the885This corresponds (to a mass AMgu70.52M... πο that q~0.41.,"This corresponds to a mass $M_{Ab} \sim 0.52$, so that $q \sim 0.41$."886 We have presented the first evidence of total eclipses (including eclipses of the faint secondarv star in { band) in the svstem $986 using an extensive series of photometric observations., We have presented the first evidence of total eclipses (including eclipses of the faint secondary star in $I$ band) in the system S986 using an extensive series of photometric observations.887 We have taken high-resolution spectroscopy. of the system and have identified a (hind star that contributes to (he light of the svstem., We have taken high-resolution spectroscopy of the system and have identified a third star that contributes to the light of the system.888 The (third star appears to be a cluster meniber. but may or may not be physically associated will the eclipsing binary.," The third star appears to be a cluster member, but may or may not be physically associated with the eclipsing binary."889 The results ol our analvsis are given in Table 5.., The results of our analysis are given in Table \ref{props}.890 The detailed analvsis of our spectroscopy and photometry for the $986 indicates that the primary star in the eclipsing binary (component Aa) is a star that is slightlv (bul significantlv) hotter than the Curnoff of the cluster., The detailed analysis of our spectroscopy and photometry for the S986 indicates that the primary star in the eclipsing binary (component Aa) is a star that is slightly (but significantly) hotter than the turnoff of the cluster.891 Two stellar explanations for this exist., Two stellar explanations for this exist.892 One possibility is that the primary is a normal main sequence star (hat is in a relatively short lived phase of its evolution., One possibility is that the primary is a normal main sequence star that is in a relatively short lived phase of its evolution.893 The gap in the CMD of M67 with 12.85<V«13.1 corresponds to a rapid phase before and after core hydrogen exhaustion during which the central convection zone disappears aud a shell fusion source is established., The gap in the CMD of M67 with $12.85 < V < 13.1$ corresponds to a rapid phase before and after core hydrogen exhaustion during which the central convection zone disappears and a shell fusion source is established.894 The size of the eap depends on exactly when the evolutionary timescale is small enough that few or no stars are likely to be lound in the phase. given the total population of stars in the cluster.," The size of the gap depends on exactly when the evolutionary timescale is small enough that few or no stars are likely to be found in the phase, given the total population of stars in the cluster."895 Several other members of M67 exist in the same portion of the CMD as component Aa (8439. 8602. 5610. $615. S12T1. 51503. and $1575: Sandequist 2003). which may lend some credence to {his idea.," Several other members of M67 exist in the same portion of the CMD as component Aa (S489, S602, S610, S615, S1271, S1503, and S1575; Sandquist 2003), which may lend some credence to this idea."896 Decause turnolf stars in clusters of M678 age have small but significant convective cores. (hev pul difficult constraints on the theory of convective overshooting (hat have nol been satisfied as vet.," Because turnoff stars in clusters of M67's age have small but significant convective cores, they put difficult constraints on the theory of convective overshooting that have not been satisfied as yet."897 Once they are. the CMD position of component Aa can be re-evaluated.," Once they are, the CMD position of component Aa can be re-evaluated."898 A second explanation is that component Aa is a blue strageler., A second explanation is that component Aa is a blue straggler.899 It is somewhat difficult lo piece together a scenario (hat can explain the system's orbital and photometric properties. but the light eurve analvsis makes it clear that component Ab is a relatively normal main sequence star and (that (he (wo stars are completely detached.," It is somewhat difficult to piece together a scenario that can explain the system's orbital and photometric properties, but the light curve analysis makes it clear that component Ab is a relatively normal main sequence star and that the two stars are completely detached."900 Component D is also consistent wilh being a normal main sequence star., Component B is also consistent with being a normal main sequence star.901 As such. scenarios involving anv kind of mass transfer (o star Aa are unlikelv.," As such, scenarios involving any kind of mass transfer to star Aa are unlikely."902" Our detection of Li in component Aa is consistent with the abundances of stars on the edge of the ""Li gap” (centered at 7,5;26700 IX)."," Our detection of Li in component Aa is consistent with the abundances of stars on the edge of the “Li gap” (centered at $T_{eff} \approx9036700$ K)."904 On the other hand. there has not been a detection of Li in a blue strageler in M67 to date.," On the other hand, there has not been a detection of Li in a blue straggler in M67 to date."905 If component Aa was created in the merger of (wo stars. the detection of Li would require that the more massive star lo have retained. a substantial amount of surface lithium in the time belore the collision. that little," If component Aa was created in the merger of two stars, the detection of Li would require that the more massive star to have retained a substantial amount of surface lithium in the time before the collision, that little"906"1980)), the hypothesis of a uniform distribution of the objects in the Universe is rejected at a confidence level of ~98% (<V./Va>=0.616+ 0.046).","), the hypothesis of a uniform distribution of the objects in the Universe is rejected at a confidence level of $\sim 98\%$ $<V_e/V_a> = 0.616 \pm 0.046$ )."907 Assuming a pure luminosity evolution model with an evolutionary form ος(1+zY€ we finda best fit parameter of C~2.7 with an associated confidence interval of 1.9-3.0., Assuming a pure luminosity evolution model with an evolutionary form $\propto (1+z)^C$ we find a best fit parameter of $\simeq$ 2.7 with an associated confidence interval of 1.9-3.0.908" This value of cosmological evolution is consistent, within the errors, both with the results obtained in the soft (E<3 keV) energy band using the Extended Medium Sensitivity Survey (C=2.56+0.17; Maccacaroet 1991,, DellaCecaetal. 1992)) and the EMSS+Rosat AGN samples (C=2.6+0.1; Pageetal. 1997)) and with the results in the 2-10 keV energy range reported in Uedaetal.(2003) (C= 2.70*057) and LaFrancaetal.(2005) (C= 3.2205)."," This value of cosmological evolution is consistent, within the errors, both with the results obtained in the soft $\ls 3$ keV) energy band using the Extended Medium Sensitivity Survey $C=2.56\pm 0.17$; \citealt{maccacaro1991}, , \citealt{dellaceca1992}) ) and the EMSS+Rosat AGN samples $C=2.6\pm 0.1$; \citealt{page1997}) ) and with the results in the 2-10 keV energy range reported in \cite{ueda2003} $C=2.70^{+0.17}_{-0.25}$ ) and \cite{lafranca2005} $C=3.22^{+0.13}_{-0.26}$ )."909" However it is now well established that a Luminosity Dependent Density Evolution (LDDE) model provides a better description of the evolutionary properties of AGN, both in the X-ray energy range (Hasingeretal.2005;; Uedaetal.2003;; LaFrancaetal.2005;; Silvermanetal.2007)) and in the optical domain (Bongiornoetal.2007))."," However it is now well established that a Luminosity Dependent Density Evolution (LDDE) model provides a better description of the evolutionary properties of AGN, both in the X-ray energy range \citealt{hasinger2005}; \citealt{ueda2003}; \citealt{lafranca2005}; \citealt{silverman2007}) ) and in the optical domain \citealt{bongiorno2007}) )."910" To test this evolutionary behavior, we assume here an LDDE model with the parametrization as introduced by Uedaetal.(2003), where Ζς corresponds to the redshift where the direction of the evolution changes sign."," To test this evolutionary behavior, we assume here an LDDE model with the parametrization as introduced by \cite{ueda2003}, where $_{\rm c}$ corresponds to the redshift where the direction of the evolution changes sign."911" It is worth noting that z, is a function of the intrinsic luminosity of the object; if we assume the best fit parameters of p2=-1.15; z;=2.49; a=0.20; Log L,=45.80 (adapted to Ho=65) as reported in LaFrancaetal.(2005),, then z, is 0.7,1.1,1.7 for AGN with Lx 10%,10*,, respectively."," It is worth noting that $_{\rm c}$ is a function of the intrinsic luminosity of the object; if we assume the best fit parameters of p2=-1.15; $_{\rm c}^*=2.49$; $\alpha$ =0.20; Log $_a$ =45.80 (adapted to $_0$ =65) as reported in \cite{lafranca2005}, then $_{\rm c}$ is $\sim 0.7,1.1,1.7$ for AGN with $_{\rm X}$ $\sim 10^{43}, 10^{44}, 10^{45}$, respectively."912" Given the coverage in the luminosity-redshift plane of the HBSS unabsorbed AGN sample, for each luminosity the objects are below z;, implying that we are unable to derive p2, z;, a and LogL,."," Given the coverage in the luminosity-redshift plane of the HBSS unabsorbed AGN sample, for each luminosity the objects are below $_{\rm c}$, implying that we are unable to derive p2, $_{\rm c}^*$, $\alpha$ and $_a$ ."913" For this reasons we have fixed them from LaFrancaetal.(2005) and we have used the V,/V, test to constrain pl.", For this reasons we have fixed them from \cite{lafranca2005} and we have used the $V_e/V_a$ test to constrain p1.914 We obtain a best fit pl=6.5 with an associated confidence interval of 3.5 - 10.0., We obtain a best fit p1=6.5 with an associated confidence interval of 3.5 - 10.0.915" The distribution of the derived V,/V, values is consistent with being uniformly distributed between 0 and 1 according to a KS test (KS probability 9596).", The distribution of the derived $V_e/V_a$ values is consistent with being uniformly distributed between 0 and 1 according to a KS test (KS probability $\sim 95\%$ ).916" We have also checked that, given the coverage of the luminosity-redshift plane of the HBSS AGN sample, the best fit pl is virtually insensitive to the other parameters of the model; ie. pl does not change by varying all the other parameters within their lo range as derived from LaFrancaetal.(2005)."," We have also checked that, given the coverage of the luminosity-redshift plane of the HBSS AGN sample, the best fit p1 is virtually insensitive to the other parameters of the model; i.e., p1 does not change by varying all the other parameters within their $1\sigma$ range as derived from \cite{lafranca2005}."917". The derived best fit value for pl is consistent, within the errors, with that reported in LaFrancaetal.(2005) (ρ1--4.62+ 0.26) and is in very good agreement with those recently obtained, in the optical domain, by Bongiornoet(2007) using a sample of 130 broad line AGN with redshift up to z=5 from the VIMOS-VLT Deep Survey (p1=6.54) and from Hopkinsetal.(2007) using a large data set of AGN selected in the Mid-IR, optical, soft X-ray and hard X-ray (p1=5.95+0.23)."," The derived best fit value for p1 is consistent, within the errors, with that reported in \cite{lafranca2005} $4.62\pm 0.26$ ) and is in very good agreement with those recently obtained, in the optical domain, by \cite{bongiorno2007} using a sample of 130 broad line AGN with redshift up to z=5 from the VIMOS-VLT Deep Survey (p1=6.54) and from \cite{hopkins2007} using a large data set of AGN selected in the Mid-IR, optical, soft X-ray and hard X-ray $5.95\pm 0.23$ )."918 Because of their number statistics (22 objects in total) and their distribution in the Ly—z plane the cosmological evolution is unconstrained for the absorbed AGN sample (note that the absorbed AGN are sampled only up to z~0.8)., Because of their number statistics (22 objects in total) and their distribution in the $L_X-z$ plane the cosmological evolution is unconstrained for the absorbed AGN sample (note that the absorbed AGN are sampled only up to $\sim 0.8$).919" Therefore in the following, and in line with the Unification Scheme of AGN, we will make the assumptionthat this class of sources evolve withcosmic time (and within the reshift range sampled at the HBSS flux limit) in a similar way as the unabsorbed ones."," Therefore in the following, and in line with the Unification Scheme of AGN, we will make the assumptionthat this class of sources evolve withcosmic time (and within the reshift range sampled at the HBSS flux limit) in a similar way as the unabsorbed ones."920We are particularly eratelul to E.,We are particularly grateful to E.921"data (Φ”=0.00016+0.0004Mpc,0.3Mgyr!,a=—1.51 40.08) gives psrr=(25E1.7)x107?Meyt! Μρς ","data $\Phi^* = 0.00016\pm0.0004\; \mathrm{Mpc}^{-3},\; \psi^*=9.2\pm0.3\;\mathrm{M}_{\sun} \; \mathrm{yr}^{-1}, \;\alpha=-1.51\pm0.08$ ) gives $\rho_\mathrm{SFR} = (25\pm1.7) \times 10^{-3} \;\mathrm{M}_{\sun}\; \mathrm{yr}^{-1}\; \mathrm{Mpc}^{-3}$ ."922This is in good agreementὃ. with most recent derivations of this result: see Table 1 for a compilation of recent results., This is in good agreement with most recent derivations of this result: see Table \ref{tab1} for a compilation of recent results.923" There is a relatively large spread in the derived values of the SFR volume density - greater than a factor of two, beyond the errors quoted on the individual measurements."," There is a relatively large spread in the derived values of the SFR volume density - greater than a factor of two, beyond the errors quoted on the individual measurements."924" This is discussed briefly by ? (who derive their own 1.4 GHz-based value of (21+5)x107?Meyr! 5), who attribute the discrepancy to a systematic underestimationΜρςε of the extinction using the Balmer decrement in some emission line-based studies."," This is discussed briefly by \cite{2002MNRAS.330..621S} (who derive their own 1.4 GHz-based value of $(21\pm5) \times 10^{-3}\;\mathrm{M}_{\sun}\; \mathrm{yr}^{-1}\; \mathrm{Mpc}^{-3}$ ), who attribute the discrepancy to a systematic underestimation of the extinction using the Balmer decrement in some emission line-based studies."925" The total value of psrr can also be decomposed into ‘UV’ and ‘IR’ components, by integrating the value of i?Φ(Φ) derived from each component individually."," The total value of $\rho_\mathrm{SFR}$ can also be decomposed into `UV' and `IR' components, by integrating the value of $\psi \,\Phi(\psi) $ derived from each component individually."926" Doing so leads to values of psrr(IR)=0.011Meyr!Mpc?, and psreR(UV)=0.012MeyrMpc?."," Doing so leads to values of $\rho_\mathrm{SFR}(\mathrm{IR}) = 0.011\; \mathrm{M}_{\sun}\; \mathrm{yr}^{-1}\; \mathrm{Mpc}^{-3}$, and $\rho_\mathrm{SFR}(\mathrm{UV}) = 0.012\; \mathrm{M}_{\sun}\; \mathrm{yr}^{-1}\; \mathrm{Mpc}^{-3}$."927 The LVL contribution is 0.0007Mayr!Mpc?., The LVL contribution is $0.0007\; \mathrm{M}_{\sun}\; \mathrm{yr}^{-1}\; \mathrm{Mpc}^{-3}$.928" This is4796,50%,, of the total for the IR, UV, and LVL components respectively."," This is, of the total for the IR, UV, and LVL components respectively."929" This result - that about half of the energy from the total cosmic star formation budget is re-processed by dust - is well known, and is in line with previous studies."," This result - that about half of the energy from the total cosmic star formation budget is re-processed by dust - is well known, and is in line with previous studies."930" ? found that of their derived total SFR. volume density (19x10?MoyrΜρο ?), was from dust-reprocessed For !consistency (and because our statistical AGN removal involves some uncertainty), we have checked the value of psrn calculated from the sample the statistical correction for AGN contamination (as per 833.1)."," \cite{Takeuchi:2005aa} found that of their derived total SFR volume density $19 \times 10^{-3} \; \mathrm{M}_{\sun}\; \mathrm{yr}^{-1}\; \mathrm{Mpc}^{-3}$ ), was from dust-reprocessed For consistency (and because our statistical AGN removal involves some uncertainty), we have checked the value of $\rho_\mathrm{SFR}$ calculated from the sample the statistical correction for AGN contamination (as per 3.1)."931" As the correction is only significant at the upper end (beyond φ”), the value only changes slightly: without any AGN correction applied, we calculate psrr=(26+2.2)x107?Meyt! Μρς "," As the correction is only significant at the upper end (beyond $\psi^*$ ), the value only changes slightly: without any AGN correction applied, we calculate $\rho_\mathrm{SFR} = (26\pm2.2) \times 10^{-3}\;\mathrm{M}_{\sun}\; \mathrm{yr}^{-1}\; \mathrm{Mpc}^{-3}$ ."932We may also ὃ.compute the fraction of the local cosmic star formation rate density occurring in starburst environments., We may also compute the fraction of the local cosmic star formation rate density occurring in starburst environments.933" For the purposes of such an analysis, we define a starburst as a system forming stars at 210 yr|."," For the purposes of such an analysis, we define a starburst as a system forming stars at $\geq$ 10 $_{\sun}\; \mathrm{yr}^{-1}$ ."934" Using the star formation rate density distribution,Mo we can thus integrate from 10 Meyr! to infinity: For our data, this value is 0.0049+0.00039 Moyr!Mpc?, or of the total star formation rate volume density; by our (admittedly somewhat crude) definition, one fifth of the starformation in the local Universe is provided by starbursts."," Using the star formation rate density distribution, we can thus integrate from 10 $_{\sun}\; \mathrm{yr}^{-1}$ to infinity: For our data, this value is $0.0049\pm 0.00039$ $_{\sun}\; \mathrm{yr}^{-1}\; \mathrm{Mpc}^{-3}$, or of the total star formation rate volume density; by our (admittedly somewhat crude) definition, one fifth of the starformation in the local Universe is provided by starbursts."935 This is consistent with the values found by ? using specific star formation rates from SDSS., This is consistent with the values found by \cite{2004MNRAS.351.1151B} using specific star formation rates from SDSS.936" Interestingly, ? also find that of star formation in the dwarf galaxy population is concentrated in high Ho equivalent width systems."," Interestingly, \cite{2009ApJ...692.1305L} also find that of star formation in the dwarf galaxy population is concentrated in high $\alpha$ equivalent width systems."937" 'There are many interesting values that can be derived from the distribution shown in Fig. 5,"," There are many interesting values that can be derived from the distribution shown in Fig. \ref{fig:sfr_den},"938" including the starburst fraction (discussed above), the ‘dividing’ SFR at which of the star formation is happening both above and below, and so on."," including the starburst fraction (discussed above), the `dividing' SFR at which of the star formation is happening both above and below, and so on."939" Rather than providng list of values for various integration limits, it is more enlighteninga to consider the behaviour of the cumulative fraction of star formation rate volume density, which is shown in Fig. 6.."," Rather than providng a list of values for various integration limits, it is more enlightening to consider the behaviour of the cumulative fraction of star formation rate volume density, which is shown in Fig. \ref{fig:cum_sfr_den}."940" This shows SFR, plotted against the fraction of the total star formation volume density coming from SFRs than that SFR."," This shows SFR, plotted against the fraction of the total star formation volume density coming from SFRs than that SFR."941" The data show a power-law increase in star formation rate volume density fraction, over 5 orders of magnitude until the truncation at ~20Mc,yr’."," The data show a power-law increase in star formation rate volume density fraction, over 5 orders of magnitude until the truncation at $\sim20 \;\mathrm{M}_{\sun}\; \mathrm{yr}^{-1}$."942" From this it can be seen that the *5076"" divide occurs at ~3M;yr!, about the SFR of the Milky Way (e.g. ?))."," From this it can be seen that the ' divide occurs at $\sim 3\; \mathrm{M}_{\sun}\; \mathrm{yr}^{-1}$, about the SFR of the Milky Way (e.g. \citealt{2006A&A...459..113M}) )."943 It is also interesting to consider the contribution to the total star formation rate volume density from LIRGs and ULIRGs., It is also interesting to consider the contribution to the total star formation rate volume density from LIRGs and ULIRGs.944" These IR-bright galaxies (defined as havingLm>10!Lc and >1013Lo, respectively) are rare in the local Universe, but become more and more important with lookback time, becoming an increasingly dominant componentof the total star formation rate volume density at higher redshifts (?;; ?;; ?))."," These IR-bright galaxies (defined as having$\mathrm{L}_{\mathrm{IR}} > 10^{11}\;\mathrm{L}_{\sun}$ and $> 10^{12}\;\mathrm{L}_{\sun}$ respectively) are rare in the local Universe, but become more and more important with lookback time, becoming an increasingly dominant componentof the total star formation rate volume density at higher redshifts \citealt{2005ApJ...619L..47S}; ; \citealt{2009A&A...496...57M}; ; \citealt{2010arXiv1008.0859G}) )."945 Fig., Fig.946 7 shows the star formation rate distribution, \ref{fig:ULIRG} shows the star formation rate distribution947"Here R, P, and B1» are the neutron star radius, rotation period (in s), and magnetic field (in 1013 G), respectively.","Here $R$ , $P$ , and $B_{12}$ are the neutron star radius, rotation period (in s), and magnetic field (in $10^{12}$ G), respectively."948" Accordingly, yioo=7/100, vaHz is the wave frequency in GHz, and A,=A/10!, where A=me/ngj is the multiplicity of the particle creation near magnetic poles (na; ΩΒ/2ποε is the Goldreich-Julian number density)."," Accordingly, $\gamma_{100} = \gamma/100$, $\nu_{\rm GHz}$ is the wave frequency in GHz, and $\lambda_{4} = \lambda/10^{4}$, where $\lambda = n_{\rm e}/n_{\rm GJ}$ is the multiplicity of the particle creation near magnetic poles $n_{\rm GJ} = \Omega B/2 \pi c e$ is the Goldreich-Julian number density)."949" On the other hand, the transverse extraordinary wave with the refractive index (X-mode) is to propagate freely."," On the other hand, the transverse extraordinary wave with the refractive index (X-mode) is to propagate freely."950 As the radius rA is much smaller than the escape radius resc (Cheng Ruderman 1979; Andrianov Beskin 2010) one can consider the effects of refraction and limiting polarization separately., As the radius $r_{\rm A}$ is much smaller than the escape radius $r_{\rm esc}$ (Cheng Ruderman 1979; Andrianov Beskin 2010) one can consider the effects of refraction and limiting polarization separately.951" In particular, this implies that one can consider the propagation of waves in the region rresc as rectilinear."," In particular, this implies that one can consider the propagation of waves in the region $r \sim r_{\rm esc}$ as rectilinear."952" Below for simplicity we assume that both two outgoing modes are generated at the same heights rem (few to tens NS radii), where the magnetic field can be considered as a rotating dipole Here = is the corresponding pulsar rotation phase."," Below for simplicity we assume that both two outgoing modes are generated at the same heights $r_{\rm em}$ (few to tens NS radii), where the magnetic field can be considered as a rotating dipole Here = is the corresponding pulsar rotation phase."953"2),we have we have In the rotating vector model (RVM) the p.a. is determined purely by the projection of magnetic field on the sky’s plane, so it coincides with $;,.",",we have we have In the rotating vector model (RVM) the ${\it p.a.}$ is determined purely by the projection of magnetic field on the sky's plane, so it coincides with $\phi_{m}$."954" The sign of the arctan term is determined by the p.a. measuredcounter-clockwise in the picture plane, as is common in radio astronomy (Everett Weisberg 2001)."," The sign of the arctan term is determined by the ${\it p.a.}$ measured in the picture plane, as is common in radio astronomy (Everett Weisberg 2001)."955" As the aberration angle at the emission point is approximately Qrem/c, i.e., it is much smaller than the angular size of the emission cone 1/», we can easily find the position of the emission point, at which the magnetic field line is along the line of sight."," As the aberration angle at the emission point is approximately $\Omega r_{\rm em}/{c}$, i.e., it is much smaller than the angular size of the emission cone $1/\gamma$, we can easily find the position of the emission point, at which the magnetic field line is along the line of sight."956" This point rem=(rem;Jem;Pem) in the XYZ frame is given by the spherical angles as Note that the impact angle )isthesmallestanglebetweenlineof sightandmagneticmomentm, isgivenby — )."," This point ${\bf r_{\rm em}} = (r_{\rm em},\theta_{\rm em},\phi_{\rm em})$ in the $XYZ$ frame is given by the spherical angles as Note that the impact angle is the smallest angle between line of sight and magnetic moment ${\bf m}$, is given by -."957".Asaresult, thetrajectoryoftheextraordinarywaveintheXY 7 f rameisgiver 'This relation allows us to determine magnetic field and all plasma characteristics along the ray."," As a result, the trajectory of the extraordinary wave in the $XYZ$ frame isgivenby the simple relation This relation allows us to determine magnetic field and all plasma characteristics along the ray."958range covered by the data.,range covered by the data.959 In those cases. the tail of the broad gaussian just serves to attenuate the emission of the source at long wavelengths.," In those cases, the tail of the broad gaussian just serves to attenuate the emission of the source at long wavelengths."960 Furthermore. we find no clear trend in the central energy or the width of the line.," Furthermore, we find no clear trend in the central energy or the width of the line."961 We find that the ratio of the spectra of the last and the first observation is close to a power law., We find that the ratio of the spectra of the last and the first observation is close to a power law.962 We therefore fit the data to an empirical model that consists of a blackbody multiplied by a power law ET. all affected by interstellar absorption.," We therefore fit the data to an empirical model that consists of a blackbody multiplied by a power law $E^{\Gamma}$, all affected by interstellar absorption."963 While the index of the multiplicative power law is allowed to change between observations. for these fits we constrain the parameters of the blackbody and the interstellar absorption to be the same in all observations.," While the index of the multiplicative power law is allowed to change between observations, for these fits we constrain the parameters of the blackbody and the interstellar absorption to be the same in all observations."964 While it is difficult to assign a physical interpretation to this model. it provides an acceptable description of the data in the RGS range ( 10 - 38A.. see Table 2). it has fewer parameters than the gaussian absorption model and. in addition. the index of the power law increases steadily over the course of the observations.," While it is difficult to assign a physical interpretation to this model, it provides an acceptable description of the data in the RGS range ( 10 - 38, see Table 2), it has fewer parameters than the gaussian absorption model and, in addition, the index of the power law increases steadily over the course of the observations."965 Starting from the raw data. we first produce a lst of calibrated events.," 	 Starting from the raw data, we first produce a list of calibrated events."966 To reduce pile-up. in the next step we select only single events as well as events that are not affected by some of the imperfections (bad columns. hot pixels. ete.)," To reduce pile-up, in the next step we select only single events as well as events that are not affected by some of the imperfections (bad columns, hot pixels, etc.)"967 of the CCDs., of the CCDs.968 We extract events withina 39 aresee circle centred on the source., We extract events withina $39$ arcsec circle centred on the source.969 We barycenter these events using the SAS routine BARYCEN version 1.13.4. and we then separate the events according to their energy in. 3 event lists: the bands that we use are 0.1 to 1.2 keV. O.I to 0.4 keV. and 0.4 to 0.8 keV. respectively.," We barycenter these events using the SAS routine BARYCEN version 1.13.4, and we then separate the events according to their energy in 3 event lists; the bands that we use are 0.1 to 1.2 keV, 0.1 to 0.4 keV, and 0.4 to 0.8 keV, respectively."970 For each observation we find the best period in the full band using an epoch folding technique: m all cases we find a period of 8.39] s. consistent with the value previously found for this source by ?..," For each observation we find the best period in the full band using an epoch folding technique; in all cases we find a period of 8.391 s, consistent with the value previously found for this source by \citet{kaplan03}."971 We then produce folded light curves in the three bands. and we also compute a folded hardness-ratio light curve from the ratio of the 0.4-0.8 keV and the 0.1—0.4 keV light curves.," We then produce folded light curves in the three bands, and we also compute a folded hardness-ratio light curve from the ratio of the 0.4–0.8 keV and the 0.1–0.4 keV light curves."972 In Figure 2 we show the 0.1-1.2 keV and the hardness- light curves., In Figure \ref{pulse} we show the 0.1-1.2 keV and the hardness-ratio light curves.973 For each observation we define the phase such that the maximum of the full-band light curve occurs at phase zero: the phase of the hardness ratio light curves is the same as for the full-band light curves., For each observation we define the phase such that the maximum of the full-band light curve occurs at phase zero; the phase of the hardness ratio light curves is the same as for the full-band light curves.974 The pulse profile in the 0.1—1.2 keV band. as well as the hardness-ratio pulse profile. change from one observation to the other.," The pulse profile in the 0.1–1.2 keV band, as well as the hardness-ratio pulse profile, change from one observation to the other."975 The first panel in Figure 2 shows a sinusoidal fit to the pulse profile during the first observation; the same sine function is overplotted to the full-band pulse profiles obtained from the other observations., The first panel in Figure \ref{pulse} shows a sinusoidal fit to the pulse profile during the first observation; the same sine function is overplotted to the full-band pulse profiles obtained from the other observations.976 It is apparent that the pulse profile becomes narrower with time., It is apparent that the pulse profile becomes narrower with time.977 At the same time. the hardness-ratio pulse. profile also changes.," At the same time, the hardness-ratio pulse profile also changes."978 lr the first observation there is a clear modulation. and the hardness-ratio profile leads the full-band light curve by (0.061+0.017 in phase.," In the first observation there is a clear modulation, and the hardness-ratio profile leads the full-band light curve by $0.064 \pm 0.017$ in phase."979 In the following observations the amplitude of the hardness-ratio modulation decreases and the phase difference between the full-band and the hardness-ratio light curves is consistent with zero., In the following observations the amplitude of the hardness-ratio modulation decreases and the phase difference between the full-band and the hardness-ratio light curves is consistent with zero.980 Eventually. in the last observation the modulation increases again. but now the hardness-ratio light curve lags the full band-light curve by 0.126+0.010 in phase.," Eventually, in the last observation the modulation increases again, but now the hardness-ratio light curve lags the full band-light curve by $-0.126 \pm 0.010$ in phase."981 The ddata of sshow that the spectrum of the source changes on a time scale of years. the first time ever that the X-ray spectrum of an isolated neutron star. other then soft gamma-ray repeaters or anomalous X-ray pulsars. is seen to change.," The data of show that the spectrum of the source changes on a time scale of years, the first time ever that the X-ray spectrum of an isolated neutron star, other then soft gamma-ray repeaters or anomalous X-ray pulsars, is seen to change."982 Whereas the changes are most pronounced in the last observation. we think that the actual change ts gradual. as witnessed by a gradual increase in the temperatures derived from the blackbody fits: or by a gradual increase in the index of the powerlaw in the fits with a blackbody multiplied with a power law reftemp and reffluxed)).," Whereas the changes are most pronounced in the last observation, we think that the actual change is gradual, as witnessed by a gradual increase in the temperatures derived from the blackbody fits; or by a gradual increase in the index of the powerlaw in the fits with a blackbody multiplied with a power law \\ref{temp} and \\ref{fluxed}) )."983 The spectral changes are accompanied by an energy-dependent change in the pulse shape: in particular the pulse phase where the spectrum is hardest has moved with respect to the phase of maximum flux refpulse))., The spectral changes are accompanied by an energy-dependent change in the pulse shape; in particular the pulse phase where the spectrum is hardest has moved with respect to the phase of maximum flux \\ref{pulse}) ).984 The phase aangle) dependent spectrum of single neutron stars is currently not explained., The phase angle) dependent spectrum of single neutron stars is currently not explained.985 The broad absorption features have been interpreted as a proton-cyclotron absorption feature (?).., The broad absorption features have been interpreted as a proton-cyclotron absorption feature \citep{haberl03a}. .986 In pulsars with a strong field (probably stronger than the limit for JO720.4-3125)) the absorption feature, In pulsars with a strong field (probably stronger than the limit for ) the absorption feature987"a dispersion of 0.1 magnitudes and the observational errors as 0.23 magnitudes, which are approximately the averages of the observational errors of the presently available SNe Ia (???)..","a dispersion of $0.1$ magnitudes and the observational errors as $0.23$ magnitudes, which are approximately the averages of the observational errors of the presently available SNe Ia \citep{Riess:2006fw, WoodVasey:2007jb, Davis:2007na}."988 The total error in our generated distance moduli for SN Ia is therefore V0.1?+0.23? magnitudes., The total error in our generated distance moduli for SN Ia is therefore $\sqrt{0.1^2+0.23^2}$ magnitudes.989 We assume an uniform distribution for SNe Ia along the redshifts., We assume an uniform distribution for SNe Ia along the redshifts.990" For GRBs, instead of generating mock data about the five luminosity relations (see ?)), we directly generate distance moduli like we do for SNe Ia for simplicity."," For GRBs, instead of generating mock data about the five luminosity relations (see \citet{Schaefer:2006pa}) ), we directly generate distance moduli like we do for SNe Ia for simplicity."991" The intrinsic scatter is set to be 0.65 magnitudes, which is approximately the average of the errors of the GRBs’ average distance moduli presented in ?,, and we ignore the measurement uncertainties, which are less than the intrinsic scatter."," The intrinsic scatter is set to be $0.65$ magnitudes, which is approximately the average of the errors of the GRBs' average distance moduli presented in \citet{Schaefer:2006pa}, and we ignore the measurement uncertainties, which are less than the intrinsic scatter."992 We consider two kinds of distributions for GRBs in the redshift bin 1.8«z<7., We consider two kinds of distributions for GRBs in the redshift bin $1.8 < z < 7$.993" One is the uniform distribution, the other a very rough approximation to the distribution presented by Fig."," One is the uniform distribution, the other a very rough approximation to the distribution presented by Fig."994" 2 in ?,, i.e. P(z)«exp(—z/7)."," 2 in \citet{Bromm:2005ep}, i.e. $P(z) \propto \exp (-z/7)$."995 We will see that our results are independent of the GRB distributions., We will see that our results are independent of the GRB distributions.996 Figures | and 2 show our results for the constraints from GRBs distributed in the redshift bin 1.8<z7 on the dark energy EOS parameter w(1.8«z7)., Figures \ref{fig:pw_GRB_hz_uni} and \ref{fig:pw_GRB_hz_bl} show our results for the constraints from GRBs distributed in the redshift bin $1.8 < z < 7$ on the dark energy EOS parameter $w (1.8 < z < 7)$.997" We can see that, for a few hundred GRBs, the constraints are only the steep drop at about zero that is seen in the probability function of the EOS parameter P(w)."," We can see that, for a few hundred GRBs, the constraints are only the steep drop at about zero that is seen in the probability function of the EOS parameter $P(w)$."998 This is consistent with the results in ?.., This is consistent with the results in \citet{Qi:2008zk}.999 Only when we have more than about 5000 GRBs can we begin to get concrete constraints on the EOS parameter., Only when we have more than about $5000$ GRBs can we begin to get concrete constraints on the EOS parameter.1000" The GRBs’ distributions have little impact on the conclusion; i.e., it is difficult to constrain the dark energy EOS parameters beyond the redshifts of SNe Ia with GRBs unless some new luminosity relations for GRBs with smaller scatters are discovered."," The GRBs' distributions have little impact on the conclusion; i.e., it is difficult to constrain the dark energy EOS parameters beyond the redshifts of SNe Ia with GRBs unless some new luminosity relations for GRBs with smaller scatters are discovered."1001" However, this does not mean that high-redshift GRBs contribute little to constraining the dark energy EOS parameters."," However, this does not mean that high-redshift GRBs contribute little to constraining the dark energy EOS parameters."1002" It has been demonstrated in ? that, even with the presently available 69 GRBs (?),, the constraints could be improved significantly at redshifts 0.5<zx1.8."," It has been demonstrated in \citet{Qi:2008zk} that, even with the presently available 69 GRBs \citep{Schaefer:2006pa}, , the constraints could be improved significantly at redshifts $0.5 \lesssim z \lesssim 1.8$."1003 Part of the improvement stems from GRBs beyond redshift 1.8., Part of the improvement stems from GRBs beyond redshift $1.8$.1004" Because the luminosity distances of standard candles depend on the behavior of the dark energy through an integration over the redshift, high-redshift GRBs put constraints on dark energy at lower redshifts, where dark energy is important in determining the cosmic expansion."," Because the luminosity distances of standard candles depend on the behavior of the dark energy through an integration over the redshift, high-redshift GRBs put constraints on dark energy at lower redshifts, where dark energy is important in determining the cosmic expansion."1005" And since there are few GRBs at low redshifts, the contributions from GRBs would lie primarily in the middle redshifts."," And since there are few GRBs at low redshifts, the contributions from GRBs would lie primarily in the middle redshifts."1006 In Figs., In Figs.1007 3 and 4 we explicitly show the constraints from GRBs distributed in the redshift bin 1.8«z7 on the dark energy EOS parameter w(0.5«z1.8)., \ref{fig:pw_GRB_mz_uni} and \ref{fig:pw_GRB_mz_bl} we explicitly show the constraints from GRBs distributed in the redshift bin $1.8 < z < 7$ on the dark energy EOS parameter $w (0.5 < z < 1.8)$.1008" For comparison, we also plot the constraints from SNe Ia uniformly distributed in the redshift bin 0.5«z1.8 on the dark energy EOS parameter w(0.5«z1.8) in Fig. 5.."," For comparison, we also plot the constraints from SNe Ia uniformly distributed in the redshift bin $0.5 < z < 1.8$ on the dark energy EOS parameter $w (0.5 < z < 1.8)$ in Fig. \ref{fig:pw_SNIa_mz_uni}."1009 We can see that the contributions from GRBs are comparable to that from SNe Ia. We explored the GRBs' contributions in constraining the dark energy EOS at high redshifts (1.8«z 7) and at middle redshifts (0.5«z 1.8)., We can see that the contributions from GRBs are comparable to that from SNe Ia. We explored the GRBs' contributions in constraining the dark energy EOS at high redshifts $1.8 < z < 7$ ) and at middle redshifts $0.5 < z < 1.8$ ).1010" When constraining the dark energy EOS in a certain redshift range, we allow the dark energy EOS parameter to vary only in that redshift bin and fix EOS parameters elsewhere to —1."," When constraining the dark energy EOS in a certain redshift range, we allow the dark energy EOS parameter to vary only in that redshift bin and fix EOS parameters elsewhere to $-1$."1011 We find that it is difficult to constrain the dark energy EOS parameters beyond the redshifts of SNe Ia with GRBs unless some new luminosity relations for GRBs with smallerscatters are discovered., We find that it is difficult to constrain the dark energy EOS parameters beyond the redshifts of SNe Ia with GRBs unless some new luminosity relations for GRBs with smallerscatters are discovered.1012" However, at middle redshifts, GRBs have contributions comparable with SNe Ia in constraining the dark energy EOS."," However, at middle redshifts, GRBs have contributions comparable with SNe Ia in constraining the dark energy EOS."1013limes.,times.1014 This figure5 clearly shows that. even starting5 from a disk in equilibrium. the Molfatian eravity does not maintain the exponential-Spitzer disk with the same initial density profile.," This figure clearly shows that, even starting from a disk in equilibrium, the Moffatian gravity does not maintain the exponential-Spitzer disk with the same initial density profile."1015 As time 5goes on. the profile turns 5gradually and is delinitely dilferent from the exponential profile.," As time goes on, the profile turns gradually and is definitely different from the exponential profile."1016 This shows that simulating models are à more robust tool than simply adjust profiles in static models. because the evolution of the svstem cannot be followed in this last approach.," This shows that simulating models are a more robust tool than simply adjust profiles in static models, because the evolution of the system cannot be followed in this last approach."1017 In conclusion. an alternative gravitational law must explain not only the rotation curves of spiral galaxies. but also their density profiles.," In conclusion, an alternative gravitational law must explain not only the rotation curves of spiral galaxies, but also their density profiles."1018 In (his way. simulations can be a powerful tool to deal with such an issue.," In this way, simulations can be a powerful tool to deal with such an issue."1019 Note that depending on (the values of ryü ancl üAdy. the Newtonian ogravitation would be naturally recovered.," Note that depending on the values of $r_0$ and $M_0$, the Newtonian gravitation would be naturally recovered."1020 Therefore. as an additional test we examine such an issue. whieh could help one to see how the structure of a disk galaxy would be modified by an alternative gravity law.," Therefore, as an additional test we examine such an issue, which could help one to see how the structure of a disk galaxy would be modified by an alternative gravity law."1021 We start [rom a Moffatian disk. just the one present. for example. in the first snapshot of Figure 8.. whose initial rotation curve is shown in Figure 7..," We start from a Moffatian disk, just the one present, for example, in the first snapshot of Figure \ref{fig8}, whose initial rotation curve is shown in Figure \ref{fig7}. ."1022" Then. we set ry=1000/pe and Af,—1x10! AL. and follow how the disk evolves."," Then, we set $r_0 = 1000 kpc$ and $M_0=1 \times 10^{10}$ $M_{\odot}$ and follow how the disk evolves."1023 The results of this simulation are shown in Figure 15. aud 16.., The results of this simulation are shown in Figure \ref{fig13} and \ref{fig14}.1024 For comparison. we also performed simulations using the Newtonian Gadget-2.," For comparison, we also performed simulations using the Newtonian Gadget-2."1025 Both the calculations produce identical results., Both the calculations produce identical results.1026 Therefore. the Newtonian calculation is recovered.," Therefore, the Newtonian calculation is recovered."1027 In particular. note in Figure 15. (he rotation curvealter 1 Gyr of simulated time: for largee values of R. the velocity is a decreasinge functionof ΠΠ. as expected for a Newtonian disk.," In particular, note in Figure \ref{fig13} the rotation curveafter 1 Gyr of simulated time; for large values of $R$, the velocity is a decreasing functionof $R$ , as expected for a Newtonian disk."1028Studying the structure aud dyuamics of the Milky Way is complicated by our location witlin it. and the resultant obscuration aloug the liue-oC-sight. but nevertheless it has established that our,"Studying the structure and dynamics of the Milky Way is complicated by our location within it, and the resultant obscuration along the line-of-sight, but nevertheless it has established that our"1029in transient black-hole N-ray binaries (Toman&Belloui2005).,in transient black-hole X-ray binaries \citep{hobe2005}.1030 It should be noted that there is ambiguity iu some of these discussions about the definition ofM., It should be noted that there is ambiguity in some of these discussions about the definition of.1031. Some authors imaplicity define aas the mass transfer rate from the companion to the compact object Roche lobe. while others take the mass flow rate through the inner disk or the accretiou rate onto the neutron star surface as the more relevant definition.," Some authors implicity define as the mass transfer rate from the companion to the compact object Roche lobe, while others take the mass flow rate through the inner disk or the accretion rate onto the neutron star surface as the more relevant definition."1032 Others explicitly distinguish various cconiponents., Others explicitly distinguish various components.1033 In the presence of the various proposed flows in the accretion/ejection process. such as disk and equatorial boundary laver flows. spherical inflows. magnetically donunated polar flows. possible disk winds and jets. clearly this is a complex issue to which we shall return in refsecidiscussion..," In the presence of the various proposed flows in the accretion/ejection process, such as disk and equatorial boundary layer flows, spherical inflows, magnetically dominated polar flows, possible disk winds and jets, clearly this is a complex issue to which we shall return in \\ref{sec:discussion}."1034 luterpreting the evolution along the Z source tracks has been iore difficult. owing to the fact that motion along the Z source tracks corresponds to relatively simall (less than a factor of —2) and non-nuonotonic iuteusitv varlatious.," Interpreting the evolution along the Z source tracks has been more difficult, owing to the fact that motion along the Z source tracks corresponds to relatively small (less than a factor of $\sim$ 2) and non-monotonic intensity variations."1035 For Z sources it was suggested that Hucreases from the horizontal brauch to the flaring branch (IHasiugeretal.1990).. although other scenarios have been put forward as well: e.g. cchaneineg in the opposite direction (Churchetal.2006).. ov unot changing at all (ILloiianetal.2002).," For Z sources it was suggested that increases from the horizontal branch to the flaring branch \citep{havaeb1990}, although other scenarios have been put forward as well: e.g., changing in the opposite direction \citep{chhaba2006}, or not changing at all \citep{hovajo2002}."1036. Based on their spectral analysis of the Z tracks. LRITO09 sugecst that motion along the Z tracks may occur at a nearly constantAY. with the branches being the result of cüffereut mstabilities in the aaccretion flow.," Based on their spectral analysis of the Z tracks, LRH09 suggest that motion along the Z tracks may occur at a nearly constant, with the branches being the result of different instabilities in the accretion flow."1037 More detailed analyses of the data presented im this work. dealing with different aspects of162.. can be found iu a umuber of other papers: spectral analysis (LRIIOO9). type-I N-orav bursts (Linetal.2009a).. kHz QPOs (Sannaetal.2010).. broad-band variability CAresu ct 22010. in prep.).," More detailed analyses of the data presented in this work, dealing with different aspects of, can be found in a number of other papers: spectral analysis (LRH09), type-I X-ray bursts \citep{lialho2009}, kHz QPOs \citep{sameal2010}, broad-band variability (Aresu et 2010, in prep.),"1038 aud the rapid decay into quiescence (Fridikssouetal.2010)., and the rapid decay into quiescence \citep{frhowi2010}.1039. Hore. we preseut au overview of the outburst of that focuses on aspects of the evolution of Hu which the change frou Z source to atoll source is nost clearly seeu: the CD/IIID tracks. high-frequency QPOs. and broad-band variability.," Here, we present an overview of the outburst of that focuses on aspects of the evolution of in which the change from Z source to atoll source is most clearly seen: the CD/HID tracks, high-frequency QPOs, and broad-band variability."1040 Du particular. we find hat selectious of data groups based on low-energy count rate allow for a more detailed study of the evolution of he CD/IIID tracks than in H7 aud LBRIIO9.," In particular, we find that selections of data groups based on low-energy count rate allow for a more detailed study of the evolution of the CD/HID tracks than in H07 and LRH09."1041 This also »ernits a more precise comparison of the observed tracks or wwith those found in the various NS-LMXD sub-classes., This also permits a more precise comparison of the observed tracks for with those found in the various NS-LMXB sub-classes.1042 Ins refsec:data we sununurize our data set aud analysis techniques., In \\ref{sec:data} we summarize our data set and analysis techniques.1043 Our results are presented in refsec:results aud in refsecidiscussion these results are interpreted ancl discussed within the— framework of various scenarios for the role of in driving the evolution between NS-LAINB subclasses and along the CD/IIID tracks of NS-LAINBs., Our results are presented in \\ref{sec:results} and in \\ref{sec:discussion} these results are interpreted and discussed within the framework of various scenarios for the role of in driving the evolution between NS-LMXB subclasses and along the CD/HID tracks of NS-LMXBs.1044 We analyzed all 865 pointed citepbiroswl1993 observations of nuuade between 2006 January 19 (MJD 53751) and 2007 Aue 29 (AITD 51311)., We analyzed all 865 pointed \\citep{brrosw1993} observations of made between 2006 January 19 (MJD 53754) and 2007 Aug 29 (MJD 54341).1045 Five of them were discarded from further analysis because proportional counter unit 2 (DCU2) was not working or because the length of usable data intervals was too short (<256s) for our variability analysis., Five of them were discarded from further analysis because proportional counter unit 2 (PCU2) was not working or because the length of usable data intervals was too short $<$ 256s) for our variability analysis.1046 The remaining 860 observations had a total combined exposure time of ~2.73 Ms. For our analysis we ouly made use of data from the Proportional Counter Array (PCA:Jahodactal.2006)., The remaining 860 observations had a total combined exposure time of $\sim$ 2.73 Ms. For our analysis we only made use of data from the Proportional Counter Array \citep[PCA;][]{jamara2006}.1047.. We followed the same analysis steps as described iu IH0T7. the ouly differeuce απο that in addition to background corrections. the data used for the light curves aud CDz/IIIDs in refsec:le-cd were also corrected for dead time.," We followed the same analysis steps as described in H07, the only difference being that in addition to background corrections, the data used for the light curves and CDs/HIDs in \\ref{sec:lc-cd} were also corrected for dead time."1048 All cout rates and colors given in the text aud used in the figures are for PCU2 only: for our power spectral analysis we made use of all active PCUs., All count rates and colors given in the text and used in the figures are for PCU2 only; for our power spectral analysis we made use of all active PCUs.1049 Dates will be referred to as days since 2006 January 19 (ALJTD 53751)., Dates will be referred to as days since 2006 January 19 (MJD 53754).1050" Iu Figure 2 we plot RANTE/PCA light curves of Hu two energv bands: ~2 2.9 keV and —9.1 1s.1 keV. corresponding to channels 123 and 2010. respectively,"," In Figure \ref{fig:lc} we plot /PCA light curves of in two energy bands: $\sim$ 2–2.9 keV and $\sim$ 9.4–18.1 keV, corresponding to channels 1–3 and 20--40, respectively."1051 The two light curves have a strikinely different appearance., The two light curves have a strikingly different appearance.1052 Except for the first 30 davs of the outburst aud occasional short drops in iuteusity between davs 30 and 130 (see imset in roffe:leaa). the low-cucrey light curve shows little short- variability.," Except for the first 30 days of the outburst and occasional short drops in intensity between days 30 and 130 (see inset in \\ref{fig:lc}a a), the low-energy light curve shows little short-term variability."1053" Smooth loung-teriu modulations with periods of ~2050 davs are preseut. until the source starts its descent iuto quiescence,"," Smooth long-term modulations with periods of $\sim$ 20–50 days are present, until the source starts its descent into quiescence."1054 The high-cucrey liebt curve. ou the other haud. shows strong short-term flaring. which. as we discuss later. corresponds mostly to motion along the Z source flaring brauch.," The high-energy light curve, on the other hand, shows strong short-term flaring, which, as we discuss later, corresponds mostly to motion along the Z source flaring branch."1055 This flaring starts to weaken around the time at which the lone-term low-enerev nodulatious cud. aud it abruptly subsides when the decay at low energies accelerates (dav d7550).," This flaring starts to weaken around the time at which the long-term low-energy modulations end, and it abruptly subsides when the decay at low energies accelerates (day $\sim$ 550)."1056 After day 7560. the count rates reach a very low. but non-zero. level of ~2 ctsss+ per PCU (full cnerey band).," After day $\sim$ 560, the count rates reach a very low, but non-zero, level of $\sim$ 2 $^{-1}$ per PCU (full energy band)."1057 This residual enüssiou can be attributed to diffuse Calactic cnussion (Fricvikssonetal.2010).. but has not been subtracted from our data.," This residual emission can be attributed to diffuse Galactic emission \citep{frhowi2010}, but has not been subtracted from our data."1058 The times of the three type I N-vav bursts that were detected near the cud of the outburst (Linetal.2009a) are indicated by the short vertical lines in Figure 2.., The times of the three type I X-ray bursts that were detected near the end of the outburst \citep{lialho2009} are indicated by the short vertical lines in Figure \ref{fig:lc}.1059 As shown by II07 and LRIIO0. ddisplavs strong secular changes in its CD aud UID.," As shown by H07 and LRH09, displays strong secular changes in its CD and HID."1060 Creating a single CD/IIID for the cutive outburst results in a complicated set of overlapping tracks with varving shapes (see. eg. Fieure 6 in LRIIO9).," Creating a single CD/HID for the entire outburst results in a complicated set of overlapping tracks with varying shapes (see, e.g., Figure 6 in LRH09)."1061 Tuuc-based selections. such as the ones nude by IIO? and LRITO9. also eucouuter strong secular motion associated with the 20.50 day modulations. which causes the shape aud position of the tracks to change on a time scale of a few davs.," Time-based selections, such as the ones made by H07 and LRH09, also encounter strong secular motion associated with the 20–50 day modulations, which causes the shape and position of the tracks to change on a time scale of a few days."1062" Fortunately, we have found that the low-energv"," Fortunately, we have found that the low-energy"1063of a variely of multi-wavelength distance determinations. which place the host galaxy. at a distance of about 700 kpe. comparable to that of M31. the Andromeda nebula.,"of a variety of multi-wavelength distance determinations, which place the host galaxy at a distance of about 700 kpc, comparable to that of M31, the Andromeda nebula."1064 Consistent wilh its high Galactic latitude. the foreground Galactic extinction towards IC. 1613 appears to be low. with estimates ranging [rom E(D-V) = 0.025 mag (Schlegel οἱ al.," Consistent with its high Galactic latitude, the foreground Galactic extinction towards IC 1613 appears to be low, with estimates ranging from E(B-V) = 0.025 mag (Schlegel et al."1065 1993) to E(D-V) = (0.005 mag (Burstein IIeiles 1932)., 1998) to E(B-V) = 0.005 mag (Burstein Heiles 1982).1066 Cepheids in IC. 1613 were first discovered by. Hubble. Mavall and Daade in the 1930s (as reported by Saucdage 1971). but it was not until about 40 vears later Chat Sandage published Baade's data on that galaxy.," Cepheids in IC 1613 were first discovered by Hubble, Mayall and Baade in the 1930s (as reported by Sandage 1971), but it was not until about 40 years later that Sandage published Baade's data on that galaxy."1067 OF the 59 variable stars reported at least. were considered to be bona fide Cepheids., Of the 59 variable stars reported at least thirty-seven were considered to be bona fide Cepheids.1068 Ouly D-band photographie photometry was available at that (me., Only B-band photographic photometry was available at that time.1069 Carlson Saucage (1990) updated the periods ancl the D-band light curves for 16 of the faintest Cepheids in IC 1613. extending the PL relation down to about 2 davs.," Carlson Sandage (1990) updated the periods and the B-band light curves for 16 of the faintest Cepheids in IC 1613, extending the PL relation down to about 2 days."1070" The first multi-wavelength DVRI CCD observations of Cepheids in IC. 1613 were made by Freedman (1988). allowing a simultaneous fit for the reddening and (rue distance modulus which were determined to be E(B-V) = 0.04-£0.04 mag and jr, = 24.30-0.10 mag. respectivelv."," The first multi-wavelength $BVRI$ CCD observations of Cepheids in IC 1613 were made by Freedman (1988), allowing a simultaneous fit for the reddening and true distance modulus which were determined to be E(B-V) = $\pm$ 0.04 mag and $\mu_o$ = $\pm$ 0.10 mag, respectively."1071 In. (he meantime more recent optical studies of Cepheids in IC. 1613 include the unfiltered. (white light) CCD survevs by Antonello et al. (, In the meantime more recent optical studies of Cepheids in IC 1613 include the unfiltered (“white light”) CCD surveys by Antonello et al. (10721999. 2000). Mantegazza. et al. (,"1999, 2000), Mantegazza, et al. ("10732001). and the VI CCD monitoring project of Udalski et al. (,"2001), and the VI CCD monitoring project of Udalski et al. ("10742001) which raised the numbers of known Cepheids in IC. 1613 to at least 138). and the DVRI sparse-sampling. follow-up study of Antonello et al. (,"2001) which raised the numbers of known Cepheids in IC 1613 to at least 138), and the BVRI sparse-sampling, follow-up study of Antonello et al. ("1075"2006) which concluded (hat E(D-V) = 0.072:0.08 mae and ff, = 24.23-50.20 mag.",2006) which concluded that E(B-V) = $\pm$ 0.08 mag and $\mu_o$ = $\pm$ 0.20 mag.1076" Near infrared H-band observations of 10. Cepheids in IC 1613 were first made by MeA]ary. Madore Davis (1984) giving yr, = 24.8140.12 mag. and these were more recently complemented by a major survey of 29 Cepheids at J aud Ix wavelengths published by Pietazvnski et al. ("," Near infrared H-band observations of 10 Cepheids in IC 1613 were first made by McAlary, Madore Davis (1984) giving $\mu_o$ = $\pm$ 0.12 mag, and these were more recently complemented by a major survey of 29 Cepheids at J and K wavelengths published by Pietrzynski et al. ("10772006).,2006).1078" They derived a reddening of E(B-V) = 0.0940.02 mae and a true distance modulus of jj, = 24.29+0.04 mag.", They derived a reddening of E(B-V) = $\pm$ 0.02 mag and a true distance modulus of $\mu_o$ = $\pm$ 0.04 mag.1079 As part of Guaranteed Time observations Gehrz (PID: 128) obtained a series of observations of IC 1613 resulting in an average integration time of about 16 min/pixel for all four mid-Ih channels., As part of Guaranteed Time observations Gehrz (PID: 128) obtained a series of observations of IC 1613 resulting in an average integration time of about 16 min/pixel for all four mid-IR channels.1080 Six uncrowded Cepheids were measured at the shortest (wo wavelengths., Six uncrowded Cepheids were measured at the shortest two wavelengths.1081 All but two of the Cepheids were either undetected or confused at S.0jan. No Cepheids in IC. 1613 were confidently measured in IC 1613 at 5.8;m. The very long-period (146 day) Cepheid IC 1613:/571]) V22 was measured in all three bands: however its period puts it bevond the limits of our standard calibration aud it was not used in (his determination of a distance {ο IC) 1613., All but two of the Cepheids were either undetected or confused at $\mu$ m. No Cepheids in IC 1613 were confidently measured in IC 1613 at $\mu$ m. The very long-period (146 day) Cepheid IC 1613:[S71] V22 was measured in all three bands; however its period puts it beyond the limits of our standard calibration and it was not used in this determination of a distance to IC 1613.1082 We do note. however. that V22 does conform to the trend noticed for these very long-period Cepheids (known as Leavitt Variables. Grieve. Madore Welch 1985) in that," We do note, however, that V22 does conform to the trend noticed for these very long-period Cepheids (known as Leavitt Variables, Grieve, Madore Welch 1985) in that"10831967).,.1084". The implied accretion rate is about L<10TAL, b (asstmming adiabatic. conservative mass trausfer aud a zero-teniperature equation of state for the secondary star)."," The implied accretion rate is about $4\times 10^{-11} M_\odot$ $^{-1}$ (assuming adiabatic, conservative mass transfer and a zero-temperature equation of state for the secondary star)."1085 At a fiducial distance of «0.5 kpc. the expected eravitatioual wave strain is 2310.7°. which is similar to the Le detection threshold of (c.¢..seerecentdis-cussionsaboutAMCVnbinariesandLZSA. 2005).," At a fiducial distance of $<$ 0.5 kpc, the expected gravitational wave strain is $h > 3\times108610^{-23}$, which is similar to the $1\sigma$ detection threshold of \citep[e.g., see recent discussions about AM~CVn binaries and {\it1087LISA} ."1088 Iu summary. along with the original SDSS AM CVu found bv Roelofsetal.(2001.2005).. the £ additional new SDSS finds presented here provide a vield of 5 SDSS AM CVn candidates thus far: this is a substantial addition to the elite. AM. οδα subclass. compared to the dozen other cases previously known.," In summary, along with the original SDSS AM CVn found by \citet{roe04,roe05}, the 4 additional new SDSS finds presented here provide a yield of 5 SDSS AM CVn candidates thus far; this is a substantial addition to the elite AM CVn subclass, compared to the dozen other cases previously known."1089 Two of these five SDSS objects are also now strougly confirmed as nlizachort-period 1inanes (SDSS J1210-0159 bv Roclofs et al., Two of these five SDSS objects are also now strongly confirmed as ultrashort-period binaries (SDSS J1240-0159 by Roelofs et al.1090 2005. aud J0926]|3621 iu this paper).," 2005, and J0926+3624 in this paper)."1091 SDSS J0926]|23621 reported here is the first coufideut example of au eclipsing AM. CVu., SDSS J0926+3624 reported here is the first confident example of an eclipsing AM CVn.1092 Our initial approximate considerations presented above for SDSS J0926|3621 presage that future detailed modeling of the 28.3 1umute eclipsing liebiteurve aud its long-terui teiiporal stability. double-peaked spectral line profiles. and follow-on radial velocity studies and multivaveleusthi observations. should provide an excellent ορπο] testbed of various models for AM. CV systems.," Our initial approximate considerations presented above for SDSS J0926+3624 presage that future detailed modeling of the 28.3 minute eclipsing lightcurve and its long-term temporal stability, double-peaked spectral line profiles, and follow-on radial velocity studies and multiwavelength observations, should provide an excellent empirical testbed of various models for AM CVn systems."1093pixclization library.,pixelization library.1094 It cau inchide several subroutines aud operating programs., It can include several subroutines and operating programs.1095 The basic program of the second level. shown as a big rectangle. interacts with the first level subroutines.," The basic program ' of the second level, shown as a big rectangle, interacts with the first level subroutines."1096 These subroutines are shown bv small rectaneles aud call external Hibraries for the Foumier transtorm aud Legeudre polynomial calculations., These subroutines are shown by small rectangles and call external libraries for the Fourier transform and Legendre polynomial calculations.1097 The package reads and writes data both in ASCII table aud FITS formats., The package reads and writes data both in ASCII table and FITS formats.1098 More than 10 programs of the GLESP package operate in the GLESP zone., More than 10 programs of the GLESP package operate in the GLESP zone.1099 The prescut development of the package has also parallel calculation nuplemieutation., The present development of the package has also parallel calculation implementation.1100 Visualization procedures in GCL have been developed at IaO. Cambridge.," Visualization procedures in GL have been developed at IaO, Cambridge."1101 Three tests allow us to check the code., Three tests allow us to check the code.1102" The first of them is from the analytical maps to calculate a;,,.", The first of them is from the analytical maps to calculate $a_{\ell m}$.1103 The code reproduces the theoretical Gon better than 10.*., The code reproduces the theoretical $a_{\ell m}$ better than $10^{-7}$.1104" The secoud test is to reproduce an analytical map AG.0)2YuGeo) from a eiven ep, These tests check the caleulatious of the map and spherical cocficicuts incdependcutly."," The second test is to reproduce an analytical map $\Delta T(x,\phi)=Y_{\ell m}(x,\phi)$ from a given $a_{lm}$ These tests check the calculations of the map and spherical coefficients independently."1105 The third test is the reconstruction of αμ after the calculations of the map. ATGre.o). and back.," The third test is the reconstruction of $a_{\ell m}$ after the calculations of the map, $\Delta T(x,\phi)$, and back."1106 This test allows oue to check orthogonality., This test allows one to check orthogonality.1107 If the transformation is based ou really orthogonal functious it has to return after forward and backward calculation the same κ values., If the transformation is based on really orthogonal functions it has to return after forward and backward calculation the same $a_{\ell m}$ values.1108 Precision of the code cau be estimated by introduction of a set of τν=1 and recoustruction of them., Precision of the code can be estimated by introduction of a set of $a_{\ell m}=1$ and reconstruction of them.1109" This test showed that using relation (13)) we can reconstruc the introduced 24;,, with the precision 10.* limited only by sinele precision of float point data recording aud with the precision 10.? for relation (11))."," This test showed that using relation \ref{legm}) ) we can reconstruct the introduced $a_{\ell m}$ with the precision $\sim111010^{-7}$ limited only by single precision of float point data recording and with the precision $\sim 10^{-5}$ for relation \ref{legl}) )."1111 Fie., Fig.1112 7. demonstrates the accuracy of C5 caleulatious using HEALPix audGLESTI?., \ref{hp_compare} demonstrates the accuracy of $C_\ell$ calculations using HEALPix and.1113. It should be noted that unlike the IIEALPix code. the GLESP method does not needed amy iteration for calculation of the αν coefficients and therefore is much faster.," It should be noted that unlike the HEALPix code, the GLESP method does not needed any iteration for calculation of the $a_{\ell m}$ coefficients and therefore is much faster."1114" Our definition of the e;,, coefficients is exactly the same as in HEALDix as an estimator of the anisotropy power spectrui: Auv re-pixelization procedure will cause loss of information and thereby introduce uncertainties aud errors.", Our definition of the $a_{\ell m}$ coefficients is exactly the same as in HEALPix as an estimator of the anisotropy power spectrum: Any re-pixelization procedure will cause loss of information and thereby introduce uncertainties and errors.1115 The GLESP code has procedures for map re- based on two cliffercut methods iu the AT(0.0) domain: the first one consists in averaging," The GLESP code has procedures for map re-pixelization based on two different methods in the $\Delta T(\theta,\phi)$ –domain: the first one consists in averaging"1116is no reason to expect that of those remaining will coutain the true value of the parameter.,is no reason to expect that of those remaining will contain the true value of the parameter.1117 This is because iustead: of suunuaime over all values of iy to eet a probability that exceeds.. we are siunmniug ouly over those values ercater than the detection threshold.," This is because instead of summing over all values of $\nS$ to get a probability that exceeds, we are summing only over those values greater than the detection threshold."1118 This results ina form of aud is ciscussed in detail im rets:eddington.., This results in a form of and is discussed in detail in \\ref{s:eddington}.1119 Tn a Bavesiau setting. probability is used f) quantity uncertainty in knowledge and iu this regard paralucters are typicalv viewed as random quantities.," In a Bayesian setting, probability is used to quantify uncertainty in knowledge and in this regard parameters are typically viewed as random quantities."1120 This distinction leads to amore intuitive interpretation of the credible interva1., This distinction leads to a more intuitive interpretation of the credible interval.1121 A credible interval at the £% level. for exa]e. is auv interval that contains the true value of the parameor EY of the time accoring fo its posterior ¢istribution. (," A credible interval at the $L$ level, for example, is any interval that contains the true value of the parameter $L$ of the time according to its posterior distribution. ("1122See Park et al.,See Park et al.1123 2008 for discussion on interval selection.), 2008 for discussion on interval selection.)1124" Thus. from a Bayοσα perspective, it is proper to sav that there is au L'A chance that the source intensity is coutaimed iu t16 reported credible interval."," Thus, from a Bayesian perspective, it is proper to say that there is an $L$ chance that the source intensity is contained in the reported credible interval."1125 The corresponding credible intervals look similar to he confidence intervals iu Figure 1.. at least i1 Ligh countscenarios’.," The corresponding credible intervals look similar to the confidence intervals in Figure \ref{fig:CI}, at least in high count."1126 So far we have considered a very simple probenm with oulv oue unknown parameter. As.," So far we have considered a very simple problem with only one unknown parameter, $\lamS$."1127 The situation Is more complicated if trere are unknownparameters. such as Ap.," The situation is more complicated if there are unknown, such as $\lamB$."1128 In this case. frequency based intervals typically are constructed using asviiptotic arguments and/or by conditioning on ancillary statistics that vield a conditional sampling distribution tha does not depend on the nuisauce parameter.," In this case, frequency based intervals typically are constructed using asymptotic arguments and/or by conditioning on ancillary statistics that yield a conditional sampling distribution that does not depend on the nuisance parameter."1129 Ideutitving ancillary statistics can be a subtle task aud the resulting intervals may not be unique., Identifying ancillary statistics can be a subtle task and the resulting intervals may not be unique.1130 Bayesian intervals. can be coustructed using a simple and clear principle known as11argiualization.," Bayesian intervals, can be constructed using a simple and clear principle known as."1131 Forexample. if Ap is unknown. the mareinal posterior distribution of As is simply Credible intervals for Ag are computed just as before. but using the marginal posterior distribution.," Forexample, if $\lamB$ is unknown, the marginal posterior distribution of $\lamS$ is simply Credible intervals for $\lamS$ are computed just as before, but using the marginal posterior distribution."1132 Weeuphasize that neither confidence nor credible intervals directly quantity the detection seusitivitv of an experiment., We emphasize that neither confidence nor credible intervals directly quantify the detection sensitivity of an experiment.1133 To do this we cousicer the detecfiou problem in detail. which frou a statistical point of view is a test of the hypothesis tha there is no source emission in the given energy baud. ic. a test of," To do this we consider the detection problem in detail, which from a statistical point of view is a test of the hypothesis that there is no source emission in the given energy , i.e., a test of"1134where Qíqgo) is the Heaviside step function.,"where $\Theta1135{(y_2) }$ is the Heaviside step function."1136 Note that & is the caustic curvature at the origin which enters explicitly into the amplification formula.," Note that $\kappa$ is the caustic curvature at the origin \citep {Gaudi,alzh_03}1137 which enters explicitly into the amplification formula."1138 Formula (16)) vields an effective approximation for the point source magnification near the coordinate origin provided ju yo>0. and οντ is not too small (see the term containing &).," Formula \ref{point amplification}) ) yields an effective approximation for the point source magnification near the coordinate origin provided that $y_2> 0$, and ${y_2}/{y_1^2}$ is not too small (see the term containing $\kappa$ )."1139 For a fixed source position. this can be satisfied always » àn appropriate choice of the coordinate origin. so that the source will be situated almost on a normal to the tangent to 1ο CAUSLIC.," For a fixed source position, this can be satisfied always by an appropriate choice of the coordinate origin, so that the source will be situated almost on a normal to the tangent to the caustic."1140 If the source is on the caustic tangent or in the region between the caustic and the tangent. then formula (16)) does not represent a good approximation to the point source magnification.," If the source is on the caustic tangent or in the region between the caustic and the tangent, then formula \ref{point1141amplification}) ) does not represent a good approximation to the point source magnification."1142 Nevertheless. in case of an extended source. we will show ju result. (16)) can be used to obtain approximations to the amplification of this source even as it intersects the caustic.," Nevertheless, in case of an extended source, we will show that result \ref{point amplification}) ) can be used to obtain approximations to the amplification of this source even as it intersects the caustic."1143 However. to do this. we need to redefine correctly the convolution of (16)) with a brightness distribution.," However, to do this, we need to redefine correctly the convolution of \ref{point amplification}) ) with a brightness distribution."1144 Let L(y) be a surface brightness distribution of an extended source., Let $I({\bmath y})$ be a surface brightness distribution of an extended source.1145 HE the source center is located at the point Y=(3.313) in the source plane. then the total microlensed Dux from the source is where the point source amplification A(y)=SoA; is the sum of amplifications of all the images.," If the source center is located at the point ${\bmath{Y}}=(Y_1,Y_2)$ in the source plane, then the total microlensed flux from the source is where the point source amplification $K( {\bmath y} ) =1146\sum\limits_i {K_i } $ is the sum of amplifications of all the images."1147 The result of using the first integral [rom Iq. (18)), The result of using the first integral from Eq. \ref{flux_extended}) )1148 obviously is equivalent to the result of the well-known ray-tracing method (when the pixel sizes tend to zero)., obviously is equivalent to the result of the well-known ray-tracing method \citep{schneider_92} (when the pixel sizes tend to zero).1149" Near a caustic. one can approximate A(y)=Au|fis fy). where Au is an amplification ofall noncritical images that is supposed to be constant during LAL. and AG, is the amplification of the critical images."," Near a caustic, one can approximate $K( {\bmath y} )=K_0 + K_{cr} (1150{\bmath y})$ , where $K_0 $ is an amplification of all noncritical images that is supposed to be constant during HAE, and $K_{cr}$ is the amplification of the critical images."1151" Formula (16)) contains the non-integrable term OCp)(yo)""7.", Formula \ref{point amplification}) ) contains the non-integrable term $\sim\Theta(y_{2}) ( {y_2 })^{ - 3 /2} $.1152 Therefore. the question arises of how formula (16)) can be used in situation when the extended. source intersects a caustic and some part of the source is in the zone between the tangent and the caustic.," Therefore, the question arises of how formula \ref{point amplification}) ) can be used in situation when the extended source intersects a caustic and some part of the source is in the zone between the tangent and the caustic."1153 In view of Section 3.2.. Ht is evident that the mentioned term is a result of the expansion of the root Viedyp/2| «in the approximate solution (11--14)).," In view of Section \ref{ss2.2}, it is evident that the mentioned term is a result of the expansion of the root $\sqrt1154{y_2 + \kappa y_1^2 t^2/2+...}$ in the approximate solution \ref{new1}- \ref{new1Z}) )."1155 Any non-integrable terms in Avi; does not arise without using this expansion., Any non-integrable terms in $K_{cr}$ does not arise without using this expansion.1156" Lt is easy to show that. in order to define A, correctly. one must replace the term OCyo)Cy)7/2 in (16)) bv the clistribution (generalized function) (jo)77 (Golfand&Shilov1964)."," It is easy to show that, in order to define $K_{cr}$ correctly, one must replace the term $\Theta(y_2)1157( y_2 )^{ - 3 /2} $ in \ref{point amplification}) ) by the distribution (generalized function) $( y_2 )_+^{ - 3/2}$ \citep{Gel'fand_64}."1158.. We recall that the distribution /57 of the variable Hy is defined by the expression [or any test function f(y)., We recall that the distribution $ y _+^{ - 3/2}$ of the variable $y$ is defined by the expression for any test function $f(y)$ .1159 After this redefinition. we have Ες formula can be used to correctly derive an approximate magnification of a sullicientlv smooth extended source including the case where the source crosses the caustic.," After this redefinition, we have This formula can be used to correctly derive an approximate magnification of a sufficiently smooth extended source including the case where the source crosses the caustic."1160 Now we use formula (19)) to derive the magnification of a Gaussian source with the brightness distribution where the parameter £L characterizes the source size., Now we use formula \ref{generalized Kcr}) ) to derive the magnification of a Gaussian source with the brightness distribution where the parameter $L$ characterizes the source size.1161" The amplification of an extended source is defined as the ratio of the lensed Hux (18)) to the Hux of the unlensed source Ly=Ir1(g)dy,dyo which is equal to 1 in case of formula (200).The amplification of a Gaussian source Ive; is obtained by the substitution of (200) and (19)) into (18))"," The amplification of an extended source is defined as the ratio of the lensed flux \ref{flux_extended}) ) to the flux of the unlensed source $F_0 = \int\!\!\!\int I \left( {\rm {\bmath y}}1162\right)dy_1 dy_2 $ which is equal to 1 in case of formula \ref{gaussian distribution}) ).The amplification of a Gaussian source $K_G$ is obtained by the substitution of \ref{gaussian distribution}) ) and \ref{generalized Kcr}) ) into \ref{flux_extended}) )."1163" Further. we introduce thedimensionless coordinates s=Y,/L.hYS/L of the source centre and the functions"," Further, we introduce thedimensionless coordinates $s = Y_1/L,\, h1164= Y_2/ L$ of the source centre and the functions"1165properties.,properties.1166" In order to reproduce the observed properties the mergers are required to happen at high-redshift (z> 1), between progenitors of different mass ratio (at least 3:1) and with a significant fraction of the total mass in the form of gas (Le., >10 percent)."," In order to reproduce the observed properties the mergers are required to happen at high-redshift $z \geq 1$ ), between progenitors of different mass ratio (at least 3:1) and with a significant fraction of the total mass in the form of gas (i.e., $\geq 10$ percent)."1167" However, this formation scenario is not able to recreate the the observed mass-metallicity gradient relation of these low-luminosity galaxies etal. 2009a;; Paper II)."," However, this formation scenario is not able to recreate the the observed mass-metallicity gradient relation of these low-luminosity galaxies \citealt{spolaor09a}; Paper II)."1168" A further interpretation of our results is that low-luminosity galaxies were originally late-type galaxies, whose star formation has been truncated by removal of gas (ie., strangulation) and subsequently the disc has been dynamically heated by high velocity encounters (i.e., galaxy harassment) in the cluster environment."," A further interpretation of our results is that low-luminosity galaxies were originally late-type galaxies, whose star formation has been truncated by removal of gas (i.e., strangulation) and subsequently the disc has been dynamically heated by high velocity encounters (i.e., galaxy harassment) in the cluster environment."1169 Simulations have shown that late-type galaxies entering in a rich cluster can undergo a significant morphological transformation into spheroidals by encounters with brighter galaxiesand the cluster's tidal field (Mooreetal.1996;; Mastropietroetal. 2005))., Simulations have shown that late-type galaxies entering in a rich cluster can undergo a significant morphological transformation into spheroidals by encounters with brighter galaxiesand the cluster's tidal field \citealt{moore96}; \citealt{mastropietro05}) ).1170" In this scenario, we expect the original disc to be dynamically heated by the interactions such that stellar orbits acquire a significant velocity component perpendicular to the disc."," In this scenario, we expect the original disc to be dynamically heated by the interactions such that stellar orbits acquire a significant velocity component perpendicular to the disc."1171 The imprint of their previous morphological nature is preserved in the form of an embedded stellar disc (e.g.; DeRijckeetal.2005: Chilingarianetal. 2008)).," The imprint of their previous morphological nature is preserved in the form of an embedded stellar disc (e.g., \citealt{rijcke03}; \citealt{chilingarian08}) )."1172" For example, Beasleyetal.(2009) reported significant rotation at large radii (i.e., 4—7r.) of two luminous Virgo dwarf ellipticals, using globular cluster systems as tracers of galaxy dynamics."," For example, \cite{beasley09} reported significant rotation at large radii (i.e., $4 -7 r_{e}$ ) of two luminous Virgo dwarf ellipticals, using globular cluster systems as tracers of galaxy dynamics."1173 They show that the detection of such large amount of rotation in the outer galactic regions support the idea that luminous dwarf ellipticals were originally disc galaxies., They show that the detection of such large amount of rotation in the outer galactic regions support the idea that luminous dwarf ellipticals were originally disc galaxies.1174" Numerical simulations (Mastropietroetal. 2005)) predict values of the anisotropy parameter (υ/σ)” similar to those of our galaxies, and also disky isophotes with similar B4 values."," Numerical simulations \citealt{mastropietro05}) ) predict values of the anisotropy parameter $(v/\sigma)^{*}$ similar to those of our galaxies, and also disky isophotes with similar $\overline{B_{4}}$ values."1175" Moreover, the lack of counter rotation and the high incidence of coupled rotation between disc and bulge observed in our sample galaxies may favour a disc-heating scenario, whereby stars of the original disc contribute towards the bulge population while retaining some of the angular momentum."," Moreover, the lack of counter rotation and the high incidence of coupled rotation between disc and bulge observed in our sample galaxies may favour a disc-heating scenario, whereby stars of the original disc contribute towards the bulge population while retaining some of the angular momentum."1176" However, this scenario is more difficult to reconcile with the stellar population properties, and in particular the mass-metallicity gradient relation, observed in our galaxies."," However, this scenario is more difficult to reconcile with the stellar population properties, and in particular the mass-metallicity gradient relation, observed in our galaxies."1177 We expect the star formation to be truncated in the disc due to the interactions., We expect the star formation to be truncated in the disc due to the interactions.1178" Thus, metallicity gradients are required to form in the late-type galaxies and to be somehow preserved during the high velocity encounters."," Thus, metallicity gradients are required to form in the late-type galaxies and to be somehow preserved during the high velocity encounters."1179" We conclude that although the kinematic and isophotal features in our galaxy sample can be interpreted in the context of a morphological transformation from late to early types, further detailed numerical simulations are needed to understand if such a scenario can also explain the stellar population trends observed."," We conclude that although the kinematic and isophotal features in our galaxy sample can be interpreted in the context of a morphological transformation from late to early types, further detailed numerical simulations are needed to understand if such a scenario can also explain the stellar population trends observed."1180 We have investigated the kinematic and photometric properties at large galactocentric radii for a sample of 14 low-luminosity early-type galaxies., We have investigated the kinematic and photometric properties at large galactocentric radii for a sample of 14 low-luminosity early-type galaxies.1181" The radial extent considered in our analysis, ie. ~1— 3re, allows us to"," The radial extent considered in our analysis, i.e. $\sim 1 - 3 r_{e}$ , allows us to"1182with the ereater rate of bGE.2) is dominant all the wav from redshift z* to :.,"with the greater rate of $b(E,z)$ is dominant all the way from redshift $z^\star$ to $z$."1183" The transfer equation is solved (Montiuerle1977). to obtain the CCR energy spectruui from a CR burst at τς, where O;uQE.=@AL.lgjego) is) the normalized flux τνof τν)/ per comoving volune with Q;(E.:.:,)=INE. i). 3 and 3” are the velocities corresponding to enerev E aud £%. respectively."," The transfer equation is solved \citep{mon1977} to obtain the CCR energy spectrum from a CR burst at $z_s$, where $\Phi_{i,{\rm H}}(E,z,z_s)\equiv \Phi_i(E,z,z_s)/n_{\rm H}(z)$ is the normalized flux of $i$ per comoving volume with $\Phi_i(E,z,z_s)\equiv1184\beta N_i(E,z)_{z_s}$ , $\beta$ and $\beta'$ are the velocities corresponding to energy $E$ and $E'_s$, respectively."1185 μη] is the present average nmuuber density of protons iu the universe., $n_{\rm H}^0$ is the present average number density of protons in the universe.1186 © is an effect resulting when the nuclear destruction is considered. aud given as After analysis with Eq. (13)).," $\xi$ is an effect resulting when the nuclear destruction is considered, and given as After analysis with Eq. \ref{eq13}) ),"1187 oue can estimate l9:ΟΙ|epomELS]tldsfeel.1o aud find au expression for c; The production rate of ποτ clement / of energy. E. produced at redshift 2 is elven by where oj);4CE.EY) is a cross section of a process between a CR unclide / with energv per uncleon E aud a backeround species j to make a eiven liebt clement 7 with E. aud »j(:) aud D) are background nunber abuudance of a uuclide j aud KEENnuuber ratio ofj to proton. respectively.," one can estimate $|\partial1188z^\star / \partial E'|_{E'=E'_s}=|b(E'_s,z_s)|^{-1} |dz/dt|_{z=z_s}$ and find an expression for $\Phi_{i, {\rm H}}$ The production rate of light element $l$ of energy $E$ , produced at redshift $z$ is given by where $\sigma_{ij \rightarrow l}(E,E')$ is a cross section of a process between a CR nuclide $i$ with energy per nucleon $E'$ and a background species $j$ to make a given light element $l$ with $E$, and $n_j(z)$ and $K_{jp}^{\rm IGM}(z)$ are background number abundance of a nuclide $j$ and number ratio of $j$ to proton, respectively."1189 When the destruction of the liebt clement / after production is neelected. the total production rate is calculated as wheregit7j|GE!) is the total cross section of a reaction i|po>X. with anv OX.," When the destruction of the light element $l$ after production is neglected, the total production rate is calculated as where $\sigma_{ij \rightarrow l}^{\rm tot}(E')$ is the total cross section of a reaction $i+j \rightarrow l+X$, with any $X$."1190" I adopt cross sections from ReadViola(1981).. aud particularly for the a|α reaction. exponcutial-plus-constaut cross section for | —9Li aud exponential one for { =""Li trom Merceretal. (2001)."," I adopt cross sections from \citet{rea1984}, and particularly for the $\alpha+\alpha$ reaction, exponential-plus-constant cross section for $l=^6$ Li and exponential one for $l=^7$ Li from \citet{mer2001}."1191. The resulting light. clement abundauce is obtained as the CR production added to the BBN vield., The resulting light element abundance is obtained as the CR production added to the BBN yield.1192 The vield by CR uncleosvuthesis is the integration of those produced at z/ πο CRs generated at z4 over +! ando. thus I also caleulate the. LiDoD production i the universe by the secoudarv process. L6. [pn]es [CO]imar >[LiBeBlisar.," The yield by CR nucleosynthesis is the integration of those produced at $z'$ from CRs generated at $z_s$ over $z'$ and $z_s$, thus I also calculate the LiBeB production in the universe by the secondary process, i.e., $p\alpha$ $_{\rm CR}$ $_{\rm1193ISM}\rightarrow$ $_{\rm ISM}$."1194 Since the C. and— ο abundances of the ISALD in structures are about two orders of magnitude higher than those of the ICAL (seeFie.1linDaignueetal.2006).. the secondary LiBeB production in the ICAL is uot important.," Since the C and O abundances of the ISM in structures are about two orders of magnitude higher than those of the IGM \citep[see Fig. 11 in][]{dai2006}, the secondary LiBeB production in the IGM is not important."1195 I expect that the LiBeB abundances in the ISAL are enhanced b a contribution of the secondary process., I expect that the LiBeB abundances in the ISM are enhanced by a contribution of the secondary process.1196 Iu fact. the reactions of [paler Ομ»[LiDeD]i make light elements in the ISALD anc the mass acerction to the structures from the IGAL dilutes the ISM. abuudanuces in the framework of this model involviug a hierarchical structure formation.," In fact, the reactions of $p\alpha$ $_{\rm CR}$ $_{\rm1197ISM}\rightarrow$ $_{\rm ISM}$ make light elements in the ISM and the mass accretion to the structures from the IGM dilutes the ISM abundances in the framework of this model involving a hierarchical structure formation."1198 Note that from the assumption that the confinement of CRs by a iiagnuetic field is ineffective. the CRs do not stav in the structures.," Note that from the assumption that the confinement of CRs by a magnetic field is ineffective, the CRs do not stay in the structures."1199 The πο clement abundances produced by the secondary reactions are then eiven with a parameter: the fraction of barvous at redshift + which are in structures where fpaQM.2) is the distribution function of halos taken from the Sheth&Tormen(1999) inodification the Press-Schechter function (Press&Schechter1971L) converted iuto the mass function (Jemlksinsetal.2001) bv a code provided Jn A. Jenkins (2007. priva5 conmuimnication).," The light element abundances produced by the secondary reactions are then given with a parameter: the fraction of baryons at redshift $z$ which are in structures where $f_{\rm PS}(M,z)$ is the distribution function of halos taken from the \citet{she1999} modification to the Press-Schechter function \citep{pre1974} converted into the mass function \citep{jen2001} by a code provided by A. Jenkins (2007, private communication)."1200 Tassie that the primordial power spectral slope is (—1. the rus amplitucle for mass deusity fluctuations iu a sphere of radius 8 5.1 Mpc is oy=0.9. and the Boud&Efstathiou(1981). fit to the trauster function for cold dark matter is used in geuerating a nass function.," I assume that the primordial power spectral slope is $n$ =1, the rms amplitude for mass density fluctuations in a sphere of radius 8 $h^{-1}$ Mpc is $\sigma_8=0.9$, and the \citet{bon1984} fit to the transfer function for cold dark matter is used in generating a mass function."

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