diff --git "a/batch_s000022.csv" "b/batch_s000022.csv" new file mode 100644--- /dev/null +++ "b/batch_s000022.csv" @@ -0,0 +1,10270 @@ +source,target +. This prescription aims to model the balance between the dissociation of molecules by Lyman-Werner band photons. and the formation of molecules on dust grains.," This prescription aims to model the balance between the dissociation of molecules by Lyman-Werner band photons, and the formation of molecules on dust grains." + We refer the readers to the aforementioned papers for the full derivation. and simply repeat the numerical prescription here.," We refer the readers to the aforementioned papers for the full derivation, and simply repeat the numerical prescription here." + The molecular fraction is given by: for s«2 and fg»= Ofors= 2., The molecular fraction is given by: for $s<2$ and $f_{\rm H2} = 0$ for $s\geq 2$ . +"5=In(1|0.6\0.014 2)/(0.67.). where y=0.76(1|3.12779), and τι=0.066Xa(Μιpe7) Z'."," $s = {\rm ln} +(1+0.6\chi + 0.01\chi^2)/(0.6\tau_{\rm c})$ , where $\chi = +0.76(1+3.1Z'^{0.365})$, and $\tau_{\rm c} = 0.066\Sigma_{\rm + cloud}/(\msun {\rm pc^{-2}})\times Z'$ ." + Z'is the metallicity divided by the solar metallicity., $Z'$is the metallicity divided by the solar metallicity. + This formalism for deriving fg» assumes chemical equilibrium., This formalism for deriving $f_{\rm H2}$ assumes chemical equilibrium. + It is worth a quick note that there are numerous prescriptions for determining the bbalance in the ISM of simulations. some of which include time-dependent chemistry.," It is worth a quick note that there are numerous prescriptions for determining the balance in the ISM of simulations, some of which include time-dependent chemistry." + developed an empirical pressure-based methodology for calculating the ffraction in the neutral ISM. based on observations of local galaxies.," developed an empirical pressure-based methodology for calculating the fraction in the neutral ISM, based on observations of local galaxies." + Similarly. both semi-analytic models2009).. as well as full numerical solutions exist which model the effect of dissociating photons through models of galaxies2010).," Similarly, both semi-analytic models, as well as full numerical solutions exist which model the effect of dissociating photons through models of galaxies." +. We motivate our usage of the analytic prescription of for two reasons., We motivate our usage of the analytic prescription of for two reasons. + First. some observational evidence suggests that on small scales (< is only mareially detected in the GSD spectrin., We only use the 3 UDS spectra as $\beta$ is only marginally detected in the GSD spectrum. + The enussion line ratios are remarkably similar for all 3 objects: IL) contributes 1/8 to the combined line huninosity. sugeesting a very low ietallicity (sec.e.g...Salzeretal.2005:Amorin2010.for conrparisons)..," The emission line ratios are remarkably similar for all 3 objects: $\beta$ contributes 1/8 to the combined line luminosity, suggesting a very low metallicity \citep[see, e.g.,][for +comparisons]{salzer05, amorin10}." + Because the flux is dominated by the lino aud is therefore more directly related to our |OII]s007observations. we show the inferred συν EWs in Figure 5. (also sce Table 13).," Because the flux is dominated by the $_{5007}$ line and is therefore more directly related to our observations, we show the inferred $_{5007}$ EWs in Figure \ref{mv_ew} (also see Table \ref{tab}) )." + However. we model the observations by fitting the inferred IL) EWs to the SB99 predictions.," However, we model the observations by fitting the inferred $\beta$ EWs to the SB99 predictions." + These are assumed to be always l/sth of the combined EW., These are assumed to be always 1/8th of the combined EW. + The unavoidable iutrinsic scatter in this couversion is, The unavoidable intrinsic scatter in this conversion is +Empirical mass loss formulas are pivotal lor the construction of empirical and semiempirical stellar atmosphere and wind models. stellar evolution computations and studies of the interstellar medium. among other (topics.,"Empirical mass loss formulas are pivotal for the construction of empirical and semiempirical stellar atmosphere and wind models, stellar evolution computations and studies of the interstellar medium, among other topics." +" Historically. the mass loss rate M ol late-tvpe elants and supergiants has been described by “Reimers” law’. given as M=jrDE 1971).. with L.. R,. M, as stellar luminosity. raclius. and mass. respectively. given in solar units. and 7 is a fitting parameter."," Historically, the mass loss rate $\dot{M}$ of late-type giants and supergiants has been described by “Reimers' law"", given as $\dot{M} = \eta \cdot \frac{L_* R_*}{M_*}$ \citep{rei75,rei77}, , with $L_*$, $R_*$, $M_*$ as stellar luminosity, radius, and mass, respectively, given in solar units, and $\eta$ is a fitting parameter." + Other empirical mass loss formulas have been presented by Lamers(1981).. deJager.Nieuwenhuijzen.&vanderIlucht (1983).. and Nieuwenhuijzen&deJager(1990).. but they do not distinguish between the strong. ancl now well-described dust-driven winds (e.g.Wachterοἱal.2002).. ancl the physically. very dillerent case of nondust-driven winds.," Other empirical mass loss formulas have been presented by \cite{lam81}, \cite*{dej88}, and \cite{nie90}, but they do not distinguish between the strong, and now well-described dust-driven winds \cite[e.g.,][]{wac02}, and the physically very different case of nondust-driven winds." + Despite its wide-ranging success. (he mass loss formula by Reimers sulfers [rom two important deficiencies.," Despite its wide-ranging success, the mass loss formula by \citeauthor{rei75} suffers from two important deficiencies." + First. it is solely based. on dimensional scaling arguments without anv physical interpretation.," First, it is solely based on dimensional scaling arguments without any physical interpretation." + In. particular. the appearance of (he stellar luminosity in the formula is awkward noting that for cool star winds. with the exception of molecule-driven and cdust-diven winds. the huninosity of the star is not expected to be relevant 1985).," In particular, the appearance of the stellar luminosity in the formula is awkward noting that for cool star winds, with the exception of molecule-driven and dust-driven winds, the luminosity of the star is not expected to be relevant \cite[e.g.,][]{hol85}." +". In fact. the Reimers law seems (o suggest that a certain fraction of the stellar luminosity L, is utilized to lift the wind material from (he photosphere."," In fact, the Reimers law seems to suggest that a certain fraction of the stellar luminosity $L_*$ is utilized to lift the wind material from the photosphere." + The second deficiency. consists in the necessity of adjustimg the fitting parameter η. as different 7 values are required ad hoe (o match observed mass-Ioss rates from different tvpes of giants and supergiants.," The second deficiency consists in the necessity of adjusting the fitting parameter $\eta$, as different $\eta$ values are required ad hoc to match observed mass-loss rates from different types of giants and supergiants." + The same is (rue. if reasonable mass loss vields and final masses are {ο be achieved through stellar evolution models with prescribed mass loss.," The same is true, if reasonable mass loss yields and final masses are to be achieved through stellar evolution models with prescribed mass loss." + For more evolved AGB egiants. the Reimers relation is better replaced by. e.g.. deJagerοἱal.(1983).. which sugeests up to three times as much mass-loss for the tip-AGB (Schroder&Sedlmavr2001).," For more evolved AGB giants, the Reimers relation is better replaced by, e.g., \cite{dej88}, which suggests up to three times as much mass-loss for the tip-AGB \citep{schr01}." +. More recently. the Reimers relation also fails to describe revised mass loss rates [rom Ix ancl AL eiant stars. based on updated Ca II ionization balances which consider photoionization raciation deduced from FUSE spectra (larperetal.2004).," More recently, the Reimers relation also fails to describe revised mass loss rates from K and M giant stars, based on updated Ca II ionization balances which consider photoionization radiation deduced from FUSE spectra \citep{har04}." +. For further updated information on mass-loss mechanisms see. e.g.. the review by Willson(2000).," For further updated information on mass-loss mechanisms see, e.g., the review by \cite{wil00}." +. In the present work. we overcome these deficiencies bv adopting a more physical picture.," In the present work, we overcome these deficiencies by adopting a more physical picture." + In our approach. the non-radiative energy input into the wind is assumed to be given by the turbulent energy. density. within the chromosphere or underneath. possibly related to the manifestation of (magneto-)acoustic waves.," In our approach, the non-radiative energy input into the wind is assumed to be given by the turbulent energy density, within the chromosphere or underneath, possibly related to the manifestation of (magneto-)acoustic waves." + This approach appears to be consistent with the major conclusion by Judge&Stencel(1991).. who presented a detailed empirical analysis of the global thermodyvnanmical properties of the outer atmosphlieres and. winds of a set of well-studied cool giant and supergiant stars.," This approach appears to be consistent with the major conclusion by \cite{jud91}, who presented a detailed empirical analysis of the global thermodynamical properties of the outer atmospheres and winds of a set of well-studied cool giant and supergiant stars." + They concluded that7[...] mass loss rates are not strongly dependent on the actual physical processes driving the winds [suggesting] that, They concluded that“[...] mass loss rates are not strongly dependent on the actual physical processes driving the winds [suggesting] that +The preseuce of absorbing material alone the iue of sight is generally believed. to be the only difference between Type 2 and a Type 1 Active Calactic Nuclei (AGN).,The presence of absorbing material along the line of sight is generally believed to be the only difference between Type 2 and a Type 1 Active Galactic Nuclei (AGN). + This material obscures oth the cussion lines from) the Broad Line Reeion (BLR) aud the N-rav spectrum. being he main ineredient5 of the so-called Unificatiou Model.," This material obscures both the emission lines from the Broad Line Region (BLR) and the X-ray spectrum, being the main ingredient of the so-called Unification Model." + It is usually euvisaged as a compact ‘tors’. ocated at a peo scale distance from the nucleus (e.g.2)..," It is usually envisaged as a compact `torus', located at a pc scale distance from the nucleus \citep[e.g.][]{antonucci93}." +" This distance is basically confirmed both wo dudiect techniques. such απ considerations owed on photoionization codes (e.g.?77).. aud direct imaeiueoe of the torus itself (οι,°?).. IToor therewo"," This distance is basically confirmed both by indirect techniques, such as considerations based on photoionization codes \citep[e.g.][]{bmi01,mass06}, and direct `imaging' of the torus itself \citep[e.g.][]{jaffe04}." + oqueds expeselenceoidcne that. thisla simplc«d5 scenario NOVO.mav not hold for all objects.," However, there is evidence that this simple scenario may not hold for all objects." +" The a. Compton-thick -torus ⋅aud∖↽↴∖⊳∖∢ a ""mECompton cii 2,≓⊳↽⋅⋈⋠thin material. on a nmch larger scale. seenis to better account extendedfor the observed pheuoumnenoloss (ee.2h."," The co-existence of a Compton-thick torus and a Compton-thin material, extended on a much larger scale, seems to better account for the observed phenomenology \citep[e.g.][]{matt00b}." +" The latter absorber mav be naturalh associated to dust-lanes (οιο,» 2).. or to molecular eas in. the ealactic. disks. (7).."," The latter absorber may be naturally associated to dust-lanes \citep[e.g.][]{mvr98}, , or to molecular gas in the galactic disks \citep{lamastra06}." + The presence of. obscuring1. matterHt on 1laree AM--(pe-kpe)] scales1 iuxi detached from the unclear torus is also supported . ↴⋝↖↽∣≲∣⇂∣↑−↙↙↕∣⊽↴∖↴↑⋯∐↸∖↴∖↴∪↕⋀∖∐↕↴↕∏∐∐∐∪∏↴∖↴≺∣∏⋜↧↴∖↴⋜∐⋅↴∖↴⋜↧↑; ⋅ hnieh⋅⋅ z which⋅ are very likely. hosted bv dusty ealaxies− (c.g.⋅⋅2?) Mor ο”... Jtat a anuabo: of Sevtert 2s presents showsignificantd variabilitylarge of the absorbing cobluun deusitv (Ng) on timescales as low as months. thus sugeesting that the absorbing material. should be ich closer to the uucleus than . ⋅ ⋅ pl ⋅⊔∪↥⋅⋯∐↖↽⇀−∙↖↖↽↸∖∐⋅≺⊔∪↴∖↴↸∖≼⋪↧↴∖↴↥⋅⋪⊔," The presence of obscuring matter on large (pc-kpc) scales and detached from the nuclear torus is also supported by studies of MIR luminous quasars at high z which are very likely hosted by dusty galaxies \citep[e.g.][]{poll08,ms06} + Moreover, \citet{risa02b} showed that a large number of Seyfert 2s presents significant variability of the absorbing column density $\mathrm{N_H}$ ) on timescales as low as months, thus suggesting that the absorbing material should be much closer to the nucleus than assumed for the torus, possibly in the BLR itself." +∖∩⊾↖↽ picture ↴⋅⋅secs the ouly tenable for the. objects. .o ⋅⇁ ⋅⋅ list↥⋅∪⋯↓↖∏∖↸∖↨↘↽↑∪⋜∏⋝∪∏↑∩⋯∪∐↑∐∖↴∙⋜↧∐∪↖↖↽∐↓∶↴⋁∏↴∖↴ within davs- or even hours: NGC 1388NN ]o (C2). NGC 1365 (2) and NOC 1151 (2)...," This picture seems the only tenable for the objects, which present the most rapid $\mathrm{N_H}$ variations ever observed, within days or even hours: NGC 4388 \citep{elvis04}, NGC 1365 \citep{ris05} and NGC 4151 \citep{puc07}." + Is this the cud of the torus paradie1i?, Is this the end of the torus paradigm? + Or is it only au exception on a laudful of peculiar objects?, Or is it only an exception on a handful of peculiar objects? + NGC“cic are7582 (z=0.0053).ra being ∙∙included iu. the ? catalog. has targeted by most Acay Clescopes: been (%).. (2). CH). Einstei," NGC 7582 (z=0.0053), being included in the \citet{pic82} catalog, has been targeted by most X-ray telescopes: \citep{mp81}, \citep{tp89}, \citep{war93}, \citep{schac98,xue98}." +nThe (?).. emerged Cringefron hese studies4 was that of a pictureflat thatS-ray spectrum dominated by heavy obscuration., The picture that emerged from these studies was that of a flat X-ray spectrum dominated by heavy obscuration. + Thauks to the -BeppoSAN⋟∏∙DEM broad‘ baudpass.ALL: .? reported] for. he first time∙ the detection ofj a more couples geometryeconmoetrv of the absorbing material. likely constituteconstituted w two differentof components. one of which This scenario was confirmed by a combined inaeiug analysis performed with andHST.. which suggested. that the Conptou-thick orus coexists with a large-scale Comptou-tlin naterial associated with the dust lane aud cireumnelear eas is photoionized by the ACN alone torus-free LBies of sight (?)..," Thanks to the BeppoSAX broad bandpass, \citet{turn00} reported for the first time the detection of a more complex geometry of the absorbing material, likely constituted by two different components, one of which This scenario was confirmed by a combined imaging analysis performed with and, which suggested that the Compton-thick torus coexists with a large-scale Compton-thin material associated with the dust lane and circumnuclear gas is photoionized by the AGN along torus-free lines of sight \citep{bianchi07b}." + The most interesting results came frou the alysis of the two observations. aken [ wears apart. in 2001 aud 2005 (7).," The most interesting results came from the analysis of the two observations, taken 4 years apart, in 2001 and 2005 \citep{pico07}." +. Both clearly show a completely different spectral and Hux state with respect to the 1998 BeppoSAX 6sorvation., Both clearly show a completely different spectral and flux state with respect to the 1998 BeppoSAX observation. + The spectrum can ve well described by a imodel consisting of a conibination. of. a heavily. absorbed (Ng-~--107! chiz7) power law aud a pure reflection. component. soth obseured. by a column density of few ο1022 ," The spectrum can be well described by a model consisting of a combination of a heavily absorbed $\mathrm{N_H}\sim10^{24}$ $^{-2}$ ) power law and a pure reflection component, both obscured by a column density of few $\times10^{22}$ $^{-2}$." +"Notably.of ? detect a significant iucrease oa factor ~2 in the cohuun density of the inner, thicker absorber covering the primary ray source, between 2001 and 2005."," Notably, \citet{pico07} detect a significant increase by a factor $\sim2$ in the column density of the inner, thicker absorber covering the primary X-ray source, between 2001 and 2005." + Iu this paper. we preseut a monitorug canrpaign. of DAP.NGC Lr7582. which.. together with. a now observation.. confinus the ↖↽⋜∐⋅↕⋜∏⋝↕∐↑⋅↖↽∪↕↑∐↸∖⋯↕⋯⊔∐≼∐∖∐↴∖↴↕↑⋅↖↽∪↕↑∐↸∖∐∐∐∖↥⋅⋅⋅⋅ . . . . absorber. but down to timescales⋅ smaller thia clay.," In this paper, we present a monitoring campaign of NGC 7582, which, together with a new observation, confirms the variability of the column density of the inner absorber, but down to timescales smaller than a day." + During⋅⋝ the second Aunouncecmieut of. 0BODENtunity ⋜↧↴∖↴↴∖↴⋯⊔↸∖≼⊔∪↥⋅∐↸∖↑∪↥⋅∏↴∖↴∙↻∪↴∖↴↴∖↴↕↴⋝↕∙↖⇁∐↕↑∐↸∖↕≧∫⇀↕⊰↕↑↴∖↴↸∖∐∙(A02) Ni .. beat observe NGC 7582 prepat different timescales. This . . ↖↖⇁∐↕↸⊳↕⊓∐⋅↸∖↴∖↴↸∖∐↑↑∐∖⋯∪↴∖↴↑↥⋅⋜∏⋯↧⋀∖∐↖↽⋜∐⋅↕⋜↕⊓∪∐↴∖↴↸∖↖⇁↸∖↥⋅ . . probe ‘distances as1| :close asthe ‘the BLEBLR iau observed.⋅⋅ almost as far as the traditional torus.," During the second Announcement of Opportunity (AO2), we proposed a strategy to observe NGC 7582 at different timescales, from 1 week to about 6 months, allowing us to probe distances as close as the BLR and almost as far as the traditional torus." + Moreover. his campaign complemented the scales of the order of vears already. tested withNewton.," Moreover, this campaign complemented the scales of the order of years already tested with." + Therefore. NGC 7582 was observed four tics v du 2007 (PE AL Cliaberee): on Max Ist aud 28th. aud November 9th aud 16th.," Therefore, NGC 7582 was observed four times by in 2007 (PI: M. Chiaberge): on May 1st and 28th, and November 9th and 16th." +" rav huagine Spectrometer (NIS) aud IbLbud X-rav Detector (IND) event files were reprocessed with the latest calibration files available (2008- release). using 6.5 and Suzaku software.VersionEP 9. adopting"" standard filtering:∙⋡"," X-ray Imaging Spectrometer (XIS) and Hard X-ray Detector (HXD) event files were reprocessed with the latest calibration files available (2008-07-09 release), using 6.5 and Suzaku softwareVersion 9, adopting standard filtering procedures." + Source⋅ ⋅↴↴⋅and background spectran for procedures. all the three NIS“Te detectors were extracted frou. circular regions of 2.9 arcnmün radius. avoiding," Source and background spectra for all the three XIS detectors were extracted from circular regions of 2.9 arcmin radius, avoiding" +Tn ow sample 59% of the X-ray detected Sevfert 1 ealaxies show significant N-rvav variability during the ROSAT AlbSky Survey aud ROSAT pointed observations.,In our sample $59\%$ of the X-ray detected Seyfert 1 galaxies show significant X-ray variability during the ROSAT All-Sky Survey and ROSAT pointed observations. + The corresponding X-rav light curves are shown in Appcuclix AppendixC:.., The corresponding X-ray light curves are shown in Appendix \ref{tables_light}. +" Iu Πο,", In fig. + 7 we compare the ROSAT All-Sky Survey count rate with the count rate measured iu ROSAT PSPC pointed observations., \ref{fig_varias1} we compare the ROSAT All-Sky Survey count rate with the count rate measured in ROSAT PSPC pointed observations. + The most extreme factor of variability is found for NCC 3516 (a factor of about 33 ou a timescale of 718 days)., The most extreme factor of variability is found for NGC 3516 (a factor of about 33 on a timescale of 718 days). + For interacting and isolated Sevtert 2 ealaxies no indication for significant X-ray variability on timescales above 0.5 vears is found by comparing the ROSAT AII-Sky Survey and ROSAT PSPC pointed observations (Fie. S))., For interacting and isolated Seyfert 2 galaxies no indication for significant X-ray variability on timescales above 0.5 years is found by comparing the ROSAT All-Sky Survey and ROSAT PSPC pointed observations (Fig. \ref{fig_varias2}) ). + The galaxy NGC 5506 is classified by Lipovetski ct al. (, The galaxy NGC 5506 is classified by Lipovetski et al. ( +1987) as Sevtert type 2.,1987) as Seyfert type 2. + This source exhibits the largest factor of variability of about 2.7 on a timescale of 375 clays., This source exhibits the largest factor of variability of about 2.7 on a timescale of 375 days. + ILowever. for three out of the 36 Sevfert 2 ealaxies. NGC 10685. NGC. [388 and ΠΑΡ FOI175-07I0. indications for X-ray variability are) found iu ROSAT pointed observations.," However, for three out of the 36 Seyfert 2 galaxies, NGC 1068, NGC 4388 and IRAS F01475-0740, indications for X-ray variability are found in ROSAT pointed observations." + In fig. (op) the pointed observation light curve o [the Sevfert 2 galaxy NCC LOGS is shown., In \ref{fig_NGC1068} ) the pointed observation light curve of the Seyfert 2 galaxy NGC 1068 is shown. + An Increase in count rate from 1.823 to 2.080 countss |. correspouding to a factor of 1.11 or Acps=0.256. within 2cays is detected.," An increase in count rate from 1.823 to 2.080 $\rm counts\;s^{-1}$ , corresponding to a factor of 1.14 or $\Delta\rm cps = 0.256$, within 2days is detected." + A coustant model fit using the 4? test cau be rejected with a probability of 99.83%. corresponding to 30.," A constant model fit using the $\chi^2$ test can be rejected with a probability of $99.83\%$, corresponding to $\sigma$." + Tndicatious for N-rav variability in NGC 1068 are also found in other pointed observations (cf., Indications for X-ray variability in NGC 1068 are also found in other pointed observations (cf. + fig. Bj)., fig. \ref{fig_NGC1068b}) ). + The ROSAT PSPC lieht curve for the Sevfert 2 ealaxy IRAS 01175-0718 is shown in fig., The ROSAT PSPC light curve for the Seyfert 2 galaxy IRAS 01475-0748 is shown in fig. + 9. Griddle)., \ref{fig_NGC1068} ). + A decrease m the count rate from 1.061 to 0.021 countss+ within 12.9 hours is detected., A decrease in the count rate from 0.064 to 0.021 $\rm counts\;s^{-1}$ within 12.9 hours is detected. + This variability correspouds to a factor of 3 aud to a chanee iu the count rate of Acps=0.013., This variability corresponds to a factor of 3 and to a change in the count rate of $\Delta\rm cps = 0.043$. + A constant model fit eives a probability of (1o)., A constant model fit gives a probability of $\%$ $\sigma$ ). + Iu fie., In fig. + 9 (bottom) the ταν light curve of NGC [388 is shown., \ref{fig_NGC1068} ) the X-ray light curve of NGC 4388 is shown. + The count rate decreases from 0.0586 to 0.0322 countss! corresponding to a factor of variabilitv of about 1.8 aud a chauge in the count rate of Acps=0.026 within 21 days., The count rate decreases from 0.0586 to 0.0322 $\rm counts\ s^{-1}$ corresponding to a factor of variability of about 1.8 and a change in the count rate of $\Delta \rm cps = 0.026$ within 21 days. +" A constant model fit can be rejected with a probability of 97.5964. corresponding to 2a,"," A constant model fit can be rejected with a probability of $\%$, corresponding to $\sigma$." + Recently. Ceorgantopoulos Papadakis (2000) found evidence for spectral (and timing) variability for four Sevtert 2 ealaxics in RATE observations.," Recently, Georgantopoulos Papadakis (2000) found evidence for spectral (and timing) variability for four Seyfert 2 galaxies in RXTE observations." +the Spruit-Tayler dyanamo.,the Spruit-Tayler dyanamo. + The binary system initially consists of a 18Meo star and a 17Mo star in a 4 day orbit., The binary system initially consists of a $18~\mathrm{M_\odot}$ star and a $17~\mathrm{M_\odot}$ star in a 4 day orbit. +" Mass transfer starts at t=8.09x10°yr, when the helium mass fraction in the hydrogen burning core has increased to 0.94."," Mass transfer starts at $t= 8.09 +\times 10^{6}~\mathrm{yr}$, when the helium mass fraction in the hydrogen burning core has increased to 0.94." +" The mass transfer rate rises up to 8x10-4 Moyr-!, which roughly corresponds to M1/tTKH1 where M; and tTxKH,1 denote the mass and the Kelvin-Helmoltz time scale of the primary star, respectively."," The mass transfer rate rises up to $8\times10^{-4}~\mathrm{M_\odot yr^{-1}}$ , which roughly corresponds to $M_\mathrm{1}/\tau_\mathrm{KH,1}$ where $M_\mathrm{1}$ and $\tau_\mathrm{KH,1}$ denote the mass and the Kelvin-Helmoltz time scale of the primary star, respectively." + The primary mass decreases to 7.5Mo by the end of the Case A transfer (see Fig. 4))., The primary mass decreases to $7.5~\mathrm{M_\odot}$ by the end of the Case A transfer (see Fig. \ref{fig:chem}) ). + The second Roche-lobe overflow begins at t=8.513x10°yr when the envelope of the primary star expands due to hydrogen shell burning during the helium core contraction phase (Case AB mass transfer)., The second Roche-lobe overflow begins at $t= 8.513\times 10^{6}~\mathrm{yr}$ when the envelope of the primary star expands due to hydrogen shell burning during the helium core contraction phase (Case AB mass transfer). +" The primary star loses most of the hydrogen envelope as a result, exposing its helium core of 3.95Mo having a small amount of hydrogen (My=0.04 Μο)) in the outermost layers, as shown in the third panel of Fig. 4.."," The primary star loses most of the hydrogen envelope as a result, exposing its helium core of $3.95~\mathrm{M_\odot}$ having a small amount of hydrogen $M_\mathrm{H} = +0.04$ ) in the outermost layers, as shown in the third panel of Fig. \ref{fig:chem}." +" Although the star remains compact (R«0.9 Ro) during core helium burning, helium shell burning activated after core helium exhaustion leads to the expansion of the envelope up to ~12Ro (see Fig. 3))"," Although the star remains compact $R < 0.9~\mathrm{R_\odot}$ ) during core helium burning, helium shell burning activated after core helium exhaustion leads to the expansion of the envelope up to $\sim 12~\mathrm{R_\odot}$ (see Fig. \ref{fig:hrseq9}) )" + during core carbon burning., during core carbon burning. +" A Case ABB mass transfer does notoccur, however, due to the large orbital separation (A=~121 Ro) at this stage, while it does"," A Case ABB mass transfer does notoccur, however, due to the large orbital separation $A = \sim +121~\mathrm{R_\odot}$ ) at this stage, while it does" +(6)) and (7)). but using the full 7-parameter Kepler formalism. not just the three Ixepler parameters displaved in equations (1)) aud (5)).,"\ref{eqn:bij}) ) and \ref{eqn:fi}) ), but using the full 7-parameter Kepler formalism, not just the three Kepler parameters displayed in equations \ref{eqn:basicform}) ) and \ref{eqn:trueform}) )." + That is. even though the adopted orbits are circular ancl edge-on. I allow for [vee fits to the eccentricity and inclination. ancl so [or correlations between (hese parameters (as well as the (wo remaining Kepler parameters) and (he parameters of interest (aunplitude and period).," That is, even though the adopted orbits are circular and edge-on, I allow for free fits to the eccentricity and inclination, and so for correlations between these parameters (as well as the two remaining Kepler parameters) and the parameters of interest (amplitude and period)." + The effect of allowing for these covariances is lo increase (he errors in semi-unplitude ancl period bv modest amounts relative to what would be obtained using equation (5))., The effect of allowing for these covariances is to increase the errors in semi-amplitude and period by modest amounts relative to what would be obtained using equation \ref{eqn:trueform}) ). + Panels(a) and (b) of Figure 1. show the ratios of the true errors for the amplitude aud period. respectively. relative to the naive equations (8)) aud (9)). for both the RV (green) and astrometric (red) cases.," Panels(a) and (b) of Figure \ref{fig:apm} show the ratios of the true errors for the amplitude and period, respectively, relative to the naive equations \ref{eqn:massfrac}) ) and \ref{eqn:periodfrac}) ), for both the RV ) and astrometric ) cases." + In fact. as Ε will discuss in 4.. for P?=T. the errors depends on phase as well as period.," In fact, as I will discuss in \ref{sec:phase}, for $P\ga T$, the errors depends on phase as well as period." + Figure 1l therefore shows the root-mean-square of the errors. averaged over all phases.," Figure \ref{fig:apm} therefore shows the root-mean-square of the errors, averaged over all phases." + Note that the RV amplitude errors follow the naive form until P/T~LA and then deteriorate relatively gracefullv., Note that the RV amplitude errors follow the naive form until $P/T\sim 1.1$ and then deteriorate relatively gracefully. + By contrast. the astrometric errors beein deviaüng al P/T~0.75 and then deteriorate much more quickly," By contrast, the astrometric errors begin deviating at $P/T\sim 0.75$ and then deteriorate much more quickly." + For the period errors. deterioration begins al P/1~0.85 for RV and 2/7~0.65 for astrometry. but the overall pattern is qualitatively similar.," For the period errors, deterioration begins at $P/T\sim 0.85$ for RV and $P/T\sim 0.65$ for astrometry, but the overall pattern is qualitatively similar." + The mass estimates for astrometry and RY depend on dillerent combinations of amplitude and period. Ilence the fractional error in the mass (or misin/ in the case of BV) is related to the errors in (he [it parameters bv In the limit P«&T. e(m)/m—ofay)/ay. but for P2 T. the period error and the correlations become important.," The mass estimates for astrometry and RV depend on different combinations of amplitude and period, Hence the fractional error in the mass (or $m\sin i$ in the case of RV) is related to the errors in the fit parameters by In the limit $P\ll T$, $\sigma(m)/m\rightarrow \sigma(a_1)/a_1$, but for $P\ga T$ , the period error and the correlations become important." + Figure lec shows the results of caleulations that apply equation (11))., Figure \ref{fig:apm}c c shows the results of calculations that apply equation \ref{eqn:masscovar}) ). + Ol course. (he star may have more (han one companion (planetary or otherwise). and one may imagine arbitrarily complicated configurations.," Of course, the star may have more than one companion (planetary or otherwise), and one may imagine arbitrarily complicated configurations." + Here I restrict myself to the next level of complication. a second companion that is sufficiently [ar away Chat its effect on the star may be (treated as uniform acceleration.," Here I restrict myself to the next level of complication, a second companion that is sufficiently far away that its effect on the star may be treated as uniform acceleration." + Even if no such acceleration is identified. one might decide to fit lor it on the grounds that there aay be such a companion that has," Even if no such acceleration is identified, one might decide to fit for it on the grounds that there be such a companion that has" +low mass stars. the material does not form stars but remains as cooled gas. or the cooling flow model is incorrect.,"low mass stars, the material does not form stars but remains as cooled gas, or the cooling flow model is incorrect." + Consequently. (here was considerable excitement when X-ray observations Claimed (o discover large amounts of cooled gas in galaxy. clusters wilh approximately (he masses expected from a long-lived cooling flow (Whiteetal.1991). (hereafter WFJMA).," Consequently, there was considerable excitement when X-ray observations claimed to discover large amounts of cooled gas in galaxy clusters with approximately the masses expected from a long-lived cooling flow \citep{wfjma} (hereafter WFJMA)." + Thev used Einstein SSS data [or 21 clusters. corrected for a (üme-dependent ice build-up. and their spectral fits vielded an absorption column which they compared to the Galactic value obtained from the large-beam Bell Labs survey (Starketal.1992)..," They used Einstein SSS data for 21 clusters, corrected for a time-dependent ice build-up, and their spectral fits yielded an absorption column which they compared to the Galactic value obtained from the large-beam Bell Labs survey \citep{sgwblhh}." + About half of the clusters (12/21) had. N-ray. absorption columns in excess of (he Galactic HI column bv al least 3o. and the excess was correlated with the deduced rate of cooling gas.," About half of the clusters (12/21) had X-ray absorption columns in excess of the Galactic HI column by at least $3\sigma$, and the excess was correlated with the deduced rate of cooling gas." + The mass of absorbing gas within the cluster was determined to be 3xLOM—10.AL... which is approximately the amount of cooled gas that would be produced by a cooling flow over its lifetime.," The mass of absorbing gas within the cluster was determined to be $3\tenup{11}-10^{12}$, which is approximately the amount of cooled gas that would be produced by a cooling flow over its lifetime." + The WFJMA study led to searches at other wavelengths for cold gas in cooling flow clusters. since LOM—107 oo! III or wwould be easily detected. if ils properties were simular to Galactic eas.," The WFJMA study led to searches at other wavelengths for cold gas in cooling flow clusters, since $10^{11}-10^{12}$ of HI or would be easily detected if its properties were similar to Galactic gas." + Observational searches for HI usually vielded upper limits (Jalfe1987.1991:Dwarakanath.vanGorkom&Owen1994:ODea.Gallimore&Bani 1995).. and when HI was detected. it was (vpically two orders of magnitude lower than the expected HI mass 1995)..," Observational searches for HI usually yielded upper limits \citep{jaf87,jaf91,dvo,ogb}, and when HI was detected, it was typically two orders of magnitude lower than the expected HI mass \citep{jaf90,mob,ngjh,hjn}." + One concern was that the ILE mieht have a velocity dispersion similar to the cluster. making it difficult to detect in narrow bandwidth studies.," One concern was that the HI might have a velocity dispersion similar to the cluster, making it difficult to detect in narrow bandwidth studies." + ILowever. a recent wide bandwidth search for III rules out such emission. (wpically at a level of 5xLO? citepopk..," However, a recent wide bandwidth search for HI rules out such emission, typically at a level of $5\tenup{9}$ \\citep{opk}." + searches [ον molecular hydrogen have often focused on emission or absorption Irom CO millimeter lines. which have led to stringent upper limits (AleNamara&Jaffe1994:ODeaetal.1994:Braine&DuprazDraine 1995).," Searches for molecular hydrogen have often focused on emission or absorption from CO millimeter lines, which have led to stringent upper limits \citep{mj,obmts,bd,bwrhl}." +. Recently. searches have emploved the infrared lines. usually the ((1-0)9C1) line. and emission has been detected in a lew cases (Jaffe&Bremer1997:Falcke 1998).," Recently, searches have employed the infrared lines, usually the (1-0)S(1) line, and emission has been detected in a few cases \citep{jb,frrsw}." +. In their analysis of the detections. Jalle&Bremer(1997). deduce masses that are about. 107.10AL... still inadequate by two orders of magnitude to be in agreement with the X-rav observations.," In their analysis of the detections, \citet{jb} deduce masses that are about $10^{10}$, still inadequate by two orders of magnitude to be in agreement with the X-ray observations." + Given the limits on HI andII5.. theoretical investigations have examined whether the eas could be hidden in a form that would be clilficult to detect.," Given the limits on HI and, theoretical investigations have examined whether the gas could be hidden in a form that would be difficult to detect." + The work of, The work of +considering the collision events of each ταν will the source surface. the quantities of interest may be read off.,"considering the collision events of each ray with the source surface, the quantities of interest may be read off." + In the stellar-source case. however. i( is necessary to solve for the initial direction of a photon so that it will reach the observer.," In the stellar-source case, however, it is necessary to solve for the initial direction of a photon so that it will reach the observer." + Hence we have a boundary-value problem., Hence we have a boundary-value problem. + Figure | is à schematic illustration of our method., Figure \ref{example} is a schematic illustration of our method. + Photons are emitted from nearby spacetime points on the stellar orbits aud travel to the observer., Photons are emitted from nearby spacetime points on the stellar orbits and travel to the observer. + In the picture. the star emits “Minkowski photons” which feel no space curvature ancl travel in straight lines: redshift depends only on the velocity and time dilation οἱ the star.," In the left-hand picture, the star emits “Minkowski photons” which feel no space curvature and travel in straight lines; redshift depends only on the velocity and time dilation of the star." + This is in effect the approximation used in previous work., This is in effect the approximation used in previous work. + In (he middle picture. (he star emits “Schwarzschild photons” which [eel space curvature.," In the middle picture, the star emits “Schwarzschild photons” which feel space curvature." +" In the right-hand picture. (he star emits “frame drageine photons"" which feel spin as well as space curvalure."," In the right-hand picture, the star emits “frame dragging photons” which feel spin as well as space curvature." + Below. ?? details the problem to be solved and the method used [ον caleulatioΕν of the redshilt.," Below, \ref{Algorithm} details the problem to be solved and the method used for calculation of the redshift." + The Matlab scripts implementing our algorithm are available as an online supplement., The Matlab scripts implementing our algorithm are available as an online supplement. + Then 2.2. presents the black-hole model ancl associated metrics which we use in our approach. and ?? «derives how (he various effects scale with orbit size.," Then \ref{theMetric} presents the black-hole model and associated metrics which we use in our approach, and \ref{scalesec} derives how the various effects scale with orbit size." + We apply our algorithm to the star $2. and detail the results in Section ??..," We apply our algorithm to the star S2, and detail the results in Section \ref{Results}." + In order to calculate the redshilt of à moving star as observed by a fixed observer. we need to solve the geodesic equations for both the star and for photons.," In order to calculate the redshift of a moving star as observed by a fixed observer, we need to solve the geodesic equations for both the star and for photons." + Geoclesic equations are commonlv expressed in terms of (he Lagrangian. with cols denoting derivatives with respect to the affine parameter.," Geodesic equations are commonly expressed in terms of the Lagrangian, with dots denoting derivatives with respect to the affine parameter." + Bul an equivalent formulation exists in Cerms of a Hamiltonian, But an equivalent formulation exists in terms of a Hamiltonian +the velocity at small 0p the spectral index is —1.76+0.02 using the global mean field compared to —1.9740.02 using the local mean field.,the velocity at small $\theta_B$ the spectral index is $-1.76 \pm 0.02$ using the global mean field compared to $-1.97 \pm 0.02$ using the local mean field. + This is because the magnetic field fluctuations are large enough that the local mean field direction seen by an eddy is not the same as the global mean field direction., This is because the magnetic field fluctuations are large enough that the local mean field direction seen by an eddy is not the same as the global mean field direction. +" If the fluctuations are in critical balance, the angle between the local and global mean fields is B/Bo©kj/k ."," If the fluctuations are in critical balance, the angle between the local and global mean fields is $\delta\mathbf{B}_\perp/B_0\approx k_\para/k_\perp$." +" This suggests that when using the global mean field, the parallel scaling cannot be correctly distinguished from the perpendicular scaling, even for small óB,/Bo, because the angle of measurement to the local mean field needs to be less than ky/k,."," This suggests that when using the global mean field, the parallel scaling cannot be correctly distinguished from the perpendicular scaling, even for small $\delta\mathbf{B}_\perp/B_0$, because the angle of measurement to the local mean field needs to be less than $k_\para/k_\perp$." + This interpretation is in agreement with previous solar wind studies that have used local and global mean field methods., This interpretation is in agreement with previous solar wind studies that have used local and global mean field methods. +" Those that use the global mean field method do not detect spectral index anisotropy (Sari&Valley1976;Tesseinetal.2009) and those that use a local mean field method do detect it (Horburyetal.2008;Podesta2009;Luo&Wu2010;Wicksetal.2010, 2011)."," Those that use the global mean field method do not detect spectral index anisotropy \citep{sari76,tessein09} and those that use a local mean field method do detect it \citep{horbury08,podesta09a,luo10,wicks10a,wicks11}." +". A similar situation is also seen in simulations, where scaling anisotropy is detected when a local mean field is used (Cho&Vishniac2000;Maron&Goldreich2001) but not when a global mean field is used (Grappin&Müller2010)."," A similar situation is also seen in simulations, where scaling anisotropy is detected when a local mean field is used \citep{cho00,maron01} but not when a global mean field is used \citep{grappin10}." +". Here, we have shown that when keeping all other parameters constant, it is indeed the use of the global or local mean field that determines whether the anisotropic scaling is measured."," Here, we have shown that when keeping all other parameters constant, it is indeed the use of the global or local mean field that determines whether the anisotropic scaling is measured." +" It seems, therefore, that the ffluctuations, both in solar wind turbulence and forced RMHD turbulence simulations, are more sensitive to the local mean field at the scale of the fluctuations than the global large scale field."," It seems, therefore, that the fluctuations, both in solar wind turbulence and forced RMHD turbulence simulations, are more sensitive to the local mean field at the scale of the fluctuations than the global large scale field." +" In the decaying simulation (not shown in Fig. 8)),"," In the decaying simulation (not shown in Fig. \ref{fig:localvsglobal}) )," +" the local and global mean field methods are much more similar, with the parallel scaling being steeper than —2 in all cases."," the local and global mean field methods are much more similar, with the parallel scaling being steeper than $-2$ in all cases." +" One possible reason for this is that the scale separation between the global mean field and the fluctuations is not large, meaning that the global and local mean fields are similar."," One possible reason for this is that the scale separation between the global mean field and the fluctuations is not large, meaning that the global and local mean fields are similar." +" This, combined with the smaller fluctuation amplitudes in the decaying simulation, could account for the observed behaviour."," This, combined with the smaller fluctuation amplitudes in the decaying simulation, could account for the observed behaviour." + This could be tested by performing a decaying simulation with a larger inertial range., This could be tested by performing a decaying simulation with a larger inertial range. +" In this paper, we measure the power and spectral index anisotropy of tturbulence in the solar wind and RMHD simulations using second-order structure functions."," In this paper, we measure the power and spectral index anisotropy of turbulence in the solar wind and RMHD simulations using second-order structure functions." +" The analysis technique is essentially the same for both, allowing us to make a direct comparison."," The analysis technique is essentially the same for both, allowing us to make a direct comparison." +" In the slow solar wind, we find that the magnetic field power and spectral index are anisotropic with respect to the local magnetic field direction."," In the slow solar wind, we find that the magnetic field power and spectral index are anisotropic with respect to the local magnetic field direction." + This anisotropy has now been seen by several different methods in both fast and slow wind., This anisotropy has now been seen by several different methods in both fast and slow wind. + In both forced and decaying simulations we also find that the power and spectral index are anisotropic in both the velocity and magnetic field., In both forced and decaying simulations we also find that the power and spectral index are anisotropic in both the velocity and magnetic field. +" In the solar wind, the perpendicular spectral index of the magnetic field is close to —5/3, in agreement with the theory of Goldreich&Sridhar(1995)."," In the solar wind, the perpendicular spectral index of the magnetic field is close to $-5/3$, in agreement with the theory of \citet{goldreich95}." +". In the forced simulation, the perpendicular spectral indices are close to —5/3 for velocity and —3/2 for the magnetic field."," In the forced simulation, the perpendicular spectral indices are close to $-5/3$ for velocity and $-3/2$ for the magnetic field." +" We are not aware of any theory that can account for this difference, although it may be caused by the velocity forcing."," We are not aware of any theory that can account for this difference, although it may be caused by the velocity forcing." +" In the decaying simulation, the perpendicular spectral index is close to —5/3 for both the velocity and magnetic field."," In the decaying simulation, the perpendicular spectral index is close to $-5/3$ for both the velocity and magnetic field." +" In all cases, the spectral index steepens at small angles to the magnetic field."," In all cases, the spectral index steepens at small angles to the magnetic field." +" The parallel scaling obtained in the solar wind and forced simulations is close to —2, which agrees with the theories based on critical balance of both Goldreich&Sridhar(1995) and Boldyrev(2006)."," The parallel scaling obtained in the solar wind and forced simulations is close to $-2$, which agrees with the theories based on critical balance of both \citet{goldreich95} and \citet{boldyrev06}." +". The parallel spectral indices in the decaying simulation are —2.33+0.03 for the velocity and —2.30+0.03 for the magnetic field, which are steeper than the critical balance predictions."," The parallel spectral indices in the decaying simulation are $-2.33 \pm 0.03$ for the velocity and $-2.30 \pm 0.03$ for the magnetic field, which are steeper than the critical balance predictions." +We based our initial classification on the ratios of diagnostic cussion lines.,We based our initial classification on the ratios of diagnostic emission lines. + Previous studies used iustead a conibinatioun of line ratios and equivalent widths (see the Iutroduction) that can be more affected Gn particular when only upper hits can be derived) by the quality of the data and bv the contrast with the continu -τσLl.sion., Previous studies used instead a combination of line ratios and equivalent widths (see the Introduction) that can be more affected (in particular when only upper limits can be derived) by the quality of the data and by the contrast with the continuum emission. +4. Similarly. we only used ratios of lines with small wavelength separation. not affected by the possible effects oe-ernal reddening. that cau be particularly severe when considering e.g. the 10 ΠΙΛΟΤΟΥ line.," Similarly, we only used ratios of lines with small wavelength separation, not affected by the possible effects of internal reddening, that can be particularly severe when considering e.g. the [O $\lambda$ 3727 line." + Thus our procedure is expected to produce a rather robust method of spectral identification., Thus our procedure is expected to produce a rather robust method of spectral identification. + Nonetheless. our classificatious are overall in good agreement with those found in the iterature ou a object by object basis.," Nonetheless, our classifications are overall in good agreement with those found in the literature on a object by object basis." + For example. comparing our results with those of Willottetal.(1999) for the 3CRR sources we fouud 52 objects in common.," For example, comparing our results with those of \citet{willott99} for the 3CRR sources we found 52 objects in common." + Leaving aside 2 objects of the newly iutroduced. class of ELEC. aud 3 objects that we consider as unclassitied. (2 reported as LEC. namely 3€ 035 aud 3€ 319. 1 as TEC. 3C 138) the identification i the various classes coiucides with oulv 3 exceptions for the remaining £7 radio-galaxies.," Leaving aside 2 objects of the newly introduced class of ELEG, and 3 objects that we consider as unclassified (2 reported as LEG, namely 3C 035 and 3C 319, 1 as HEG, 3C 438) the identification in the various classes coincides with only 3 exceptions for the remaining 47 radio-galaxies." + These are: 3€ 388. à LEG from our analysis (with an excitation index of E.L20.62) against the previous TEC identification. and two galaxies. 3C 079 aud 3C 223. where we do not see a broad linecoumponcut?.. contrasting with their sugeestedOO membership in the class of Weak Quasars.," These are: 3C 388, a LEG from our analysis (with an excitation index of E.I.=0.62) against the previous HEG identification, and two galaxies, 3C 079 and 3C 223, where we do not see a broad line, contrasting with their suggested membership in the class of Weak Quasars." + Ledlow&Owen(1996) conrpared the optical Ro band magnitude of the host galaxies with the total radio cluission at 1.[ GIIz., \citet{ledlow96} compared the optical R band magnitude of the host galaxies with the total radio emission at 1.4 GHz. + They found that sources locate in different areas of the plot depending ou their radio morphology: as already. known frou the pioneering study of Εαπατο&Riley(1971) FR II sources have higher radio powers than FR I sources and they separate at a huninosity of ~2«4107? W |! at 178 MIIEz., They found that sources locate in different areas of the plot depending on their radio morphology: as already known from the pioneering study of \citet{fanaroff74} FR II sources have higher radio powers than FR I sources and they separate at a luminosity of $\sim 2\times10^{25}$ W $^{-1}$ at 178 MHz. + The novel result of Ledlow&Owen(1996) cousists in the fact that the FR I/II division shows a depeudeuce on Mj., The novel result of \citet{ledlow96} consists in the fact that the FR I/II division shows a dependence on $M_{\rm host}$. + FR I sources hosted bv the nore lunünous galaxies cau have radio powers higher than the average ER I/FR II separation., FR I sources hosted by the more luminous galaxies can have radio powers higher than the average FR I/FR II separation. + The separation between FR I and FR IT is rather sharp over the whole range of radio power., The separation between FR I and FR II is rather sharp over the whole range of radio power. + Iu Fig., In Fig. + 10. (left panel) we plotted the 3CR sources in the plane radio huninosity (at 178 MIIz) versus the naenitude in IT head ofthe ost galaxy (reported in Table 2))., \ref{ledlow} (left panel) we plotted the 3CR sources in the plane radio luminosity (at 178 MHz) versus the magnitude in H band of the host galaxy (reported in Table \ref{speclas}) ). + We selected the IT band since it provides the most complete coverage (~ ) for the 3€CR sample bv using neasurclcuts from the 2ALASS (Skrutskieetal.2006) or. When this is not available. from IST images (Donzellietal. 2007).," We selected the H band since it provides the most complete coverage $\sim$ ) for the 3CR sample by using measurements from the 2MASS \citep{skrutskie06} or, when this is not available, from HST images \citep{donzelli07}." +. For the BLO we also corrected the host iuninositv for the coutribution of their brigh IR unelei. ucasured by Baldietal.(2009).," For the BLO we also corrected the host luminosity for the contribution of their bright IR nuclei, measured by \citet{baldi09}." +. In order to compare our results with those of Ledlow&Owen(1996) we used the color correction from Manuuncecietal.(2001).. R- II 2 2.5. and scaled the 1.1 CUz data to 178 MITz adopting a radio spectriun in the form FyXvU.T," In order to compare our results with those of \citet{ledlow96} we used the color correction from \citet{mannucci01}, R - H = 2.5, and scaled the 1.4 GHz data to 178 MHz adopting a radio spectrum in the form $F_{\nu} \propto \nu^{-0.7}$." + The relative scarcity of FR Tsources in the 3CR sample prevents us from exploring in detail the host maenitude- separation between the FR classes., The relative scarcity of FR I sources in the 3CR sample prevents us from exploring in detail the host magnitude-dependent separation between the FR classes. + However. the FR location for our sample is consistent with the separation introduced bv Ledlow&Owen(1996).," However, the FR location for our sample is consistent with the separation introduced by \citet{ledlow96}." +. We also checked that this result holds using radio ποσάπως at 1.1 1) as well as host magnitude in other bands (ic. V xd)., We also checked that this result holds using radio luminosities at 1.4 GHz as well as host magnitude in other bands (i.e. V band). + Du line with their results we fud a few exceptions. associated with FR Isources of extremely high radio powers m vorv massive hosts.," In line with their results we find a few exceptions, associated with FR I sources of extremely high radio powers in very massive hosts." + Iun the rieht xuel woe iutroduced the optical spectroscopic classification. separating the 3C'R sources iuto WEG and LEC.," In the right panel we introduced the optical spectroscopic classification, separating the 3CR sources into HEG and LEG." + For the LEG class we further consider the FR type., For the LEG class we further consider the FR type. + WEG and LEG/FR II sources are well mixed above the FR I/FR II separation. having the same median in terius of radio power. and oulv a small offset iu the," HEG and LEG/FR II sources are well mixed above the FR I/FR II separation, having the same median in terms of radio power, and only a small offset in the" +and Fedunetal.(2011). have indicated how vortex motions generate a significant amount of Povnting Ilux directed outwards from the photosphere. and. as a result. may be (he source of various observed. MIID wave moces.,"and \citet{fedun11} have indicated how vortex motions generate a significant amount of Poynting flux directed outwards from the photosphere, and, as a result, may be the source of various observed MHD wave modes." + In this paper. we use high spatial and temporal resolution observations. in addition to numerical simulations. to determine (he velocity distribution of a large sample of ΔΙ)».," In this paper, we use high spatial and temporal resolution observations, in addition to numerical simulations, to determine the velocity distribution of a large sample of MBPs." + The observations and munerical simulations are described in 2.. while the methodology used. and the values obtained for the velocities of AIBP structures. are detailed in 3..," The observations and numerical simulations are described in \ref{obs}, while the methodology used, and the values obtained for the velocities of MBP structures, are detailed in \ref{analy}." + As our tracking algorithm can detect and monitor bright point chains. as well as isolated brghtenings and merger events. we believe (hat (his is a unique study of the. dynamics of AIBPs in the solar photosphere.," As our tracking algorithm can detect and monitor bright point chains, as well as isolated brightenings and merger events, we believe that this is a unique study of the dynamics of MBPs in the solar photosphere." + Differences between (he velocity characteristics of MDPs. and (those that undergo mergers wilh other bright points. are discussed in 3..," Differences between the velocity characteristics of non-merging MBPs, and those that undergo mergers with other bright points, are discussed in \ref{analy}." + Finally. our concluding remarks are given in 1..," Finally, our concluding remarks are given in \ref{conc}." + The data emploved in this study. were obtained using the Rapid Oscillations in the Solar Atmosphere (ROSA:Jessetal.2010) instrument. which is installed as a user facility at the 76 em Dunn Solar Telescope (DST). in New Mexico. USA.," The data employed in this study were obtained using the Rapid Oscillations in the Solar Atmosphere \citep[ROSA;][]{Jess10} instrument, which is installed as a common-user facility at the 76 cm Dunn Solar Telescope (DST), in New Mexico, USA." + Observations were obtained during a period of excellent seeing on 2009 May. 28. using a 9.2 wide filter centred al 43805 (G-band).," Observations were obtained during a period of excellent seeing on 2009 May 28, using a $9.2$ wide filter centred at $4305$ (G-band)." +" We observed a 70x10"" quiet Sun region at disk centre for ~50 minutes. achieving diffraction-limited imaging with 0"".069 !."," We observed a $70'' \times 70''$ quiet Sun region at disk centre for $\sim$ 50 minutes, achieving diffraction-limited imaging with $0''.069$ $^{-1}$ ." +" The images were reconstructed using Speckle algorithms (Wógeretal.2003).. while image ce-stretching was performed using a 40x grid (equatingtoaz1"".7separationbetweenspatialsamples:etal.2007. 2008)."," The images were reconstructed using Speckle algorithms \citep{Wog08}, while image de-stretching was performed using a $40 \times 40$ grid \citep[equating to a $\approx1''.7$ separation between +spatial samples;][]{Jess07, Jess08}." +. These processes were implemented to remove (he effects of atmospheric seeing from the dataset., These processes were implemented to remove the effects of atmospheric seeing from the dataset. + G-band images were taken at a raw cadence of 0.033 s. while alter speckle reconstruction the cadence was reduced to 0.528 s. Reconstructed images were then binned into consecutive groups of four to improve the signal-to-noise anc reduce (he overall volume of the dataset. providing a final image cadence of 2.1 s. simulated G-band images were produced using the detailed radiative transport technique described by Shelvagetal.(2004)... with the solar photospheric magneto-convection models for the radiative transport calculations provided by the MUBRAM radiative MIID code 2005).," G-band images were taken at a raw cadence of 0.033 s, while after speckle reconstruction the cadence was reduced to 0.528 s. Reconstructed images were then binned into consecutive groups of four to improve the signal-to-noise and reduce the overall volume of the dataset, providing a final image cadence of 2.1 s. Simulated G-band images were produced using the detailed radiative transport technique described by \citet{Shel04}, with the solar photospheric magneto-convection models for the radiative transport calculations provided by the MURaM radiative MHD code \citep{Vog05}." +.. A computational domain of size 12x1.4 Mm. was emploved [or the simulations. resolved by 480x100 grid cells. providing a horizontal (wo-pixel resolution of 50 km.," A computational domain of size $12\times12\times1.4$ $^3$, was employed for the simulations, resolved by $480\times480\times100$ grid cells, providing a horizontal two-pixel resolution of 50 km." + The level corresponding to the visible solar surface is located approximately GOO kin below the upper boundary of thedomain., The level corresponding to the visible solar surface is located approximately 600 km below the upper boundary of thedomain. + Side boundariesof the domain are periodic. while the upper boundary is closed [or vertical ancl stress-free horizontal plasma motions and," Side boundariesof the domain are periodic, while the upper boundary is closed for vertical and stress-free horizontal plasma motions and" + (o: M.. aw (e.g..Johnson1981.1987:1993.2003;Stelzer2004).," $\alpha\omega$ $M_\odot$ $\alpha\omega$ \citep[e.g.,][]{johnson81,johnson87,tagliaferri90,drake96,fleming00,rutledge00,fleming93,fleming03,stelzer04}." + (a7 (e.g..Durneyetal.," $\alpha^2$ \citep[e.g.,][]{durney93}." +1993).. Ha (Gizisetal.2000:Mohanty&Basri2003).. (e.g..Fleming," $\alpha$ \citep{gizis00,mohanty03}. \citep[e.g.,][]{fleming93,fleming03}." +etal.1993.2003).. Berger(2002) Putnam2005).," \citet{berger02} \citep{berger05,burgasser05}." +. regime with the Australia Telescope Compact Array (ATCA)., regime with the Australia Telescope Compact Array (ATCA). + Our target. ε Ind Bab. is the closest known brown dwarf and is composed of two objects with spectral types ΤΙ and Τό separated by 0773 (2.65 AU at a distance of 3.626 pe; Scholz2004)).," Our target, $\epsilon$ Ind Bab, is the closest known brown dwarf and is composed of two objects with spectral types T1 and T6 separated by $0\farcs 73$ $2.65$ AU at a distance of $3.626$ pc; \citealt{scholz03,smith03,volk03,mccaughrean04}) )." + We list the binary’s main characteristics in Table 1I.., We list the binary's main characteristics in Table \ref{tab:epsind}. + Blank(2005) failed to detect e Ind Bab with ATCA. but our radio observation goes deeper.," \citet{blank05} failed to detect $\epsilon$ Ind Bab with ATCA, but our radio observation goes deeper." + Despite our best effort to coordinate the and ATCA observations of the e Ind Bab binary. the X-ray observations were delayed by a few days due to satellite safety reasons.," Despite our best effort to coordinate the and ATCA observations of the $\epsilon$ Ind Bab binary, the X-ray observations were delayed by a few days due to satellite safety reasons." + A log of the observations is given in Table 2.., A log of the observations is given in Table \ref{tab:log}. + The ATCA was in a long-baseline configuration (6D); we used 4.8 GHz and 8.64 GHz receivers with bandwidths of 128 MHz., The ATCA was in a long-baseline configuration (6D); we used 4.8 GHz and 8.64 GHz receivers with bandwidths of 128 MHz. +" Observing scans ranged from 10 min to 20 min on source. depending on the weather conditions. whereas we used 3 min scans for the phase calibrator,"," Observing scans ranged from 10 min to 20 min on source, depending on the weather conditions, whereas we used 3 min scans for the phase calibrator." +" About 5 minutes at the start of each observing round were spent on the flux calibrator,", About 5 minutes at the start of each observing round were spent on the flux calibrator. + The observing conditions on the first day were average with cloud coverage: however. the last three hours of the first day of observation were essentially useless due to strong winds and a thunderstorm.," The observing conditions on the first day were average with cloud coverage; however, the last three hours of the first day of observation were essentially useless due to strong winds and a thunderstorm." + In contrast. the weather conditions were much better during the second day with generally a cloud-free sky.," In contrast, the weather conditions were much better during the second day with generally a cloud-free sky." + We combined both observing rounds and reduced the ATCA data using the MIRIAD software (Saultetal.1995)., We combined both observing rounds and reduced the ATCA data using the MIRIAD software \citep{sault95}. + We detected 9 sources in the 4.8 GHz map: we used boxes of about width centered on these sources and applied a CLEAN algorithm using uniform. weighting., We detected 9 sources in the 4.8 GHz map; we used boxes of about width centered on these sources and applied a CLEAN algorithm using uniform weighting. + About 5.4 mJy were thus removed in 202 iterations (we stopped when a negative value was encountered)., About $5.4$ mJy were thus removed in 202 iterations (we stopped when a negative value was encountered). + Although no sources were visible in the dirty map at 8.64 GHz. we used the boxes around the first five brightest sources detected at longer wavelengths and performed a CLEAN algorithm.," Although no sources were visible in the dirty map at 8.64 GHz, we used the boxes around the first five brightest sources detected at longer wavelengths and performed a CLEAN algorithm." + About 0.5 mJy were removed after 38 iterations., About $0.5$ mJy were removed after 38 iterations. + The rms noise levelinthecleaned mapsreached 26.4 and 37.3 at 4.8 and 8.64 GHz. respectively.," The rms noise levelinthecleaned mapsreached $26.4$ and $37.3$ at 4.8 and 8.64 GHz, respectively." + The values are close to thetheoreticalvalues (25.1 and 35.6 jiJy))., The values are close to thetheoreticalvalues $25.1$ and $35.6$ ). + No source was, No source was +Let us now discuss the conditions required for the strong-cooling model developed in the preceding sections to be valid.,Let us now discuss the conditions required for the strong-cooling model developed in the preceding sections to be valid. + First. an obvious necessary. coudiGon for the strong-cooling. strong-compression regime is (hat equation (2.4)) has a large-;1 solution. Ac1.," First, an obvious necessary condition for the strong-cooling, strong-compression regime is that equation \ref{eq-entropy-A}) ) has a $A$ solution, $A\gg 1$." + However. the actual situation is somewhat more subtle.," However, the actual situation is somewhat more subtle." + The condition sls>1 is just the condition for the of a stationary stronglv-cooled. state of the reconnection laver., The condition $A\gg 1$ is just the condition for the of a stationary strongly-cooled state of the reconnection layer. + In addition. however. we must impose an extra evolutionary condition for the svstem to be able to reach this state.," In addition, however, we must impose an extra evolutionary condition for the system to be able to reach this state." + As we shall see below. this will result in a certain requirement for the radiative cooling function.," As we shall see below, this will result in a certain requirement for the radiative cooling function." + The picture thal we have in mind here is the following., The picture that we have in mind here is the following. + The ambient plasma upstream of the reconnection laver is rather tenuous: when it just enters (he laver. it becomes subject to ohmic heating ancl its temperature rises. whereas ils density does not change appreciably ab first.," The ambient plasma upstream of the reconnection layer is rather tenuous; when it just enters the layer, it becomes subject to ohmic heating and its temperature rises, whereas its density does not change appreciably at first." + If radiative cooling can be neglected. one always gets the classical SweetParker laver solution. with relatively low density η2ny and relatively high temperature TT4 (corresponding to “lt7 1).," If radiative cooling can be neglected, one always gets the classical Sweet–Parker layer solution, with relatively low density $n\simeq n_0$ and relatively high temperature $T\simeq T_{\rm eq}$ (corresponding to $A\simeq 1$ )." + The transition to the strong-cooling. strong-compression 12» reeime described in the previous sections happens only if that η. (1)]y. where we used equation (2.4)) in the last step.," For this to happen, we must require that the radiative cooling of the corresponding $A\simeq 1$ Sweet–Parker solution be stronger that the corresponding Ohmic heating, i.e.: [n_0, (n_0)] > [n_0, (n_0)], where we used equation \ref{eq-Q_ohm-2}) ) in the last step." + Now. assuming that a stationary strong-cooling solution with slc1 does exist. it is convenient to make use of the corresponding heating-cooling balance equation," Now, assuming that a stationary strong-cooling solution with $A\gg 1$ does exist, it is convenient to make use of the corresponding heating-cooling balance equation" +Results for (&) obtained by dividing the inner galaxy into radial bins of width LR. are shown on figure 9.,Results for $\left< \kappa \right>$ obtained by dividing the inner galaxy into radial bins of width $\frac{1}{30} R_{\odot}$ are shown on figure 9. + The histogram shows an arithmetic average over (lie various lines ol sight through each annulus., The histogram shows an arithmetic average over the various lines of sight through each annulus. + Also shown on figure 9 as small circles are the individual channel values of 7 in (he absorption spectra. converted to & by mulliplving by the velocity eradient. a given by the rotation curve (see Burton. 1055. [or a review of the significance ol the velocity graclient).," Also shown on figure 9 as small circles are the individual channel values of $\tau$ in the absorption spectra, converted to $\kappa$ by multiplying by the velocity gradient, $\frac{dv}{ds}$, given by the rotation curve (see Burton, 1988, for a review of the significance of the velocity gradient)." + The curves on figure 9 indicate observational selection based on our noise level in 7 for the case of G328.4240.22. one of our brighter sources.," The curves on figure 9 indicate observational selection based on our noise level in $\tau$ for the case of G328.42+0.22, one of our brighter sources." + The lower curve shows the opacity which would result [rom optical depth equal to one sigma. as defined bv the emission fluctuations discussed above.," The lower curve shows the opacity which would result from optical depth equal to one sigma, as defined by the emission fluctuations discussed above." + Weaker absorption (han (his is not detectable. so multiplving by the velocity eradient eives (he corresponding lower limit for detectable opacity.," Weaker absorption than this is not detectable, so multiplying by the velocity gradient gives the corresponding lower limit for detectable opacity." +" Spectra toward Lainter sources (hat give higher o, will have higher lower limits.", Spectra toward fainter sources that give higher $\sigma_{\tau}$ will have higher lower limits. + Points near or below this curve on ligure 9 are upper limits on &., Points near or below this curve on figure 9 are upper limits on $\kappa$. +" On the high side. when the absorption lines are very deep. the noise prevents us from distinguishing between optical depths greater than 7,4,=—ln(20;}."," On the high side, when the absorption lines are very deep, the noise prevents us from distinguishing between optical depths greater than $\tau_{max}=-\ln \left( 2 \sigma_{\tau} \right)$." +" The line saturates al this point (typically 7 3). ancl we set the optical depth to this value ibe*«2o,."," The line saturates at this point (typically $\tau \sim 3$ ), and we set the optical depth to this value if $e^{-\tau}< 2 \sigma_{\tau}$." + Multiplied by the velocity gradient. (his maximum detectable 7 gives an upper limit on the measurable &. shown for the case of G328.42+0.22 by the upper curve.," Multiplied by the velocity gradient, this maximum detectable $\tau$ gives an upper limit on the measurable $\kappa$, shown for the case of G328.42+0.22 by the upper curve." + Again. for spectra wilh higher noise level (he upper limit is lower. as evidenced by chains of points al various levels corresponding (o saturated lines.," Again, for spectra with higher noise level the upper limit is lower, as evidenced by chains of points at various levels corresponding to saturated lines." + Points near the upper curve on figure 9 are (hus lower limits on &., Points near the upper curve on figure 9 are thus lower limits on $\kappa$. + The velocity integrals of (he absorption spectra are given on table 1. columns 6 and 7.," The velocity integrals of the absorption spectra are given on table 1, columns 6 and 7." + Column 6 gives (he integral over the entire negative velocily range corresponding to the inner galaxy., Column 6 gives the integral over the entire negative velocity range corresponding to the inner galaxy. + Column 7 gives the integral over therestricted velocity range corresponding to the points on figure 9. i.e. [rom zero km ! to the recombination line velocity.," Column 7 gives the integral over therestricted velocity range corresponding to the points on figure 9, i.e. from zero km $^{-1}$ to the recombination line velocity." + Whether the region is at the near or [ar distance. we can be confident that at least over (his velocity range onlv (he near-side gas can contribute to the absorption.," Whether the region is at the near or far distance, we can be confident that at least over this velocity range only the near-side gas can contribute to the absorption." + For the regions we stop 3km ! short of the recombination line velocity. (o avoid the deep absorption usually seen just bevond the region's velocity.," For the regions we stop 3 km $^{-1}$ short of the recombination line velocity, to avoid the deep absorption usually seen just beyond the region's velocity." + The SNR. G328.42+0.22. is known to be bevond the solar circle on Che far side of the Galaxy (Gaensler. Dickel. and Green. 2000): in this case we carry the velocity integration to the terminal velocity at (his longitude. (," The SNR G328.42+0.22, is known to be beyond the solar circle on the far side of the Galaxy (Gaensler, Dickel, and Green, 2000); in this case we carry the velocity integration to the terminal velocity at this longitude. (" +Varving the 3 km | offset to 10 or even 15 km ! has minimal effect on the opacities on figure 9. although it reduces the number of lines of sight contributing to some of the annuli.),"Varying the 3 km $^{-1}$ offset to 10 or even 15 km $^{-1}$ has minimal effect on the opacities on figure 9, although it reduces the number of lines of sight contributing to some of the annuli.)" + Figure 10 shows the geometrv of the Galactic plane in the fourth. cquacdrant (from MeClue-GQrffiths et al., Figure 10 shows the geometry of the Galactic plane in the fourth quadrant (from McClure-Griffiths et al. + 2001)., 2001). + The sun's location is assumed to be al (roy)=(0.8.5). and we plot lines of sight at longitude ancl3337... the boundaries of the test region studied in (his paper.," The sun's location is assumed to be at $(x,y)=(0,8.5)$, and we plot lines of sight at longitude and, the boundaries of the test region studied in this paper." + Annuli ave plotted with radii from 0.4 to 1.0 Ro. and the major spiral features," Annuli are plotted with radii from 0.4 to 1.0 $R_{\odot}$ , and the major spiral features" +"N-rav- endssion associated with radio jets in extragalactic sources now cones ina large variety of diverse characteristics,",X-ray emission associated with radio jets in extragalactic sources now comes in a large variety of diverse characteristics. + When this sort of Cluission was first isolated (c.g. the radio ealaxy AST with the EINSTEIN OBSERVATORY. Schreier. Gorenstein. Feigelsou 1982) aud there were oulv a few examples. it was tempting to work on the assumption that the ΟΡΙΟ process was definable aud would apply to all examples.," When this sort of emission was first isolated (e.g. the radio galaxy M87 with the EINSTEIN OBSERVATORY, Schreier, Gorenstein, Feigelson 1982) and there were only a few examples, it was tempting to work on the assumption that the emission process was definable and would apply to all examples." + This notion persisted into the ROSAT era until a couvincing case was iade that the terminal hotspots of Cyenus A represented svuchrotrou selt-Conmptou (SSC) emission. (Warris. Carilli. Perley. 1991).," This notion persisted into the ROSAT era until a convincing case was made that the terminal hotspots of Cygnus A represented synchrotron self-Compton (SSC) emission (Harris, Carilli, Perley, 1994)." + With the advent of the CUANDRA OBSERVATORY. he uuuber of sources has alinost tripled (from 7 to at least 19) ye there remain substantial problems in deternünius the cussion process responsible or the N-rays in some sources.," With the advent of the CHANDRA OBSERVATORY, the number of sources has almost tripled (from 7 to at least 19) yet there remain substantial problems in determining the emission process responsible for the X-rays in some sources." +" Althoueli broken oower laws connecting the radio. optical. aud. X-rav data are still viable spectral models for a few sources, a uunmboer of other sources are observed to rave such a low flux deusitv iu the optical that the indicated cutoff iu the spectrum would preclude a simple conection to the N-ray data."," Although broken power laws connecting the radio, optical, and X-ray data are still viable spectral models for a few sources, a number of other sources are observed to have such a low flux density in the optical that the indicated cutoff in the spectrum would preclude a simple connection to the X-ray data." + The introduction of the beaming model (Tavecchio et al., The introduction of the 'beaming model' (Tavecchio et al. + 2000. Celotti et al.," 2000, Celotti et al." + 2001) in the particular case of PISSOG37 was presented as an escape from this dilemuna., 2001) in the particular case of PKS0637 was presented as an escape from this dilemma. + Iu this model. the euhancement of," In this model, the enhancement of" +»ulse observed in high-energv channel is narrower than in ower-energv. channel. which is manifested by the fact that he FAWHIAIs of the pulses in separated energy. channels decrease with the energy in à power-law form.,"pulse observed in high-energy channel is narrower than in lower-energy channel, which is manifested by the fact that the FWHMs of the pulses in separated energy channels decrease with the energy in a power-law form." + However. he pulse narrowing we obtained is less prominent than hat observed in real GRBs for which pulse width decay »ower-law. index -0.4: while the pulse width decay index we obtained. for instance in the case of Figure 2. (one-sided exponential decay emission profile). is -0.13.," However, the pulse narrowing we obtained is less prominent than that observed in real GRBs for which pulse width decay power-law index $\sim$ -0.4; while the pulse width decay index we obtained, for instance in the case of Figure \ref{expfig} (one-sided exponential decay emission profile), is -0.13." +" Other than the ""Band"" spectrum. we also used. an alternative function - a low-energy power [aw plus the . . ⋅∕⋅ ↓⊔⋏∙≟↓↥⊣⋅⊔⋖⊾↓⋅⋏∙≟∙∖⇁⋖⋅⇀∖↓≻∪⊔⋖⋅⊔⇂⋯↓≼↛⋯−∪∐⋜⊔∆↗∣−⇂∪↓⋅↿↓⊔⋅↓⋅∢⋅⊳∖⇂−∐⋅⋜⋯↓⋖⊾⋅ spectrum."," Other than the “Band” spectrum, we also used an alternative function - a low-energy power law plus the high-energy exponential cut-off at $E_p'$ - for the rest-frame spectrum." + For the typical values of the parameters we have used. this changing of spectrum only narrows the Channel 4 pulse by ~6%.. hence hardly changes the slope of the pulse width versus the energy.," For the typical values of the parameters we have used, this changing of spectrum only narrows the Channel 4 pulse by $\sim$, hence hardly changes the slope of the pulse width versus the energy." + The spectral lag is an important observational property of je pulse in GRBs in that it may be usec to derive the 'osmological distribution of (ας (Norris 2002) ancl to iscriminate the internal shock signature and the external shock signature in the pulses (e.g.. Llakkila Ciblin 2004).," The spectral lag is an important observational property of the pulse in GRBs in that it may be used to derive the cosmological distribution of GRBs (Norris 2002) and to discriminate the internal shock signature and the external shock signature in the pulses (e.g., Hakkila Giblin 2004)." + This motivates us to probe the dependences of the peak lags oin other physical parameters of the simple model., This motivates us to probe the dependences of the peak lags on other physical parameters of the simple model. + We choose le symmetric Gaussian. profile as the intrinsic emission profile. which includes an intrinsic rising phase.," We choose the symmetric Gaussian profile as the intrinsic emission profile, which includes an intrinsic rising phase." +" We alter the Lorentz factor E. the spectral parameters of the rest frame emission (a. 3 and £7,7 ). the radius of the radiation surface H. and the rest-frame duration ἐς of the intrinsic radiation. respectively. and see how the Channel 1/3 and the Channel 1/4 peak lags vary. with these changes."," We alter the Lorentz factor $\Gamma$, the spectral parameters of the rest frame emission $\alpha$, $\beta$ and $E_p'$ ), the radius of the radiation surface $R$, and the rest-frame duration $t_d'$ of the intrinsic radiation, respectively, and see how the Channel 1/3 and the Channel 1/4 peak lags vary with these changes." + Figure 4 shows that the lag decreases with the Lorentz factor following Lag xLot., Figure \ref{lag_gamma} shows that the lag decreases with the Lorentz factor following Lag $\propto \Gamma^{-1}$. + We think this is a natural outcome of the relativistic boosting of the time structure., We think this is a natural outcome of the relativistic boosting of the time structure. + ‘Those pulses whose lags are larger may come from colliding shells with low Lorentz factors. according to the current standard models (e.g. Piran 1999).," Those pulses whose lags are larger may come from colliding shells with low Lorentz factors, according to the current standard models (e.g., Piran 1999)." +bv an equivalent deviation An of the differential antenna direction.,by an equivalent deviation $\Delta\bf{n}$ of the differential antenna direction. + The deviation induced by {he pseudo-dipole signal in a released WMAP map can be easily modeled., The deviation induced by the pseudo-dipole signal in a released WMAP map can be easily modeled. + For each measured temperature difference in the TOD used to produce the map. we substitute Cae pseudo-dipole signal caleulated by Eq.," For each measured temperature difference in the TOD used to produce the map, we substitute the pseudo-dipole signal calculated by Eq." + 2 for an assumed An (o produce a new., 2 for an assumed $\Delta\bf{n}$ to produce a new. + The temperature map produced by map [rom ihe new TOD can be used as a model of the pseudo-dipole signal in the released map., The temperature map produced by map from the new TOD can be used as a model of the pseudo-dipole signal in the released map. + In calculation we use the spacecraft coordinate svstem (N.Y.Z). where the X. axis is parallel to plane of radiators. —Z is the anti-sun direction of the spin axis. and Y is perpendicular to both.," In calculation we use the spacecraft coordinate system $(X, Y, Z)$ , where the $X$ axis is parallel to plane of radiators, $-Z$ is the anti-sun direction of the spin axis, and $Y$ is perpendicular to both." + The WMAP spacecraft scans the skv with a livbrid motion mode consists of rotation and precessing., The WMAP spacecraft scans the sky with a hybrid motion mode consists of rotation and precessing. + In spacecralt coordinates. (he LOS unit vectors of its (wo antennas are close lo Cr.y.z)=(0.0.94.20.33) aud Ce.y.2)=(0.—0.94. —0.33). and the spacecraft rotation is around the Z-axis.," In spacecraft coordinates, the LOS unit vectors of its two antennas are close to $(x,y,z)=(0, 0.94, -0.33)$ and $(x,y,z)=(0, -0.94, -0.33)$ , and the spacecraft rotation is around the $Z$ -axis." +" Suppose the overall LOS error An from all such effects is made up of three small vectors (0.0.0). (0.0.0) and (0.0.0) with ὁ= 0.01. each alone on the final map induces its own full-sky distribution of deviation 90/,. 9/, and 9/.. respectively,"," Suppose the overall LOS error $\Delta\bf{n}$ from all such effects is made up of three small vectors $(\delta, 0, 0)$, $(0,\delta, 0)$ and $(0, 0, \delta)$ with $\delta=0.01$ , each alone on the final map induces its own full-sky distribution of deviation $\delta t_x$ , $\delta t_y$ and $\delta t_z$, respectively." +" The induced deviation upon the released WAITAPT vear-1 Ql1-band map. 0/,. 0/,. and of. are shown in Fig."," The induced deviation upon the released WMAP7 year-1 Q1-band map, $\delta t_x$, $\delta t_y$, and $\delta t_z$ are shown in Fig." + 1., 1. + Results lor other vears and other bands are similar., Results for other years and other bands are similar. + It is easy to see [rom Fig., It is easy to see from Fig. +" 1 that 9/, and of. are highly correlated.", 1 that $\delta t_y$ and $\delta t_z$ are highly correlated. +" In. order (o avoid degeneracy issue we only use οἱ, and οἱ, in model fitting.", In order to avoid degeneracy issue we only use $\delta t_x$ and $\delta t_y$ in model fitting. +" The clean full skv temperature map where // is the corresponding WAIAP CAMB temperature map and the coellicients ο, and e, can be determined by minimizing /7,,,,.", The clean full sky temperature map where $t'$ is the corresponding WMAP CMB temperature map and the coefficients $c_x$ and $c_y$ can be determined by minimizing $t_{clean}^2$. +" Usinge the standard IDL programex “reeress”e we gel e,=—0.35. e,=—0.18 for the WMAPT vear-1 QlI-band map."," Using the standard IDL program ""regress"" we get $c_x=-0.35$, $c_y=-0.78$ for the WMAP7 year-1 Q1-band map." + We also model and remove the pseudo-dipole signal from the released WAIAP7T vear-1 to vear-7 maps of QI. Q2. Vl. V2. WI. W2. W3 and W4 bands.separatelv.," We also model and remove the pseudo-dipole signal from the released WMAP7 year-1 to year-7 maps of Q1, Q2, V1, V2, W1, W2, W3 and W4 bands,." +. From the clean maps we calculate (heir power spectraand residual quadruples., From the clean maps we calculate their power spectraand residual quadruples. + Table 1lists the obtained residual cquacdrupoles ofdifferent bands., Table 1lists the obtained residual quadrupoles ofdifferent bands. + The overallaverage clean quadiupole power for all bands is found to be, The overallaverage clean quadrupole power for all bands is found to be +Iu any case. due to the degeneracy of the material iu the density aud temperature ranges considered heroe. the computed ignition times (or the fits) rarely differ between the two cases more than,"In any case, due to the degeneracy of the material in the density and temperature ranges considered here, the computed ignition times (or the fits) rarely differ between the two cases more than." +50.. niaiu-sequence star comes frou the CNO aud °°FeimmeleiMostoftheinitialmctallicity inherited frou its ambient interstellar iuediuni at birth., Most of the initial metallicity of main-sequence star comes from the CNO and } nuclei inherited from its ambient interstellar medium at birth. + The slowest step in the CNO cvele is , The slowest step in the hydrogen-burning CNO cycle is proton capture onto }. +"ThisresultsinalltheCNO catalysts piling up into hwdrogeu-buruimg1ENwhenlydrogenprotoncaptureoutoHN. burning ou παπάς, all of the themainsequenceiscompleted.", This results in all the CNO catalysts piling up into } when hydrogen burning on the main sequence is completed. +Divinghelimm !Nisconvertediuto??No.," During helium burning, all of the } is converted into }." + Asa proxy for investigating the effects of metallicity in our a-chain based reaction network. we consider ignition while increasing the fraction of Νο(audthus this surrogate by usiug," Asa proxy for investigating the effects of metallicity in our $\alpha$ -chain based reaction network, we consider the ignition of a $\cfrac = 0.5$ constant-pressure ignition while increasing the fraction of } (and thus decreasing the abundance of oxygen)." + Neinlaveernetworks.decreasingtheabuudauceofoxvecu).We'llverify, We'll verify this surrogate by using } in larger networks. + The effects of increasingBS. from 0 to 0.05. and then further to 0.1 and 0.2. is shown in Fie. 5..," The effects of increasing from 0 to 0.05, and then further to 0.1 and 0.2, is shown in Fig. \ref{fig:nediff}. ." + Addition of even fairly modest amounts of neon can siguificautly 201) reduce the ignition times for, Addition of even fairly modest amounts of neon can significantly ) reduce the ignition times for + It is now fairly well-established that WofRavet (WR) stars av display two distinct (but pr'bably nou mutually exclusive) spectroscopic p)otterust of variability: (a) small-scale enuüission features servations:1ically moving from the line ceuter to the line on| an ⋅hourly Igitimescale le(c.g.?d .of Lépine1998)): (5) ιατ]ςnoetric‘ally larger line-profile deformations operating ou mich contimmun. onegcr basis ( davs. e.g.. Sunith&Willis199," It is now fairly well-established that Wolf-Rayet (WR) stars may display two distinct (but probably non mutually exclusive) spectroscopic patterns of variability: (a) small-scale emission features systematically moving from the line center to the line wings on an hourly timescale (e.g., \cite{Lepinephd}) ); (b) dramatically larger line-profile deformations operating on a much longer basis $\sim$ days, e.g., \cite{Smithwillis}) )." +" 1)). i the first phenomenon. observed ii most. (Gf not all) WR stars. is believed to be the consequence of the ↕⋟↥⋅⋜↧∶↴∙⊾⋯↸∖∐↸∖≼↧∙↻∪↴∖∷∖↴∏⋝↕↖⇁↑↿∐⋅↴⋝∏↕↸∖∐↑∐⋜↧⊓∐⋅↸∖∪↕≯↑∐↸∖⋯↕↑∏∪↖↖⇁∙↑↕↓↸∖ origi⋅⋅o of the ⋡↾↕↕⇈‘latter 4tvpeY of, variabiliUtiili vods still very much elusive."," Although the first phenomenon, observed in most (if not all) WR stars, is believed to be the consequence of the fragmented, possibly turbulent nature of the outflow, the origin of the latter type of variability is still very much elusive." +1 Remarkable; in. this. respect. is. the existence of a wel-estalished (although strougv epoch-cdepeudcut) large-scale. pattern of varjabilitv iu tjio two apparcutly single WR stars (P = 2Miwaτουpan’ + 0.002 d: Firmianiὁal. 1980)) and (P 227 + O01 d MeCandlissetal.199111 Moreletal. 1999)).," Remarkable in this respect, is the existence of a well-established (although strongly epoch-dependent) large-scale, pattern of variability in the two apparently single WR stars $\cal P$ = 3.763 $\pm$ 0.002 d; \cite{Firmani}) ) and $\cal P$ = 2.27 $\pm$ 0.04 d; \cite{McCandliss94}; \cite{Morel98b}) )." +" A majx observaional effort has been cirected on cstablising the true nature of these peculiar ohjects. Ίνα, whether this evelical variability is imduced by an orbiting uuseen (colapsed?)"," A major observational effort has been directed on establishing the true nature of these peculiar objects, i.e., whether this cyclical variability is induced by an orbiting unseen (collapsed?)" + companion or bv the LOational modulation of large-scale wind structures (6.8... Vreuxctal.1992:: Morel1 908: Ihuriesetal. 1999... aud reerences therein).," companion or by the rotational modulation of large-scale wind structures (e.g., \cite{Vreux}; \cite{Morel98phd}; \cite{Harries}, and references therein)." + Αλλοιeh the exact nature of these stews has vet to be muahicuouslv. settled. these studies reveal that rotatioial iioc.lation constitutes an attractive alernative to the|iuuv livothesis. especiaIv considering the recent recoenilon tha sole © stars (ti6 progenitors of WR stars) might possess such aziniutliaIv structured 0!tilows (Fullerto1etal.!997: Ikapereta. 1997)).," Although the exact nature of these stars has yet to be unambiguously settled, these studies reveal that rotational modulation constitutes an attractive alternative to the binary hypothesis, especially considering the recent recognition that some O stars (the progenitors of WR stars) might possess such azimuthally structured outflows \cite{Fullerton}; \cite{Kaper}) )." +" A prime target for furt1er Investigations is the seldom, apparentv single WN 5 star (ID lool) that has receutlv been shown to prese ioa spectral"," A prime target for further investigations is the seldom-studied, apparently single WN 5 star (HD 4004) that has recently been shown to present a spectral" +be possible only on high-mass acereting WDs (Mj&1 AL. ).,be possible only on high-mass accreting WDs $M_{1} \gtappeq 1$ $_{\odot}$ ). + Moreover. Ne are the only class of novae in which the WD is expected to gain more mass between eruptions than it loses during them.," Moreover, RNe are the only class of novae in which the WD is expected to gain more mass between eruptions than it loses during them." + This would make E Pyx a strong candidate Type la supernova progenitor., This would make T Pyx a strong candidate Type Ia supernova progenitor. + However. the recent study of the system by Schaefer.Pagnotta&Shara(2000). (see also Selvellietal. 2003)) suggests. first. that P. Pyx.js. in fact. in a transient evolutionary state. and. second. that. integrated over many nova eruptions. its WD does lose more mass than it. gains.," However, the recent study of the system by \cite{b18} (see also \citealp{b20}) ) suggests, first, that T Pyx, in fact, in a transient evolutionary state, and, second, that, integrated over many nova eruptions, its WD does lose more mass than it gains." + Alore specifically. Schaefer.Pagnotta&Shara(2009) suggest that T Pyx was an ordinary cataclysmic variable until it erupted as a nova in. 1866.," More specifically, \cite{b18} suggest that T Pyx was an ordinary cataclysmic variable until it erupted as a nova in 1866." +" This eruption triggered a winel-clriven supersoft: X-ray phase (as. first. suggested bv Ἱνηίσσο,Wine&Patterson 2000)). resulting in an unusually high. luminosity and. acerction rate."," This eruption triggered a wind-driven supersoft X-ray phase (as first suggested by \citealp{b7}) ), resulting in an unusually high luminosity and accretion rate." +" However. unlike in the original scenario proposed by WKnigee.Wine&Patterson (2000). Che supersoft phase is not self-sustaining. so that the aceretion rate has. been declining ever. since the 1866 nova eruption. Fron. AL~lo"" M. vero to 10 M."," However, unlike in the original scenario proposed by \cite{b7}, the supersoft phase is not self-sustaining, so that the accretion rate has been declining ever since the 1866 nova eruption from $\dot{M} \sim 10^{-7}$ $_{\odot}$ $^{-1}$ to $10^{-8} $ $_{\odot}$ $^{-1}$." + As a result. T Pyx has faded: by almost 2 magnitudes since the nova eruption (Schaefer.Pagnotta&Shara 2009)).," As a result, T Pyx has faded by almost 2 magnitudes since the nova eruption \citealp{b18}) )." + Dased on this. and the fact that T Pvx has already passed. its mean recurrence time by more than 20 vears. Schaefer.Pagnotta&Shara(2009) argue that Po Pyx might no longer even. be a recurrent. nova.," Based on this, and the fact that T Pyx has already passed its mean recurrence time by more than 20 years, \cite{b18} argue that T Pyx might no longer even be a recurrent nova." + Lf these ideas are correct. T Pyx is not a viable SN. la progenitor. ancl its remaining Lifetime can be substantially longer than a few million vears.," If these ideas are correct, T Pyx is not a viable SN Ia progenitor, and its remaining lifetime can be substantially longer than a few million years." + However. if all its ordinary nova eruptions are followed by. relatively long-lived ( 100. vrs) intervals of winel-clriven evolution at. high AL. its secular evolution may nevertheless be strongly affected. with significant implications for CV evolution more generally (sce also Section 5)).," However, if all its ordinary nova eruptions are followed by relatively long-lived (> 100 yrs) intervals of wind-driven evolution at high $\dot{M}$, its secular evolution may nevertheless be strongly affected, with significant implications for CV evolution more generally (see also Section \ref{SD}) )." + A kev assumption in virtually all of these arguments is that the photometric period measured by Pattersonοἱ(1998). is. in fact. the orbital period of the system.," A key assumption in virtually all of these arguments is that the photometric period measured by \cite{b13} is, in fact, the orbital period of the system." + So far. there has only been one attempt to obtain a spectroscopic period for P Pyx. by. Vogt.ctal.(1990)... who reporte a spectroscopic modulation with P=344 hours.," So far, there has only been one attempt to obtain a spectroscopic period for T Pyx, by \cite{b26}, who reported a spectroscopic modulation with $P=3.44$ hours." + Such a long orbital period above the CV period gap would. be much more consistent with the high accretion rate four in T Pyx., Such a long orbital period above the CV period gap would be much more consistent with the high accretion rate found in T Pyx. + In this study. we present the first. definitive spectroscopic determination of the orbital period of T Pyx. showing that it ijs. in fact. consistent with Patterson e al," In this study, we present the first definitive spectroscopic determination of the orbital period of T Pyx, showing that it is, in fact, consistent with Patterson et al." +s photometric period.,'s photometric period. +" We also use our. time-resolvec spectroscopy to estimate the main system parameters; such as the velocity semi-amplitude of the white cwarl (A1). the mass-ratio (q). the masses (M, anc AM») and the orbita inclination. (7)."," We also use our time-resolved spectroscopy to estimate the main system parameters, such as the velocity semi-amplitude of the white dwarf $K1$ ), the mass-ratio (q), the masses $M_{1}$ and $M_{2}$ ) and the orbital inclination $i$ )." + Finally. we discuss the implications of our results for the evolution of P Pyx and related svstenis.," Finally, we discuss the implications of our results for the evolution of T Pyx and related systems." + Alulti-Bibre Spectroscopy. of T. Pyx was obtained. during five nights in 2004 and 2005 with the GLIILAEFISFLAALES instrument mounted on the Unit Telescope 2 of the VET at ESO Paranal. Chile.," Multi-fibre Spectroscopy of T Pyx was obtained during five nights in 2004 and 2005 with the GIRAFFE/FLAMES instrument mounted on the Unit Telescope 2 of the VLT at ESO Paranal, Chile." + Phe data were taken in the integrated lieldeunit mode., The data were taken in the integrated field-unit mode. +" “Phe total field. of view in this mode is about 11.5"" 7.3"" and thus covers most of T Pyx's 10"" diameter nove shell (Williams1982))."," The total field of view in this mode is about 11.5"" $\times$ 7.3"" and thus covers most of T Pyx's 10"" diameter nova shell \citealp{b29}) )." +. We used. the fibre system ARGUS. which consists of BIT fibres. cüstributed across the field. of which 5 are pointing to a calibration unit ancl 15 are pointing to sky.," We used the fibre system ARGUS, which consists of 317 fibres distributed across the field, of which 5 are pointing to a calibration unit and 15 are pointing to sky." + Ehe grating order was 4. which gives à resolution of Ro12000.," The grating order was 4, which gives a resolution of R=12000." + Phe wavelength range was chosen between 4501 to 5078AL. so that the emission-line speetrum would include the Bowen blend at 4645 4650 and the Hell at 4686A.," The wavelength range was chosen between 4501 to 5078, so that the emission-line spectrum would include the Bowen blend at 4645 – 4650 and the HeII at 4686." + With this setup. the dispersion is 0.2 pix. corresponding to about 12.5 pix.," With this setup, the dispersion is 0.2 /pix, corresponding to about 12.5 $^{-1}$ /pix." + The full widths at. half-maximum (EWILMsS) of a few spectral lines obtained simultaneously with the science spectra from libres pointing to the calibration unit. indicate. that. the spectral resolution is about 0.4A., The full widths at half-maximum (FWHMs) of a few spectral lines obtained simultaneously with the science spectra from fibres pointing to the calibration unit indicate that the spectral resolution is about 0.4. + A log of the observations can be found in Table L.., A log of the observations can be found in Table \ref{tab:obs}. + The initial steps in the data reduction were performed using the ESO pipeline for CEILAEFEIS., The initial steps in the data reduction were performed using the ESO pipeline for GIRAFFE. + Ehe pipeline is based on the reduction software BLDRS from the Observatory of Geneva., The pipeline is based on the reduction software BLDRS from the Observatory of Geneva. + Phe basie functions. of the pipeline. are to oovide master calibration data and. dispersion. solutions., The basic functions of the pipeline are to provide master calibration data and dispersion solutions. + The pipeline also provides an image of the reconstructed icld of view. which can be used to associate a specific fibre o à given object.," The pipeline also provides an image of the reconstructed field of view, which can be used to associate a specific fibre to a given object." + In order to extract the spectrum. from he desired. fibre and to correct. for the contribution from he sky. background: and. cosmic ravs. the output. from the pipeline was processed. further in LRAF.," In order to extract the spectrum from the desired fibre and to correct for the contribution from the sky background and cosmic rays, the output from the pipeline was processed further in IRAF." + The PSE of our arget. T Pyx. is spread out over several fibres and 6 single ibre spectra containing significant target [Tux were extracted and median combined after weighting cach spectrum by the mean Fux in the region 4660 - 4710 A(covering Holl at 4686 A)).," The PSF of our target, T Pyx, is spread out over several fibres and 6 single fibre spectra containing significant target flux were extracted and median combined after weighting each spectrum by the mean flux in the region 4660 - 4710 (covering HeII at 4686 )." + Cosmic rays were removed by first binning the spectra over 7 pixels (the cosmic ravs have a typical width of 2 6 pixels)., Cosmic rays were removed by first binning the spectra over 7 pixels (the cosmic rays have a typical width of 2 $-$ 6 pixels). + Phe smoothed spectra were then subtracted from the corresponding fibre spectra to only. leave the residuals and the cosmic rays., The smoothed spectra were then subtracted from the corresponding fibre spectra to only leave the residuals and the cosmic rays. + Cosmic ravs were then removed and the residuals added back to the target spectra., Cosmic rays were then removed and the residuals added back to the target spectra. + Fibres containing the sky were extracted and combined to ereate a master-sky spectrum., Fibres containing the sky were extracted and combined to create a master-sky spectrum. + Finally. the master-sky. was subtracted from the combined science spectrum.," Finally, the master-sky was subtracted from the combined science spectrum." + T Pyx was observed again during four nights in March 2008. this time on the 6.5 meter Baacle telescope Magellan Lat Las Campanas. Chile (see Table L for a log of the observations).," T Pyx was observed again during four nights in March 2008, this time on the 6.5 meter Baade telescope Magellan I at Las Campanas, Chile (see Table \ref{tab:obs} for a log of the observations)." +" Long-«lit. spectroscopy. was obtained with the instrument INLACS using the Cra-L200-17.45 grating with a 0.9"" slit. resulting in a clispersion of 0.386. —pix. corresponcling o about 25 pix."," Long-slit spectroscopy was obtained with the instrument IMACS using the Gra-1200-17.45 grating with a 0.9"" slit, resulting in a dispersion of 0.386 /pix, corresponding to about 25 $^{-1}$ /pix." + We estimate that the spectral resolution of these observations is about 1.5A. as measured rom the EWIIMSs of a few spectral lines in the arc-Iamp spectra.," We estimate that the spectral resolution of these observations is about 1.5, as measured from the FWHMs of a few spectral lines in the arc-lamp spectra." + The overall spectra span over four CCDs and cover a total wavelength range of 4000 500A., The overall spectra span over four CCDs and cover a total wavelength range of 4000 – 4800. +. ATE frames from he four CCDs were treated separately during both the 2D and LD reduction steps., All frames from the four CCDs were treated separately during both the 2D and 1D reduction steps. + The speetra were reduced. in. LAF using. standard packages., The spectra were reduced in IRAF using standard packages. + A master bias produced. from combining all bias Tames obtained during the four nights was subtracted from he science frames and the overscan region was used. to remove the residual bias., A master bias produced from combining all bias frames obtained during the four nights was subtracted from the science frames and the overscan region was used to remove the residual bias. + A master fat-Hield. corrected. for illumination effects was produced.," A master flat-field, corrected for illumination effects was produced." + The spectra were then lat-Giclel corrected. ancl extracted., The spectra were then flat-field corrected and extracted. + Line. iclentifications of, Line identifications of +xocessius.,processing. +" However. the existeuce of Πο would have Oo be taken iuto account. because old svstenis with donors that have undergone significant mass loss could wave Ny;=2.105 and would thus have high nova rates, regardless of the accreted moetallicitv."," However, the existence of $^3$ He would have to be taken into account, because old systems with donors that have undergone significant mass loss could have $X_3\gtrsim2\E{-3}$ and would thus have high nova rates, regardless of the accreted metallicity." +. A proper wecdiction of the effect of donor composition requires a population-svuthesis calculation that includes further colplications such as binary aud donor evolutiou., A proper prediction of the effect of donor composition requires a population-synthesis calculation that includes further complications such as binary and donor evolution. + We cave this exercise for future work., We leave this exercise for future work. + To date. most observations only report ealactically-averaged ova rates. although some ΑΟ studies (Ciarcdulloetal.1987:Capaccioli1989:Daruleyal.2006) have found that NM31*s bulee produces more πονας per stellar huuinositv than its disk by a factor of ~5.," To date, most observations only report galactically-averaged nova rates, although some M31 studies \citep{ciar87,cap89,darn06} have found that M31's bulge produces more novae per stellar luminosity than its disk by a factor of $\sim 5$." + On the other haud. ealactically-averaged uova rates do not see any imnorphologv depeudeuce. finding instead that the huninosity-specific nova rate (LSNR) is roughly across all galaxy types at a value of δν| constantaoeLoa) (Williams&Shatter2001).. where Log is the A-—band solar huninositv.," On the other hand, galactically-averaged nova rates do not see any morphology dependence, finding instead that the luminosity-specific nova rate (LSNR) is roughly constant across all galaxy types at a value of $2 \pm 1$ $^{-1}$ $(10^{10} \ L_{\odot, \, K})^{-1}$ \citep{ws04}, where $L_{\odot, \, K}$ is the -band solar luminosity." + The LAIC and SAIC (and possibly Vireo chwart elliptical ealaxies: Neill&Shara 2005)). which have LSNRs higher by a factor of 3. are exceptions.," The LMC and SMC (and possibly Virgo dwarf elliptical galaxies; \citealt{ns05}) ), which have LSNRs higher by a factor of 3, are exceptions." + These mneasurenmieuts have large error bars due to μπα πο statistics and issues of completion caused by. both extinction and iufrequeut observations., These measurements have large error bars due to small number statistics and issues of completion caused by both extinction and infrequent observations. + A better measurement of nova rates will conie with new deep optical surveys with high cadeuces such as Pan-STARRS-1. Pau-STARRBS-1. iud the Large Synoptic Survey Telescope. which will see thousauds of novae every vear.," A better measurement of nova rates will come with new deep optical surveys with high cadences such as Pan-STARRS-1, Pan-STARRS-4, and the Large Synoptic Survey Telescope, which will see thousands of novae every year." + These will reduce the nova rate error bars and also possibly allow us to measure rates in different populations within other galaxies besides M21, These will reduce the nova rate error bars and also possibly allow us to measure rates in different populations within other galaxies besides M31. + Tn addition to this population-averaged observable. the composition could also have a detectable effect on individual systems.," In addition to this population-averaged observable, the composition could also have a detectable effect on individual systems." + Ta particular. the depletion of fuel can significantly increase the surface Ηχος] above the baseline set by the entropy released ching compression of the accreted laver (see Figs.," In particular, the depletion of fuel can significantly increase the surface luminosity above the baseline set by the entropy released during compression of the accreted layer (see Figs." + 10 and 11))., \ref{fig:lumz} and \ref{fig:lumx3}) ). + While this increase is still well below the accretiou lIuimunositv associated with eravitational energy release. it would be visible while the svstemi was du disk quiescence.," While this increase is still well below the accretion luminosity associated with gravitational energy release, it would be visible while the system was in disk quiescence." + Recurrent novae. in particular. would be ideal systenis in which to observe this brightening in quiesceut DIunünositv due to their short recurrence times of ~30 vr.," Recurrent novae, in particular, would be ideal systems in which to observe this brightening in quiescent luminosity due to their short recurrence times of $\sim 30 $ yr." + These observables are depeudent on the assuiptio- that convection is not initiated in C-cuhauced material., These observables are dependent on the assumption that convection is not initiated in C-enhanced material. + If instead U-vich euvelope material penetrates into C-rich material aud triggers convection there. the accreted composition will have little effect.," If instead H-rich envelope material penetrates into C-rich material and triggers convection there, the accreted composition will have little effect." + Thus. if these colmpositiou-dependcut effects are observed. they will provide evidence that convection for imu novae is initiated iu C-poor material aud that CNO euricluneut for these novae is due to convective shear mixiug or overshoot.," Thus, if these composition-dependent effects are observed, they will provide evidence that convection for many novae is initiated in C-poor material, and that CNO enrichment for these novae is due to convective shear mixing or overshoot." + We thank D. Towuslev for discussions. D. Paxton aud F. Tiuuues for valuable assistance with MESA. aud J. Steiufadt for nova rate calculations.," We thank D. Townsley for discussions, B. Paxton and F. Timmes for valuable assistance with MESA, and J. Steinfadt for nova rate calculations." + This work was supported bv the National Science Foundation uuder evauts PITY 05-51161 aud AST 07-07633, This work was supported by the National Science Foundation under grants PHY 05-51164 and AST 07-07633. +This suggests that. bv studying the backgrounds behind dwarl stars. we can predict the limes of future events and plan frequent. sensitive. high-resolution observations to test [or evidence of the planet's effect as a lens (2)..,"This suggests that, by studying the backgrounds behind dwarf stars, we can predict the times of future events and plan frequent, sensitive, high-resolution observations to test for evidence of the planet's effect as a lens \citep{DiStefano2005}." + What can we learn [rom (targeted observations?, What can we learn from targeted observations? + We can determine if (here is a planet in the habitable zone: we will either discover evidence of it. or place a quantifiable limit on the existence of one.," We can determine if there is a planet in the habitable zone: we will either discover evidence of it, or place a quantifiable limit on the existence of one." + If there is a planet. we can. under ideal circumstances. measure ils mass and its projected distance [rom the star.," If there is a planet, we can, under ideal circumstances, measure its mass and its projected distance from the star." + To plan such observations. we must identilv a large reservoir of potential lenses ling in [ront of dense backerounds.," To plan such observations, we must identify a large reservoir of potential lenses lying in front of dense backgrounds." +" In. front of the Magellanie Clouds. e.g.. we expect there to be approximately 200 (1600) dwarf stars with D,«50 pe (CD,<200 pe)."," In front of the Magellanic Clouds, e.g., we expect there to be approximately $200$ $1600$ ) dwarf stars with $D_L < 50$ pc $D_L < 200$ pc)." + Equation (4) indicates that. if observations with small values of fy and/or ον can be conducted. roughly 1056 of these stars. will produce detectable events within a decade.," Equation (4) indicates that, if observations with small values of $f_T$ and/or $\theta_{mon}$ can be conducted, roughly $10\%$ of these stars will produce detectable events within a decade." + The first step. therefore. is to study the backgrounds behind the known dwarf stars Iviug in front of the chosen background field. to determine which are the ones most likely to produce events in the near future. and (o predict the likely event ünmes so (hat appropriate monitoring observations can be planned for the duration of the predicted event.," The first step, therefore, is to study the backgrounds behind the known dwarf stars lying in front of the chosen background field, to determine which are the ones most likely to produce events in the near future, and to predict the likely event times so that appropriate monitoring observations can be planned for the duration of the predicted event." + For dwarl stars that do not lie in front of dense fields. serendipitous events are nevertheless possible: one such event has been observed (?7?)..," For dwarf stars that do not lie in front of dense fields, serendipitous events are nevertheless possible; one such event has been observed \citep{Gaudi2007, Fukui2007}." + between the positions of nearby dwarf stars and the poistions of more distant sources of light may identify future positional coincidences (hat can be predicted with hieh accuracy (?).., Cross-correlation between the positions of nearby dwarf stars and the poistions of more distant sources of light may identify future positional coincidences that can be predicted with high accuracy \citep{SalimGould}. . + Targeted lensing observations have been suggested by a variety of authors (??7??).. but have not vet been carried out.," Targeted lensing observations have been suggested by a variety of authors \citep{Feibelman1986, PaczynskiNearby, SalimGould, +DiStefano2005}, but have not yet been carried out." + Instead. astronomers have conducted large observing prograis in which (μον have monitored tens of millions of stars per night. (???)..," Instead, astronomers have conducted large observing programs in which they have monitored tens of millions of stars per night \citep{MACHO5.7, +OGLEIIIcatalog, EROSII3year}." + More than 3.500 microlensing event candidates have been discovered to date.," More than $3,500$ microlensing event candidates have been discovered to date." + The microlenses tend to be located al distances greater (han several kiloparsecs. and their presence is revealed (hrough (heir action as lenses.," The microlenses tend to be located at distances greater than several kiloparsecs, and their presence is revealed through their action as lenses." + While theoretical work has explored the discovery of nearby lenses by these programs (?).. several examples of nearby lenses suggest that dwarf stars constitute as many as LO-20% of the lenses producing detectable events (????)..," While theoretical work has explored the discovery of nearby lenses by these programs \citep{DiStefano2007}, several examples of nearby lenses suggest that dwarf stars constitute as many as $10-20\%$ of the lenses producing detectable events \citep{Nguyen2004, Kallivayalil2006, +Gaudi2007, Fukui2007}." + For monitoring programs. the expected rate of events caused by nearby dwarfs. with constant spatial density. Ny. in front of a sourcefield of area Q. is," For monitoring programs, the expected rate of events caused by nearby dwarfs, with constant spatial density $N_L,$ in front of a sourcefield of area $\Omega,$ is" +to orbital phase over more than one rotation period iu cach season (e.g. 1996.. Busaetal. 19993).,"to orbital phase over more than one rotation period in each season (e.g. \citealt{1996ApJ...470.1172D}, \citealt{1999A&A...350..571B}) )." + Iu this work we analyse the short aud long-term claomospheric activity of the nou-eclipsiug RS CVni stars most observed by IUE aud we compare the chromospheric and photospheric patterus of variability., In this work we analyse the short and long-term chromospheric activity of the non-eclipsing RS CVn stars most observed by IUE and we compare the chromospheric and photospheric patterns of variability. + Iu particular. in Section refsec.calibbaja.. we derive a relation to determine the Mouut Wilson iudex from the Me line-core fluxes measured on IUE low-resolution spectra.," In particular, in Section \\ref{sec.calibbaja}, we derive a relation to determine the Mount Wilson index from the Mg line-core fluxes measured on IUE low-resolution spectra." + As an application of this calibration. iu Section refsec.rscvn owe studv the Mount Wilson indices we derived from both IVE hieh aud low-resolution spectra of the RS CVn stars ΠΟ 22168 (V711 Tau. UR 1099). TD 21212 (UN Ari) and ΠΟ 221085 (II Peg).," As an application of this calibration, in Section \\ref{sec.rscvn} we study the Mount Wilson indices we derived from both IUE high and low-resolution spectra of the RS CVn stars HD 22468 (V711 Tau, HR 1099), HD 21242 (UX Ari) and HD 224085 (II Peg)." + Iu Paper πο iute-calibrated the iudex 5 aud Mg Hhxes using quasi-multaueous IUE high-resolution observations for a set of dwarf stars with spectral types F to I. Since in the present work we inteud to use this calibration to study the activity of RS CV svstems. which have sub-egiauts as their primary star. we check the accuracy of applying this calibration to cool sub-eiauts.," In Paper I we inter-calibrated the index $S$ and Mg fluxes using quasi-simultaneous IUE high-resolution observations for a set of dwarf stars with spectral types F to K. Since in the present work we intend to use this calibration to study the activity of RS CVn systems, which have sub-giants as their primary star, we check the accuracy of applying this calibration to cool sub-giants." + To do so. we obtained the IVE Ale fiuxes for those cool sub-giaut stars also observed at Alot Wilson Observatory.," To do so, we obtained the IUE Mg fluxes for those cool sub-giant stars also observed at Mount Wilson Observatory." + In Fig., In Fig. + 1 we show the calibration of Paper L aud we include these sub-eiauts.," \ref{fig.calibS_alta} we show the calibration of Paper I, and we include these sub-giants." + It cau be seen that these stars follow this calibration within the statistical OCYYOIS., It can be seen that these stars follow this calibration within the statistical errors. + Since the IUE database also provides a large number of low-resolution spectra of stars. in particular RS CVu stars. it is inportaut to incorporate to the svsteniatic studies of magnetic activity.," Since the IUE database also provides a large number of low-resolution spectra of late-type stars, in particular RS CVn stars, it is important to incorporate to the systematic studies of magnetic activity." + To this cud. in what follows we analyse the relation between the Me line-core fixes derivedfrom IUE low-resolution spectra aud the Mouut Wilson iudex.," To this end, in what follows we analyse the relation between the Mg line-core fluxes derivedfrom IUE low-resolution spectra and the Mount Wilson index." + Iu Fig., In Fig. + 2. we preseut some examples of IVE low-resolution spectra of three F. € aud IK iain sequence stars.," \ref{fig.esp_b} we present some examples of IUE low-resolution spectra of three F, G and K main sequence stars." + These spectra present a resolution of R=100 at 2700A.. they are available from the IUE public library (at /sdc.laeff.esa.es/cgi-ines/IUEdbsMY)). aud have been calibrated using the NEWSIPS (New Spectral nage Processing System) algorithin (Carhartetal. 1997)..," These spectra present a resolution of $R=400$ at 2700, they are available from the IUE public library (at ), and have been calibrated using the NEWSIPS (New Spectral Image Processing System) algorithm \citep{1997IUENN..57....1G}. ." + The iuterual accuracy of the low-resolution flux calibration is (Massa&Fitzpatrick 2000).., The internal accuracy of the low-resolution flux calibration is \citep{2000ApJS..126..517M}. . +where D is the distance to the svstem.,where $D$ is the distance to the system. + The quantities on the rhs of (his equation can all be measured. astrometicallv., The quantities on the rhs of this equation can all be measured astrometically. + We will assume that M. the mass of the more huninous component. can be estimated photometrically or spectroscopicallv.," We will assume that $M$, the mass of the more luminous component, can be estimated photometrically or spectroscopically." + And we will focus on the case in which the companion is known to be dark (or at least extremely. dim compared to the primary). /«L.," And we will focus on the case in which the companion is known to be dark (or at least extremely dim compared to the primary), $l\ll L$." + Under (hese assumptions. it is straightforward to determine i. the mass of the dark companion. Irom the astrometric observations.," Under these assumptions, it is straightforward to determine $m$, the mass of the dark companion, from the astrometric observations." + In general. a can be measured with approximately (he same precision as (he parallax. π.," In general, $\alpha$ can be measured with approximately the same precision as the parallax, $\pi$." + OL course this does not hold exactly., Of course this does not hold exactly. + Even for circular binary orbits. the inclination of the orbit will not match exactly the ecliptic latitude (1.e.. the inclination of the parallactic circle). so there will be either more or less information about the binary orbit than about (he reflex motion of (he Earth's orbit (parallax).," Even for circular binary orbits, the inclination of the orbit will not match exactly the ecliptic latitude (i.e., the inclination of the parallactic circle), so there will be either more or less information about the binary orbit than about the reflex motion of the Earth's orbit (parallax)." + Moreover. for certain binary orbits. notably edee-on highly eccentric orbits that “point” in our direction. the errors in a will be much larger (han the parallax errors because (he binary will show almost no astrometric motion.," Moreover, for certain binary orbits, notably edge-on highly eccentric orbits that “point” in our direction, the errors in $\alpha$ will be much larger than the parallax errors because the binary will show almost no astrometric motion." +" Nevertheless. [rom the standpoint of making an estimate of the errors lor a random ensemble of binaries. setting σι,~8, is a good approximation."," Nevertheless, from the standpoint of making an estimate of the errors for a random ensemble of binaries, setting $\sigma_\alpha \sim \sigma_\pi$ is a good approximation." +" This is confirmed by Figure 1.. where we plot a,/σι lor astrometric binaries will orbital solutions (i.e.. binaries of (wpe Ὁ} in the llipparcos catalog (ESA1997.Vol.10).."," This is confirmed by Figure \ref{fig:one}, where we plot $\sigma_\alpha/\sigma_\pi$ for astrometric binaries with orbital solutions (i.e., binaries of type `O') in the Hipparcos catalog \citep[Vol.\ 10]{hip}." + While these fits macle use of some auxiliary ground- spectroscopic information (uainly to establish the period). or constrained orbits to be circular. this should not have a major impact on the errors in a for periods P<3.3vi. the duration of the mission.," While these fits made use of some auxilliary ground-based spectroscopic information (mainly to establish the period), or constrained orbits to be circular, this should not have a major impact on the errors in $\alpha$ for periods $P\la 3.3\,\yr$, the duration of the mission." + While the figure shows some scatter. the two errors are roughly equal o1 average.," While the figure shows some scatter, the two errors are roughly equal on average." + Figure 2. shows (he sensilivily (50 detection) of Hipparcos to dark companions as a function of stellar (wpe. i.e.. the number ofLipparcos stars that can be probed lor companions ol a given mass.," Figure \ref{fig:two} shows the sensitivity $5\,\sigma$ detection) of Hipparcos to dark companions as a function of stellar type, i.e., the number of stars that can be probed for companions of a given mass." + These (vpes were assigned based on position in the color-amagnitude diagram when the parallaxes were sufficiently accurate. and on position in (he reduced proper-notion diagram otherwise.," These types were assigned based on position in the color-magnitude diagram when the parallaxes were sufficiently accurate, and on position in the reduced proper-motion diagram otherwise." + In the latter case. cistances were assigned based on stellar (ype and color and magnitude.," In the latter case, distances were assigned based on stellar type and color and magnitude." +" The figure shows that white dwarf (WD). NS. and DII companions of mass 0.6. 1.4 and 7 M... are respectively detectable among39%...G8Y%.. and of allHipparcos stars (Nii,— 118.000)."," The figure shows that white dwarf (WD), NS, and BH companions of mass 0.6, 1.4 and 7 $M_\odot$, are respectively detectable among, and of all stars $N_{Hip}=118,000$ )." + For periods of P=1.5vr. these fractions fall to21%.," For periods of $P=1.5\,\yr$, these fractions fall to,." +..47%...52%... At P~dva.sensitivity is seriously compromised by parallax aliasing and at shorter periods the sensititv. falls off rapidly.," At $P\sim 1\,\yr$,sensitivity is seriously compromised by parallax aliasing and at shorter periods the sensitity falls off rapidly." + On the other hand. for P23.8vr. orbital solutions become rapidly unstable.," On the other hand, for $P\ga 3.3\,\yr$, orbital solutions become rapidly unstable." + Hence. the sensitivities peak fairly sharply at ?~3.3ντ.," Hence, the sensitivities peak fairly sharply at $P\sim 3.3\,\yr$." + The overwhelming majority of theseMipparcos stars ave F ancl G cdwarfs. or giant stars whose progenilors are overwhelmingly F and G dwarls.," The overwhelming majority of these stars are F and G dwarfs, or giant stars whose progenitors are overwhelmingly F and G dwarfs." + The Ireequency of companions per log period for P~3.3vr among such stars is dfy/dlogP~17 (Duquennov&Mavor 1991)).," The frequency of companions per log period for $P\sim 3.3\,\yr$ among such stars is $df_b/d\log P\sim 7\%$ \citealt{DM91}) )." + From the previous paragraph. is sensitive to companions over about hall a dex," From the previous paragraph, is sensitive to companions over about half a dex" +We apply the same offset technique to metallicities as a function of mass.,We apply the same offset technique to metallicities as a function of mass. + The total stellar mass-metallicity relation of unbarred galaxies is fit with a second order polynomial and A O/H is defined as the otfset between the metallicity of a barred galaxy and the value predicted for its total stellar mass: The O/H residuals Gin bins of stellar mass) of the unbarred control sample have median values around. zero and scatter ypically less than 0.02 dex., The total stellar mass-metallicity relation of unbarred galaxies is fit with a second order polynomial and $\Delta$ O/H is defined as the offset between the metallicity of a barred galaxy and the value predicted for its total stellar mass: The O/H residuals (in bins of stellar mass) of the unbarred control sample have median values around zero and scatter typically less than 0.02 dex. + Note that. unlike the SPRs. no attempt is made to correct he abundance value to a total metallicity.," Note that, unlike the SFRs, no attempt is made to correct the abundance value to a total metallicity." + The metallicity values used throughout this paper are fibre values., The metallicity values used throughout this paper are fibre values. + Kewlev et al. (, Kewley et al. ( +2005) ound that covering fractions of >20% should yield abundances hat are representative of integrated light spectra over the entire galaxy.,2005) found that covering fractions of $>$ should yield abundances that are representative of integrated light spectra over the entire galaxy. + The majority of our galaxies have tibre covering fractions «20t.. so that imposing such a cut would leave a sample hampered by small number statistics.," The majority of our galaxies have fibre covering fractions $<$, so that imposing such a cut would leave a sample hampered by small number statistics." + However. considering the fibre stellar mass-metallicity relation circumvents the issue of aperture bias. under the assumption that the unbarred galaxies have a similar distribution of radial coverage to the barred sample.," However, considering the fibre stellar mass-metallicity relation circumvents the issue of aperture bias, under the assumption that the unbarred galaxies have a similar distribution of radial coverage to the barred sample." + The consistent distributions of mass and redshift between the barred and unbarrec galaxies indicate that this is a reasonable assumption., The consistent distributions of mass and redshift between the barred and unbarred galaxies indicate that this is a reasonable assumption. + The upper panel of Figure 4. shows AO/H as a function of total stellar mass., The upper panel of Figure \ref{delta_oh} shows $\Delta \rm{O/H}$ as a function of total stellar mass. +" The metallicities of barred galaxies are higher than the unbarred sample by «0.06 dex when the total mass of the galaxy M, > 10! M..", The metallicities of barred galaxies are higher than the unbarred sample by $\sim$ 0.06 dex when the total mass of the galaxy $_{\star}$ $>$ $^{10}$ $_{\odot}$. + This is a similar transition mass to the enhanced star formation rates in Figure 3.., This is a similar transition mass to the enhanced star formation rates in Figure \ref{delta_sfr}. + The lower panel of the same figure shows the offset from the mass-metallicity relation., The lower panel of the same figure shows the offset from the mass-metallicity relation. + The metallicities of barred galaxies are now higher by ~ 0.06 dex across the entire mass range., The metallicities of barred galaxies are now higher by $\sim$ 0.06 dex across the entire mass range. + The appearance of enhanced metallicities at low masses when tibre quantities are considered can be understood by plotting the fraction of mass in the fibre as a function of total stellar mass (Figure 51)., The appearance of enhanced metallicities at low masses when fibre quantities are considered can be understood by plotting the fraction of mass in the fibre as a function of total stellar mass (Figure \ref{delta_mass}) ). +" Since barred galaxies with M, « 10! M. are dominated by late-types (Nair Abraham 2010b) whose bulges and bars are small compared to their disks. the fibre contains a smaller fraction of the total galaxy mass (see also Figure 1)."," Since barred galaxies with $_{\star}$ $<$ $^{10}$ $_{\odot}$ are dominated by late-types (Nair Abraham 2010b) whose bulges and bars are small compared to their disks, the fibre contains a smaller fraction of the total galaxy mass (see also Figure \ref{bar_images}) )." +" Above M, > 10! M.. there is a rapid transition to a population dominated by early-type spirals. whose bulge fraction is much higher."," Above $_{\star}$ $>$ $^{10}$ $_{\odot}$, there is a rapid transition to a population dominated by early-type spirals, whose bulge fraction is much higher." + The low fraction of mass covered by the tibrefor low stellar mass galaxies results in a more pronounced ditference in the fibre mass-metallicity oftsets in the lower panel of Figure 4.., The low fraction of mass covered by the fibrefor low stellar mass galaxies results in a more pronounced difference in the fibre mass-metallicity offsets in the lower panel of Figure \ref{delta_oh}. . +We have searched for C» and CN emission bands.,We have searched for $_2$ and CN emission bands. + Figure 8. presents the observed spectra obtained in the 3700-4000 rrange (CN band). and Fig.," Figure \ref{f:cn} presents the observed spectra obtained in the 3700-4000 range (CN band), and Fig." + 9. presents the 4800-5200 rregion (C+ bands) after subtraction of the solar spectrum., \ref{f:c2} presents the 4800-5200 region $_2$ bands) after subtraction of the solar spectrum. + A theoretical spectrum of both CN and C» emission bands has been superimposed on these spectra., A theoretical spectrum of both CN and $_2$ emission bands has been superimposed on these spectra. + We computed the CN spectrum by using the model described in ?.., We computed the CN spectrum by using the model described in \cite{zucconi:1985}. +" We computed the C spectrum with the model described in ? with transition moments |[D,-yF=[D107? aatomie unit.", We computed the $_2$ spectrum with the model described in \cite{rousselot:2000} with transition moments $|D_{a-X}|^2=|D_{c-X}|^2=3.5\times 10^{-6}$ atomic unit. + Both spectra were computed for similar heliocentric distance and velocity km.s! ) and convolved with an instrument response function similar to that of FORS | in the mode used during our observations oof FWHM)., Both spectra were computed for similar heliocentric distance and velocity (-3.097 $^{-1}$ ) and convolved with an instrument response function similar to that of FORS 1 in the mode used during our observations of FWHM). + As we've seen. no CN nor C» emission lines are apparent.," As we've seen, no CN nor $_2$ emission lines are apparent." + It is only possible to derive an upper limit for both of these species., It is only possible to derive an upper limit for both of these species. +" In the case of CN the brightest possible CN emission band can be estimated to have an intensity equal to about 2.0x107"" 7.s eerg.cmA! (corresponding to a 4-sigma detection", In the case of CN the brightest possible CN emission band can be estimated to have an intensity equal to about $2.0\times 10^{-17}$ $^{-2}$ $^{-1}.$ $^{-1}$ (corresponding to a 4-sigma detection + , +fits the data well.,fits the data well. + The temperature of the seed photons is again fixed at 0.3 keV. As for the global spectrum. we remark that the absorption column returned from the fit with this model is slightly higher than the value obtained with CPL.," The temperature of the seed photons is again fixed at 0.3 keV. As for the global spectrum, we remark that the absorption column returned from the fit with this model is slightly higher than the value obtained with CPL." + We note a significant evolution of the absorption column density and of the power law photon index between the two intervals., We note a significant evolution of the absorption column density and of the power law photon index between the two intervals. + In order to check whether the evolution of both was real. we re-performed the fits freezing Ny to its mean value (Table 6)).," In order to check whether the evolution of both was real, we re-performed the fits freezing $N_{\mathrm H}$ to its mean value (Table \ref{tab:rxtefit}) )." + The spectral parameters obtained for both fits are compatible with those found leaving all parameters free to vary. except the power law photon index which tends to a softer value in interval 1 (EF.=2.11+ 0.05). and a to harder one for interval 2 (PV=1.38+ 0.03).," The spectral parameters obtained for both fits are compatible with those found leaving all parameters free to vary, except the power law photon index which tends to a softer value in interval 1 $\Gamma=2.11\pm 0.05$ ), and a to harder one for interval 2 $\Gamma=1.38\pm0.03$ )." + Since Ny and E are tightly correlated. we also re-performed the fit freezing Γ to its mean value. and allowing Ny to vary.," Since $N_{\mathrm H}$ and $\Gamma$ are tightly correlated, we also re-performed the fit freezing $\Gamma$ to its mean value, and allowing $N_{\mathrm H}$ to vary." + While for interval 2 the spectral parameters obtained in this case are close to the ones obtained when everything is free to vary. this method yields a poor fit for interval 1.," While for interval 2 the spectral parameters obtained in this case are close to the ones obtained when everything is free to vary, this method yields a poor fit for interval 1." + We take these results as evidence that both F and Ny vary between both intervals., We take these results as evidence that both $\Gamma$ and $N_{\mathrm H}$ vary between both intervals. + Note that this likely variation of the absorption is reinforced by the variations of Ny we observe between Obs., Note that this likely variation of the absorption is reinforced by the variations of $N_{\mathrm H}$ we observe between Obs. + |. 2 and 3 (Table 6)).," 1, 2 and 3 (Table \ref{tab:rxtefit}) )." + As mentioned previously in all the and spectra. an iron Ka fluorescence line i5 required in the spectral fits.," As mentioned previously in all the and spectra, an iron $\alpha$ fluorescence line is required in the spectral fits." + The parameters of the line obtained from the spectral fit to each observation are reported in Table 8.., The parameters of the line obtained from the spectral fit to each observation are reported in Table \ref{tab:line}. + Note that these are obtained from the fits with the phenomenological models. but no significant differences are found in the spectra where a model is used.," Note that these are obtained from the fits with the phenomenological models, but no significant differences are found in the spectra where a model is used." + One could wonder whether the line is intrinsic to itself. or whether it could originate from the Galactic background.," One could wonder whether the line is intrinsic to itself, or whether it could originate from the Galactic background." + The main argument that points towards an origin intrinsic to the system is that if the line was due to the Galactic ridge. we would expect its flux to be roughly constant.," The main argument that points towards an origin intrinsic to the system is that if the line was due to the Galactic ridge, we would expect its flux to be roughly constant." + This is obviously not the case here., This is obviously not the case here. +" It is interesting to note that in almost all cases. (except in the “Bright” and ""Faint states). the parameters inferred for the line could be indicative of a narrow line. rather than a broad line."," It is interesting to note that in almost all cases, (except in the “Bright"" and ""Faint"" states), the parameters inferred for the line could be indicative of a narrow line, rather than a broad line." + In fact for both instruments the upper limit on the line width indicates that we are limited by the instrumental spectral resolution., In fact for both instruments the upper limit on the line width indicates that we are limited by the instrumental spectral resolution. + The case of the faint and bright states seem different since our fits indicate a broad line (Table 8))., The case of the faint and bright states seem different since our fits indicate a broad line (Table \ref{tab:line}) ). + Our spectral fits to the data (Sec. 3.2.1)), Our spectral fits to the data (Sec. \ref{sec:integspec}) ) +" 1dicate that the ""Bright"" state is spectrally intermediate between the “Faint” state and the ""Ultra-bright one. as we will discuss further below."," indicate that the “Bright” state is spectrally intermediate between the “Faint” state and the “Ultra-bright” one, as we will discuss further below." + In particular in the soft X-rays (4-8 keV). a black body component could be present in the spectra of the “Bright” state. and represents the data well for the faint state.," In particular in the soft X-rays (4–8 keV), a black body component could be present in the spectra of the “Bright” state, and represents the data well for the faint state." + In both cases. a fit to the data with a black body and a Gaussian (besides the power law) does not converge on sensitive. parameters for either of the components.," In both cases, a fit to the data with a black body and a Gaussian (besides the power law) does not converge on sensitive parameters for either of the components." +" The broad line we found instead could be indicative of a ""mixture"" of faint black body emission (poorly constrained given the 4 keV lower boundary of our fits) and a Gaussian line.", The broad line we found instead could be indicative of a “mixture” of faint black body emission (poorly constrained given the 4 keV lower boundary of our fits) and a Gaussian line. + This possibility is compatible with the evolution between the three “states”. as clearly seen of Fig. 2..," This possibility is compatible with the evolution between the three “states”, as clearly seen of Fig. \ref{fig:integspec}," +" where black body emission dominates the soft X-ray in the “Faint state"" (when either no line is needed or a very broad one). to the ""Ultra Bright"" state. where no black body is detected. and with a good constraint on the We performed a thorough spectral analysis of the source using a well-sampled high energy monitoring with in 2003 March-May. and adding 3RXTE observations performed at different epochs."," where black body emission dominates the soft X-ray in the “Faint state” (when either no line is needed or a very broad one), to the “Ultra Bright” state, where no black body is detected, and with a good constraint on the We performed a thorough spectral analysis of the source using a well-sampled high energy monitoring with in 2003 March–May, and adding 3 observations performed at different epochs." + As already observed (Paper 1). is highly variable on timescales from months down to hours. and it can show variations on shorter timescales as seen during observation 3 (Fig. 5)).," As already observed (Paper 1), is highly variable on timescales from months down to hours, and it can show variations on shorter timescales as seen during observation 3 (Fig. \ref{fig:PCAHXT}) )." + This behaviour is reminiscent of Galactic X-ray binaries (XRB). and our deep analysis further confirms the Galactic nature of IGR 71914040951. already proposed in other publications (Paper|. Corbet et al.," This behaviour is reminiscent of Galactic X-ray binaries (XRB), and our deep analysis further confirms the Galactic nature of IGR J19140+0951, already proposed in other publications (Paper1, Corbet et al." + When observed withRXTE. the source was dim. with a |- keV (unabsorbed) luminosity of ~3.4x 10°°x(D/10 Κρο)” erg/s (Obs.3). and a spectrum typical of Comptonisation of soft photons by a low temperature plasma (AT~5 keV) with a relatively high optical depth (7~ 5).," When observed with, the source was dim, with a 1-200 keV (unabsorbed) luminosity of $\sim 3.4 \times 10^{36}\times$ (D/10 $^2$ erg/s (Obs.3), and a spectrum typical of Comptonisation of soft photons by a low temperature plasma $kT\sim 5$ keV) with a relatively high optical depth $\tau \sim 5$ )." +" This could Correspone to the ""ultra faint state” which seems to be the state in which the source spends most of its time as indicated by our monitoring.", This could correspond to the “ultra faint state” which seems to be the state in which the source spends most of its time as indicated by our monitoring. + During the observations. the luminosity is up to about 10 times higher. with a maximum of ~3.7x10 «D/IO kpey erg/s. Here significant spectral evolution is observed since in one case a," During the observations, the luminosity is up to about 10 times higher, with a maximum of $\sim 3.7 \times 10^{37}\times$ (D/10 $^2$ erg/s. Here significant spectral evolution is observed since in one case a" +Once loggg is set. Chere is a direct relation between the eravitw of the belt loggii and ils velocity Viu.,"Once $\log{g_{wd}}$ is set, there is a direct relation between the gravity of the belt $\log{g_{belt}}$ and its velocity $V_{belt}$." +" For the accretion belt plus WD composite models. we created a grid in WD temperature Tip from 16.000IX. to 35.000Ix. in steps of 1000Ilx. and in accretion belt temperature {νι from 25.000IX (to 55.000IN. in steps of 100019. However. the results are nol verv sensitive to the value of loggpa as long as logi4;<7.5. corresponding to Visinizz3.000—4.000 km !. where the lower limit corresponds to loggj.)=8.37 (a 0.8687. WD) and the upper limit corresponds to logguy=8.54 (a 0.96AM,, WD). ancl we have assumed 7=60 degrees."," For the accretion belt plus WD composite models, we created a grid in WD temperature $T_{eff}$ from 16,000K to 35,000K in steps of 1000K, and in accretion belt temperature $T_{belt}$ from 25,000K to 55,000K in steps of 1000K. However, the results are not very sensitive to the value of $\log{g_{belt}}$ as long as $\log{g_{belt}} < 7.5$, corresponding to $V_{belt} \sin{i} \approx 3,000-4,000$ km $^{-1}$, where the lower limit corresponds to $\log{g_{wd}}=8.37$ (a $0.86 M_{\odot}$ WD) and the upper limit corresponds to $\log{g_{wd}}=8.54$ (a $0.96 M_{wd}$ WD), and we have assumed $i=60$ degrees." + In the case of the WD plus belt the distance d is given in a way similar to the WD only case with where we sel d=65 pe., In the case of the WD plus belt the distance $d$ is given in a way similar to the WD only case with where we set d=65 pc. +" The best-litting white dwarf plus accretion belt fit with fixed distance (d=65pc) and a free radius A; vielded 7,,;—23. 000K. Si abundance = 2.0 x solar. C abundance = 0.2 x solar. V,sini= 4O0knm J|. with a radius Ry=0.0087... corresponding (o a mass Moyo=0.96.U. or logg=8.54."," The best-fitting white dwarf plus accretion belt fit with fixed distance (d=65pc) and a free radius $R_{wd}$ yielded $T_{wd} = 23,000$ K, Si abundance = 2.0 $\times$ solar, C abundance = 0.2 $\times$ solar, $V_{rot}\sin{i}= 400$ km $^{-1}$ , with a radius $R_{wd}=0.0087R_{\odot}$, corresponding to a mass $M_{wd}=0.96 M_{\odot}$ or $\log{g}=8.54$." + The belt temperature was {γι=48. 000Ix. with a velocity of Vigsin£24. 000km !.," The belt temperature was $T_{belt} = 48,000$ K, with a velocity of $V_{belt}\sin{i} \approx 4,000$ km $^{-1}$." + In this model. the white dwarf contributed of the FUV flux and the accretion belt of the FUV flus. and the fractional area of the accretion belt was24%.," In this model, the white dwarf contributed of the FUV flux and the accretion belt of the FUV flux, and the fractional area of the accretion belt was." +.. The 42 value of this fit was 7.06., The $\chi^2_{\nu}$ value of this fit was 7.06. + This best-fitting white dwarf plus accretion belt composite model is displaved in figure 5 aud in Table 2 (model 12)., This best-fitting white dwarf plus accretion belt composite model is displayed in figure 5 and in Table 2 (model 12). + We find this composite fit to be clearly superior to the single temperature and accretion disk - only fits., We find this composite fit to be clearly superior to the single temperature and accretion disk - only fits. + The remarkable lowering of the reduced 42 value for the accretion belt fit is additional confirmation of the findings by Sionetal.(1996.1997.2001). and Gansicke&Benermann(1996) that VW llis white dwarl has an inhomogeneous temperature distribution and that the most likely explanation is that of an accretion belt of higher temperatureat its equatorial latitudes.," The remarkable lowering of the reduced $\chi^2_{\nu}$ value for the accretion belt fit is additional confirmation of the findings by \citet{sio96,sio97,sio01} and \citet{gan96} that VW Hyi's white dwarf has an inhomogeneous temperature distribution and that the most likely explanation is that of an accretion belt of higher temperatureat its equatorial latitudes." + On the other hand. the best-litting combination WD plus accretion belt model with a fixed WD radius and distance(model 13 in Table 2. M=0.86... ). had a 472 = 10.9.," On the other hand, the best-fitting combination WD plus accretion belt model with a fixed WD radius and distance(model 13 in Table 2, $M=0.86 M_{\odot}$ ), had a $\chi^2_{\nu}$ = 10.9." + The stellar and belt parameters corresponding to (hiis best-fit are as follows., The stellar and belt parameters corresponding to this best-fit are as follows. +" The WD has an average surface temperature Typp = 22.000. V;,;sin= 400knm b with solar abundances."," The WD has an average surface temperature $T_{eff}$ = 22,000K, $V_{rot}\sin{i}= 400$ km $^{-1}$, with solar abundances." +" The accretion belt has the parameters 77,5; = 50.000. and τιsin;= 3.000km !."," The accretion belt has the parameters $T_{belt}$ = 50,000K, and $V_{belt} \sin{i}= 3,000$ km $^{-1}$." + The bell area is of the WD surface and the belt contributes of the total flux while the WD contributes of flux., The belt area is of the WD surface and the belt contributes of the total flux while the WD contributes of flux. + This composite two-lemperature fit is shown in figure 6., This composite two-temperature fit is shown in figure 6. + It is interesting to note that irrespective of whether the radius (and consequently the mass) of the white dwarf was kept fixed or not in the models. (he best fit models with a lower AZ andwith parameters (Mu. d. /) consistent with the values assessed for the system," It is interesting to note that irrespective of whether the radius (and consequently the mass) of the white dwarf was kept fixed or not in the models, the best fit models with a lower $\chi^2_{\nu}$ andwith parameters $M_{wd}$ , $d$ , $i$ ) consistent with the values assessed for the system" +of the ages have been given in that paper: occasionally thev max be as large as a factor of 2 to 3: errors that large will uot detract frou our main conclusions.,of the ages have been given in that paper; occasionally they may be as large as a factor of 2 to 3; errors that large will not detract from our main conclusions. + Our sample has been selected from the catalogue of stars within pc from the Sun by Woolleyctal.(1970): this catalogue is definitely incomplete and so iust be our saluple., Our sample has been selected from the catalogue of stars within pc from the Sun by \citet{wool:70}; this catalogue is definitely incomplete and so must be our sample. + Even within the distance Bits eiven in Table l1 stars will exist that we could have inchided but did uot., Even within the distance limits given in Table \ref{tab:distlimits} stars will exist that we could have included but did not. + This incompleteness does not. however. iutroduce a statistical bias: we have checked that for a given spectral type the distribution of the stellar distances is the same for stars with a disk as for stars without a disk: this is illustrated by the average distances in Table 7..," This incompleteness does not, however, introduce a statistical bias: we have checked that for a given spectral type the distribution of the stellar distances is the same for stars with a disk as for stars without a disk; this is illustrated by the average distances in Table \ref{tab:distances}." + Fig., Fig. + 6 presets eraphically the fraction of the (visual) stellar light recmutted im the infrared bv the disk as a function of the stellar age., \ref{fig:tau-of-age} presents graphically the fraction of the (visual) stellar light reemitted in the infrared by the disk as a function of the stellar age. + Similar diagrams based mainly on IRAS results. have been published before- sec. for example. Tollandetal.(1998).," Similar diagrams based mainly on IRAS results, have been published before- see, for example, \citet{holl:98}." +". À eeneral. continuous correlation appears: disks around PMS-stars (οιο, Herbie AeDoe) are more massive than disks around stars like 3 Pic and Vega. and the disk around the Sun is still less massive,"," A general, continuous correlation appears: disks around PMS-stars (e.g. Herbig AeBe) are more massive than disks around stars like $\beta$ Pic and Vega, and the disk around the Sun is still less massive." + These earlier diagrams have almost no data on the age range shown in Fig., These earlier diagrams have almost no data on the age range shown in Fig. + 6 aud the new ISO data fill in an important hole., \ref{fig:tau-of-age} and the new ISO data fill in an important hole. +" Table & suniuanizes the detections at GO. separatelv for sars of different agen and of ciffereut spectral type together with the same nunibers for stars with a disk: iu the column marked “tot” the total umber of stars (disks plus no-disks) is shown and uuder the heading ""disk the iuuber of stars with a disk.", Table \ref{tab:detstat} summarizes the detections at 60 separately for stars of different age and of different spectral type together with the same numbers for stars with a disk; in the column marked “tot” the total number of stars (disks plus no-disks) is shown and under the heading “disk” the number of stars with a disk. + The total count is Sl mscad of 81 because for three of our target stars (two A-stars iud one IK-star) the age could not be estimated ina satisfying manner., The total count is 81 instead of 84 because for three of our target stars (two A-stars and one K-star) the age could not be estimated in a satisfying manner. + Table & shows that the stars with a etected disk are systematically vounger than the stars without disk: out of the 15 stars vouuger than LOO Ayr uine (6054)) have a disk: out of the 66 older stars ouly five have a disk (1)., Table \ref{tab:detstat} shows that the stars with a detected disk are systematically younger than the stars without disk: out of the 15 stars younger than 400 Myr nine ) have a disk; out of the 66 older stars only five have a disk ). + Eurthermore. there exists a more or less sharply defined age aove Which a star has no longer a disk.," Furthermore, there exists a more or less sharply defined age above which a star has no longer a disk." + This is best demonstrated by the A-stars., This is best demonstrated by the A-stars. + Six A-stars have a disk: the stellar ages are 220. 2LO. 280. 350. 360. 380 Myr.," Six A-stars have a disk; the stellar ages are 220, 240, 280, 350, 360, 380 Myr." + For the A-stars without disk the corresponding ages are 300. 320. 350. 380. 120. 150. 5LO. 890. 1230 My: 350 to LOO Ner is a well-defined transition region.," For the A-stars without disk the corresponding ages are 300, 320, 350, 380, 420, 480, 540, 890, 1230 Myr: 350 to 400 Myr is a well-defined transition region." + We couclude that the A stars in genera arive on the Dualn-sequeuce with a disk. but that hey loose the disk within 50 Myr when they are about 350.3vr old.," We conclude that the A stars in general arrive on the main-sequence with a disk, but that they loose the disk within 50 Myr when they are about 350 Myr old." + Is what is true for he A-stars also valid or the stars of other spectral types?, Is what is true for the A-stars also valid for the stars of other spectral types? +" Our answer is ""probably ves”: of the five EF. C. and Is stars vounecr than LOO Ny. three (GO%)) have a disk."," Our answer is “probably yes”: of the five F, G, and K stars younger than 400 Myr three ) have a disk." + Of the GI. EF. €. aud K stars older than LOO Myr five iive a disk (one in twelve or )).," Of the 61 F, G, and K stars older than 400 Myr five have a disk (one in twelve or )." + The percentages are he same as for the A-stars out the for voung Cc and Is-sars Is based on only three detections., The percentages are the same as for the A-stars but the for young G- and K-stars is based on only three detections. + Tt secs that the disks around EF. €. aud I& stars decay in a sinularly short time after arrival on the main sequence.," It seems that the disks around F, G, and K stars decay in a similarly short time after arrival on the main sequence." + An inuuediate question is: do stars arrive at the nai sequence with a disk?, An immediate question is: do stars arrive at the main sequence with a disk? + Studies of EC-MWUL-SCquchce stars show that disks are common. mt whether they always exist is unknown.," Studies of pre-main-sequence stars show that disks are common, but whether they always exist is unknown." + The sequence| of ages of the A-stars shows that thie three voungest A-stars have a disk., The sequence of ages of the A-stars shows that the three youngest A-stars have a disk. + This sueeestsOO that all stars arrive on he main secpuede? with a disk. but the sugecstionOO is based on simall-uimuber," This suggests that all stars arrive on the main sequence with a disk, but the suggestion is based on small-number" +This is the same form as used in Yang et al. (,This is the same form as used in Yang et al. ( +"2008), with scaling parameters: logM;= 9.8, logΜι,=10.7, a=0.6 and 8=2.9.","2008), with scaling parameters: $log~M_s = 9.8$ , $log~M_h = 10.7$ , $\alpha = 0.6$ and $\beta = 2.9$." + Halo masses for the spiral galaxies in our sample were estimated using the spiral galaxy relation of Mandelbaum et al. (, Halo masses for the spiral galaxies in our sample were estimated using the spiral galaxy relation of Mandelbaum et al. ( +"2006), also shown in Fig. 1..","2006), also shown in Fig. \ref{fig1}." + Note the data in Fig., Note the data in Fig. +" 2 show a similar form to the relationship adopted between galaxy stellar and halo mass (Fig. 1)),"," \ref{fig2} show a similar form to the relationship adopted between galaxy stellar and halo mass (Fig. \ref{fig1}) )," + with only an offset in the X-axis values., with only an offset in the X-axis values. + Galaxy stellar masses are taken from Spitler et al. (, Galaxy stellar masses are taken from Spitler et al. ( +2008) and Peng et al. (,2008) and Peng et al. ( +2008).,2008). + For the Spitler et al. (, For the Spitler et al. ( +"2008) estimates, the Chabrier (2003) initial stellar mass function is used to match the Mandelbaum et al. (","2008) estimates, the Chabrier (2003) initial stellar mass function is used to match the Mandelbaum et al. (" +2006) relation.,2006) relation. + There is a small (0.07 dex in logMstetiar) systematic offset between the masses derived using the Spitler et al. (, There is a small (0.07 dex in $log~M_{stellar}$ ) systematic offset between the masses derived using the Spitler et al. ( +2008) technique and those published in Peng et al. (,2008) technique and those published in Peng et al. ( +2008).,2008). + This offset is removed from the Peng et al. (, This offset is removed from the Peng et al. ( +2008) masses before analysis.,2008) masses before analysis. + The GC system numbers in Spitler et al. (, The GC system numbers in Spitler et al. ( +2008) were converted to GC system total masses by multiplying the numbers by the average GC mass of 4x10° Mo.,2008) were converted to GC system total masses by multiplying the numbers by the average GC mass of $4\times10^5$ $_{\odot}$. + Peng et al. (, Peng et al. ( +2008) summed the total stellar mass of all GCs in each galaxy.,2008) summed the total stellar mass of all GCs in each galaxy. +" For galaxies in common, the Spitler et al. ("," For galaxies in common, the Spitler et al. (" +2008) GC masses were used because they come from wide-field imaging where the entire spatial coverage of the GC system was observed.,2008) GC masses were used because they come from wide-field imaging where the entire spatial coverage of the GC system was observed. + The NGC 3311 GC system number estimate is from Wehner et al. (, The NGC 3311 GC system number estimate is from Wehner et al. ( +2008).,2008). +" For reference, a table is available online with relevant properties of the main sample."," For reference, a table is available online with relevant properties of the main sample." +" The GC system mass of Local Group (LG) dwarf galaxies is estimated by summing the individual GC stellar masses inferred from V-band photometry (Harris 1996; Webbink 1985; Da Costa Mould 1988) and applying a mass-to-light ratio of 2.2 for an old, metal-poor stellar population (Bruzual Charlot 2003)."," The GC system mass of Local Group (LG) dwarf galaxies is estimated by summing the individual GC stellar masses inferred from V-band photometry (Harris 1996; Webbink 1985; Da Costa Mould 1988) and applying a mass-to-light ratio of 2.2 for an old, metal-poor stellar population (Bruzual Charlot 2003)." + LG dwarf galaxy stellar masses are from V-band absolute magnitudes (Lotz et al., LG dwarf galaxy stellar masses are from V-band absolute magnitudes (Lotz et al. + 2004) with appropriate mass-to-light ratios from Bruzual Charlot (2003) for the age and metallicity of the stellar populations (Lotz et al., 2004) with appropriate mass-to-light ratios from Bruzual Charlot (2003) for the age and metallicity of the stellar populations (Lotz et al. + 2004)., 2004). +" Total masses (Miotalος06, where σο is the central velocity dispersion) and distances to these galaxies are from Mateo (1998)."," Total masses $M_{total}\propto\sigma_0^2$, where $\sigma_0$ is the central velocity dispersion) and distances to these galaxies are from Mateo (1998)." + The analysis includes five galaxy clusters selected because their central galaxy has a reliable GC system number measurement available., The analysis includes five galaxy clusters selected because their central galaxy has a reliable GC system number measurement available. +" GCs associated with galaxy clusters will reside in the central cluster galaxy, around satellite galaxies and in the intracluster medium (see refresults))."," GCs associated with galaxy clusters will reside in the central cluster galaxy, around satellite galaxies and in the intracluster medium (see \\ref{results}) )." +" The total mass of GCs associated with satellite galaxies was approximated by integrating the observed cluster galaxy mass functions (Sandage, Bingegeli, Tammann et al."," The total mass of GCs associated with satellite galaxies was approximated by integrating the observed cluster galaxy mass functions (Sandage, Bingegeli, Tammann et al." + 1985; Ferguson Sandage 1991; Yagi et al., 1985; Ferguson Sandage 1991; Yagi et al. +" 2002; Trentham, Tully Mahdavi 2006) after convolving them with a quadratic fit to data in Fig. 2.."," 2002; Trentham, Tully Mahdavi 2006) after convolving them with a quadratic fit to data in Fig. \ref{fig2}." + No global constraint on an intracluster GC population exists., No global constraint on an intracluster GC population exists. +" We therefore use a prediction from computer simulations of galaxy clusters (Bekki Yahagi 2006) that intracluster GCs make up (with RMS = 5%)) of the total cluster GC mass, independent of the clusters total mass."," We therefore use a prediction from computer simulations of galaxy clusters (Bekki Yahagi 2006) that intracluster GCs make up (with RMS = ) of the total cluster GC mass, independent of the clusters total mass." +" Because the study of Bekki Yahagi (2006) was limited to a rudimentary GC formation prescription, formal uncertainties on these total cluster GC masses are taken to be40%."," Because the study of Bekki Yahagi (2006) was limited to a rudimentary GC formation prescription, formal uncertainties on these total cluster GC masses are taken to be." +. Cluster halo masses are taken from the following sources: Virgo and Hydra clusters (Girardi et al., Cluster halo masses are taken from the following sources: Virgo and Hydra clusters (Girardi et al. +" 1998), NGC 1407 (Brough et al."," 1998), NGC 1407 (Brough et al." +" 2006), Antlia (Nakazawa et al."," 2006), Antlia (Nakazawa et al." +" 2000), and Fornax (Drinkwater, Gregg Colless 2001)."," 2000), and Fornax (Drinkwater, Gregg Colless 2001)." + In Fig., In Fig. +" ὃ we show that GC system masses (Macs) are directly proportional to the total halo mass of its host galaxy, with a scatter comparable to the observational uncertainties."," \ref{fig3} we show that GC system masses $M_{GCS}$ ) are directly proportional to the total halo mass of its host galaxy, with a scatter comparable to the observational uncertainties." + The form of the line in Fig., The form of the line in Fig. + 3 is logMnato=logMacs+ 4.15., \ref{fig3} is $log~M_{halo} = log~M_{GCS}+4.15$ . +" This can be related to the initial total baryon mass of a galaxy, by assuming the universal baryon fraction (i.e. Miaryon/Mnato£2Ώυ/Ώπι&0.17; Komatsu et al."," This can be related to the initial total baryon mass of a galaxy, by assuming the universal baryon fraction (i.e. $M_{baryon}/M_{halo}\approx\Omega_{b}/\Omega_{m}\approx0.17$; Komatsu et al." + 2008) applies on all galactic scales in the early Universe., 2008) applies on all galactic scales in the early Universe. +" For galaxies with Mnato>5x10!!Mo, the relationship in Fig."," For galaxies with $M_{halo}>5\times10^{11} M_{\odot}$, the relationship in Fig." + 3 appears to be invariant to the local environment and to the morphological type of the galaxy (see discussion in Spitler et al., \ref{fig3} appears to be invariant to the local environment and to the morphological type of the galaxy (see discussion in Spitler et al. + 2008)., 2008). +" In contrast, the statistical relationships between stellar and halo mass depend on whether the galaxy is a spiral or an elliptical type (see Fig. 1))."," In contrast, the statistical relationships between stellar and halo mass depend on whether the galaxy is a spiral or an elliptical type (see Fig. \ref{fig1}) )." +" Furthermore, the statistical relationship between galaxy stellar mass and the halo mass is strongly non-linear."," Furthermore, the statistical relationship between galaxy stellar mass and the halo mass is strongly non-linear." + 'This means that for very massive galaxies their halo masses derived from the stellar mass relation are poorly constrained., This means that for very massive galaxies their halo masses derived from the stellar mass relation are poorly constrained. + 'The direct proportionalitybetween GCsystem masses and their host halo is consistent with our current understanding of GC formation., The direct proportionalitybetween GCsystem masses and their host halo is consistent with our current understanding of GC formation. + While stars in a galaxy, While stars in a galaxy +the integral of f between the maximum aud minimum value of μις,the integral of $f$ between the maximum and minimum value of $N_{HI}$. +" We normalize the theoretical distribution such as to give a number of detectious with Nyy,>1.6κ104 ? equal to the observed one.", We normalize the theoretical distribution such as to give a number of detections with $N_{HI}\ge 1.6\times 10^{17}$ $^{-2}$ equal to the observed one. + Two maxima for the Likelihood are fouud: ΤΙe >68.356. > . aud >99% coulidence levels in the X—a plane are shown in Figure | where the filled dots indicates the location of the maxima as in eq. (15))," Two maxima for the Likelihood are found: The $>68.3\%$, $>95.5\%$ , and $>99\%$ confidence levels in the $X-\alpha$ plane are shown in Figure 4 where the filled dots indicates the location of the maxima as in eq. \ref{bestfit1}) )" + and (16))., and \ref{bestfit2}) ). + The self gravitaing gas solution (4j=0. a= 1.63. X= 3.33) lies wel outside the >99% conticence leve (we woild need the 99.999% confidence level to include it) aixd therefore it is not consistent witl the data.," The self gravitating gas solution $\eta=0$, $\alpha=4.63$ , $X=3.33$ ) lies well outside the $>99\%$ confidence level (we would need the $\%$ confidence level to include it) and therefore it is not consistent with the data." + We have also checked that a similar concusion hoks if we use |ve exact self gravitating eas soltou. as giveu by eq. (7)).," We have also checked that a similar conclusion holds if we use the exact self gravitating gas solution, as given by eq. \ref{sigma_sg}) )," + in deriving the JVμιNu !elation., in deriving the $N_{HI\perp}-N_{H\perp}$ relation. + For this case both N au the best fit a value are withi 1% of the values obalned usie eq. (5)), For this case both $X$ and the best fit $\alpha$ value are within $1\%$ of the values obtained using eq. \ref{density}) ) + aicy =0 for the vertica gas stratification., and $\eta=0$ for the vertical gas stratification. + In Figure 5 we compare te observed valie of te cunmulative funetion with the theoretical ones derived from the integral of te projected HI coluuii deusity: we show resuls for the two best fit inodels (the two maxima in FEigure [) ard fo ‘two models cor'esponcding t«) the highest and lowest X values on the >95.5% conidence level of Figure {., In Figure 5 we compare the observed value of the cumulative function with the theoretical ones derived from the integral of the projected HI column density; we show results for the two best fit models (the two maxima in Figure 4) and for two models corresponding to the highest and lowest X values on the $>95.5\%$ confidence level of Figure 4. + For points which lave Lo defined μι. Le. which have large errors. we tleni coiupiute treir best clistribttiou [or a give vf N spreadiug the data in the alowed range of Ij accoring o f weighted wih he redslit yatha.," For points which have no defined $N_{HI}$ , i.e. which have large errors, we then compute their best distribution for a given $f$ by spreading the data in the allowed range of $N_{HI}$ according to $f$ weighted with the redshift path." + Between all the possible periiiatious of poins with undetermined Nyy; we t choose hose wlich satisfies best the UÜ-tes on the deviatious between tlie observed aud the ex)ecLed eundative functions over the error interval. /2. and over Nyy. C (see Paper ΠΠ lor more detals and for the use of a numerical siiulatio1 to proof the validity of this approac1).," Between all the possible permutations of points with undetermined $N_{HI}$ we then choose those which satisfies best the $U$ -test on the deviations between the observed and the expected cumulative functions over the error interval, $R$, and over $N_{HI}$, $C$ (see Paper II for more details and for the use of a numerical simulation to proof the validity of this approach)." + For X—« viide the 99% confidence level of Figure 1 he Ix-8 tests on f aud C are satisfied o the 99.9% level., For $X-\alpha$ inside the $99\%$ confidence level of Figure 4 the K-S tests on $R$ and $C$ are satisfied to the $\%$ level. + We |ave proved that tle gas clistribution beween the LLS axl the DLS region follows a single power law with index a>2 if the ionization level is such that less than 1% of the total gas is neutral when Nyy=1.6x10! > 7., We have proved that the gas distribution between the LLS and the DLS region follows a single power law with index $\alpha > 2$ if the ionization level is such that less than $1\%$ of the total gas is neutral when $N_{HI}=1.6 \times 10^{17}$ $^{-2}$ . + There is 1o need of a dist{bution more complicated than a power law once one takes iito account lonizatiol effects., There is no need of a distribution more complicated than a power law once one takes into account ionization effects. + Our results on a and X still hold even if we do not iuclude in the daa set the clampect lires with 5€W<104A oor if we exclude a certain percentage of these liies due to possible bleudiug withsinaller lines., Our results on $\alpha$ and $X$ still hold even if we do not include in the data set the damped lines with $5\le W\le 10$ or if we exclude a certain percentage of these lines due to possible blending withsmaller lines. + We shall discussbere some results relative to the best-fit values ofWY and a as given in eq. (15)), We shall discusshere some results relative to the best-fit values of$X$ and $\alpha$ as given in eq. \ref{bestfit1}) ) + aud in eq. (16)).," and in eq. \ref{bestfit2}) )," + and to the twomost extreme values of XN ou the >95.5% confidence level.," and to the twomost extreme values of $X$ on the $>95.5\%$ confidence level," +is constrained form the observed level of [Ti/Fe] among halo stars (seeKobayashietal.2006).,is constrained form the observed level of [Ti/Fe] among halo stars \citep[see][]{Kobayashi_06}. +". For [O/Fe] and the observed properties, i.e., a large scatter at a [Mg/Fe],low-metallicity and an overall decreasing trend, are well reproduced."," For [O/Fe] and [Mg/Fe], the observed properties, i.e., a large scatter at a low-metallicity and an overall decreasing trend, are well reproduced." +" For [Ti/Fe], the observed data around [Ti/Fe] ~+0.3 is lacking."," For [Ti/Fe], the observed data around [Ti/Fe] $\sim$ +0.3 is lacking." +" However, medium-resolution observations suggest the presence of stars exhibiting such a high ratio (Kirbyetal.2010)."," However, medium-resolution observations suggest the presence of stars exhibiting such a high ratio \citep{Kirby_10}." +". Note that an unusual upward Ti/Fe feature for [Fe/H] -1 is reproduced by the combination of low and high Ti/Fe yields in SNe II and SNe Ia, respectively."," Note that an unusual upward Ti/Fe feature for [Fe/H] -1 is reproduced by the combination of low and high Ti/Fe yields in SNe II and SNe Ia, respectively." +" Since Ca is also synthesized highly in SNe Ia, our model predicts a similar upward feature for Ca/Fe."," Since Ca is also synthesized highly in SNe Ia, our model predicts a similar upward feature for Ca/Fe." + This is indeed observed in the Fnx dSph (Letarteetal.2010)., This is indeed observed in the Fnx dSph \citep{Letarte_10}. +". Our model anticipates that the observed dispersion in both and at a low-metallicity is an end result of [Ba/Fe]the IMF [Mg/Fe]variation which yields a high [Ba/Fe] and a low [Mg/Fe] by m,=25 and a reverse correlation by m,=50 Mo..", Our model anticipates that the observed dispersion in both [Ba/Fe] and [Mg/Fe] at a low-metallicity is an end result of the IMF variation which yields a high [Ba/Fe] and a low [Mg/Fe] by $m_u$ =25 and a reverse correlation by $m_u$ =50. +" Figure 6 demonstrates that the predicted correlation of [Ba/Fe] and [Mg/Fe] is broadly compatible with the observed one given by the data of the Fnx GC, though this analysis should be validated by much more data."," Figure 6 demonstrates that the predicted correlation of [Ba/Fe] and [Mg/Fe] is broadly compatible with the observed one given by the data of the Fnx GC, though this analysis should be validated by much more data." +" Observed unusual Ba enhancement relative to Fe, a- elements, and Eu in some dSphs as well as in the LMC at their late evolution is investigated by modeling the Fornax dSph galaxy case."," Observed unusual Ba enhancement relative to Fe, $\alpha$ -elements, and Eu in some dSphs as well as in the LMC at their late evolution is investigated by modeling the Fornax dSph galaxy case." +" Our claim is that its effect occurs because the IMF's truncate a high mass end at around 25Mo,, that causes the reduction of a-elements and Fe but no (little) influence on r- or s-process elements in their ejection, associated with the death of stars covering a wide range of masses."," Our claim is that its effect occurs because the IMFs truncate a high mass end at around 25, that causes the reduction of $\alpha$ -elements and Fe but no (little) influence on $r$ - or $s$ -process elements in their ejection, associated with the death of stars covering a wide range of masses." + Such a truncated IMF is assured by the theoretical agument given by the IGIMF scheme in which the number of massive stars depends on the SFR in galaxies., Such a truncated IMF is assured by the theoretical agument given by the IGIMF scheme in which the number of massive stars depends on the SFR in galaxies. +" In addition, the star formation history of the Fnx dSph revealed by recent surveys, together with a large dispersion in elemental ratios such as [a/Fe] and suggests a rather complex chemical history not [Ba/Fe],represented by a single model but composed of a few evolutionary paths resulting from different speed of star formation as well as from a differenta form of the IMF."," In addition, the star formation history of the Fnx dSph revealed by recent surveys, together with a large dispersion in elemental ratios such as $\alpha$ /Fe] and [Ba/Fe], suggests a rather complex chemical history not represented by a single model but composed of a few evolutionary paths resulting from a different speed of star formation as well as from a different form of the IMF." +" Previous work on the chemical evolution of dSphs interpret the lower [a/Fe] ratios in these galaxies as being due to a combination of the time-delay model and a low SFR (e.g.,Carigietal.2002;Ikuta&ArimotoLanfranchi&Matteucci2003;Kirbyetal. 2011)."," Previous work on the chemical evolution of dSphs interpret the lower $\alpha$ /Fe] ratios in these galaxies as being due to a combination of the time-delay model and a low SFR \citep[e.g.,][]{Carigi_02, Ikuta_02, Lanfranchi_03, Kirby_11}." +". This interpretation can explain the observed [Ba/Eu] ratios in dSphs with the inclusion of the galactic wind effect (Lanfranchietal.2008);; however, it does not favor the same increasing [Ba/Fe] trend as [Ba/Eu] (see,however,tionongalacticwindfortheSculptor dSph).."," This interpretation can explain the observed [Ba/Eu] ratios in dSphs with the inclusion of the galactic wind effect \citep{Lanfranchi_08}; however, it does not favor the same increasing [Ba/Fe] trend as [Ba/Eu] \citep[see, however,][as the model with a different assumption on galactic wind for the Sculptor dSph]{Fenner_06}." +" Further, it confronts the fact that a massive dwarf galaxy, i.e., the LMC, exhibits the same level of increase in [Ba/Fe] as"," Further, it confronts the fact that a massive dwarf galaxy, i.e., the LMC, exhibits the same level of increase in [Ba/Fe] as" +11330).,1334). + Finally. the GIS30AT aud CAGOAL spectra were co-aligned aud. co-added using lines of the same species .11260 vs .11526).," Finally, the G130M and G160M spectra were co-aligned and co-added using lines of the same species 1260 vs 1526)." + Co-addition was performed by a snuple stim of counts. after aliguiment.," Co-addition was performed by a simple sum of counts, after alignment." + For cach pixel. we tracked the wavelength. umber of counts upper aud lower error estimates due to Poisson statistics. and the effective exposure time.," For each pixel, we tracked the wavelength, number of counts, upper and lower error estimates due to Poisson statistics, and the effective exposure time." + We applied a flat-field correction by takine the STScI COS team 1d flats (D. Alassa. priv.," We applied a flat-field correction by taking the STScI COS team 1d flats (D. Massa, priv." + col).," comm.)," + processed with a low-pass filter. to remove the high-frequency noise.," processed with a low-pass filter, to remove the high-frequency noise." + These flats account for the erid-wire pattern in the COS FUV detectors. aud are applied to the effective exposure tine for cach pixel (note that they are not applied to the counts directly. since we use the counts to caleulated the Poisson errors).," These flats account for the grid-wire pattern in the COS FUV detectors, and are applied to the effective exposure time for each pixel (note that they are not applied to the counts directly, since we use the counts to calculated the Poisson errors)." + Since we acciunulate counts. the spectra contain sliarp discontinuities in regions where the waveleneth οποιο resulted imm a larger effective exposure time. or iu regions affected by the eridewire pattern.," Since we accumulate counts, the spectra contain sharp discontinuities in regions where the wavelength dithering resulted in a larger effective exposure time, or in regions affected by the grid-wire pattern." + Thus our counts spectra do not have a sinooth coutimmun but the countrate spectrin does., Thus our counts spectra do not have a smooth continuum but the count spectrum does. + Finally. we normalized the count-rate spectrum by piecewise fitting of low-order Chebyshev polvuomials to chunks of spectrum ~50LOOA lone.," Finally, we normalized the count-rate spectrum by piecewise fitting of low-order Chebyshev polynomials to chunks of spectrum $\sim 50-100\A$ long." + Our procedure vields a normalized spectrum with both upper aud lower error estimates., Our procedure yields a normalized spectrum with both upper and lower error estimates. + In regions of hieh counts (2 30). these estimates couveree to the usual eaussian approximation of VN. with the upper aud lower estimates the same (1.6. converging to the usual lo errors).," In regions of high counts $\simgt 30$ ), these estimates converge to the usual gaussian approximation of $\sqrt{N}$, with the upper and lower estimates the same (i.e. converging to the usual $\sigma$ errors)." + To be couservative. when quoting errors on nieasured quantities; we quote the larger of these two error estimates.," To be conservative, when quoting errors on measured quantities, we quote the larger of these two error estimates." + The S/N of the resulting spectra varies from ~| per resolution at the shortest waveleugths (~ A). peaking at ~8 per rescl at ~LLOOA. and decliniug to ~203 per resel at the red euc of the spectrmm (1500 A).," The S/N of the resulting spectra varies from $\sim 4$ per resolution at the shortest wavelengths $\sim 1135\A$ ), peaking at $\sim 8$ per resel at $\sim 1400\A$, and declining to $\sim 2-3$ per resel at the red end of the spectrum $\sim 1800\A$ )." + By choosing multiple appropriate central waveleneth settings for cach erating. we ensured continuous waveleneth coverage (ie. no gaps) at the expense of lower S/N in the waveleneth reeious with only one erating setting.," By choosing multiple appropriate central wavelength settings for each grating, we ensured continuous wavelength coverage (i.e. no gaps), at the expense of lower S/N in the wavelength regions with only one grating setting." +" We obtained a high resolution optical spectrumof oon 26 March 2010 using the Tieh Resolution. Echelle Spectrometer (IIIRES:?). on Weck 1. We employed the UV cross-disperser aud the C1 decker (slit width 0.86"")). resultiug in a resolution of ~L800 or —Glins|."," We obtained a high resolution optical spectrumof on 26 March 2010 using the High Resolution Echelle Spectrometer \citep[HIRES;][]{vogt-etal-94-HIRES} on Keck I. We employed the UV cross-disperser and the C1 decker (slit width ), resulting in a resolution of $\sim +48000$ or $\sim 6\kms$." + The erating angles were set to give coverage down to 3050À. in order to detect low-: aabsorptiou.," The grating angles were set to give coverage down to $3050\A$, in order to detect $z$ absorption." + The data were reduced. with the ITIBRedux pipeline included with the NIDLpackage., The data were reduced with the HIRedux pipeline included with the XIDL. +.. Tudividual orders were normalized after extraction with a series of Chebyshev polvnouuals to remove the echelle blaze function. and then combined iuto a final 1D spectrin.," Individual orders were normalized after extraction with a series of Chebyshev polynomials to remove the echelle blaze function, and then combined into a final 1D spectrum." + After the (ος obscrvations were conducted we obtained spectra of several galaxies in the field close to the QSO with the Low Resolution Imaging Spectrometer (LRIS:?) ou the Keck I telescope., After the COS observations were conducted we obtained spectra of several galaxies in the field close to the QSO with the Low Resolution Imaging Spectrometer \citep[LRIS;][]{oke-etal-95-LRIS} on the Keck I telescope. + We obtained long-slit spectra of 1 galaxies on 25 March 2010., We obtained long-slit spectra of 4 galaxies on 25 March 2010. + We eiiploved the delichroic.A with the 600/7500 erating on the red side. aud the 600/L000 eria on the blue side.," We employed the dichroic, with the 600/7500 grating on the red side, and the 600/4000 grism on the blue side." + The slit size was1.. yielding a FWIIM resolution of L7A (~200]aus.+) over a wavelength range of 5600200A on the red side: the blue side covered the range 00605500A at a resolution of 3.9LIA FWOAL (~300k1misly," The slit size was, yielding a FWHM resolution of $4.7\A$ $\sim 200\kms$ ) over a wavelength range of $5600 - 8200\A$ on the red side; the blue side covered the range $3000 - 5500\A$ at a resolution of $3.9-4.1\A$ FWHM $\sim 300\kms$ )." + The data were reduced using the LRIS pipeline iu the NIDL package., The data were reduced using the LRIS pipeline in the XIDL package. + Fig 1l shows an nuage of the field taken from the SDSS. centered ou the QSO position.," Fig \ref{fig: keck_field} shows an image of the field taken from the SDSS, centered on the QSO position." + Objects classified as galaxies iu SDSS are labeled in a polar co-ordinate svstena. with a position anuele (degrees east of north) and an aneular distance from the QSO (iu aresec).," Objects classified as galaxies in SDSS are labeled in a polar co-ordinate system, with a position angle (degrees east of north) and an angular distance from the QSO (in arcsec)." + Galaxies for which we obtained spectroscopic redshifts are euclosed in red boxes. aud the measured redshifts iucluded. in the label," Galaxies for which we obtained spectroscopic redshifts are enclosed in red boxes, and the measured redshifts included in the label." + Objects classified as galaxies in SDSS but which lack spectroscopic redshifts are enclosed in erecu diunonds., Objects classified as galaxies in SDSS but which lack spectroscopic redshifts are enclosed in green diamonds. + The maxim range of the SDSS photometric redshift estimates are listed., The maximum range of the SDSS photometric redshift estimates are listed. + We have also examined the photometric redshift probability distributions for these objects produced by. 7.., We have also examined the photometric redshift probability distributions for these objects produced by \citet{cunha-etal-09-SDSS-photoz}. + None of these objects are cousistent with being at the redshift of the absorbers. although we note that contamination of objects very close to the QSO by the QSO light may be an issue. and it would be ideal to obtain further spectroscopy follow-up for these galaxies.," None of these objects are consistent with being at the redshift of the absorbers, although we note that contamination of objects very close to the QSO by the QSO light may be an issue, and it would be ideal to obtain further spectroscopy follow-up for these galaxies." + Uulabele objects in Figure 1— are classified as stars., Unlabeled objects in Figure \ref{fig: keck_field} are classified as stars. + Higher resolution imaeimug with ce. TST. is au ongoing conrponeut of our multiiustrüment project. aud woul be helpful in the future for quantitative micasures of ealaxy morphology.," Higher resolution imaging with e.g. HST, is an ongoing component of our multi-instrument project, and would be helpful in the future for quantitative measures of galaxy morphology." + Iu Figure 2. we show the absorption lines affiliated with the ealaxy227_19., In Figure \ref{fig: stack-plot} we show the absorption lines affiliated with the galaxy. +". We plot the contimmin jorinalized spectra iu a velocity space. with respect to he spectroscopic redshitt of the galaxy. z,4]cea=0.3529 (all velocities iu this paper are with respect to this "," We plot the continuum normalized spectra in a velocity space, with respect to the spectroscopic redshift of the galaxy, $\zgal = 0.3529$ (all velocities in this paper are with respect to this zero-point)." +Ate=|365kms| we detect strong saturated aabsorptiou., At $v = +365\kms$ we detect strong saturated absorption. + The first 5 lines are saturated. and the svsteni breaks iuto two hain conponeuts in the higher order μαι lines. at velocities of e=|365.Ebims.!.," The first 5 lines are saturated, and the system breaks into two main components in the higher order Lyman lines, at velocities of $v += +365, +445\kms$." + Both coniponeuts lave associated weak aabsorptiou., Both components have associated weak absorption. + The spectriun also shows a hint of possible aabsorptiou. but these features are only significant at the 20 level. aud we consider them non-detectious.," The spectrum also shows a hint of possible absorption, but these features are only significant at the $2\sigma$ level, and we consider them non-detections." + Higher quality data would be required to confirm these features., Higher quality data would be required to confirm these features. +" Significantly. we detect no aabsorption in the TIRES data to very sensitive upper Πατ»,"," Significantly, we detect no absorption in the HIRES data to very sensitive upper limits." + Due to its lack of strong metal liue. absorption. we describe this cloud as “metal-poor. a name we will justify in Section [.1..," Due to its lack of strong metal line absorption, we describe this cloud as “metal-poor”, a name we will justify in Section \ref{subsec: metal-poor}. ." + This svstem also contains a acl, This system also contains a much +The differential equation possesses the right properties both at small and at large distances.,The differential equation possesses the right properties both at small and at large distances. + At a large distance from the disk. the modulus in the complete elliptic integrals tends to zero.," At a large distance from the disk, the modulus in the complete elliptic integrals tends to zero." + We have then . Since the total mass of the disk is given by the expression the aboveVain ODE can then be rearranged into As this equation must be satisfied for any s». we must have which is the expected behavior (the disk is no longer distinguishable from a point mass).," We have and then Since the total mass of the disk is given by the expression the above ODE can then be rearranged into As this equation must be satisfied for any $s$, we must have which is the expected behavior (the disk is no longer distinguishable from a point mass)." + This also implies that rn perform ⋀↾⋅≏⊔∣⋯∣↑⋔⋋↾∐∏∁⊖⋅≏∐⋪⋂∐⋯↿⋔⊖⋂⊓∶↔↾⋯⋖∣↜⊜⊽∣⋅≪∠∣⋯⋟⋅∖∖⇁⊜∁∐∏ a second order expansion of the S-term by expanding the elliptic integral accordingly (?)..," This also implies that At a short distance around the origin (i.e. $r \ll \ain$ ), we can perform a second order expansion of the $S$ -term by expanding the elliptic integral accordingly \citep{gradryz65}." + We find and then the ODE becomes whose solution is At second order. the potential in the inner domain (7< diy) IS quadratic with the cylindrical radius R (while. the gravitational acceleration is linear).," We find and then the ODE becomes whose solution is At second order, the potential in the inner domain $r \ll \ain$ ) is quadratic with the cylindrical radius $R$ (while the gravitational acceleration is linear)." + As in ?.. we consider a vertical stratification of the form for |<]€f (and 0 elsewhere). where po is the density at the disk midplane. / the local semi-thiekness (both a function of the radius « ?..," As in \cite{hp09}, we consider a vertical stratification of the form for $|z| \le h$ (and $0$ elsewhere), where $\rho_0$ is the density at the disk midplane, $h$ the local semi-thickness (both a function of the radius $a$ \cite{hp09}," +objects randomly. distributed within their allowed: volume.,objects randomly distributed within their allowed volume. + We now calculate. cach galaxys isophotal magnitude. a corrected magnitude and their total magnitude and sum the final number distribution according to absolute magnitude.," We now calculate each galaxy's isophotal magnitude, a corrected magnitude and their total magnitude and sum the final number distribution according to absolute magnitude." + This is plotted in Fig 4 for total. corrected and isophotal absolute magnitucles.," This is plotted in Fig \ref{fig:N_M} for total, corrected and isophotal absolute magnitudes." + We then reconstruct. the luminosity function using a ων prescription (as our simulations contain no clustering this should be an optimal estimator)., We then reconstruct the luminosity function using a $1/V_{Max}$ prescription (as our simulations contain no clustering this should be an optimal estimator). + Fig., Fig. + 5 shows the recovered luminosity. functions., \ref{fig:lfs} shows the recovered luminosity functions. + The LEs of 5, The LFs of Fig. + demonstrate. the impact of surface. brightness selection as they are all drawn from the same DDE: the only cilferenee is the limiting isophote and the choice of magnitude measurement., \ref{fig:lfs} demonstrate the impact of surface brightness selection as they are all drawn from the same BBF; the only difference is the limiting isophote and the choice of magnitude measurement. + The range of published values is shown as the shaded. area (excluding the LORS Lin ct al., The range of published values is shown as the shaded area (excluding the LCRS Lin et al. + 1996)., 1996). + Also shown is the limit solution. for our model BBE.," Also shown is the limit solution, for our model BBF." + The left panel assumes isophotal magnitudes are measured. the central panel assumes. Caussian corrected: magnitudes were used and the right panel assumes some procedure has been implemented. to recover the total magnitudes.," The left panel assumes isophotal magnitudes are measured, the central panel assumes Gaussian corrected magnitudes were used and the right panel assumes some procedure has been implemented to recover the total magnitudes." + The results are also tabulatec in Table 2.., The results are also tabulated in Table \ref{table2}. + If isophotal magnitudes. are adopted. and the surface brightness limit is bright. the luminosities of galaxies are severely uncerestimated.," If isophotal magnitudes are adopted and the surface brightness limit is bright, the luminosities of galaxies are severely underestimated." + Thus both the number density and the A value are severely unclerestimatec (see Table. 2))., Thus both the number density and the $M^*$ value are severely underestimated (see Table \ref{table2}) ). + The variation in O° is upto and in M? upto 1.0 mags., The variation in $\phi^*$ is upto and in $M^*$ upto 1.0 mags. +" This tallies well with the range of Schechter values recovered (see $2) over the range tested. (230κqua,<26).", This tallies well with the range of Schechter values recovered (see 2) over the range tested $23<\mu_{lim}<26$ ). + To some extent is it surprising that @° is not more drastically ellected: this is because the observed distribution of galaxies is skewed towards the faint end. see Fig. 4..," To some extent is it surprising that $\phi^*$ is not more drastically effected; this is because the observed distribution of galaxies is skewed towards the faint end, see Fig. \ref{fig:N_M}." + As à simple l/V4í; correction or maximum likelihood estimator based on the isophotal magnitudes alone does not take into account surface brightness issues. especially Dight loss. a smaller volume is calculated than for total magnitudes. leacling to an overestimate of the number density. see Fig 3...," As a simple $1/V_{max}$ correction or maximum likelihood estimator based on the isophotal magnitudes alone does not take into account surface brightness issues, especially light loss, a smaller volume is calculated than for total magnitudes, leading to an overestimate of the number density, see Fig \ref{fig:V_M}." + This is tempered by a lower number density at. brighter absolute magnituces., This is tempered by a lower number density at brighter absolute magnitudes. + Perhaps most surprising is the robustness of the faint end slope whose value is recovered correctly regardless of the isophote., Perhaps most surprising is the robustness of the faint end slope whose value is recovered correctly regardless of the isophote. + Alost surveys attempt to correct their isophotal magnitudes to total magnitudes., Most surveys attempt to correct their isophotal magnitudes to total magnitudes. + We used a Gaussian. correction as described. above., We used a Gaussian correction as described above. + Fig., Fig. + 5— and Table 2— demonstrate that corrected. magnitudes recover of the Iuminosity density at 24. mag 2 compared to. the that isophotal magnitudes recover and the that total magnitudes. recover., \ref{fig:lfs} and Table \ref{table2} demonstrate that corrected magnitudes recover of the luminosity density at 24 mag $^{-2}$ compared to the that isophotal magnitudes recover and the that total magnitudes recover. + As with isophotal magnitudes. corrected. magnitudes give a luminosity function. biased. at all values of AZ. although the bias has been significantly. reclucecL.," As with isophotal magnitudes, corrected magnitudes give a luminosity function biased at all values of $M$, although the bias has been significantly reduced." + If some method is emploved to correct the galaxies to total magnitudes (e.g. Kron magnitudes or Petrosian magnitucdes) we find that the parameters are very. robust for. fts=24 mag arcsec, If some method is employed to correct the galaxies to total magnitudes (e.g. Kron magnitudes or Petrosian magnitudes) we find that the parameters are very robust for $\mu_{lim} \geq 24$ mag $^{-2}$. +" llowever. at nj,=28 mag arcsec2 the number density is. uncderestimatecl throughout the distribution."," However, at $\mu_{lim}=23$ mag $^{-2}$ the number density is underestimated throughout the distribution." + Fig 3.illustrates why this occurs., Fig \ref{fig:V_M} illustrates why this occurs. +" The volume has almost no surface brightness dependeney for the thresholds 24 $ 2500 km $^{-1}$, i.e. in the way not to take into account nearest objects with the large angular diameter." + Such a volume limiting also helps us to avo influence of Virgo cluster where strong peculiar motion exists., Such a volume limiting also helps us to avoid influence of Virgo cluster where strong peculiar motion exists. + We checked: additionally all pairs of galaxies with a small angular resolution and. excluded. identical. objects (parts of galaxies). which are presented twice and more in SDSS survey.," We checked additionally all pairs of galaxies with a small angular resolution and excluded identical objects (parts of galaxies), which are presented twice and more in SDSS survey." +" All galaxy velocities Vj, were corrected. for the Local Group centroidVc; accordingly to Ixarachentsev Makarov (1996).", All galaxy velocities $V_{h}$ were corrected for the Local Group centroid$V_{LG}$ accordingly to Karachentsev Makarov (1996). + When we πας applied the high-order Voronoi tessellation method to SDSS catalogue we limited our sample 3000 kim Vier: 9500 kni +., When we had applied the high-order Voronoi tessellation method to SDSS catalogue we limited our sample 3000 km $^{-1}$ $\leq V_{LG} \leq$ 9500 km $^{-1}$ . + We did not, We did not +"probability is μπα,",probability is small. + A very promising possibility is a damped absorber iu (2206-199. at 2=2.559. with a low metallicity aud very narrow lines (Pettini et al.," A very promising possibility is a damped absorber in Q2206-199, at $z=2.559$, with a low metallicity and very narrow lines (Pettini et al." + 1991)., 1994). + The iuterloper problem is πιο simaller here. both because of the very ligh column aud the low redshift.," The interloper problem is much smaller here, both because of the very high column and the low redshift." + The low redshift requires UST. but with STIS the ecutive Lyman series can be seen at once so this is a practical program. currently approved for cycle 7.," The low redshift requires HST, but with STIS the entire Lyman series can be seen at once so this is a practical program, currently approved for cycle 7." + There is certainly HIT absorption between the identified lines of the a forest., There is certainly HI absorption between the identified lines of the $\alpha$ forest. + As spectra of higher signal-to-noise ratio are obtained they reveal absorption of progressively lower optical depth., As spectra of higher signal-to-noise ratio are obtained they reveal absorption of progressively lower optical depth. + In HII however. even at the highest S/N so far available (about 100 at high resolution). the IIT absorption does not vet fill redshift space.," In HI however, even at the highest S/N so far available (about 100 at high resolution), the HI absorption does not yet fill redshift space." + Limits ou III coutiunous optical depth (or “Camu-Peterson effect”) provide useful coustraiunts on diffuse eas density. subject," Limits on HI continuous optical depth (or “Gunn-Peterson effect”) provide useful constraints on diffuse gas density, subject" +brown-dwarf companion and a well-determined astrometric orbit.,brown-dwarf companion and a well-determined astrometric orbit. +" After determining the orbital inclination from astrometry, we compared it to the orientation of the stellar spin axis."," After determining the orbital inclination from astrometry, we compared it to the orientation of the stellar spin axis." +" The inclination i;4 of the stellar spin axis is defined with respect to the line of sight (i4,=0? or 180? for a pole-on view) and can be derived from the spectroscopic estimate of 4.2 km s! (?)..", The inclination $i_\mathrm{rot}$ of the stellar spin axis is defined with respect to the line of sight $i_\mathrm{rot}=0\degr$ or $180\degr$ for a pole-on view) and can be derived from the spectroscopic estimate of $ \upsilon \sin i_\mathrm{rot} = 4.2$ km $^{-1}$ \citep{Santos:2010fk2}. +" The authors did not give an error bar for this measurement and we assumed a conservative uncertainty of 1 km s!. On the basis of the activity indicator logRink determined from the HARPS spectra, we used the calibration of ? to derive the stellar rotation period Py."," The authors did not give an error bar for this measurement and we assumed a conservative uncertainty of 1 km $^{-1}$ On the basis of the activity indicator $\log R'_{H,K}$ determined from the HARPS spectra, we used the calibration of \cite{Mamajek:2008fk} to derive the stellar rotation period $P_\mathrm{rot}$ ." +" Assuming an effective temperature of Teg=6297+32 (?),, the apparent visual magnitude my=6.839+0.001 (?),, and the parallax @ given in Table 2,, we derived the star’s absolute magnitude, luminosity(L=4.5 0.919). and radius (R=1.8+0.1 Re), using standard formulae and Monte Carlo resampling."," Assuming an effective temperature of $T_\mathrm{eff} = 6297 \pm 32$ \citep{Santos:2010fk2}, the apparent visual magnitude $m_V = 6.839 \pm 0.001$ \citep{:2007kx}, , and the parallax $\varpi$ given in Table \ref{tab:2}, we derived the star's absolute magnitude, luminosity$L = 4.5 \pm 0.3\, L_{\sun}$ ), and radius $R = 1.8 \pm 0.1 \,R_{\sun}$ ), using standard formulae and Monte Carlo resampling." + Bolometric corrections were computed using the ? parameters given by ?.., Bolometric corrections were computed using the \cite{Flower:1996qy} parameters given by \cite{Torres:2010uq}. +" Using the stellar radius and rotation period, we derived the equatorial rotation velocity to be v=10+3 ss!, and then the inclination of the spin axis by calculating ijo;=arcsin(vsinijo: /v)."," Using the stellar radius and rotation period, we derived the equatorial rotation velocity to be $\upsilon = 10 \pm 3$ $^{-1}$, and then the inclination of the spin axis by calculating $i_\mathrm{rot} = \arcsin( \upsilon \sin i_\mathrm{rot} / \upsilon)$ ." +" Because we cannot determine the star's sense of rotation, the angle ig, hasa 180° ambiguity and we first considered the value that falls into the same quadrant as ioi, ie. a prograde configuration."," Because we cannot determine the star's sense of rotation, the angle $i_\mathrm{rot}$ hasa $180^\circ$ ambiguity and we first considered the value that falls into the same quadrant as $i_\mathrm{orbit}$, i.e. a prograde configuration." +" The astrometric analysis yielded the distribution of init, obtained from 1000000 Monte Carlo simulations."," The astrometric analysis yielded the distribution of $i_\mathrm{orbit}$, obtained from 000 Monte Carlo simulations." +" To obtain the i;4,-distribution, we performed 106 Monte Carlo simulations."," To obtain the $i_\mathrm{rot}$ -distribution, we performed $10^6$ Monte Carlo simulations." + We finally compared these two distributions by drawing 2:107 pairs of values [iomit. trot] and obtained the distribution of the orbit obliquity or angle y by computing y=ioi—dot.," We finally compared these two distributions by drawing $2\cdot10^7$ pairs of values $[i_\mathrm{orbit}$ , $i_\mathrm{rot}]$ and obtained the distribution of the orbit obliquity or angle $\psi$ by computing $\psi = i_\mathrm{orbit} -i_\mathrm{rot}$." +" Figure 3. shows the probability density functions (PDF) of ioi, ioi, and y."," Figure \ref{fig:inclinations} shows the probability density functions (PDF) of $i_\mathrm{orbit}$ , $i_\mathrm{rot}$, and $\psi$." +" The io,pix-distribution is very narrow and peaks around 178.3°, whereas the ij4-distribution is broad with its maximum at 155? and the two distributions show a very small overlap."," The $i_\mathrm{orbit}$ -distribution is very narrow and peaks around $ 178.3^\circ$ , whereas the $i_\mathrm{rot}$ -distribution is broad with its maximum at $ \sim\!155^\circ$ and the two distributions show a very small overlap." +" The median values and confidence intervals of τοι, igi, and the obliquity y are given in Table 3.."," The median values and confidence intervals of $i_\mathrm{rot}$, $i_\mathrm{orbit}$, and the obliquity $\psi$ are given in Table \ref{tab:spin}." +" We found that wy is larger than 4.4? and 19.3? with a probability of and 68.3%,, respectively, and its nominal value with 1c confidence intervals is y.=29105 in prograde configuration, which indicates that the orientations of stellar spin and orbital axis differ substantially."," We found that $\psi$ is larger than $4.4\degr$ and $19.3\degr$ with a probability of and 68.3, respectively, and its nominal value with $1\,\sigma$ confidence intervals is $\psi= 23_{- 8}^{+10\,\circ}$ in prograde configuration, which indicates that the orientations of stellar spin and orbital axis differ substantially." +" In retrograde configuration, the obliquity would be y=153130."," In retrograde configuration, the obliquity would be $\psi'=153_{-10}^{+ 8\,\,\circ}$." +" We note that these values of y and w’ are lower limits, becausethe ascending node £X, of the spin axis is not constrained and we assumed that Q=€, in their derivation."," We note that these values of $\psi$ and $\psi'$ are lower limits, becausethe ascending node $\Omega_\mathrm{rot}$ of the spin axis is not constrained and we assumed that $\Omega = \Omega_\mathrm{rot}$ in their derivation." +" As illustrated in Fig. 4,,"," As illustrated in Fig. \ref{fig:inc}, ," +" y increases if the two ascending nodes Ώχοι and Q do not coincide, creating an additional uncertainty in y of 2-(180?—iowit)=3.4? in the prograde configuration."," $\psi$ increases if the two ascending nodes $\Omega_\mathrm{rot}$ and $\Omega$ do not coincide, creating an additional uncertainty in $\psi$ of $2\cdot (180\degr-i_\mathrm{orbit}) = 3.4 \degr$ in the prograde configuration." +"For a retrograde orbit, thisuncertainty is larger at 51°.","For a retrograde orbit, thisuncertainty is larger at $51 \degr$ ." +" In summary, the obliquity is y=23*0E941 ?and ψ’=1535511? for prograde and retrogradeorbits, respectively, where theadditional uncertainties are denotedin square brackets."," In summary, the obliquity is $\psi= 23_{- 8}^{+10\,[+3.4]\,\circ}$ and $\psi'=153_{-10}^{+ 8\, [+51]\,\circ}$ for prograde and retrogradeorbits, respectively, where theadditional uncertainties are denotedin square brackets." +" We performed these calculations using the Pyo.-calibration by ?,, which yielded a value of 8.8+1.6 days and an obliquity ofyΞ22133, in agreementwith the result obtained with the"," We performed these calculations using the $P_\mathrm{rot}$ -calibration by \cite{Noyes:1984qy}, , which yielded a value of $8.8 \pm 1.6$ days and an obliquity of $\psi= 22_{- 7}^{+9\,\circ}$, in agreementwith the result obtained with the" +Permanent superhumps have been observed so far in about 20 cataclysmic variables (CVs) (Patterson 1999).,Permanent superhumps have been observed so far in about 20 cataclysmic variables (CVs) (Patterson 1999). + These show superhumips (quasi-perioclicitics shifted by a few percent from their orbital periods) in their optical light curves during normal brightness state., These show superhumps (quasi-periodicities shifted by a few percent from their orbital periods) in their optical light curves during normal brightness state. + In contrast. SU UMa systems (see Warner 1995 for a review of SU UMa systems and CVs in general) have superhumps only during their bright chwarl nova outbursts (superoutbursts)," In contrast, SU UMa systems (see Warner 1995 for a review of SU UMa systems and CVs in general) have superhumps only during their bright dwarf nova outbursts (superoutbursts)." +" Permanent superhumps can either be a few percent longer than the orbital periods and they are called ""positive superhumps'. or shorter ""negative superhumps'."," Permanent superhumps can either be a few percent longer than the orbital periods and they are called $\bf positive$ $\bf superhumps$ ', or shorter – $\bf negative$ $\bf superhumps$ '." + The positive superhump is explained. as the beat between the binary motion and the precession of an accretion disc in, The positive superhump is explained as the beat between the binary motion and the precession of an accretion disc in +LEGOs observed in the field of 0322 fill out the sampled volume. with a mean redshift of 3.155 and a standard eviation of 0.019.,"LEGOs observed in the field of $-$ 0322 fill out the sampled volume, with a mean redshift of 3.155 and a standard deviation of 0.019." + On the contrary. the redshifts of LEGOs —1 the field of 4427 have a mean of 2.858 and a tandard deviation of only 0.006. corresponding to a velocity Cvispersion of 470 km !.," On the contrary, the redshifts of LEGOs in the field of $-$ 4427 have a mean of 2.858 and a standard deviation of only 0.006, corresponding to a velocity dispersion of 470 km $^{-1}$." +" A significant part of this velocity vwpread must be caused by peculiar velocities or offsets between the Lya and systemic redshifts. and therefore. the Hubble flow ""Septh of the structure should be even less."," A significant part of this velocity spread must be caused by peculiar velocities or offsets between the $\alpha$ and systemic redshifts, and therefore, the Hubble flow depth of the structure should be even less." + The mean observed redshift is close to the redshift of the DLA absorber toward 4427 (z=2.851)., The mean observed redshift is close to the redshift of the DLA absorber toward $-$ 4427 (z=2.851). + This indicates the presence of a large-scale structure of galaxies. e.g. a pancake-like structure at the redshift of the DLA absorber. surrounded by voids.," This indicates the presence of a large-scale structure of galaxies, e.g. a pancake-like structure at the redshift of the DLA absorber, surrounded by voids." + Independent evidence for this comes from the observation of strong metal absorption lines at the same redshift in two nearby QSOs (Francis Hewitt 1993: D'Odorico et al., Independent evidence for this comes from the observation of strong metal absorption lines at the same redshift in two nearby QSOs (Francis Hewitt 1993; D'Odorico et al. + 2002)., 2002). + The redshift distribution of LEGOS in the field of 4427 is similar to that of LEGOs in the fields of radio galaxies (Pentericei et al., The redshift distribution of LEGOs in the field of $-$ 4427 is similar to that of LEGOs in the fields of radio galaxies (Pentericci et al. + 2000: Venemans et al., 2000; Venemans et al. + 2002)., 2002). + In a subsequent paper (Ledoux et al..," In a subsequent paper (Ledoux et al.," + in prep.).," in prep.)," + we will address the properties of the DLA absorber., we will address the properties of the DLA absorber. + Most of the candidates that we did not confirm are faint in the narrow-band images and/or have low EWs (see Fig. 4))., Most of the candidates that we did not confirm are faint in the narrow-band images and/or have low EWs (see Fig. \ref{select}) ). + These candidates could either have been missed by the slitlets. be too faint for the follow-up spectroscopy (due to the bad seeing we did not reach the planned detection limit). or simply not be LEGOs.," These candidates could either have been missed by the slitlets, be too faint for the follow-up spectroscopy (due to the bad seeing we did not reach the planned detection limit), or simply not be LEGOs." + As seen in Fig. 3..," As seen in Fig. \ref{colcol}," + the unconfirmed candidates tend to have redder colours R(AB) = 0.9-1.8) than the confirmed candidates (see Fig. 3))., the unconfirmed candidates tend to have redder colours $-$ R(AB) = 0.9–1.8) than the confirmed candidates (see Fig. \ref{colcol}) ). + The confirmed emission- sources detected in the broad bands indeed have blue colours (typically R(AB)<0.8)., The confirmed emission-line sources detected in the broad bands indeed have blue colours (typically $-$ $<$ 0.8). + However. the fact that one of the confirmed candidates. LEGO2138.331. has colours and flux very similar to the unconfirmed candidates makes it," However, the fact that one of the confirmed candidates, 31, has colours and flux very similar to the unconfirmed candidates makes it" +"Some simple properties of the Dirac-Milne universe are common to those of a purely linear cosmology studied in ?,, ??,, and ?..","Some simple properties of the Dirac-Milne universe are common to those of a purely linear cosmology studied in \citet{Simmering98}, , \citet{Kaplinghat99, Kaplinghat00}, , and \citet{Sethi05}." + We briefly recall some of these properties., We briefly recall some of these properties. + Using Eq. (5))," Using Eq. \ref{fried1}) )," +" it is straightforward to obtain the relation between the age of the Universe and the redshift, hence the temperature where Tp is the present temperature of the Universe, as measured by CMB experiments, To=2.725+0.001K (?).."," it is straightforward to obtain the relation between the age of the Universe and the redshift, hence the temperature where $T_0$ is the present temperature of the Universe, as measured by CMB experiments, $T_0=2.725\pm 0.001\;\rm{K}$ \citep{Fixsen2002}." + This relation between time and temperature is valid throughout the whole history of the universe and implies that the thermal history of the Dirac-Milne universe is drastically modified from the evolution in the standard ACDM cosmology., This relation between time and temperature is valid throughout the whole history of the universe and implies that the thermal history of the Dirac-Milne universe is drastically modified from the evolution in the standard $\Lambda$ CDM cosmology. + Figure (1)) represents the age of the Universe as a function of the temperature for the Dirac-Milne and the ACDM models., Figure \ref{age}) ) represents the age of the Universe as a function of the temperature for the Dirac-Milne and the $\Lambda$ CDM models. +" It can be seen that, at high temperatures, the Dirac-Milne universe is much older than the corresponding ACDM cosmology."," It can be seen that, at high temperatures, the Dirac-Milne universe is much older than the corresponding $\Lambda$ CDM cosmology." +" For instance, the traditional 1 MeV-1 sec approximation for the standard model becomes 1 MeV - 3.3 years in the Dirac-Milne cosmology."," For instance, the traditional 1 $\sim$ 1 sec approximation for the standard model becomes 1 MeV $\sim$ 3.3 years in the Dirac-Milne cosmology." +" As noted in ?,, this difference has profound implications for big-bang nucleosynthesis calculations, and is discussed in section 4.."," As noted in \citet{Simmering98}, this difference has profound implications for big-bang nucleosynthesis calculations, and is discussed in section \ref{sec_bbn}." + Another temperature of interest is the temperature of the quark-gluon-plasma (QGP) transition., Another temperature of interest is the temperature of the quark-gluon-plasma (QGP) transition. +" ? proposed that matter-antimatter separation occurred around that temperature, owing to a putative repulsive interaction between nucleons and antinucleons."," \citet{Omnes1972} proposed that matter-antimatter separation occurred around that temperature, owing to a putative repulsive interaction between nucleons and antinucleons." + The maximum size of a domain of (anti)matter was controlled by the diffusion of neutrons., The maximum size of a domain of (anti)matter was controlled by the diffusion of neutrons. +" ? found a maximum size of 7x107cm at a temperature of T~330 MeV, which was at this epoch the estimated temperature of the QGP transition."," \citet{Aly_sep1974} found a maximum size of $7\times 10^{-4}\;\rm{cm}$ at a temperature of $T\sim330 $ MeV, which was at this epoch the estimated temperature of the QGP transition." + This size was later found to differ from the minimum size a domain should have in order to ensure a production of primordial helium compatible with observations (??)..," This size was later found to differ from the minimum size a domain should have in order to ensure a production of primordial helium compatible with observations \citep{Combes75,Aly1978}." + The situation is rather different in the Dirac-Milne universe as the timescale of the QGP transition is much longer., The situation is rather different in the Dirac-Milne universe as the timescale of the QGP transition is much longer. +" Since the temperature of the transition is estimated today to be around T~170 MeV (?),, it corresponds to an age of 6x10?sec in the Dirac-Milne universe, which is a factor ~10!° older than in the standard case."," Since the temperature of the transition is estimated today to be around $T \sim 170$ MeV \citep{Schwarz2003}, it corresponds to an age of $6\times 10^{5}\;\rm{sec}$ in the Dirac-Milne universe, which is a factor $\sim 10^{10}$ older than in the standard case." + This implies that the maximum size to which a domain could possibly grow (assuming the existence of an efficient separation mechanism) is five orders of magnitude higher., This implies that the maximum size to which a domain could possibly grow (assuming the existence of an efficient separation mechanism) is five orders of magnitude higher. +" For this reason, the Dirac-Milne universe is far more weakly constrained by observations than the Omnéss cosmology."," For this reason, the Dirac-Milne universe is far more weakly constrained by observations than the Omnèss cosmology." + A fundamental example of the modifications induced by a linear scale factor can be seen in the epoch of decoupling of the weak interactions., A fundamental example of the modifications induced by a linear scale factor can be seen in the epoch of decoupling of the weak interactions. +" This example was analyzed extensively in ?,, so we only provide here the main In the standard model, weak decoupling occurs at a temperature T~1MeV."," This example was analyzed extensively in \citet{Simmering98}, so we only provide here the main In the standard model, weak decoupling occurs at a temperature $T\sim 1\;\rm{MeV}$." +" In the Dirac-Milne universe, this decoupling happens at a lower temperature of around T~80keV, because of the slower variation and the lower value of the expansion rate."," In the Dirac-Milne universe, this decoupling happens at a lower temperature of around $T\sim 80 \;\rm{keV}$, because of the slower variation and the lower value of the expansion rate." + This effect is illustrated in Fig. 2.., This effect is illustrated in Fig. \ref{wkrates}. + Weak interactions control the n«€p equilibrium., Weak interactions control the $n \leftrightarrow p $ equilibrium. +" At low temperatures, this reaction is limited to the free neutron disintegration (green short-dashed line), but at temperatures sx than 80 keV, the equilibrium between proton and higheneutrons remains possible."," At low temperatures, this reaction is limited to the free neutron disintegration (green short-dashed line), but at temperatures higher than 80 keV, the equilibrium between proton and neutrons remains possible." + The long-dashed line represent the proton conversion rate as a function of the temperature for the Dirac-Milne universe (red) and thestandard cosmology (blue)., The long-dashed line represent the proton conversion rate as a function of the temperature for the Dirac-Milne universe (red) and thestandard cosmology (blue). + The analytical expressions for these reaction rates come from ? and ?.., The analytical expressions for these reaction rates come from \citet{Wagoner69} and \citet{Dicus82}. + Weak interactions decouple when the expansion rate becomes higher than the p©n rate., Weak interactions decouple when the expansion rate becomes higher than the $p \leftrightarrow n$ rate. + The small difference in the p€n rate between the two cosmologies is caused by a difference in the neutrino background temperature., The small difference in the $p \leftrightarrow n$ rate between the two cosmologies is caused by a difference in the neutrino background temperature. +" As the weak interactions decouple at a temperature of T~80 keV, neutrinos indeed also decouple from the photonbackgroundalso at this temperature, but only after the annihilation of most"," As the weak interactions decouple at a temperature of $T\sim 80\;\rm{keV}$ , neutrinos indeed also decouple from the photonbackgroundalso at this temperature, but only after the annihilation of most" +" AGNs in Section 4 (see, for example, Figure 5)) is a narrow-line/linelessphysical effect, robust beyond the choice of black hole mass estimator.","narrow-line/lineless AGNs in Section 4 (see, for example, Figure \ref{fig:acchistogram}) ) is a physical effect, robust beyond the choice of black hole mass estimator." +" We highlight the range and limitations of the AGN sample in Figure 4,, which shows bolometric luminosities and black hole masses for the broad-line, narrow-line, and lineless AGNs."," We highlight the range and limitations of the AGN sample in Figure \ref{fig:lbolmbh}, which shows bolometric luminosities and black hole masses for the broad-line, narrow-line, and lineless AGNs." +" Objects in the upper left have the highest specific accretion rates, while those in the lower right are weakly accreting AGNs."," Objects in the upper left have the highest specific accretion rates, while those in the lower right are weakly accreting AGNs." +" While the total sample spans 3 orders of magnitude in both luminosity and black hole mass, our narrow-line and lineless AGNs are generally less luminous and more massive than broad-line AGNs."," While the total sample spans 3 orders of magnitude in both luminosity and black hole mass, our narrow-line and lineless AGNs are generally less luminous and more massive than broad-line AGNs." + The lack of low-mass narrow-line and lineless AGNs is due to the selection limits of the survey: such objects are too faint to be detected in COSMOS., The lack of low-mass narrow-line and lineless AGNs is due to the selection limits of the survey: such objects are too faint to be detected in COSMOS. +" It is suggestive that these higher mass narrow-line and lineless AGNs are at z«1 and are less luminous: this is consistent with "" downsizing,"" with more massive AGNs becoming less active at lower redshift"," It is suggestive that these higher mass narrow-line and lineless AGNs are at $z<1$ and are less luminous: this is consistent with ” downsizing,” with more massive AGNs becoming less active at lower redshift." +2007).. Figure 4 shows that at a given mass or luminosity there are generally all types of AGNs present in our sample., Figure \ref{fig:lbolmbh} shows that at a given mass or luminosity there are generally all types of AGNs present in our sample. + For this reason we do not expect that the differences between broad-line and AGNs are biased by selected samples from different narrow-line/linelessmasses or luminosities., For this reason we do not expect that the differences between broad-line and narrow-line/lineless AGNs are biased by selected samples from different masses or luminosities. +" In addition, despite the different redshifts of most broad-line and AGNs, we do not expect their differences to be narrow-line/linelesscaused by redshift."," In addition, despite the different redshifts of most broad-line and narrow-line/lineless AGNs, we do not expect their differences to be caused by redshift." +" There is evidence that AGN obscuration properties depend on redshift2009a),, but these AGNs are unobscured."," There is evidence that AGN obscuration properties depend on redshift, but these AGNs are unobscured." +" The AGN central engine, meanwhile, does not change with redshift in terms of ionization parameters2004), spectral energy distributions(Vignali2008),, or metallicity 2010)."," The AGN central engine, meanwhile, does not change with redshift in terms of ionization parameters, spectral energy distributions, or metallicity ." +". Limiting the sample to z< 1,85«log(Mpg)9, or 44«log(Lint)45 does not significantly change the differences between the broad-line and AGN samples seen in Figures 5, 6, 7, narrow-line/linelessor 8."," Limiting the sample to $z<1$, $8.5<\log(M_{BH})<9$, or $44<\log(L_{int})<45$ does not significantly change the differences between the broad-line and narrow-line/lineless AGN samples seen in Figures 5, 6, 7, or 8." +" We estimate errors for each of our specific accretion rates, propagating the errors from both the intrinsic luminosity estimate and the black hole mass estimate."," We estimate errors for each of our specific accretion rates, propagating the errors from both the intrinsic luminosity estimate and the black hole mass estimate." + Our intrinsic luminosityis subject to three major uncertainties:, Our intrinsic luminosityis subject to three major uncertainties: +values up to about 12LI... most notably the large hole.,"values up to about 12, most notably the large hole." + The high column density region is fairly well demarcated by the 8 cecontour., The high column density region is fairly well demarcated by the 8 contour. + Outside of the optical galaxy the velocity dispersion drops. and values in the extended eas are of order 5|.," Outside of the optical galaxy the velocity dispersion drops, and values in the extended gas are of order 5." + Thus. the velocity dispersions in the in DDO 43 appear to be quite normal.," Thus, the velocity dispersions in the in DDO 43 appear to be quite normal." + llowever. (he second moment map of the galaxy does not tell the whole story.," However, the second moment map of the galaxy does not tell the whole story." + To better examine (he kinematics in the kknots and holes. using the ccube we plotted (he spectra of pixels (averaged across a beamwicltli) for several of the knots and the large hole.," To better examine the kinematics in the knots and holes, using the cube we plotted the spectra of pixels (averaged across a beamwidth) for several of the knots and the large hole." + The spectra of the knots are complex., The spectra of the knots are complex. + Many exhibit a central double peak. often with smaller peaks. sometimes on both sides of the bright peak. sometimes only ralsible as broad wings on one or both sides.," Many exhibit a central double peak, often with smaller peaks, sometimes on both sides of the bright peak, sometimes only visible as broad wings on one or both sides." + We fil gaussians to the ILanning-smoothed beam-averaged spectra of the brightest knot and the laree hole: the spectra are shown in Figure 28.., We fit gaussians to the Hanning-smoothed beam-averaged spectra of the brightest knot and the large hole; the spectra are shown in Figure \ref{fig:spectra}. + For the knot. we were able to successfully fit tree components to 19 of the 28 spectra and two components to six spectra.," For the knot, we were able to successfully fit three components to 19 of the 28 spectra and two components to six spectra." + Three spectra had large uncertainties to the fits aud so were not included in our analysis., Three spectra had large uncertainties to the fits and so were not included in our analysis. + For the 19 spectra with good fits to three components. the average dillerence in velocity between the central and (wo side components is ~£15kms...," For the 19 spectra with good fits to three components, the average difference in velocity between the central and two side components is $\sim \pm 15$." + The average amplitucles are 2. 11. ancl 4 mJv/D going trom hieh to low velocity.," The average amplitudes are 2, 11, and 4 mJy/B going from high to low velocity." + The central and low velocity components are broad. with an average width of ~17!.," The central and low velocity components are broad, with an average width of $\sim 17$." +. The hieh velocity component is narrower. wilh an average width of roughly half (hat.," The high velocity component is narrower, with an average width of roughly half that." + The beam-averaged spectra of the laree hole are more complex (han those of the |vs10s. with most being fit by four components.," The beam-averaged spectra of the large hole are more complex than those of the knots, with most being fit by four components." + Three of the 13 spectra were fit with three components. and one was fit wil two.," Three of the 18 spectra were fit with three components, and one was fit with two." + Labelling the components 1.+ from high to low central velocities. Components 1 and 3 have average widths of approximately 10!|.. while components 2 and 4 have average widths of around 16|.," Labelling the components 1–4 from high to low central velocities, components 1 and 3 have average widths of approximately 10, while components 2 and 4 have average widths of around 16." + The average amplitudes are low as expected for a depression in the gas. ranging Irom 2.2 (component 1) to 5.2 mJv/B (component 2).," The average amplitudes are low as expected for a depression in the gas, ranging from 2.2 (component 1) to 5.2 mJy/B (component 2)." + The components are separated by 18. 1H. and 13 oon average.," The components are separated by 18, 14, and 13 on average." + The high dispersions associated with this region are reflected in (lese spectra: the eas seems to be somewhat churned up., The high dispersions associated with this region are reflected in these spectra; the gas seems to be somewhat churned up. + With these complex spectra. we do not believe that we detect expansion in the hole.," With these complex spectra, we do not believe that we detect expansion in the hole." + The hole itself is not clearly idenüfiable in the channel maps. nor is (here any leature in the position-velocitv diagrams at the location and velocity (7 350-360 1) of the hole that would indicate expansion or even blowout Walter Brinks 1999).," The hole itself is not clearly identifiable in the channel maps, nor is there any feature in the position-velocity diagrams at the location and velocity $\sim$ 350-360 ) of the hole that would indicate expansion or even blowout Walter Brinks 1999)." +where dV. is the volume element ancl We define Aly=OEmy(lknisty8238.Ot. so that AM.M.r=AlonM(7bet)Eσι,"where $dV$ is the volume element and We define $\dot M_0 = \pi G^2 {\rm M}_\odot^2 m_p (1 {\rm km~s^{-1}})^{-3} += 3.8 \times 10^{14}$, so that $\dot M(n,M,v) = +\dot M_0 n M^2 (v^2+c_s^2)^{-3/2}$." + pora elven mass and sound speed. we can define the minimum number density required. for accretion at a rate greater than A: /(ALjAL=).," For a given mass and sound speed, we can define the minimum number density required for accretion at a rate greater than $\dot M$ : $n > n_0 = \dot M c_s^3/(\dot M_0 M^2)$ ." + Using equations (1)) ane (3)). wecan first carry out the b integration analytically. where rg=CMonM7/M)ος.," Using equations \ref{bondi}) ) and \ref{dndm}) ), wecan first carry out the $v$ integration analytically, where $v_0^2=(\dot M_0 n M^2/\dot M)^{2/3} -c_s^2$." + The remaining two integrals we compute numerically., The remaining two integrals we compute numerically. + 2mm In Figure 1: we plot the function «EN/d4M for the various phases of the interstellar medium at the solar circle., 2mm In Figure 1 we plot the function $dN/d\dot M$ for the various phases of the interstellar medium at the solar circle. + The densest eas (GMCs) dominates the highest accretion rates. while the hottest gas dominates the lowest accretion rates.," The densest gas (GMCs) dominates the highest accretion rates, while the hottest gas dominates the lowest accretion rates." + For the hot LLL accretion is subsonic and p is assumed to be constant. so Mx07.," For the hot HII, accretion is subsonic and $n$ is assumed to be constant, so $\dot M \propto M^2$." +" hus. dN/dAMxM.3777, spanning a range in Al of (AdoΑΛ}. or two decades."," Thus, $dN/d\dot M \propto +\dot M^{-(1+\gamma)/2}$, spanning a range in $\dot M$ of $(M_2/M_1)^2$, or two decades." + This is consistent with the numerical spectrum shown in Figure 1., This is consistent with the numerical spectrum shown in Figure 1. + The other phases have more complicated accretion-rate distributions since a.2 ὃς., The other phases have more complicated accretion-rate distributions since $\sigma_v > c_s$ . + To compute the expected. total number of black holes in the Galaxy accreting at a rate M. we integrate the Luminosity functions (assumed to be constant) over the gas filling fraction times the number density of black holes as a function of position over the entire Galaxy. Figure2(a) shows N(.M)=fydal’(dNdal) for both black holes anc neutron stars.," To compute the expected total number of black holes in the Galaxy accreting at a rate $\dot M$, we integrate the luminosity functions (assumed to be constant) over the gas filling fraction times the number density of black holes as a function of position over the entire Galaxy, Figure 2(a) shows $N(>{\dot M})=\int_{\dot M}^\infty d\dot M' +(dN/d\dot M')$ for both black holes and neutron stars." +" For neutron stars. we choose Al=14AL. δ0 per cent with a. =175kms tand14 per cent with a,=100 km t (CordesChernolI 1998). N=5.2.107 "," For neutron stars, we choose $M=1.4 {\rm M}_\odot$ , 86 per cent with $\sigma_v = 175$ km $^{-1}$ and14 per cent with $\sigma_v=700$ km $^{-1}$ (CordesChernoff 1998), $N_\odot = 5.2\times 10^5$ " +The lisht variation of SN 2001V was followed ou 18 nights. starting from f=S days (with respect to B. maxi). extending up tot=162 davs.,"The light variation of SN 2001V was followed on 18 nights, starting from $t = -8$ days (with respect to $B-$ maximum), extending up to $t = +62$ days." + The applied telescopes aud detectors are listed in Table 1., The applied telescopes and detectors are listed in Table 1. + All data were collected through standard Jolinsou-Cousis BVRE filters., All data were collected through standard Johnson-Cousins $BVRI$ filters. +" The CCD-frames have been reduced inLRAE"".", The CCD-frames have been reduced in. +. First. the instrumental magnitudes of the SN and the sclected conrparison stars (Fie...) were derived with aperture photometry using the taskdyiphot/apphot.," First, the instrumental magnitudes of the SN and the selected comparison stars (Fig.1) were derived with aperture photometry using the task." + The radius of the aperture was 6 pixels (about 2 x FWHAL see Table 1). while the sky level was determined in a 5 pixel- aunulus with iuuer radius of LO pixels.," The radius of the aperture was 6 pixels (about 2 x FWHM, see Table 1), while the sky level was determined in a 5 pixel-wide annulus with inner radius of 10 pixels." + Because the SN is located close to the “tip” of NGC 3987. most of the jxels in the annulus were uot affected significaitlv by the ight from tie host ealaxy.," Because the SN is located close to the “tip” of NGC 3987, most of the pixels in the annulus were not affected significantly by the light from the host galaxy." + The sky level was «etermined w calculating the modal average (3 X median 2x nean) of the intensities in the annulus., The sky level was determined by calculating the modal average (3 x median $-$ 2 x mean) of the intensities in the annulus. +" The calculations were done interactively, aud the results were uotted on he screen and inspected visually in order to detect any obvious systematic errors."," The calculations were done interactively, and the results were plotted on the screen and inspected visually in order to detect any obvious systematic errors." + The average sky level arouud he SN was always very close to the background. around he comparison stars. no clear svstematic effect could be omc.," The average sky level around the SN was always very close to the background around the comparison stars, no clear systematic effect could be found." + Secoud. the whole dataset have been reaeuced Using PSF-photometry (diyiphot/duophot). as also advised by he referee of this paper.," Second, the whole dataset have been re-reduced using PSF-photometry ), as also advised by the referee of this paper." + PSF-photometry is a superior yhotometric method if the background strongly varies around the objects. and its removal is complicated.," PSF-photometry is a superior photometric method if the background strongly varies around the objects, and its removal is complicated." + Since SN 2001V is somewhat contaminated by its host. the use of PSF-photometry nay be useful to separate the light of the SN from that of he galaxy.," Since SN 2001V is somewhat contaminated by its host, the use of PSF-photometry may be useful to separate the light of the SN from that of the galaxy." + This method requires bright stars with hieh S/N to cousruct a good PSF., This method requires bright stars with high S/N to construct a good PSF. + Because there are only a few of such stars iu the fiedof NGC 3987. and also the field of view of nost of the telescopes used in this study was quite αμα]. a lot of framies contained ouly lL - 5 stars around the SN.," Because there are only a few of such stars in the field of NGC 3987, and also the field of view of most of the telescopes used in this study was quite small, a lot of frames contained only 4 - 5 stars around the SN." +" Nevertjicless. the PSF of each frame was determines luteractively,"," Nevertheless, the PSF of each frame was determined interactively." + The analytic component of the PSF was approximated by the »üilt-in function iu.daoplhiot. but im most cases it was based on ouly 2-3 stars.," The analytic component of the PSF was approximated by the built-in function in, but in most cases it was based on only 2-3 stars." + The funes mace with the Schinidt-telescope (Table 1) contained unch more field objects. l1t the PSF ou these frames showed siguificaut positional dependence.," The frames made with the Schmidt-telescope (Table 1) contained much more field objects, but the PSF on these frames showed significant positional dependence." + Therefore. a secoud-order variable PSF model has been constructed for tlese pictures. while cousaut PSF was cletermined for all other frames.," Therefore, a second-order variable PSF model has been constructed for these pictures, while constant PSF was determined for all other frames." + Tudividua skv levels were calculated for a] objects. and i6 backeround was subtracted iteratively durius the fitting of 10 PSF indeophot/allstar.," Individual sky levels were calculated for all objects, and the background was subtracted iteratively during the fitting of the PSF in." + Then. the residuals were exandued visually on the subtracted frames.," Then, the residuals were examined visually on the subtracted frames." +" The stars as well as the SN were adequately removed from most yanues, but slight residuals were preseut at the position of ie brightest stars on some frames."," The stars as well as the SN were adequately removed from most frames, but slight residuals were present at the position of the brightest stars on some frames." + This was probably caused by the muacertaimty of the PSF due to the small nuuber of PSF-stars., This was probably caused by the uncertainty of the PSF due to the small number of PSF-stars. + Differential magnitudes of ον 2001V have been colmputed using the comparison stars labeled in Fie.l (see also Table 2 below)., Differential magnitudes of SN 2001V have been computed using the comparison stars labeled in Fig.1 (see also Table 2 below). + After trausforming them to he staudard svsteii (Vinkóetal. 2001)). the brightuess of the SN was calculated from the calibratedΤΠ uaenitudes of cach comparison star (see below).," After transforming them to the standard system \cite{2ke}) ), the brightness of the SN was calculated from the calibrated magnitudes of each comparison star (see below)." + Then. he SN maguitudes belonging to the same frame were averaged.," Then, the SN magnitudes belonging to the same frame were averaged." + lu order to search for auv systematic effec caused w the reduction. procedure. we have compared the SN uaenitudes from the aperture- and PSE-phoolnetry.," In order to search for any systematic effect caused by the reduction procedure, we have compared the SN magnitudes from the aperture- and PSF-photometry." + Fig.2 preseuts the aperture minus PSFAanagnuitudes in all filters as a function of time., Fig.2 presents the aperture minus PSF-magnitudes in all filters as a function of time. + It is apparent that most of the differences are within 40.1 mae., It is apparent that most of the differences are within $\pm 0.1$ mag. + Naturally. the differences are higher at later phases. when the SN became faiuter. mt there is no visible systematic trend im the data.," Naturally, the differences are higher at later phases, when the SN became fainter, but there is no visible systematic trend in the data." + We couclude that boh the aperture- aud PSF-photometry of SN 2001V preseued here is affected by apxoxinatelv the παλιο amount of randoni errors at the ΕΕ. mag level. mainly due to the technical liuutations of the applied iustrumnenuts (lower S/N. smal field of view. very few PSE-stars).," We conclude that both the aperture- and PSF-photometry of SN 2001V presented here is affected by approximately the same amount of random errors at the $\pm 0.1$ mag level, mainly due to the technical limitations of the applied instruments (lower S/N, small field of view, very few PSF-stars)." +" In order to reduce the ""uncertainties introduced "" the reduction iiethod. the SN magnitudes resulted from both aperture- aud PSF-phoolnetry were averaged. aud these magnitudes were accepted as the final result."," In order to reduce the uncertainties introduced by the reduction method, the SN magnitudes resulted from both aperture- and PSF-photometry were averaged, and these magnitudes were accepted as the final result." + At first. the magnitudes of the comparison stays were calibrated via Landolt standards. observed at Calar Alto Observatory with twe 1.2 in Casseerain. under photometric conditions ou Augll. 2001.," At first, the magnitudes of the comparison stars were calibrated via Landolt standards, observed at Calar Alto Observatory with the 1.2 m Cassegrain, under photometric conditions on Aug.11, 2001." + The rcliabilitw of this dataset have been checked by using the calibrated photometry of some of the field stars made by the CEA Supernova Croup at the F. L. Whipple Observatory., The reliability of this dataset have been checked by using the calibrated photometry of some of the field stars made by the CfA Supernova Group at the F. L. Whipple Observatory. + Because the comparison stars used iu this study. and," Because the comparison stars used in this study, and" +"If the target photon field is characterized by a peak energy 5, (hen (he maximum injection rate in the blob occurs at energy llowever. we have to note that depending on the slope of the primary 5-ray spectrum. this value can change significantly.","If the target photon field is characterized by a peak energy $\varepsilon$, then the maximum injection rate in the blob occurs at energy However, we have to note that depending on the slope of the primary $\gamma$ -ray spectrum, this value can change significantly." + Since the svnchrotron cooling time of these electrons. is very short (compared to both the tvpical time scales for the svstem and the Compton cooling time of electrons). the entire absorbed energy will be immediately released by secondary electrons through the svuchrotvon channel.," Since the synchrotron cooling time of these electrons, is very short (compared to both the typical time scales for the system and the Compton cooling time of electrons), the entire absorbed energy will be immediately released by secondary electrons through the synchrotron channel." + In the case of large internal absorption or high bulk Lorentz Iactor. the secondary svuchrotron component has a broad distribution centerecl al The variability time-scale of (he svnchirotron radiation of secondary pairs is determined bv the change of the injection. ie. by the change of primary y-ray component.," In the case of large internal absorption or high bulk Lorentz factor, the secondary synchrotron component has a broad distribution centered at The variability time-scale of the synchrotron radiation of secondary pairs is determined by the change of the injection, i.e. by the change of primary $\gamma$ -ray component." + In (he case of small internal opacity ancl assuming (hat. protons are distributed over (he energy interval between 1GeV. and 10*TeV with E7 7-tvpe spectrum. the luminosity of the secondary svnchrotron radiation is estimated as," In the case of small internal opacity and assuming that protons are distributed over the energy interval between $1\,\rm GeV$ and $10^7\, \rm TeV$ with $E^{-2}$ -type spectrum, the luminosity of the secondary synchrotron radiation is estimated as" +"where ko,(6000) is expressed in mag airmass!, and N(O3) is expressed in DU.","where $k_{\rm{O}_3}(6000)$ is expressed in mag $^{-1}$ , and $_3$ ) is expressed in DU." + From this we derive an average O3 column density of 258 DU (the RMS deviation is 14 DU)., From this we derive an average $_3$ column density of 258 DU (the RMS deviation is 14 DU). +" To cross-check this result, we run an independent analysis of the ozone variability using the satellite data provided by the Ozone Monitor Instrument (OMI) on board of NASAAURA?."," To cross-check this result, we run an independent analysis of the ozone variability using the satellite data provided by the Ozone Monitor Instrument (OMI) on board of NASA." +. OMI derives the daytime ozone column density by comparing the amount of back-scattered solar radiation in the UV and in the optical., OMI derives the daytime ozone column density by comparing the amount of back-scattered solar radiation in the UV and in the optical. +" The OMI O; column density over Paranal collected between 2007 and 2009 clearly shows a seasonal trend (see Fig. 8)),"," The OMI $_3$ column density over Paranal collected between 2007 and 2009 clearly shows a seasonal trend (see Fig. \ref{fig:ozone}) )," +" with maxima attained around August, September and October (~300 DU), and minima reached in February, March and April (~240 DU)."," with maxima attained around August, September and October $\sim$ 300 DU), and minima reached in February, March and April $\sim$ 240 DU)." +" The average value during the PARSEC campaign was about 260 DU, which is slightly larger than the value given by the LBLRTM model (~240 DU; see previous section)."," The average value during the PARSEC campaign was about 260 DU, which is slightly larger than the value given by the LBLRTM model $\sim$ 240 DU; see previous section)." + A closer inspection to the OMI data shows that the ozone content steadily decreased during the time covered by our observations., A closer inspection to the OMI data shows that the ozone content steadily decreased during the time covered by our observations. + The peak-to-peak variation is about25%., The peak-to-peak variation is about. +". Thisturns into a maximum variation of ~0.01 mag airmass""! at 6000 during the time covered by our observations.", Thisturns into a maximum variation of $\sim$ 0.01 mag $^{-1}$ at $\sim$ 6000 during the time covered by our observations. +" An inspection of the time evolution of ko,(6000) shows no traces of such a steady decrease, and the fluctuations appear to be dominated by short timescale variations, partially attributable to random errors."," An inspection of the time evolution of $k_{\rm{O}_3}(6000)$ shows no traces of such a steady decrease, and the fluctuations appear to be dominated by short timescale variations, partially attributable to random errors." +" Molecular oxygen shows two main O» vibrational absorption bands centred at 6870 and7605A,, usually indicated as B and A bands, respectively (Fig. 9))."," Molecular oxygen shows two main $_2$ vibrational absorption bands centred at 6870 and, usually indicated as B and A bands, respectively (Fig. \ref{fig:h2o}) )." +" Their typical equivalent widths (EW) are ~6A and ~28A,, which make them easily detectable in low resolution spectra."," Their typical equivalent widths (EW) are $\sim$ and $\sim$, which make them easily detectable in low resolution spectra." +" To quantify the variability of O2 column density, and its effect on the extinction, we have measured the EW of the B band in the red setting spectra."," To quantify the variability of $_2$ column density, and its effect on the extinction, we have measured the EW of the B band in the red setting spectra." +" The A band is severely affected by fringing, and so no very accurate measurements were possible."," The A band is severely affected by fringing, and so no very accurate measurements were possible." +" However, the integrated strengths of the two bands are well correlated, as demonstrated by a series of LBLRTM simulations run for different values of the column density N(O2)."," However, the integrated strengths of the two bands are well correlated, as demonstrated by a series of LBLRTM simulations run for different values of the column density $_2$ )." +" Additionally, they both follow a linear dependency on airmass, down to X—2.5."," Additionally, they both follow a linear dependency on airmass, down to $X$ =2.5." +" The measurements clearly show the EW airmass dependency, which is well reproduced by the following best fit relation: where EWeg79 is expressed inA."," The measurements clearly show the EW airmass dependency, which is well reproduced by the following best fit relation: where $EW_{6870}$ is expressed in." +". With the aid of this relationship one can correct the observed values to zenith, and derive the column density using a standard curve of growth procedure."," With the aid of this relationship one can correct the observed values to zenith, and derive the column density using a standard curve of growth procedure." + For this purpose we computed a number of LBLRTM models varying N(02) between 8.4x10? cm? and 6.7x10? cm?., For this purpose we computed a number of LBLRTM models varying $_2$ ) between$\times$ $^{23}$ $^{-2}$ and $\times$ $^{24}$ $^{-2}$ . +" Subsequently we measured the EW of the B band on the output spectra, after convolving them with"," Subsequently we measured the EW of the B band on the output spectra, after convolving them with" +severe for only one extra parameter.,severe for only one extra parameter. + It follows from our decision rule that the Type error rate is quite low., It follows from our decision rule that the Type I error rate is quite low. +" Indeed, for the standard decisive ratio of e?I—148, the Type error rates are exceedingly small — the decision rule is very conservativeI at these noise ratios."," Indeed, for the standard decisive ratio of $e^5=148$, the Type I error rates are exceedingly small – the decision rule is very conservative at these signal-to-noise ratios." +" On the other hand, clearly if Ηι is true we will often find values below the critical value and so the power is not large."," On the other hand, clearly if $H_1$ is true we will often find values below the critical value and so the power is not large." + Ultimately we can trace this to the width of the prior on the satellite line height; we are too vague about what we are looking for to have high power., Ultimately we can trace this to the width of the prior on the satellite line height; we are too vague about what we are looking for to have high power. + This point arises again in the next example., This point arises again in the next example. +" The utility of the proposed decision rule is summarized in Fig. 7,,"," The utility of the proposed decision rule is summarized in Fig. \ref{figure6}," + which shows the power and Type I error rate as a function of decision threshold (the chosen critical evidence ratio) and signal-to-noise ratio., which shows the power and Type I error rate as a function of decision threshold (the chosen critical evidence ratio) and signal-to-noise ratio. +" This diagram is specific to the problem at hand, but interesting points emerge."," This diagram is specific to the problem at hand, but interesting points emerge." +" Evidently, the combination of the critical evidence and the signal-to-noise ratio determines where the decision rule places one in the diagram."," Evidently, the combination of the critical evidence and the signal-to-noise ratio determines where the decision rule places one in the diagram." + Standard decisive thresholds like e? result in low power and a very small Type I error rate — less than 1/500 with our number of repetitions of the Monte Carlo simulation., Standard decisive thresholds like $e^5$ result in low power and a very small Type I error rate – less than 1/500 with our number of repetitions of the Monte Carlo simulation. + This may not be what is needed., This may not be what is needed. +" For comparison, we also apply a Bayesian Information Criterion (BIC; see e.g. Liddle 2007)."," For comparison, we also apply a Bayesian Information Criterion (BIC; see e.g. Liddle 2007)." + In our case this means we pick the model with the smallest value of the normalized sum of squares plus the penalty term In(number of data points) x (number of model parameters)., In our case this means we pick the model with the smallest value of the normalized sum of squares plus the penalty term $\ln$ (number of data points) $\times$ (number of model parameters). + The number of data points is the number of spectral channels — evidently this number is somewhat vague as not all channels are equally informative., The number of data points is the number of spectral channels – evidently this number is somewhat vague as not all channels are equally informative. +" The BIC rule, while offering no choices, sits in a useful place in the diagram for this relatively simple problem and is no worse in power than the evidence ratio."," The BIC rule, while offering no choices, sits in a useful place in the diagram for this relatively simple problem and is no worse in power than the evidence ratio." +" Finally, we note that different decision rules (for example, accepting Ho if the evidence for it is bigger than the evidence for H1) result in a different diagram."," Finally, we note that different decision rules (for example, accepting $H_0$ if the evidence for it is bigger than the evidence for $H_1$ ) result in a different diagram." +" For a second example, we consider trying to decide if a line profile is Gaussian (Ho) or Lorentzian (H1)."," For a second example, we consider trying to decide if a line profile is Gaussian $H_0$ ) or Lorentzian $H_1$ )." +" Here we have The simulation proceeds very much as in the first case, except that we assume the priors are the same for the two models; this"," Here we have The simulation proceeds very much as in the first case, except that we assume the priors are the same for the two models; this" +from that of the MP.,from that of the MP. + Note that the position angle of the AIP raciation is determined by the magnetic Geld direction in the emission region. whereas the position angle of the LEC radiation should reflect the magnetic field orientation in the scattering region.," Note that the position angle of the MP radiation is determined by the magnetic field direction in the emission region, whereas the position angle of the LFC radiation should reflect the magnetic field orientation in the scattering region." + Because of the magnetosphere rotation. the ray emitted alone the magnetic Geld makes he angle r/2r; with the local magnetic field. direction (seePetrova2008a.andSect.4above)..," Because of the magnetosphere rotation, the ray emitted along the magnetic field makes the angle $\sim r/2r_L$ with the local magnetic field direction \citep[see][and Sect. 4 above]{p07a}." + Thus. the magnetic ield orientations in the scattering and emission regions ciller woσε. the dillerence between the position angles of he original8 and scattered. radiation. being& approximatelyap he same.," Thus, the magnetic field orientations in the scattering and emission regions differ by $\sim r/2r_L$, the difference between the position angles of the original and scattered radiation being approximately the same." + For the scattering taking place close to the ligh cvlinder this dillerence is 30°., For the scattering taking place close to the light cylinder this difference is $\sim 30^\circ$. + Ht is worthy to. poin out that in our consideration the position angle shift. of he scattered. component roughly equals. its. longitudina separation from the MP., It is worthy to point out that in our consideration the position angle shift of the scattered component roughly equals its longitudinal separation from the MP. + Ες is indeed the case for the LEC ol the Crab pulsar (Molfett&LIankins1999) and is believe o be a distinctive feature of the scattered. components in other pulsars., This is indeed the case for the LFC of the Crab pulsar \citep{mh98} and is believed to be a distinctive feature of the scattered components in other pulsars. + Lligh percentage of linear polarization is another characteristic feature of the scattered. components., High percentage of linear polarization is another characteristic feature of the scattered components. + In case of the scattering in a strong magnetic field. the scatterec radiation is dominated by the waves of ordinary polarization. whose electric vector lies in the plane of the wavevector anc he external magnetic field.," In case of the scattering in a strong magnetic field, the scattered radiation is dominated by the waves of ordinary polarization, whose electric vector lies in the plane of the wavevector and the external magnetic field." + In the original radio beam. only he ordinary waves are subject to the scattering below the resonance. whereas both types of waves. the ordinary. an extraordinary ones. undergo equally etlicient. scattering a he harmonies of the gvrofrequencey.," In the original radio beam, only the ordinary waves are subject to the scattering below the resonance, whereas both types of waves, the ordinary and extraordinary ones, undergo equally efficient scattering at the harmonics of the gyrofrequency." + In the Crab. as well as in other pulsars. the PR component is known to have almos complete linear polarization.," In the Crab, as well as in other pulsars, the PR component is known to have almost complete linear polarization." + Although the percentage. of inear polarization of the LEC is lower. ~40%. it stil exceeds that of the ALD.," Although the percentage of linear polarization of the LFC is lower, $\sim 40\%$, it still exceeds that of the MP." + One can expect that the LEC radiation sullers depolarization., One can expect that the LFC radiation suffers depolarization. + This can be understood. as follows., This can be understood as follows. + A noticeable sweep of the position angle across the LEC (Mollett&Llankins1999) implies that this component is formed. by the radiation coming from somewhat cilferent altitudes in the magnetosphere. which results. from. the scattering of somewhat cdilferent frequencies.," A noticeable sweep of the position angle across the LFC \citep{mh98} implies that this component is formed by the radiation coming from somewhat different altitudes in the magnetosphere, which results from the scattering of somewhat different frequencies." + Lone take into account the finite width of the MP. at a fixed pulse longitude within the LEC there should be radiation from cillerent altitucles and. therefore with cillerent position angles.," If one take into account the finite width of the MP, at a fixed pulse longitude within the LFC there should be radiation from different altitudes and therefore with different position angles." + The superposition of the waves with dillerent position angles may actually lead to a substantial depolarization of the resultant raciation., The superposition of the waves with different position angles may actually lead to a substantial depolarization of the resultant radiation. + The LEC and PR of the Crab. pulsar are. known to exhibit. pronounced. frequeney. evolution (Molfett&Lank-ins 1996)., The LFC and PR of the Crab pulsar are known to exhibit pronounced frequency evolution \citep{mh96}. +. Phe PR component is significant at the lowest frequencies. the LEC becomes strong at. frequencies ~1 CGlIIz. and at higher frequencies both components vanish.," The PR component is significant at the lowest frequencies, the LFC becomes strong at frequencies $\sim 1$ GHz, and at higher frequencies both components vanish." +" To analvze the spectral behaviour of the scattered components in our model let us turn to equation (28) and consider the ratio of the scattering elliciencies given that the frequencies of the scattered: radiation are equal. £j,νι."," To analyze the spectral behaviour of the scattered components in our model let us turn to equation (28) and consider the ratio of the scattering efficiencies given that the frequencies of the scattered radiation are equal, $\nu_{1_0}=\nu_{1_s}$." + Phen we have νο~GonybengfaePe+t ie. the role of the scattering at the harmonies of the evrofrequeney increases with frequeney. Py/Pyxvf3.," Then we have $\Gamma_s/\Gamma_0\sim(\nu_s\eta/\nu_{1_s}\eta_1)^{1-\alpha} +(\gamma_0/\theta\gamma)^{2s-4}$, i.e. the role of the scattering at the harmonics of the gyrofrequency increases with frequency, $\Gamma_s/\Gamma_0\propto\nu_{1_s}^{\alpha-1}$." +" πας, the LEC is expected to dominate at somewhat higher frequencies. which is in accordance with the observed. trend."," Thus, the LFC is expected to dominate at somewhat higher frequencies, which is in accordance with the observed trend." + On the way in the magnetosphere. both scattered components. the PR and. LEC. may be further subject to scattering.," On the way in the magnetosphere, both scattered components, the PR and LFC, may be further subject to scattering." + Because of magnetosphere rotation their inclination to the ambient magnetic field rapidly. increases with distance. while the magnetic field. strength rapidly decreases.," Because of magnetosphere rotation their inclination to the ambient magnetic field rapidly increases with distance, while the magnetic field strength rapidly decreases." + Similarly to the. MI the components may. be involved in the induced transverse scattering in a moderately strong magnetic field. in which case the radiation is scattered backwards (forthegeneraltheoryofthisprocessseePetrova2008b).," Similarly to the MP, the components may be involved in the induced transverse scattering in a moderately strong magnetic field, in which case the radiation is scattered backwards \citep[for the general theory of this process +see][]{p07b}." +. The consequences of the backward: scattering of the components will be studied. in detail in à separate paper., The consequences of the backward scattering of the components will be studied in detail in a separate paper. + Lt will be shown that this process may give rise to the high-frequency. components in the profile of the Crab pulsar: the backscattering of the PR can account for the LP’. whereas the scattering of the LEC can explain the LECT and 1Ο2.," It will be shown that this process may give rise to the high-frequency components in the profile of the Crab pulsar: the backscattering of the PR can account for the IP', whereas the scattering of the LFC can explain the HFC1 and HFC2." + Lt will also be demonstrated that the elieiency of the induced. transverse scattering increases with frequency. and. corresponcdinelv. at high enough frequencies the PLR and LEC vanish. their intensities being almost completely transferred to the backward components.," It will also be demonstrated that the efficiency of the induced transverse scattering increases with frequency and, correspondingly, at high enough frequencies the PR and LFC vanish, their intensities being almost completely transferred to the backward components." + The scattering elliciencies given by equations (26) and (27) depend on the intensity of the incident. radio beam and on the number density and the characteristic Lorentz-[actor of the scattering plasma particles., The scattering efficiencies given by equations (26) and (27) depend on the intensity of the incident radio beam and on the number density and the characteristic Lorentz-factor of the scattering plasma particles. + All these quantities may show marked: pulse-to-pulse Γιοπατος. so that. the scattering elliciencies may vary as well.," All these quantities may show marked pulse-to-pulse fluctuations, so that the scattering efficiencies may vary as well." + I£ the scattering is so strong that the component growth is at the stage of saturation. .r »1. the luctuations of E do not alfect the intensity of the scattered: component significantly.," If the scattering is so strong that the component growth is at the stage of saturation, $x\gg 1$ or $y\gg +1$, the fluctuations of $\Gamma$ do not affect the intensity of the scattered component significantly." + On condition that pr~Lory 1. however. even small Ductuations of the scattering ellieiency may [ead o drastic variations of the scattered component.," On condition that $x\sim 1$ or $y\sim 1$, however, even small fluctuations of the scattering efficiency may lead to drastic variations of the scattered component." + According o equations. (26)-(27). this condition may be. satisfied in a number of pulsars. which have large enough racio uminosities. strong magnetic fields and short periods.," According to equations (26)-(27), this condition may be satisfied in a number of pulsars, which have large enough radio luminosities, strong magnetic fields and short periods." + Such oulsars are believed to exhibit. occasional activity at. the απο longitudes. preceding the MP., Such pulsars are believed to exhibit occasional activity at the pulse longitudes preceding the MP. + Namely. these pulsars are expected to show the transient. components with the spectral and polarization properties similar to those known or the PR and LEC of the Crab pulsar.," Namely, these pulsars are expected to show the transient components with the spectral and polarization properties similar to those known for the PR and LFC of the Crab pulsar." + Furthermore. the ransient components resulting from the higher-harmonic scattering can also be present in pulsar profiles. in particular. in the Crab pulsar.," Furthermore, the transient components resulting from the higher-harmonic scattering can also be present in pulsar profiles, in particular, in the Crab pulsar." + The components of pulsar. profiles outside of the MP. are known to exhibit a number of peculiar. properties. and at the same time the pulse-to-pulse Iuctuations generally testify to a physical relation of these components to the ALD.," The components of pulsar profiles outside of the MP are known to exhibit a number of peculiar properties, and at the same time the pulse-to-pulse fluctuations generally testify to a physical relation of these components to the MP." + We believe that the components outside of the MP originate as a result. of induced: scattering of the pulsar radio beam into the background. with different types ofthe components corresponding to cilferent scattering regimes.," We believe that the components outside of the MP originate as a result of induced scattering of the pulsar radio beam into the background, with different types of the components corresponding to different scattering regimes." + In the present. paper. we have considered. the magnetized induced scattering olf the spiraling particles. which may be present in the outer magnetosphere of a pulsar.," In the present paper, we have considered the magnetized induced scattering off the spiraling particles, which may be present in the outer magnetosphere of a pulsar." + In this case the scattering at the harmonics of the particle &vrofrequeney may be eflicient., In this case the scattering at the harmonics of the particle gyrofrequency may be efficient. + Our investigation is aimed at explaining. at least partially. the extremely complex radio emission pattern of the Crab. pulsar.," Our investigation is aimed at explaining, at least partially, the extremely complex radio emission pattern of the Crab pulsar." + Lt has been demonstrated. that. the scattering from the first harmonic of the evrofrequency into the state below the resonance can account for the formation, It has been demonstrated that the scattering from the first harmonic of the gyrofrequency into the state below the resonance can account for the formation +The global. simultaneous fit gives a reduced y7=1.055.,"The global, simultaneous fit gives a reduced $\chi^2_{\nu}$ =1.055." + Overall there are 25 free parameters common to all time intervals that. therefore. are constrained by the full 2 10° photon statistics.," Overall there are 25 free parameters common to all time intervals that, therefore, are constrained by the full 2 $^5$ photon statistics." + Each time interval has its own set of 8 free parameters. three for the continuum (Ny>. CF and powerlaw normalization) and five for the absorption Fe lines (velocity and individual depth).," Each time interval has its own set of 8 free parameters, three for the continuum $\rm N_{H,2}$, $\rm CF$ and powerlaw normalization) and five for the absorption Fe lines (velocity and individual depth)." + Fig., Fig. + 3. shows the spectra and the resulting fit in two representative time intervals (T8 and T12. as marked in Fig. 2)).," \ref{spec_ind} shows the spectra and the resulting fit in two representative time intervals (T8 and T12, as marked in Fig. \ref{eclipses}) )," + clearly displaying a strong variation of absorption between the two time intervals., clearly displaying a strong variation of absorption between the two time intervals. + In the following we will mostly focus on the variations of the column density Ny» and of the Covering Factor (CF) of the partial absorber. whose resulting best-fit values in the various time intervals are shown in Fig.," In the following we will mostly focus on the variations of the column density $\rm N_{H,2}$ and of the Covering Factor $\rm CF$ ) of the partial absorber, whose resulting best-fit values in the various time intervals are shown in Fig." + 2bb and c. One possible concern is whether these two quantities are degenerate. given the reduced statistics available in each time interval.," \ref{eclipses}b b and c. One possible concern is whether these two quantities are degenerate, given the reduced statistics available in each time interval." + We found this not to be the case in any of the time intervals (except for the last interval. which does not require a second absorber).," We found this not to be the case in any of the time intervals (except for the last interval, which does not require a second absorber)." + As an example. Fig.," As an example, Fig." + 4. shows the confidence levels in the Ny> versus CF plane. for the time interval T8: although there is some correlation between the two parameters," \ref{contour} shows the confidence levels in the $\rm N_{H,2}$ versus $\rm CF$ plane, for the time interval T8: although there is some correlation between the two parameters" +regions of the Galaxy.,regions of the Galaxy. + Although the model has some points of similarity with the present study. there are also large differences.," Although the model has some points of similarity with the present study, there are also large differences." + The disk in Chandran’s model is assumed to have a uniform rotation and (he gravitational potential is assumed (o correspond (ο a constant background mass densitv (so that the gravitational acceleration increases linearly with radius)., The disk in Chandran's model is assumed to have a uniform rotation and the gravitational potential is assumed to correspond to a constant background mass density (so that the gravitational acceleration increases linearly with radius). + In contrast. we assume that the disk is differentiallv rotating and (hat the gravitational potential corresponds to that of a compact mass al the center.," In contrast, we assume that the disk is differentially rotating and that the gravitational potential corresponds to that of a compact mass at the center." + ILowever. Chandran considers a compressible eas whereas we simplify our problem by taking (he gas to be incompressible.," However, Chandran considers a compressible gas whereas we simplify our problem by taking the gas to be incompressible." + has derived a formula (his eqs. |, has derived a formula (his eqs. [ +91] and [92]) for the oscillation frequency when there is no magnetic field and the density contrast parameter j(=+1.,91] and [92]) for the oscillation frequency when there is no magnetic field and the density contrast parameter $\mu =\pm 1$. + His results are consistent with our analvtical results for a disk with constant angular velocity (see our eq. 1960)., His results are consistent with our analytical results for a disk with constant angular velocity (see our eq. ]). + In particular. the results confirm that the disk vorticity has the effect of stabilizing the modes.," In particular, the results confirm that the disk vorticity has the effect of stabilizing the modes." + The authors thank the anonvmous referee for several useful comments., \acknowledgements The authors thank the anonymous referee for several useful comments. + LXL's research was supported by NASA through Chandra Postdoctoral Fellowship grant number PFE1-20018 awarded by the Chandra X-ray Center. which is operated by the Smithsonian Astrophysical Observatory for NASA under contract NASS-39073.," LXL's research was supported by NASA through Chandra Postdoctoral Fellowship grant number PF1-20018 awarded by the Chandra X-ray Center, which is operated by the Smithsonian Astrophysical Observatory for NASA under contract NAS8-39073." + RN was supported in part by NASA erant. NACG5-10780 and NSF grant. AST 0307433., RN was supported in part by NASA grant NAG5-10780 and NSF grant AST 0307433. +The broad component of the Bahuer lines iu this τν=0.1511 quasar are bluc-shüfted (~3100 En with respect to NLs.,"The broad component of the Balmer lines in this $z_{\rm NL}=0.1514$ quasar are blue-shifted $\sim 3\,100$ ) with respect to NLs." + The line profile is boxy. with no sjeuificaut asvunuetiv.," The line profile is boxy, with no significant asymmetry." + The fux ratio is —5. constant over the velocity rauge.," The flux ratio is $\sim 5$, constant over the velocity range." + This object was not iucluded inthe analysis by Shenetal.(2010).., This object was not included inthe analysis by \citet{shen10a}. + Stratevaetal.(2003). and Bianetal.(2007) listed this source as a DPE., \citet{strateva03} and \citet{bian07} listed this source as a DPE. + The bulk of the BLs of this quasars is redshifted (~1200 +)) with respect to NLs.," The bulk of the BLs of this quasars is redshifted $\sim 1\,200$ ) with respect to NLs." + The red wine is brighter., The red wing is brighter. + The flux ratio is [in the blue wing and around 3 iu the red wine., The flux ratio is $\sim4$ in the blue wing and around 3 in the red wing. + This object was labeled asa DPE caudidate by Sheuetal.(2010).., This object was labeled as a DPE candidate by \citet{shen10a}. +. The line of this source peaks at ~23700 bluewrds of the NLs. aud shows an extended red wing.," The line of this source peaks at $\sim 3\,700$ blue-wards of the NLs, and shows an extended red wing." + The hue profile is similar., The line profile is similar. + The properties of this quasar are half the wav between the objects with asvuunetric line profiles (0.9... JLIS1)0131) aud the typical DPEs. though this source has not been included in any previous compilation of DPEs.," The properties of this quasar are half the way between the objects with asymmetric line profiles (e.g., J1154+0134) and the typical DPEs, though this source has not been included in any previous compilation of DPEs." + The peculiar properties of this object were first reported bx Borosou&Lauer(2009)., The peculiar properties of this object were first reported by \citet{boroson09}. +. The broad dines show two peaks. one consistent with the rest-frame of the ealaxy as set by NLs. the other significantly bluc-slüfted (~3100m 13).," The broad lines show two peaks, one consistent with the rest-frame of the galaxy as set by NLs, the other significantly blue-shifted $\sim3\,400$ )." + Boroson&Lauer(2009) proposed the BUB interpretation for this source.," \citet{boroson09} + proposed the BHB interpretation for this source." + However. following observations covering the red wing of revealed the presence of a bump in the line wing (Choruock 2010).. a feature conunouly observed in DPEs.," However, following observations covering the red wing of revealed the presence of a bump in the line wing \citep{chornock10}, a feature commonly observed in DPEs." +emitter or From the spectroscopic point of view. the properties of this source are simular to those of J0927|29[3.," or From the spectroscopic point of view, the properties of this source are similar to those of J0927+2943." + The Spectruni presents three sets of lines at two different redshifts: Broad bahuer dines (driving the redshift estimate by the SDSS. pipeline) aud faint narrow lines are detected at τι=0.1993., The spectrum presents three sets of lines at two different redshifts: Broad balmer lines (driving the redshift estimate by the SDSS pipeline) and faint narrow lines are detected at $z_1=0.1993$. + Another set of (brigliter) narrow lues is observed at το=0.2263., Another set of (brighter) narrow lines is observed at $z_2=0.2263$. + The corresponding velocity shift is ~6600.," The corresponding velocity shift is $\sim +6\,600$." + A careful inspection of the SDSS image of this source reveals an extended stellar wing South-wards of the quasar., A careful inspection of the SDSS image of this source reveals an extended stellar wing South-wards of the quasar. + If this belongs to the quasar host galaxy. then it would reveal a strongly perturbed morphology.," If this belongs to the quasar host galaxy, then it would reveal a strongly perturbed morphology." + Ou the other hand. it could be that this is a superposed galaxy.," On the other hand, it could be that this is a superposed galaxy." + Iu this case. since τμ]<$ 000 ) and rather faint emission lines." + The main peak of these lues show huge velocity shifts (>5000 1)) with respect to the NLs.," The main peak of these lines show huge velocity shifts $>5\,000$ ) with respect to the NLs." +" For a conparison. oulv 5 objects out of 138 in Stratevaetal.(2003). have a shift of the brighter peak of Luger than 50000 ον, and none of them exceed τος Ἐ"," For a comparison, only 5 objects out of 138 in \citet{strateva03} have a shift of the brighter peak of larger than 000 , and none of them exceed 000 ." +"ν, Note that the vextreme double-peaked enütter"" explanation is possible also for oue of the BITB candidates already discussed m literature 2010).."," Note that the “extreme double-peaked emitter” explanation is possible also for one of the BHB candidates already discussed in literature \citep[J1000+2233,][]{decarli_4c2225}. ." +As discussed above. the sizes of the known populaloli of both AIBCs and disrupted asteroids. from which these generalizatious are drawn. are extremely sniall. and so the typical caveats associated with siiall-uuuber statistics certainly apply.,"As discussed above, the sizes of the known populations of both MBCs and disrupted asteroids, from which these generalizations are drawn, are extremely small, and so the typical caveats associated with small-number statistics certainly apply." + However. for the above reasons. we sugecstfelon] that repeated activity is the least ambiguous and most reliably obtainable indicator available a the current time that comet-like activity is sublimation-driven for a particular object.," However, for the above reasons, we suggest that repeated activity is the least ambiguous and most reliably obtainable indicator available at the current time that comet-like activity is sublimation-driven for a particular object." +" While ouly two o| the seven currently known comet-like main-belt objects(he, both MIBCs aud disrupted asteroids) have been obxcyved to exhibit recurrent activity to date. we note tha the remaining five objects were discovered ax come-like bodies recently enough that they have not actually vet conipleted. full orbits since their respective disco‘TIES,"," While only two of the seven currently known comet-like main-belt objects, both MBCs and disrupted asteroids) have been observed to exhibit recurrent activity to date, we note that the remaining five objects were discovered as comet-like bodies recently enough that they have not actually yet completed full orbits since their respective discoveries." + As such. continued monitoring of all of these objects to search for recurrent activity will be importaut for validating their identi&cation as AIBCs or disrupted asteroids.," As such, continued monitoring of all of these objects to search for recurrent activity will be important for validating their identification as MBCs or disrupted asteroids." + We lave conducted a photometric. spectroscopic. ancl ανασα. study of comet-like main-belt asteroid (5096) Scheila. and report the following findings:," We have conducted a photometric, spectroscopic, and dynamical study of comet-like main-belt asteroid (596) Scheila, and report the following findings:" +with y and help to exploit fully the ability of the XLF data to constrain γ.,with $\gamma$ and help to exploit fully the ability of the XLF data to constrain $\gamma$. +" To demonstrate the impacts of these datasets, Figure 5 shows the constraints in the €,"" (left panel) and cs,"" (right panel) planes for various subsets of data."," To demonstrate the impacts of these datasets, Figure \ref{fig:datasets} shows the constraints in the $\Omega_{\rm m}, \gamma$ (left panel) and $\sigma_8, \gamma$ (right panel) planes for various subsets of data." + The red contours show the constraints from the fzas data (i.e. only cluster data); the green contours show the results from adding SNIa data (i.e. fzas--SNIa); the blue contours from adding BAO to the XLF--rest; and the gold (smallest) contours from adding CMBdata??., The red contours show the constraints from the $f_{\rm gas}$ data (i.e. only cluster data); the green contours show the results from adding SNIa data (i.e. $f_{\rm gas}$ +SNIa); the blue contours from adding BAO to the rest; and the gold (smallest) contours from adding CMB. +". The left panel of Figure 5 demonstrates again the absence of any strong correlation between (34, and ¥ (see also Section 6.1)).", The left panel of Figure \ref{fig:datasets} demonstrates again the absence of any strong correlation between $\Omega_{\rm m}$ and $\gamma$ (see also Section \ref{sec:growth}) ). +" These results (see also Table 1)) show that simply improving our knowledge of Qm, and therefore the"," These results (see also Table \ref{table:params}) ) show that simply improving our knowledge of $\Omega_{\rm m}$ , and therefore the" +sample clistjbutious iu Figure [ do not look that similar. aud the bieh siguificaice Once agaln reflects the act that the Ix-9 test has a higher seusitivity to the median values of clisributious than to the spreads in distributions.,"sample distributions in Figure 4 do not look that similar, and the high significance once again reflects the fact that the K-S test has a higher sensitivity to the median values of distributions than to the spreads in distributions." + In Fiere 2 we compare the two timescale να]es (Tyas ad Torn) to each otler for the four samples., In Figure 5 we compare the two timescale values $\tau_{gas}$ and $\tau_{form}$ ) to each other for the four samples. + Figure 5 shows a general correlation of τρως with 55; (as should be expected since both axes siare a common denominator)., Figure 5 shows a general correlation of $\tau_{gas}$ with $\tau_{form}$ (as should be expected since both axes share a common denominator). + The main reason for the relatively good correlation iu Figure 5 is that the gas-rich dwarf galaxies generally show a limited range in NM(HI)/L(B) (Skillimau 1996)., The main reason for the relatively good correlation in Figure 5 is that the gas-rich dwarf galaxies generally show a limited range in M(HI)/L(B) (Skillman 1996). + The dotted line in Figure 5 representsan equality between Tyas and 7555. or. equivalently. M(H/L(B) = 1.0.," The dotted line in Figure 5 representsan equality between $\tau_{gas}$ and $\tau_{form}$, or, equivalently, M(HI)/L(B) $=$ 1.0." + The couclusious of Figure 3 aud. [are supported., The conclusions of Figure 3 and 4 are supported. + While the Sculptor (ορ cds aud the Local Croup dis tend to fall into the region of the graph that is well populated by the larger LSB anc isolatec di samples. it is interesting that the Sculptor group dls lie at preferentially higher values of log(tyas) with the majority above 10.5. while the Local Group dls lie at. preferentially lower values of logt7yos) with the 1ajority below 10.5.," While the Sculptor Group dIs and the Local Group dIs tend to fall into the region of the graph that is well populated by the larger LSB and isolated dI samples, it is interesting that the Sculptor group dIs lie at preferentially higher values of $\tau_{gas}$ ) with the majority above 10.5, while the Local Group dIs lie at preferentially lower values of $\tau_{gas}$ ) with the majority below 10.5." + It interesting that. when normalized by SER. the LSB ealaxies clo not devia ar from the trend.," It is interesting that, when normalized by SFR, the LSB galaxies do not deviate far from the trend." + Nzively. oue might expect ilem to deviate to thetyper right. (higher gas cont and lower |uninmos. but. in fact. they c) 10 appear to listinetish themselves in this diagrOsic diagram.," Naively, one might expect them to deviate to the upper right (higher gas content and lower luminosity), but, in fact, they do not appear to distinguish themselves in this diagnostic diagram." + This is simply due to the fact tha 1ie. dynamic range ii the SE Rois much larger than the ¢ynaiic range in M(HL)/L(B)., This is simply due to the fact that the dynamic range in the SFR is much larger than the dynamic range in M(HI)/L(B). + Finally. iu Figure 6. we have plotted he SER ve‘sus gas mass with both noTueized to the galaxy luminosity (SFR/Ly versus Myj/Lp)*.," Finally, in Figure 6, we have plotted the SFR versus gas mass with both normalized to the galaxy luminosity $_B$ versus $_{HI}$ $_B$." + In thi jaguostic diagram excurslous are much nore proninen., In this diagnostic diagram excursions are much more prominent. + The high relative SFR eaanxies [roi Local Group are uot. uimStally gas rich., The high relative SFR galaxies from the Local Group are not unusually gas rich. + 'The Sculxor Group galaxies tend toward larger gas [heions and lower values of SER (uote the arge nuliber o ‘them in the lower right eqacdraut)., The Sculptor Group galaxies tend toward larger gas fractions and lower values of SFR (note the large number of them in the lower right quadrant). + TIe Isolated cls show a large ange in values. reaching οΑΓΙ the extremes seen in the two group sauples.," The isolated dIs show a large range in values, reaching toward the extremes seen in the two group samples." + It would appear that the isolated cls sample of van Zee (2000. 2001) covers the range of proyerties of cls with the possie exception of he lowest lumilosity systenis.," It would appear that the isolated dIs sample of van Zee (2000, 2001) covers the range of properties of dIs with the possible exception of the lowest luminosity systems." + Ol course. the very large values of τρως seen ii severa ol the Sculptor Dwarf cls «lo uot represeut au upper bound: there are several Sculptor Group dls wit1 HI detected but no Ha emission detected. and these would have τρως values of infinity.," Of course, the very large values of $\tau_{gas}$ seen in several of the Sculptor Dwarf dIs do not represent an upper bound; there are several Sculptor Group dIs with HI detected but no $\alpha$ emission detected, and these would have $\tau_{gas}$ values of infinity." + Suc1 galaxies are not limited to the Seulptor Cirotp: iu the Local Group we have LC5-3. Autlia. aud DDO 210 as examples of dls with detectable HI but uo detectable Ha emission (Mateo 1995).," Such galaxies are not limited to the Sculptor Group; in the Local Group we have LGS-3, Antlia, and DDO 210 as examples of dIs with detectable HI but no detectable $\alpha$ emission (Mateo 1998)." +" Tlese gaaxies are often referred to as ""hrausitlon galaxies or dIrr/dSph ", These galaxies are often referred to as “transition” galaxies or dIrr/dSph . +Mateo (1998) aso incldes Pegasus aud Phoeuix 1u this category., Mateo (1998) also includes Pegasus and Phoenix in this category. +spectra plotted against the 8-10 keV flux.,spectra plotted against the 8-10 keV flux. + We find that the normal spectral variability of NGC 3227 is very similar to that found in other Sevfert galaxies., We find that the 'normal' spectral variability of NGC 3227 is very similar to that found in other Seyfert galaxies. + At low flux levels the spectral index steepens rapidly with increasing flux: at higher flux levels the increase of the spectral slope levels off and saturates at D—2.0., At low flux levels the spectral index steepens rapidly with increasing flux; at higher flux levels the increase of the spectral slope levels off and saturates at $\Gamma \sim 2.0$. + Similar flux - slope relations have been found in NGC 4051 (Lamer et al., Similar flux - slope relations have been found in NGC 4051 (Lamer et al. + 2002) and MCG-6-30-15 (Shih. Iwasawa Fabian 2002).," 2002) and MCG-6-30-15 (Shih, Iwasawa Fabian 2002)." + On the other hand. the data points from the 2001 event clearly fall outside the normal range in the flux - index plane.," On the other hand, the data points from the 2001 event clearly fall outside the normal range in the flux - index plane." + The indices are much harder and do not strongly correlate with changes in the 8-10 keV flux., The indices are much harder and do not strongly correlate with changes in the 8-10 keV flux. + Having ruled out simple. flux-correlated variability as the source of the hard-spectrum event. we next consider the possibility that it is caused by transient obscuration by a large column of gas.," Having ruled out simple, flux-correlated variability as the source of the hard-spectrum event, we next consider the possibility that it is caused by transient obscuration by a large column of gas." + The apparent symmetry of the event supports this possibiliat suggesting that a symmetric (.e. spherical) cloud passed in front of the X-ray source.," The apparent symmetry of the event supports this possibility, suggesting that a symmetric (i.e. spherical) cloud passed in front of the X-ray source." + From the flux of hard X-rays and the normal flux - index relation in NGC 3227 (Fig. 2)), From the flux of hard X-rays and the normal flux - index relation in NGC 3227 (Fig. \ref{fluxgamma}) ) + we estimate an intrinsic photon index of F=1.6 during the absorption event., we estimate an intrinsic photon index of $\Gamma = 1.6$ during the absorption event. + We repeated the model fitting with the power law + Gaussian line model with the photon index fixed at P=1.6 and the absorption column density left free to vary., We repeated the model fitting with the power law + Gaussian line model with the photon index fixed at $\Gamma = 1.6$ and the absorption column density left free to vary. + Fig., Fig. + 3 shows the resulting column density for the assumption of a neutral absorber., \ref{nhcurve} shows the resulting column density for the assumption of a neutral absorber. +" We fitted the protile of column density changes with two simple models. a uniform sphere and a -model of the form Ny=Naas/(1(rfI)""7 (see Fig. 3))."," We fitted the profile of column density changes with two simple models, a uniform sphere and a $\beta$ -model of the form $N_{\rm H}=N_{\rm H,max}/(1+(r/R)^2)^{0.5}$ (see Fig. \ref{nhcurve}) )." + The J-model gave a much better fit (reduced X7.70.98 versus 47o1.85 for the uniform sphere model). for a «7 index of 0.5. suggesting that the cloud density is not uniform but increases towards the centre.," The $\beta$ -model gave a much better fit (reduced $\chi^{2}\simeq0.98$ versus $\chi^{2}\simeq1.85$ for the uniform sphere model), for a $\beta$ index of $\sim0.5$, suggesting that the cloud density is not uniform but increases towards the centre." + The column density peaks at 2.6-107 em.7., The column density peaks at $N_{\rm H} \sim 2.6 \cdot 10^{23}$ $^{-2}$. + However. bused on theRXTE data alone. we cannot absolutely discount the possibility that the hard-spectrum event is caused by very unusual variability of the primary continuum. which is not simply correlated with flux.," However, based on the data alone, we cannot absolutely discount the possibility that the hard-spectrum event is caused by very unusual variability of the primary continuum, which is not simply correlated with flux." + Fortunately. NGC 3227 was observed by early in the event. and it is to this data that we now turn.," Fortunately, NGC 3227 was observed by early in the event, and it is to this data that we now turn." + NGC 3227 was observed by around MID 51877. during an early phase of the hard spectrum event (see Fig 3)).," NGC 3227 was observed by around MJD 51877, during an early phase of the hard spectrum event (see Fig \ref{nhcurve}) )." + We performed joint model titting on the EPIC MOSI. MOS? and PN spectra.," We performed joint model fitting on the EPIC MOS1, MOS2 and PN spectra." +" The hard bands ¢ 2 keV) can be modeled by a strongly absorbed (Ny~5-I07em. 7) power law spectrum and a narrow Fe Ix, fluorescence line.", The hard bands $>$ 2 keV) can be modeled by a strongly absorbed $N_{\rm H} \sim 5 \cdot 10 ^{22} {\rm cm^{-2}}$ ) power law spectrum and a narrow Fe ${\rm K_{\alpha}}$ fluorescence line. + The absorbing column density is consistent with the value measured byAXTE at the same time (see Fig. 35., The absorbing column density is consistent with the value measured by at the same time (see Fig. \ref{nhcurve}) ). + In the soft range below | keV an unabsorbed power law spectrum dominates (see below and Fig. 4)., In the soft range below 1 keV an unabsorbed power law spectrum dominates (see below and Fig. \ref{xmmspec}) ). + UsingNSPEC. we fitted 4 different partial covering models to the EPIC spectra: l.," Using, we fitted 4 different partial covering models to the EPIC spectra: 1." + Single power law model with partial absorption:ZGAUSS)). with the two power law components having identical slopes.," Single power law model with partial absorption:, with the two power law components having identical slopes." + 2., 2. + Double power law model:ZGAUSS)). both power law indices are free to vary.," Double power law model:, both power law indices are free to vary." + 3., 3. + Double power law model with warm absorber as partial coverer: 4+., Double power law model with warm absorber as partial coverer: 4. + Single power law with Compton reflection and warm absorber: The results of the spectral fitting are summarized in table [.. and the double power law + warm absorber model is shown in Figure 4..," Single power law with Compton reflection and warm absorber: The results of the spectral fitting are summarized in table \ref{specfit}, and the double power law + warm absorber model is shown in Figure \ref{xmmspec}." +" In all of the three models a narrow iron νι, fluorescence line with rest frame energy 6.4 keV and equivalent width ~ 240 eV is required.", In all of the three models a narrow iron ${\rm K_{\alpha}}$ fluorescence line with rest frame energy 6.4 keV and equivalent width $\sim$ 240 eV is required. +" The neutral. unredshifted absorption in all three models is consistent with the Galactic value (2.2107"" 7)."," The neutral, unredshifted absorption in all three models is consistent with the Galactic value $2.2\times10^{20}$ $^{-2}$ )." + From model 3. we tind that constraints on Ny and the ionisation parameter. £ of the absorbing gas suggest that the obscuring cloud is not neutral. but ionised. albeit with a low ionisation parameter (see Fig. 59).," From model 3, we find that constraints on $N_{\rm H}$ and the ionisation parameter, $\xi$ of the absorbing gas suggest that the obscuring cloud is not neutral, but ionised, albeit with a low ionisation parameter (see Fig. \ref{xinhcont}) )." + Note that the absorbed power-law component is rather hard (D.— 1.3). as expected due to the low 8-10 keV flux (2.210.7 erg 7 +) measured during theobservation," Note that the absorbed power-law component is rather hard $\Gamma\sim1.3$ ), as expected due to the low 8-10 keV flux $2.2\cdot10^{-12}$ erg $^{-2}$ $^{-1}$ ) measured during the (see Fig." + (see Fig. 2. for comparison with the ‘normal’ photon index-flux relation)., \ref{fluxgamma} for comparison with the `normal' photon index-flux relation). + The unabsorbed power law component in the soft range has a normalization of about of the absorbed power law component., The unabsorbed power law component in the soft range has a normalization of about of the absorbed power law component. + The best fit parameters of models 2 and 3 (also see Fig. 49) , The best fit parameters of models 2 and 3 (also see Fig. \ref{xmmspec}) ) +also show that the unabsorbed component is intrinsically softer than the absorbed component., also show that the unabsorbed component is intrinsically softer than the absorbed component. + There are three possible reasons for this finding: |., There are three possible reasons for this finding: 1. + We see two components emitted from different regions of the AGN. e.g. the softer. unabsorbed power law arises froma more extended emitting region. which," We see two components emitted from different regions of the AGN, e.g. the softer, unabsorbed power law arises froma more extended emitting region, which" +We begin with 71 published lighteurves of SNe Ia [rom the SNLSproject.. described in Astierοἱal.(2006).,"We begin with 71 published lightcurves of SNe Ia from the SNLS, described in \citet[][]{ASTIER_SNLS06}." +". The SNLS is a 5-vear rolling"" SN-Ia survey. using the [οσααι wide field imager on the 3.6 m Canacda-France-Lawaii Telescope."," The SNLS is a 5-year `rolling' SN-Ia survey, using the MegaCam wide field imager on the 3.6 m Canada-France-Hawaii Telescope." + The fiekls are imaged in [our bands. similar to the Sloan Digital Sky Survey οἱal. 2006).. with limiting magnitudes in ; of the order of 24.5mag.," The fields are imaged in four bands, similar to the Sloan Digital Sky Survey \citep{FUKUGITA_96,ASTIER_SNLS06}, with limiting magnitudes in $i$ of the order of $24.5~\textrm{mag}$." + The SN canudidates are confirmed using spectroscopy from 5-10 m class telescopes., The SN candidates are confirmed using spectroscopy from 8-10 m class telescopes. + The SNe in our sample are all spectroscopically confirmed SNe Ia al z=0.25—1. with a median of z=0.6.," The SNe in our sample are all spectroscopically confirmed SNe Ia at $z=0.25-1$, with a median of $z=0.6$ ." + Typical photometric errors are smaller (han 0.1mag., Typical photometric errors are smaller than $0.1~\textrm{mag}$. + Since our main focus is on classification by means of three bands. we ignore at first g-band data (but see relbands)). and use for each SN only those data combinations which have same-cay (X1) photometry mέν," Since our main focus is on classification by means of three bands, we ignore at first -band data (but see \\ref{bands}) ), and use for each SN only those data combinations which have same-day $\pm1$ ) photometry in." +"ο, This produces a sample of 172 ‘objects’. extracted [rom 58 SNe."," This produces a sample of 172 `objects', extracted from 58 SNe." + This selection does not affect the redshift distribution. which remains similar to the distribution of the original sample.," This selection does not affect the redshift distribution, which remains similar to the distribution of the original sample." + since (hese SNe have spectroscopic redshifts. we create simulated photometric redshilts. Lund. Dv adding to each objects redshift a normally distributed (with zero mean and σι standard deviation) error. and create a Gaussian z-pxdf of width o». centered on the noise-added redshift. To evaluate the impactof the precision of redshift determination. we have run (le [for various combinations of σι ancl o» values.," Since these SNe have spectroscopic redshifts, we create simulated photometric redshifts, $z_{\mathrm{rand}}$, by adding to each object's redshift a normally distributed (with zero mean and $\sigma_1$ standard deviation) error, and create a Gaussian z-pdf of width $\sigma_2$, centered on the noise-added redshift, To evaluate the impactof the precision of redshift determination, we have run the SN-ABC for various combinations of $\sigma_1$ and $\sigma_2$ values." + For every SN. we perform several specilic μαμα realizations. and average (he outcomes.," For every SN, we perform several specific $z_{\mathrm{rand}}$ realizations, and average the outcomes." +" In Figure 1. we present the SN-ABC output Pj, distributions (left) for various precisions of redshift determinations. and the posterior redshift compared to the spectroscopic one Gight)."," In Figure \ref{SNLSIa} we present the SN-ABC output $P_{Ia}$ distributions (left) for various precisions of redshift determinations, and the posterior redshift compared to the spectroscopic one (right)." + We start with σι=0 and oe»=0.01. which can represent well-determined. ie.. spectroscopic. redshifts.," We start with $\sigma_1=0$ and $\sigma_2=0.01$, which can represent well-determined, i.e., spectroscopic, redshifts." + In this case ~97% of the SNe are correctly classified by the, In this case $\sim97\%$ of the SNe are correctly classified by theSN-ABC. + With o4=o» 0.1. a reasonable precision for photometric redshilts in most surveys and redshift ranges (e.g..Grazianetal.2006:Coe 2006).. this result remains unchanged.," With $\sigma_1=\sigma_2=0.1$ , a reasonable precision for photometric redshifts in most surveys and redshift ranges \citep[e.g.,][]{Grazian_06,COE_06}, , this result remains unchanged," +the other haad. the flux rope configuration provides a natural explanation for the three-part structure of CMESs and (heir quiescent counterparts. i.e.. helmet streamers (Low1996.2001).,"the other hand, the flux rope configuration provides a natural explanation for the three-part structure of CMEs and their quiescent counterparts, i.e., helmet streamers \citep{low96, low01}." +. CAMEs that exhibit circular intensity. patterns have also been interpreted as a manifestation of helical magnetic fields. therefore being termed flux-rope CMESs (e.g..Dereetal.1999)..," CMEs that exhibit circular intensity patterns have also been interpreted as a manifestation of helical magnetic fields, therefore being termed flux-rope CMEs \citep[e.g.,][]{dere99}. ." + Recently. Gary&Moore(2004) reported the eruption of a multi-turn helix from within a region of sheared magnetic field.," Recently, \citet{gm04} reported the eruption of a multi-turn helix from within a region of sheared magnetic field." + The presence of (wisting and kinking motions in eruptive prominences further argues for (he existence of (Iux ropes in the corona (e.g..Alexauderetal.2007b).," The presence of twisting and kinking motions in eruptive prominences further argues for the existence of flux ropes in the corona \citep[e.g.,][]{alg06,lag07}." +". While these morphological studies demonstrate that [Iux ropes are indeed associated wilh CMESs. it is still unknown whether (μον are present. prior to solar eruptions. although their presence ""alter"" (he eruption have been confirmed by observations of rotating magnetic fields (Durlagaetal.1981)."," While these morphological studies demonstrate that flux ropes are indeed associated with CMEs, it is still unknown whether they are present prior to solar eruptions, although their presence “after” the eruption have been confirmed by observations of rotating magnetic fields \citep{burlaga81}." +. The inflation of coronal fields can be attributed either to the shearing of the magnetic footpoints. or to the emergence of new flux.," The inflation of coronal fields can be attributed either to the shearing of the magnetic footpoints, or to the emergence of new flux." + However. the eruption of the whole PEA such as the 2005 August 22 event ία.€)) poses a severe constraint on the energetics of (he eruption. since it has been demonstrated that a bipolar force-free field is at its maximum energvwhen the field is completely “open” (Alv1984.1991:Sturrock1991).," However, the eruption of the whole PEA such as the 2005 August 22 event (a–c)) poses a severe constraint on the energetics of the eruption, since it has been demonstrated that a bipolar force-free field is at its maximum energywhen the field is completely “open” \citep{aly84, aly91, sturrock91}." +.. A multipolar topology as proposed in the break-out model (Antiochosetal.1999) can help to circumvent the so-called Alv-Sturrock limit. since only one of the bipolar arcacles is opened up.," A multipolar topology as proposed in the break-out model \citep{adk99} can help to circumvent the so-called Aly-Sturrock limit, since only one of the bipolar arcades is opened up." + Indeed Ah 10798 that hosted the 2005 August 22 PEA displays a quadrupolar field topology. as demonstrated by the contours of the MDI magnetogram LO((a)).," Indeed AR 10798 that hosted the 2005 August 22 PEA displays a quadrupolar field topology, as demonstrated by the contours of the MDI magnetogram (a))." + Alternatively. studies have shown that the AlwStirrock limit can be byvpassed if the coronal field contains a detached flux rope (e.g..Wolfson2003:Flyerοἱal.2004).," Alternatively, studies have shown that the Aly-Sturrock limit can be bypassed if the coronal field contains a detached flux rope \citep[e.g.,][]{wolfson03,flyer04}." +. Intviguinely. a swirling structure can be seen in the center of the 2005 August 22 arcade as early as 12:12 UT 4((b)). and was most obvious at 12:36 UT. 10((a)). over [our hours before the onset of the M5.6 flare at about 1646 UT.," Intriguingly, a swirling structure can be seen in the center of the 2005 August 22 arcade as early as 12:12 UT (b)), and was most obvious at 12:36 UT (a)), over four hours before the onset of the M5.6 flare at about 16:46 UT." + Ambieuity in interpreting {his structure exists due to the limitation of the two-dimensional observation., Ambiguity in interpreting this structure exists due to the limitation of the two-dimensional observation. + It. could be composed of two sheared loops as illustrated in 10((b). or a truly twisted structure as in 1θ((ο).," It could be composed of two sheared loops as illustrated in (b), or a truly twisted structure as in (c)." + The former configuration. however. requires (he two loops to be sheared in opposite directions on both sides of the neutral line (denoted bv the dashed line).," The former configuration, however, requires the two loops to be sheared in opposite directions on both sides of the neutral line (denoted by the dashed line)." + Hence. the latter configuration. namely. a flux rope. offers a more natural explanation.," Hence, the latter configuration, namely, a flux rope, offers a more natural explanation." + For the 2005 the rising arcade via nonlinear force-Iree-field modeling.," For the 2005 January 15 event 2.2.1), \citet{cheng10} + showed that a flux rope was located below the rising arcade via nonlinear force-free-field modeling." + As part of the PEA. the flux rope must be generated in the corona. via three possible wavs. viz..," As part of the PEA, the flux rope must be generated in the corona, via three possible ways, viz.," + a) reconnection of sheared magnetic fields (e.g.. 1989): b) reconnection within the flux rope involved in (he preceding eruption. which is therefore a partial eruption(Gilbertοἱal. 2007): and c) the emergence of a lresh magnetic," a) reconnection of sheared magnetic fields \citep[e.g.,][]{vm89}; b) reconnection within the flux rope involved in the preceding eruption, which is therefore a partial eruption\citep{gal07}; ; and c) the emergence of a fresh magnetic" +aclequate description of the r-process conditions in core-collapse events.,adequate description of the r-process conditions in core-collapse events. + For example. results from multidimensional hvdrodynamies calculations suggest that the instabilities resulting from those calculations may ultimately be shown to produce the entropy required for making the heaviest r-process nuclei (Burrowsetal.2006).," For example, results from multidimensional hydrodynamics calculations suggest that the instabilities resulting from those calculations may ultimately be shown to produce the entropy required for making the heaviest r-process nuclei \citep{burrows06}." +. Interesüinelv. these instabiliGes may generate the neutron star kicks (Burrowsetal.2006:Guilet.Sato.&Foglizzo2010) that eive rise to high space velocities of some pulsars (Arzoumanianetal.2002).," Interestingly, these instabilities may generate the neutron star kicks \citep{burrows06, guilet10} that give rise to high space velocities of some pulsars \citep{arzou02}." +. It will also be necessary to include all of the detailed neutrino physics (Burrows&Thomson2002:Roberts.Woosley.&Hoffman2010:Liebendoerferetal.2005) (o aclequately characterize (he neutron richness in matter expelled [rom the supernova.," It will also be necessary to include all of the detailed neutrino physics \citep{burrows02, roberts10, liebendoerfer05} + to adequately characterize the neutron richness in matter expelled from the supernova." + Future work will determine whether more advanced core-collapse supernova models will provide the conditions needed [or the r-process., Future work will determine whether more advanced core-collapse supernova models will provide the conditions needed for the r-process. + For the purposes of the present paper. we will simply assume that neutrino-driven winds in core-collapse supernovae are al least one of the sites of r-process nucleosvuthesis.," For the purposes of the present paper, we will simply assume that neutrino-driven winds in core-collapse supernovae are at least one of the sites of r-process nucleosynthesis." + To study the truncated r-process in the neutrino-driven wind. we applied the basic idea behind the study of Woosleyetal.(1994).. which assumed that the r-process occurred in the neutrino wind from a core collapse supernova.," To study the truncated r-process in the neutrino-driven wind, we applied the basic idea behind the study of \citet{woosley94}, which assumed that the r-process occurred in the neutrino wind from a core collapse supernova." +" La (hat study. a succession of 40 ""trajectories"" (Chat is. (hin shell wind elements). all assumed to have originated deep within the (assumed spherically «νοτο) star. but having imitially different conditions of density. temperature. entropy. and electron fraction. were emitted into the interstellar medium. (hus contributing to the total r-process nucleosvnthesis."," In that study, a succession of 40 “trajectories” (that is, thin shell wind elements), all assumed to have originated deep within the (assumed spherically symmetric) star, but having initially different conditions of density, temperature, entropy, and electron fraction, were emitted into the interstellar medium, thus contributing to the total r-process nucleosynthesis." + The bubble was evolving in lime. so that the conditions under which the individual trajectories were processed changed with the identity of the trajectory.," The bubble was evolving in time, so that the conditions under which the individual trajectories were processed changed with the identity of the trajectory." + We assumed that the dillerent trajectories were emitted [rom the star successively. but ceased to be emitted when the collapse to the black hole occurred.," We assumed that the different trajectories were emitted from the star successively, but ceased to be emitted when the collapse to the black hole occurred." + This would be consistent with Wooslevetal.(1994).. who assumed successive emissions of the trajectories io generate what turned out to be a good representation of the Solar r-process abundances.," This would be consistent with \citet{woosley94}, who assumed successive emissions of the trajectories to generate what turned out to be a good representation of the Solar r-process abundances." + For our r-process calculations. we used a network code based on libaucnet. a library of C codes for storing and managing nuclear reaction networks (Mever&Adams2007).," For our r-process calculations, we used a network code based on libnucnet, a library of C codes for storing and managing nuclear reaction networks \citep{meyer07}." +. The nuclear and reaction data for the calculations were taken [from the JINA reaclib database (Cyburtetal.2010)., The nuclear and reaction data for the calculations were taken from the JINA reaclib database \citep{cyburt10}. +. We perlormed caleulations for trajectories 24 - 40 in the Wooslev hvdrodsynamies model., We performed calculations for trajectories 24 - 40 in the \citet{woosley94} hydrodynamics model. + For each trajectory. reaction network calculations were performed for Ty «2.5 using initial abundances derived trom the Woosleyetal.(1994) results.," For each trajectory, reaction network calculations were performed for $_9<$ 2.5 using initial abundances derived from the \citet{woosley94} + results." + Our calculations were simplified by assuming an initial abundance of massive nuclei [rom a single nucleus heavy seed with a mass A equal to the average mass al To=2.5 and an, Our calculations were simplified by assuming an initial abundance of massive nuclei from a single nucleus heavy seed with a mass A equal to the average mass at $_9$ =2.5 and an +To exemplifs. we simulate the transit o£ a planet kleutical to Saturn and its riugs. with 30-days period aud 89° orbital inclination.,"To exemplify, we simulate the transit of a planet identical to Saturn and its rings, with 30-days period and $^\circ$ orbital inclination." + The trausit is modeled for two cases: that witli the noise level of CoRoT aud the other with that of Ixepler telescope., The transit is modeled for two cases: that with the noise level of CoRoT and the other with that of Kepler telescope. + In both cases. the light curve was subinitted toa fit process assuming only the presence of the planet.," In both cases, the light curve was submitted to a fit process assuming only the presence of the planet." + The result of this preliminary fit is shown in Figure 9 aud Table I., The result of this preliminary fit is shown in Figure \ref{fig:saturno_planetas} and Table \ref{tab:ajuste_aneis_planetas}. + From the analysis of the residual plotted on Figure 9 aud the Q value in Table {.. we see that the fit considering only the planet vields a satisfactory. result only for the CoRoT noise level (Figure 9(b))).," From the analysis of the residual plotted on Figure \ref{fig:saturno_planetas} and the Q value in Table \ref{tab:ajuste_aneis_planetas}, we see that the fit considering only the planet yields a satisfactory result only for the CoRoT noise level (Figure \ref{fig:saturno_planeta_kepler}) )." + This indicates that a ring system such as that of Saturn could only be detected by the lxepler satellite., This indicates that a ring system such as that of Saturn could only be detected by the Kepler satellite. + The ColtoT satellite would identify this light curve as that produced by a ejant planet with a radius slightly larger than that of Saturn (123.3 %)). but without riugs.," The CoRoT satellite would identify this light curve as that produced by a giant planet with a radius slightly larger than that of Saturn (12.3 ), but without rings." + Next. we fit only the light curve plotted in Figure 9(b) but now consideriug the presence of rings. that is the rine parameters are taken into accouut.," Next, we fit only the light curve plotted in Figure \ref{fig:saturno_planeta_kepler} but now considering the presence of rings, that is the ring parameters are taken into account." + The resulting fit. parameters are listed in Table 5.. whereas the result of the fit is plotted in Figure 10..," The resulting fit parameters are listed in Table \ref{tab:ajuste_saturno_kepler}, whereas the result of the fit is plotted in Figure \ref{fig:fit_saturno_kepler}." + Comparing the residual of Figures aud 10.. one can see that the fit is much better for the model where the rings were iuclucec.," Comparing the residual of Figures \ref{fig:saturno_planeta_kepler} and \ref{fig:fit_saturno_kepler}, one can see that the fit is much better for the model where the rings were included." + The Q value in Table 5 aud the residuals in Figure 10. show that the [it was satisfactory., The Q value in Table \ref{tab:ajuste_saturno_kepler} and the residuals in Figure \ref{fig:fit_saturno_kepler} show that the fit was satisfactory. +mass limit.,mass limit. + predict an influence on the EME of the forming star cluster. and. so do who investigated this question of crowding further.," predict an influence on the IMF of the forming star cluster, and so do who investigated this question of crowding further." + They. concluded that erowding should be relevant in the most massive clusters (e.g. progenitors of globular clusters) leading to a top-heavy IME. because the croweleck medium: would have a higher low-mass limit for star formation and therefore more massive stars need to be build to result in the same total mass.," They concluded that crowding should be relevant in the most massive clusters (e.g. progenitors of globular clusters) leading to a top-heavy IMF, because the crowded medium would have a higher low-mass limit for star formation and therefore more massive stars need to be build to result in the same total mass." + constructed a three-component LAL mocdel from these results., constructed a three-component IMF model from these results. + further showed that the ellect. of crowding must have an inlluence on the IME in starburst clusters., further showed that the effect of crowding must have an influence on the IMF in starburst clusters. + While ancl? present models for the IME in a starburst they do not discuss the overall integrated LATIF for a whole galaxy with a starburst., While and present models for the IMF in a starburst they do not discuss the overall integrated IMF for a whole galaxy with a starburst. + Certainly. in massive clusters. or UCDs. the IME. will be elected by erowding ?2).. but. the question remains if this change is large enough to inlluence the IGIME significantlv.," Certainly, in massive clusters, or UCDs, the IMF will be effected by crowding , but the question remains if this change is large enough to influence the IGIMF significantly." + In Fig., In Fig. + 1 the croweling is illustrated., \ref{fig:crowding} the crowding is illustrated. + Lt shows how many proto-stars of a fixed. pre-stellar cloud core size can be fitted into a spherical proto-cluster with a radius of 1 pe., It shows how many proto-stars of a fixed pre-stellar cloud core size can be fitted into a spherical proto-cluster with a radius of 1 pc. + This is done by taking a range of proto-cluster masses and dividing these masses by the mean mass of the canonical LME (Wien& 0.36 AL.) in order to get the expected number of stars. Noxpee. in the cluster.," This is done by taking a range of proto-cluster masses and dividing these masses by the mean mass of the canonical IMF $m_\mathrm{mean} \approx$ 0.36 $M_\odot$ ) in order to get the expected number of stars, $N_\mathrm{expec}$ , in the cluster." + Nexpec is then multiplied by the volume of three different: pre-stellar cloud. core sizes - 1000 AU linc). 5000 AU tine). and 10000 AU l," $N_\mathrm{expec}$ is then multiplied by the volume of three different pre-stellar cloud core sizes - 1000 AU ), 5000 AU ), and 10000 AU )." +ine)., Fig. + Vig. 1 shows the volume of the proto-cluster divided by the total volume of the pre- cloud. cores., \ref{fig:crowding} shows the volume of the proto-cluster divided by the total volume of the pre-stellar cloud cores. + For clusters with more than z107Al. crowding will be a problem.," For clusters with more than $\approx 10^{5}\,M_{\odot}$ crowding will be a problem." + Lt is therefore appropriate to assume that such high-density environments may have an inlluence on the IME within such star clusters., It is therefore appropriate to assume that such high-density environments may have an influence on the IMF within such star clusters. + An alternative or additional mechanism which. mav induce star bursts leading to top-heavy IMES. may. be through the heating of the molecular eas by supernova eencrated cosmic ravs(?)., An alternative or additional mechanism which may induce star bursts leading to top-heavy IMFs may be through the heating of the molecular gas by supernova generated cosmic rays. +. While the above discussion. suggests that the IME may become top-heavy. it remains. unfortunately. unclear as to how a systematic variation of the IME with increasing M4 ought to be realised.," While the above discussion suggests that the IMF may become top-heavy, it remains, unfortunately, unclear as to how a systematic variation of the IMF with increasing $M_\mathrm{ecl}$ ought to be realised." + and already. presented descriptions of the change of an ΤΗΣ in starbursts., and already presented descriptions of the change of an IMF in starbursts. + They. based. their nmocels on a log-normal EME but we use the multi-power law formulation of the stellar LME., They based their models on a log-normal IMF but we use the multi-power law formulation of the stellar IMF. + The modelling of the IGLME starts from a SER which determines the upper mass limit of the EC'ME according to eq. 2.., The modelling of the IGIMF starts from a SFR which determines the upper mass limit of the ECMF according to eq. \ref{eq:eclmax}. + In order to calculate the total amount of stars formed in a star-forming period the SER. is multiplied bv a time-step which is assumed to be 10 Myr., In order to calculate the total amount of stars formed in a star-forming period the SFR is multiplied by a time-step which is assumed to be 10 Myr. + With the use of the total mass the ECME can be normalised for the time-step., With the use of the total mass the ECMF can be normalised for the time-step. + The EXME is then divided in 1000 logarithmic bins., The ECMF is then divided in 1000 logarithmic bins. + As the embedded cluster mass limits the most-massive star in each cluster. the upper limit of the IME in cach EC'ME-bin can be caleulated.," As the embedded cluster mass limits the most-massive star in each cluster, the upper limit of the IMF in each ECMF-bin can be calculated." + As the number of clusters per bin is eiven bv the normalised ECME. the λος of each EC'ME-bin can be multiplied bv the number of clusters in order to eive the integrated galactic EME of the time-step.," As the number of clusters per bin is given by the normalised ECMF, the IMFs of each ECMF-bin can be multiplied by the number of clusters in order to give the integrated galactic IMF of the time-step." + The slope of this IGIME above 1.5 AM. can then be computed by a least-squares fit to the caleulated EGLIME., The slope of this IGIMF above 1.3 $M_\odot$ can then be computed by a least-squares fit to the calculated IGIMF. + Phe value of the so-derived ay gives a rough indication of the top-heaviness. while detailed: astrophysical parameters would. be derived [rom using the actually computed IGIME.," The value of the so-derived $\alpha_3$ gives a rough indication of the top-heaviness, while detailed astrophysical parameters would be derived from using the actually computed IGIMF." + In order to include the possible effect of croweling into the framework of the IGIME theory 2.2)) the results of Alarks. INroupa Dabringhausen (in preparation) on the high-mass ΙΔΗΣ slope in globular clusters anc UCDs are used.," In order to include the possible effect of crowding into the framework of the IGIMF theory \ref{sub:crowding}) ) the results of Marks, Kroupa Dabringhausen (in preparation) on the high-mass IMF slope in globular clusters and UCDs are used." + “Phev derive the following dependence of the EME slope for stars more massive than 1 AZ. and for clusters with initial masses M4 2 2:107 ALL. The limit of 2.107 AZ. is chosen because for clusters with masses below this limit. Marks. Ixroupa. Dabringhausen (in preparation) results infer a Salpeter slope.," They derive the following dependence of the IMF slope for stars more massive than 1 $M_\odot$ and for clusters with initial masses $M_\mathrm{ecl}$ $\ge$ $\times +10^5$ $M_\odot$, The limit of $\times 10^5$ $M_\odot$ is chosen because for clusters with masses below this limit Marks, Kroupa Dabringhausen (in preparation) results infer a Salpeter slope." + Note that while the parametrisation in eq., Note that while the parametrisation in eq. + 3. rests on empirical globular cluster data which have heen corrected [or stellar and dynamical evolution. the parametrisation we acopt in eq.," \ref{eq:a3M} rests on empirical globular cluster data which have been corrected for stellar and dynamical evolution, the parametrisation we adopt in eq." + 3 is not to be seen as an established dependence of ay on Ma., \ref{eq:a3M} is not to be seen as an established dependence of $\alpha_3$ on $M_\mathrm{ecl}$. + Rather. while giving a good clue asto how the IGIME may. change with increasing SER. the calculations performed here are independent of the parametrisation and may thus be easily adopted for dillerent. parametrisations.," Rather, while giving a good clue asto how the IGIMF may change with increasing SFR, the calculations performed here are independent of the parametrisation and may thus be easily adopted for different parametrisations." +Accreting black holes show variations over a broad range of timescales.,Accreting black holes show variations over a broad range of timescales. + In the well-studied Galactic Black hole binaries (BHBs) their power spectra may include broad-band noise. band-limited noise (BLN) and quasi-periodic oscillations (QPOs). distinguished by their relative frequency widths reviews).," In the well-studied Galactic Black hole binaries (BHBs) their power spectra may include broad-band noise, band-limited noise (BLN) and quasi-periodic oscillations (QPOs), distinguished by their relative frequency widths ." +.. The exact origin of the variability and its characteristic frequencies remain elusive. although strong correlations between frequencies of ditferent power-spectral components have been observed as wel as correlations between frequencies and spectral parameters 222).," The exact origin of the variability and its characteristic frequencies remain elusive, although strong correlations between frequencies of different power-spectral components have been observed as well as correlations between frequencies and spectral parameters ." + QPOs are observed over a range of frequencies in BHBs anc S. in BHBs they are commonly described as either low frequency « 50 Hz or high frequency 7100 Hz(2).," QPOs are observed over a range of frequencies in BHBs and NS, in BHBs they are commonly described as either low frequency $<$ 50 Hz or high frequency $>$ 100 Hz." +. Low frequency QPOs are often observed with further harmonies and sub harmonies anc heir formation mechanism is unclear., Low frequency QPOs are often observed with further harmonics and sub harmonics and their formation mechanism is unclear. +" The three main types are commonly classified as A. B or C(22222), with types A and B observed in the soft intermediate states. and displaying ditferen jurmonie and phase lag behaviours. and the type Cs observed in yard states G.e low-hard and hard intermediate) with strong band noise."," The three main types are commonly classified as A, B or C, with types A and B observed in the soft intermediate states, and displaying different harmonic and phase lag behaviours, and the type Cs observed in hard states (i.e low-hard and hard intermediate) with strong broad-band noise." + The frequency of type C QPOs is known to correlate with spectral properties of the source. the photon index. dise inner radius. dise temperature and both power law and dise fluxes although there is as yet no consensus on the physical origin of QPOs(?2?).," The frequency of type C QPOs is known to correlate with spectral properties of the source, the photon index, disc inner radius, disc temperature and both power law and disc fluxes although there is as yet no consensus on the physical origin of QPOs." +. One of the simplest and most stable relationships observed between variability properties is the rms-flux relation. which connects the rms amplitude of variations to the mean flux level by a positive linear correlation that appears to operate over a wide range of timescales where the power spectra remain similar(22).," One of the simplest and most stable relationships observed between variability properties is the rms-flux relation, which connects the rms amplitude of variations to the mean flux level by a positive linear correlation that appears to operate over a wide range of timescales where the power spectra remain similar." + This relation is inherent to the short-term variability of sources with an otherwise-stationary (or close to stationary) power-spectral shape., This relation is inherent to the short-term variability of sources with an otherwise-stationary (or close to stationary) power-spectral shape. + Longer-term changes in rms ean be caused by changes in power-spectral shape which correlate with the spectral evolution of the source within and between the different spectral states. but these are different to the rms-flux relation which appears to be a fundamental aspect of the variability process itself.," Longer-term changes in rms can be caused by changes in power-spectral shape which correlate with the spectral evolution of the source within and between the different spectral states, but these are different to the rms-flux relation which appears to be a fundamental aspect of the variability process itself." + The linear rms-flux relation was initially observed in the BHB Cygnus X-I. to date the same linear rms-flux relation has been observed in Active Galactic Nuclei (2222).. one neutron star X-ray binary and one Ultra-Luminous X-ray source (ULX)(2).. it has also recently been observed over long timescales in the BHB GX 339-4(?).," The linear rms-flux relation was initially observed in the BHB Cygnus X-1, to date the same linear rms-flux relation has been observed in Active Galactic Nuclei , one neutron star X-ray binary and one Ultra-Luminous X-ray source (ULX), it has also recently been observed over long timescales in the BHB GX 339-4." +. This relation is observed in the noise components of the power spectrum. and in the 401 Hz pulsation of the neutron star system SAX I1808.41-3658(?).. but to date has not been studied for QPOs.," This relation is observed in the noise components of the power spectrum, and in the $401$ Hz pulsation of the neutron star system SAX J1808.4-3658, but to date has not been studied for QPOs." + Arguably the most promising explanation for the linear rms- relation observed for the broad-band noise of accreting systems is the “propagating fluctuation’ model (see discussion and references in ???2))., Arguably the most promising explanation for the linear rms-flux relation observed for the broad-band noise of accreting systems is the `propagating fluctuation' model (see discussion and references in ). + In this general model long timescale fluctuations in the accretion rate originate from large radii in an accretion dise. (perhaps as random variations in. viscosity) and propagate inwards. modulating shorter timescale variations originating at smaller radii222)... and eventually modulating the accretion rate in the innermost. X-ray producing regions.," In this general model long timescale fluctuations in the accretion rate originate from large radii in an accretion disc (perhaps as random variations in viscosity) and propagate inwards, modulating shorter timescale variations originating at smaller radii, and eventually modulating the accretion rate in the innermost, X-ray producing regions." + This simple scheme naturally explains X-ray emission that varies on a wide range of timescales. and a linear rms-flux relation due to the," This simple scheme naturally explains X-ray emission that varies on a wide range of timescales, and a linear rms-flux relation due to the" +dinenusouless representation with δν aud V/IL.R as wand y-axes. respectively. oue may couvenieutlv describe different dwuamical regions of the svstei (See Fig.1)).,"dimensionless representation with $R/R_{\rm v}$ and $V/H_{\rm v}R_{\rm v}$ as $x$ - and $y$ -axes, respectively, one may conveniently describe different dynamical regions of the system (See \ref{fig1}) )." + Writing the total mechanical energy as LE-aAGAL/R.. there is a mininuiun energy curve correspouding to a=3ο," Writing the total mechanical energy as $E = -\alpha \,GM/R_{\rm v}$, there is a minimum energy curve corresponding to $\alpha = \frac{3}{2}$." + Test particles ejected from the reeion of bound orbits CR< Ry} cannot appear below this curve for R2Ry., Test particles ejected from the region of bound orbits $R < R_{\rm v}$ ) cannot appear below this curve for $R > R_{\rm v}$. + In fac. the mininuun energv curve can be used to give an upper lait to the local DE deusity or a lower limit to Ry. whici iav be stricter than that obtained from the size aud mass of the svsteui.," In fact, the minimum energy curve can be used to give an upper limit to the local DE density or a lower limit to $R_{\rm v}$ which may be stricter than that obtained from the size and mass of the system." + The physical seuse of thIS WMI enerev curve Is that it corresponds to ejectio san infiuitelv long time ago., The physical sense of this minimum energy curve is that it corresponds to ejections an infinitely long time ago. + Hence. any upper limit for the age provides a still stricter lower-limit curve.," Hence, any upper limit for the age provides a still stricter lower-limit curve." +" Consider the vacuum Επο]ο time l/IL. where The vacuum IIubble time Zi is larger than the elobal Ihibble time by the factor (11p,p)?=(QU)V? fora flat universe and for pj= the global DE density."," Consider the vacuum Hubble time $T_{\rm v} = 1/H_{\rm v}$ , where The vacuum Hubble time $T_{\rm v}$ is larger than the global Hubble time by the factor $(1+\rho_m/\rho_{\rm v})^{1/2} = (\Omega_{\rm v})^{-1/2}$ for a flat universe and for $\rho_{\rm v} =$ the global DE density." + Thus τς is a natural upper lit for the age., Thus $T_{\rm v}$ is a natural upper limit for the age. + Iu the standard model T.=1610? vis and the age of the universe (13.610? vrs) is about 0.85\Ti.," In the standard model $T_{\rm v} = 16\, 10^9$ yrs and the age of the universe $13.6\,10^9$ yrs) is about $0.85 \times T_{\rm v}$." +" The dight time from the ceuter of the eroup (ry< 1) to the normalized distance «=r/R. for a particle with encreyv E—oGMT can be parametrized in terms of the vacua IIubble time T=1/28: de, while the normalized velocity y is related to. as v One can calculate for each location ως the required enerev o for a particle to reach this disance after the flight time £f. and thus the normalized velocity y."," The flight time from the center of the group $x_0 \ll 1$ ) to the normalized distance $x = r/R_{\rm v}$, for a particle with energy $E = -\alpha \, GM/R_{\rm v}$ can be parametrized in terms of the vacuum Hubble time $T_{\rm v} = 1/H_{\rm v}$: t = (x^2 + 2/x dx, while the normalized velocity $y$ is related to $x$ as y = (x^2 + 2/x - One can calculate for each location $x$ the required energy $\alpha$ for a particle to reach this distance after the flight time $t$, and thus the normalized velocity $y$." + This is similar to what has been done iu Lemaittre-Tolinan solutious (6.2. Peirani de Freitas Pacheco 2006.. 2008)).," This is similar to what has been done in Lemaîttre-Tolman solutions (e.g. Peirani de Freitas Pacheco \cite{peirani06}, \cite{peirani08}) )." +" As an example. in the normalized ciagrai of Fig.l we have indicated the predicted current distance-velocity curve for the age f/T,=(0.85 for he case where the local DE deusity is equal to the global one (eq.5 or 7 with pis py)."," As an example, in the normalized diagram of \ref{fig1} we have indicated the predicted current distance-velocity curve for the age $t/T_{\rm v} = 0.85$ for the case where the local DE density is equal to the global one \ref{integral1} or \ref{integral2} with $\rho_{\rm loc} =\rho_{\rm v}$ )." + The straight line above the vacuna IIubble dow (gy= ow) is the eloba Ilubble law with Π=(O.)Ἠτῆν for ὡς=0.77.," The straight line above the vacuum Hubble flow $y = x$ ) is the global Hubble law with $H = (\Omega_{\rm v})^{-1/2} H_{\rm v}$ for $\Omega_{\rm v} = +0.77$." + Tn Fig.2 we illustrate how the increasing flight time (0.85. 1.5. and 2.0 T.) influences the distaucc-volocitv relation in the normalized IIubble diagram.," In \ref{fig2} we illustrate how the increasing flight time (0.85, 1.5, and 2.0 $\times T_{\rm v}$ ) influences the distance-velocity relation in the normalized Hubble diagram." + Note that at large distances aud long times the flow approches the vacuum flow y—.rc., Note that at large distances and long times the flow approches the vacuum flow $y=x$. + The ναι flow is also the asviutotic line for the zero-energv aud the minima enuergev curves. as can be seen from eq.6..," The vacuum flow is also the asymtotic line for the zero-energy and the minimum energy curves, as can be seen from \ref{y-x}." + From the y=g(Qc) we can obtain the locus of preseut distance-velocity positions as (Ry. gIE IU).," From the $y = y(x)$ we can obtain the locus of present distance-velocity positions as $xR_{\rm v}$, $yH_{\rm v}R_{\rm v}$ )." + So. fixing the uass AF and the DE density p. Gvhich give the distance Ry. and the vactuun Hubble constant Z4. needed in the jormalization). aud the flight time £/TA. (sav. tle age of the universe) we can calculate the velocitv-distauce relation or the ordinary ITubble diagram.," So, fixing the mass $M$ and the DE density $\rho_{\rm v}$ (which give the distance $R_{\rm v}$ and the vacuum Hubble constant $H_{\rm v}$ needed in the normalization), and the flight time $t/T_{\rm v}$ (say, the age of the universe) we can calculate the velocity-distance relation for the ordinary Hubble diagram." + For example. iu Chorniu et al. (20093) ," For example, in Chernin et al. \cite{chernin09}) )" +the mass was varied and the predicted IIubble relation was compared with the outflow around he Local Group. asstuning that the local DE deusity is he same as the global one.," the mass was varied and the predicted Hubble relation was compared with the outflow around the Local Group, assuming that the local DE density is the same as the global one." +Although in a sample like VCVeat it is difficult to take into account all of the selection ellects that might be active. since the Sloan Digital Skv Survey (SDSS) sources are likely to make up the largest single portion of the sample the target selection process in (hat survey is worth examining.,"Although in a sample like VCVcat it is difficult to take into account all of the selection effects that might be active, since the Sloan Digital Sky Survey (SDSS) sources are likely to make up the largest single portion of the sample the target selection process in that survey is worth examining." + First. (he survey is sensitive to all redshifts lower than z = 5.8. and the overall completeness is expected to be over 90% (Richardsetal.2002).," First, the survey is sensitive to all redshifts lower than $z$ = 5.8, and the overall completeness is expected to be over $90\%$ \citep{ric02}." +. Extended. sources were also targeted. as low-redshift quasar candidates im order (o investigate the evolution ol AGN at the faint end of the luminosity [unetion., Extended sources were also targeted as low-redshift quasar candidates in order to investigate the evolution of AGN at the faint end of the luminosity function. + During the color selection process no distinction was made between quasars aud the less luminous Sevfert nuclei., During the color selection process no distinction was made between quasars and the less luminous Seyfert nuclei. + Objects that had the colors of Iow-redshift AGN galaxies were targeted even if they were resolved., Objects that had the colors of low-redshift AGN galaxies were targeted even if they were resolved. + This policy was in contrast to some other quasar survevs that reject extended objects. (hereby imposing a lower limit to the redshift. distribution of the survey (Richardsetal.2002).," This policy was in contrast to some other quasar surveys that reject extended objects, thereby imposing a lower limit to the redshift distribution of the survey \citep{ric02}." +.. In addition to selecting normal quasars. the selection algorithm also makes it sensitive to alwpical AGN such as broad absorption line quasars and heavily reddened quasars (Bichardsetal.2002).," In addition to selecting normal quasars, the selection algorithm also makes it sensitive to atypical AGN such as broad absorption line quasars and heavily reddened quasars \citep{ric02}." +. In addition to the detection limit set bv the sensitivity of the observing svstem the 5D55 also contains (wo additional observer. or program-mposed. limits.," In addition to the detection limit set by the sensitivity of the observing system the SDSS also contains two additional observer, or program-imposed, limits." + One of (hese was a [aint-edge limit at / = 19.1m. and the other was a bright-edge cut-off al 7 = 15m. The reasons why these limits were imposed ean be found in Richardsetal.(2002).," One of these was a faint-edge limit at $i^{*}$ = 19.1m, and the other was a bright-edge cut-off at $i^{*}$ = 15m. The reasons why these limits were imposed can be found in \citet{ric02}." +". Although color-selected. quasar candidates below z = 3 were only targeted (o a Galactic 7” magnitude of 19.1. as noted above. since we are only examining the bright edge ol the logz-m, plot. this faint edge limit is not expected to have allected the results."," Although color-selected quasar candidates below z = 3 were only targeted to a Galactic extinction-corrected $i^{*}$ magnitude of 19.1, as noted above, since we are only examining the bright edge of the $z$ $_{v}$ plot, this faint edge limit is not expected to have affected the results." +" However. the bright edge cut-off al /* = 15m could have affected the shape of the bright edge of the logz-m, plot aud (his needs to be examined more closely."," However, the bright edge cut-off at $i^{*}$ = 15m could have affected the shape of the bright edge of the $z$ $_{v}$ plot and this needs to be examined more closely." +" In Fig 2. for 0.7R, the rays are parallel and the flux is constant."," Since $\,D\gg R$, the rays are parallel and the flux is constant." +" In this one application we assume X=| instead of X=0.7, i.e. pure hydrogen with Ha= land,= 0.5."," In this one application we assume $X=1$ instead of $X=0.7$, i.e. pure hydrogen with $\mu_{\rm n}=1$ and $\mu_{\rm i}=0.5$ ." +" The neutral gas is assumed to be at T,=100K."," The neutral gas is assumed to be at $T_{\rm n}=100\,{\rm K}$." +" The sound speeds are therefore c,=0.9kms!and c;= 12.8kms!."," The sound speeds are therefore $c_{\rm n}=0.9\,{\rm km}\,{\rm s}^{-1}$and $c_{\rm i}=12.8\,{\rm km}\,{\rm s}^{-1}$ ." +" The simulation uses N,,,=3x10° particles, and self-gravity is taken into account."," The simulation uses ${\cal N}_{_{\rm SPH}}=3\times10^5$ particles, and self-gravity is taken into account." + The simulation is terminatedat t=2.5 Myr.," The simulation is terminatedat $t=2.5\,{\rm Myr}$ ." +In its journey from the binary companion to the neutron star core. a parcel of matter releases a tremendous amount of energy. and the rate of this energy release is directly proportional to the rate ad which matter falls onto the stellar surface.,"In its journey from the binary companion to the neutron star core, a parcel of matter releases a tremendous amount of energy, and the rate of this energy release is directly proportional to the rate at which matter falls onto the stellar surface." + Thus. it is not surprising that the thermal profile of an accreting neutron star is very sensitive to the accretion rate.," Thus, it is not surprising that the thermal profile of an accreting neutron star is very sensitive to the accretion rate." +" To varving degrees of importance. the accretion rate affects the thermal profile in four different Waves,"," To varying degrees of importance, the accretion rate affects the thermal profile in four different ways." + Most of the energv released by an infalhng parcel of accreted material is from the eravitational enerev released when the matter impacts the stellar surface., Most of the energy released by an infalling parcel of accreted material is from the gravitational energy released when the matter impacts the stellar surface. + Most of this energy is racdiated outward., Most of this energy is radiated outward. + Nevertheless. it determines the temperature at the stellar surface ancl thereby sets a boundary condition.," Nevertheless, it determines the temperature at the stellar surface and thereby sets a boundary condition." + The calculation is rather insensitive to (his temperature. however. lor the thermal prolile near the surface approaches a radiative-zero solution.," The calculation is rather insensitive to this temperature, however, for the thermal profile near the surface approaches a radiative-zero solution." + As accretion continues. nuclear [nel accumulates and eventually burns either stably or unstably.," As accretion continues, nuclear fuel accumulates and eventually burns either stably or unstably." + The time-averaged rate of nuclear energy generation is proportional to (he accretion rate., The time-averaged rate of nuclear energy generation is proportional to the accretion rate. + Although the nuclear enerey per eram of accretecl material released via [usion is roughly forty times less than that released [rom gravitational energy. the nuclear energy is generated well below the stellar surface.," Although the nuclear energy per gram of accreted material released via fusion is roughly forty times less than that released from gravitational energy, the nuclear energy is generated well below the stellar surface." + Thus the nuclear energy generation ean have a significant effect upon the thermal profile of the crust. in particular the superburst ignition region (see also 833.2).," Thus the nuclear energy generation can have a significant effect upon the thermal profile of the crust, in particular the superburst ignition region (see also 3.2)." + Additionally. continious accretion causes both compressional heating throughout the crust and deep crustal heating via non-equilibrium reactions.," Additionally, continuous accretion causes both compressional heating throughout the crust and deep crustal heating via non-equilibrium reactions." + The compressional heating is rather small compared to other sources. and it is therefore often. neglected in other studies.," The compressional heating is rather small compared to other sources, and it is therefore often neglected in other studies." + The deep crustal heating is roughly five times less than that [rom hydrogen. ancl helium burning. but it can have a non-negligible elfect upon the thermal profile of the crust. especially if the conductive opacity of the inner crust is large.," The deep crustal heating is roughly five times less than that from hydrogen and helium burning, but it can have a non-negligible effect upon the thermal profile of the crust, especially if the conductive opacity of the inner crust is large." + We plot the temperature and Παν profiles for (wo neutron stars accreting al cdillerent rates in Figure 2., We plot the temperature and flux profiles for two neutron stars accreting at different rates in Figure 2. + The energy flux is normalized by the maximum nuclear burning energy Εν available in the accreting gas: The parameter [ace=M/Mya is the accretion rate normalized to the Eddington limit. where Mya=ἀπM(1o- Mets. with s— 0.4engg!.," The energy flux is normalized by the maximum nuclear burning energy flux available in the accreting gas: The parameter $l_{\mathrm{acc}}= \dot{M} / \dot{M}_{\mathrm{Edd}}$ is the accretion rate normalized to the Eddington limit, where $\dot{M}_{\mathrm{Edd}} = 4 \pi G M (1+z)/c z \kappa_{\mathrm{es}}$ , with $\kappa_{\mathrm{es}} = 0.4$ $\mathrm{cm}^{2}\,\mathrm{g}^{-1}$." + The temperature outer boundary condition. which is shown at the left end of the left panel. is determined by the rate of eravitational energy liberated at the surface.," The temperature outer boundary condition, which is shown at the left end of the left panel, is determined by the rate of gravitational energy liberated at the surface." + Changes in the slope of the temperature prolile are associated with localized energv sources. and (μον are reflected. by rapid changes in the flux.," Changes in the slope of the temperature profile are associated with localized energy sources, and they are reflected by rapid changes in the flux." + Thus. hydrogen and helium burning causes (he peak in the (thermal profile aud," Thus, hydrogen and helium burning causes the peak in the thermal profile and" + A kev question in the study. of the ultraluminous X-ray sources (ULXs) is whether or not the X-ray. emission. is uned., A key question in the study of the ultraluminous X-ray sources (ULXs) is whether or not the X-ray emission is beamed. +" Lf the X-rays are beamed. then the ULXs. may rc accreting ""normal mass (« 2OAL.) black holes or even neutron stars."," If the X-rays are beamed, then the ULXs may be accreting “normal” mass $< 20 +M_{\odot}$ ) black holes or even neutron stars." + Wing et ((2001) have suggested that ULXs are high-mass X-ray binaries with super-Edcinegton mass ransfer rates in which the N-ray emission is funnelled. xoducing high observed. X-ray fluxes for observers near the »aming axis.," King et (2001) have suggested that ULXs are high-mass X-ray binaries with super-Eddington mass transfer rates in which the X-ray emission is funnelled, producing high observed X-ray fluxes for observers near the beaming axis." + Motivated by the recent suggestion that jets may contribute a significant fraction of the observed. X-ray lux in Galactic binaries previously thought to be dominated ov disk and coronal emission. (MarkolL..Faleke.&|Fender 2001).. Ixórrding et ((2002) have suggested that the ULXs may be stellar-mass black holes in which relativistic beaming in jets aligned nearly along our line of sight produce the high apparent X-ray [luxes.," Motivated by the recent suggestion that jets may contribute a significant fraction of the observed X-ray flux in Galactic binaries previously thought to be dominated by disk and coronal emission \cite{markoff01}, Körrding et (2002) have suggested that the ULXs may be stellar-mass black holes in which relativistic beaming in jets aligned nearly along our line of sight produce the high apparent X-ray fluxes." + If the ULNs are. not. stronely beamed. then. the masses required. for the sources to be emitting below heir LEedeington luminosities are Large. well above the maximum possible mass ( 20M.) for a black hole woduced. at. the endpoint of the evolution of a normal star.," If the ULXs are not strongly beamed, then the masses required for the sources to be emitting below their Eddington luminosities are large, well above the maximum possible mass $\sim 20 M_{\sun}$ ) for a black hole produced at the endpoint of the evolution of a normal star." +" Hence. the compact objects would be ""intermeciate-mass” black holes (Colbert&Alushotzky1999)."," Hence, the compact objects would be ``intermediate-mass'' black holes \cite{colbert99}." +.. This ms potentially interesting consequences., This has potentially interesting consequences. + Latermeciiate-mass lack holes may be excellent sources of gravitational radiation (IEbisuzakietal.2001:Miller&Llamilton2002).," Intermediate-mass black holes may be excellent sources of gravitational radiation \cite{ebisuzaki01,miller02}." +. ον may be relies of the first generation of star formation (Macau&Rees2001).. where. due to the absence of metals. extremely massive stars were likely to have formed (Larson 1998).," They may be relics of the first generation of star formation \cite{madau01}, where, due to the absence of metals, extremely massive stars were likely to have formed \cite{larson98}." +. Or. they may be important in the formation of supermassive black holes (Ptak&Crilliths1999).," Or, they may be important in the formation of supermassive black holes \cite{ptak99}." +. Pakull Alironi (2002). discovered. an A4686 emission line nebula in the ROSAT error box for the ULX in the dwarf irregular galaxy. Holmberg HL at a cistance of 3.05 Alpe (Lloessel.Saha.&Danielson1998)., Pakull Mironi (2002) discovered an $\lambda 4686$ emission line nebula in the ROSAT error box for the ULX in the dwarf irregular galaxy Holmberg II at a distance of 3.05 Mpc \cite{hoessel98}. +. X-ray emission was first detected from. ομήρους HL in the ROSAT all-sky survey and then localized in ROSAT ΤΙ observations to, X-ray emission was first detected from Holmberg II in the ROSAT all-sky survey and then localized in ROSAT HRI observations to +For given central cuegiue parameters this range is large if 3; is snall. and vice versa.,"For given central engine parameters this range is large if $Y_e$ is small, and vice versa." +" This is because when Y. is siuall the fireball material is neutrou rich] 2,/5, cau be large while still leaving a substautial portion of the energy iu the neutron component."," This is because when $Y_e$ is small the fireball material is neutron rich) $\gamma_p / +\gamma_n$ can be large while still leaving a substantial portion of the energy in the neutron component." + Eq., Eq. + 9 only applies for £>1 initially aud driven to unity through spreading., \ref{tltgt} only applies for $\xi > 1$ initially and driven to unity through spreading. +" Note that when &>ms, we can neglect ms."," Here, since $M_{\rm c} \gg m_{\rm s}$, we can neglect $m_{\rm s}$." +" The number2008).. density of stars in spiral arms is given by n,= /((z?)!/2M.), where (z?)!/? is the scale height of the disk and X, is the surface density of the spiral arms."," The number density of stars in spiral arms is given by $n_{\rm c} = \Sigma_{\rm c}/(\langle z^2\rangle ^{1/2}M_{\rm c})$ , where $\langle z^2 \rangle ^{1/2}$ is the scale height of the disk and $\Sigma_{\rm c}$ is the surface density of the spiral arms." +" The scale height (22)!/? is given by (22)!/?~o,/Q, where o; is the vertical velocity dispersion and €) is the angular speed of the disk."," The scale height $\langle z^2\rangle ^{1/2}$ is given by $\langle z^2\rangle ^{1/2} \simeq \sigma _z/\Omega$, where $\sigma _z$ is the vertical velocity dispersion and $\Omega$ is the angular speed of the disk." +" In a disk system, o;~v (e.g.,Kokubo&Ida 1992),, the relaxation time of a disk can be written as By definition, the relaxation time is tg=mua"," In a disk system, $\sigma _z \simeq v$ \citep[e.g.,][]{KI92}, the relaxation time of a disk can be written as By definition, the relaxation time is $t_{\rm g} = \frac{v^2}{{dv^2}/{dt}}$." +" 'The change of velocity dispersion is written as We assume that the mass and surface density of each clump of the spiral arms are given by where Ma and X are the total mass and surfacedensity of the disk, and m and A,, are the number and amplitude of the spiral arms."," The change of velocity dispersion is written as We assume that the mass and surface density of each clump of the spiral arms are given by where $M_{\rm d}$ and $\Sigma$ are the total mass and surfacedensity of the disk, and $m$ and $A_m$ are the number and amplitude of the spiral arms." +" Substituting Equations (4)), (6)), and (7)) to Equation (5)), we obtain From Equation (2)), the time derivative ofQ is where we assumed that κ and © are constants."," Substituting Equations \ref{eq:tg}) ), \ref{eq:a}) ), and \ref{eq:b}) ) to Equation \ref{eq:dvdt}) ), we obtain From Equation \ref{eq:Q}) ), the time derivative of$Q$ is where we assumed that $\kappa$ and $\Sigma$ are constants." +" Assuming that the three-dimensional velocity dispersion is v= νοσῃ, from Equations (8)) and (9)), we obtain"," Assuming that the three-dimensional velocity dispersion is $v=\sqrt{3}\sigma_R$ , from Equations \ref{eq:dvdt2}) ) and \ref{eq:dQdt}) ), we obtain" +side. these conclusious are based on measurements of the orientation of lincar polarization (E vector). which reveal coherent structures across jet dmages.,"side, these conclusions are based on measurements of the orientation of linear polarization $\mathbf E$ vector), which reveal coherent structures across jet images." + This iudicates that magnetic fields. which are predominantly perpeucdicular to the electric vectors. are also prefercutially aligned. although iu different sources or in different parts of the jet the inaguetie fields can be mainly orthogonal (Wardle or parallel (Jouesetal.1985:BuskaudSeaquist/1985) to the projected jet orieutation.," This indicates that magnetic fields, which are predominantly perpendicular to the electric vectors, are also preferentially aligned, although in different sources or in different parts of the jet the magnetic fields can be mainly orthogonal \citep{war98} or parallel \citep{jon85,rus85} to the projected jet orientation." + From the theoretical poiut of view. ordered jet magnetic field is expected when shocks compress au iuitiallv random field (Laing1980.1981:MarscherandCrear1985:ITushesetal.1989:WardleaudRoberts1991). (B perpendicular to the jet axis) or when such initial fields are sheared to lie ina plane (Laing1980.1981:Beechnan.Rees1981). CB parallel to the jet axis).," From the theoretical point of view, ordered jet magnetic field is expected when shocks compress an initially random field \citep{lai80,lai81,mer85,hug89,war94} $\mathbf B$ perpendicular to the jet axis) or when such initial fields are sheared to lie in a plane \citep{lai80,lai81,beg84} $\mathbf B$ parallel to the jet axis)." + Circular polarization (CP) is a common feature of quasars and blazars (Ravueretal.2000:Tomanct 2001). is usually characterized by au approximately flat spectrun. and is ecnerated near svuchrotron sclbabsorbed jet cores (TomanaudWardle1990).," Circular polarization (CP) is a common feature of quasars and blazars \citep{ray00,hom01}, is usually characterized by an approximately flat spectrum, and is generated near synchrotron self-absorbed jet cores \citep{hom99}." +. CP is detected iu about of these objects., CP is detected in about of these objects. + Measured degrees of CP are geuerallv lower than the levels of line polarizatiou and usually ranee between 0.1 and (Tomandle1999:Tlomanetal. 2001).," Measured degrees of CP are generally lower than the levels of linear polarization and usually range between 0.1 and \citep{hom99,hom01}." +. As reported by. Macequartetal.(2000) for the Intraday variable source PISS 1519- the CP of variable componcuts of intensity can be much higher than the overall circular polarization levels.," As reported by \citet{mar00} for the intraday variable source PKS 1519-273, the CP of variable components of intensity can be much higher than the overall circular polarization levels." + Observations of proper motion of CP-produciug regions iu the quasar 3€ 273 (TomanandWardle1999) sueecst that circular polarization is intrinsic to the source. as opposed to being due to foreground effects.," Observations of proper motion of CP-producing regions in the quasar 3C 273 \citep{hom99} suggest that circular polarization is intrinsic to the source, as opposed to being due to foreground effects." + Most muiportantly. comparisons of CP measurements made within the last 30 vears (WeilerauddePater1983:Iomesaroffetal.1981:TomanandWardle1999) with the most recent observations reveal that. despite CP variability. its sign is a persistent feature of ACN. which must therefore be related to a small net unidirectional component of magnetic field in jets.," Most importantly, comparisons of CP measurements made within the last 30 years \citep{wei83,kom84,hom99} with the most recent observations reveal that, despite CP variability, its sign is a persistent feature of AGN, which must therefore be related to a small net unidirectional component of magnetic field in jets." + The most obvious candidate for explaining circular polarization of compact radio sources is mnfrinsic Clissiol (LeseandWestfold1968)., The most obvious candidate for explaining circular polarization of compact radio sources is intrinsic emission \citep{leg68}. +. Athough iutriusic CP is roughly Wineο...Lo where 5 is the Lorentz actor of vacating clectrous. iu a realistic source it will uxt likely be strongly suppressed by the taieled magnetic field aud possibly the emissivity from e!© pairs. whic1 do not contribute CP.," Although intrinsic CP is roughly $\pi_{c, \rm int}\sim\gamma^{-1}$ where $\gamma$ is the Lorentz factor of radiating electrons, in a realistic source it will most likely be strongly suppressed by the tangled magnetic field and possibly the emissivity from $e^{+}-e^{-}$ pairs, which do not contribute CP." +" Specifically. iuw~(ByWRBrus4FMoaSE Ίο, where B, aud Buy are the 1unidirectional couponent of the maenetic feld projected onto the linc-of-ight and the fluctuating component «Xf the field. respectively. ο—(nnl'yfinni)x 1."," Specifically, $\pi_{c, \rm int}\sim\gamma^{-1}(B_{u}/B_{\rm rms})f_{\rm pair}\ll 1\%$ , where $B_{u}$ and $B_{\rm rms}$ are the unidirectional component of the magnetic field projected onto the line-of-sight and the fluctuating component of the field, respectively, and $f_{\rm pair}\equiv(n^{-}-n^{+})/(n^{-}+n^{+})\le 1$." +Trerefore. intrinsic CP appears to be inadequate to explain the observed polarization.," Therefore, intrinsic CP appears to be inadequate to explain the observed polarization." + Other mechauisiis have also been proposed. amoug which the most popular ones are coherent radiation processes (BeutordaudTzach2000).. scintillation (AlacquartandAIclrose2000). and Faraday conversionL99s).," Other mechanisms have also been proposed, among which the most popular ones are coherent radiation processes \citep{ben00}, scintillation \citep{marm00} and Faraday conversion." +. The first of these mechanisms produces polarization in a narrow frequency range which now seems to be ruled out by iultiband observations., The first of these mechanisms produces polarization in a narrow frequency range which now seems to be ruled out by multiband observations. + The receutlv proposed scintillation 1iechiauisui im which circular polarization is stochastically produced by a birefrinegcut screen located between the jet and the observer. fails to explain the persistent sien of circular polarization as the time-averaged CP signal is predicted to vanish.," The recently proposed scintillation mechanism, in which circular polarization is stochastically produced by a birefringent screen located between the jet and the observer, fails to explain the persistent sign of circular polarization as the time-averaged CP signal is predicted to vanish." + The last mechanisi Faraday conversion — seenis to be the most promising one and in the next subsection we discuss it iu more detail., The last mechanism — Faraday conversion — seems to be the most promising one and in the next subsection we discuss it in more detail. + The polarization of radiation changes as it propagates through any mediuu in which modes are characterized bv different plasima speeds., The polarization of radiation changes as it propagates through any medium in which modes are characterized by different plasma speeds. + In the case of cold plasiua the modes are circularly polarized., In the case of cold plasma the modes are circularly polarized. + The left and right 3rcular nodes have different phase velocities aud therefore the linear polarization vector of the propagating radiation rotates., The left and right circular modes have different phase velocities and therefore the linear polarization vector of the propagating radiation rotates. + This effect is called Faraday rotation aud it is often used to estimate maeuectic field strength iu the oeiterstellar iuediuni and to estinate pulsar distances., This effect is called Faraday rotation and it is often used to estimate magnetic field strength in the interstellar medium and to estimate pulsar distances. + Note that Faraday rotation does not alter the degree of circular polarization. since auv circular polarization cau be decomposed into two independent linearly polarized waves.," Note that Faraday rotation does not alter the degree of circular polarization, since any circular polarization can be decomposed into two independent linearly polarized waves." + Faraday rotation is a specific example of a more eeneral phenomenon called birefriugeuce., Faraday rotation is a specific example of a more general phenomenon called birefringence. + Ta a medina whose natural modes are linearly or clliptically polarized. such as a plasma of relativistic particles. birefriugence leads to the partial evelic conversion between linearly aud circularly polarized radiatio ras the phase relationships between the modes along tlie rav change with position.," In a medium whose natural modes are linearly or elliptically polarized, such as a plasma of relativistic particles, birefringence leads to the partial cyclic conversion between linearly and circularly polarized radiation as the phase relationships between the modes along the ray change with position." + This effect is best visualizeL by means of the Poincaré sphere (MelroseandMePrehau1991:Kennet[οιrose 1998).," This effect is best visualized by means of the Poincaré sphere \citep{mel91,ken98}." +. An arbitrary cJliptieal polavization cau be represented by a vector P wit hits tip wing ou the Poincaré sphere aud characterize by Cartesian coordinates (QUVfL. where Q.U.V and Jo are the Stokes paralcters (soe Fie.," An arbitrary elliptical polarization can be represented by a vector $\mathbf P$ with its tip lying on the Poincaré sphere and characterized by Cartesian coordinates $(Q,U,V)/I$, where $Q,U,V$ and $I$ are the Stokes parameters (see Fig." + D)., 1). + Tlis. the north aud south poles correspond to right aud let circular polarizatiouns aud points onu the equator to linear polarization.," Thus, the north and south poles correspond to right and left circular polarizations and points on the equator to linear polarization." + Different azinuthal positious ou the sphere correspond. to differeut orientations of the polarization ellipses., Different azimuthal positions on the sphere correspond to different orientations of the polarization ellipses. + The polarization of natural modes of the mediunu is represented by a diagonal axis whose polar angle measured from the vertical axis depends on whether the medium is dominated we cold (0°) or highly relativistic particles (90°).," The polarization of natural modes of the medium is represented by a diagonal axis, whose polar angle measured from the vertical axis depends on whether the medium is dominated by cold $(0^{\rm o})$ or highly relativistic particles $(90^{\rm o})$." + As he radiation passes through the mecdinm. birefringence causes the tip of the polarization vector to rotate at a constant latitude around the axis of the natural plasia nodes.," As the radiation passes through the medium, birefringence causes the tip of the polarization vector to rotate at a constant latitude around the axis of the natural plasma modes." + In this picture. Faraday rotation corresponds to he case where the natural modes axis is vertical and he polarization vector P rotates around it.," In this picture, Faraday rotation corresponds to the case where the natural modes axis is vertical and the polarization vector $\mathbf P$ rotates around it." + Note that. even if radiation initially has no circular polarization (1.6.. P les in the equatorial plane) aud then eucouuters a uediunu in which the normal modes are elliptical. it will develop an clliptically polarized component.," Note that, even if radiation initially has no circular polarization (i.e., $\mathbf P$ lies in the equatorial plane) and then encounters a medium in which the normal modes are elliptical, it will develop an elliptically polarized component." + Au interesting xopertv of a relativistic birefringeut plasina is that it can eoncrate circular polarization even if it is coniposed alinost entirely of clectron-positron pairs., An interesting property of a relativistic birefringent plasma is that it can generate circular polarization even if it is composed almost entirely of electron-positron pairs. + At first this may secu xwadoxical as one would expect electrous and positrons o contzibute to CP with opposite signs.," At first this may seem paradoxical, as one would expect electrons and positrons to contribute to CP with opposite signs." + However. despite," However, despite" +"clensily is where ay is the electron scattering opacily per unit mass. ancl M,=0.0177 is the rest-mass accretion rate in code units.","density is where $\kappa_T$ is the electron scattering opacity per unit mass, and $\dot{M}_c=0.0177$ is the time-averaged rest-mass accretion rate in code units." + By fortunate coincidence. optical depths dependonly on. L/(L4:). which we abbreviate as im. because the unit of length is xM.," By fortunate coincidence, optical depths depend on $L/(\eta L_E)$ , which we abbreviate as $\dot m$, because the unit of length is $\propto M$." + Because our accretion [ow is Far from spherically svannmetric. (he location of the photosphere is a function of the observers position.," Because our accretion flow is far from spherically symmetric, the location of the photosphere is a function of the observer's position." + We imagine. then. that numerous “cameras” are placed on a grid in polar angle 9 and azimuthal angle 4? on a very large sphere (radius 105 ) centered on the black hole.," We imagine, then, that numerous “cameras"" are placed on a grid in polar angle $\vartheta$ and azimuthal angle $\varphi$ on a very large sphere (radius $10^6M$ ) centered on the black hole." + From each camera. we define a bundle of geodesics that run through the problem volume.," From each camera, we define a bundle of geodesics that run through the problem volume." + These are parameterized by an alline parameter A normalized so that an observer in the local fluid frame would measure the dillerential length along a rav as where v is (he Irequency of the photon as measured by (hat observer., These are parameterized by an affine parameter $\lambda$ normalized so that an observer in the local fluid frame would measure the differential length along a ray as where $\nu$ is the frequency of the photon as measured by that observer. + IP NY—da/dÀ is the 4-vector tangent to the null rav then where z is the redshift factor between the local fluid. [rame observer and the camera frame: In the numerator of this ratio. the 4-velocitv is that of the camera: in the denominator. ibis that of the [Iuid at some point along the rav.," If $N^\mu = dx^\mu/d\lambda$ is the $4$ -vector tangent to the null ray then where $z$ is the redshift factor between the local fluid frame observer and the camera frame: In the numerator of this ratio, the 4-velocity is that of the camera; in the denominator, it is that of the fluid at some point along the ray." + We then integrate the optical depth along these geodesics in order to determine the location of the photospheric surface for that camera., We then integrate the optical depth along these geodesics in order to determine the location of the photospheric surface for that camera. + The photosphere surface is defined (o lie at a constant 7=7.. which we set to unity. Le.. το=1.," The photosphere surface is defined to lie at a constant $\tau = \tau_\circ$, which we set to unity, i.e., $\tau_\circ=1$." + Once the location of the photosphere is determined. we integrate the emissivily along these geodesics from the photosphereout to (he camera: we assume no scattering (takes place along these ravs:," Once the location of the photosphere is determined, we integrate the emissivity along these geodesics from the photosphereout to the camera; we assume no scattering takes place along these rays:" +correlation on HX waveband. using both flux. densities and Iuminosities for this purpose.,"correlation on IR waveband, using both flux densities and luminosities for this purpose." + Their work confirmed that a radioLR. correlation exists. and that it is strongest. in the mid-IR (Spearman-Rank correlation coellicients: 0.73 at pm: 0.64 at pim. both with significance >99.9 percent).," Their work confirmed that a radio–IR correlation exists, and that it is strongest in the mid-IR (Spearman-Rank correlation coefficients: 0.73 at $\mu$ m; 0.64 at $\mu$ m, both with significance $>99.9$ percent)." + This causes no surprise as both the dust and the ionized gas are thought to form. part of the CS envelope in svmbiotic binary systems., This causes no surprise as both the dust and the ionized gas are thought to form part of the CS envelope in symbiotic binary systems. + Figures 2 and 3 show the most complete sample of radio and Hi measurements of symbiotic stars to date. a total οἱ 60 sources for which both{115 and 3.6cem data exist. together with the measurements of the colour mimics.," Figures 2 and 3 show the most complete sample of radio and IR measurements of symbiotic stars to date, a total of 60 sources for which both and cm data exist, together with the measurements of the colour mimics." +7/45 flux densities for the svmbioties were drawn from Munari Ivison (in preparation) and Ixenvon et ((1988)), flux densities for the symbiotics were drawn from Munari Ivison (in preparation) and Kenyon et (1988). + For the Lgvmbiotics. the correlation between both 12 and jam Lux ensities and the 3.6cem {lux density is clear to the eve. especially for the D-tvpes.," For the symbiotics, the correlation between both 12 and $\mu$ m flux densities and the cm flux density is clear to the eye, especially for the D-types." + The correlation improves further if the very slow novae. VIOIG C€veg. LIAL See and RR. Tel. are ignored.," The correlation improves further if the very slow novae, V1016 Cyg, HM Sge and RR Tel, are ignored." + We note that the position of 36 on this iagram olfers some credence to the idea. propounclect by Allen (1983). that this system has also experienced a very slow nova-like event.," We note that the position of $-$ 36 on this diagram offers some credence to the idea, propounded by Allen (1983), that this system has also experienced a very slow nova-like event." + lt ds immecliately clear even without recourse to statistical tests that there is virtually no similarity between our sample of OLL/LIt colour mimics and the radio-Iuminous D-type symbiotic Miras., It is immediately clear even without recourse to statistical tests that there is virtually no similarity between our sample of OH/IR colour mimics and the radio-luminous D-type symbiotic Miras. + Nor is there any similarity between S- or D'-tvpe svmbioties and the colour mimies., Nor is there any similarity between S- or $'$ -type symbiotics and the colour mimics. + This inipression is confirmed by a 2-D Ixolmogorov-Smirnowv test (ignoring>e upper limits for the svmbioties whilst. treatingIn upper limits for the colour mimies as detections) which vields a probability p<10'7 that the two samples are rawn from the same population.," This impression is confirmed by a 2-D Kolmogorov-Smirnov test (ignoring upper limits for the symbiotics whilst treating upper limits for the colour mimics as detections) which yields a probability $p < +10^{-7}$ that the two samples are drawn from the same population." + A 1-D test using survival unalvsis methods (Feigelson Nelson 1985: Isobe. Feigelson Nelson 1986) on a sample restricted to the range of LR tux ensities occupied by the color mimics vields p«107.," A 1-D test using survival analysis methods (Feigelson Nelson 1985; Isobe, Feigelson Nelson 1986) on a sample restricted to the range of IR flux densities occupied by the color mimics yields $p < +10^{-4}$." + AL upper limits are included in the latter test., All upper limits are included in the latter test. + In only one case. iu of | 3333. is there any. possibility of an ionized nebula approaching the scale of those found in. svmbiotic Miras.," In only one case, that of $+$ 3333, is there any possibility of an ionized nebula approaching the scale of those found in symbiotic Miras." + Even for | 3333. the 3.6-em lux density is more dan an order of magnitude lower than svmbiotic Miras with equivalent levels of mid-L1. emission.," Even for $+$ 3333, the 3.6-cm flux density is more than an order of magnitude lower than symbiotic Miras with equivalent levels of mid-IR emission." + Thus it is clear that if the colour mimics possess hot companions. then the size of the tonizecl zone is relatively small.," Thus it is clear that if the colour mimics possess hot companions, then the size of the ionized zone is relatively small." + “Phe racio detected svmbioties are nearly all density bounded (91ΤΟ). and it is therefore likely that the colour mimics are radiation bounded.," The radio detected symbiotics are nearly all density bounded (SKT93), and it is therefore likely that the colour mimics are radiation bounded." + In terms of the binary model considered by Taylor Scaquist (1984) this is equivalent to stating that the ionization parameter No«1/3. where .X measures essentially the ratio of the UV. luminosity to the available mass in the envelope.," In terms of the binary model considered by Taylor Seaquist (1984) this is equivalent to stating that the ionization parameter $X < 1/3$, where $X$ measures essentially the ratio of the UV luminosity to the available mass in the envelope." + Lt is possible to estimate the upper limit on the radio continuum flux. density for such a svstem if the distance ancl binary separation are assumed., It is possible to estimate the upper limit on the radio continuum flux density for such a system if the distance and binary separation are assumed. + A rough estimate of the distance for the colour mimics mav be obtained by comparing them with the eroup of D-type symbioties in Figures 2 and 3 occupying the same range in LR [lux density anc a broadly similar range in colour., A rough estimate of the distance for the colour mimics may be obtained by comparing them with the group of D-type symbiotics in Figures 2 and 3 occupying the same range in IR flux density and a broadly similar range in colour. + The median distance for svmbioties in this eroup for which there are available distance estimates SSIXT903) is about 2kkpe., The median distance for symbiotics in this group for which there are available distance estimates SKT93) is about kpc. + Then for an assumed. binary . ⊳∖∢⊾↓≻⋜⊔⋅⋜∐↓∪⊔∪⇂⋅↱≻↓∪⊓∼⊔↓⊳↿↓↕∢⋅⋡↓⊔⋜⊔⋅∙∖⇁⊔↓⇜⇂⋖⊾↓∙∖⇁⊓⋅↓∠⇂⊳∖⋜↧∆∫≻⊳≼⊢⋅ ⊥⊥ . . ⋅⋅ ≼⇍⊔↓↓⇂∟∖∠⇂⋖⊾⊔⊳∖⊲⊔∙∖⇁↓∢⋅⊳∖⊳∖⇂↓⋯⊔↓∪∪∕∣↼∙∖⇁⊳⊔∪⇂∖⇁⋖⋅↓⋅∙∖⇁∠⇂↕↓↥⋅∢⊾↓⋅⋖⋅↓↕∐⋅∪⊔↓ the observed. limits for the colour mimics.," Then for an assumed binary separation of $5 \times 10^{14}$ cm, the binary model yields a 3.6-cm flux density less than $\mu$ Jy, not very different from the observed limits for the colour mimics." + Note also that if IU Aqr. a probable raciation-bounded: system. (SINT93). were placed at 2kkpe. then its continuum flux density would be near our detectable limit. and its LILO maser emission would also be undetectable. though its SiO maser emission night be detectable.," Note also that if R Aqr, a probable radiation-bounded system (SKT93), were placed at kpc, then its continuum flux density would be near our detectable limit, and its $_2$ O maser emission would also be undetectable, though its SiO maser emission might be detectable." + Furthermore. a line of slope unity through Ro Aqr in. Figures 2 and 3 passes close to the one detection in our sample. thus if Ro Aer. were displaced in distance so that its LR lux. matehec that of the detected object. its radio Lux would be comparable to our detected. source. suggesting perhaps that most of the colour mimics are stronely racliation bounced if they contain a hot component at all.," Furthermore, a line of slope unity through R Aqr in Figures 2 and 3 passes close to the one detection in our sample, thus if R Aqr were displaced in distance so that its IR flux matched that of the detected object, its radio flux would be comparable to our detected source, suggesting perhaps that most of the colour mimics are strongly radiation bounded if they contain a hot component at all." + his may be due either to an underluminous hot companion. excessive mass-Ioss rate or small binary separation when compared to the D-type svmbioties of similar colour.," This may be due either to an underluminous hot companion, excessive mass-loss rate or small binary separation when compared to the D-type symbiotics of similar colour." + The search for cem free-[ree emission from a sample of ΟΙΑΗ colour mimics with no OLI masers viclded negative results with possibly one exception., The search for cm free-free emission from a sample of OH/IR colour mimics with no OH masers yielded negative results with possibly one exception. + The conclusion is that [or all but one of these objects the suspected hot companion does not ionize sullicient gas to reveal its presence as a, The conclusion is that for all but one of these objects the suspected hot companion does not ionize sufficient gas to reveal its presence as a +tvpically short. compared. to cadence of the WASP survey (S10 minutes).,typically short compared to cadence of the WASP survey (8–10 minutes). + We therefore ignore the detailed shape of the ingress and ceress phases ancl modelled. the transit signatures as simple box-like profiles., We therefore ignore the detailed shape of the ingress and egress phases and modelled the transit signatures as simple box-like profiles. +" To cover the orbital period-planet. radius parameter space we selected seven trial periods spaced approximately ogarithmically (2?=0.08. 0.22. 0.87. 1.56. 3.57. 8.30 anc 4.72 days). and five planet radit Z,=10.0. 1.0. 0.6. 0.34 andt"," To cover the orbital period-planet radius parameter space we selected seven trial periods spaced approximately logarithmically $P=0.08$, 0.22, 0.87, 1.56, 3.57, 8.30 and 14.72 days), and five planet radii $R_{\rm p}=10.0$, 1.0, 0.6, 0.34 and." +es We modelled. the set. of synthetic. light curves by injecting lake transit signals into phase-folded light curves a he trial period with a random transit epoch fy in the range )edyο, We modelled the set of synthetic light curves by injecting fake transit signals into phase-folded light curves at the trial period with a random transit epoch $t_0$ in the range $03 Gyr. 7»5 Gyr): in WINGS. instead. a large number of SOs are SDGs (see Figure 2)).," Practically all S0s are SDGs (see Figure \ref{fig:all}) ) and most of them are old have Luminosity-weighted-age $>3$ Gyr, $>5$ Gyr); in WINGS, instead, a large number of S0s are SDGs (see Figure \ref{fig:morph}) )." + On the other hand. among the WINGS SDGs with SO morphology. only have ages lower than the corresponding llookback time. wwere most likely morphologically changed at redshifts lower thanEDisCS.," On the other hand, among the WINGS SDGs with S0 morphology, only have ages lower than the corresponding lookback time, were most likely morphologically changed at redshifts lower than." +. This ts an indication that for the largest galaxies the majority of the morphological transformations took place a few billion years ago. while for most of the compact galaxies both the quenching of star formation and the final morphological type were reached at earlier epochs.," This is an indication that for the largest galaxies the majority of the morphological transformations took place a few billion years ago, while for most of the compact galaxies both the quenching of star formation and the final morphological type were reached at earlier epochs." + It is clear that when comparing high- with low-z samples. it is of paramount importance to keep in mind that morphologically selecting galaxies at different epochs introduces an apparent. but spurious size evolution with redshift. which instead is a selection effect.," It is clear that when comparing high- with low-z samples, it is of paramount importance to keep in mind that morphologically selecting galaxies at different epochs introduces an apparent, but spurious size evolution with redshift, which instead is a selection effect." + Although it is from the WINGS data to recover which galaxies were early-types at the EDisCS’ss epoch. our findings support the hypothesis that the main reason why the median size of WINGS early-type galaxies (dashed line in Figure 2)) is much more consistent with the median size of all gealaxies (dotted line. see also Table 2)) than with the size of only EDisCS early-types is that the largest late-type EDisCS'ss galaxies have gradually become earlier types by the WINGS epoch.," Although it is from the WINGS data to recover which galaxies were early-types at the s epoch, our findings support the hypothesis that the main reason why the median size of WINGS early-type galaxies (dashed line in Figure \ref{fig:morph}) ) is much more consistent with the median size of all galaxies (dotted line, see also Table \ref{tab:fac}) ) than with the size of only EDisCS early-types is that the largest late-type s galaxies have gradually become earlier types by the WINGS epoch." +" We have found that of eegalaxies with M.~4<10'""M are SDGs.", We have found that of galaxies with $\sm\sim4\per10^{10}\msol$ are SDGs. + Their properties are similar to WINGS SDGs. apart.. for a significantly different morphological mix: the prevalence of SOs in WINGS is not found inEDisCS.," Their properties are similar to WINGS SDGs, apart for a significantly different morphological mix: the prevalence of S0s in WINGS is not found in." +. Such a result is not unexpected. given our previous findings: in VIO we have found that (for the mass limits and radii adopted here) of WINGS clusters members at z~0 are SDGs.," Such a result is not unexpected, given our previous findings: in V10 we have found that (for the mass limits and radii adopted here) of WINGS clusters members at $z \sim 0$ are SDGs." + More than of them have stellar ages older than 9Gyr. a clear indication that they were already old and compact at the EDisCS'ss epoch.," More than of them have stellar ages older than 9Gyr, a clear indication that they were already old and compact at the s epoch." + The evolution of the SDG fraction in clusters with redshift is expected if SDGs are massive and old galaxies. formed in clusters seeds and preferentially found in today's massive clusters. while they are rarer in the field (seeTayloretal.2009) and therefore in the population of galaxies infalling into clusters at later and later times.," The evolution of the SDG fraction in clusters with redshift is expected if SDGs are massive and old galaxies, formed in clusters seeds and preferentially found in today's massive clusters, while they are rarer in the field \citep[see][]{taylor09} and therefore in the population of galaxies infalling into clusters at later and later times." + We find that when galaxies of all morphological types are considered. the median size of cluster galaxies at z~0.7 is only a factor 1.18 smaller than the local median.," We find that when galaxies of all morphological types are considered, the median size of cluster galaxies at $z \sim 0.7$ is only a factor 1.18 smaller than the local median." + We conclude that from z0.7 to z— 0.04. there is at most a verymodest evolution in galaxy sizes in clusters.," We conclude that from $z\sim0.7$ to $z\sim0.04$ , there is at most a verymodest evolution in galaxy sizes in clusters." + Similarly to our VIO analysis of age selection effects. we have shown that comparing high-z morphologically selected samples with local ones can be misleading.," Similarly to our V10 analysis of age selection effects, we have shown that comparing high-z morphologically selected samples with local ones can be misleading." + In agreement, In agreement +- A second mechanism can also provide evaporation of frostted volatiles: the pareut bodies can slowly evaporate if their orbit xogressivolv euters the evaporation limit.,- A second mechanism can also provide evaporation of ted volatiles: the parent bodies can slowly evaporate if their orbit progressively enters the evaporation limit. + Tn fact. the evaporation rate is very dependent on the distance to the star (—rr20 Fie.," In fact, the evaporation rate is very dependent on the distance to the star $\sim r^{-20}$, Fig." + 3 of LVF). aud the distance below which the gas evaporates can thus be considered as very sharp.," 3 of LVF), and the distance below which the gas evaporates can thus be considered as very sharp." + The consequence of such evaporation of bodies still on quasi-civcular orbits is that the dust can remain on elliptical orbit around the star., The consequence of such evaporation of bodies still on quasi-circular orbits is that the dust can remain on elliptical orbit around the star. + For typical erain size distribution and assuming that the largest erains are larger than LOgan. oue can estimate that less than of the mass ds ejected on a hvperbolie orbit in the dust tail the remaiming is distribute on a large disk structure (LVF).," For typical grain size distribution and assuming that the largest grains are larger than $\mu$ m, one can estimate that less than of the mass is ejected on a hyperbolic orbit in the dust tail, the remaining is distributed on a large disk structure (LVF)." + Chiron is subject to such evaporation (Lut Jewitt 1990)., Chiron is subject to such evaporation (Luu Jewitt 1990). + Tlowever his cannot happen frequently iu the Solar System because he evaporation of the common volatiles takes place inside the planetary svstem., However this cannot happen frequently in the Solar System because the evaporation of the common volatiles takes place inside the planetary system. + There. massive planets are responsible for stroug eravitational perturbations aud put he evaporating bodies ou very ecceutrie orbit: these are hen observed as classical comets.," There, massive planets are responsible for strong gravitational perturbations and put the evaporating bodies on very eccentric orbit; these are then observed as classical comets." + This is also why Chiron jas à Chaotic orbit and will not remain a slow evaporating ουν for a long time (Scholl 1979)., This is also why Chiron has a chaotic orbit and will not remain a slow evaporating body for a long time (Scholl 1979). + Ou the contrary. this slow evaporation can occur iu an extrasolar planetary svstem if the evaporation lint is outside the massive planets orbits.," On the contrary, this slow evaporation can occur in an extra-solar planetary system if the evaporation limit is outside the massive planets orbits." + For exiuuple. this could be the case if a planetary svsteu simular to the Solar System was present around a star brighter than the Sun.," For example, this could be the case if a planetary system similar to the Solar System was present around a star brighter than the Sun." +" Iu LVF. we have estimated. the total mass of dust associated. with the observed CO around > pictoris. if it is produced iu such a slow evaporation of orbiting bodies,"," In LVF, we have estimated the total mass of dust associated with the observed CO around $\beta\:$ Pictoris, if it is produced in such a slow evaporation of orbiting bodies." + With reasonable paraicters tle mass is found to be consistent with the total mass of observed dust(see also Sect. 3 )):, With reasonable parameters the mass is found to be consistent with the total mass of observed dust(see also Sect. \ref{number of parent bodies}) ); + this provide an evidence that the » ddust disk can be supplied dyEvaporating-Dodies., this provide an evidence that the $\beta\:$ dust disk can be supplied by. +enierges. however.,"emerges, however." + Taken at [ace value. (hese results imply (hat Jupiter formed by disk instability. in the protoplanetary disk while Saturn formed by core accretion.," Taken at face value, these results imply that Jupiter formed by disk instability in the protoplanetary disk while Saturn formed by core accretion." + It is rather unlikely (hat the two planets formed by such different mechanisms. however.," It is rather unlikely that the two planets formed by such different mechanisms, however." + We speculate that the only wav to reconcile the formation processes of Jupiter and Saturn is that both of them formed by core accretion and that for Jupiter. the subsequent accretion of the gaseous II/IIle envelope resulted in partial or complete mixing of the core with the gas. increasing Mz al the expense OL Ms.," We speculate that the only way to reconcile the formation processes of Jupiter and Saturn is that both of them formed by core accretion and that for Jupiter, the subsequent accretion of the gaseous H/He envelope resulted in partial or complete mixing of the core with the gas, increasing $M_{\sss Z}$ at the expense of $M_{\rm core}$." + The larger accretion rate in (he proto-Jupiter may have caused larger mixing (han in the proto-Saturn (Guillotetal...2003)., The larger accretion rate in the proto-Jupiter may have caused larger mixing than in the proto-Saturn \citep{gshs03}. +. On the other hand. Jupiter models computed with the LALA EOS have core masses thal are (barely) consistent with the mass required lor formation with core accretion formation (10 ).," On the other hand, Jupiter models computed with the LM-A EOS have core masses that are (barely) consistent with the mass required for formation with core accretion formation $\sim 10\,M_\oplus$ )." + In this case. mixing of the core of proto-Jupiter with the accreting envelope would not be required ancl both planets would form bv the same process.," In this case, mixing of the core of proto-Jupiter with the accreting envelope would not be required and both planets would form by the same process." + The LM-À EOS was constructed to fit the NOVA (P.V.T) Iugoniot as well as the gas gun reshock temperatures.," The LM-A EOS was constructed to fit the NOVA $(P,V,T)$ Hugoniot as well as the gas gun reshock temperatures." + It represents the soltest and coolest EOS allowed by the experiments., It represents the softest and coolest EOS allowed by the experiments. + The reshock temperatures measurements may be too low. however. and a reevaluation of these measurements may well rule out the LM-À EOS.," The reshock temperatures measurements may be too low, however, and a reevaluation of these measurements may well rule out the LM-A EOS." + This study has been conducted with the point of view of learning about the interiors of Jupiter and Saturn from our current knowledge of the EOS of hydrogen and the associated uncertainties., This study has been conducted with the point of view of learning about the interiors of Jupiter and Saturn from our current knowledge of the EOS of hydrogen and the associated uncertainties. + The opposite approach can also be considered: Can astrophysical knowledge contribute to the debate on the hieh-pressure EOS of hydrogen?, The opposite approach can also be considered: Can astrophysical knowledge contribute to the debate on the high-pressure EOS of hydrogen? + Because much astrophysical knowledge is not amenable (o direct. observation or experimentation. our knowledge of processes (hat are hidden from view or that ave no longer taking place is verv sketchy.," Because much astrophysical knowledge is not amenable to direct observation or experimentation, our knowledge of processes that are hidden from view or that are no longer taking place is very sketchy." + l1 is usually diffieult to draw strong conclusions about the underlying microphysies when only the elobal properties of a complex. natural object are known.," It is usually difficult to draw strong conclusions about the underlying microphysics when only the global properties of a complex, natural object are known." + The ability of a given EOS to eive acceptable models depends somewhat ou the assumptions for the model structure., The ability of a given EOS to give acceptable models depends somewhat on the assumptions for the model structure. + In eeneral. more elaborate models (wilh more parameters) can accommodate a wider range of EOS.," In general, more elaborate models (with more parameters) can accommodate a wider range of EOS." + Nevertheless. we venture to comment on interesting patterns that emerge in (le more extreme cases thal we have encountered in (his stud.," Nevertheless, we venture to comment on interesting patterns that emerge in the more extreme cases that we have encountered in this study." + We could not obtain satisfactory models of Jupiter with the original SESAME EOS because il is relatively sill between 0.1 and Mbar. ancl relatively soft at higher pressures along Jupiter's adiabat.," We could not obtain satisfactory models of Jupiter with the original SESAME EOS because it is relatively stiff between 0.1 and $\,$ Mbar, and relatively soft at higher pressures along Jupiter's adiabat." +" Both of these effects combine to decrease the core mass but even with A4,=0 models that fit the gravitational moments could not be obtained with this EOS."," Both of these effects combine to decrease the core mass \citep{guillot99} + but even with $M_{\rm core}=0$ models that fit the gravitational moments could not be obtained with this EOS." + It is only alter it was patched at low pressures and that a uncertaintv in (he EOS was introduced that acceptable models could be found (SESAME-p EOS)., It is only after it was patched at low pressures and that a uncertainty in the EOS was introduced that acceptable models could be found (SESAME-p EOS). + Similarly. we could not obtain satisfactory models of Jupiter with the LAI-B EOS," Similarly, we could not obtain satisfactory models of Jupiter with the LM-B EOS" +Tu the case of PSR B1133|16. Malofeev et al. (,"In the case of PSR B1133+16, Malofeev et al. (" +"1996) extrapolated the critical frequency 7, to a value of around TOO MITz.",1996) extrapolated the critical frequency $\nu_c$ to a value of around 700 MHz. + Tlowever. inspecting Fig.," However, inspecting Fig." + 2 we realize that this pulsar is clearly in the strong sciutillation regime at 1112 MIIz., \ref{flux1133} we realize that this pulsar is clearly in the strong scintillation regime at 1412 MHz. + Bhat et al. (, Bhat et al. ( +1999) measured three differeut scintillation bandwidths at a frequency of 327. MIT.,1999b) measured three different scintillation bandwidths at a frequency of 327 MHz. + Using the mean value of those and a frequency scaling of Amasxvbt and AfqgasXrb. we estimate the transition frequency to be about vw.~2 GIIz insteack with scintillation parameters as listed in Table 1..," Using the mean value of those and a frequency scaling of $\Delta \nu_{\rm ISS} \propto \nu^{4.4}$ and $\Delta t_{\rm ISS}\propto \nu^{1.2}$, we estimate the transition frequency to be about $\nu_c \sim 2$ GHz instead, with scintillation parameters as listed in Table \ref{obstab}." + At 311 MIIz we expect to sample a mummber of scintles. resulting in only little modulation.," At 341 MHz we expect to sample a number of scintles, resulting in only little modulation." + In coutrast. at the other frequencies the observing bandwidth is of sane size or wich smaller thaw the de-correlation baudwidth.," In contrast, at the other frequencies the observing bandwidth is of same size or much smaller than the de-correlation bandwidth." + Strong intensity variation should be expected ou a timescale of 6 min at 626 MIIZ aud 16 iin at 1112. MIIz which seems. im particular when cousidering the involved uncertaiuties. to be in good agreement with the observations (Fie. 2)).," Strong intensity variation should be expected on a timescale of 6 min at 626 MHz and 16 min at 1412 MHz which seems, in particular when considering the involved uncertainties, to be in good agreement with the observations (Fig. \ref{flux1133}) )." + Iu the following we present a procedure which is aimed at separating fiux density wauriatious of iutriusic origin and those caused by ISS., In the following we present a procedure which is aimed at separating flux density variations of intrinsic origin and those caused by ISS. + We note that in addition to diffractive sciutillatiou. ao refractive branch exists as well (Sicher 1982).," We note that in addition to diffractive scintillation, a refractive branch exists as well (Sieber \nocite{sie82}." +" Timescales associated with refractive sciutillatiou are much longer while the involved modulations are much weaker (οιο, Rickett We can try to estimate the expected refractive timescale in stroug scintillation regine by using our derived diffractive scintillation parameters and the relation where « is the streneth of scattering given bw the ratio of Fresucl aud coherence scale (c.g. Rickett 1990. Stinebring Condon 1990)."," Timescales associated with refractive scintillation are much longer while the involved modulations are much weaker (e.g. Rickett \nocite{ric90} We can try to estimate the expected refractive timescale in strong scintillation regime by using our derived diffractive scintillation parameters and the relation where $u$ is the strength of scattering given by the ratio of Fresnel and coherence scale (e.g. Rickett 1990, Stinebring Condon 1990)." + For v=11I12 MIIz. we derive for PSR Bo329|51. Afpiss~830 iin. being much longer than our total observing time.," \nocite{sc90a} For $\nu = 1412$ MHz, we derive for PSR B0329+54, $\Delta t_{\rm RISS} \sim 830$ min, being much longer than our total observing time." + For this pulsar. Stinebring et al. (," For this pulsar, Stinebring et al. (" +1996). studied the refractive scintillation properties in detail. observing flux deusity variations at 610 MIIz of about30%.,"1996) \nocite{sfm96} studied the refractive scintillation properties in detail, observing flux density variations at 610 MHz of about." +.. This is consistent with the results obtaiuec by Stinebring et al., This is consistent with the results obtained by Stinebring et al. + and those by Bhat et al. (, \nocite{ssh+00} and those by Bhat et al. ( +1999a) at 327 MIIz who also obtained measurements for PSR Bi133|16.,1999a) at 327 MHz who also obtained measurements for PSR B1133+16. + For the latter pulsar. we estimate Agescδ min at 1112 ΣΠ which is the same as our observing time for this pulsar.," For the latter pulsar, we estimate $\Delta t_{\rm RISS} \sim 80$ min at 1412 MHz which is the same as our observing time for this pulsar." + Based on the results bv Stinebring et al. (, Based on the results by Stinebring et al. ( +1996. 2000). Bhat et al. (,"1996, 2000), Bhat et al. (" +1990012) and au expected fequeuev scaling of mgXVO (o.@. Stinebring et al.,1999b) and an expected frequency scaling of $m_{\rm RISS}\propto \nu^{\sim 0.56}$ (e.g. Stinebring et al. + 2000). we expect modulation iudices due to RISS for both pulsars of μιςSOL at 1110 AIIIz.," 2000), we expect modulation indices due to RISS for both pulsars of $m_{\rm RISS}\la 0.4$ at 1410 MHz." + We note that even such moderate values can lead to fairlv large deviations of the dux from the mean value, We note that even such moderate values can lead to fairly large deviations of the flux from the mean value + GCVE.&2) Ad~1.2. of We thank Federica Govoni for the deep radio image of the cluster.," $\mathcal{M} \ga +2$ $\mathcal{M} \sim 1.2$ We thank Federica Govoni for the deep radio image of the cluster." + Support for this work was provided by the National Aeronautics and Space Administration through, Support for this work was provided by the National Aeronautics and Space Administration through +The complex morphology aud change of the jet direction observed iu LOL5|352 may result from (1) a merecr. (2) a jet precession. or (3) jet-cloud iuteractious.,"The complex morphology and a change of the jet direction observed in 1045+352 may result from (1) a merger, (2) a jet precession, or (3) jet-cloud interactions." + Below. we discuss possible origius of the multiple radio structures aud their misaliguiuent.," Below, we discuss possible origins of the multiple radio structures and their misalignment." + Observations Iudicate. that about of voung AGN contain double nuclei iu their host galaxies or exhibit morphological distortions that are supposed tobe due to the past mereing events (O'Dea19908:Lin200L).," Observations indicate, that about of young AGN contain double nuclei in their host galaxies or exhibit morphological distortions that are supposed to be due to the past merging events \citep{odea98,liu04}." +. Although there are no obvious signs of merger event in the optical image of 10151352 (from the Sloan Dieital Skv Survey. SDSS). the radio distortious imdicate this possibility.," Although there are no obvious signs of merger event in the optical image of 1045+352 (from the Sloan Digital Sky Survey, SDSS), the radio distortions indicate this possibility." + Therefore we discuss below the possible scenario of a 1uereer event in QSO 1015|352., Therefore we discuss below the possible scenario of a merger event in QSO 1045+352. + As shown by Liu (2001). the spin axis of the black hole formed after the merger chauges its orientation from the vertical wit1 respect to the outer accretion disk to the aligned. wit1 the rotation axis of the binary on timescale 10? vr.," As shown by Liu (2004), the spin axis of the black hole formed after the merger changes its orientation from the vertical with respect to the outer accretion disk to the aligned with the rotation axis of the binary on timescale $10^{5}$ yr." + The angle by which the jet müght lave precessed iu 10151352 is difficult to be determined observationallv. due to oricutation effects," The angle by which the jet might have precessed in 1045+352 is difficult to be determined observationally, due to orientation effects." + The inclination angle of the À|C structure (jet axis) to the line of sight is about 30°, The inclination angle of the A+C structure (jet axis) to the line of sight is about $30^{\circ}$. + Iu the case of the older components Ay and D it secs o be rather 0~617., In the case of the older components $A_{1}$ and B it seems to be rather $\theta\sim61\degr$. + The images of the radio structures are projected outo the plane of the sky., The images of the radio structures are projected onto the plane of the sky. + Therefore even or a very small precession angle. e.g. 107. the musalignecd structure will appear shifted by a large anele on the 2-D nap. e.g. 907. due to the projection effect.," Therefore even for a very small precession angle, e.g. $10^{\circ}$, the misaligned structure will appear shifted by a large angle on the 2-D map, e.g. $90^{\circ}$, due to the projection effect." + Iu the case of 101512352. a timescale for the most distaut structure 43 (1.7 kpe. in projection) will be equal o f—5.5«Lot sas if we assume the jet velocity of 0.1e. and f=L8«10! ves for 03e.," In the case of 1045+352, a timescale for the most distant structure $A_{3}$ $1.7$ kpc, in projection) will be equal to $t=5.5\times 10^{4}$ yrs if we assume the jet velocity of $0.1 c$, and $t=1.8\times 10^{4}$ yrs for $0.3 c$." + Therefore in this source. we nw be witnessne an ougoine process of the disk realiguinent after à imierger event. which took place after structure ολο3 was ignited.," Therefore in this source, we may be witnessing an ongoing process of the disk realignment after a merger event, which took place after structure $A_{3}$ was ignited." + Iu this section. we apply the accretion disk instability model to explain the “reactivation” of the 1015|352 core.," In this section, we apply the accretion disk instability model to explain the ""reactivation"" of the 1045+352 core." + Below. we describe in brief the basic properties of this model. which was described in iore detail elsewhere (Janiketal.2002:Czerux2009).," Below, we describe in brief the basic properties of this model, which was described in more detail elsewhere \citep{jan02,czerny}." +. Tustabilities of the accretion disks have heen shown to operate ou long aud short timescales (Janisetal.2002:ανct2009). depending ou their nature (the dwarf-nova type of instability. caused by the partial ionization of lvdrogen: or the radiation pressure instability. stucied iu nicroquasars).," Instabilities of the accretion disks have been shown to operate on long and short timescales \citep{jan02,czerny} , depending on their nature (the dwarf-nova type of instability, caused by the partial ionization of hydrogen; or the radiation pressure instability, studied in microquasars)." + Scaling the outbursts of the Calactie microquasar CRS 1915|105. lasting about 2000 seconds for a black hole 11ass of 10A/.. to the quasar hosting a supermassive black hole. gives outbursts ou timescales of 10210? years.," Scaling the outbursts of the Galactic microquasar GRS 1915+105, lasting about $-$ 2000 seconds for a black hole mass of $10 +M_{\odot}$, to the quasar hosting a supermassive black hole, gives outbursts on timescales of $10^{2}-10^{5}$ years." + The unstable disk surrounding a black hole is subject to thermal aud viscous instability if the radiation pressure domunates over the eas pressure., The unstable disk surrounding a black hole is subject to thermal and viscous instability if the radiation pressure dominates over the gas pressure. +" If the accretion rate outside the unstable region 1νο, the πασά accretion rate) is such that the disk is iu the unstable mode. the source eaters a cycle of bright. hot states; separated by cold. quiescent states."," If the accretion rate outside the unstable region (i.e. the mean accretion rate) is such that the disk is in the unstable mode, the source enters a cycle of bright, hot states, separated by cold, quiescent states." + Iu the hot state. the hunünous quasar could power a radio jet. while during the cold state the radio activity ceases.," In the hot state, the luminous quasar could power a radio jet, while during the cold state the radio activity ceases." + The quantitative results. ic. the outburst amplitudes and duratious. are sensitive the model parameters: lack hole mass aud viscosity coefficieut.," The quantitative results, i.e. the outburst amplitudes and durations, are sensitive to the model parameters: black hole mass and viscosity coefficient." + Iu addition. he description of the heating is essential.," In addition, the description of the heating is essential." + If the heating is proportional to the total pressure. the outburst auplitudes are very large.," If the heating is proportional to the total pressure, the outburst amplitudes are very large." + The heating proportional to he square root of the eas times the total pressure reduces he amplitude of the disk outbursts., The heating proportional to the square root of the gas times the total pressure reduces the amplitude of the disk outbursts. + We compute the time dependent accretion disk modcl for several combinations of the maim parameters: four values of the mean accretion rate. 00.36.0.68.0.7 aud 1.0 uuits of the Eddiugton accretion rate: three values of inthe viscosity parameter: a=0.01.0.09 and 0.1: three values of black hole mass AL= and LstheLOSAL.. (see Table 3: models are labeled with A. D. and M).," We compute the time dependent accretion disk model for several combinations of the main parameters: four values of the mean accretion rate, $\dot m=0.36, 0.68, 0.7$ and 1.0 in units of the Eddington accretion rate; three values of the viscosity parameter: $\alpha=0.01, +0.03$ and 0.1; and three values of the black hole mass, $M= 2\times +10^{7}, 5.6\times 10^{7}$ and $4\times 10^{8} M_{\odot}$ (see Table 3; models are labeled with A, B, and M)." + The aceretion rate is iu, The accretion rate is in +(NUV-J) and (NUV-H) colour gradients caused by a metallicity gradient and hence enhanced line blanketing in the core.,(NUV-J) and (NUV-H) colour gradients caused by a metallicity gradient and hence enhanced line blanketing in the core. + In these cases we can be confident that the FUV residual does indeed show the distribution of the stars giving rise to the FUV excess., In these cases we can be confident that the FUV residual does indeed show the distribution of the stars giving rise to the FUV excess. +" In a number of other galaxies (e.g. NGC1407, NGC4365, NGC4649, NGC4839 and NGC4889) the NUV residual image shows extended positive excess NUV emission, which we attribute to recent star formation in the core."," In a number of other galaxies (e.g. NGC1407, NGC4365, NGC4649, NGC4839 and NGC4889) the NUV residual image shows extended positive excess NUV emission, which we attribute to recent star formation in the core." +" This will also contribute to the FUV residual, but cannot account for it all."," This will also contribute to the FUV residual, but cannot account for it all." +" For instance for NGC4649, which shows the strongest positive NUV residual, we find from the fits to the residual images described below that the magnitude of the excess is 16.26 in FUV and 17.13 in NUV."," For instance for NGC4649, which shows the strongest positive NUV residual, we find from the fits to the residual images described below that the magnitude of the excess is 16.26 in FUV and 17.13 in NUV." + Bianchi et al. (, Bianchi et al. ( +2005) present some single stellar population and continuous star formation models (their Figure 5) and they find that (FUV-NUV) lies in the range -0.2 to 0.0 for models with ages between 3 and 32Myr.,2005) present some single stellar population and continuous star formation models (their Figure 5) and they find that (FUV-NUV) lies in the range -0.2 to 0.0 for models with ages between 3 and 32Myr. +" Thus even in the unlikely event of the NGC4649 NUV excess being due to such a young starburst, this can still contribute at most of the excess flux in the FUV."," Thus even in the unlikely event of the NGC4649 NUV excess being due to such a young starburst, this can still contribute at most of the excess flux in the FUV." +" Liners, such as NGC1052, NGC4278, NGC4486 and NGC4552, show unresolved NUV and FUV excess which we attribute to the non-thermal nuclear source, in the latter two cases there is clearly extended FUV residual emission as well."," Liners, such as NGC1052, NGC4278, NGC4486 and NGC4552, show unresolved NUV and FUV excess which we attribute to the non-thermal nuclear source, in the latter two cases there is clearly extended FUV residual emission as well." +" In NGC1399, in addition to a strong extended FUV residual emission, and extended negative NUV residual, there is an excess in both bands right in the core."," In NGC1399, in addition to a strong extended FUV residual emission, and extended negative NUV residual, there is an excess in both bands right in the core." +" This occurs in the H-band as well and is an indication that the Sérrsic function is an inadequate fit to the surface brightness profile, there is extra light (c.f."," This occurs in the H-band as well and is an indication that the Sérrsic function is an inadequate fit to the surface brightness profile, there is extra light (c.f." + Kormendy et al., Kormendy et al. + 2009) above the Sérrsic fit in all wavebands in the core of this galaxy., 2009) above the Sérrsic fit in all wavebands in the core of this galaxy. +" For a smaller subsample, the signal-to-noise ratio in the FUV residual images is sufficient that we can use to determine their structure."," For a smaller subsample, the signal-to-noise ratio in the FUV residual images is sufficient that we can use to determine their structure." +" Our procedure is to fit a Sérrsic function to the residual image, adopting the square root of the original FUV counts image (i.e. the GALEX archive image multiplied by the exposure time) as a noise image."," Our procedure is to fit a Sérrsic function to the residual image, adopting the square root of the original FUV counts image (i.e. the GALEX archive image multiplied by the exposure time) as a noise image." + The results of the fits are given in Table 3.., The results of the fits are given in Table \ref{tab:UVexcess}. +" In this Table, column 2 gives the extinction corrected FUV apparent magnitude of the Sérrsic model of the residual, column 3 the effective radius Re and column 4 the Sérrsic index n of the residual image."," In this Table, column 2 gives the extinction corrected FUV apparent magnitude of the Sérrsic model of the residual, column 3 the effective radius $_e$ and column 4 the Sérrsic index $n$ of the residual image." +" Column 5 gives the magnitude difference between the model of the residual and the model of the galaxy image, the latter is calculated from columns 3 and 4 of Table 2.."," Column 5 gives the magnitude difference between the model of the residual and the model of the galaxy image, the latter is calculated from columns 3 and 4 of Table \ref{tab:properties}." +" The magnitude difference can be as little as 0.58 magnitudes, meaning that the central residual component can contribute up to of the FUV flux, although values of - are more typical."," The magnitude difference can be as little as 0.58 magnitudes, meaning that the central residual component can contribute up to of the FUV flux, although values of - are more typical." +" The upper limit to this magnitude difference of some 3.5 magnitudes, equivalent to a residual component of of total FUV flux, represents only our inability to measure smaller contributions with this technique."," The upper limit to this magnitude difference of some 3.5 magnitudes, equivalent to a residual component of of total FUV flux, represents only our inability to measure smaller contributions with this technique." +" Similarly we find that Κε for the residual component is much smaller than for the galaxy image in the FUV passband, if it were not then our procedure would not recover the residual, so we cannot rule out the existence of a more extended and more luminous FUV component with a scale length equal to"," Similarly we find that $_e$ for the residual component is much smaller than for the galaxy image in the FUV passband, if it were not then our procedure would not recover the residual, so we cannot rule out the existence of a more extended and more luminous FUV component with a scale length equal to" +(he experimental conditions one may wish to simulate.,the experimental conditions one may wish to simulate. + Through additional steps. which would involve the calculation of the nuclear trasparency [unction (defined as the probability that at some impact parameter the projectile will pass through the target without interacting). the mean free path is closely related to the nuclear reaction cross section.," Through additional steps, which would involve the calculation of the nuclear trasparency function (defined as the probability that at some impact parameter the projectile will pass through the target without interacting), the mean free path is closely related to the nuclear reaction cross section." + Thus. analvses of reaction cross section data can ultimately shed light on the target density. (a much. needed inlormation for nuclei with large neutron skin aud. (hus. harcl-to-probe density distributions).," Thus, analyses of reaction cross section data can ultimately shed light on the target density (a much needed information for nuclei with large neutron skin and, thus, hard-to-probe density distributions)." + On the other hand. a crucial input for the equations written above are the two- cross sections. for which parametrizations ol free-space NN cross sections are often adopted.," On the other hand, a crucial input for the equations written above are the two-body cross sections, for which parametrizations of free-space NN cross sections are often adopted." + This may not be reliable. and we suggest that keeping in touch with microscopic predictions can be of help when taving to constrain observables which depend on several (essentially unknown) degrees of Ireedom.," This may not be reliable, and we suggest that keeping in touch with microscopic predictions can be of help when trying to constrain observables which depend on several (essentially unknown) degrees of freedom." + Financial support from the U.S. Departament of Energy under grant number is acknowledged., Financial support from the U.S. Department of Energy under grant number DE-FG02-03ER41270 is acknowledged. +2002. Tornatore et al.,"2002, Tornatore et al." + 2003). aceretion shocks (Tozzi Norman 2001: Babul et al.," 2003), accretion shocks (Tozzi Norman 2001; Babul et al." +" 2002). quasar outflows (Nath Rovchowdlaury 2002).x aud ""effervesceut heating” (Rovchowdhnury et al."," 2002), quasar outflows (Nath Roychowdhury 2002), and “effervescent heating” (Roychowdhury et al." + 20014: hereafter: RRNBOL)., 2004; hereafter RRNB04). + More information on various heating models can be fouud iu a review bv Cardi Ricker (2001)., More information on various heating models can be found in a review by Gardini Ricker (2004). + Iu a receut study Croston ot al. (, In a recent study Croston et al. ( +"2001) preseuted the huuinosity-temperature relationμα for groups aud separated the sample iuto ""radio loud” or ""quiet? objects.",2004) presented the luminosity-temperature relation for groups and separated the sample into “radio loud” or “quiet” objects. +" Thev showed that ""radio loud” eroups deviated more frou the self-similar scaling relation thau the radio quiet ones.", They showed that “radio loud” groups deviated more from the self-similar scaling relation than the radio quiet ones. + This aremuent adds amore credibility to the idea that Αλλο are responsible for the entropy “floor” and deviations from self-sinilar scaling relations., This argument adds more credibility to the idea that AGNs are responsible for the entropy “floor” and deviations from self-similar scaling relations. + Iu a recent paper. we lave studied the effect of buovaut bubbles which deposit energy into the ICAL as they rise and expand iu the cluster atinosphere (RRNBOL).," In a recent paper, we have studied the effect of buoyant bubbles which deposit energy into the ICM as they rise and expand in the cluster atmosphere (RRNB04)." +" We studied the evolution of the density. temperature aud eutropy profiles of the ICM under the effect of ""effervescenut heatiues"" from buovant bubbles. radiative cooling aud convection. and deduced the energw required from the AGN to satisfv the eutrox observations of he ICAL."," We studied the evolution of the density, temperature and entropy profiles of the ICM under the effect of “effervescent heating” from buoyant bubbles, radiative cooling and convection, and deduced the energy required from the AGN to satisfy the entropy observations of the ICM." + Although the constraints from cutropy observations at wo differcut radi (0.179590 aud Fs00) were sati«fied. the cluperature aud cutropy profiles were somewhat different roni observed profiles. in that the eutropy profiles had a Hattened core and the teniperature in the mner regions were enhanced (see RRNBOL for details).," Although the constraints from entropy observations at two different radii $0.1 r_{200}$ and $r_{500}$ ) were satisfied, the temperature and entropy profiles were somewhat different from observed profiles, in that the entropy profiles had a flattened core and the temperature in the inner regions were enhanced (see RRNB04 for details)." + To resolve this issue. woe studyv the effect of thermal couductiou iu this oper.," To resolve this issue, we study the effect of thermal conduction in this paper." + The role of thermal conduction in the intracluster uediunu has generated a lot of mterest iu recent times., The role of thermal conduction in the intracluster medium has generated a lot of interest in recent times. + Its role. however. has mostly been discussed or studied iu detail in reference to cooling flows in the central regious of clusters.," Its role, however, has mostly been discussed or studied in detail in reference to cooling flows in the central regions of clusters." + May authors have investigated whether thermal conduction alone can act as à heating source in the centre of clusters to stop the eas from radiatively cooling to very low temperatures (0.9.. Zakauska Naravan. 2003: Voit 2002: Loeb 2002).," Many authors have investigated whether thermal conduction alone can act as a heating source in the centre of clusters to stop the gas from radiatively cooling to very low temperatures (e.g., Zakamska Narayan, 2003; Voigt 2002; Loeb 2002)." +" It has also been studied along with other heating mechauisiis like ""effervesceut heating” again in the coutext of cooling flows in the centers of clusters (Ruszkowski Beechuan. 2002)."," It has also been studied along with other heating mechanisms like “effervescent heating” again in the context of cooling flows in the centers of clusters (Ruszkowski Begelman, 2002)." + In this paper. we study the effect of thermal conduction along with heating via ACN in changing the cutropy profile of the ICM.," In this paper, we study the effect of thermal conduction along with heating via AGN in changing the entropy profile of the ICM." + Until receuthy it was only N-ray observations that vielded information about the cutropy excess., Until recently it was only X-ray observations that yielded information about the entropy excess. + Due to advances in detectors aud uew obscrving strategies (Birkinshaw 1999. Caeeo et al.," Due to advances in detectors and new observing strategies (Birkinshaw 1999, Grego et al." + 2001: Cwainge et al., 2001; Grainge et al. + 2002: Reese et al., 2002; Reese et al. + 2002: Zhane Wu 2000). the thermal Suuvaev-Zeldovich (SZ) effect (Sunvaev Zeldovich 1972. 1980) is Clucreine as anindependent test of the deusity and the thermal structure of clusters. thus equivalently of the entropy excess.," 2002; Zhang Wu 2000), the thermal Sunyaev-Zeldovich (SZ) effect (Sunyaev Zeldovich 1972, 1980) is emerging as an test of the density and the thermal structure of clusters, thus equivalently of the entropy excess." + Alauv authors lave investigated the role of excess eutropy iu clusters on the SZ effect aud tried to quantity it (White et al., Many authors have investigated the role of excess entropy in clusters on the SZ effect and tried to quantify it (White et al. + 2002: Springel et al., 2002; Springel et al. + 2001: da Silva et al., 2001; da Silva et al. + 2001. 2001: Cavaliere Moencei 2001: Holder Carlstrom 2001 MeCarthy et al.," 2001, 2004; Cavaliere Menci 2001; Holder Carlstrom 2001 McCarthy et al." + 2003a. 20035).," 2003a, 2003b)." + IIolder Carlstrom (2001). Cavaliere Moeuci (2001) aud MeCrtliv οἳ al. (," Holder Carlstrom (2001), Cavaliere Menci (2001) and McCarthy et al. (" +2003a) have also examined a few SZ scaling relatious for individual clusters.,2003a) have also examined a few SZ scaling relations for individual clusters. + Thev have shown that the SZ decrement is reduced ii individual clusters as a result of enerey injection aud that the SZ scaling relations deviate from the sclfsimilar predictions., They have shown that the SZ decrement is reduced in individual clusters as a result of energy injection and that the SZ scaling relations deviate from the self-similar predictions. + Iu a iore recent effort. Lapi et al.," In a more recent effort, Lapi et al." + 2003 have estimated the cubancements in the SZ cect due to trausieut blastwaves from quasars aud the depressions when the hydrostatic equilibrium is recovered., 2003 have estimated the enhancements in the SZ effect due to transient blastwaves from quasars and the depressions when the hydrostatic equilibrium is recovered. +" Tn this paper we further explore the consequences of heating the iutrachister iedimm via the ""effervescent heating” mechanisin (Degehuan 2001. BRuszkowski Beechnan 2002. RRNBOL) and thermal conduction."," In this paper we further explore the consequences of heating the intracluster medium via the “effervescent heating” mechanism (Begelman 2001, Ruszkowski Begelman 2002, RRNB04) and thermal conduction." + We also focus on the SZ decrement resulting from this heating model and calculate the angular power spectrum of the CXIB due to effervescent heating aud thermal conduction., We also focus on the SZ decrement resulting from this heating model and calculate the angular power spectrum of the CMB due to effervescent heating and thermal conduction. + Using the eutropy data. we also put constraints ou the relation between the black hole mass aud the cluster mass.," Using the entropy data, we also put constraints on the relation between the black hole mass and the cluster mass." + We show that it is las to be noulincar in analogy to the black holegalaxy halo relation that is expected to hold on stnaller scales., We show that it is has to be nonlinear in analogy to the black hole—galaxy halo relation that is expected to hold on smaller scales. + The paoer Is organized as follows., The paper is organized as follows. + T1 Section 2 we brieflv describe our model., In Section 2 we briefly describe our model. +" In Section 3 we extimate the ceutral SZ cdecremens,", In Section 3 we estimate the central SZ decrements. + We also sinulate the eveution of the «ΗΤΤΑ SZ senual due to AGN heating. cooine and conduction.," We also simulate the evolution of the central SZ signal due to AGN heating, cooling and conduction." + Iu Section [| woe estimate the angular power spectrum of he SZ temperature decrement in our models., In Section 4 we estimate the angular power spectrum of the SZ temperature decrement in our models. + We present our results and discussion in Section 5., We present our results and discussion in Section 5. + In Section 6 we discuss the relation between the mass of the central black role and the mass of the cluster., In Section 6 we discuss the relation between the mass of the central black hole and the mass of the cluster. + Finally. our conclusions are sununarized in Section 7.," Finally, our conclusions are summarized in Section 7." +" We asstune throughout the paper O40.71. Oy= 29. Q),=OOLF aud 5h=0.71 which are the best fit xuneters frou WALAP (Sperecl et al."," We assume throughout the paper $\Omega_{\rm\Lambda} \, = \, 0.71$ , $\Omega_{0} \, +=\,0.29$ , $\Omega_{\rm b} \,={\,0.047}$ and $h\,=\,0.71$ which are the best fit parameters from WMAP (Spergel et al." + 2003)., 2003). + The details of the initial conditions of our model are simular to those adopted by RRNDOL, The details of the initial conditions of our model are similar to those adopted by RRNB04. + Iu brief. we assume that the ICM is characterized by a “universal temperature profile” iu the range 0.015rfinge<1 eiven by where CD; is the ciissiou-weighted temperature. 1.33. a=rq and 6=1.6.," In brief, we assume that the ICM is characterized by a “universal temperature profile” in the range $0.04\le r/r_{\rm vir}\le 1$ given by where $\langle T\rangle$ is the emission-weighted temperature, $b=1.33$ , $a=r_{\rm vir}$ and $\delta = 1.6$." + This choice of the teiiperature profile as the initial temperature profile stems from the results of receut simulation of adiabatic evolution of clusters (Loken et al., This choice of the temperature profile as the initial temperature profile stems from the results of recent simulation of adiabatic evolution of clusters (Loken et al. + 2002)., 2002). + Since our goal is determine the effect of cucrey input from ACN. the most natural choice for an initial profile is that which arises from cluster evolution without cherev input.," Since our goal is determine the effect of energy input from AGN, the most natural choice for an initial profile is that which arises from cluster evolution without energy input." + Also. as Rovchowdlury Natl (2003) have shown. this initial temperature profile results iu cutropy profiles closer to observations than other profiles used previously in literature.," Also, as Roychowdhury Nath (2003) have shown, this initial temperature profile results in entropy profiles closer to observations than other profiles used previously in literature." + The choice of this temperature profile therefore decreases the discrepancy in entropy and therefore provides moreconservative estimate of the enerev required frou ACN., The choice of this temperature profile therefore decreases the discrepancy in entropy and therefore provides moreconservative estimate of the energy required from AGN. +"When we fit the DE models (5)) ancl (7)) to the observational data. we have four parameters QO,,. Op. tg and wy.","When we fit the DE models \ref{lind}) ) and \ref{wzeq}) ) to the observational data, we have four parameters $\Omega_m$ , $\Omega_k$, $w_0$ and $w_a$." + The MCAIC method is used to explore the. parameter space., The MCMC method is used to explore the parameter space. + The marginalized probability of Q; is shown in Fig. 1.., The marginalized probability of $\Omega_k$ is shown in Fig. \ref{fig1}. + It is obvious that the cosmic curvature cannot be well constrained for the DE model (5))., It is obvious that the cosmic curvature cannot be well constrained for the DE model \ref{lind}) ). + As discussed in Elgaroy&Mul- ancl Wang&Mukherjee(2007).. the combination of the shift parameter ancl the angular scale of the sound horizon at recombination gives much better constraints on cosmological parameters.," As discussed in \citet{lar} and \citet{wang07}, the combination of the shift parameter and the angular scale of the sound horizon at recombination gives much better constraints on cosmological parameters." +" So we add the angular scale of the sound horizon atrecombination (Wang&Mukhlerjee2007) where the sound speed c,=1//3(14-Ry). B=3150000,52/,,,/2.IN).). a is the scale factor. and Oh?=0.02173+J.0.00082 (Wang&Mukherjee2007)."," So we add the angular scale of the sound horizon atrecombination \citep{wang07} + where the sound speed $c_s=1/\sqrt{3(1+\bar{R_b} a)}$, $\bar{R_b}=315000\Omega_b h^2(T_{cmb}/2.7{\rm K})^{-4}$, $a$ is the scale factor, and $\Omega_b h^2=0.02173\pm 0.00082$ \citep{wang07}." +". To implement the WAMAPS3 data.we need to add three fitting parameters 2. /, and Q;/7."," To implement the WMAP3 data,we need to add three fitting parameters $R$, $l_a$ and $\Omega_b h^2$." +" So we need to add the term τονHr;vj))Ar; to C. where c;=CR.1.OU?) denote the three parameters for WMAP3 data, Xr)=ry)—27 and ον.j) is the covariance matrix for the three parameters."," So we need to add the term $\Delta +x_i {\rm Cov}^{-1}(x_i,x_j)\Delta x_j$ to $\chi^2$, where $x_i=(R,\ +l_a,\ \Omega_b h^2)$ denote the three parameters for WMAP3 data, $\Delta x_i=x_i-x_i^{obs}$ and $(x_i,x_j)$ is the covariance matrix for the three parameters." + Follow Wang and Mukherjee. we use the covariance matrix for ry=(2.1.Ομ) derived in Wang&Mukherjee(2007).," Follow Wang and Mukherjee, we use the covariance matrix for $x_i=(R,\ l_a,\ \Omega_b h^2)$ derived in \citet{wang07}." +. Since the covariance matrix for the six quantities in Wane&Mukherjee(2007) is defined as the pair correlations for those variables. so each element in the matrix is obtained by marginalizing over all other variables.," Since the covariance matrix for the six quantities in \citet{wang07} is defined as the pair correlations for those variables, so each element in the matrix is obtained by marginalizing over all other variables." + Therefore. the covariance matrix between .r; andr; is the three by three sub-matrix of the full six by six malrixin Wane&Mukherjee(2007).," Therefore, the covariance matrix between $x_i$ and $x_j$ is the three by three sub-matrix of the full six by six matrix in \cite{wang07}." +.. The marginalized probability of ος is shown in Fig. 1.., The marginalized probability of $\Omega_k$ is shown in Fig. \ref{fig1}. +" We see that the cosmic curvature is constrained better with the acldition of the angular scale /, of the sound horizon at recombination.", We see that the cosmic curvature is constrained better with the addition of the angular scale $l_a$ of the sound horizon at recombination. +" since (he angular scale of (he sound horizon depends on (he early history of the Universe. so il strongly depends on ,."," Since the angular scale of the sound horizon depends on the early history of the Universe, so it strongly depends on $\Omega_r$." + However. we can neglect (he effect of ο when we evaluate the distance modules j4((z) and the shift parameter 2 because the Universe is matter dominated.," However, we can neglect the effect of $\Omega_r$ when we evaluate the distance modules $\mu(z)$ and the shift parameter $R$ because the Universe is matter dominated." +" so only when we implement the CMD data with /,. we need to consider the effect of Q,."," So only when we implement the CMB data with $l_a$, we need to consider the effect of $\Omega_r$." +" We know the enerey density p, of radiation. so thedependence of Q,=8x6p,/(3117) is manifested by the Hubble constant Z7."," We know the energy density $\rho_r$ of radiation, so thedependence of $\Omega_r=8\pi G\rho_r/(3 H_0^2)$ is manifested by the Hubble constant $H_0$." + Since we can neglect the effect of £ in fitting SN la data. so the effect of the observed value of {{ can be neglected by marginalizing over it.," Since we can neglect the effect of $\Omega_r$ in fitting SN Ia data, so the effect of the observed value of $H_0$ can be neglected by marginalizing over it." +" Therefore. we use (he IIubble constant {1η asa lee parameter instead of O,."," Therefore, we use the Hubble constant $H_0$ asa free parameter instead of $\Omega_r$." + The marginalized probabilities of Ως [or Hj=65 km/s/Mpce aud fy=72 kmn/s/Mpc are shown in Fie. 2.., The marginalized probabilities of $\Omega_k$ for $H_0=65$ km/s/Mpc and $H_0=72$ km/s/Mpc are shown in Fig. \ref{fig2}. . + We see that the resultsindeed depend on £44., We see that the resultsindeed depend on $H_0$ . +" As discussed in (Elearov&Multoanáki 2007).. the combination of 2 and /, approximates the WAIAPS clata and the WMAP3 data depends on ff, through /,. a"" "," As discussed in \citep{lar}, the combination of $R$ and $l_a$ approximates the WMAP3 data and the WMAP3 data depends on $H_0$ through $l_a$ ." +"So. as expected. /, also depends on fy."," So, as expected, $l_a$ also depends on $H_0$ ." + From now on wealso take Lf) as a filling parameter. and impose a prior of [fy=7248 km/s/Mpc (Freecdinan:2001 )..," From now on wealso take $H_0$ as a fitting parameter, and impose a prior of $H_0=72\pm 8$ km/s/Mpc \citep{freedman}. ." +solar r-process distribution.,solar $r$ -process distribution. + The peaks made by trajectory 2 lie several mass units above the corresponding solar r-process abundance peaks., The peaks made by trajectory 2 lie several mass units above the corresponding solar $r$ -process abundance peaks. + This is mainly due to the rather extensive exposure (o neutron capture for this trajectorv: there are still about 15 [ree neutrons per heavy nucleus at the end of the run., This is mainly due to the rather extensive exposure to neutron capture for this trajectory: there are still about 15 free neutrons per heavy nucleus at the end of the run. + The reason why trajectories 1 and 2 are able to produce heavy. neutron-rich nuclei despite (he zero to low iniüal neutron excess is (he persistent a-particle disequilibrium discussed by Meyer(2002)..," The reason why trajectories 1 and 2 are able to produce heavy, neutron-rich nuclei despite the zero to low initial neutron excess is the persistent $\alpha$ -particle disequilibrium discussed by \citet{2002PhRvL..89w1101M}." + Iu these expansions. (he initial distribution of nuclei is quickly broken down into nuclear statistical equilibrium. which is dominated by [ree neutrons and protons.," In these expansions, the initial distribution of nuclei is quickly broken down into nuclear statistical equilibrium, which is dominated by free neutrons and protons." + As the material expands ancl cools. the free nucleons assenible into oa-particles and heavier nuclei.," As the material expands and cools, the free nucleons assemble into $\alpha$ -particles and heavier nuclei." + Because of the rapidness of the expansion. however. the free nucleons do not assemble into heavier species (particularly a-particles) as quickly as equilibrium demands.," Because of the rapidness of the expansion, however, the free nucleons do not assemble into heavier species (particularly $\alpha$ -particles) as quickly as equilibrium demands." + This leaves a large excess of these [ree nucleons. which push the heavy nuclei to very. high mass.," This leaves a large excess of these free nucleons, which push the heavy nuclei to very high mass." + For example. for trajectory 2. al Lozz4. (he abundance distribution is dominated by [ree neutrons ancl protons. a-parlicles. and nuclei with mass nunmber vlee140.," For example, for trajectory 2, at $T_9 \approx 4$, the abundance distribution is dominated by free neutrons and protons, $\alpha$ -particles, and nuclei with mass number $A \approx 140$." + Specifically. (he mass fractions of [ree neutrons ancl protons. a-particles. and heavy nuclei at this temperature are zz1.356...0.356...97.655... and 0.6%.. respectively.," Specifically, the mass fractions of free neutrons and protons, $\alpha$ -particles, and heavy nuclei at this temperature are $\approx 1.3$, and , respectively." + The heavy nuclei serve as the seeds for the subsequent. r-process nucleosvntliesis., The heavy nuclei serve as the seeds for the subsequent $r$ -process nucleosynthesis. + We expect that the final abundance distribution will depend on the details of the trajectories of the mass elements at late times., We expect that the final abundance distribution will depend on the details of the trajectories of the mass elements at late times. + Indeed. we note that for trajectory 2. expansion occurs so rapidly (hat reaction [reezeout occurs because (he densitv drops to such a low value that neutron-capture (ünmescales become long. not because the neutrons are all consumed.," Indeed, we note that for trajectory 2, expansion occurs so rapidly that reaction freezeout occurs because the density drops to such a low value that neutron-capture timescales become long, not because the neutrons are all consumed." + The result is that there are still about 15 free neutrons per heavy nucleus al the end of the run (the final mass fractions of free neutrons. a-particles. and heavy nuclei are g0.256...Οδ. and 2%.. respectively).," The result is that there are still about 15 free neutrons per heavy nucleus at the end of the run (the final mass fractions of free neutrons, $\alpha$ -particles, and heavy nuclei are $\approx 0.2$, and , respectively)." + We confirmed this bv running a caleulation identical to trajectory 2 except that (hie expansion slowed at late (mes and allowed (he neutrons to be all consumed., We confirmed this by running a calculation identical to trajectory 2 except that the expansion slowed at late times and allowed the neutrons to be all consumed. + The resulting patteri was broadly similar (o (hat in the lower panel of Fig. 1.. ," The resulting pattern was broadly similar to that in the lower panel of Fig. \ref{fig:fig1}, ," +but the contrast between the peaks and vallevs was smaller., but the contrast between the peaks and valleys was smaller. + We also followed trajectories 1 and 2’. which were identical to trajectories 1 and 2 except that neutrino reactions were included.," We also followed trajectories $'$ and $'$, which were identical to trajectories 1 and 2 except that neutrino reactions were included." + The neutrino interactions had negligible effects on the abundance patterns., The neutrino interactions had negligible effects on the abundance patterns. + This is because expansion carried (he material away so rapidly (hat the total number of neutrino interactions per nucleon or nucleus was«1 during the expansion., This is because expansion carried the material away so rapidly that the total number of neutrino interactions per nucleon or nucleus was$\ll 1$ during the expansion. +phenomena discussed here. but it does show the possibility of a presupernova outburst. even in the II-poor case.,"phenomena discussed here, but it does show the possibility of a presupernova outburst, even in the H-poor case." + A model similar to that developed here was presented by and applied to the Type Ib SN 2008D. We thank Claes Fransson for discussions., A model similar to that developed here was presented by \cite{balberg11} and applied to the Type Ib SN 2008D. We thank Claes Fransson for discussions. + This research was supported in part by NSF erant. AST-0807127., This research was supported in part by NSF grant AST-0807727. +"οασε 0.00025. 0.01900+ 0.00035. 0.019604- 0.00025. 1.02[50+0.00025. and 0.02500+0.00025 dot,","$0.01644\pm0.00025$ , $0.01900\pm0.00035$ , $0.01960\pm0.00025$ , $0.02450\pm0.00025$, and $0.02500\pm0.00025$ $^{-1}$." + A substantial fraction of the 571 poteutial sources are extragalactic targets such as active galactic nuclei. extended Galactic targets such as supernova remnants. or N-rav binaries that have been in quiescence since the einning of the RNTE wission and for which we have ιο expectation of finding detectable pertocdicitics.," A substantial fraction of the 571 potential sources are extragalactic targets such as active galactic nuclei, extended Galactic targets such as supernova remnants, or X-ray binaries that have been in quiescence since the beginning of the RXTE mission and for which we have no expectation of finding detectable periodicities." + The oower spectra of these sources act effectively as controls iat show the actual statistics of the power spectra aud iat bring attention to periodicitics that πας be the roduct of statistical fluctuations or artifacts., The power spectra of these sources act effectively as controls that show the actual statistics of the power spectra and that bring attention to periodicities that must be the product of statistical fluctuations or artifacts. + Tucecd. 1ο search procedure deseribed here was tailored iu art by examination of the results on the “controls”," Indeed, the search procedure described here was tailored in part by examination of the results on the “controls”." + Furthermore. since it would be dif&cult to understand 1c reality of peaks that exceed the detection threshold iu 1e power spectra of these sources. the effective umber of sources must be less than 571.," Furthermore, since it would be difficult to understand the reality of peaks that exceed the detection threshold in the power spectra of these sources, the effective number of sources must be less than 571." + We have not adjusted je significance thresholds downward to account for this ffect., We have not adjusted the significance thresholds downward to account for this effect. + Since we searched large uuubers of bins. the thresholds or the detection of previously unreported periodicitics even in Table 2. are high.," Since we searched large numbers of bins, the thresholds for the detection of previously unreported periodicities given in Table \ref{tbl:tmscls} are high." + When a periodicitv has xeviouslv been reported. it may be confirmed even if he power at or very close to the previously reported requencev is below the threshold eiveu iu the table.," When a periodicity has previously been reported, it may be confirmed even if the power at or very close to the previously reported frequency is below the threshold given in the table." + Unconmpressed power deusitv spectra are useful for xecise estimation of the frequencies of the detected periodicities., Uncompressed power density spectra are useful for precise estimation of the frequencies of the detected periodicities. +" Since the unconipressed spectra were not saved in the original analysis for smoothing time scales less than or equal to 30.0 days. the analyses that produced the most significaut detection of cach periodicity were repeated. if necessary. aud the resulting ""nconpressed spectra were saved."," Since the uncompressed spectra were not saved in the original analysis for smoothing time scales less than or equal to 30.0 days, the analyses that produced the most significant detection of each periodicity were repeated, if necessary, and the resulting uncompressed spectra were saved." + For cach periodicitv a small frequency rauge arouud the major peak was fit with a Gaussian to obtain estimates of the central frequency. its uncertaiutv. aud the peak width.," For each periodicity a small frequency range around the major peak was fit with a Gaussian to obtain estimates of the central frequency, its uncertainty, and the peak width." + The uncertaiutv im the frequency may be estimated based. ou the result of IIorne aud DBaliuuas (1986) that where T ds the leneth of the time interval covered by the light curve and P. is the peak power in a normalized PDS., The uncertainty in the frequency may be estimated based on the result of Horne and Baliunas (1986) that where $T$ is the length of the time interval covered by the light curve and $P_r$ is the peak power in a normalized PDS. + We also use the simple estimate which. in most cases. should be a conservative upper limit to the uncertainty (but. if the periodicity persisted for only a fraction of the time covered by the heht curve. the uncertainty could be larger than this value).," We also use the simple estimate which, in most cases, should be a conservative upper limit to the uncertainty (but, if the periodicity persisted for only a fraction of the time covered by the light curve, the uncertainty could be larger than this value)." + In the estimates of frequencies and periods that we present below. the uncertainty derived using eq. (," In the estimates of frequencies and periods that we present below, the uncertainty derived using eq. (" +8) is given first and the uncertainty derived using eq.(9) isgiven secoudin square brackets.,8) is given first and the uncertainty derived using eq.(9) isgiven secondin square brackets. +on the wide redshift distribution (6.=0.10). which is uost relevant to the current observations.,"on the wide redshift distribution $\sigma_{z}=0.4$ ), which is most relevant to the current observations." + The intrinsic (523 we predict is a sinall fraction of the measured. value on all scales. except possibly for the largest scale poiu roni WWL. which. as those authors poiut out is an interesting null detection.," The intrinsic $\shear$ we predict is a small fraction of the measured value on all scales, except possibly for the largest scale point from KWL, which, as those authors point out is an interesting null detection." + The intrinisic (57) ix also a a sunaller level than the leo errors for the observational neasureiuents., The intrinisic $\shear$ is also at a smaller level than the $1\sigma$ errors for the observational measurements. + It is therefore not really a factor whet- interpreting the current results. but may become a bi nore of au issue when the surveved areas mnuerease aud the statistical errors become simaller.," It is therefore not really a factor when interpreting the current results, but may become a bit more of an issue when the surveyed areas increase and the statistical errors become smaller." + If we now turn to tlic other two curves. we can see that for the narrow redshift distributions. the jutrinsic (57) liegins to approach the current measurements. at least on large scales.," If we now turn to the other two curves, we can see that for the narrow redshift distributions, the intrinsic $\shear$ begins to approach the current measurements, at least on large scales." + On small scales. although the errors are large (Fig. 9)).," On small scales, although the errors are large (Fig. \ref{limbervsimcatshear}) )," + there appears to be relatively less signal., there appears to be relatively less signal. + We have κος Nobody simulatious to male predictious or intrinsic correlations of galaxw cllipticitics. under the assuniptiou that ealaxy shapes follow the shapes of their dark matter halos.," We have used Nbody simulations to make predictions for intrinsic correlations of galaxy ellipticities, under the assumption that galaxy shapes follow the shapes of their dark matter halos." +" Measurements of the ellipticity correlation ""unuctions dim fhree-dineusious eive a distinctive signal. which we measure with relatively μαμα uucertaiuties on scales from ~0.5307.!Mpe."," Measurements of the ellipticity correlation functions in three-dimensions give a distinctive signal, which we measure with relatively small uncertainties on scales from $\sim 0.5-30 \hmpc$." + These correlations vary w oless than a factor of ~2 for different halo finding echniques and different simulation resolutious., These correlations vary by less than a factor of $\sim 2$ for different halo finding techniques and different simulation resolutions. + We project hese three dimensional correlations iuto angular statistics. including the shear variance.," We project these three dimensional correlations into angular statistics, including the shear variance." + We have done this both analytically. using a modified Limbers equation. aud bv naking direct iieasureimenuts from simulated suveys coustructedrestlts * projectius the simulation boxes.," We have done this both analytically, using a modified Limber's equation, and by making direct measurements from simulated surveys constructed by projecting the simulation boxes." + We find that the auplitude of the angular statistics depeuds strougly ou ie redshift width of the galaxy distribution., We find that the amplitude of the angular statistics depends strongly on the redshift width of the galaxy distribution. + With widths —xppropriate to present dav surveys. we find that the ityinsic correlations we predict are around 1020% of je currently measured signal. somewhat smaller than the lo errors ou the measurements.," With widths appropriate to present day surveys, we find that the intrinsic correlations we predict are around $10-20\%$ of the currently measured signal, somewhat smaller than the $1 \sigma$ errors on the measurements." + Since the area of the sky surveyed for weals lensing is oewcreasing rapidly. the iutrinisic correlation may become etectable from these deep aud wide surveys in the future.," Since the area of the sky surveyed for weak lensing is increasing rapidly, the intrinisic correlation may become detectable from these deep and wide surveys in the future." + Iu any case. if seenus to be worth bearing m imunud that rere could be this sort of contamination.," In any case, it seems to be worth bearing in mind that there could be this sort of contamination." +" Iu particular. one possible way of extracting nore iuforniatfion frou eusine which has received attention is the use of pj0toietric redshift information. to break dow ithe background galaxy distribution iuto a uuuber of ""crecus’."," In particular, one possible way of extracting more information from lensing which has received attention is the use of photometric redshift information, to break down the background galaxy distribution into a number of “screens”." +" This woud euale oloeraphy to be carried out (οιοι, IIu 1999)."," This would enable tomography to be carried out (e.g., Hu 1999)." + We 1lave SCC rowever that the iutrinsic correlajon nav be qiite laronex or these narrow redshift bius. so that it mieht become conrparable to the weak lensing signal (Fie. 11)).," We have seen however that the intrinsic correlation may be quite large for these narrow redshift bins, so that it might become comparable to the weak lensing signal (Fig. \ref{shearobs}) )." + Of course. the extra information available in the form of photometric redshifts is likely to be very useful for deciding whether there is au intrinsic coniponent. and if it exists. to separate it from the leusing signal.," Of course, the extra information available in the form of photometric redshifts is likely to be very useful for deciding whether there is an intrinsic component, and if it exists, to separate it from the lensing signal." + For example he cross-correlation of ellipticities (or co-variance of the shear) between different redshift bius cau be compared to he correlation within bius. with ouly the later responding o intrinsic correlations.," For example the cross-correlation of ellipticities (or co-variance of the shear) between different redshift bins can be compared to the correlation within bins, with only the later responding to intrinisic correlations." + Something aloug these lines las already been carried out by IWL. albeit with two colour wands which both give wide redshift distributions (but with one deeper than the other).," Something along these lines has already been carried out by KWL, albeit with two colour bands which both give wide redshift distributions (but with one deeper than the other)." + These authors find a üeher shear signal for the deeper redshift sample. which is consistent with lensing. but iu the wrong direction for intrinsic correlations.," These authors find a higher shear signal for the deeper redshift sample, which is consistent with lensing, but in the wrong direction for intrinsic correlations." + For the cross-correlation between saluples. they do fud shehthy anomalous results. however.," For the cross-correlation between samples, they do find slightly anomalous results, however." + Another way of trving to measure anv intrinsic ellipticitv correlations would be to stick to the local universe. aud to measure the three dimensional correlation fuuctious (833) from a redshift survey.," Another way of trying to measure any intrinsic ellipticity correlations would be to stick to the local universe, and to measure the three dimensional correlation functions 3) from a redshift survey." + Tf there really is a signal like that plotted iu Fig. 3..," If there really is a signal like that plotted in Fig. \ref{xie}," + then this could be measurable from a relatively small survey (by todavs standards). with a few thousand galaxies.," then this could be measurable from a relatively small survey (by todays standards), with a few thousand galaxies." + Even without redshifts. one nuelt expect to find a measurable intrinsic signal frou a relatively nearby aneular sample of galaxies. like the APM survey (Maddox 1990). or Sloan Digital Sky Survey (Gunn Weinberg 1995).," Even without redshifts, one might expect to find a measurable intrinsic signal from a relatively nearby angular sample of galaxies, like the APM survey (Maddox 1990), or Sloan Digital Sky Survey (Gunn Weinberg 1995)." + Tf there are infact some measurable correlations between real galaxy cllipticitics. then this cau be understood iu the framework of structure formation bv gravitational instability. with the ellipticities being linked to the angular momenta of galaxies. which are in turn set up by tidal torques from the shear in the initial density field (c.e.. Peebles 1969. Darues Efstathiou 1987. Catelan aud 'Theuus 1996a.b).," If there are in fact some measurable correlations between real galaxy ellipticities, then this can be understood in the framework of structure formation by gravitational instability, with the ellipticities being linked to the angular momenta of galaxies, which are in turn set up by tidal torques from the shear in the initial density field (e.g., Peebles 1969, Barnes Efstathiou 1987, Catelan and Theuns 1996a,b)." + This may explain why the ellipticity correlation functions we measure have simular functional forms to those caused by weak-lIeusiue: both are responding to a cosmic shear field., This may explain why the ellipticity correlation functions we measure have similar functional forms to those caused by weak-lensing: both are responding to a cosmic shear field. + Detection of correlated ellipticities. if they exist. πας be useful for the study of galaxy formation (e.g.. Sugerman 2000). or even cosmology (Lee Pen 2000).," Detection of correlated ellipticities, if they exist, may be useful for the study of galaxy formation (e.g., Sugerman 2000), or even cosmology (Lee Pen 2000)." + It is also Likely that the signal due to the intrinsic correlation will give qualitatively and measurably differeut from weak leusing for soie statistics we lave not considered here., It is also likely that the signal due to the intrinsic correlation will give qualitatively and measurably different results from weak lensing for some statistics we have not considered here. + For example. the probability distribution of the lensing convergence is predicted to have a iieasurable skewness. something which can be used to determine © (Bernardeau 1997).," For example, the probability distribution of the lensing convergence is predicted to have a measurable skewness, something which can be used to determine $\Omega$ (Bernardeau 1997)." + Measurements of this parameter roni our sniulated surveys by L. Vau Waerbeke (private conumnmnication) vield a uull result. the convergence pdf eiue cousisteut with a Caussian distribution.," Measurements of this parameter from our simulated surveys by L. Van Waerbeke (private communication) yield a null result, the convergence pdf being consistent with a Gaussian distribution." + The iutriuisic correlations do not therefore appear to iuterfere with our ability to do cosmology in this wav. and should not act as nore than au additional source of noise (albeit correlated) when reconstructed mass maps are made.," The intrinisic correlations do not therefore appear to interfere with our ability to do cosmology in this way, and should not act as more than an additional source of noise (albeit correlated) when reconstructed mass maps are made." + Ou the simulation side. one important issue is the act that our results have apparently not converged with resolution.," On the simulation side, one important issue is the fact that our results have apparently not converged with resolution." + Although we find that the higher resolution of two simulations cives iore iutrinsic correlations. it is possible that eiven even higher resolution. thines wi1 beein to go the other wav.," Although we find that the higher resolution of two simulations gives more intrinsic correlations, it is possible that given even higher resolution, things will begin to go the other way." + Clearly this needs to be testec1 somehow iu the future., Clearly this needs to be tested somehow in the future. + Also. perhaps most important of all. we have asstned a very simple relatiouship betwee- projected halo ellipticities and projected galaxy ellipticities.," Also, perhaps most important of all, we have assumed a very simple relationship between projected halo ellipticities and projected galaxy ellipticities." + Tt is possible that adding eas dvuaiiics and star formation to simulations will result in their being no siguificaut correlation between the two., It is possible that adding gas dynamics and star formation to simulations will result in their being no significant correlation between the two. + The tests which we lave carried out which have most beariug on this are the use of two sets of different fieuds of frieuds eroups. which respond to cllipticities cither of the whole halo. or just the dense central region.," The tests which we have carried out which have most bearing on this are the use of two sets of different friends of friends groups, which respond to ellipticities either of the whole halo, or just the dense central region." + As we find results for the two which are verv simular. this is at least some evideuce that the lutrinsic correlation may be fuudaueutal.," As we find results for the two which are very similar, this is at least some evidence that the intrinsic correlation may be fundamental." + As this paper was being completed. we became aware of simular work bv Ieaveus (2000).," As this paper was being completed, we became aware of similar work by Heavens (2000)." + These authors use, These authors use +of the molecular gas associated with will focus on Component |.,of the molecular gas associated with will focus on Component 1. + The kinematics of Component | was studied by using position-velocity maps across selected strips., The kinematics of Component 1 was studied by using position-velocity maps across selected strips. + The map obtained along (corresponding to clump A) is shown in the upper panel of Fig. 4.., The map obtained along (corresponding to clump A) is shown in the upper panel of Fig. \ref{fig:pos-vel}. + A noticeable velocity gradient is observed at velocities from about —23 to about -28.., A noticeable velocity gradient is observed at velocities from about $-23$ to about $-28$. + Additional support to the existence of this gradient can be obtained through à moment analysis., Additional support to the existence of this gradient can be obtained through a moment analysis. + Due to the large angular dimensions of Component | and the spatial sampling of NANTEN observations. 28 independient CO profiles were observed towards the region enclosed by the 0.42 K-contour line in Fig. 3..," Due to the large angular dimensions of Component 1 and the spatial sampling of NANTEN observations, 28 independient CO profiles were observed towards the region enclosed by the 0.42 K-contour line in Fig. \ref{fig:comp12y3}." + Having these spectra a high signal-to-noise ratio10).. they are well suited to study in some detail possible variations of the CO profiles across Component I.," Having these spectra a high signal-to-noise ratio, they are well suited to study in some detail possible variations of the CO profiles across Component 1." + With this aim. we used the AIPS package to calculate the first three moments (integrated area. temperature weighted meat radial velocity. and velocity dispersion) of the CO profiles.," With this aim, we used the AIPS package to calculate the first three moments (integrated area, temperature weighted mean radial velocity, and velocity dispersion) of the CO profiles." + It the lower panel of Fig. 4..," In the lower panel of Fig. \ref{fig:pos-vel}," + the temperature weighted meat radial velocity distribution of CO is shown., the temperature weighted mean radial velocity distribution of CO is shown. + A clear velocity gradient is observed along Component |. and particulary ii the region of clump A (depicted by the dotted ellipse). with mean radial velocities more negative toward the position of.," A clear velocity gradient is observed along Component 1, and particulary in the region of clump A (depicted by the dotted ellipse), with mean radial velocities more negative toward the position of." +. A velocity shift of about ~ 1.4 is observec across the region of clump A. which at a distance of 2.9 kpe translates to a gradient w = 0.15 pe.," A velocity shift of about $\sim$ 1.4 is observed across the region of clump A, which at a distance of 2.9 kpc translates to a gradient $\omega$ $\approx$ 0.15 $^{-1}$." + This panel also shows that the CO emission corresponding to elump B does not show a significant velocity gradient., This panel also shows that the CO emission corresponding to clump B does not show a significant velocity gradient. + In order to offer a complete picture of the kinematical properties of clump A. we show in Fig.," In order to offer a complete picture of the kinematical properties of clump A, we show in Fig." + 6— the spatial distribution of the CO emission within the velocity range from -27.4 to 223.4., \ref{fig:mosaico1} the spatial distribution of the CO emission within the velocity range from –27.4 to –23.4. +. Every image depicts mean --values (in contours) over a velocity interval of superimposed on the 5.13 μπι eemission (in greyscale)., Every image depicts mean -values (in contours) over a velocity interval of superimposed on the 8.13 $\mu$ m emission (in greyscale). + In the velocity range from —27.4 to -26.4 the molecular emission arising from clump A is slightly displaced from the brightest MSX emission located at = (289255. 907111).," In the velocity range from –27.4 to –26.4 the molecular emission arising from clump A is slightly displaced from the brightest MSX emission located at $\approx$ 5, 11)." + As we move towards more positive velocities. the maximum of the CO emission gradually shifts westwards.," As we move towards more positive velocities, the maximum of the CO emission gradually shifts westwards." + Following ?.. we analyze the excitation temperature (Το) obtained from the CO data to probe the surface conditions of Component [.," Following \citet{U09}, we analyze the excitation temperature $T_{\rm exc}$ ) obtained from the CO data to probe the surface conditions of Component 1." +" The excitation temperature of the 'CO line can be obtained considering that 'CO is optically thick (7, >> η.", The excitation temperature of the $^{12}$ CO line can be obtained considering that $^{12}$ CO is optically thick $\tau_{\nu}$ $>>$ 1). +" Then. the peak temperature of this line is given by (?) where J, is the Planck function at a frequency v."," Then, the peak temperature of this line is given by \citep{di78} where $J_{\nu}$ is the Planck function at a frequency $\nu$." + Assuming gaussian profiles for the CO line.combining the order zero moment map (.e.. integrated area) with the order two moment map (re. velocity dispersion). and using Eq.," Assuming gaussian profiles for the $^{12}$ CO line,combining the order zero moment map (i.e., integrated area) with the order two moment map (i.e., velocity dispersion), and using Eq." + 2 we obtain the 7... distribution map5)., \ref{eq:tpeak} we obtain the $T_{\rm exc}$ distribution map. +. As expected. the 7... distribution is quite similar to the CO emission distribution of Component 1. reaching a maximum of ~ 17.7 K at+0811).," As expected, the $T_{\rm exc}$ distribution is quite similar to the CO emission distribution of Component 1, reaching a maximum of $\sim$ 17.7 K at." +" It is worth noting that the obtained value of 7, towards the center of clump A is lower than the obtained by ? towardsK).", It is worth noting that the obtained value of $T_{exc}$ towards the center of clump A is lower than the obtained by \citet{U09} towards. +. This difference may be explained in terms of a beam smearing of our NANTEN data. which implies that the values of 7... shown in Fig.," This difference may be explained in terms of a beam smearing of our NANTEN data, which implies that the values of $T_{\rm exc}$ shown in Fig." + 5 must be considered as lower limits., \ref{fig:momento} must be considered as lower limits. + Themass of the molecular gas associated with can be derived making use of the empirical relationship between the molecular hydrogen column density. NCH2). and the integrated molecular emission. dv).," Themass of the molecular gas associated with can be derived making use of the empirical relationship between the molecular hydrogen column density, $N(\rm H_2)$ and the integrated molecular emission, ." + The conversion between /:co and N(H>) 1s given byf the equation, The conversion between $I_{{\rm ^{12}CO}}$ and $N(\rm H_2$ ) is given by the equation +field.,field. + The inteeral over all azimuthal aneles iu the cisk is uot affected by a translation in azimuthal anele resulting from the pitch angle of the magnetic field., The integral over all azimuthal angles in the disk is not affected by a translation in azimuthal angle resulting from the pitch angle of the magnetic field. + Table5. eives values for the parameters in the models that are compared with the data., Table\ref{model_par-tab} gives values for the parameters in the models that are compared with the data. + Model 7 corresponds with the values adopted by Beck(2007b) for NGC 6916., Model 7 corresponds with the values adopted by \citet{beck2007} for NGC 6946. + The filling factor of ionized gas f; aud the thickness of the disk 2/ were kept constant. because thei effect on the models is simular to that of the electron density aud the magnetic field.," The filling factor of ionized gas $f_{i}$ and the thickness of the disk $2h$ were kept constant, because their effect on the models is similar to that of the electron density and the magnetic field." + Model curves of fractional polarization as a function of inclination are shown in Figure 1.., Model curves of fractional polarization as a function of inclination are shown in Figure \ref{diskpol_model-fig}. +" Three funuilies of models are shown {Table 5)). with fp= 1. 2, and 3."," Three families of models are shown (Table \ref{model_par-tab}) ), with $f_{\rm B} = $ 1, 2, and 3." +" For each value of £p. model curves are shown for n.=O0.03 Ὁ, B=h pO (solid curves). i.=0.08 cuο, B= 1059G (dashed curves). aud a,=0.09 cn? D—5 pO (dotted curves)."," For each value of $f_{\rm B}$, model curves are shown for $n_e = 0.03$ $^{-3}$ , $B = 5\ \mu$ G (solid curves), $n_e = 0.03$ $^{-3}$, $B = +10 \mu$ G (dashed curves), and $n_e = 0.09$ $^{-3}$ , $B = 5\ \mu$ G (dotted curves)." + At low inclination. the models are mainly distiueuished by the value of fp.," At low inclination, the models are mainly distinguished by the value of $f_{\rm B}$." + The line-ofsight component of the regular magnetic feld is siall at low inclination. and the main depolarization niechanisiis are wavelength independent depolarization aud Faraday dispersion.," The line-of-sight component of the regular magnetic field is small at low inclination, and the main depolarization mechanisms are wavelength independent depolarization and Faraday dispersion." + At inclination /2507. differential Faraday rotation along the line of sight becomes increasingly importaut. aud sieuificaut effects of the streneth of the regular magnetic feld and the deusitv of thermal electrous are found.," At inclination $i \gtrsim 50\degr$, differential Faraday rotation along the line of sight becomes increasingly important, and significant effects of the strength of the regular magnetic field and the density of thermal electrons are found." + This effect already occurs at low iuclination. where the hue-ofsight component of the magnetic field near the niajor axis increases proportionally to ἐν but the path leugth through the disk ~l/cos/ is coustaut to first order in ;.," This effect already occurs at low inclination, where the line-of-sight component of the magnetic field near the major axis increases proportionally to $i$, but the path length through the disk $\sim +1/\cos i$ is constant to first order in $i$." + The result is that models that tuchide Faraday depolarization predict ahiyher degree of polarization at low inclinations than models that do not iuclude Faraday depolarization (Stiletal.2007).., The result is that models that include Faraday depolarization predict a degree of polarization at low inclinations than models that do not include Faraday depolarization \citep{stil2007a}. +" The presen models also predict a higher fractional polarization a low inchuation if the electron deusitv 0, or the streneth of the regular maenetic field is iucreased. if the ratio of randoni magnetic field to regular maguctic field streueth is not too high."," The present models also predict a higher fractional polarization at low inclination if the electron density $n_e$ or the strength of the regular magnetic field is increased, if the ratio of random magnetic field to regular magnetic field strength is not too high." + The models more or less cover the same area of Figure laa as the data., The models more or less cover the same area of Figure \ref{diskpol_model-fig}a a as the data. + This result supports the idea tha the observed integrated polarization of spiral galaxies is related to the large-scale field in the disk., This result supports the idea that the observed integrated polarization of spiral galaxies is related to the large-scale field in the disk. + The mos notable difference between the data aud the models is the observed low Ty€2% of some galaxies with intermediate inclination. οςες607.," The most notable difference between the data and the models is the observed low $\Pi_0 +\lesssim 2\%$ of some galaxies with intermediate inclination, $40\degr +\lesssim i \lesssim 60\degr$." + Tt is difficult to change av suele parameter in the model to obtain a fractional polarization T=2% in this inchnation range. uuless lieher values of fj are assumed.," It is difficult to change any single parameter in the model to obtain a fractional polarization $\Pi +\lesssim 2\%$ in this inclination range, unless higher values of $f_{\rm B}$ are assumed." + The results iu the previous sections suggest that the integrated [8 GIIz enüssion of spiral galaxies can show substantial polarization., The results in the previous sections suggest that the integrated 4.8 GHz emission of spiral galaxies can show substantial polarization. + Deep polarization survevs cau detect distant unresolved spiral galaxies., Deep polarization surveys can detect distant unresolved spiral galaxies. + Wow niu spiral galaxies can be detected. and the interpretation of unresolved galaxies detected in polarization. is determined by the probability deusity fiction (PDF) of the fractional polarization of spiral galaxies.," How many spiral galaxies can be detected, and the interpretation of unresolved galaxies detected in polarization, is determined by the probability density function (PDF) of the fractional polarization of spiral galaxies." + The wavelength dependence of integrated polarization 1s also best sumunarized bv imeaus of the PDF of fractional polarization., The wavelength dependence of integrated polarization is also best summarized by means of the PDF of fractional polarization. + In this section we diseuss the expected shape of the PDF of fractional polarization for uuresolved spiral ealaxies at La GIIz aud 1.1 GITz., In this section we discuss the expected shape of the PDF of fractional polarization for unresolved spiral galaxies at 4.8 GHz and 1.4 GHz. + We also discuss the PDF of Wy in the special case of low-inclination ealaxics (/Xm 307). where the integrated polarization depends mostly ou Faraday dispersion. but the actual value of the inclination cannot be determuned reliably roni the optical axial ratio.," We also discuss the PDF of $\Pi_0$ in the special case of low-inclination galaxies $i \lesssim 30\degr$ ), where the integrated polarization depends mostly on Faraday dispersion, but the actual value of the inclination cannot be determined reliably from the optical axial ratio." + The models for the iutegrated fractional polarization as a function of inclination can be used to derive a xobabilitv density function (PDF) for Wy of uuresolved. randomly oriented spiral galaxies.," The models for the integrated fractional polarization as a function of inclination can be used to derive a probability density function (PDF) for $\Pi_0$ of unresolved, randomly oriented spiral galaxies." + This PDF cau be used o predict thenuniber of spiral galaxies detectable iu deep polarization surveys based on population models of he total intensity source comnts (Stiletal.2007).., This PDF can be used to predict thenumber of spiral galaxies detectable in deep polarization surveys based on population models of the total intensity source counts \citep{stil2007a}. + The shape of the PDF cau be modeled as a function of wavelength aud fitted to observations., The shape of the PDF can be modeled as a function of rest-frame wavelength and fitted to observations. + Taylorctal. used Moute-Carlo simulations of noise statistics and observational sclection effects. and derived the shape of the PDF for Il; for faint polarized sources from a πιααπ likelihood fit to the data.," \citet{taylor2007} used Monte-Carlo simulations of noise statistics and observational selection effects, and derived the shape of the PDF for $\Pi_0$ for faint polarized sources from a maximum likelihood fit to the data." + A similar approach can be usec in the future to compare the PDF of Wy for ealaxies at Ligh redshift with the PDF for local galaxies., A similar approach can be used in the future to compare the PDF of $\Pi_0$ for galaxies at high redshift with the PDF for local galaxies. + The PDF for Uy follows from the probability P(/) to observe a galaxy at inclination between / aud i|di. The probabilitv. to fud a fractional polarization between Wy aud Wy|AI is equal to the probability to findaealaxy with inclination in one of up to two inclination ranges Ai fo ὅμως that vield the same fractional polarization.," The PDF for $\Pi_0$ follows from the probability $P(i)$ to observe a galaxy at inclination between $i$ and $i+di$, The probability to find a fractional polarization between $\Pi_0$ and $\Pi_0+\Delta\Pi_0$ is equal to the probability to findagalaxy with inclination in one of up to two inclination ranges $i_{{\rm min}}$ to $i_{{\rm max}}$ that yield the same fractional polarization." +" Therefore. Iu most cases, [IN— 2. except at the παπι of I. where NV= 1."," Therefore, In most cases, $N=2$ , except at the maximum of $\Pi_0$ , where $N=1$ ." +The remaining viable texture structures which have phenomenological implications are 2D. 3E. 4B. GC. The corresponding values of ον. slo and Ay for these texture structures are given in Table 2.,"The remaining viable texture structures which have phenomenological implications are 2D, 3F, 4B, 6C. The corresponding values of $A_1$ , $A_2$ and $A_3$ for these texture structures are given in Table 2." + All these textures give normal. inverted aad quasidegenerate mass spectra.," All these textures give normal, inverted and quasidegenerate mass spectra." + For class 2DCNII. QD). we get unconstrained parameter space i.e. (here are no strong predictions.," For class 2D(NH, QD), we get unconstrained parameter space i.e. there are no strong predictions." +" However. for 2D(IID). the Dirac tvpe CP- violating phase ὁ is constrained to the range 90°—270"". while the Majorana twpe CP- violating phase a takes the value 0.180°."," However, for 2D(IH), the Dirac type CP- violating phase $\delta$ is constrained to the range $90^o - +270^o$, while the Majorana type CP- violating phase $\alpha$ takes the value $0^o, 180^o$." +" A lower bound on the Elfective Majorana mass AM,0.05 eV is obtained.", A lower bound on the Effective Majorana mass $M_{ee}> 0.05$ eV is obtained. +" The aüimospheric mixing angle. 054 lies below maximalily ie. Pa,«45° (Fig.3(a))."," The atmospheric mixing angle, $\theta_{23}$ lies below maximality i.e. $\theta_{23}< 45^o$ (Fig.3(a))." + Class 3F(111) has similar predictions and bounds for all parameters as in class 2D(III) except θ which is above maximal., Class 3F(IH) has similar predictions and bounds for all parameters as in class 2D(IH) except $\theta_{23}$ which is above maximal. +" For class 4B aud 6C. unconstrainecl parameter space is obtained [or inverted and quasidegenerate mass hierarchy,"," For class 4B and 6C, unconstrained parameter space is obtained for inverted and quasidegenerate mass hierarchy." + However. 4B(N11) and 6CCNILT) give some strong predictions for parameters under investigation.," However, 4B(NH) and 6C(NH) give some strong predictions for parameters under investigation." +" A lower bound. AZ,20.01 eV is obtained for both these cases.", A lower bound $M_{ee}> 0.01$ eV is obtained for both these cases. + The atmospheric mixing angle 954 is above maximal for 6C(NII) and below maximal for 4B(NID)., The atmospheric mixing angle $\theta_{23}$ is above maximal for 6C(NH) and below maximal for 4B(NH). +" There are some projects like Tokai- to- Ixamioka- NKorea (CI2IxXIxX) which plans to resolve the octant degeneracy of Ao; (i.e. 854—45° or Go,>45°) [25].", There are some projects like Tokai- to- Kamioka- Korea (T2KK) which plans to resolve the octant degeneracy of $\theta_{23}$ (i.e. $\theta_{23}<45^{o} $ or $\theta_{23}>45^{o}$ ) \cite{25}. +". All the phenomenologieally viable textures with a texture zero and a zero minor in V, discussed in (his work can be realized in a simple wav in models based on seesaw mechanism with a abelian flavor symmetry |14].", All the phenomenologically viable textures with a texture zero and a zero minor in $M_\nu$ discussed in this work can be realized in a simple way in models based on seesaw mechanism with a abelian flavor symmetry \cite{14}. +". For constructing the required leptonic mass matrices. we consider three left-handed Standard Model (SAL) lepton doublets D,,(a—1.2.3) aud three right handed charged lepton singlets /j,."," For constructing the required leptonic mass matrices, we consider three left-handed Standard Model (SM) lepton doublets $D_{La}$ (a=1,2,3) and three right handed charged lepton singlets $l_{Ra}$." + To this we add three right handed neutrino singlets rj; inorder to enable the see-saw mechanism for suppressing the neutrino masses., To this we add three right handed neutrino singlets $\nu_{Ra}$ inorder to enable the see-saw mechanism for suppressing the neutrino masses. + For each non zero entry in M; or My we need, For each non zero entry in $M_l$ or $M_D$ we need +disks which lave been resolved at present. observed structures have even been used to suggest the location of uuseen plauets.,"disks which have been resolved at present, observed structures have even been used to suggest the location of unseen planets." + Uunedreds more stars have had their disks characterised from their SEDs showing that these disks are the extrasolar equivalents of the Kuiper aud asteroid belts in the Solar System., Hundreds more stars have had their disks characterised from their SEDs showing that these disks are the extrasolar equivalents of the Kuiper and asteroid belts in the Solar System. + Iu this Legacy survey. we will use 390 hours of SCUBA- tune on the JOMT to observe 500 nearby. miadin-sequence stars to search for debris disk signatures.," In this Legacy survey, we will use 390 hours of SCUBA-2 time on the JCMT to observe 500 nearby main-sequence stars to search for debris disk signatures." + This survey will be the first unbiased one since IRAS. as xevious far-IR surveys have had to out many stars.," This survey will be the first unbiased one since IRAS, as previous far-IR surveys have had to omit many stars." + The crucial value of the swbuullimeter is that the stellar shotospheric signal is nvelevaut and so auv star cau jo examined., The crucial value of the submillimeter is that the stellar photospheric signal is irrelevant and so any star can be examined. + The output of our survey will be robust statistics ou the incidence of debris disks plus discovery of he nuderlving causes (in terms of the stellar cuvirommieut aud historv)., The output of our survey will be robust statistics on the incidence of debris disks plus discovery of the underlying causes (in terms of the stellar environment and history). + The nearer svstenis may also be resolved. contributing to planetary detection and planning for ulssious such as TPF/Darwin.," The nearer systems may also be resolved, contributing to planetary detection and planning for missions such as TPF/Darwin." + The data products will be unique. comprising deep and uniform searches for debris without amy bias owards particular stellar properties.," The data products will be unique, comprising deep and uniform searches for debris without any bias towards particular stellar properties." + This has never jen done at any waveleneth. and particularly not in the submillimeter where a new cold population of disks is barely explored.," This has never been done at any wavelength, and particularly not in the submillimeter where a new cold population of disks is barely explored." + The SUNSS will exceed the uodest. uubiased. Cedwarf SCUBA survey (Creaves&Wratt2003). bv forty-fold in stellar nuubers while cine substantially deeper.," The SUNSS will exceed the modest, unbiased G-dwarf SCUBA survey \citep{gw03} by forty-fold in stellar numbers while being substantially deeper." + The SCUBA-2 sensitivity will approach the I&uiper belt dust level for the closest Solar analogues: a disk around these targets could actually ο detected in our survey before the equivalent has COL mapped around the Sun., The SCUBA-2 sensitivity will approach the Kuiper belt dust level for the closest Solar analogues; a disk around these targets could actually be detected in our survey before the equivalent has been mapped around the Sun. + The survey can never be done better until laree far-IR telescopes fly in space resolving the disk spatially from the stellar photosphere a prospect cousicderably downstream of JWST., The survey can never be done better until large far-IR telescopes fly in space – resolving the disk spatially from the stellar photosphere – a prospect considerably downstream of JWST. +" The Science Legacy lies in answers to the five kev outconies: With these answers iu παπα, we will be able to nuderstaud for the first time the relation of debris disks tracing planetesimals up to tens of km across iu orbits at tens of AU to the inner planetary systems detected by other methods."," The Science Legacy lies in answers to the five key outcomes: With these answers in hand, we will be able to understand for the first time the relation of debris disks – tracing planetesimals up to tens of km across in orbits at tens of AU – to the inner planetary systems detected by other methods." + The results. especially when combined with shorter waveleneth data to coustrain teniperature and mass. will test mocels of plauct formation spanning across the scale of our Solar System (from inside Alereurvs orbit to bevoud Neptune's).," The results, especially when combined with shorter wavelength data to constrain temperature and mass, will test models of planet formation spanning across the scale of our Solar System (from inside Mercury's orbit to beyond Neptune's)." + The images of disks will be followed iu the next decade by ligh-resolution inagiug that may indicate perturbing plaucts. even following their orbital perturbations iu real time.," The images of disks will be followed in the next decade by high-resolution imaging that may indicate perturbing planets, even following their orbital perturbations in real time." + The results will be vital for the detection of extrasolar Earths with coronaeraplis., The results will be vital for the detection of extrasolar Earths with coronagraphs. +eq. (8)),eq. \ref{eq:sfr}) ) + this leads to a global birthrate for the group of bicc0.15., this leads to a global birthrate for the group of $b_{\rm tot} \simeq 0.15$. +" To much extent, such a low figure is mostly induced by the prevailing contribution of early-type galaxies among the more massive members of the NGC 5044 group (see the disaggregated distribution of Fig. 9))."," To much extent, such a low figure is mostly induced by the prevailing contribution of early-type galaxies among the more massive members of the NGC 5044 group (see the disaggregated distribution of Fig. \ref{f9}) )." +" As a result, animportant fraction of resides in nearly quiescent stellar aggregates (see Fig. M;,)(tot)10)),"," As a result, animportant fraction of $M^*_{\rm gal}({\rm tot})$ resides in nearly quiescent stellar aggregates (see Fig. \ref{f10}) )," + while only very low-mass systems (mostly dSph and Im types) are still able to feed fresh stars to the global environment., while only very low-mass systems (mostly dSph and Im types) are still able to feed fresh stars to the global environment. +" Even at this small mass scale, therefore, the emerging picture seems consistent with the so-called down-sizing mechanism (Cowieetal.1996;Gavazzi 1993),, that is an inverse dependence of the birthrate with galaxy mass as the imposing paradigm for galaxy formation in the Universe."," Even at this small mass scale, therefore, the emerging picture seems consistent with the so-called down-sizing mechanism \citep{cowie96,gavazzi93}, that is an inverse dependence of the birthrate with galaxy mass as the imposing paradigm for galaxy formation in the Universe." +" A preliminary analysis of the spectroscopic material collected along our survey has already been provided in Cellone&Buzzoni(2005,seeTable1therein),, where redshift measurements have been presented for 14 galaxies of the sample."," A preliminary analysis of the spectroscopic material collected along our survey has already been provided in \citet[][see Table~1 therein]{cb05}, where redshift measurements have been presented for 14 galaxies of the sample." +" For a total of 10 objects, the paper confirmed group membership, while 4 galaxies resulted to lie in the background."," For a total of 10 objects, the paper confirmed group membership, while 4 galaxies resulted to lie in the background." +" After thorough reconsideration of the data, also including the observing sessions, we can further expand here the original output by including 7 more objects, for which a confident redshift measure can be obtained together with a rough morphological classification according to the detected spectral features."," After thorough reconsideration of the data, also including the observing sessions, we can further expand here the original output by including 7 more objects, for which a confident redshift measure can be obtained together with a rough morphological classification according to the detected spectral features." +" For a further set of 3 spectra no definite conclusions can be achieved, mostly due to the extremely poor S/N level."," For a further set of 3 spectra no definite conclusions can be achieved, mostly due to the extremely poor S/N level." +" Our spectroscopic results, then, extend and complement the works of Mendeletal.(2008, 2009),, which provided 103 (mostly new) redshifts for galaxies in the NGC 5044 Group catalog, as well as a stellar population analysis through Lick indices for a subset of 67 groupmembers."," Our spectroscopic results, then, extend and complement the works of \citet{mendel08,mendel09}, which provided 103 (mostly new) redshifts for galaxies in the NGC 5044 Group catalog, as well as a stellar population analysis through Lick indices for a subset of 67 groupmembers." +" The summary of our results is presented in Table 7,, which also recollects the data of Cellone&Buzzoni(2005) for reader's better convenience."," The summary of our results is presented in Table \ref{t7}, which also recollects the data of \citet{cb05} for reader's better convenience." +" Out of the 25 objects considered by the observations, 10 galaxies, plus NGC 5044, belong to the same physical group, while behind one may guess the presence of at least three galaxy aggregations, that also match the Mendeletal.(2008) data, located respectively at z~0.045,0.095, and 0.28, the farthest one actually confirmed by the coherent X-ray emission studied by XMM-Newton (Gastaldelloetal.2007a)."," Out of the 25 objects considered by the observations, 10 galaxies, plus NGC 5044, belong to the same physical group, while behind one may guess the presence of at least three galaxy aggregations, that also match the \citet{mendel08} data, located respectively at $z \sim 0.045, 0.095$, and 0.28, the farthest one actually confirmed by the coherent X-ray emission studied by XMM-Newton \citep{gastaldello07}." +". The most distant galaxy in our sample is object B5, located at z=0.42."," The most distant galaxy in our sample is object B5, located at $z = 0.42$." +" According to Table 7,, a roughly similar fraction of member and background galaxies is not a surprising feature, of course, given our observing strategy, that included a “bonus” object for each target pointing, as explained in Sec."," According to Table \ref{t7}, a roughly similar fraction of member and background galaxies is not a surprising feature, of course, given our observing strategy, that included a “bonus” object for each target pointing, as explained in Sec." + 2.2., 2.2. +" In this regard we stress the very high reliability of morphological membership assignment by Ferguson&Sandage (1990),, which reaches ~91% for Me=1 galaxies (Mendeletal. 2008).."," In this regard we stress the very high reliability of morphological membership assignment by \citet{fs90}, , which reaches $\sim 91$ for $m_c=1$ galaxies \citep{mendel08}. ." +" As a reference for possible future investigations, we report in Table A5 the"," As a reference for possible future investigations, we report in Table \ref{a4} the" +The outbursts of long period X-ray binaries involve accretion rates close to the Eddington limit.,The outbursts of long period X-ray binaries involve accretion rates close to the Eddington limit. + Consequently. the evolution of the massive accretion discs in these objects is expected to be highly influenced by mass loss and irradiation by the central X-ray source.," Consequently, the evolution of the massive accretion discs in these objects is expected to be highly influenced by mass loss and irradiation by the central X-ray source." + Outbursts of this nature are thought to power the most luminous stellar X-ray sources such as the galactic microquasars and at least some of the recently discovered ultra-Iuminous X-ray sources in nearby galaxies (King.2002)., Outbursts of this nature are thought to power the most luminous stellar X-ray sources such as the galactic microquasars and at least some of the recently discovered ultra-luminous X-ray sources in nearby galaxies \citep{kin02}. +.. In this paper we investigate the evolution of accretion dises and the origin of the long-term variability in the outbursts of long period X-ray transients. using the galactic microquasar GRS 19154105 as an example system.," In this paper we investigate the evolution of accretion discs and the origin of the long-term variability in the outbursts of long period X-ray transients, using the galactic microquasar GRS 1915+105 as an example system." + The galactic mieroquasar GRS 19154105 (V1I487 Αα) was discovered as an X-ray transient in 1992 (Castro-Tirado.Brandt&Lundt 1992).. and has been observed to be extremely luminous ever since.," The galactic microquasar GRS 1915+105 (V1487 Aql) was discovered as an X-ray transient in 1992 \citep{cas}, and has been observed to be extremely luminous ever since." + This binary system contains a 14 AL. black hole (Greiner.Cuby&MeCaughrean2001) accreting from a late-type giant of mass 0.5+0.5ML. (Harlaftis&Greiner2004). via Roche lobe overflow., This binary system contains a 14 $\msol$ black hole \citep{gre01a} accreting from a late-type giant of mass $0.8 \pm 0.5 \msol$ \citep{har} via Roche lobe overflow. + GRS 19154103 is unique among accreting Galactic black 10les spending much of its time at super-Eddington luminosities (Done.Wardzinski&Gierlinski2004)., GRS 1915+105 is unique among accreting Galactic black holes spending much of its time at super-Eddington luminosities \citep{don}. + It is an extremely variable source. exhibiting dramatic. aperiodie variability on a wide range of imescales. from milliseconds to months.," It is an extremely variable source, exhibiting dramatic, aperiodic variability on a wide range of timescales, from milliseconds to months." + Figure | shows the Rossi X-ray Timing Explorer All-Sky Monitor observations of X-ray flux rom GRS 19154103 over the past decade., Figure \ref{obs} shows the Rossi X-ray Timing Explorer All-Sky Monitor observations of X-ray flux from GRS 1915+105 over the past decade. + The fundamental origin of this spectacular behaviour is hought to be an outburst similar to those exhibited by other X- transients. but of a much longer duration.," The fundamental origin of this spectacular behaviour is thought to be an outburst similar to those exhibited by other X-ray transients, but of a much longer duration." + The outbursts of X-ray transients are believed to be initiated by a thermal-viscous accretion dise instability. and prolonged by the heating effect of the central. irradiating X-ray source (King&Ritter1998:Dubus.Hameury&Lasota2001:Trussetal. 2002).," The outbursts of X-ray transients are believed to be initiated by a thermal-viscous accretion disc instability, and prolonged by the heating effect of the central, irradiating X-ray source \citep{kin98,dub,tru02}." +. The extremely long time-scale of the outburst of GRS 19154105 is a consequence of its long 33.5 day orbital period. which implies a very large dise size Rane~31077 cm).," The extremely long time-scale of the outburst of GRS 1915+105 is a consequence of its long 33.5 day orbital period, which implies a very large disc size $R_{\rmn{disc}} \sim 3 \times 10^{12}~\rmn{cm}$ )." + Such a large dise can accumulate an enormous amounto of mass during quiescence. which is able to support a subsequent super-Eddington outburst over many decades.," Such a large disc can accumulate an enormous amount of mass during quiescence, which is able to support a subsequent super-Eddington outburst over many decades." + So far. most models of the variability of GRS 19154105 have concentrated on explaining the origin of the short time-scale luminosity changes associated with the inner regions of the accretion dise (for example. Belloni et al.," So far, most models of the variability of GRS 1915+105 have concentrated on explaining the origin of the short time-scale luminosity changes associated with the inner regions of the accretion disc (for example, Belloni et al." + 1997). although Kingetal.(2004) have proposed a mechanism for generating variability on a wider range of time-scales. in which outflows of mass from the dise are driven by localised magnetic dynamo processes.," 1997), although \citet{kin04} have proposed a mechanism for generating variability on a wider range of time-scales, in which outflows of mass from the disc are driven by localised magnetic dynamo processes." + However. the origin of longer-term. aperiodic variations on timescales of hundreds of days remain poorly understood as these are most likely driven by dynamical evolution of the outer disc.," However, the origin of longer-term, aperiodic variations on timescales of hundreds of days remain poorly understood as these are most likely driven by dynamical evolution of the outer disc." + In this paper we present the results of two-dimensional (2D) calculations of the long-term evolution of an accretion dise in a long-period X-ray binary accreting close to the Eddington limit. using GRS 191541053 as an example system.," In this paper we present the results of two-dimensional (2D) calculations of the long-term evolution of an accretion disc in a long-period X-ray binary accreting close to the Eddington limit, using GRS 1915+105 as an example system." + We include the effects of tidal instability. central irradiation and mass loss on the dise evolution.," We include the effects of tidal instability, central irradiation and mass loss on the disc evolution." + We show that the interplay of these effects in the outer regions of the disc can induce similar variability to that observed in GRS 19154105., We show that the interplay of these effects in the outer regions of the disc can induce similar variability to that observed in GRS 1915+105. + In this section we discuss several key refinements that have been made to an existing smooth particle hydrodynamics (SPH) code., In this section we discuss several key refinements that have been made to an existing smooth particle hydrodynamics (SPH) code. + SPH is a Lagrangian scheme used to describe the dynamics of fluid flow., SPH is a Lagrangian scheme used to describe the dynamics of fluid flow. + A continuous gas is described by an ensemble of particles moving with the local fluid velocity., A continuous gas is described by an ensemble of particles moving with the local fluid velocity. + Local properties such as velocity. density and temperature are determined by an interpolation over the neighbouring particles and in this way the fluid equations may be solved.," Local properties such as velocity, density and temperature are determined by an interpolation over the neighbouring particles and in this way the fluid equations may be solved." + In the continuum limit (that is. for a large enough number of neighbour particles). the SPH equations," In the continuum limit (that is, for a large enough number of neighbour particles), the SPH equations" +We also quantilv the distinction between tighüly aud loosely wound circimmnuclear spirals by setting aas the delineation between “small” and “laree” pitch angles.,We also quantify the distinction between tightly and loosely wound circumnuclear spirals by setting as the delineation between “small” and “large” pitch angles. + This division roughly corresponds to that of Sb galaxies (Nennicut( 1931)., This division roughly corresponds to that of Sb galaxies (Kennicutt 1981). + Previously. the differentiation between TW aud LW was done purely bv eve. and also took into account arm morphology.," Previously, the differentiation between TW and LW was done purely by eye, and also took into account arm morphology." +" Specifically. for a nuclear spiral to be classified as ""σαι wound.” the arms had to be traceable through al least one complete revolution. aud therefore the classification was potentially subject to signal-to-noise ratio bias (for an arm to remain coherent about an entire revolution. aud thus be classified as TW. a hisher SNR was needed)."," Specifically, for a nuclear spiral to be classified as “tightly wound,” the arms had to be traceable through at least one complete revolution, and therefore the classification was potentially subject to signal-to-noise ratio bias (for an arm to remain coherent about an entire revolution, and thus be classified as TW, a higher SNR was needed)." + We measure pitch angles wilh an interactive PGPlot program which fits logarithmic spirals (to a deprojected image of (he structure map., We measure pitch angles with an interactive PGPlot program which fits logarithmic spirals to a deprojected image of the structure map. + Five points of increasing radius on a single prominent spiral arm of the galaxy. are chosen within an annulus given by of the bulge radius. or of of D»; if the galaxy is either bulgeless or there is no available effective bulge radius The program then fils logarithmic spirals to each consecutive pair of points. averaging the resulting four pitch angles to give the pitch angle lor the entire arm.," Five points of increasing radius on a single prominent spiral arm of the galaxy are chosen within an annulus given by of the bulge radius, or of of $D_{25}$ if the galaxy is either bulgeless or there is no available effective bulge radius The program then fits logarithmic spirals to each consecutive pair of points, averaging the resulting four pitch angles to give the pitch angle for the entire arm." + As found by Kennieutt(1981). for spirals. (he nuclear spirals are not well fit bv logarithmic spiralsa given arm does nol have constant pitch angle as a function of radius.," As found by \citet{kennicutt81} for large-scale spirals, the nuclear spirals are not well fit by logarithmic spirals—a given arm does not have constant pitch angle as a function of radius." +" Still. (his method vields an ""average"" pitch angle for (he arm."," Still, this method yields an “average” pitch angle for the arm." + The observed non-constant pitch angle along a spiral arm implies that (he region is experiencing differential rotation which is inconsistent wilh constant rotational velocily (Alaciejewski2004).., The observed non-constant pitch angle along a spiral arm implies that the region is experiencing differential rotation which is inconsistent with constant rotational velocity \citep{maciejewski04a}. + We also note that the pitch angle often varies between clilferent arms in a single galaxy., We also note that the pitch angle often varies between different arms in a single galaxy. + Notwithstanding (hese caveats. we find that this method sulffices for determining whether or not the pitch angle is above or below107.. thus cdifferentiating between TW and LW nuclear spirals.," Notwithstanding these caveats, we find that this method suffices for determining whether or not the pitch angle is above or below, thus differentiating between TW and LW nuclear spirals." +" Finally. the ""central region” used in classifving the N class of objects was previously defined as a ""few hundred parsecs” (Martiniοἱal.2003a)."," Finally, the “central region” used in classifying the N class of objects was previously defined as a “few hundred parsecs” \citep{martini03a}." +. We have clarified this so that (he central region is specific to each galaxy. namely. a circle of radius r..," We have clarified this so that the central region is specific to each galaxy, namely, a circle of radius $r_c$." + While in general ihe entire region within 0.0505; is used [or classification. the region within r. is also used as a guide in deciding between different classifications: if a galaxy is seen to have a different morphology al small radii (han at large radii. such as is seen in NGCLOGS. the classification ab small racii is used.," While in general the entire region within $0.05D_{25}$ is used for classification, the region within $r_c$ is also used as a guide in deciding between different classifications; if a galaxy is seen to have a different morphology at small radii than at large radii, such as is seen in NGC1068, the classification at small radii is used." + This decision also led to changes in the classifications of several galaxies from those reported in previous papers., This decision also led to changes in the classifications of several galaxies from those reported in previous papers. + Though this distinction is subject to the definition ol r.. only two galaxies. Νας10605 and NGC3227. would have their classifications changed (LW to C and CS to C. respectively) if r7. were defined to be of Da; for all galaxies.," Though this distinction is subject to the definition of $r_c$, only two galaxies, NGC1068 and NGC3227, would have their classifications changed (LW to C and CS to C, respectively) if $r_c$ were defined to be of $D_{25}$ for all galaxies," +] avoid positions at the first NAM tine step. nlL. because the treatinent of the initial condition in equaion (3.2)) iu the discrete form in equation (3.2)) is a rough approxi:αἱlon.,"I avoid positions at the first NAM time step, $n=1$, because the treatment of the initial condition in equation \ref{eq:eomi}) ) in the discrete form in equation \ref{eq:NAMi}) ) is a rough approximation." + The forward fromH these Hinitialm conditionsm a De2000 time steps leaso well reoroduces t j»resent. positions of the massive bodies οἱven to the NAN computation., The forward from these initial conditions at $p_x=2000$ time steps reasonably well reproduces the present positions of the massive bodies given to the NAM computation. + computed positio ‘the LMC is more in e‘ror. typically by a ew tens of kilop:usecs.," The computed position of the LMC is more in error, typically by a few tens of kiloparsecs." + Since t comparable to the ‘eset clisance between the LMC and MW it must be corrececd. and the si perturbation to t yath of A131 by the LNC inay be co‘rectecLioo.," Since that is comparable to the present distance between the LMC and MW it must be corrected, and the smaller perturbation to the path of M31 by the LMC may be corrected too." +" This is do1 by adjustir initial te, bet le SIX Cartesian Components of tle differences between the comp present galactocentric positious of the LMC aud M31 anc the &iven present positious.", This is done by adjusting the initial Let $e_a$ be the six Cartesian components of the differences between the computed present galactocentric positions of the LMC and M31 and the given present positions. + Write t components of the iritial positious of these two galaxies as rg., Write the six components of the initial positions of these two galaxies as $r_b$. +" Nuimericaly comyute the clerivativ dap=Oe,fry."," Numerically compute the derivatives $d_{a,b}=\partial e_a/\partial r_b$." +" Livet this 6 by 6 matrix to get corrections to the initia j»ositions. dr,EHd,con"," Invert this 6 by 6 matrix to get corrections to the initial positions, $\delta r_b=-\beta d^{-1}_{b,c}e_c$." + [t helps to let the constant? be less than unity for a ew iterations. ater which ;?=1 usually quickly drives the present. positious Crom the forward iitegration to tle positious given to NANI to machine precision.," It helps to let the constant $\beta$ be less than unity for a few iterations, after which $\beta=1$ usually quickly drives the present positions from the forward integration to the positions given to NAM to machine precision." + This procedure slightly perturbs he present posiion of the third massive body. but that does not matter because this position was chosen at random in the search for an acceptable solution.," This procedure slightly perturbs the present position of the third massive body, but that does not matter because this position was chosen at random in the search for an acceptable solution." + The LC galaxies are assigned present heliocentric positious = 121.171. bb = —21.573. dd = = 20.165. bb = —32.888. dd = = 302.707. bb = —11.299. dd =," The LG galaxies are assigned present heliocentric positions = 121.174, b = -21.573, d = = 280.465, b = -32.888, d = = 302.797, b = -44.299, d =" +The esseutial clement of thie cooling flow problem is that iu the ceuters of galaxy chsters the intracluster medi (ICAI) should cool on a timescale much shorter than the Πιο]e time (Fabian1991).,The essential element of the cooling flow problem is that in the centers of galaxy clusters the intracluster medium (ICM) should cool on a timescale much shorter than the Hubble time \citep{fabian94}. +. However. observational evidence from aud revealed that only reatively sinall amounts of eas cools to low temperatures (Davidetal.2001:Peterson2003:Ikaastraetal.2(00 0).," However, observational evidence from and revealed that only relatively small amounts of gas cools to low temperatures \citep{david01,peterson03,kaastra04}." +.. The most commonly accepted resolution of this prodenm is the (2cheating of the ICAL by the central active ealactic uucleus (ACN)(c.g.miChu-razovetal.2001:Peerson&Fal," The most commonly accepted resolution of this problem is the (re)heating of the ICM by the central active galactic nucleus (AGN) \citep[e.g.][]{churazov01,peterson06}." +ian 2006).. ealaxy clusters the most direct signature of the interaction of AGN outbursts aud he ICM is the detection of ταν cavities (e.g.Bochrinecretal.1993:Forman2005).," In galaxy clusters the most direct signature of the interaction of AGN outbursts and the ICM is the detection of X-ray cavities \citep[e.g.][]{boehringer93,forman05}." +. Outbursts fom powerful radio sources can significantly increase the eutropy of the ICAL thereby inflating the eas distribution aud reducing the eas density., Outbursts from powerful radio sources can significantly increase the entropy of the ICM thereby inflating the gas distribution and reducing the gas density. + Hence at the position of radio lobes a decrement in the X-ray surface brightness becomes observable., Hence at the position of radio lobes a decrement in the X-ray surface brightness becomes observable. + Abell 191. shown in Fig. l.," Abell 194, shown in Fig. \ref{fig:dss_image}," +" is a poor cluster at a redshift of 2=0.018. aud hosts two lIuuuuous racio sources, 3€ LOB (wide anele tail radio galaxy WAT). associated with NCCSL7. aud 3€ LOA (nazrow angle tail radio galaxy NAT). associated with NCC5 (O'Deaetal 1985)."," is a poor cluster at a redshift of $z=0.018$, and hosts two luminous radio sources, 3C 40B (wide angle tail radio galaxy – WAT), associated with NGC547, and 3C 40A (narrow angle tail radio galaxy – NAT), associated with NGC541 \citep{odea85}." + The jet cimanatine from theLL latter is believed tobe respousible for triggering star-foriiation i Aliukowski* Object(wanBreugecletal.L985:Brodical. 1985).," The jet emanating from the latter is believed to be responsible for triggering star-formation in Minkowski's Object \citep{breugel85,brodie85}." +". The ""uded [-alpha emissiou from 3€ 10D (e.g.Daunetal.LOSS) is associated with a dust disk aud diffuse UY emission (Allenetal.2002).. the latter likely due to star formation."," The extended H-alpha emission from 3C 40B \citep[e.g.][]{baum88} is associated with a dust disk and diffuse UV emission \citep{allen02}, the latter likely due to star formation." + The nucleus is not detected at 11.5 mücrons (vanderWolketal.2010) and the optical cnussion Lue spectrum is low excitation (Duttiglioneetal.2009. 2010).. which indicate that the AGN accretion disk is faint = cousisteut with a low accretion rate.," The nucleus is not detected at 11.8 microns \citep{wolk10} and the optical emission line spectrum is low excitation \citep{buttiglione09,buttiglione10}, which indicate that the AGN accretion disk is faint – consistent with a low accretion rate." + Abcll 19 Lis one of the most striking “linear” clusters of ealaxies. as its ealaxv distribution aud X-ray cussion are both linearly elongated along the northeast-soutlivest direction (Chapmanetal.1988:Nikogossvinct1999:Jones&Forman 1999).," Abell 194 is one of the most striking “linear” clusters of galaxies, as its galaxy distribution and X-ray emission are both linearly elongated along the northeast-southwest direction \citep{chapman88,nikogossyan99,jones99}." + The optical bridge between NGOC515/NGC5[7 and δις (Croftctal.2006) indicates past and/or recent interactions.ο thereby sugeesting that Abell 191 is not a relaxed cluster.," The optical bridge between NGC545/NGC547 and NGC541 \citep{croft06} indicates past and/or recent interactions, thereby suggesting that Abell 194 is not a relaxed cluster." + As a consequence of the linear distribution of Abell 19L. it has uot been clear whether any of the massive radio galaxies are in the center of the cluster. aud whether Abell 191 is uudereoius a major merger event.," As a consequence of the linear distribution of Abell 194, it has not been clear whether any of the massive radio galaxies are in the center of the cluster, and whether Abell 194 is undergoing a major merger event." + Receutlv.," Recently," +Our hypothesis is that such fundamental mechanism is (he mass hierarchy. in fermions or possibly neutrinos.,Our hypothesis is that such fundamental mechanism is the mass hierarchy in fermions or possibly neutrinos. + If (hose black holes are formed by the overweight FDFSs. we can estimate ihe masses of those neutrinos as in Table 2.," If those black holes are formed by the overweight FDFSs, we can estimate the masses of those neutrinos as in Table 2." + The corresponding masses of fermions. except ος. ος] Eq.(1)) ave [ar heavier (han eV and we may iclentify those fermions as more massive sterile neutrinos.," The corresponding masses of fermions, except $\nu _{e,\mu ,\tau }$, through \ref{Mfermi}) ) are far heavier than eV and we may identify those fermions as more massive sterile neutrinos." + Lighter neutrino of mass LOb=10.7 eV would vield FDFSs much extended dilute structures whose sizes well exceed the Horizon size., Lighter neutrino of mass $10^{-1}-10^{-3}$ eV would yield FDFSs much extended dilute structures whose sizes well exceed the Horizon size. + In the above. we have approximate values.," In the above, we have approximate values." + However. the lower limit of the black hole mass within a class vields (he precise value of the corresponding neutrino mass.," However, the lower limit of the black hole mass within a class yields the precise value of the corresponding neutrino mass." + The existence of such a lower limit would be the kev ingredient of the FDFS model., The existence of such a lower limit would be the key ingredient of the FDFS model. + We have examined the possible structures formed bv the fully degenerate sell-gravitating fermions (FDFS) at various scales. such as the mass concentration of a cluster of galaxies. the eiat black holes at the center of à galaxy and the intermediate black holes in galaxies.," We have examined the possible structures formed by the fully degenerate self-gravitating fermions (FDFS) at various scales, such as the mass concentration of a cluster of galaxies, the giant black holes at the center of a galaxy and the intermediate black holes in galaxies." + As an order estimation. their characteristic masses directly reflect the constituent fermion masses through the simple. relation.. Mp;=Gοly»?-m/m.," As an order estimation, their characteristic masses directly reflect the constituent fermion masses through the simple relation, $M_{fermi}=G^{-3/4}m^{-2}=m_{pl}^{3}/m^{2}$." + For (he purpose. of. a «quantitative. analvsis. exact masses and detailed mass densitwv profiles of FDFSs were examined from nonrelativistic to relativistic situation. using (he formalism of Oppenheimer ancl VolkolL.," For the purpose of a quantitative analysis, exact masses and detailed mass density profiles of FDFSs were examined from nonrelativistic to relativistic situation, using the formalism of Oppenheimer and Volkoff." + These results were applied to the cluster of galaxies. ALGS9. whose mass distribution has been observationally obtained.," These results were applied to the cluster of galaxies, A1689, whose mass distribution has been observationally obtained." + We converted the observed. column density profile to a volume density. profile assuming spherical symmetry. ancl compared the observed and model 3D encircled mass profiles.," We converted the observed column density profile to a volume density profile assuming spherical symmetry, and compared the observed and model 3D encircled mass profiles." + We found that the f[Iat-top nature of the observed. profile is reproduced by (he model and the particle mass range is between 2 eV and 30 eV depending on (he actual seale of the degenerate structure., We found that the flat-top nature of the observed profile is reproduced by the model and the particle mass range is between 2 eV and 30 eV depending on the actual scale of the degenerate structure. + For about black holes. our scenario will provide alternative mechanism of the black hole formation.," For about black holes, our scenario will provide alternative mechanism of the black hole formation." + Most of the present theories assume (he coalescence of stellar mass black holes in the gravitational potential., Most of the present theories assume the coalescence of stellar mass black holes in the gravitational potential. + Such processes seem (o be quite complex compared to the FDFS scenario. ancl therefore it would be much difficult to explain. lor example. the observed. universal relation between the black hole mass at the center of a galaxy and the bulee mass: Mg/My;&0.002. This point will be discussed in detail in our future work.," Such processes seem to be quite complex compared to the FDFS scenario, and therefore it would be much difficult to explain, for example, the observed universal relation between the black hole mass at the center of a galaxy and the bulge mass: $M_{BH}/M_{bul} +\approx 0.002.$ This point will be discussed in detail in our future work." + We thank Nobuo Arimoto lor comments on the manuscript., We thank Nobuo Arimoto for comments on the manuscript. + This study was motivated bv a very interesting talk given by Tom DBroadhurst in 2004 at NAOJ. Mitaka. Japan.," This study was motivated by a very interesting talk given by Tom Broadhurst in 2004 at NAOJ, Mitaka, Japan." +10565|2118). 12 mergers. aud { old mnereers.,"10565+2448), 12 mergers, and 4 old mergers." + The ULIRGS in the merger stage tend to present higher surface brightucss. so our analysis of spatial eradicuts in Daher absorption is heavily weighted towards this merger phase.," The ULIRGS in the merger stage tend to present higher surface brightness, so our analysis of spatial gradients in Balmer absorption is heavily weighted towards this merger phase." + We examined the positional dependence of the lue profile using ai sliding aperture for spectral extraction., We examined the positional dependence of the line profile using a sliding aperture for spectral extraction. + We matched the aperture width to a seenmg element (~ 07.8) and extracted a spectrim at each line of he spectrogram., We matched the aperture width to a seeing element $\sim0''.8$ ) and extracted a spectrum at each line of the spectrogram. + At some spatial positions. as illustrated in Fie. l..," At some spatial positions, as illustrated in Fig. \ref{fig:hbprofile}," + the spectra present a two-compoucut iue profile., the spectra present a two-component line profile. + A broad absorption trough underlies the jurow Cluission line., A broad absorption trough underlies the narrow emission line. + We ft the absorption and Cluission colmponcuts siuultauecouslv using non-linear cast-squares fitting with AIPFIT in IDL., We fit the absorption and emission components simultaneously using non-linear least-squares fitting with MPFIT in IDL. + These spectra exhibit countiuuous chanec from position to position due o atinospheric smieariug. so parameters found from fitting one aperture position were supplied as the euess or the fit of the next position.," These spectra exhibit continuous change from position to position due to atmospheric smearing, so parameters found from fitting one aperture position were supplied as the guess for the fit of the next position." + The simall. gray poiutsiu Figure 2 show the result.," The small, gray pointsin Figure \ref{fig:ew_im} show the result." +" Over scales of a few kpc. this analysis often reveals an merease in aabsorption cquivalent width.j,5.. with distance from the peak coutiuuun emission iu the Ro baud."," Over scales of a few kpc, this analysis often reveals an increase in absorption equivalent width, with distance from the peak continuum emission in the R band." + To cliaminate effects due to correlated errors we extracted spatially separated spectra based on the shape of these racial aabsorptiou and continuum surface brightness trends.," To eliminate effects due to correlated errors, we extracted spatially separated spectra based on the shape of these radial absorption and continuum surface brightness trends." +" These spectra are shown in Figure 3.. where the larger black points in Figure 2. show the aabsorptiou equivalent width obtained by fitting these spectra,"," These spectra are shown in Figure \ref{fig:stack_09111}, where the larger black points in Figure \ref{fig:ew_im} show the absorption equivalent width obtained by fitting these spectra." + We measured ssurface brightness in these same apertures., We measured surface brightness in these same apertures. + The Ines could only. be fitted iu more than 3 apertures for oue object., The lines could only be fitted in more than 3 apertures for one object. + To correct the eenission for unudoerlviug stellar aabsorption. we measured the aabsorptiou equivaleut width aud assumed the aabsorptiou equivalent width was two-thirds as larec.," To correct the emission for underlying stellar absorption, we measured the absorption equivalent width and assumed the absorption equivalent width was two-thirds as large." + Tuspection of svuthetic spectra computed for stellar population inodels (7) verified that this scaling works over a broad range of star formation models. including those with truncated star formation histories.," Inspection of synthetic spectra computed for stellar population models \citep{bc03} verified that this scaling works over a broad range of star formation models, including those with truncated star formation histories." + The masxiunun value of the correction.3A.. is small compared to the emission equivalent width.," The maximum value of the correction, is small compared to the emission equivalent width." + The flux iu eenission is also corrected for extinction., The flux in emission is also corrected for extinction. + We determined the color excess. E(B V). per aperture by measuring the Balmer decrement aud using a standard reddening law (Ry = LOS = Ay-/E(B V)) aud the extinction law from ?..," We determined the color excess, E(B – V), per aperture by measuring the Balmer decrement and using a standard reddening law $_V$ = 4.05 = $_V$ /E(B – V)) and the extinction law from \cite{calzetti00}." + When significant. we discuss the correction for atteuuation by Galactic dust ou a galaxy-by-galaxy basis in Section 3.2..," When significant, we discuss the correction for attenuation by Galactic dust on a galaxy-by-galaxy basis in Section \ref{sect:spat_res}. ." + We estimate areal star formation, We estimate areal star formation +"Combining the equations (2)). (3)) and (9)) we can express µ in terms of the sound speed ce; as Accordingly. the energy of the flow £ in equation (3)) can be explicitly rewritten as a [function of e, which is conserved along the flow except at a shock front.","Combining the equations \ref{eq:polytropic}) ), \ref{eq:mu}) ) and \ref{eq:sound}) ) we can express $\mu$ in terms of the sound speed $c_s$ as Accordingly, the energy of the flow $E$ in equation \ref{eq:energy}) ) can be explicitly rewritten as a function of $c_s$ which is conserved along the flow except at a shock front." + That is. across a shock Iront. the enerev / and the angular momentum £ will both decrease in such a wav that the ratio =L/E is continuous across (he shock.," That is, across a shock front, the energy $E$ and the angular momentum $L$ will both decrease in such a way that the ratio $\lambda \equiv L/E$ is continuous across the shock." + Using equation (3)) and (10)) the barvon rest-1nass density can be rewritten as We define the mass-accretion rate AL as where // represents the vertical scale-heieht of the flow defined as from the conventional hydrostatic equilibrium assumption., Using equation \ref{eq:mu}) ) and \ref{eq:mu2}) ) the baryon rest-mass density can be rewritten as We define the mass-accretion rate $\dot{M}$ as where $H$ represents the vertical scale-height of the flow defined as from the conventional hydrostatic equilibrium assumption. + Here. am?) is the Weplerian angular velocity.," Here, $\Omega_K(r) \equiv m^{1/2}/(r^{3/2}+a m^{1/2})$ is the Keplerian angular velocity." + Note that for accretion we have 4<0., Note that for accretion we have $u^r<0$. + As often assumed. we only consider a constant mass-accretion rate in (his paper. alihough a variable accretion rate has been discussed in the literature. (e.g..Blandford&|Degelman.1999).," As often assumed, we only consider a constant mass-accretion rate in this paper, although a variable accretion rate has been discussed in the literature \citep[e.g.,][]{BB99}." +. Eliminating py from equations (12)) and (13)) we rewrite 1 as Similarly to. / and L. the mass-accretion rate M is also conserved along the flow except at à shock location.," Eliminating $\rho_0$ from equations \ref{eq:rho}) ) and \ref{eq:mdot1}) ) we rewrite $\dot{M}$ as Similarly to $E$ and $L$, the mass-accretion rate $\dot{M}$ is also conserved along the flow except at a shock location." + After defining all the physical quantities necessary to solve for black hole accretion. we will describe below the (ransonic properties of the physical accretion solutions.," After defining all the physical quantities necessary to solve for black hole accretion, we will describe below the transonic properties of the physical accretion solutions." +acecretion. ratios (Alathur CGrupe 2005).,accretion ratios (Mathur Grupe 2005). + Greene 1ο (2004) presented. a sample of 19 AGNs with low-mass black roles from Sloan Digital Sky Survey (SDSS) Data Relcasc One (DRI)., Greene Ho (2004) presented a sample of 19 AGNs with low-mass black holes from Sloan Digital Sky Survey (SDSS) Data Release One (DR1). + These 19 AGNs can be classified as NLSμα »ecause Of their Ho EWA less than12., These 19 AGNs can be classified as NLS1s because of their $\alpha$ FWHM less than. + Barth. Greene Lo (2005) measured o in these 19 NLSIs.," Barth, Greene Ho (2005) measured $\sigma$ in these 19 NLS1s." + Thev founcl these NLSIs follow the Mjo relation., They found these NLS1s follow the $M_{bh} - \sigma$ relation. + Ehe linewidth of © LLL indeed typically overestimates & comparing to the direct. measurement of ao, The linewidth of [O III] indeed typically overestimates $\sigma$ comparing to the direct measurement of $\sigma$. + Botte et al. (, Botte et al. ( +2005) also reaches his result.,2005) also reaches this result. + As we known. the O LL) profile is usually bluewarels asvmmetric. Le. with more Ilux on the short-wavelength side of lino than on the lone-wavelcneth side (Peterson 1997).," As we known, the [O III] profile is usually bluewards asymmetric, i.e. with more flux on the short-wavelength side of line than on the long-wavelength side (Peterson 1997)." + And the strong Fe Lb multiples would blend. the OO. 11) and. 1:2 lines in NLSIs., And the strong Fe II multiples would blend the [O III] and $\beta$ lines in NLS1s. + Multi-component profile and. be LH template are needed to model the Ο HI] lines in NLSIs., Multi-component profile and Fe II template are needed to model the [O III] lines in NLS1s. + Greene Lo (2005a) recently suggested that the core of ο LL after removing its asymmetric blue wing can trace e in narrow line (type 2) galaxies., Greene Ho (2005a) recently suggested that the core of [O III] after removing its asymmetric blue wing can trace $\sigma$ in narrow line (type 2) galaxies. + Is it true for NLSIs?, Is it true for NLS1s? + We used the largest. published sample of 150 NLSIs to investigate this problem (Williams. Pogee Mathur 2002).," We used the largest published sample of 150 NLSls to investigate this problem (Williams, Pogge Mathur 2002)." + Their spectra have been analyzed using multi-component model to investigate the O LLL blueshift in NLSIs. ancl we Found seven “blue outliers” (Bian. Yuan Zhao 2005a).," Their spectra have been analyzed using multi-component model to investigate the [O III] blueshift in NLS1s, and we found seven ""blue outliers"" (Bian, Yuan Zhao 2005a)." +" In this paper. We want to investigate whether NLSIs follow the A,om relation when we used the narrow/core component of O LU) line to trace σ."," In this paper, We want to investigate whether NLS1s follow the $M_{bh} - \sigma$ relation when we used the narrow/core component of [O III] line to trace $\sigma$." + In Sec., In Sec. + 2. we hbrielly introduce the data and the analysis.," 2, we briefly introduce the data and the analysis." + Our results and. discussion. are given in Sec., Our results and discussion are given in Sec. + 3., 3. + X conclusion is presented in the final section., A conclusion is presented in the final section. + All of the cosmological calculations in this paper assume Πας15kms|Alpe+. Qj203. Q4—0.7.," All of the cosmological calculations in this paper assume $H_{0}=75 \rm {~km ~s^ {-1}~Mpc^{-1}}$, $\Omega_{M}=0.3$, $\Omega_{\Lambda} = 0.7$." + There are many samples of NLSIs: (1) an optically selected sample of 46 NLSIs with extremely steep soft N-ray spectra observed. with ROSAT. (Boller et al.1996): (2) à compiled sample of G4 NLS1s (Veron-Cetty. Verron Cloncalves 2001): (3) a sample of 150 NLSIs found within SDSS IZarlv Data Release (EDR) (Williams et al.," There are many samples of NLS1s: (1) an optically selected sample of 46 NLS1s with extremely steep soft X-ray spectra observed with ROSAT (Boller et al.1996); (2) a compiled sample of 64 NLS1s (Veron-Cetty, Verron Cloncalves 2001); (3) a sample of 150 NLS1s found within SDSS Early Data Release (EDR) (Williams et al." + 2002): (4) 50 NLSIs rom a complete sample of 110 soft X-ray selected AGNs (Cirupe et al., 2002); (4) 50 NLS1s from a complete sample of 110 soft X-ray selected AGNs (Grupe et al. + 2004): (5) 19 AGNs with low-mass black holes rom SDSS DRI presented by Greene Ho (2004)., 2004); (5) 19 AGNs with low-mass black holes from SDSS DR1 presented by Greene Ho (2004). + Hore we used the 150 SDSS NLSIs sample because it is the largest xiblished NLS1s sumple., Here we used the 150 SDSS NLS1s sample because it is the largest published NLS1s sample. + Because of the lack of the ο 11) inc. SDSS 153243.67-004342.5 is ignored in our analysis.," Because of the lack of the [O III] line, SDSS J153243.67-004342.5 is ignored in our analysis." + Considering strong Fe IL multiples and the asvmmetrvy of ο ΓΣ lines. we reduced. their SDSS spectra. by he multicomponent fitting task SPECLIL (Ixriss 1994) in the IILAE-STS. package.," Considering strong Fe II multiples and the asymmetry of [O $\beta$ lines, we reduced their SDSS spectra by the multicomponent fitting task SPECFIT (Kriss 1994) in the IRAF-STS package." + Phe components are(1) the Galactic interstellar reddening curve: (2) Fe LL template: (3) power-law continuum: (4) three sets of (wo-eaussian profiles for O. HJAA4959.. 5007 ancl 113 lines.," The components are(1) the Galactic interstellar reddening curve; (2) Fe II template; (3) power-law continuum; (4) three sets of two-gaussian profiles for [O $\lambda\lambda$ 4959, 5007 and $\beta$ lines." + For the doublet ο AAL959.5007. We take the same finewidth or each component. and fix the Dux ratio of O L11]A4959 o O UYA5007 to be 1:3.," For the doublet [O $\lambda \lambda$4959,5007, We take the same linewidth for each component, and fix the flux ratio of [O $\lambda$ 4959 to [O $\lambda$ 5007 to be 1:3." + We didn't consider the starligh contribution because of no obvious stellar lines (Cu et al., We didn't consider the starlight contribution because of no obvious stellar lines (Gu et al. + 2005)., 2005). + For more details. please refer to Bian. Yuan Zhao (2005a)," For more details, please refer to Bian, Yuan Zhao (2005a)." + As we mentioned above. the —O LH]. profile is. usually bluewares asvmmetric.," As we mentioned above, the [O III] profile is usually bluewards asymmetric." + We calculated the blueshift of the broad component relative to the narrow component (AAMovead Anerrow) for the O LL and Le? lines.," We calculated the blueshift of the broad component relative to the narrow component $\Delta +\lambda=\lambda_{broad}-\lambda_{narrow}$ ) for the [O III] and $\beta$ lines." + In Fig.1. we showed the distribution of AA for the Lb? ancl O HI] lines.," In Fig.1, we showed the distribution of $\Delta +\lambda$ for the $\beta$ and [O III] lines." + Lt is obvious that the ο LLL profiles tend to be bluewards while the LL? profiles tend to be bluewards or recdwards., It is obvious that the [O III] profiles tend to be bluewards while the $\beta$ profiles tend to be bluewards or redwards. + In our two-component mocel. we found that for some objects the optical Fe HE multiples seriously. blend with the lines of LE? and. OO HIAA4959. 5007.," In our two-component model, we found that for some objects the optical Fe II multiples seriously blend with the lines of $\beta$ and [O $\lambda\lambda$ 4959, 5007." + In some cases. Fe LE multiples showed almost the seme magnitude of Dux to that of O LL] line (see fig.," In some cases, Fe II multiples showed almost the same magnitude of flux to that of [O III] line (see fig." + 3 in Dian. Yuan Zhao 2005a).," 3 in Bian, Yuan Zhao 2005a)." + Dian Zhao (2004a) directly measure the ο IH]A5007 linewidth Thereafter £11 44A277(O111])]. using one-Gaussian profile model., Bian Zhao (2004a) directly measure the [O $\lambda$ 5007 linewidth [hereafter $FWHM^{one}([O III])$ ] using one-Gaussian profile model. + The spectrum resolution It is about 1800. which is equivalent to 1.," The spectrum resolution R is about 1800, which is equivalent to ." + Phe typical error of £MLM(OIL) is about LO per cent., The typical error of $FWHM^{one}([O III])$ is about 10 per cent. + For the, For the +images is expected. sooner than one due to disappearing critical images.,images is expected sooner than one due to disappearing critical images. + The probabilities for cusp events are similar to those for events due to disappearing critical images. making cistinguishing these cillicult before the event event has reached its maximum.," The probabilities for cusp events are similar to those for events due to disappearing critical images, making distinguishing these difficult before the event event has reached its maximum." + However cusp events are far rarer than caustic crossings., However cusp events are far rarer than caustic crossings. + We have checked the effect on our triggering function of different combinations of assumptions for the size of photometric error in the monitoring data. the fraction of smooth matter content and the direction. of the galactic transverse velocity.," We have checked the effect on our triggering function of different combinations of assumptions for the size of photometric error in the monitoring data, the fraction of smooth matter content and the direction of the galactic transverse velocity." + We find. Little systematic dependence on these quantities., We find little systematic dependence on these quantities. + We have placed. limits on the intrinsic variation in (2237|0305 and shown that (except for the smaller triggers) the predictions should not be οοσο by intrinsic source variation., We have placed limits on the intrinsic variation in Q2237+0305 and shown that (except for the smaller triggers) the predictions should not be effected by intrinsic source variation. + A svstematic uncderestimation (the largest possible) of. 2 in our previous estimation of source size would produce an underestimate in the arrival time., A systematic underestimation (the largest possible) of $\times 2$ in our previous estimation of source size would produce an underestimate in the arrival time. + The unclerestimation is most serious for large triggers preceding a caustic crossing high magnification event., The underestimation is most serious for large triggers preceding a caustic crossing high magnification event. + Predictions from smaller clerivatives are less alfected., Predictions from smaller derivatives are less affected. + Computation of the distributions of the separation between a trigger and subsequent high magnification event [or clilferent sampling rates determines the appropriate sampling rate for the prediction of caustic crossings from regular monitoring., Computation of the distributions of the separation between a trigger and subsequent high magnification event for different sampling rates determines the appropriate sampling rate for the prediction of caustic crossings from regular monitoring. + We find that the triggering function is insensitive to sampling rate for sampling rates of 2 weeks or less., We find that the triggering function is insensitive to sampling rate for sampling rates of $\sim 2$ weeks or less. + Hf caustic crossing probabilities are calculated. from monitoring data with a higher sampling rate. the derivative," If caustic crossing probabilities are calculated from monitoring data with a higher sampling rate, the derivative" + In this section we summarise the main properties of the improved A-variance analysis proposed in paper L focusing on the new points. not covered in the original A-variance definition by Stutzkiet," In this section we summarise the main properties of the improved $\Delta$ -variance analysis proposed in paper I, focusing on the new points, not covered in the original $\Delta$ -variance definition by \citet{Stutzki}." +"al.(1998). The A-variance measures the amount of structure on a given scale / in a map f(r) by filtering the map with a spherically symmetric wavelet of size / and computing the variance of the thus filtered map: where. the average is taken over the area of the map. the symbol stands for a convolution. and (2, describes the filter function composed of positive inner ""core"" and a negative annulus. both normalised to integral values of unity We have studied the ""French-hat filter with constant values in both parts: and a ""Mexican hat” consisting of two Gaussian functions: where / is the core diameter and v is the diameter ratio between the annulus and the core of the filter."," The $\Delta$ -variance measures the amount of structure on a given scale $l$ in a map $f(\vec{r})$ by filtering the map with a spherically symmetric wavelet of size $l$ and computing the variance of the thus filtered map: where, the average is taken over the area of the map, the symbol $*$ stands for a convolution, and $\bigodot_l$ describes the filter function composed of positive inner “core” and a negative annulus, both normalised to integral values of unity We have studied the “French-hat” filter with constant values in both parts: and a “Mexican hat” consisting of two Gaussian functions: where $l$ is the core diameter and $v$ is the diameter ratio between the annulus and the core of the filter." + Plotting the A-variance as a function of the filter size / then provides a spectrum showing the relative amount of structure in a given map as a function of the structure size., Plotting the $\Delta$ -variance as a function of the filter size $l$ then provides a spectrum showing the relative amount of structure in a given map as a function of the structure size. + The effective filter size. given by the average distance of points in the core and the annulus. deviates from the core diameter / as Thus structures with a particular size should show up as prominent peaks in the A-variance spectrum on a scale /r corresponding to that size.," The effective filter size, given by the average distance of points in the core and the annulus, deviates from the core diameter $l$ as Thus structures with a particular size should show up as prominent peaks in the $\Delta$ -variance spectrum on a scale $l\sub{eff}$ corresponding to that size." + Test with artificial data sets in paper I have shown. however. that the peak positions always falls this systematic offset into account we can nevertheless reliably calibrate the spatial resolution of the A-variance analysis.," Test with artificial data sets in paper I have shown, however, that the peak positions always falls this systematic offset into account we can nevertheless reliably calibrate the spatial resolution of the $\Delta$ -variance analysis." + A major improvement of the new A-variance algorithm was the introduction of a weighting function to the data Waaua(”)., A major improvement of the new $\Delta$ -variance algorithm was the introduction of a weighting function to the data $w\sub{data}(\vec{r})$. + This simultaneously solved the problems of the edge treatment of finite maps and the analysis of data with a variable uncertainty across the map., This simultaneously solved the problems of the edge treatment of finite maps and the analysis of data with a variable uncertainty across the map. + The weight function varies between O and |. representing the reliability of the individual data points. and it extends beyond the original map size. padding it with zeros at the boundaries.," The weight function varies between 0 and 1, representing the reliability of the individual data points, and it extends beyond the original map size, padding it with zeros at the boundaries." + Instead of the original map f(r). an extended map. fpadded()=fxWoah) inside the original data area. fusag(r)=0 outside. is analysed.," Instead of the original map $f(\vec{r})$, an extended map, $f\sub{padded}(\vec{r})=f(\vec{r}) \times w\sub{data}(\vec{r})$ inside the original data area, $f\sub{padded}(\vec{r})=0$ outside, is analysed." + This padded map can be periodically continued. without. wrap-around effects. so that the filter convolution can be efficiently computed in Fourier space involving a fast Fourier transform and a map multiplication.," This padded map can be periodically continued without wrap-around effects, so that the filter convolution can be efficiently computed in Fourier space involving a fast Fourier transform and a map multiplication." + To avoic that data points within the padded area or with a low weighting are counted like normal zero-value data. but disregarded in the computation of the variance. the filter has to be re-normalised at each position in the map in such a way that the integral weights of core and annulus remain unity when excluding the padded points and when taking the weighting of the normal data points into account.," To avoid that data points within the padded area or with a low weighting are counted like normal zero-value data, but disregarded in the computation of the variance, the filter has to be re-normalised at each position in the map in such a way that the integral weights of core and annulus remain unity when excluding the padded points and when taking the weighting of the normal data points into account." + Instead of one convolution (Eq. 1).," Instead of one convolution (Eq. \ref{eq_basicdelta}) )," + one has to compute four convolutions and combine the results while re-normalising with the effective filter weight for the valid data From the actual filter weight computed for each point in the map we can derive a significance function as the product of both normalisation factors This provides the actual significance of the data points in the convolved map which is used when computing the A- variance of the whole map With this generalisedDanap concept. the A-variance analysis can be applied to arbitrary. data sets.," one has to compute four convolutions and combine the results while re-normalising with the effective filter weight for the valid data From the actual filter weight computed for each point in the map we can derive a significance function as the product of both normalisation factors This provides the actual significance of the data points in the convolved map which is used when computing the $\Delta$ -variance of the whole map With this generalised concept, the $\Delta$ -variance analysis can be applied to arbitrary data sets." +" They must be projected onto some regular grid but they do not need to contain regular boundaries as the corresponding ""empty"" grid points can be marked with a zero significance.", They must be projected onto some regular grid but they do not need to contain regular boundaries as the corresponding “empty” grid points can be marked with a zero significance. + Varying noise or other changes in the data reliability can be expressed in the significance function μμ)., Varying noise or other changes in the data reliability can be expressed in the significance function $w\sub{data}(\vec{r})$. + This applies e.g. to maps where not all points are observed with the same integration time so that they show a different noise level., This applies e.g. to maps where not all points are observed with the same integration time so that they show a different noise level. + In paper I we used a weighting function given by the inverse noise RMS and in Sect., In paper I we used a weighting function given by the inverse noise RMS and in Sect. + 3.2 we will study the impact of the selection of the weighting function for observed data., \ref{sect_andre} we will study the impact of the selection of the weighting function for observed data. + The only remaining requirement for the applicability of the A-variance analysis ts a sufficiently large spatial dynamic range, The only remaining requirement for the applicability of the $\Delta$ -variance analysis is a sufficiently large spatial dynamic range +"Recall that g=Q/2 in dust-dominated FRW models. with Q=30/0? aud p representing the deusity of the matter in the w,-lrame.","Recall that $q=\Omega/2$ in dust-dominated FRW models, with $\Omega=3\rho/\Theta^2$ and $\rho$ representing the density of the matter in the $u_a$ -frame." + Noting that Q may also be seen as the ellective density parameter of patel CA). the tilded observers will experience accelerated expausion if Whether this couclit ∩∐↥⊳∖⊳∖⋜↕∏⊳∖↥∎∐↵≺⇂≺∐⋅∐∩↕⋜↕∐≺⊔∐↩⋜↕∐⇀≺↵∢∙↕≺↵≺⊳∖∢∙⋜↕↥≺↵↸⋮↥⋅≺↵⋅↕∐≺↲⊳∖↥∠≺↵∩↥∎↥↽≻⋜⋯∙∐⋖↜≵≩⋝↥∐ Fig. 2)).," Noting that $\Omega$ may also be seen as the effective density parameter of patch $A$ ), the tilded observers will experience accelerated expansion if Whether this condition is satisfied or not and the affected scale (i.e. the size of patch $B$ ) in Fig. \ref{fig:pvel}) )," + depends on the value of 2 and ou the ratio 7/0., depends on the value of $\Omega$ and on the ratio $\vartheta/\Theta$. + To estimate the latter we need to know the bulk velocities of drift motions on scales far beyoud that of our Local Group., To estimate the latter we need to know the bulk velocities of drift motions on scales far beyond that of our Local Group. + Peculiar velocities are clifficult to measure. since direct measurements ouly provide their radial component.," Peculiar velocities are difficult to measure, since direct measurements only provide their radial component." + One also needs to subtract the Hubble expansion. which requires iudependenut kuowledge of the galaxys distance.," One also needs to subtract the Hubble expansion, which requires independent knowledge of the galaxy's distance." + As a result. bulk peculiar velocities are estimated by meaus of statistical methods (Strauss&Willick1995).," As a result, bulk peculiar velocities are estimated by means of statistical methods \citep{SW}." +. Recent independent reports have claimed large-scale coherent drift velocities siguificautly higher than those anticipated by the concordance AC DMI model., Recent independent reports have claimed large-scale coherent drift velocities significantly higher than those anticipated by the concordance $\Lambda$ CDM model. + These surveys extend to lengths of LOO tMpe (Watkinsetal2009:Feldman2009).. 3004.1 Mpe and 5004.1 Mpe (IXashlinskyetal2008.2009a.b).. with // being the Hubble parameter in units of 100 MMpe.," These surveys extend to lengths of $h^{-1}$ Mpc \citep{WFH,FWH}, $h^{-1}$ Mpc and $h^{-1}$ Mpc \citep{KA-BKE1,KA-BKE2,KA-BEEK}, with $h$ being the Hubble parameter in units of 100 Mpc." + The results show bulk velocities as large as 500 Καιρού (Watkinsetal2000: and up to 1000 ki/sec (Ixashlinskyetal2008.2009a.b) on the corresponding scales.," The results show bulk velocities as large as 500 km/sec \citep{WFH,FWH} and up to 1000 km/sec \citep{KA-BKE1,KA-BKE2,KA-BEEK} on the corresponding scales." + Ou sinaller lengths (between 30) and 60 Mpc) the work of Li&Schwarz(2008). suggests a (positive) variance in the local Hubble rate up to1056., On smaller lengths (between 30 and 60 Mpc) the work of \cite{LS} suggests a (positive) variance in the local Hubble rate up to. +.. With the possible exception of the last survey. there is currently uo way of kuowiug whether the reported bulk flows are of the desired type (Le. with )> 0).," With the possible exception of the last survey, there is currently no way of knowing whether the reported bulk flows are of the desired type (i.e. with $\vartheta>0$ )." + Nevertheless. in the abseuce of better data. we will use the maeuituces of the aforementioned peculiar velocities to infer reasonable (order-of-inagnitude) estimates [or 1.," Nevertheless, in the absence of better data, we will use the magnitudes of the aforementioned peculiar velocities to infer reasonable (order-of-magnitude) estimates for $\vartheta$." + In addition. mainly [or algebraic simplicity and illustration purposes. we will also consider the intermediate value of 700 km/sec as a yardstick peculiar velocity.," In addition, mainly for algebraic simplicity and illustration purposes, we will also consider the intermediate value of 700 km/sec as a yardstick peculiar velocity." + Note that this value is very close to the drift velocity of our Local Group., Note that this value is very close to the drift velocity of our Local Group. + setting the Hubble parameter at 70 MMpe and extrapolating to 50 Mpc. 100 Mpc and 1000 Mpc. we find that 2/0 is close to 1/5. 1/10 and 1/100 Then. following condition (9)). the tilded observer will 1neasure! negative deceleration parameter within a regioi oL up to 50 Mpe (in an otherwise decelerating universe) iO17 we find a~LYΤΟ1, jy eood agreement with the models of Dekel Silk."," If we limit this fit to the fainter LMCGs at $_{V} > -17$ we find $\sigma \sim L^{0.18\pm0.12}$, in good agreement with the models of Dekel Silk." + After converting the sizes aud velocity dispersions listed in Cela et al. (, After converting the sizes and velocity dispersions listed in Geha et al. ( +2002) iuto a pseudo-total mass using he relationship A4cem.o.0? we find that the Miora/Ly ratios for these Vireo LAICGs increases. at ower huuimosities.,"2002) into a pseudo-total mass using the relationship $M_{\rm total} \approx +\epsilon {\rm r_{e}} \times \sigma^{2}$ we find that the $M_{\rm total}/L_{V}$ ratios for these Virgo LMCGs increases at lower luminosities." + Fitting these two quantities together we find MorayLpo ~LE829%!21 ποσατν consistent with he Dekel Silk slope predictions.," Fitting these two quantities together we find $M_{\rm total}/L_{V}$ $\sim L^{-0.25\pm0.24}$, broadly consistent with the Dekel Silk slope predictions." + In general. the above arguments sugeest that the limited nuuber of LAICCs with measured internal velocitics are consistent with maving evolved through a sclfeurichment supernova wiud outflow model. such as that proposed by Dekel Silk. although these internal velocity samples are dominated oulv bv a few brieht LAICCs that tend to follow eiaut ealaxy scaling relatiouships.," In general, the above arguments suggest that the limited number of LMCGs with measured internal velocities are consistent with having evolved through a self-enrichment supernova wind outflow model, such as that proposed by Dekel Silk, although these internal velocity samples are dominated only by a few bright LMCGs that tend to follow giant galaxy scaling relationships." + The most complete previous analysis of the stellar populations for a sizable population of LAICGs is that of Rakos ct al. (, The most complete previous analysis of the stellar populations for a sizable population of LMCGs is that of Rakos et al. ( +2001). who estunated the ages and metallicities of 27 Fornax cluster dEs.,"2001), who estimated the ages and metallicities of 27 Fornax cluster dEs." + Bakos et al. (, Rakos et al. ( +2001) find that there is a broad age aud imotallicitv distribution for this sample of Fornax dEs. with |Fe/II| values raugiug from -1.6 to -0. Laud ages from 9 to 12 Civys.,"2001) find that there is a broad age and metallicity distribution for this sample of Fornax dEs, with [Fe/H] values ranging from -1.6 to -0.4 and ages from 9 to 12 Gyrs." + From this. aud the analvsis iu 83.1 where we couclude that τος Perseus LAICGs can not be metal poor objects. it is difficult for all LAICGs to be primordial objects formed through the e.g.. Dekel Silk paracigia as we would expect to have a population of objects with homogeneously old and poor stellar populations.," From this, and the analysis in 3.4 where we conclude that red Perseus LMCGs can not be metal poor objects, it is difficult for all LMCGs to be primordial objects formed through the e.g., Dekel Silk paradigm as we would expect to have a population of objects with homogeneously old and metal-poor stellar populations." + We also argue that not all LAICGs cau. form: in a siuple carly collapse by directly comparing our data to CDAL simulations that predict the properties of low-anass ealaxies that all formed carly in the universe., We also argue that not all LMCGs can form in a simple early collapse by directly comparing our data to CDM simulations that predict the properties of low-mass galaxies that all formed early in the universe. + Ii Figure 13 we plot the coloranaguitude diagram for the Perseus ealaxies together with the liinesities and colors derived from predictious of low-mass galaxies from the ACDAL lydrodvuamiic models of Nagamine et al. (, In Figure 13 we plot the color-magnitude diagram for the Perseus galaxies together with the luminosities and colors derived from predictions of low-mass galaxies from the $\Lambda$ CDM hydrodynamic models of Nagamine et al. ( +2001) which are based on simple feedback mechanisms that do not take into account environmental effects.,2001) which are based on simple feedback mechanisms that do not take into account environmental effects. + The high stellar mass objects im these simulatious. with Moca: 72«109 tAD... have a wide range in stellar ages aud metals due to the hierarchical nature of their formation over time.," The high stellar mass objects in these simulations, with $_{\rm stellar}$ $>2\times10^{9}$ $^{-1}$, have a wide range in stellar ages and metals due to the hierarchical nature of their formation over time." + The low-mass galaxies with Mas<2.lool +AL... ou the other haud. expericuce only a brief epoch of star formation. with few new stars produced after the universe is ~2 Civrs old.," The low-mass galaxies with $_{\rm stellar} < 2 \times 10^{8}$ $^{-1}$, on the other hand, experience only a brief epoch of star formation, with few new stars produced after the universe is $\sim 2$ Gyrs old." + The conversion between metallicity aud color for the Nagamine et al. (, The conversion between metallicity and color for the Nagamine et al. ( +2001) simulated ealaxics was achieved by adopting the Milky Wavy elobular based relation (eq.,2001) simulated galaxies was achieved by adopting the Milky Way globular cluster-based relation (eq. + 3)., 3). + There is a general agreement between the simulated Nagauuue et al. (, There is a general agreement between the simulated Nagamine et al. ( +2001) and Perseus cluster ealaxics properties. except at the faint and bright ends of the huninosity function.,"2001) and Perseus cluster galaxies properties, except at the faint and bright ends of the luminosity function." + Bright Perseus galaxies are redder than the simulated points. and these ACDAL models do not predict the observed population of red low-mass galaxies.," Bright Perseus galaxies are redder than the simulated points, and these $\Lambda$ CDM models do not predict the observed population of red low-mass galaxies." + It does. however. appear that the ACDM simulated objects. based on simple feedback moechauisius. can reproduce the blue LALCCs as metal-poor and old ealaxies.," It does, however, appear that the $\Lambda$ CDM simulated objects, based on simple feedback mechanisms, can reproduce the blue LMCGs as metal-poor and old galaxies." + If the correlation of color and magnitude for bright ealaxies represents a total massnetallicitv. relatiouship and LAICGs are primordial aud evolve through selt-chrichiment. then the fact that the color-magnitude relation breaks down could be the result of varving tota uass to light (Αννα) ratios.," If the correlation of color and magnitude for bright galaxies represents a total mass-metallicity relationship and LMCGs are primordial and evolve through self-enrichment, then the fact that the color-magnitude relation breaks down could be the result of varying total mass to light $M_{\rm total}/L$ ) ratios." + That is. LAICCs coulk contain large amounts of dark matter.," That is, LMCGs could contain large amounts of dark matter." + A verv high tota uass to lieht ratio could account for objects that lave Heh metallicitfies. but appear faint. such as the rec LAICGs in the supernova - selteuricliieut scenario.," A very high total mass to light ratio could account for objects that have high metallicities, but appear faint, such as the red LMCGs in the supernova - self-enrichment scenario." + That is. when metals are produced durius star formation in hese dark-natter-domuuated galaxies they are not ejectec into the intracluster medimu due to the large eravitationa xteutial of the galaxy. which essentially traps the metals ong enough for subsequeut generations of more metal rich stars to form.," That is, when metals are produced during star formation in these dark-matter-dominated galaxies they are not ejected into the intracluster medium due to the large gravitational potential of the galaxy, which essentially traps the metals long enough for subsequent generations of more metal rich stars to form." + The likelihood of this scenario cau be examined using he coloranaenitude auc massuetallicitv relationships and properties of the red LAICGs., The likelihood of this scenario can be examined using the color-magnitude and mass-metallicity relationships and properties of the red LMCGs. + For LAICGs at (5Ryy~ Ll to be at a similar location of the mass-uctallicityfcolor-magnitude relationship as a brighter elliptical galaxy at the same color would require/ a total nass ~3 magnitudes hieher. and thus a total mass to ight ratio of Αν [τν (2.5)! «GossDcttiprieals 7," For LMCGs at $(B-R)_{0}$$\sim$ 1.4 to be at a similar location of the mass-metallicity/color-magnitude relationship as a brighter elliptical galaxy at the same color would require a total mass $\sim 3$ magnitudes higher, and thus a total mass to light ratio of $M_{\rm total}/L$ $\sim$ $^{3}$ $\times (M_{\rm total}/L)_{\rm +ellipticals}$ $\sim$ 15 $\times (M_{\rm total}/L)_{\rm +ellipticals}$." + ο we take the Aftoraif£ values or Cllipticals οcommuted using galaxy-ealaxy lensing bx Alelkav et al. (, If we take the $M_{\rm total}/L$ values for ellipticals computed using galaxy-galaxy lensing by McKay et al. ( +2002). which ave 1254351 aud 221426 in he Sloan Digitized Survey οἳ aud r bands. then the inferved LMCG ALjgafh~6<107.,"2002), which are $\pm$ 51 and $\pm$ 26 in the Sloan Digitized Survey g' and r' bands, then the inferred LMCG $M_{\rm total}/L \sim +6\times 10^{3}$." +" This would require an enormous dark matter content and is about 10 times arecr than auv suele galaxw Αα, vet derived (6.8... Mateo 1998: Wlevna et al."," This would require an enormous dark matter content and is about 10 times larger than any single galaxy $M_{\rm total}/L$ yet derived (e.g., Mateo 1998; Kleyna et al." + 2002)., 2002). + ITowever the iutracluster nedit im clusters could have stripped gas from low-1ass wos carly through ram-pressure (Comm Cott 1972) fore significant star formation and without removing any dark matter. thereby producing a galaxy with a high MisL ratio.," However the intracluster medium in clusters could have stripped gas from low-mass halos early through ram-pressure (Gunn Gott 1972) before significant star formation and without removing any dark matter, thereby producing a galaxy with a high $M_{\rm total}/L$ ratio." +" The best way to determine ifthe LAICCs have these high mass to lieht ratios would be to measure their internal velocity dispersious out to a laree radius ίσιο, EKlevua et al."," The best way to determine if the LMCGs have these high mass to light ratios would be to measure their internal velocity dispersions out to a large radius (e.g., Kleyna et al." + 2002)., 2002). + This type of information docs not vet exist for auv LAICGs., This type of information does not yet exist for any LMCGs. + In fact. the ouly velocity dispersion measurements are those in the central parts of LAICCs (Pedraz et al.," In fact, the only velocity dispersion measurements are those in the central parts of LMCGs (Pedraz et al." + 2002: Celia ct al., 2002; Geha et al. + 2002) where dark matter is nof found to be present in laree amounts, 2002) where dark matter is not found to be present in large amounts. + Future observations through radial velocities of dE globular clusters or velocity dispersion profiles out to considerable distances are needed to determine total LAICC masses within a relatively large radius., Future observations through radial velocities of dE globular clusters or velocity dispersion profiles out to considerable distances are needed to determine total LMCG masses within a relatively large radius. +totally unexpected. considering various statistical errors ancl hiclen svstematic uncertainties (e.g.. in the mass-to-light ratio aud in the spatial and spectral modeling).,"totally unexpected, considering various statistical errors and hiden systematic uncertainties (e.g., in the mass-to-light ratio and in the spatial and spectral modeling)." + We note that adopting the M32 stellar emissivitv (o remove the stellar contribution in wwould enhance the hot gas contribution in and around the bbulge. but. would not qualitatively alter (he picture of the diffuse emission presented in 2.2 and below.," We note that adopting the M32 stellar emissivity to remove the stellar contribution in would enhance the hot gas contribution in and around the bulge, but would not qualitatively alter the picture of the diffuse emission presented in \ref{subsec:dif} and below." + The characterization of the diffuse hot eas sheds important insights into the energv balance in the bbulge., The characterization of the diffuse hot gas sheds important insights into the energy balance in the bulge. +" The estimated Iuminositv of the hot gas (2.5x109eress!) is only about of the expected SNe mechanical energv input. ~4x10ores&I,"," The estimated luminosity of the hot gas $2.5\times10^{38}{\rm~ergs~s^{-1}}$ ) is only about of the expected SNe mechanical energy input, $\sim$$4\times10^{40}{\rm~ergs~s^{-1}}$." + As mentioned in 1.. this indicates that the input energv may be removed primarily in an outflow.," As mentioned in \ref{sec:intro}, this indicates that the input energy may be removed primarily in an outflow." + Dynamically. such an outflow tends to lind its way along sleeper pressure gradient against (he gravity. of the ealaxv. consistent with the observed bi-polar morphology of the diffuse X-ray emission.," Dynamically, such an outflow tends to find its way along steeper pressure gradient against the gravity of the galaxy, consistent with the observed bi-polar morphology of the diffuse X-ray emission." + If (he gas were quasistatic. one would expect its distribution to follow that of the eravitational potential. i.e.. more extended along the major-axis.," If the gas were quasi-static, one would expect its distribution to follow that of the gravitational potential, i.e., more extended along the major-axis." + However. (he gas may not be hot enough to ultimately escape Irom the deep gravitational potential ofM31: it is also not clear how the outflow interacts with the large-scale halo of aad how the mechanical energy is dissipated.," However, the gas may not be hot enough to ultimately escape from the deep gravitational potential of; it is also not clear how the outflow interacts with the large-scale halo of and how the mechanical energy is dissipated." + Similar considerations also challenge the studies of X-ray-laint elliptical galaxies (e.g.. David et al.," Similar considerations also challenge the studies of X-ray-faint elliptical galaxies (e.g., David et al." + 2006)., 2006). + Ongoing numerical simulations would help to understand the nature of the hot gas and its role in the evolution of these svslens., Ongoing numerical simulations would help to understand the nature of the hot gas and its role in the evolution of these systems. + Our unambiguous detection of the diffuse hot gas in and around the bbulge also helps to understand the soft X-ray enhancement observed toward the inner region of our Galaxy., Our unambiguous detection of the diffuse hot gas in and around the bulge also helps to understand the soft X-ray enhancement observed toward the inner region of our Galaxy. + The temperature of the hot gas associated with the bbulge. 0.4 keV. is similar to that with the Galactic bulge. as estimated from the ROSAT all-sky survey (Snowclen et al.," The temperature of the hot gas associated with the bulge, 0.4 keV, is similar to that with the Galactic bulge, as estimated from the ROSAT all-sky survey (Snowden et al." + 1997)., 1997). + Dased on a hydrostatie model of the Galactic bulge X-rav emission developed by Wang (1997). Almy et al. (," Based on a hydrostatic model of the Galactic bulge X-ray emission developed by Wang (1997), Almy et al. (" +"2000) further inferred a total 0.5-2 keV luminosity of ~8x10eress.|, about four times greater than our estimated bbulge luminosity.","2000) further inferred a total 0.5-2 keV luminosity of $\sim8 \times +10^{38}{\rm~ergs~s^{-1}}$, about four times greater than our estimated bulge luminosity." + The relatively high. luminosity of the Galactic bulge manifests in the large extent of the soft. N-rayv enhancement from the Galactic bulge., The relatively high luminosity of the Galactic bulge manifests in the large extent of the soft X-ray enhancement from the Galactic bulge. + At Galactic lattitudes be—15* (2 kpe from Che plane). for example. where both the confusion with (he foreground enission features and the interstellar absorption are relatively small. (he intensity has an averaged. value of —6(4)x10.|ROSATPSPCciss!avemin7 in the 0.75 (1.5) keV band (Snowclen et al.," At Galactic lattitudes $b\sim-15^\circ$ $\sim$ 2 kpc from the plane), for example, where both the confusion with the foreground emission features and the interstellar absorption are relatively small, the intensity has an averaged value of $\sim$$6 (4){\times}10^{-4} {\rm~ROSAT~PSPC~cts~s^{-1}~arcmin^{-2}}$ in the 0.75 (1.5) keV band (Snowden et al." + 1997)., 1997). + Had this emission been detected from bby the ACIS-L. it would be measured with an intensity of ~10(3)x10etssl|aremin in the 0.5-1 (1-2) keV band. about 2-4 times higher than the observed. vvalues represented by (he tails (Fie.," Had this emission been detected from by the ACIS-I, it would be measured with an intensity of $\sim$$10 (3){\times}10^{-4}{\rm~cts~s^{-1}~arcmin^{-2}}$ in the 0.5-1 (1-2) keV band, about 2-4 times higher than the observed values represented by the tails (Fig." + fbb)., \ref{fig:rsb}b b). + The intensity drops slowly and even shows local, The intensity drops slowly and even shows local +1908: Macquart. et al.,1998; Macquart et al. + 2000: Ravner. Norris Sault 2000: lloman. Attridge Warele 2001) have been used in an attempt to probe directly the composition and distribution of the particles in the jets from these supermassive black holes.," 2000; Rayner, Norris Sault 2000; Homan, Attridge Wardle 2001) have been used in an attempt to probe directly the composition and distribution of the particles in the jets from these supermassive black holes." + Closer to home. circular polarisation has been detected from the (probable) Iow-Iuminosity AGN (LLAGN) Ser A* al the ealactic centre {Bower. Faleke Backer 1999: Sault Marquart 1999) and. the related: nearby radio core in ASI (Brunthaler et al.," Closer to home, circular polarisation has been detected from the (probable) low-luminosity AGN (LLAGN) Sgr A* at the galactic centre (Bower, Falcke Backer 1999; Sault Marquart 1999) and the related nearby radio core in M81 (Brunthaler et al." + 2001)., 2001). + In 2000 Alay we discovered circularly polarised radio emission from the famous galactic jet source SS 433 (Fender et al., In 2000 May we discovered circularly polarised radio emission from the famous galactic jet source SS 433 (Fender et al. + 2000)., 2000). + This X-ray. binary was clearly detected at four frequencies between 19 Cllz with a CP spectrum decreasing with increasing Lrequency., This X-ray binary was clearly detected at four frequencies between 1–9 GHz with a CP spectrum decreasing with increasing frequency. + Llowever. our lack of ability to resolve the variable extended structure of SS 433 with the Australia Telescope Compact Array (APCA) did not enable us to determine accurately the fractional CP spectrum and hence get a clear grip on the physical process which might be responsible.," However, our lack of ability to resolve the variable extended structure of SS 433 with the Australia Telescope Compact Array (ATCA) did not enable us to determine accurately the fractional CP spectrum and hence get a clear grip on the physical process which might be responsible." + Furthermore. SS 433 seems to be unique amongst relativistic jet sources as it appears to have a fixed jet velocity of 0.266 and displays optical / infrared / X-rav emission lines which seem to clearly indicate a large barvonic fraction (e.g. Margon 1984: lxotani et al.," Furthermore, SS 433 seems to be unique amongst relativistic jet sources as it appears to have a fixed jet velocity of $0.26c$ and displays optical / infrared / X-ray emission lines which seem to clearly indicate a large baryonic fraction (e.g. Margon 1984; Kotani et al." + 1994)., 1994). + The X-ray binary GRS 1915]105. was the first. galactic system to display apparent superluminal motions within our galaxy (CMirabel Roclriguez 1994). implving large bulk velocities maybe comparable to those in AGN.," The X-ray binary GRS 1915+105 was the first galactic system to display apparent superluminal motions within our galaxy (Mirabel Rodriguez 1994), implying large bulk velocities maybe comparable to those in AGN." + The svstem has been directly resolved. on multiple occasions. into highly relativistic jets which display dillerent patterns of behaviour closely linked to the X-ray state of the source (Fender et al.," The system has been directly resolved, on multiple occasions, into highly relativistic jets which display different patterns of behaviour closely linked to the X-ray state of the source (Fender et al." + 1999: Dhawan. Mirabel Itodriguez 2000: IxIcin-Wolt ct al.," 1999; Dhawan, Mirabel Rodriguez 2000; Klein-Wolt et al." + 2002)., 2002). + Whilst clisplavine a highly complex pattern of X-ray behaviour (e.g. Belloni et al., Whilst displaying a highly complex pattern of X-ray behaviour (e.g. Belloni et al. + 2000). the source does at times exhibit recognisable patterns.," 2000), the source does at times exhibit recognisable patterns." + For example. it seems that the system regularly. perhaps always. follows extended hard X-rav periods Cplateaux) with major ejections (Fender ct al.," For example, it seems that the system regularly, perhaps always, follows extended hard X-ray periods (`plateaux') with major ejections (Fender et al." + 1999: Wlhein-Wolt et al., 1999; Klein-Wolt et al. + 2002)., 2002). + These plateaux are themselves associated with powerful compact jets (Dhawan οἱ al., These plateaux are themselves associated with powerful compact jets (Dhawan et al. + 2000b: ) which have spectral similarities with self-absorbed jets from other black hole candidate (DIIC) systems. in sitnilar hard X-ray. states (Fender 2001)., 2000b; ) which have spectral similarities with self-absorbed jets from other black hole candidate (BHC) systems in similar hard X-ray states (Fender 2001). +" Furhermore. the observation o| apparent superlumina motions from several other NIB BUCS (c.g. Mirabel 1tocdriguez 999) and the arly typical ""vadio loudness’ (Lener Wttulkers 2001) imply that the jets of GRS 1915|105. may be far more vpical of those from NBs than the relatively slow. cool. jets of SS 433."," Furthermore, the observation of apparent superluminal motions from several other XRB BHCs (e.g. Mirabel Rodriguez 1999) and the fairly typical `radio loudness' (Fender Kuulkers 2001) imply that the jets of GRS 1915+105 may be far more typical of those from XRBs than the relatively slow, cool, jets of SS 433." + In this paper we report the discovery of a strong and variable circularly polarised component in the radio emission rom GRS 1915|105 which we can cirectly associate with relativistic ejection events., In this paper we report the discovery of a strong and variable circularly polarised component in the radio emission from GRS 1915+105 which we can directly associate with relativistic ejection events. + 1n Fig Lowe show radio and soft X-ray monitoring of GRS 1915|105. over a 150-dav period.," In Fig 1 we show radio and soft X-ray monitoring of GRS 1915+105, over a 150-day period." + The radio monitoring data were obtained with the Itvle Telescope (IUE). at à frequeney of 15 CGllz: for a more detailed description of this monitoring program see Pooley Lender (1997).," The radio monitoring data were obtained with the Ryle Telescope (RT), at a frequency of 15 GHz; for a more detailed description of this monitoring program see Pooley Fender (1997)." + The N-rav data are from the ZossiNTE All-Skv Monitor. (ASAI) ancl measure the total {lux in the 2-12 keV band., The X-ray data are from the XTE All-Sky Monitor (ASM) and measure the total flux in the 2-12 keV band. + Phe RossiTIS ASAL is described. in Levine et al. (, The XTE ASM is described in Levine et al. ( +1996) and the publie data can be obtained atx,1996) and the public data can be obtained at. +te.mit.edu. ποσα(ος in the top panels of Fig 1 are the times of our two ATCA and multiple \UERLIN observations of CRS 1915|105., Indicated in the top panels of Fig 1 are the times of our two ATCA and multiple MERLIN observations of GRS 1915+105. + The Australia Telescope Compact Array (ATCA: Frater. Brooks Whiteoak L092) has a number of design features which enable very accurate circular polarization measurements.," The Australia Telescope Compact Array (ATCA; Frater, Brooks Whiteoak 1992) has a number of design features which enable very accurate circular polarization measurements." + “The low antenna cross-polarization and high polarization stability enable. accurate calibration. of polarization leakage terms. and the lincarly-polarized [eed design largely isolates Stokes Vo from contamination by Stokes L. ATCA observed GRS 1915|105. twice. for six hours cach. on 2001 January 17 and 2001 March 23.," The low antenna cross-polarization and high polarization stability enable accurate calibration of polarization leakage terms, and the linearly-polarized feed design largely isolates Stokes V from contamination by Stokes I. ATCA observed GRS 1915+105 twice, for six hours each, on 2001 January 17 and 2001 March 23." + During the January observations. simultaneous. observations at. 1384 MlIIz and 2496 MlIZ were interleaved wih observations at 4800 MllIz ancl S640 MllIz: for the March observations. only 4800 MlIz and S640 Mllz were observed.," During the January observations, simultaneous observations at 1384 MHz and 2496 MHz were interleaved with observations at 4800 MHz and 8640 MHz; for the March observations, only 4800 MHz and 8640 MHz were observed." + For both epochs the array was ina 6 km’ configuration. for which the lack of short. baselines served to reduce confusion. from. other galactic sources.," For both epochs the array was in a `6 km' configuration, for which the lack of short baselines served to reduce confusion from other galactic sources." + The observation and calibration procedures were similar to those described in Fender «t al. (, The observation and calibration procedures were similar to those described in Fender et al. ( +2000).,2000). + As discussed in Fender et al. (, As discussed in Fender et al. ( +"2000). calibration of circular polarization data requires the ""stronglv-polarized"" calibration equations (Sault. Ixilleen. Westeven. 1991). using a point-source with a lew percent linear polarization.","2000), calibration of circular polarization data requires the ""strongly-polarized"" calibration equations (Sault, Killeen Kesteven, 1991), using a point-source with a few percent linear polarization." +115 davs after the outburst ouset. while VlI was rising to τον red values. approaching those of brown dwarts.,"115 days after the outburst onset, while $V-I$ was rising to very red values, approaching those of brown dwarfs." + The reason became apparent when Desicdera aud Abunani (2002) discovered on spectra at dav 271 that the contribution from the verv cool outburstine component was less in the blue part of the spectiuu. revealing the preseuce of a fainter and hotter companion.," The reason became apparent when Desidera and Munari (2002) discovered on spectra at day 274 that the contribution from the very cool outbursting component was less in the blue part of the spectrum, revealing the presence of a fainter and hotter companion." + V838 Mon was thus shown to be a binary system. aud he hot companion was classified by Munani ct al. (," V838 Mon was thus shown to be a binary system, and the hot companion was classified by Munari et al. (" +20021) on spectra for dav X as à D3VV star.,2002b) on spectra for day 300 as a V star. + The preseuce of the hot companion was confrned on- higher resolution spectra bv Waener and Starrfield (2002)., The presence of the hot companion was confirmed on higher resolution spectra by Wagner and Starrfield (2002). + The composite nature of optical spectra o Vase Mon during this phase is illustrated im the op pane of Figure 9., The composite nature of optical spectra of V838 Mon during this phase is illustrated in the top panel of Figure 9. + Later on 100 Was an dnereasei in 16 contribution of the outhursting component a shorter wavelengths. as illustrated in the bottom paucl of Figure 9.," Later on there was an increase in the contribution of the outbursting component at shorter wavelengths, as illustrated in the bottom panel of Figure 9." + The average color of Vs3e Mon at the time of the raked visibility of the VV companion was Y=|0.68 (cf., The average color of V838 Mon at the time of the naked visibility of the V companion was =+0.68 (cf. + Figure 1 and Miimari ct al., Figure 1 and Munari et al. + 2002b)., 2002b). + Comparing with he intrinsic colors of a WV from Fitzgerald (1970) it results in £p 40.88. in excellent agreciment with the results from interstellar Nal aud IKI mes.," Comparing with the intrinsic colors of a V from Fitzgerald (1970) it results in $E_{B-V}$ =0.88, in excellent agreement with the results from interstellar NaI and KI lines." + The metallicity im the ealactic cisk at the ealactocentric distance of V838 Mon ids 0.7. about half dex lower than in the solar ucighborhood (6.8. Fric et al.," The metallicity in the galactic disk at the galactocentric distance of V838 Mon is $-$ 0.7, about half dex lower than in the solar neighborhood (e.g. Friel et al." + 2002. Tlou et al.," 2002, Hou et al." + 2003)., 2003). + The effect on theBW color of the VV. compoucut in V838 Mon of such a reduction im metallicity is a very ninor ouc. beiug on the Ravleigh-Jeans tail of the cnerev distribution of a hot star.," The effect on the color of the V component in V838 Mon of such a reduction in metallicity is a very minor one, being on the Rayleigh-Jeans tail of the energy distribution of a hot star." + Iuteeratiug the transimission profiles of the Laudolt's D aud V bauds (to which our photometry is tied) to the 2500-10500 ssvuthetic Iurucz spectral library of Mhmari et al. (, Integrating the transmission profiles of the Landolt's $B$ and $V$ bands (to which our photometry is tied) to the 2500-10500 synthetic Kurucz spectral library of Munari et al. ( +200 the net effect is just 0.007. mae.,"2004), the net effect is just 0.007 mag." + The average V. maguitude of Vass Mon at the time the V. baud was dominated by the radiation frou the VV. component is W=16.0540.05., The average $V$ magnitude of V838 Mon at the time the $V$ band was dominated by the radiation from the V component is $V$ $\pm$ 0.05. + Coupled with the Ep4-0 570.01 and au absolute magnitude My 0020.05 for à VV star from Toul (2001). it iuplies a distance of 10 kpe to Vase Mon.," Coupled with the $E_{B-V}$ $\pm$ 0.01 and an absolute magnitude $M_V$ $-$ $\pm$ 0.05 for a V star from Houk (2004), it implies a distance of 10 kpc to V838 Mon." + Two assumptiou-iudependenut methods. the interstellar atomic absorption lines and the colors of the B3 colmpanion. provide cousisteut results on the reddening affecting Vase Mon: Eg y=0.86 aud Ep y=O0.88. respectively.," Two assumption-independent methods, the interstellar atomic absorption lines and the colors of the B3V companion, provide consistent results on the reddening affecting V838 Mon: $E_{B-V}$ =0.86 and $E_{B-V}$ =0.88, respectively." + There is no differential extinction between the outburstiug star and the B3V companion., There is no differential extinction between the outbursting star and the B3V companion. + The same amount of reddeniug is derived from the modeling of the IIR diaerani of fell stars close to Va3e Mon pertrined in sect., The same amount of reddening is derived from the modeling of the HR diagram of field stars close to V838 Mon performed in sect. + 3., 3. + In fact. entering Table 2 or Figure 5 with the distance (10 spc) to V838 Mon frou the spectro-photometric parallax ο the D3V companion. Ep y—SI is obtained.," In fact, entering Table 2 or Figure 5 with the distance (10 kpc) to V838 Mon from the spectro-photometric parallax to the B3V companion, $E_{B-V}$ =0.87 is obtained." +" We therefore conclude that the extinction toward Vasa Mon follows the standard Ry=Ay/Epy=3.1 law aud the reddening amounts to Lyy=O.8TEO.OL,", We therefore conclude that the extinction toward V838 Mon follows the standard $R_{\rm V} = A_{\rm V}/E_{B-V} = $ 3.1 law and the reddening amounts to $E_{B-V}$ $\pm$ 0.01. + There are several auc independent aremments and evidences that support a long distance scale to VS38 Mon. of the order of LO kpc.," There are several and independent arguments and evidences that support a long distance scale to V838 Mon, of the order of 10 kpc." + Analvsis of the high-resolution IST poluiuetiy inaeges of the light-echo led Boud et al. (, Analysis of the high-resolution HST polarimetry images of the light-echo led Bond et al. ( +2003) to place a lower limit of 6 kpc to the distauce of Vase Mon.,2003) to place a lower limit of 6 kpc to the distance of V838 Mon. +" Working on the same UST material. Twleuda (2001) revised the distance to SE? χο,"," Working on the same HST material, Tylenda (2004) revised the distance to $\pm$ 2 kpc." + The spectro-photometric parallax to the D3V companion derived in sect., The spectro-photometric parallax to the B3V companion derived in sect. + 5 is 10 kpe., 5 is 10 kpc. + Furthermore. reversing the argument of the previous section. we can cuter Table 2 or Fiewe 5 with the reddening Ep y=O.87 (corresponding to y-=2.7) determined from he iuterstellar lines ane the colors of the D3V. companion. obtaining the same distance of 10 kpe to Vass Mon.," Furthermore, reversing the argument of the previous section, we can enter Table 2 or Figure 5 with the reddening $E_{B-V}$ =0.87 (corresponding to $A_V$ =2.7) determined from the interstellar lines and the colors of the B3V companion, obtaining the same distance of 10 kpc to V838 Mon." + Two other arguments are in favor of a large distance o Vs3e Mon. given its proxiuitv to the ealactic aue (b= 3°51 ealactic latitude).," Two other arguments are in favor of a large distance to V838 Mon, given its proximity to the galactic plane $b$ $-3^\circ$ $^\prime$ galactic latitude)." + First. we have seeu above that the Π radio observations iu the direction of Vasa Mon reveal three componcuts whose velocity natch exactly that of the lec components seen in he interstellar absorption lines.," First, we have seen above that the HI radio observations in the direction of V838 Mon reveal three components whose velocity match exactly that of the three components seen in the interstellar absorption lines." + Given the fact. that he radio observatious integrate along the whole line of sight through the Galaxy aud that no IIT is secubeyond Voa3ea Mon Gu tho sense that no corresponding interstellar ines are detected in the ligh-resolition spectra). it is straightforward to couclude that Vass Mou lies at ercat," Given the fact that the radio observations integrate along the whole line of sight through the Galaxy and that no HI is seen V838 Mon (in the sense that no corresponding interstellar lines are detected in the high-resolution spectra), it is straightforward to conclude that V838 Mon lies at great" +The study of the processes governing the formation and destruction of molecular clouds is eritical for our understanding of how galaxies have evolved in our Universe.,The study of the processes governing the formation and destruction of molecular clouds is critical for our understanding of how galaxies have evolved in our Universe. + In terms of column and local volume densities only two extreme states of cloud evolution have been systematically observed: diffuse atomic clouds traced by the cem line of (e.g.?) anc dense molecular clouds traced by rotational transitions of CO (e.g.?).., In terms of column and local volume densities only two extreme states of cloud evolution have been systematically observed: diffuse atomic clouds traced by the cm line of \citep[e.g.][]{Kalberla2009} and dense molecular clouds traced by rotational transitions of CO \citep[e.g.][]{Dame01}. + We know. however. very little about the intermediate phases of cloud evolution and the interface between diffuse and dense nolecular σας.," We know, however, very little about the intermediate phases of cloud evolution and the interface between diffuse and dense molecular gas." + Galactic Observations of Terahertz C4). a Herschel Key Project. is devoted to study the |] emission i different environments in our Galaxy.," alactic bservations of erahertz ), a Herschel Key Project, is devoted to study the ] emission in different environments in our Galaxy." + The survey will observe the u]] um line over a volume weighted sampling of 500 lines—of-sight (LOS)., The survey will observe the ] $\mu$ m line over a volume weighted sampling of 500 lines–of–sight (LOS). + Upon completion. it will provide a database of a few thousand u]]-emitting clouds distributed over the entire Galactic plane.," Upon completion, it will provide a database of a few thousand ]–emitting clouds distributed over the entire Galactic plane." + The |Cu]]| fine structure line at 158mm is an excellent tracer of the interface between diffuse and dense molecular gas., The ] fine structure line at $\mu$ m is an excellent tracer of the interface between diffuse and dense molecular gas. + The densities and temperatures in this interface allow effective collisional excitation of this line., The densities and temperatures in this interface allow effective collisional excitation of this line. +" The and H2 volume densities are a significant fractior of. or comparable to. the critical densities for collisional 10"" and 7.1x10° em? at T=100 KK. respectively). the kinetic temperatures are.100K. and the formation of CO ts inhibited by limited shielding against far-ultraviolet (FUV) photons and therefore most of the gas-phase carbon is i1 C and some ο."," The and ${\rm H}_2$ volume densities are a significant fraction of, or comparable to, the critical densities for collisional $\times10^{3}$ and $\times10^{3}$ $^{-3}$ at $T=100$ K, respectively), the kinetic temperatures are, and the formation of CO is inhibited by limited shielding against far-ultraviolet (FUV) photons and therefore most of the gas-phase carbon is in $^+$ and some $^0$." + Here we present the first results on the molecular cloud-atomic cloud interface from the project., Here we present the first results on the molecular cloud-atomic cloud interface from the project. + During the Herschel Priority Science and Performance Verification phase. we have collected data along 5 LOSs near /=340° .aand 9 LOSs near /=20° citepVelusamy2010..," During the Herschel Priority Science and Performance Verification phase, we have collected data along 5 LOSs near $l=340$ and 9 LOSs near $l=20$ \\citep{Velusamy2010}." +" The focus of this letter is to study [Cu]] components towards clouds that have sufficient column density to have significant ""CO emission.", The focus of this letter is to study ] components towards clouds that have sufficient column density to have significant $^{13}$ CO emission. + Such regions can be considered as dense Photon-Dominated Regions ( or photodissociation regions. or PDRs).," Such regions can be considered as dense Photon–Dominated Regions ( or photodissociation regions, or PDRs)." + PDRs are regions where the chemistry and thermal balance is dominated by the effects of FUV photons from young stars (?.andreferencestherein)..," PDRs are regions where the chemistry and thermal balance is dominated by the effects of FUV photons from young stars \citep[][and references + therein]{HollenbachTielens99}." + These data are therefore important for the study of the stellar feedback of newly formed massive stars in their progenitor molecular cloud., These data are therefore important for the study of the stellar feedback of newly formed massive stars in their progenitor molecular cloud. +" We combine the u]|| data with observations of ""CO and CO from the ATNF Mopra 22-m telescope to study 58 high-column density PDRs.", We combine the ] data with observations of $^{12}$ CO and $^{13}$ CO from the ATNF Mopra 22-m telescope to study 58 high–column density PDRs. + We use the πι] ο and u]]/CO integrated intensity ratios to constrain physical conditions of the line-emitting gas comparing with a grid of PDR models., We use the $^{12}$ CO and $^{13}$ CO integrated intensity ratios to constrain physical conditions of the line–emitting gas comparing with a grid of PDR models. + The Galactic plane has been studied in u]] with low velocity and spatial resolution observations with COBE (?) and BICE (?)., The Galactic plane has been studied in ] with low velocity and spatial resolution observations with COBE \citep{Bennett1994} and BICE \citep{Nakagawa1998}. + The high angular (12)) and velocity ss!) resolution of the Herschel/HIFL observations allow us to study for the first time the rich structure of molecular clouds along the line-of-sight towards the galactic plane., The high angular ) and velocity $^{-1}$ ) resolution of the Herschel/HIFI observations allow us to study for the first time the rich structure of molecular clouds along the line-of-sight towards the galactic plane. + The Kuiper Airborne Observatory allowed the study of a handful of regions with velocity resolved n]] observations (e.g.95)," The Kuiper Airborne Observatory allowed the study of a handful of regions with velocity resolved ] observations \citep[e.g.][]{Boreiko1988,Boreiko91}." + However. they were limited to massive. star-forming regions with dense and hot PDRs.," However, they were limited to massive star-forming regions with dense and hot PDRs." + The sensitivity of our observations allow us to study for the first time the population of PDRs in our galaxy that are exposedto weaker FUV radiation fields., The sensitivity of our observations allow us to study for the first time the population of PDRs in our galaxy that are exposedto weaker FUV radiation fields. +" We observed the [Cu] Pi ""Py, lie at GGHz towards 16 LOSs in the Galactic. plane with the HIFI (?) instrument on board the Herschel space observatory (?)..", We observed the ] $^2$ $_{3/2} \to ^2$ $_{1/2}$ line at GHz towards 16 LOSs in the Galactic plane with the HIFI \citep{deGraauw2010} instrument on board the Herschel space observatory \citep{Pilbratt2010}. . + We refer to ? for more details about the, We refer to \citet{Velusamy2010} for more details about the +eucrgv (GE«— 0) inflow.,energy $E<0$ ) inflow. + The fluid part of energy. per total energy. is deuoted by E/|E|—Xa44C7.Nana). where (αιμαδα cui become negative even if CXauig)n; IS positive (ITirotanictal.1992): that is. the initial positive euergy {fgjing is extracted from the plana. aud is deposited in the magnetic field tobe carried outwards.," The fluid part of energy per total energy is denoted by $E/|E|-X_{\rm em} (\equiv X_{\rm fluid})$ , where $(X_{\rm fluid})_{\rm H}$ can become negative even if $(X_{\rm fluid})_{\rm inj}$ is positive \citep{Hirotani-TNT92}; that is, the initial positive energy $(\mu u_t)_{\rm inj}$ is extracted from the plasma and is deposited in the magnetic field tobe carried outwards." + Figures 10bb and 11bb show the energy conversion between the fiuid part aud. electromagnetic part in the Sclsviuzschild eeoimetry. where βία is always vositive.," Figures \ref{fig:MHDaccA}b b and \ref{fig:MHDaccB}b b show the energy conversion between the fluid part and electromagnetic part in the Schwarzschild geometry, where $X_{\rm fluid}$ is always positive." +" Though the poloidal flow solutiou iu the black hole maguetosphere coutaius two Alfvénn radii +=aN and p=rt"" an accretion across both Alfvénn radii is possible when the injection point is located |vetween the outer Alfvénn point and the outer light surface."," Though the poloidal flow solution in the black hole magnetosphere contains two Alfvénn radii $r=r_{\rm A}^{in}$ and $r=r_{\rm A}^{out}$, an accretion across both Alfvénn radii is possible when the injection point is located between the outer Alfvénn point and the outer light surface." +" One of them corresponds to the Alfvéóun poiut or the considered flow. where the requirement of Dqv=dA >.Is satisfied.⋅⋅ and Xu,↽ does not chauge its. sie:. such a poiut is A'"" for case (1) aud AU for case Gi)."," One of them corresponds to the Alfvénn point for the considered flow, where the requirement of $u_p^2=u_{\rm AW}^2$ is satisfied, and $X_{\rm em}$ does not change its sign; such a point is $^{in}$ for case (i) and $^{out}$ for case (ii)." +" However. IX, changes its sign at the other Alfvénredis. which is not the Alfvéuu point for the cousidering. SAF-solutionB because «45Dκ there: such a rajus ds r—prt for case (3) aud r=ήν for case (i)."," However, $X_{\rm em}$ changes its sign at the other Alfvénn, which is not the Alfvénn point for the considering -solution because $u_p^2 \neq u_{\rm AW}^2$ there; such a radius is $r=r_{\rm A}^{out}$ for case (i) and $r=r_{\rm A}^{in}$ for case (ii)." +" Outside this latter Alfvéun radius. B""/D,«0 aud maguctic energy streams outward (iaENou0j o the injection point. while side this point BC/D,peo>0 and naenetic cucrey streams inward."," Outside this latter Alfvénn radius, $B^\phi/B_p<0$ and magnetic energy streams outward $nu^r |E| X_{\rm em} >0$ ) to the injection point, while inside this point $B^\phi/B_p>0$ and magnetic energy streams inward." +" The fuid part of eucrgy flux always streams inward ( na|ENand< 1)., Figure \ref{fig:MHDaccD} shows a negative energy accretion solution $\Omega_F \tilde L>1$ ). + We see that the Alfvénn point locates inside the ergosphere (see Paper D., We see that the Alfvénn point locates inside the ergosphere (see Paper I). +" The outgoiug clectromaguctic cucrey flux is always greater than the ingoine fluid energev flux (VQ,< laud Neng=1Nay> 0).", The outgoing electromagnetic energy flux is always greater than the ingoing fluid energy flux $X_{\rm em} < -1$ and $X_{\rm fluid} = -1-X_{\rm em} > 0$ ). +" The magnetic Seld lunes are trailed (BeFD, <0) everywhere due to the black hole rotation.", The magnetic field lines are trailed $B^\phi/B_p <0$ ) everywhere due to the black hole rotation. + For accretion with OpL 70° ))arepref erentiallylocatedattheedgeso f theintergranulardownf lowhenug, see BygragT hor"," Near the optical surface, vortices with a large inclination with respect to the vertical > ) are preferentially located at the edges of the intergranular downflow lanes, see Fig. \ref{fig:mapvor}." +ghtidtatheaiptichnenidaée). < 20° )Daremostlyinsidethelaneswherethedownf lowisstrong., Those with a small inclination < 20 ) are mostly inside the lanes where the downflow is strong. +" We find most of the strong vortical flows at a few hundred kilometers below the optical surface, see Fig. 3.."," We find most of the strong vortical flows at a few hundred kilometers below the optical surface, see Fig. \ref{fig:depthcov}." +" With an increasing upper limit for the swirling period, the distribution declines less steeply with depth, i.e., most of the very deep swirls are slow."," With an increasing upper limit for the swirling period, the distribution declines less steeply with depth, i.e., most of the very deep swirls are slow." + The structure at great depths is also filamentary., The structure at great depths is also filamentary. +" Horizontal swirls (dotted lines) are more numerous than vertical ones (dashed lines), consistent with isotropy."," Horizontal swirls (dotted lines) are more numerous than vertical ones (dashed lines), consistent with isotropy." +" Near and above the optical surface, the distribution of inclination angles deviates from isotropy (see next Section)."," Near and above the optical surface, the distribution of inclination angles deviates from isotropy (see next Section)." +" In Fig. 4,,"," In Fig. \ref{fig:disdens}," + we present statistical properties ofregions with large Ag., we present statistical properties ofregions with large $\lci$. +" For these analyses, we combined data from five different snapshots of Run C with a separation of about 7 minutes each."," For these analyses, we combined data from five different snapshots of Run C with a separation of about 7 minutes each." +" All grid cells are treated equally in the statistics, regardless of whether or not they form part of a larger, contiguous swirling region."," All grid cells are treated equally in the statistics, regardless of whether or not they form part of a larger, contiguous swirling region." +" In panels (b)-(h), we plot histograms normalized such as to give the fraction density with respect to the considered variable: the integral over a certain range of the variable gives the fraction of grid cells with values in that range."," In panels (b)–(h), we plot histograms normalized such as to give the fraction density with respect to the considered variable: the integral over a certain range of the variable gives the fraction of grid cells with values in that range." +" For every histogram we considered a )Ggridcells)verticalrangeabouttheindicatedheight, takingatotalo f grid cells into account."," For every histogram we considered a (5 grid cells) vertical range about the indicated height, taking a total of grid cells into account." + The individual panels of Fig., The individual panels of Fig. + 4 are described in the following. (, \ref{fig:disdens} are described in the following. ( +"a) This plot shows, as a function of height, the fraction of space occupied by swirls with \(compareFig. 3)).","a) This plot shows, as a function of height, the fraction of space occupied by swirls with (compare Fig. \ref{fig:depthcov}) )." +T hehighestoccurrenceo f these swirlsisatzz , The highest occurrence of these swirls is at z being the average height of the optical surface). +"Inwardly spiraling flows that diverge in the direction of the vortex (type 2, see Sect. 2.2))"," Inwardly spiraling flows that diverge in the direction of the vortex (type 2, see Sect. \ref{sec:vortex}) )" + are prevailing everywhere; their mean fraction with respect to all types is below and above., are prevailing everywhere; their mean fraction with respect to all types is below and above. +" The mean fraction of swirling flows of the outwardly spiraling, converging type (3) is below JanddecreasestoT%abovez"," The mean fraction of swirling flows of the outwardly spiraling, converging type (3) is below and decreases to above." +z )..Types(l)and(4)areinsignificant. (, Types (1) and (4) are insignificant. ( +"b) This plot shows histograms of the swirling period τς, normalized such that the integral over all","b) This plot shows histograms of the swirling period $\taus$ , normalized such that the integral over all" +does not exhibit an unambiguous signal.,does not exhibit an unambiguous signal. +" For u/849 nm and H, lines. no jump ts detected in the differential phase."," For /849 nm and $_\alpha$ lines, no jump is detected in the differential phase." + For the Can/866 nm line. jumps seem to be present but their amplitude with respect to the phase precision ts too low for a significant detection.," For the /866 nm line, jumps seem to be present but their amplitude with respect to the phase precision is too low for a significant detection." + The phase jumps can be explained either in. terms of an asymmetric chromosphere or an asymmetric. photosphere. which implies structure in the chromosphere and/or in. the photosphere.," The phase jumps can be explained either in terms of an asymmetric chromosphere or an asymmetric photosphere, which implies structure in the chromosphere and/or in the photosphere." + Our observations provide phase measurements for only one baseline for each line preventing us from deriving the exact photocenter positions., Our observations provide phase measurements for only one baseline for each line preventing us from deriving the exact photocenter positions. + However. the fact that phase signatures are not present with the same amplitude in all lines may indicate that structures are present in the chromosphere and not only in the photosphere.," However, the fact that phase signatures are not present with the same amplitude in all lines may indicate that structures are present in the chromosphere and not only in the photosphere." + The star ó Crt perfectly illustrates this property because an unambiguous phase jump (amplitude greater than 20° seen in the bottom left panel of Fig. 6)), The star $\delta$ Crt perfectly illustrates this property because an unambiguous phase jump (amplitude greater than $20^\circ$ seen in the bottom left panel of Fig. \ref{figdiff854}) ) +" is present in the core of the Cau/s54 nm line whereas the phase remains constant over the H, line (see Fig. 5)).", is present in the core of the /854 nm line whereas the phase remains constant over the $_{\alpha}$ line (see Fig. \ref{figdiff656}) ). + Until now. only spectroscopic methods have been used to detect and study the presence of structures in the chromosphere of single K giant. stars.," Until now, only spectroscopic methods have been used to detect and study the presence of structures in the chromosphere of single K giant stars." +" For instance. ? studied in detail the chromosphere. discriminating between different structures (plages. prominences. flares. and microflares). by analyzing the ratio of excess emission equivalent width (EW) of two iinfrared lines (Eysy2/Esios) or the ratio of EWs of two Balmer lines (£y,/£u,)."," For instance, \cite{montes00} studied in detail the chromosphere, discriminating between different structures (plages, prominences, flares, and microflares), by analyzing the ratio of excess emission equivalent width (EW) of two infrared lines $E_{8542}/E_{8498}$ ) or the ratio of EWs of two Balmer lines $E_{{\rm H_\alpha}}/E_{{\rm H_\beta}}$ )." + Our study shows that additional informations could be provided by interferometry in the future to help us understand the structures in the chromosphere of single K giant stars., Our study shows that additional informations could be provided by interferometry in the future to help us understand the structures in the chromosphere of single K giant stars. + In reality. the structure of the chromospheric network delineated by bundles of magnetic field lines could be spatially studied in the future.," In reality, the structure of the chromospheric network delineated by bundles of magnetic field lines could be spatially studied in the future." + Combinations of interferometric observations in several spectral lines will allow us to determine the characteristics (size. position. intensity) of the chromospheric structures such as plages (part of the chromospheric network of bright emission associated with concentrations of magnetic fields) and prominences or filaments (dense clouds of material suspended above the stellar surface by loops of magnetic field).," Combinations of interferometric observations in several spectral lines will allow us to determine the characteristics (size, position, intensity) of the chromospheric structures such as plages (part of the chromospheric network of bright emission associated with concentrations of magnetic fields) and prominences or filaments (dense clouds of material suspended above the stellar surface by loops of magnetic field)." + These perspectives require interferometric observations with a more complete (u.v) coverage (several baselines with different lengths and orientations) than that available from these first observations.," These perspectives require interferometric observations with a more complete $(u,v)$ coverage (several baselines with different lengths and orientations) than that available from these first observations." + The star8 Cet is the only one for which a model atmosphere including a chromosphere and a transition region has been fitted (?).., The star $\beta$ Cet is the only one for which a model atmosphere including a chromosphere and a transition region has been fitted \citep{Eriksson83}. . + The adopted atmospheric parameters for the target are given in Table 7.., The adopted atmospheric parameters for the target are given in Table \ref{Atm_carac}. + We note that ?. useda pre-Hipparcos paralax estimate of p=61 mas. which ts about twice the Hipparcos measurement (p=34 mas. ?)).," We note that \cite{Eriksson83} useda pre-Hipparcos paralax estimate of $p = 61$ mas, which is about twice the Hipparcos measurement $p = 34$ mas, \citealt{Perryman97}) )." + The star was thought to be closer. thus smaller and consequently leading to an overestimation of the surface gravity by ?..," The star was thought to be closer, thus smaller and consequently leading to an overestimation of the surface gravity by \cite{Eriksson83}." + We adopt a surface gravity based on our previously estimated interferometric radius (R=16.8 Ris) and the mass deduced from the evolutionary tracks (M.=3 M..)., We adopt a surface gravity based on our previously estimated interferometric radius $R=16.8\ R_\odot$ ) and the mass deduced from the evolutionary tracks $M = 3\ M_\odot$ ). + The uncertainties in these two parameters give a surface gravity ranging from 2.45 to 2.55., The uncertainties in these two parameters give a surface gravity ranging from 2.45 to 2.55. + We adopted a value of logg=2.45. which ts consistent with the values determined by both ? and ? from a spectroscopic analysis basedon the ionization equilibrium of iron.," We adopted a value of $\log g = 2.45$, which is consistent with the values determined by both \citet{luck95} and \citet{Kovacs83} from a spectroscopic analysis basedon the ionization equilibrium of iron." + We interpolate the model atmospheres (?) with spherical geometry for the atmospherical parameters Τομ=4830 K. logg= 2.45. |Fe/H] = 0. andZ=2 km s'. all obtained with the interpolation code," We interpolate the model atmospheres \citep{Gustafsson08} with spherical geometry for the atmospherical parameters $T_{\rm eff} = 4830$ K, $\log g =2.45$ , [Fe/H] = 0, and$\zeta = 2$ km $^{-1}$ , all obtained with the interpolation code" +mass function for all the haloes used. in the sample.,mass function for all the haloes used in the sample. + Lo compare the ciflercnt subhalo mass functions. we have rescaled the subbalo mass by dividing bv the virial mass of the parent halo.," To compare the different subhalo mass functions, we have rescaled the subhalo mass by dividing by the virial mass of the parent halo." + Each line represents the average eumulative mass function over all the haloes in each mass bin., Each line represents the average cumulative mass function over all the haloes in each mass bin. + Note tha in this paper we define the ‘virial mass’ as AMooo. the mass within a sphere of density. 200 times the critical value a redshift zero.," Note that in this paper we define the `virial mass' as $M_{200}$, the mass within a sphere of density $200$ times the critical value at redshift zero." + The lines end at dillerent. places because of he dilfering mass resolution of the simulations (see Table 1)., The lines end at different places because of the differing mass resolution of the simulations (see Table \ref{tab:tab1}) ). + We find that all four cumulative mass functions agree within the statistical errors., We find that all four cumulative mass functions agree within the statistical errors. + Finally. in the bottom righ vanel. we show the dilferential subhalo mass functions in units of rescaled mass.," Finally, in the bottom right panel, we show the differential subhalo mass functions in units of rescaled mass." + We note that the ‘universality’ of the subhalo mass unction seen here appears to be quite robust with respect o numerical resolution., We note that the `universality' of the subhalo mass function seen here appears to be quite robust with respect to numerical resolution. + In Fig., In Fig. + 2— we compare the average cumulative mass functions for haloes with mass ~10ΤΝ. from simulations B2 and M23.," \ref{fig:fig1b} we compare the average cumulative mass functions for haloes with mass $\simeq 10^{14}\,h^{-1}{\rm +M}_{\odot}$ from simulations B2 and M3." + We here averaged 5 haloes for simulations D2. and 4 for simulation. M3. to reduce the object-to-object scatter that is unavoidable for small numbers of subhalos.," We here averaged $5$ haloes for simulations B2, and $4$ for simulation M3, to reduce the object-to-object scatter that is unavoidable for small numbers of subhalos." + Despite an order of magnitude difference in numerical resolution. the agreement. between 10 simulations is good.," Despite an order of magnitude difference in numerical resolution, the agreement between the simulations is good." + We are able to resolve the right number of objects in the low-resolution simulation above its resolution limit (shown as a vertical dotted. line. in the figure)., We are able to resolve the right number of objects in the low-resolution simulation above its resolution limit (shown as a vertical dotted line in the figure). + A similar result. was obtained by 2.seetheirFig.5) using a set of 4 resimulations of the same ‘luster with svstematicallv increasing resolution. thereby allowing a cirect study of numerical convergence.," A similar result was obtained by \citet[][see their Fig.~5]{volker2} using a set of $4$ re–simulations of the same cluster with systematically increasing resolution, thereby allowing a direct study of numerical convergence." + “Phis showed in particular that the S2 simulation used here has well converged to the properties of a much higher resolution simulation above its own resolution limit. as used here.," This showed in particular that the S2 simulation used here has well converged to the properties of a much higher resolution simulation above its own resolution limit, as used here." + Further support for our results was also. found bv 7.seetheirFig. 3). ," Further support for our results was also found by \citet[][see their +Fig.~3]{felix2}. ." +Thev compared the οseries simulations from ?) with an extremely well resolved. resimulation of a MilkyWay sized halo., They compared the S–series simulations from \citet{volker2} with an extremely well resolved re--simulation of a Milky–Way sized halo. + This latter simulation used an updated: version of. the simulation code. and more conservative integration parameters than usec here (Following?).. suggesting that the subhalo mass function is à relatively robust quantity ancl that the simulations we discuss here are adequate for our purposes.," This latter simulation used an updated version of the simulation code and more conservative integration parameters than used here \citep[following][]{power}, suggesting that the subhalo mass function is a relatively robust quantity and that the simulations we discuss here are adequate for our purposes." + As a further check of the robustness. of our results we also compare the internal structure of subhalos drawn rom our cdillerent simulations., As a further check of the robustness of our results we also compare the internal structure of subhalos drawn from our different simulations. + Fig., Fig. + 3. shows the correlation oetween the substructure mass and the third. power of the maximum circular velocity. Vias. measured. clirectly from he circular velocity curve of each subhalo.," \ref{fig:fig1c} shows the correlation between the substructure mass and the third power of the maximum circular velocity, $V_{\rm max}$, measured directly from the circular velocity curve of each subhalo." + Different svnibols are used for substructures drawn from cillerent simulations., Different symbols are used for substructures drawn from different simulations. + vote that. for the range of masses shown in the. plot. substructures drawn from simulation M3 contain at least 60 xuticles.," Note that for the range of masses shown in the plot, substructures drawn from simulation M3 contain at least $60$ particles." + While the scatter is clearly large for haloes with such a low number of particles. the good general agreement )etween the runs suggests that the smallest substruetures in our lower resolution simulations have an internal structure hat is still reliably resolved. at least in a statistical fashion.," While the scatter is clearly large for haloes with such a low number of particles, the good general agreement between the runs suggests that the smallest substructures in our lower resolution simulations have an internal structure that is still reliably resolved, at least in a statistical fashion." + Our results confirm. the conclusion. drawn by ?):: he mass function of substructures appears to be almost independent of the mass of the parent halo., Our results confirm the conclusion drawn by \citet{moore2}: the mass function of substructures appears to be almost independent of the mass of the parent halo. +" While our results are consistent with such a ""scale.free’ subhalo mass function. the haloto scatter. in our simulation set ds quite large. preventing us from putting tight constraints on the accuracy with which the ‘scalefree” subhalo mass function is preserved. when halocs of different mass are considered."," While our results are consistent with such a `scale–free' subhalo mass function, the halo–to–halo scatter in our simulation set is quite large, preventing us from putting tight constraints on the accuracy with which the `scale–free' subhalo mass function is preserved when haloes of different mass are considered." + And hence there is still room for weak trends with mass., And hence there is still room for weak trends with mass. + A clear detection of these would require simulations with larger cvnamic range. and larger samples of simulated haloes for cach mass bin.," A clear detection of these would require simulations with larger dynamic range, and larger samples of simulated haloes for each mass bin." + As we discuss in more detail in Sec. 7.2..," As we discuss in more detail in Sec. \ref{sec:mah}," + our findings sugeest that the destruction of satellites due to the physical processes of dynamical friction ancl tidal stripping on one hand. and the accretion of new satellites on the other hand. cancel out in such a wav that the subhalo mass function does not depend or at. best very weakly. depends on the mass of the parent halo.," our findings suggest that the destruction of satellites due to the physical processes of dynamical friction and tidal stripping on one hand, and the accretion of new satellites on the other hand, cancel out in such a way that the subhalo mass function does not depend or at best very weakly depends on the mass of the parent halo." + Phe reason for the invariance of the subhalo mass function may lie in the physical nature of this dvnamical balance. which may be insensitive to the slightly broken seale-invariance of dark. haloes themselves.," The reason for the invariance of the subhalo mass function may lie in the physical nature of this dynamical balance, which may be insensitive to the slightly broken scale-invariance of dark haloes themselves." + Thisshows up as a mass-clependence of halo concentrations. or example.," Thisshows up as a mass-dependence of halo concentrations, for example." + Some Lully analytic models for the subhalo abundance have been developed: (c.g.2).. but they are wesenthy not able to account for mass-loss ancl dvnamical riction self-consistently. and so provide Little guidance o answer this interesting question.," Some fully analytic models for the subhalo abundance have been developed \citep[e.g.][]{ravi}, but they are presently not able to account for mass-loss and dynamical friction self-consistently, and so provide little guidance to answer this interesting question." + A full understanding of the apparent ‘conspiracy’ that establishes an almost miass-invariant subhalo mass function will therefore require turther simulations., A full understanding of the apparent `conspiracy' that establishes an almost mass-invariant subhalo mass function will therefore require further simulations. + In this section we investigate whether the properties of the largest substructures depend on the mass of the parent halo., In this section we investigate whether the properties of the largest substructures depend on the mass of the parent halo. + ‘This is interesting since the largest substructures mark the sites where one expects to find the brightest galaxies., This is interesting since the largest substructures mark the sites where one expects to find the brightest galaxies. +" 1n the following. AZ, refers to the mass of the mos massive subhalo and. AJ» to the mass of the second. nios massive subhalo within the virial radius of à given objec of virial mass Afsoy."," In the following, $M_1$ refers to the mass of the most massive subhalo and $M_2$ to the mass of the second most massive subhalo within the virial radius of a given object of virial mass $M_{200}$." + Note that we have excluded from our analysis the subhalo associated. with the FOL group itself., Note that we have excluded from our analysis the subhalo associated with the FOF group itself. + 1n a semi-analvtic scheme. it is this ‘subhalo’ that woulc host the brightest cluster galaxy (BCC).," In a semi-analytic scheme, it is this `subhalo' that would host the brightest cluster galaxy (BCG)." + In Sec., In Sec. + 7.2 we wil show that. once accreted onto a massive halo. substructures suller significant stripping. an elfect that is more importan for substructures accreted at higher redshift.," \ref{sec:mah} we will show that, once accreted onto a massive halo, substructures suffer significant stripping, an effect that is more important for substructures accreted at higher redshift." + Ht is thenlikely. that the largest substructures we find within the virial radius ab the present time were acereted at relatively low redshift., It is thenlikely that the largest substructures we find within the virial radius at the present time were accreted at relatively low redshift. + In Fig. 4..," In Fig. \ref{fig:fig2}," + we plot AlpΛου às a function of Afous for 434 haloes crawn from all the simulations listed in Table 1L.., we plot $M_1/M_{200}$ as a function of $M_{200}$ for $434$ haloes drawn from all the simulations listed in Table \ref{tab:tab1}. . + This sample includes not only the central clusters in. our re-mulations. but also the other haloes found in the high-resolution regions around the re-simulated objects down toa mass limit of LOYA TALS.," This sample includes not only the central clusters in our re-simulations, but also the other haloes found in the high-resolution regions around the re-simulated objects down to a mass limit of $10^{13}\,h^{-1}\,{\rm + M}_{\odot}$ ." + We took carehowever to exclude haloes that contained low resolution particles., We took carehowever to exclude haloes that contained low resolution particles. + 1n simulation M3. weselected only haloes with a mass larger," In simulation $3$ , weselected only haloes with a mass larger" +"of a diagonal prior, the MSE for the prior alone is given by Npinsx(Sw?)=144. Adding the data, one could significantly NZ,.02,improve the constraints on some of the eigenmodes, thus reduce the MSE.","of a diagonal prior, the MSE for the prior alone is given by $N_{\rm bins} \times \langle \delta w^2 \rangle = N_{\rm bins}^2 +\sigma^2_{\rm m} = 144.$ Adding the data, one could significantly improve the constraints on some of the eigenmodes, thus reduce the MSE." +" As the prior is diagonal, the new eigenmodes are also eigenmodes of the prior with the same eigenvalue, given by Npinso2,=3.6 (shaded region in the upper panels of 5))."," As the prior is diagonal, the new eigenmodes are also eigenmodes of the prior with the same eigenvalue, given by $N_{\rm +bins} \sigma^2_{\rm m} = 3.6$ (shaded region in the upper panels of )." + The reduction of the MSE thus roughly tells us how many modes can be constrained compared to the prior., The reduction of the MSE thus roughly tells us how many modes can be constrained compared to the prior. +" For example, adding LSST reduces the MSE from 144 to 112, meaning that there are (144—112)/3.6~9 modes can be constrained by LSST, and similarly, the ideal 10k survey is able to constrain 7 modes."," For example, adding LSST reduces the MSE from 144 to 112, meaning that there are $(144-112)/3.6 \simeq 9$ modes can be constrained by LSST, and similarly, the ideal 10k survey is able to constrain 7 modes." +" With KDUST--LSST, one can actually constrain 10 eigenmodes."," With KDUST+LSST, one can actually constrain 10 eigenmodes." + These numbers can also be counted in the upper panel of above the prior threshold shown in shade., These numbers can also be counted in the upper panel of above the prior threshold shown in shade. +" For a correlated prior, we can analogously put a lower bound on the number of modes constrained by data using the MSE shown in2."," For a correlated prior, we can analogously put a lower bound on the number of modes constrained by data using the MSE shown in." +". For instance, for the case of z=0.1 and z=0.4, LSST combined with KDUST can at least constrain (35—18.1)/3.6~4 and (11.5—3.7)/3.6~2 modes, respectively."," For instance, for the case of $z_c=0.1$ and $z_c=0.4$, LSST combined with KDUST can at least constrain $(35-18.1)/3.6\simeq4$ and $(11.5-3.7)/3.6\simeq2$ modes, respectively." +" As we see, the number of new modes estimated in this way is reduced as the prior correlation length is increased."," As we see, the number of new modes estimated in this way is reduced as the prior correlation length is increased." +" This is as expected — as z, increases, more high frequency modes will be filtered out by the smoothness prior."," This is as expected – as $z_c$ increases, more high frequency modes will be filtered out by the smoothness prior." + Dome offers a very competitive site for studying dark energy., Dome A offers a very competitive site for studying dark energy. +" GivenA the amount of resources required to build a large telescope and run a massive survey there, one must give the highest priority to programs that cannot be easily carried out elsewhere."," Given the amount of resources required to build a large telescope and run a massive survey there, one must give the highest priority to programs that cannot be easily carried out elsewhere." +" Thus, a reasonable strategy is to focus on NIR imaging and collaborate with other surveys for optical data."," Thus, a reasonable strategy is to focus on NIR imaging and collaborate with other surveys for optical data." +" Using LSST as an example, we show that a high-resolution 5000-10,000 deg? KDUST survey in bands could improve LSST BAO+WL constraints on the dark energy EOS parameters wo and Wa by reducing the and shear measurement systematics."," Using LSST as an example, we show that a high-resolution 5000–10,000 $^2$ KDUST survey in bands could improve LSST BAO+WL constraints on the dark energy EOS parameters $w_0$ and $w_a$ by reducing the and shear measurement systematics." + A SNAP-like SN sample plus a large local and nearby SN sample from KDUST would further boost the DETF FOM by more than a factor of two., A SNAP-like SN sample plus a large local and nearby SN sample from KDUST would further boost the DETF FOM by more than a factor of two. +" In addition to forecasts for the wo-w; parametrization, we also apply à PCA approach to investigate the constraints on the dark energy EOS w(z) in a model-independent way."," In addition to forecasts for the $w_0$ $w_a$ parametrization, we also apply a PCA approach to investigate the constraints on the dark energy EOS $w(z)$ in a model-independent way." +" We find that regarding the number of the constrained eigenmodes of w(z), an ideal 10,000 deg? survey, combined withPlanck, can constrain 7 eigenmodes, while KDUST--LSST can allow us to constrain 3 more modes."," We find that regarding the number of the constrained eigenmodes of $w(z)$, an ideal 10,000 $^2$ survey, combined with, can constrain 7 eigenmodes, while KDUST+LSST can allow us to constrain 3 more modes." +" We have not discussed dark energy probes such as strong lensing, cluster counting, and higher-order statistics of the same galaxy and shear data, which could further tighten the constraints on the dark energy EOS."," We have not discussed dark energy probes such as strong lensing, cluster counting, and higher-order statistics of the same galaxy and shear data, which could further tighten the constraints on the dark energy EOS." + Strong lensing constrains dark energy through the time delay effect as well as counting of strong lenses., Strong lensing constrains dark energy through the time delay effect as well as counting of strong lenses. +" It is also an excellent probe of dark matter halo structures and, hence, can be used to measure dark matter particle properties."," It is also an excellent probe of dark matter halo structures and, hence, can be used to measure dark matter particle properties." +" With high-resolution imaging, one could extract more cosmological information from strong lensing observations."," With high-resolution imaging, one could extract more cosmological information from strong lensing observations." +" Therefore, Dome A could be particularly advantageous for strong lensing studies."," Therefore, Dome A could be particularly advantageous for strong lensing studies." +" Dark energy forecasts depend crucially on the assumed properties of the survey data, including all the systematics."," Dark energy forecasts depend crucially on the assumed properties of the survey data, including all the systematics." + Dome A has many advantages over other ground sites and has an environment close to that in space., Dome A has many advantages over other ground sites and has an environment close to that in space. +" Hence, we use well-studied LSST and SNAP as references to make crude estimates of the data for this investigation."," Hence, we use well-studied LSST and SNAP as references to make crude estimates of the data for this investigation." + Further work and detailed modeling are needed to give a more realistic assessment of the Dome A site for studying dark energy., Further work and detailed modeling are needed to give a more realistic assessment of the Dome A site for studying dark energy. +" We thank David Bacon, Rob Crittenden, Kazuya Koyama, Bob Nichol and Levon Pogosian for useful discussions."," We thank David Bacon, Rob Crittenden, Kazuya Koyama, Bob Nichol and Levon Pogosian for useful discussions." + GZ is supported by the ERC grant., GZ is supported by the ERC grant. + HZ is supported by the Bairen program from the Chinese Academy of Sciences and the National Basic Research Program of China grant No., HZ is supported by the Bairen program from the Chinese Academy of Sciences and the National Basic Research Program of China grant No. + 2010CB833000., 2010CB833000. + The work of L. Wang is partially supported by NSF grant AST-, The work of L. Wang is partially supported by NSF grant AST-0708873. + XZ is supported in part by the NSF of China., XZ is supported in part by the NSF of China. +Iu this study the attention is focused onu the properties of the relatively poor. compact. and evolved Fornax cluster. oue of the best studied galaxy clusters in the local universe (e.g. Ferguson 1989.. Ferguson Saudage 1988).,"In this study the attention is focused on the properties of the relatively poor, compact, and evolved Fornax cluster, one of the best studied galaxy clusters in the local universe (e.g. Ferguson \cite{ferg89}, Ferguson Sandage \cite{ferg88}) )." + Other uearby clusters are believed to be iu different evolutionary states., Other nearby clusters are believed to be in different evolutionary states. + Whereas Virgo (e.g. Saudage ct al. 1985.. ," Whereas Virgo (e.g. Sandage et al. \cite{sand85}, ," +Fereusou Sandage 1991)) is dominated by late type galaxies and is only half as dense iu the ceuter (unnbers of galaxies per volue) as Fornax., Ferguson Sandage \cite{ferg91}) ) is dominated by late type galaxies and is only half as dense in the center (numbers of galaxies per volume) as Fornax. + Centaurus (Jevjen Dressler 1997.. Steiu et al. 1997))," Centaurus (Jerjen Dressler \cite{jerj97b}, Stein et al. \cite {stei}) )" + and Coma (e.g. Secker Harris 1997)) show substructures. indicative of a stil ongoing cvnamical evolution. like for example cluster-cluster or cluster-eroup mereiug.," and Coma (e.g. Secker Harris \cite{seck97}) ) show substructures, indicative of a still ongoing dynamical evolution, like for example cluster-cluster or cluster-group merging." + Tn the first two papers of this series (1998a.. 19098b.. jicreafter Paper I aud Paper II) we investieated the distribution of galaxies in central Fornax fields.," In the first two papers of this series \cite{hilk99b}, \cite{hilk99a}, hereafter Paper I and Paper II) we investigated the distribution of galaxies in central Fornax fields." + We found wo compact objecta that belong to the Fornax cluster and müsht be candidates for isolated nuclei of stripped dwarf cllipticals., We found two compact objects that belong to the Fornax cluster and might be candidates for isolated nuclei of stripped dwarf ellipticals. + However. very few new members were ound compared to the study of Ferguson (1989)).," However, very few new members were found compared to the study of Ferguson \cite{ferg89}) )." + Thus. he spatial distribution aud buuinositv function of dwarf ealaxies in Fornax (Fergusou Saucdage 1988)) was confined.," Thus, the spatial distribution and luminosity function of dwarf galaxies in Fornax (Ferguson Sandage \cite{ferg88}) ) was confirmed." + Tn this paper we discuss the possibility. whether the iufall of dwarf galaxy iuto the cluster center may plav an Huportant role in the eurichineut of the ceutral elobular cluster svsteni. especially the increase of the elobular cluster specific frequency ον. as well as the formation of the exteuded cD halo.," In this paper we discuss the possibility, whether the infall of dwarf galaxy into the cluster center may play an important role in the enrichment of the central globular cluster system, especially the increase of the globular cluster specific frequency $S_N$, as well as the formation of the extended cD halo." + Iu the following section we eive a compilation of the necessary backeround of our analysis., In the following section we give a compilation of the necessary background of our analysis. + Tn their review about dwarf elliptical galaxies. Ferguson BineechSs (19913) ματ1ζος. the formation andl evolutionary scenarios that are predicted by theoretical models.," In their review about dwarf elliptical galaxies, Ferguson Binggeli \cite{ferg94}) ) summarized the formation and evolutionary scenarios that are predicted by theoretical models." + It is generally accepted that ealaxy formation started from gascous conditions in the early universe followed by the collapse of primordial density fluctuations. cooling of the gas and subsequent star formation (c.g. White Freuk 1991.. Blanchard et al. 1992..," It is generally accepted that galaxy formation started from gaseous conditions in the early universe followed by the collapse of primordial density fluctuations, cooling of the gas and subsequent star formation (e.g. White Frenk \cite{whit91}, Blanchard et al. \cite{blan}," + Cole ct al. 1991..," Cole et al. \cite{cole94}," +" Ixauffinzun et al. 100,"," Kauffmann et al. \cite{kauf93}," + Lacey et al. 1993))., Lacey et al. \cite{lace}) ). + Iu cold dark matter (CDAD) donunated models the collation of low-mass salaxies is favored. because for dwarf ealaxy halos collapsing at 2%3 10 the cooling iue is short compared to the free-fall time. thus cooling should be very cficient. and accordingly many dwarts will he onued.," In cold dark matter (CDM) dominated models the formation of low-mass galaxies is favored, because for dwarf galaxy halos collapsing at $z \simeq 3$ –10 the cooling time is short compared to the free-fall time, thus cooling should be very efficient, and accordingly many dwarfs will be formed." + A steep slope. a=2. of the initial nass function GVCAZ)dM.x AL) ds predicted (e.g. Blanchard ct al. 1992)).," A steep slope, $\alpha = -2$, of the initial mass function $N(M)$ $M \propto +M^\alpha$ ) is predicted (e.g. Blanchard et al. \cite{blan}) )." + In contrast. the faint cud slope of the observed hnuumositv functious in nearby clusters aro around à&L3840.14 (soe Ferguson Bineecli 19911).," In contrast, the faint end slope of the observed luminosity functions in nearby clusters are around $\alpha \simeq -1.3\pm0.4$ (see Ferguson Binggeli \cite{ferg94}) )." +" This contradiction is the so-called ""'overcooling xobleumr Cee. Cole 1991)).", This contradiction is the so-called “overcooling problem” (e.g. Cole \cite{cole91}) ). + Tf the CDM model prediction is correct. there must have been active some mechauisiis hat either counteracted the cooling during the collapse of dwarts or destroved the uuuerous cawarts after their ornation.," If the CDM model prediction is correct, there must have been active some mechanisms that either counteracted the cooling during the collapse of dwarfs or destroyed the numerous dwarfs after their formation." + Plausible mechanisms that mvolve internal as well as external agents are sunuuarized in the review by Fereuson Bineech (1991))., Plausible mechanisms that involve internal as well as external agents are summarized in the review by Ferguson Binggeli \cite{ferg94}) ). + Tn the following. we focus our attention ou the possibility. that uanv dwarf galaxies have merged with the central ealaxy.," In the following, we focus our attention on the possibility that many dwarf galaxies have merged with the central galaxy." + For a CDM. power spectrum in an Q=1 cosinoloey the epoch of chwart ealaxy formation is believed to be also the epoch of rapid imereine., For a CDM power spectrum in an $\Omega = 1$ cosmology the epoch of dwarf galaxy formation is believed to be also the epoch of rapid merging. + INautiinann et al. (1991)), Kauffmann et al. \cite{kauf94}) ) +" included the mereing of satellite ealaxics iu their CDM uodels and founc that most of the observationa data can be reproduced when adopting a mnoreiug timescale tha is a tenth of the tidal friction timescale. and when star formation is suppressed iu low-circula-velocity halos until they are accreted iuto larger systems,"," included the merging of satellite galaxies in their CDM models and found that most of the observational data can be reproduced when adopting a merging timescale that is a tenth of the tidal friction timescale, and when star formation is suppressed in low-circular-velocity halos until they are accreted into larger systems." + Further. eficieut mereing at all epochs results in a decrease of the faint cud slope of the LF compared to the initial predicted value of a=2.," Further, efficient merging at all epochs results in a decrease of the faint end slope of the LF compared to the initial predicted value of $\alpha = -2$." + Several authors have suggestedOO that tidal disruption (total dissolution of the ealaxy light) of ealaxies iu clusT centers as well as tidal stripping (only outer parts are affected. a remnant survives) nueht be related to the formation of ¢D halos (see references below).," Several authors have suggested that tidal disruption (total dissolution of the galaxy light) of galaxies in cluster centers as well as tidal stripping (only outer parts are affected, a remnant survives) might be related to the formation of cD halos (see references below)." + The time of formation is beiug discussed., The time of formation is being discussed. +" Most authors assiuae that the stripping processes take place after the cluster collapse (οιο, Gallagher Ostriker 1972.. Richstone 1976.. Ostriker Dausmau 1977.. Richstone Alaluuuth 1983))."," Most authors assume that the stripping processes take place after the cluster collapse (e.g. Gallagher Ostriker \cite{gall72}, Richstone \cite{richs76}, , Ostriker Hausman \cite{ostri}, Richstone Malumuth \cite{richs83}) )." + Tn contrast. Merritt (198 1)) explained the ecucral appearence of cD halos as theresult of ανασα] processes duiug the cluster collapse.," In contrast, Merritt \cite{merr}) ) explained the general appearence of cD halos as theresult of dynamical processes during the cluster collapse." +" Iu his scenario the acciuuulatiou of slowly-moving galaxies in the cluster core via dyvuauical friction ouly plavs an aportaut role for erowps or clusters with small velocity dispersion a.<500 kun Foruax: 360 kins τὸ, ", In his scenario the accumulation of slowly-moving galaxies in the cluster core via dynamical friction only plays an important role for groups or clusters with small velocity dispersion $\sigma_v \leq 500$ km $^{-1}$ (Fornax: $\sigma_v \simeq 360$ km $^{-1}$ ). +White (] 987)) argued that. in the case of fida disruption aud stripping. the distribution of stripped and disrupted material (diffuse light. dark uatter. CC's) should be Lore concentrated to. the contrer than the relaxed galaxy distribution. because galaxies closer to the center are more affected bw disruption processes than ealaxies outside.," White \cite{whit87}) ) argued that, in the case of tidal disruption and stripping, the distribution of stripped and disrupted material (diffuse light, dark matter, GCs) should be more concentrated to the center than the relaxed galaxy distribution, because galaxies closer to the center are more affected by disruption processes than galaxies outside." + Iu the case of Merritt’s inodoel. galaxics formed before the collapse. stripping occured duriug the collapse. aud finally the stripped material is distributed in the same way as the galaxies through collective relaxation.," In the case of Merritt's model, galaxies formed before the collapse, stripping occured during the collapse, and finally the stripped material is distributed in the same way as the galaxies through collective relaxation." +" Furthermore. it is interesting to note that also a large aunount of the iutrachistereas (seen as N-rav. halo) might have had its origin in dwurf galaxies. which could have expelled their gas by superneva-driven winds. or stripped off their gas (Trentham199 1, Nath"," Furthermore, it is interesting to note that also a large amount of the intraclustergas (seen as X-ray halo) might have had its origin in dwarf galaxies, which could have expelled their gas by supernova-driven winds, or stripped off their gas (Trentham\cite{tren94}, , Nath" +A laree majority of stars go through a period of high mass loss at the end of their evolution while climbing the asvinptotic giant brauch (ACB).,A large majority of stars go through a period of high mass loss at the end of their evolution while climbing the asymptotic giant branch (AGB). +" This mass loss. of the order of LO* to 10.141,yr. is the main source for replenishing interstellar space with processed materials."," This mass loss, of the order of $10^{-7}$ to $10^{-4} M_\odot +/{\rm yr}$, is the main source for replenishing interstellar space with processed materials." + Thus the mass loss mechanisin is an important subject of study., Thus the mass loss mechanism is an important subject of study. + Iu late type stars. this lieh mass loss produces a circumstellar envelope. (CSE) im which several maser species can be found.," In late type stars, this high mass loss produces a circumstellar envelope (CSE) in which several maser species can be found." + These nasers. especially SiO. IO aud OIL are excellent. tyrevers of the kinematics of the CSEs.," These masers, especially SiO, $_{2}$ O and OH, are excellent tracers of the kinematics of the CSEs." + The role of magnetic fieds du the mass loss and formations of CSEs is sill unclear., The role of magnetic fields in the mass loss and formations of CSEs is still unclear. + Polarization observations of circustellar 1Laseys Call reveal the streneth aud structure of the magnetic field throughout the CSE., Polarization observations of circumstellar masers can reveal the strength and structure of the magnetic field throughout the CSE. +" Observations of SiO uaser polarization lave shown highly ordered magnetic fields close to the ceutral star. at radii of 5-10 AU where the SiO maser cmission occurs (οιο, Ikeniball Diamond. 1997)."," Observations of SiO maser polarization have shown highly ordered magnetic fields close to the central star, at radii of 5-10 AU where the SiO maser emission occurs (e.g. Kemball Diamond, 1997)." + The measured circular polarization indicates magnetic field strenetls of z510 C. when assuni1 oa standard Zeeman interpretation.," The measured circular polarization indicates magnetic field strengths of $\approx 5-10$ G, when assuming a standard Zeeman interpretation." + However. a nou-Zecman interpretation has been proposed by Wiebe Watson (1998). which ouly requires fields of zz 30 mG. At umech lower deusities aud telperatures and generally mucji further from the star. OI maser observations nmieasure fields of z Line (e.g. sgvinezak Coleu. 1997: Masheder et al..," However, a non-Zeeman interpretation has been proposed by Wiebe Watson (1998), which only requires fields of $\approx$ 30 mG. At much lower densities and temperatures and generally much further from the star, OH maser observations measure fields of $\approx 1$ mG (e.g. Szymczak Cohen, 1997; Masheder et al.," + 1999) ancl there is little dispute of the Zecmman origi of the polarization., 1999) and there is little dispute of the Zeeman origin of the polarization. + Cutil veceuth. uo information on the maguetic fields at distances of a few hundred AU from the star was available.," Until recently, no information on the magnetic fields at distances of a few hundred AU from the star was available." +" This is the region where the WoO mascr eLulsson occurs,", This is the region where the $_{2}$ O maser emission occurs. + Because water is a non-paramaenetic nolecule. determination of the magnetic field is significantly more difficult.," Because water is a non-paramagnetic molecule, determination of the magnetic field is significantly more difficult." + The fields expected in the ΠοΟ maser region are, The fields expected in the $_{2}$ O maser region are +Gyr.,Gyr. + Figures 2 and 4 show a well-defined. inner slope with exponent 5=1.5 by 1 Gyr., Figures \ref{fig:densevol} and \ref{fig:densevSD} show a well-defined inner slope with exponent $\gamma=1.5$ by 1 Gyr. + This is consistent. with the recent work by Moore et al. (, This is consistent with the recent work by Moore et al. ( +1998) ancl [xIvpin et al. (,1998) and Klypin et al. ( +2000).,2000). + For longer evolution or noisier evolution. the inner exponent continues to evolve. although slowly (cf.," For longer evolution or noisier evolution, the inner exponent continues to evolve, although slowly (cf." + Fig. 2))., Fig. \ref{fig:densevol}) ). + In particular. this may help explain Jing Suto (2000) finding that the inner slope depends on environment. and the evolution of the scale radius ry (e.g. NEW).," In particular, this may help explain Jing Suto (2000) finding that the inner slope depends on environment and the evolution of the scale radius $r_s$ (e.g. NFW)." + However. as described in refsecimocdels.. further development needed. to address the allect of cuspy initial profiles will be necessary to. predict this trend and will be the subject of a later paper.," However, as described in \\ref{sec:models}, further development needed to address the affect of cuspy initial profiles will be necessary to predict this trend and will be the subject of a later paper." + This paper describes the evolution of a halo due to transient noise tvpical of the epoch of galaxy formation (7&1 Gyr)., This paper describes the evolution of a halo due to transient noise typical of the epoch of galaxy formation $\tau\simless1\gyr$ ). + We consider two transient. noise sources: Iv. by encounters and merging substructure (satellites)., We consider two transient noise sources: fly by encounters and merging substructure (satellites). + Both result drive the halo toward double power law profiles with inner exponent of approximately —1.5 and outer power law exponent of 3. similar to the form proposed by NEW and Moore et αἱ.," Both result drive the halo toward double power law profiles with inner exponent of approximately $-1.5$ and outer power law exponent of $-3$, similar to the form proposed by NFW and Moore et al." + Over a range of initial halo concentrations. the double power laws obtain independent of noise source and initial profile.," Over a range of initial halo concentrations, the double power laws obtain independent of noise source and initial profile." + The dynamical mechanism is simply explained., The dynamical mechanism is simply explained. + When one disturbs a halo it rings., When one disturbs a halo it rings. + This ringing is cdaniped but 10 mostly weakly. damped: modes shape the response and ominate the angular momentum transport responsible for evolution., This ringing is damped but the mostly weakly damped modes shape the response and dominate the angular momentum transport responsible for evolution. + Therefore. it doesn't matter how one hits the halo.," Therefore, it doesn't matter how one hits the halo," +The most important prerequisite of most successful astronomical observation. mainly optical observation. is no doubt a cloudless sky (see(hiestoryofGuillaumeLeGentilinthe1161/69TransitofVenus.cL.2.foraratherunlucky example)..,"The most important prerequisite of most successful astronomical observation, mainly optical observation, is no doubt a cloudless sky \citep[see the story of Guillaume Le Gentil in the 1761/69 Transit of Venus, cf.][for a rather unlucky example]{saw51}." + However. cloud cover forecast had been difficult for a long time as limited by theoretical understanding of mesoscale circulation (ie. modeling) and computation ability.," However, cloud cover forecast had been difficult for a long time as limited by theoretical understanding of mesoscale circulation (i.e. modeling) and computation ability." + Numerical simultaneous cloud cover forecast. [or astronomical observation had not been practically useful until the very end of 20th century., Numerical simultaneous cloud cover forecast for astronomical observation had not been practically useful until the very end of 20th century. + In the meteorological context. cloud plavs a kev role in radiation balance of the Earth. and is widely accepted to be the main source of uncertainty of elobal weather predictions ο.," In the meteorological context, cloud plays a key role in radiation balance of the Earth, and is widely accepted to be the main source of uncertainty of global weather predictions \citep[cf.][]{stu99,ste05}." + lt gathered much attention from atmospheric sciences community. both from modeling eroup and from observational group.," It gathered much attention from atmospheric sciences community, both from modeling group and from observational group." + The attempt to “parameterize cloud activity started in (he 1930s (οἱ.2.andreferencestherein).., The attempt to “parameterize” cloud activity started in the 1980s \citep[cf.][and references therein]{sun89}. + Several cloud schemes have been proposed since then. followed by eround- and space-based evaluation in aim for their refinement (e.g.??7)..," Several cloud schemes have been proposed since then, followed by ground- and space-based evaluation in aim for their refinement \citep[e.g.][]{hin99,luo05,yan06}." + Although many amateur and professional observatories have been (taken advantage of open access (o (he outputs of major numerical weather models for a decade. the reliability of such forecast is poorly understood.," Although many amateur and professional observatories have been taken advantage of open access to the outputs of major numerical weather models for a decade, the reliability of such forecast is poorly understood." + The meteorology community is mostly interested in parücular mesoscale events and/or particular regions. and pavs relatively little attention to the model performance over broader environment: while (here are only two studies from (he astronomy community (hat have investigated this topic: ?.. which suggested that only of cloudy nights at the European Southern Observatory sites could be identified bv the European Centre for Mecium-Hange Weather Forecasting (ECAIWF) model: and our earlier study (?).. which suggested a high detection rate accompanied with a moderate false alarm rate [rom the NCEP Global Forecast System (GES) model. based on the cloud observations from several astronomical observatories.," The meteorology community is mostly interested in particular mesoscale events and/or particular regions, and pays relatively little attention to the model performance over broader environment; while there are only two studies from the astronomy community that have investigated this topic: \citet{era01}, which suggested that only of cloudy nights at the European Southern Observatory sites could be identified by the European Centre for Medium-Range Weather Forecasting (ECMWF) model; and our earlier study \citep{ye11}, which suggested a high detection rate accompanied with a moderate false alarm rate from the NCEP Global Forecast System (GFS) model, based on the cloud observations from several astronomical observatories." + Even so. as the two studies are both limited at spatial densities aud scales. investigations of numerical cloud forecasts over global scale are still lacking.," Even so, as the two studies are both limited at spatial densities and scales, investigations of numerical cloud forecasts over global scale are still lacking." + This study is therefore. carried out in aim to assess the cloud forecast ability of a elobal numerical model to provide insight on its reliability as a reference for astronomical observation., This study is therefore carried out in aim to assess the cloud forecast ability of a global numerical model to provide insight on its reliability as a reference for astronomical observation. + In order to do this. we need: 1) output from global numerical model as forecast cata. and ii) observational data wilh appreciable temporal ancl spatial coverage.," In order to do this, we need: i) output from global numerical model as forecast data, and ii) observational data with appreciable temporal and spatial coverage." + The selection and reduction of such data will be discussed in the following section., The selection and reduction of such data will be discussed in the following section. +nass stars will uot display the fast WR wind).,mass stars will not display the fast WR wind). + Iu fact. its results cannot even be safely usec for the 35 sstar. since they depeud so critically ou the adopted parameters of the model (ass loss rates aud wind velocities for the various stages).," In fact, its results cannot even be safely used for the 35 star, since they depend so critically on the adopted parameters of the model (mass loss rates and wind velocities for the various stages)." + Aud they certainly fail to describe the situation for rotating stars. which display slow but iuteuse (and not racially sviunietrie) mass losses on the Alain sequence.," And they certainly fail to describe the situation for rotating stars, which display slow but intense (and not radially symmetric) mass losses on the Main sequence." +" Iu view of these unecertaintics. we adopt here a simplified prescription for the structure of the circtunstellar bubble. assuming spherical svuuuetry iu all cases,"," In view of these uncertainties, we adopt here a simplified prescription for the structure of the circumstellar bubble, assuming spherical symmetry in all cases." + We assiue that the winds have excavated a bubble of iy=O.01 cur? aud. consequently of radius μα my. my being the proton mass.," We assume that the winds have excavated a bubble of $n_0$ =0.01 $^{-3}$ and, consequently of radius with $\rho_0$ $n_0 \ m_p$, $m_p$ being the proton mass." + Iuside the bubble. the deusitv profile is p(r)x&.2. iecit correspouds to a steady stellar wind with mass loss rate Aly aud velocity ew. which is giveu by Our choice of py automatically fixes the p(r) profile aud corresponds to a combination of Mie aud ey values.," Inside the bubble, the density profile is $\rho(r) \propto r^{-2}$, i.e. it corresponds to a steady stellar wind with mass loss rate ${\dot M_W}$ and velocity $v_W$ , which is given by Our choice of $\rho_0$ automatically fixes the $\rho(r) $ profile and corresponds to a combination of ${\dot M_W}$ and $v_W$ values." +"Obviously. oue has Outside Ap we asstune an ISM with coustaut density Pisaral«ατα my,ο 5m","Obviously, one has Outside $R_W$ we assume an ISM with constant density $\rho_{ISM}$ =1 $m_p$ $^{-3}$." + Our approach is similar to ¢Caprioli (2011). but we do not cousider here the more complicate case of a WR wiud overtaking a RSC wind.," Our approach is similar to Caprioli (2011), but we do not consider here the more complicate case of a WR wind overtaking a RSG wind." + We follow the propagation of the forward shock first through the wind bubble aud then through the ISM with a simple model presented in Ptuskin and Zirakashvili (2005) and. in a amore concise form. in Caprioli (2011. his eqs.," We follow the propagation of the forward shock first through the wind bubble and then through the ISM with a simple model presented in Ptuskin and Zirakashvili (2005) and, in a more concise form, in Caprioli (2011, his eqs." + 3.1 to 3.9)., 3.4 to 3.9). + We start the calewlation from the frec-expansion(ejecta dominated) phase. where the swept-wp nüass is snualler than aaud which cau be described by self-similar analytical solutions.," We start the calculation from the ""free-expansion""(ejecta dominated) phase, where the swept-up mass is smaller than and which can be described by self-similar analytical solutions." + In the subsequent ST phase (swept up ass < Mr;)). the model is based ou the “thin shellapproximation (c.g. Ostriker aud Melxee 1958) which assumes that the swept wp mass is concentrated m a thin shell behind the shock.," In the subsequent ST phase (swept up mass $<$ ), the model is based on the ""thin shell""approximation (e.g. Ostriker and McKee 1988) which assumes that the swept up mass is concentrated in a thin shell behind the shock." + We solve nuuercallv. the time-dependent equations for continuity of mass. energy and momenta. to recover shock radius aud velocity as a function of time.," We solve numerically the time-dependent equations for continuity of mass, energy and momentum, to recover shock radius and velocity as a function of time." + Unlike Caprioli (2011) we asstiue full adiabaticitv iu the ST phase. ie. we do not take iuto account the energv losses of the shock through CR acceleration. which would reduce the shock velocity (x EU) by less than1056.," Unlike Caprioli (2011) we assume full adiabaticity in the ST phase, i.e. we do not take into account the energy losses of the shock through CR acceleration, which would reduce the shock velocity $\propto E_0^{0.5}$ ) by less than." + The mass swept up in the ST phase inside shock radius Rs is We follow the evolution all the wav through the ST phase. which cuds when a significant fraction of the energv of the cooling reninant is radiated away (through recombination enmuüssion) for a solar mixture this occurs at time Tn the framework of this simple model we are able to calculate the composition of the material encountered (and prestunably accelerated) by the forward shock as a function of time. or of the swept-ip mass: indeed. the inteerated mass of cach element swept up by the forward shock is eiven by au equation simular to Eq.," The mass swept up in the ST phase inside shock radius $R_S$ is We follow the evolution all the way through the ST phase, which ends when a significant fraction of the energy of the cooling remnant is radiated away (through recombination emission); for a solar mixture this occurs at time In the framework of this simple model we are able to calculate the composition of the material encountered (and presumably accelerated) by the forward shock as a function of time, or of the swept-up mass: indeed, the integrated mass of each element swept up by the forward shock is given by an equation similar to Eq." + 2 where αςτμ for Mj$, i.e. when the shock propagates in the ISM; the upper limit in the integral is given by eq. (" +10).,10). + Eq., Eq. + 12 allows one to link the stellar model. ie. the abuudance profiles IX(M). to the evolution during the ST phase through Eq.," 12 allows one to link the stellar model, i.e. the abundance profiles $X(M)$, to the evolution during the ST phase through Eq." + 10. aud to the properties of the shock wave.," 10, and to the properties of the shock wave." + Since the mass Mo swept-up in the eud of the ST phase is much larger than the wind mass im all cases fa few 10° colmpared to ~LOO at most) for the largest part of the ST phase the swept up material has ISM composition.," Since the mass $_{S2}$ swept-up in the end of the ST phase is much larger than the wind mass in all cases (a few $^3$, compared to $\sim$ 100 at most) for the largest part of the ST phase the swept up material has ISM composition." + Iu order to obtain significant deviations from the solar composition. such as the observed ratio. one should assume thatphase. when the forward shock is stronger and its velocity higher.," In order to obtain significant deviations from the solar composition, such as the observed ratio, one should assume that, when the forward shock is stronger and its velocity higher." + Fie., Fig. +" 5 (top) displays the evolution of the velocity es aud radius Rs of the forward shock aud of the mass MszRe) swept up by it. for the cases of a 20 aud a GOAL. rotating star. respectively,"," \ref{Fig:GCRaccel} (top) displays the evolution of the velocity $\upsilon_S$ and radius $R_S$ of the forward shock and of the mass $M_S( Freetmat et al.," Soft, faint, diffuse X-ray emission from our Galaxy is a possible contaminant of the background given the low Galactic latitude of Circinus $b=-3.\!^{\circ}8$; Freeman et al." + 1977)., 1977). + However. similar “esl were obtained using backe'OU spectra taken rom other long ACIS-5 observations in whict e discrete sources of X-ray etDISSo1 had been..," However, similar results were obtained using background spectra taken from other long ACIS-S observations in which the discrete sources of X-ray emission had been." +" These observations are of ""blank-sky. were taken at ilthe same focal pane e--iperature as our Cireinus observations (i.e. —120°C). alle e backeroune spectra were extrace [rom the same regions of the chip as the source spectra it OUL Circinus observations."," These observations are of “blank-sky”, were taken at the same focal plane temperature as our Circinus observations (i.e. $-120^{\circ}$ C), and the background spectra were extracted from the same regions of the chip as the source spectra in our Circinus observations." + In performing he spectral aialysis of the exended X-ray emission. we have used botl ile inaximuuu-likelihoo«. or C-statistic (method 1: Cast 1979) and the X? statistic (method 2).," In performing the spectral analysis of the extended X-ray emission, we have used both the maximum-likelihood, or C-statistic (method 1; Cash 1979) and the $\chi^{2}$ statistic (method 2)." + Mehod 1 does not requre tle data to be re-binned. aud hs avolds potentia oss of information on naTOW spectral features.," Method 1 does not require the data to be re-binned, and thus avoids potential loss of information on narrow spectral features." +" However. use of the C-staist16 'equires the backeround to be inodelled (with simple power-AWS alid Gaussians) rather thar slbt""acted clirectly. ai( there is no test for goxlness of fit."," However, use of the C-statistic requires the background to be modelled (with simple power-laws and Gaussians) rather than subtracted directly, and there is no test for goodness of fit." + The coilideuce intervals are calculate iu he sane way as or the 4 statistic. aid are usually tighter for aiv given parameter (e.g. [9]Iseκά SIue 1989).," The confidence intervals are calculated in the same way as for the $\chi^{2}$ statistic, and are usually tighter for any given parameter (e.g. Nousek Shue 1989)." + ethod 2 requires the dala to be binued sotiat there are a 1minunum of (typicaly 20 cous per spectral biu. aud the backe‘ound is subtracted cirectly from the data.," Method 2 requires the data to be binned so that there are a minimum of (typically) 20 counts per spectral bin, and the background is subtracted directly from the data." + We fiud siuilar values or the bestittiug continuum paraljeters uxing the two methods. aud so refer to only the 1jethoc 2 results i the text.," We find similar values for the best-fitting continuum parameters using the two methods, and so refer to only the method 2 results in the text." + However. inethod ] results give more precise measurements on the lije featwes. αμα so these results are referος to when giving best-fit line energies. uormalizatious. aud eqivalent widlis.," However, method 1 results give more precise measurements on the line features, and so these results are referred to when giving best-fit line energies, normalizations, and equivalent widths." +density of molecular hydrogen.,density of molecular hydrogen. +" With these simulations we explore the impact of baryons on the structure of the dark matter halos, important for many current observational studies."," With these simulations we explore the impact of baryons on the structure of the dark matter halos, important for many current observational studies." +" We investigate the shape of dark matter halos as a function of radius, important for gravitational lensing studies; the response of the radial halo profile to central condensation of baryons, for studies of the Tully-Fisher and other galactic scaling relations; the alignment of dark halos and stellar disks; and the distribution and evolution of the angular momentum of dark matter."," We investigate the shape of dark matter halos as a function of radius, important for gravitational lensing studies; the response of the radial halo profile to central condensation of baryons, for studies of the Tully-Fisher and other galactic scaling relations; the alignment of dark halos and stellar disks; and the distribution and evolution of the angular momentum of dark matter." +" We run cosmological simulations of a periodic box with comoving length Lys,=25.6h-!Mpc."," We run cosmological simulations of a periodic box with comoving length $L_\mathrm{box} = 25.6\, h^{-1}\, \mathrm{Mpc}$." +" We adopt a ACDM cosmology with a total matter density parameter Ώνιο=0.28, dark matter density Qpm,o=0.234, baryon density Ωμ=0.046, cosmological constant Q,=0.72, Hubble parameter Hg=100kkms~!Mpc™?, with h= 0.7, linearly extrapolated normalization of the power spectrum og=0.82, and spectral index n,=0.96, consistent with the Wilkinson Microwave Anisotropy Probe 7-year data (?).."," We adopt a $\Lambda$ CDM cosmology with a total matter density parameter $\Omega_{\mathrm{M},0} = 0.28$, dark matter density $\Omega_{\mathrm{DM},0} = 0.234$, baryon density $\Omega_{\mathrm{B},0} = 0.046$, cosmological constant $\Omega_{\Lambda} = 0.72$, Hubble parameter $H_0 = 100 h\, \mathrm{km}\, \mathrm{s}^{-1}\, \mathrm{Mpc}^{-1}$, with $h=0.7$ , linearly extrapolated normalization of the power spectrum $\sigma_8 = 0.82$, and spectral index $n_s = 0.96$, consistent with the Wilkinson Microwave Anisotropy Probe 7-year data \citep{2011ApJS..192...14J}." + The initial conditions were generated taking into account a non-zero DC mode (??).," The initial conditions were generated taking into account a non-zero DC mode \citep{2005ApJ...634..728S,2011ApJS..194...46G}." +" The DC mode corrects for a possible deviation of the average matter density in the box from the universal value, arising from the finite simulation volume."," The DC mode corrects for a possible deviation of the average matter density in the box from the universal value, arising from the finite simulation volume." +" It is equivalent to having a constant overdensity at redshift z=0 of ÓDC,0=Pbox,o/Punio—1."," It is equivalent to having a constant overdensity at redshift $z=0$ of $\delta_\mathrm{DC,0} \equiv \bar{\rho}_\mathrm{box,0}/\bar{\rho}_\mathrm{uni,0} - 1$." +" In general, the DC mode denotes an offset of the mean of a signal or waveform from zero."," In general, the DC mode denotes an offset of the mean of a signal or waveform from zero." +" Usually, it is common practice to ignore the DC mode, but this is already a constraint on the initial conditions and therefore the initial conditions are not a trulyrandom realization."," Usually, it is common practice to ignore the DC mode, but this is already a constraint on the initial conditions and therefore the initial conditions are not a trulyrandom realization." + The positions and velocities of particles are determined by the usual Zel'dovich approximation (???).. ," The positions and velocities of particles are determined by the usual Zel'dovich approximation \citep{1970A&A.....5...84Z, 1983MNRAS.204..891K, 1985ApJS...57..241E}. ." +"First, we ran 5 low resolution (256° particles) random realizations of the cosmological box."," First, we ran 5 low resolution $^3$ particles) random realizations of the cosmological box." +" In these low-resolution simulations, we only simulate dissipationless evolution with an N-body code PKDGRAV2 (?).."," In these low-resolution simulations, we only simulate dissipationless evolution with an N-body code PKDGRAV2 \citep{2001PhDT........21S}." +" We then selected a representative box that had the mass function of halos at redshift z=0 closest to that expected for the whole universe g.,7"," We then selected a representative box that had the mass function of halos at redshift $z=0$ closest to that expected for the whole universe \citep[e.g.,][]{1999MNRAS.308..119S}." +" This box has a DC mode of (e.g.""nc.o7.=0.571.", This box has a DC mode of $\delta_\mathrm{DC.0} = 0.571$. + In this selected box we chose to refine7 objects in the mass range Magn~1011—1015Mg at z=0 also Figure 2))., In this selected box we chose to refine 7 objects in the mass range $M_\mathrm{200b} \approx 10^{11} - 10^{13}~\Mo$ at $z=0$ (see also Figure \ref{fig:halomass}) ). +" Maoop is the mass within rooop such (seethat the enclosed density is 200pp, with pp being the background matter density."," $M_\mathrm{200b}$ is the mass within $r_\mathrm{200b}$ such that the enclosed density is $200 \rho_\mathrm{b}$, with $\rho_\mathrm{b}$ being the background matter density." +" The selected objects had a quiet merger history after z~2 but apart from that, they were selected randomly by visual examination."," The selected objects had a quiet merger history after $z \approx 2$ but apart from that, they were selected randomly by visual examination." + We used the traditional method of refining a region of interest with a large number of dark matter particles and leaving the rest at lower resolution so that we correctly account for the large-scale tidal forces (??)..," We used the traditional method of refining a region of interest with a large number of dark matter particles and leaving the rest at lower resolution so that we correctly account for the large-scale tidal forces \citep{1991ApJ...368..325K,2001ApJS..137....1B}." +" Around the 7 selected objects we refined a region of 5rogop with an effective dark matter resolution of 2048?, i.e. the high resolution dark matter particles have a mass of 1.81x10?Mo."," Around the 7 selected objects we refined a region of $5~r_\mathrm{200b}$ with an effective dark matter resolution of $2048^3$, i.e. the high resolution dark matter particles have a mass of $1.81 \times 10^5~\Mo$." +" In the surrounding region, we increased the dark matter mass in buffer zones by factors of 2?—8 until we reached the initial low resolution level."," In the surrounding region, we increased the dark matter mass in buffer zones by factors of $2^3=8$ until we reached the initial low resolution level." +" For the thickness of the buffer zones we chose 3 lengths of the top-level cells (310), where Lo= = 143 kpc "," For the thickness of the buffer zones we chose 3 lengths of the top-level cells $3 L_0$ ), where $L_0 = L_\mathrm{box}/256$ = 143 kpc (comoving)." +The gas wasLyox/256 initialized following(comoving). the same refinement pattern with the baryonic power spectrum., The gas was initialized following the same refinement pattern with the baryonic power spectrum. +" The initial composition of the gas is primordial, i.e. a hydrogen mass fraction X=0.76, helium mass fraction Y=0.24, and metal mass fraction Z=0."," The initial composition of the gas is primordial, i.e. a hydrogen mass fraction $X=0.76$, helium mass fraction $Y = 0.24$, and metal mass fraction $Z=0$." +" Further, we set Xyy=1.2x107°,Ώνιο/(Ώηο)X=1.51074 (?,equation6-119),, =2x10-9X1.52x1079 (?),, and Xy;=XXu,—Xyy—Xy,."," Further, we set $X_\mathrm{H\,\textsc{ii}} = 1.2 \times 10^{-5} \sqrt{\Omega_\mathrm{M,0}}/(\Omega_\mathrm{B,0} h) ~X = 1.5 \times 10^{-4}$ \cite[equation 6-119]{1993ppc..book.....P}, , $X_\mathrm{H_2} = 2 \times 10^{-6} ~X = 1.52 \times 10^{-6}$ \citep{2001ApJ...560..580R}, and $X_\mathrm{H\,\textsc{i}} = X - X_\mathrm{H\,\textsc{ii}} - X_\mathrm{H_2}$." +" All the helium is initially in the form of 1.6. Yuer=>Y, YueIΞ0, YueII—0. textsci,,"," All the helium is initially in the form of, i.e. $Y_\mathrm{He\,\textsc{i}} = Y$, $Y_\mathrm{He\,\textsc{ii}} = 0$, $Y_\mathrm{He\,\textsc{iii}} = 0$." +"'The starting redshift of the refined initial conditions was determined by the criterion that the root mean square of the density fluctuations is 0.1, which resulted in 210=108."," The starting redshift of the refined initial conditions was determined by the criterion that the root mean square of the density fluctuations is 0.1, which resulted in $z_\mathrm{IC} = 108$." + The simulations were run with the latest version of the gas dynamics and N-body Adaptive Refinement Tree (ART) code (????)..," The simulations were run with the latest version of the gas dynamics and $N$ -body Adaptive Refinement Tree (ART) code \citep{1997ApJS..111...73K,1999PhDT........25K,2002ApJ...571..563K,2008ApJ...672...19R}." + The Poisson and fluid equations are solved in super-comoving coordinates using cell-based adaptive mesh refinement (AMR) techniques (??)..," The Poisson and fluid equations are solved in super-comoving coordinates using cell-based adaptive mesh refinement (AMR) techniques \citep{1997ApJS..111...73K,2002ApJ...571..563K}." + ART includes 3-dimensional radiative transfer of ultraviolet (UV) radiation from individual stellar particles and from the extragalactic background (modeled according to ?)) using the Optically Thin Variable Eddington Tensor approximation (?).., ART includes 3-dimensional radiative transfer of ultraviolet (UV) radiation from individual stellar particles and from the extragalactic background (modeled according to \citealt{2001cghr.confE..64H}) ) using the Optically Thin Variable Eddington Tensor approximation \citep{2001NewA....6..437G}. +" It includes a non-equilibrium chemical network for hydrogentextsci,textscii,, and H3) and heliumtextsci,textscii, and as well as non-equilibrium cooling and heating rates, textsciii))which use the local abundances of atomic, molecular, and ionic species and the local UV intensity (?).."," It includes a non-equilibrium chemical network for hydrogen, and $_2$ ) and helium, and ) as well as non-equilibrium cooling and heating rates, which use the local abundances of atomic, molecular, and ionic species and the local UV intensity \citep{2011ApJ...728...88G}." + All these reactions are followed self-consistently in the course of a simulation., All these reactions are followed self-consistently in the course of a simulation. + An empirical model for the formation and shielding of molecular hydrogen on the interstellar dust allows for more realistic star formation recipes based on the localdensity of molecular hydrogen A, An empirical model for the formation and shielding of molecular hydrogen on the interstellar dust allows for more realistic star formation recipes based on the localdensity of molecular hydrogen \citep{2011ApJ...728...88G}. . +RT also includes metal enrichment and thermal feedback(?).. due to the TypeII and Type Ia supernovae (?).., ART also includes metal enrichment and thermal feedback due to the TypeII and Type Ia supernovae\citep{2003ApJ...590L...1K}. . +potentially capture enough objects to perform a similar analysis and obtain these constraints.,potentially capture enough objects to perform a similar analysis and obtain these constraints. + We predict an order of magnitude fewer high-frequency radio halos at low mass than the analysis of CBS06 and ?.., We predict an order of magnitude fewer high-frequency radio halos at low mass than the analysis of CBS06 and \citet{Cassano2010b}. +" Some of this discrepancy might be due to our lack of steep-spectrum halos, which get counted via inclusion of the calculation of the synchrotron break frequency, vy."," Some of this discrepancy might be due to our lack of steep-spectrum halos, which get counted via inclusion of the calculation of the synchrotron break frequency, $\nu_b$." +" Instead, we just assign a radio halo to 5% of our clusters."," Instead, we just assign a radio halo to $5\%$ of our clusters." +" We found that adjusting the spectral index to 1.9 (ie., the average spectral index found by ?)) only increased the number counts by roughly 50%, which is not nearly enough to explain the differences, a higher probability of hosting a radio halo at 150 MHz as predicted in reacceleration models could explain the differences."," We found that adjusting the spectral index to $1.9$ (i.e., the average spectral index found by \citealt{Cassano2010b}) ) only increased the number counts by roughly $50 \%$, which is not nearly enough to explain the differences, a higher probability of hosting a radio halo at 150 MHz as predicted in reacceleration models could explain the differences." +" Also, since our limited simulation volume precludes us from counting all of the most massive clusters, we will systematically underestimate our total number counts at both 1.4 GHz and 150 MHz."," Also, since our limited simulation volume precludes us from counting all of the most massive clusters, we will systematically underestimate our total number counts at both 1.4 GHz and 150 MHz." +" However,"," However," +There Is à growing consensus in the star formation community that non steady (episodic) acecretion. plays a dominant role during the formation of low-mass stars (see e.g Enoch et al.,There is a growing consensus in the star formation community that non steady (episodic) accretion plays a dominant role during the formation of low-mass stars (see e.g Enoch et al. + 2009; Vorobyov 2009: Zhu et al., 2009; Vorobyov 2009; Zhu et al. + 2010a and references therein)., 2010a and references therein). + In a recent paper (Baratfe. Chabrier. Gallardo 2009. hereafter BCGO9). we have suggested that episodic aceretion provides a viable explanation for the observed luminosity spread in young cluster Herzsprung-Russell diagrams (HRD).," In a recent paper (Baraffe, Chabrier, Gallardo 2009, hereafter BCG09), we have suggested that episodic accretion provides a viable explanation for the observed luminosity spread in young cluster Herzsprung-Russell diagrams (HRD)." + The present follow-up analysis explores in more details the effects of episodic accretion on the internal structure of young low mass stars (<] M). commonly used to derive ages of star forming regions and young clusters.," The present follow-up analysis explores in more details the effects of episodic accretion on the internal structure of young low mass stars $\leq 1\,\msol$ ), commonly used to derive ages of star forming regions and young clusters." + We show that. depending on the accretion history. the internal structure of these objects can be strongly affected for up to a few tens of Myr (32))," We show that, depending on the accretion history, the internal structure of these objects can be strongly affected for up to a few tens of Myr \ref{section_structure}) )." + Lithium depletion and. for the partly convective stars. the size of the convective envelope. in particular can strongly differ from the standard (non accreting) pre-main sequence model predictions (83)).," Lithium depletion and, for the partly convective stars, the size of the convective envelope, in particular can strongly differ from the standard (non accreting) pre-main sequence model predictions \ref{section_lithium}) )." + In section 4.. we examine the impact of episodic accretion on the observational signatures and show that taking this process into account in the young low-mass object evolution provides a consistent explanation for the puzzling observations of strong lithium depletion in several low-mass stars (LMS) belonging to young clusters (e.¢ Kenyon et al.," In section \ref{discussion}, we examine the impact of episodic accretion on the observational signatures and show that taking this process into account in the young low-mass object evolution provides a consistent explanation for the puzzling observations of strong lithium depletion in several low-mass stars (LMS) belonging to young clusters (e.g Kenyon et al." + 2005: Saeco et al., 2005; Sacco et al. + 2007) and in hosting stars (Israelian et al., 2007) and in planet-hosting stars (Israelian et al. + 2009). as well as to the recently determined peculiar abundances of refractory elements in the Sun (Melendez et al.," 2009), as well as to the recently determined peculiar abundances of refractory elements in the Sun (Melendez et al." + 2009; Ramirez et al., 2009; Ramirez et al. + 2009)., 2009). + We adopt the same input physics and the same treatment of accretion as outlined in. BCGO9., We adopt the same input physics and the same treatment of accretion as outlined in BCG09. + In standard. stellar evolution calculations. energy conservation equation for a non accreting object reads as where mis the mass enclosed 1n à sphere of radius 7 within the object. $ the specific entropy and ey the local nuclear energy generation rate.," In standard stellar evolution calculations, energy conservation equation for a non accreting object reads as where $m$ is the mass enclosed in a sphere of radius $r$ within the object, $S$ the specific entropy and $\epsilon_{\rm nuc}$ the local nuclear energy generation rate." + For very young objects. only deuterium fusion provides a contribution to e...," For very young objects, only deuterium fusion provides a contribution to $\epsilon_{\rm nuc}$." +" For aceretion proceeding at a rate M. time derivatives at fixed mass shell must account for the variation of mass with time and of entropy with accreted mass. re. (Sugimoto Nomoto 1975): g =m/M,."," For accretion proceeding at a rate $\dot M$, time derivatives at fixed mass shell must account for the variation of mass with time and of entropy with accreted mass, i.e. (Sugimoto Nomoto 1975): with $q \equiv m/\mstar$." +The mass (M -Ar)accreted during a timestep Ar is assumed to be redistributed over the entire structure. with the new mass in a shell of fixed g given by In the present calculations. we assume instantaneous and uniform redistribution of the extra source of internal energy brought by the accreted material.," The mass $\dot M \cdot \Delta t$ ) accreted during a timestep $\Delta t$ is assumed to be redistributed over the entire structure, with the new mass in a shell of fixed $q$ given by In the present calculations, we assume instantaneous and uniform redistribution of the extra source of internal energy brought by the accreted material." + In reality. mass and heat redistributions inside the accreting object depend on the thermal properties of the accreting material.," In reality, mass and heat redistributions inside the accreting object depend on the thermal properties of the accreting material." + Proto low-mass stars below about 2 M. are expected to be entirely convective (Stahler Palla 2005)., Proto low-mass stars below about 2 $\msol$ are expected to be entirely convective (Stahler Palla 2005). + For completely convective objects. given the short typical convective timescales. our assumption of uniform. mass and heat redistribution should be valid. providing the entropy of accreted matter is comparable to or less than the accreting object’s internal one. so that the infalling material can rapidly thermalize with its surroundings (see discussion in Siess Forestini 1996; Hartmann et al.," For completely convective objects, given the short typical convective timescales, our assumption of uniform mass and heat redistribution should be valid, providing the entropy of accreted matter is comparable to or less than the accreting object's internal one, so that the infalling material can rapidly thermalize with its surroundings (see discussion in Siess Forestini 1996; Hartmann et al." + 1997)., 1997). + If the aforementioned condition is not fulfilled. the accreting matter may not be able to penetrate very deep inside the object. possibly leading to Rayleigh-Taylor like instabilities in stably radiative regions.," If the aforementioned condition is not fulfilled, the accreting matter may not be able to penetrate very deep inside the object, possibly leading to Rayleigh-Taylor like instabilities in stably radiative regions." + Siess et al. (, Siess et al. ( +1997) explored the effect of mass and heat redistribution by using a penetration function.,1997) explored the effect of mass and heat redistribution by using a penetration function. + Such an approach. however. remains highly phenomenological and thus of limited reliability.," Such an approach, however, remains highly phenomenological and thus of limited reliability." + Given the complexity of the problem and the present exploratory nature of the effect of episodic accretion on young low-mass objects. not mentioning uncertainties in the accretion processes. we elected to stick to the simplest and probably most reasonable in most of the presently explored situations treatment. and assumed homogeneous. rapid heat and matter redistribution within the accreting body.," Given the complexity of the problem and the present exploratory nature of the effect of episodic accretion on young low-mass objects, not mentioning uncertainties in the accretion processes, we elected to stick to the simplest and probably most reasonable in most of the presently explored situations treatment, and assumed homogeneous, rapid heat and matter redistribution within the accreting body." +ab each of the two observed wavelengths. and take the other parameters for the svstem (planetary. and stellar radii. orbital period. etc.),"at each of the two observed wavelengths, and take the other parameters for the system (planetary and stellar radii, orbital period, etc.)" + from Knutsonetal.(2007a)., from \citet{knut07a}. +. We calculate our transit curve using the equations from Mouidel&Agol(2002). for the ease with no limb-darkening., We calculate our transit curve using the equations from \citet{mand02} for the case with no limb-darkening. + After running the chain. we search for the point in the chain where the 4? value first [alls below the median of all the 4? values in the chain (i.e. where the code had first found. the best-lit solution). and discard all the steps up to that point.," After running the chain, we search for the point in the chain where the $\chi^2$ value first falls below the median of all the $\chi^2$ values in the chain (i.e. where the code had first found the best-fit solution), and discard all the steps up to that point." + We take the median of the remaining distribution as our best-fit parameter. wilh errors calculated as the svimmetrie range about the median containing of the points in the distribution.," We take the median of the remaining distribution as our best-fit parameter, with errors calculated as the symmetric range about the median containing of the points in the distribution." + The distribution of values was very close to svimneltrie in all cases. ancl there did not appear to be any strong correlations between variables.," The distribution of values was very close to symmetric in all cases, and there did not appear to be any strong correlations between variables." + Figure 1 shows the binned data with the best fit to the detector effects overplotted. and Figure 2 shows the binned data once these trends are removed. with best-fit eclipse curves overplotted.," Figure \ref{norm_plots} shows the binned data with the best fit to the detector effects overplotted, and Figure \ref{four_eclipses} shows the binned data once these trends are removed, with best-fit eclipse curves overplotted." + DBest-fit eclipse depths and times are given in Table 1.., Best-fit eclipse depths and times are given in Table \ref{eclipse_depths}. + At longer wavelengths the flux from the star is smaller and the zodiacal background is larger: as a result we chose to use a smaller 3.5 pixel aperture al these (wo wavelengths in order to minimize the noise contribution from this increased background., At longer wavelengths the flux from the star is smaller and the zodiacal background is larger; as a result we chose to use a smaller 3.5 pixel aperture at these two wavelengths in order to minimize the noise contribution from this increased background. + As a test we also tried using a psf fit to derive the time series in the 8 channel. which has the hiehest background. using the in-flight point response functions generated Lom calibration test data7.," As a test we also tried using a psf fit to derive the time series in the 8 channel, which has the highest background, using the in-flight point response functions generated from calibration test data." + There was no improvement in the resulting time series. indicating that aperture photometry is still appropriate here.," There was no improvement in the resulting time series, indicating that aperture photometry is still appropriate here." + As a check we repeat our analvsis using apertures ranging from 3.5—5 pixels and obtain a consistent signal in all cases. but with a scatter (hat increases with the radius of the photometric aperture.," As a check we repeat our analysis using apertures ranging from $3.5-5$ pixels and obtain a consistent signal in all cases, but with a scatter that increases with the radius of the photometric aperture." + As before. we calculate the position of the star individually in each image as (he position-weighted sum of the fluxes in aTx7 pixel box. and estimate the background using a Gaussian [it to a histogram of the pixels in the corners of the array.," As before, we calculate the position of the star individually in each image as the position-weighted sum of the fluxes in a $7\times7$ pixel box, and estimate the background using a Gaussian fit to a histogram of the pixels in the corners of the array." + Fluxes in the first 10 images in each set of 64 are consistently below the median value for the set by as much asLOM... with the lowest values at the beginning of each set. so we chose to exclude the first 10 images [rom each set of G4 in our analvsis.," Fluxes in the first 10 images in each set of 64 are consistently below the median value for the set by as much as, with the lowest values at the beginning of each set, so we chose to exclude the first 10 images from each set of 64 in our analysis." + There is no intra-pixel sensilivily al these wavelengths. but (here is another well- detector effect. (INnutsonοἱal.2007b) which causes the effective gain (and thus (he measured {lis} in individual pixels to increase over time.," There is no intra-pixel sensitivity at these wavelengths, but there is another well-documented detector effect \citep{knut07b} which causes the effective gain (and thus the measured flux) in individual pixels to increase over time." + This effect has been referred, This effect has been referred +the ESW effect. from the perturbations decreases with the sound speed.,the ISW effect from the perturbations decreases with the sound speed. + For a<1 the elect is reversed. with the perturbations initially of opposite sign. and the contribution to the ISW elfect increasing as the sound speed is decreased.," For $w<-1$ the effect is reversed, with the perturbations initially of opposite sign, and the contribution to the ISW effect increasing as the sound speed is decreased." + In Fig., In Fig. +" 5 we show how the CAIB temperature anisotropies change on large scales. lor different constant ο,"," \ref{fig:cs} we show how the CMB temperature anisotropies change on large scales, for different constant $\hcs$." + We see that if we decrease the sound speed eraciually from &=1] to ὃν=0 the ISW contribution becomes smaller as the dark energy. clusters more with the matter. partly compensating the change in the potential due to the change in the background equation of state.," We see that if we decrease the sound speed gradually from $\hcs=1$ to $\hcs=0$ the ISW contribution becomes smaller as the dark energy clusters more with the matter, partly compensating the change in the potential due to the change in the background equation of state." + Pherefore cross - correlating the large scale CMD power spectrum with clirect measures of the potential (Boughn&Crittenden2003) might be an excellent probe for the sound speed of the clark enerey Component. if the equation of state is dillerent [rom w=1.," Therefore cross - correlating the large scale CMB power spectrum with direct measures of the potential \citep{Boughn:2003yz} might be an excellent probe for the sound speed of the dark energy component, if the equation of state is different from $w=-1$." + In order to stress the importance of the inelusion of clark energv perturbations we will discuss their impact on the parameter estimation with CAIB data., In order to stress the importance of the inclusion of dark energy perturbations we will discuss their impact on the parameter estimation with CMB data. + We included: the perturbations into the code (Lewisetal.2000) (based on (Seljak&Zaldarriaga 1996))) and. performed a Markov-chain Monte Carlo parameter analysis using (Lewis&Dri-cle 2002).," We included the perturbations into the code \citep{Lewis99} + (based on \citep{Seljak96}) ) and performed a Markov-chain Monte Carlo parameter analysis using \citep{cosmomc}." +" We varied six. non-dark energy cosmological parameters with [at priors: the barvon density 5,57. the cold dark matter density 57. the ratio of the sound horizon to the angular diameter distance at last scattering 6. the damping of the small scale CMDB power due to reionization ZoeE (we assume r« 0.3). the amplitude. of the Iluctuations zi, and the spectral index of the primordial power spectrum ny."," We varied six non-dark energy cosmological parameters with flat priors: the baryon density $\Omega_b h^2$, the cold dark matter density $\Omega_{\rm c} h^2$, the ratio of the sound horizon to the angular diameter distance at last scattering $\theta$ , the damping of the small scale CMB power due to reionization $Z\equiv e^{-2\tau}$ (we assume $\tau<0.3$ ), the amplitude of the fluctuations $A_s$ and the spectral index of the primordial power spectrum $n_s$." +" In addition we varied the constant equation of state parameter of the dark energy component es and where required the constant sound speed. parameter inthe range 3«log,402<2."," In addition we varied the constant equation of state parameter of the dark energy component $w$ , and where required the constant sound speed parameter in the range $-3<\log_{10} \hcs<2$." + The Hubble parameter 440 is derived from 8 (Ixosowskyetal.2002).. and the dark energy density from the requirement that the background. universe is spatially flat.," The Hubble parameter $H_0$ is derived from $\theta$ \citep{Kosowsky02}, and the dark energy density from the requirement that the background universe is spatially flat." +" We assume negligible primordial tensor modes and neutrino mass. and include priors on the Hubble parameter from the Llubble Key project. (Freedmanctal. with 4/4,=(F248)kms*\Ipe+ ane a weak prior O,h7=0.022£0.002 (1 σ) from Big Bang nuclcosynthesis Aurlesetal.(2001).."," We assume negligible primordial tensor modes and neutrino mass, and include priors on the Hubble parameter from the Hubble Key project \citep{Freedman01}, with $H_0 = (72\pm 8) \Hunit$, and a weak prior $\Omega_b h^2=0.022 \pm 0.002$ (1 $\sigma$ ) from Big Bang nucleosynthesis \cite{Burles01}. ." + In addition to the CAIB likelihood code provided by WALADP (Verdeetal.2003:LlinshawIxogutetal.2003) (including the temperature-polarization cross-correlation data). we use CBI (Pearsonοἱal.2003) and ACBAR (Ixuoetal.2002) data for the smaller scales ἐς>S00)," In addition to the CMB likelihood code provided by WMAP \citep{Verde03,Hinshaw03,Kogut03} (including the temperature-polarization cross-correlation data), we use CBI \citep{Pearson02} and ACBAR \citep{Kuo02} data for the smaller scales $\ell>800$ )." + In Fie., In Fig. +" G6 we show the posterior confidence contours in the Ον,i plane.", \ref{fig:CMBcont} we show the posterior confidence contours in the $\Omega_m-w$ plane. + Phe dashed: contours are from an analysis assuming no perturbations in the dark energy component. while the solid contours are with perturbations.," The dashed contours are from an analysis assuming no perturbations in the dark energy component, while the solid contours are with perturbations." + We clearly see the different shape of the likelihood contours and how they open up to more negative values in ew if we include perturbations., We clearly see the different shape of the likelihood contours and how they open up to more negative values in $w$ if we include perturbations. + This is a direct. result. of the ilference between Figs., This is a direct result of the difference between Figs. + 2. and 3..., \ref{fig:Clno} and \ref{fig:Clpert}. + Because the large LSW fora«— lis not present if we include perturbations this part of the parameter space can not be excluded with CM ala., Because the large ISW for $w<-1$ is not present if we include perturbations this part of the parameter space can not be excluded with CMB data. + Furthermore the inclusion of perturbationsleads to more stringent upper bounds on the equation of state 0., Furthermore the inclusion of perturbationsleads to more stringent upper bounds on the equation of state $w$. + This is becauseas we increase the large scale CAIB power ue to the perturbations (for t 1). the relatively low uacirupole and octopole disfavour these models.," This is becauseas we increase the large scale CMB power due to the perturbations (for $w>-1$ ), the relatively low quadrupole and octopole disfavour these models." + In Fig., In Fig. + 7 we show the constraints [rom additionally varving a constant sound. speed., \ref{fig:CMBcs2} we show the constraints from additionally varying a constant sound speed. + This slightly favours values of ac1. where low sound. speeds lead to a smaller. IS\W contribution at the lowest £.," This slightly favours values of $w>-1$, where low sound speeds lead to a smaller ISW contribution at the lowest $\ell$." + For εν<1 the contours broaden to include large sound: speeds which also give somewhat smaller low multipoSs., For $w<-1$ the contours broaden to include large sound speeds which also give somewhat smaller low multipoles. + Finally we performed. an analysis where we also incluclecl the data from the Supernovae Cosmology. Project (SCP) (Perlmutterctal.1999). ancl the two degree field (2b) galaxy redshift survey (Percivaletal. 2001)., Finally we performed an analysis where we also included the data from the Supernovae Cosmology Project (SCP) \citep{Perlmutter98} and the two degree field (2dF) galaxy redshift survey \citep{Percival01}. . +. The information from the 901 large scale structure combined with the prior from the Llubble Ίνον Project constrains the matter contents. while the Supernovac (SNe) information is complementary.," The information from the 2dF large scale structure combined with the prior from the Hubble Key Project constrains the matter contents, while the Supernovae (SNe) information is complementary." + In Fig., In Fig. + Swe show the result. of this combined analysis. with and without marginalizing over a varving sound: speed =.," \ref{fig:CMBall} we show the result of this combined analysis, with and without marginalizing over a varying sound speed $\hcs$." + ‘Phe mean value for scalar field models with @=1 is w=1.02. strikinely close to a cosmological constant. however the marginalized confidence limit LST«oec0.74 still allows a lot of room for dillerent. dark energy. scenarios.," The mean value for scalar field models with $\hcs=1$ is $w=-1.02$, strikingly close to a cosmological constant, however the marginalized confidence limit $-1.370 region, the x«0 solutions being deduced by symmetry arguments."," Without loss of generality, we will consider the case of a wave emitted in the $x>0$ region, the $x<0$ solutions being deduced by symmetry arguments." +" It is worth noting that is in fact the vorticity conservation equation in a (20))compressible medium, with a constant background vorticity (2—q)Q."," It is worth noting that \ref{eqParabol}) ) is in fact the vorticity conservation equation in a compressible medium, with a constant background vorticity $(2-q)\Omega$." +" In a global disk however, background vorticity is not constant and density might also depend on radius."," In a global disk however, background vorticity is not constant and density might also depend on radius." +" In this context, one would write a conservation equation for the vortensity Vxv/X which would be similar to (20)) if the background vortensity was constant."," In this context, one would write a conservation equation for the vortensity $\bm{\nabla \times v}/\Sigma$ which would be similar to \ref{eqParabol}) ) if the background vortensity was constant." +" Therefore, the wave emission model we are discussing here should be understood as a local model for a disk."," Therefore, the wave emission model we are discussing here should be understood as a local model for a disk." + The above equation admit solutions in the form of parabolic cylinder functions., The above equation admit solutions in the form of parabolic cylinder functions. +" However, to understand the physical origin of vortex waves, we present here WKB solutions."," However, to understand the physical origin of vortex waves, we present here WKB solutions." +" We first note that (20)) has a turning point at where we have introduced wa;=V/k?c2+q(2—q(?, the natural frequency of acoustic-inertial waves."," We first note that \ref{eqParabol}) ) has a turning point at where we have introduced $\omega_{ai}=\sqrt{k^2c_s^2+q(2-q)\Omega^2}$, the natural frequency of acoustic-inertial waves." + This particular location corresponds to the sonic line of the vortex., This particular location corresponds to the sonic line of the vortex. + This is the line along which the flow speed is equal to the wave speed as given by the phase velocity., This is the line along which the flow speed is equal to the wave speed as given by the phase velocity. + In the limit of large k this phase velocity becomes equal to the sound speed hence the term sonic line., In the limit of large $k$ this phase velocity becomes equal to the sound speed hence the term sonic line. +" For x«ας (“subsonic” region), the wave has an exponential shape and it corresponds to the logarithmic tail of an incompressible vortex."," For $xx, region), the wave is essentially sinusoidal and(“supersonic” can travel for very large distances."," Using first order WKB theory in the limit $x\ll x_s$, we get: On the other hand, for $x>x_s$ (“supersonic” region), the wave is essentially sinusoidal and can travel for very large distances." +" In the limit x>>ας, we obtain: where it can be shown that an outgoing wave (wave transporting angular momentum is obtained when C=0."," In the limit $x\gg x_s$, we obtain: where it can be shown that an outgoing wave (wave transporting angular momentum outward) is obtained when $C=0$." + This solution leads outward)to the long “wakes” one observes in compressible simulations of vortices., This solution leads to the long “wakes” one observes in compressible simulations of vortices. +" In particular, in the limit z>>ke,/qQ, we find that the wavefronts of the supersonic region are given by which produce a pattern similar to the wakes found in simulations (Fig. 5))."," In particular, in the limit $x\gg kc_s/q\Omega$, we find that the wavefronts of the supersonic region are given by which produce a pattern similar to the wakes found in simulations (Fig. \ref{figWakes}) )." + 'The connection of the supersonic and subsonic regions allows one to determine C and D knowing A and B., The connection of the supersonic and subsonic regions allows one to determine $C$ and $D$ knowing $A$ and $B$. + 'This can be done using asymptotic matching techniques based on Airy functions., This can be done using asymptotic matching techniques based on Airy functions. +" Although the precise derivation of these solutions is beyond the scope of this paper, we find that |C|~|D|max(|A|,|B]), i.e. the amplitude of the solution does not change significantly as one crosses the sonic line."," Although the precise derivation of these solutions is beyond the scope of this paper, we find that $|C|\sim|D|\sim {\rm max}(|A|,|B|)$, i.e. the amplitude of the solution does not change significantly as one crosses the sonic line." +" However, it should be noted that the wave amplitude in the supersonic region is significantly reduced compared to its amplitude at x=0 due to the exponential decay in the subsonic region."," However, it should be noted that the wave amplitude in the supersonic region is significantly reduced compared to its amplitude at $x=0$ due to the exponential decay in the subsonic region." + One can estimate this attenuation factor I' with:, One can estimate this attenuation factor $\Gamma$ with: +"2005),, however, the degree to which the dark matter halo would have to be prolate to accommodate the observed anisotropy around the MW and M31 would be extremely atypical (Kroupaetal.2010).",", however, the degree to which the dark matter halo would have to be prolate to accommodate the observed anisotropy around the MW and M31 would be extremely atypical \citep{Kroupa10}." +". Furthermore, the debris stream of the disrupting Sagittarius dwarf can not be modelled under the influence of such an extremely prolate dark matter halo 2009;Kelleretal.2008, 2009)."," Furthermore, the debris stream of the disrupting Sagittarius dwarf can not be modelled under the influence of such an extremely prolate dark matter halo \citep{Law09, Prior09b, Keller08, Keller09}." +. Li&Helmi(2008) present a scenario in which all satellites fall in to the MW halo in 1-2 groups and demonstrate that such an accretion history could account for the current satellite anisotropy., \citet{Li08} present a scenario in which all satellites fall in to the MW halo in 1–2 groups and demonstrate that such an accretion history could account for the current satellite anisotropy. +" D'Onghia&Lake(2008) develop a similar scenario, reminiscent of the groups of MW satellite galaxies of Lynden-Bell(1976,1982);Kunkel&Demers(1976),, in which the groups formed in LMC-like dark matter halos."," \citet{DOnghia08} develop a similar scenario, reminiscent of the groups of MW satellite galaxies of \citet{Lynden-Bell76, Lynden-Bell82, Kunkel76}, in which the groups formed in LMC-like dark matter halos." +" However, such a scenario has a number of problematic features as discussed in Kroupaetal.(2010), the frequency of such groups in the local volume is low; the group would have been comprised predominantly of dwarf spheroidal galaxies and this does not match to the morphology-density relation; and the group identity of satellites after infall is expected to be short lived (Klimentowski 2009)."," However, such a scenario has a number of problematic features as discussed in \citet{Kroupa10}, the frequency of such groups in the local volume is low; the group would have been comprised predominantly of dwarf spheroidal galaxies and this does not match to the morphology-density relation; and the group identity of satellites after infall is expected to be short lived \citep{Klimentowski09}." +. Metzetal.(2007) present a scenario in which the satellites arise from the tidal fragmentation of a large galaxy at an early epoch., \citet{Metz07} present a scenario in which the satellites arise from the tidal fragmentation of a large galaxy at an early epoch. +" Under this scenario, the kinematics of the TDGs is retained from formation as a rotationally supported disk."," Under this scenario, the kinematics of the TDGs is retained from formation as a rotationally supported disk." + Metzet2009b) confirm this: the inferred angular momentum vectors for the majority of classical MW satellites are directed within a 30? region on the sky.," \citet{Metz08,Metz09} confirm this: the inferred angular momentum vectors for the majority of classical MW satellites are directed within a $^{\circ}$ region on the sky." +" Libeskindetal.(2005,2010) present cosmological simulations that show that substructures stream through LSS filaments that feed MW-sized halos."," \citet{Libeskind05, Libeskind10} present cosmological simulations that show that substructures stream through LSS filaments that feed MW-sized halos." + This accretion occurs from preferred directions on the sky and is coherent on scales from 1 Mpc to 20 kpc., This accretion occurs from preferred directions on the sky and is coherent on scales from 1 Mpc to 20 kpc. + From simulated systems that contain at least 11 luminous satellites (i.e. comparable to the MW system) Libeskind find possess satellites with orbital angular momenta aligned to a similar degree as the MW system., From simulated systems that contain at least 11 luminous satellites (i.e. comparable to the MW system) \citet{Libeskind10} find possess satellites with orbital angular momenta aligned to a similar degree as the MW system. +" Lovelletal.(2010) find a similar result, namely that quasi-planar distributions of coherently rotating satellites arise naturally in the Aquarius simulations as subhalos fall in along the central spines of LSSf"," \citet{Lovell10} find a similar result, namely that quasi-planar distributions of coherently rotating satellites arise naturally in the Aquarius simulations as subhalos fall in along the central spines of LSS." +ilaments?.. In Figures 5 and 6 we show the orientation of the MW and M31 PoS in supergalactic coordinates (see deVaucouleursetal. 1991 for definition)., In Figures \ref{figure:SGxy} and \ref{figure:SGxz} we show the orientation of the MW and M31 PoS in supergalactic coordinates (see \citeauthor{deVaucouleurs91} \citeyear{deVaucouleurs91} for definition). + The supergalactic plane is defined by the distribution of galaxies ~ few Mpc about the MW., The supergalactic plane is defined by the distribution of galaxies $\sim$ few Mpc about the MW. + Within this volume, Within this volume +For high Mach number shocks this Equation simplifies to: The compression ratio of the subshock is given by the standard shock relation: with Mi being given by Equation ,For high Mach number shocks this Equation simplifies to: The compression ratio of the subshock is given by the standard shock relation: with $M_1$ being given by Equation \ref{eq:M1}) ). +"Equations (5)),(9)) and (11)) together (5)).show that there is a one to one relation between the compression ratio in the precursor and the downstream fractional cosmic-ray pressure for a given upstream Mach number Mo.", Equations \ref{eq:M1}) \ref{eq:w}) ) and \ref{eq:chi2}) ) together show that there is a one to one relation between the compression ratio in the precursor and the downstream fractional cosmic-ray pressure for a given upstream Mach number $M_0$. +" In order to determine the escaping energy flux carried away by particles diffusing away far upstream, we need to use the expression for conservation of energy flux across the shock, but with a modification in order to express the fact that energy flux may be lost from the system (e.g.Berezhko&Ellison1999):: with wu=P/(y—1) the internal energy, and the escaping cosmic-ray energy flux, normalized to the total kinetic energy flux of the shock."," In order to determine the escaping energy flux carried away by particles diffusing away far upstream, we need to use the expression for conservation of energy flux across the shock, but with a modification in order to express the fact that energy flux may be lost from the system \citep[e.g.][]{berezhko99}: with $u=P/(\gamma-1)$ the internal energy, and the escaping cosmic-ray energy flux, normalized to the total kinetic energy flux of the shock." +" Note that the escaping energy flux can only be taken out of the kinetic energy flux, as this is the only source of free energy."," Note that the escaping energy flux can only be taken out of the kinetic energy flux, as this is the only source of free energy." +" If we would have considered radiative losses, then the factor (1—εοςο) should have been in front of Po as well, as the usptream thermal energy can also be radiated away."," If we would have considered radiative losses, then the factor $(1-\epsilon_{\rm esc})$ should have been in front of $P_0$ as well, as the usptream thermal energy can also be radiated away." + Following Vink(2008);Helderetal.(2009) we introduce for convenience Reordering the terms and using Equation (6)) gives: This Equation completes the thermodynamic relation between the precursor compression ratio χι and downstream non-thermal pressure and overall energy flux escape.," Following \citet{vink08d, helder09} we introduce for convenience Reordering the terms and using Equation \ref{eq:P2}) ) gives: This Equation completes the thermodynamic relation between the precursor compression ratio $\chi_1$ and downstream non-thermal pressure and overall energy flux escape." +" The resulting relation between es, and w can be seen in Figure 1..", The resulting relation between $\epsilon_{\rm esc}$ and $w$ can be seen in Figure \ref{fig:epsilon}. + For high Mach number shocks the second and third terms can be omitted., For high Mach number shocks the second and third terms can be omitted. +" In the limit of γα=5/3 and Mo,M;—oo one can show that the relation between έρεο and w is well approximated by: Since realistically yr< (see Discussion), Equation (16)) serves as an upper 5/3bound on the escape flux."," In the limit of $\gamma_{\rm cr}=5/3$ and $M_0,M_1 \rightarrow \infty$ one can show that the relation between $\epsilon_{\rm esc}$ and $w$ is well approximated by: Since realistically $\gamma_{\rm cr}<5/3$ (see Discussion), Equation \ref{eq:epsw}) ) serves as an upper bound on the escape flux." +to a formal best-fit parameter set that is either unphysical or difficult to explain from the theoretical point of view.,to a formal best-fit parameter set that is either unphysical or difficult to explain from the theoretical point of view. + Therefore some priors on the parameters have to be adopted., Therefore some priors on the parameters have to be adopted. + The present work aims at probing the sensible range for some of those., The present work aims at probing the sensible range for some of those. +" With a, e and ¢ held constant at their fiducial values ϐ was varied over the range 0«8<1.25."," With $\alpha$ , $\epsilon$ and $\zeta$ held constant at their fiducial values $\beta$ was varied over the range $0<\beta<1.25$." + The predictions for galaxies are shown in Fig., The predictions for galaxies are shown in Fig. + 3 {2e 2.27) and Fig., \ref{fig:beta1} $z\approx2.27$ ) and Fig. + 4 (z& 3.54).," \ref{fig:beta2} + $z\approx3.54$ )." + Inspection of the plots show that 6 has a distinguishable effect on the distribution of the massand metallicities of the galaxies., Inspection of the plots show that $\beta$ has a distinguishable effect on the distribution of the massand metallicities of the galaxies. + At any given, At any given +this type will be available soon from instruments such as SCUBA-2 on the JCMT and SPIRE/PACS on-board theservatory. published surveys have so far been limited to an area of ~(0.5 7? (Coppin et al.,"this type will be available soon from instruments such as SCUBA-2 on the JCMT and SPIRE/PACS on-board the, published surveys have so far been limited to an area of $\sim0.5$ $^{-2}$ (Coppin et al." + 2006: Austermann et al., 2006; Austermann et al. + 2010: et al., 2010; et al. + 2009)., 2009). + One of the largest published submillimetre surveys is the SCUBA HAIf-Degree Extragalactic Survey (SHADES: Mortier et al., One of the largest published submillimetre surveys is the SCUBA HAlf-Degree Extragalactic Survey (SHADES; Mortier et al. + 2005: Coppin et al., 2005; Coppin et al. + 2006) which. due to technical problems. mapped only 0.2 deg? discovering ~100 submillimetre galaxies (SMGs).," 2006) which, due to technical problems, mapped only 0.2 $^2$ discovering $\sim100$ submillimetre galaxies (SMGs)." + Whilst this survey provided one of the largest and most uniformly selected samples of SMGs ever assembled. the area of sky surveyed is extremely small by most standards.," Whilst this survey provided one of the largest and most uniformly selected samples of SMGs ever assembled, the area of sky surveyed is extremely small by most standards." + For example. ACDM simulations predict that a dark matter halo of mass greater than a few times 10 M. at >=2 will evolve to become a very rich cluster galaxies by >=0 (e.g. Farrah et al.," For example, $\Lambda$ CDM simulations predict that a dark matter halo of mass greater than a few times $10^{14}$ $_{\odot}$ at $z=2$ will evolve to become a very rich cluster of galaxies by $z=0$ (e.g. Farrah et al." + 2006)., 2006). + However. since the surfaceof density of such massive haloes at 2.—2 is only of order 0.01 > (Evrard et al.," However, since the surface density of such massive haloes at $z\geq2$ is only of order $0.01$ $^{-2}$ (Evrard et al." + 2002). a wide-area survey would be required in order to contain one by chance.," 2002), a wide-area survey would be required in order to contain one by chance." + One promising method of locating rare structures is to target the fields of high-redshift active galactic nuclei (AGN)., One promising method of locating rare structures is to target the fields of high-redshift active galactic nuclei (AGN). + Given their huge luminosities. such objects must contain a SMBH even at very high redshifts. and therefore must represent some of the most massive objects in existence at their epochs.," Given their huge luminosities, such objects must contain a SMBH even at very high redshifts, and therefore must represent some of the most massive objects in existence at their epochs." + They should thus act as signposts to rare high-density regions of the early universe. and can be observed efficiently with existing technology.," They should thus act as signposts to rare high-density regions of the early universe, and can be observed efficiently with existing technology." + Several groups have exploited this technique to search for proto-clusters forming around high-redshift radio galaxies (e.g. Kurk et al., Several groups have exploited this technique to search for proto-clusters forming around high-redshift radio galaxies (e.g. Kurk et al. + 2000: Pentericei et al., 2000; Pentericci et al. + 2000: Ivison et al., 2000; Ivison et al. + 2000: Stevens et al., 2000; Stevens et al. + 2003: Smail et al., 2003; Smail et al. + 2003: De Breuck et al., 2003; De Breuck et al. + 2004: Greve e al., 2004; Greve et al. + 2007: Venemans et al., 2007; Venemans et al. + 2007) and quasi-stellar objects (QSOs: Stevens et al., 2007) and quasi-stellar objects (QSOs; Stevens et al. + 2004: Priddey. Ivison Isaak 2008).," 2004; Priddey, Ivison Isaak 2008)." + Most of these studies have concentrated on extreme objects. those with the highest luminosities and at the highest redshifts. and all have found over-densities of star-forming galaxies (typically Ένα emitters or SMGs) in the fields of the AGN.," Most of these studies have concentrated on extreme objects, those with the highest luminosities and at the highest redshifts, and all have found over-densities of star-forming galaxies (typically $\alpha$ emitters or SMGs) in the fields of the AGN." + Here we extend this work to investigate the environments of typical QSOs at submillimetre anc mid-infrared wavelengths., Here we extend this work to investigate the environments of typical QSOs at submillimetre and mid-infrared wavelengths. + The QSOs are selected over the redshift range 1.7<2«2.8 where the star-formation rate density and accretion luminosity density of the universe peak., The QSOs are selected over the redshift range $1.75$ mJy/beam. + This flux density threshold is based on limitations imposed by current sensitivity limits and by confusion noise. but also means that any source detected at +1. must be either an ultraluminous or hyperluminous far-infrared galaxyif the emission is from dust. and if the temperature of this dust is typical of such objects detected at low redshift.," This flux density threshold is based on limitations imposed by current sensitivity limits and by confusion noise, but also means that any source detected at $z>1$ must be either an ultraluminous or hyperluminous far-infrared galaxyif the emission is from dust, and if the temperature of this dust is typical of such objects detected at low redshift." + The observations of RX J094144.5]|385434.8 were published by Stevens et al. (, The observations of RX $094144.51+385434.8$ were published by Stevens et al. ( +2004) but are includedhere for completeness.,2004) but are includedhere for completeness. + The 5 QSOs are listed in Table | along with some basic parameters., The 5 QSOs are listed in Table \ref{table:sample} along with some basic parameters. + They are selected to CH) span the redshift range 1.7«z2.5 and (2) have 0.52 KkeV X-ray luminosities within 0.7 dex of £L. the break in the X-ray luminosity function.," They are selected to (1) span the redshift range $1.76$ ) are likely to be complimentary to the constraints at lower redshifts provided by these techniques. + lt has recenth been suggested. that observations of 21ccm intensity fluctuations might provide an additional avenue to measure the mass PS (c.g.72?2).. and that future low-frequency arrays could be used to measure the BAO scale at a range of recdshilts (???)..," It has recently been suggested that observations of cm intensity fluctuations might provide an additional avenue to measure the mass PS \citep[e.g.][]{mcquinn2006, bowman2006, +mao_tegmark2008}, and that future low-frequency arrays could be used to measure the BAO scale at a range of redshifts \citep{wlg2008,chang2008,mao2008}." + Redshifted ccm surveys are sensitive to neutral hyelrogen regardless: of whether it is part of a resolved object., Redshifted cm surveys are sensitive to neutral hydrogen regardless of whether it is part of a resolved object. + As a result. at high redshifts such surveys may be more ellicient in measuring the large-scale mass distribution than galaxy. redshift: surveys. which must icentify a very large number of individual galaxies.," As a result, at high redshifts such surveys may be more efficient in measuring the large-scale mass distribution than galaxy redshift surveys, which must identify a very large number of individual galaxies." + Furthermore. spectroscopic emission line surveys have the advantage of probing a precisely defined: redshift interval. which is unlikely to be true of a traditional galaxy survey (see?)..," Furthermore, spectroscopic emission line surveys have the advantage of probing a precisely defined redshift interval, which is unlikely to be true of a traditional galaxy survey \cite[see][]{simpson2006}." + Planned low-frequency arrays such as the Murchison Wicleficlel (MNA) and are designed. to measure the PS of 2lcem Iuctuations at 26 in order o probe the reionisation era., Planned low-frequency arrays such as the Murchison Widefield (MWA) and are designed to measure the PS of cm fluctuations at $z>6$ in order to probe the reionisation era. + ?. have argued that while he first generation of low-[requeney arrays will not. have sullicient sensitivity to precisely determine the BAO scale. future extensions could have the sensitivity to detect. the BAO scale with promisinglv small errors.," \citet{wlg2008} have argued that while the first generation of low-frequency arrays will not have sufficient sensitivity to precisely determine the BAO scale, future extensions could have the sensitivity to detect the BAO scale with promisingly small errors." + ?. assumed a semi-analytic model which predicts a scale. independent: value or the cllective bias between the linear matter PS and he 2leem PS.," \citet{wlg2008} + assumed a semi-analytic model which predicts a scale independent value for the effective bias between the linear matter PS and the cm PS." + However the 21cem bias is expected. to of strongly scale. dependent. especially toward the end. of reionisation when many ionised bubbles percolate through he intergalactic medium (GAL). ereating an excess of power on scales larger than the characteristic bubble size (c.g.?)..," However the cm bias is expected to be strongly scale dependent, especially toward the end of reionisation when many ionised bubbles percolate through the intergalactic medium (IGM), creating an excess of power on scales larger than the characteristic bubble size \citep[e.g.][]{furlanetto2004}." + In this paper we explore whether the scale dependence of he 2leem bias will compromise the ability of recdshiftec 21ccm observations to measure the BAO. scak (?).., In this paper we explore whether the scale dependence of the cm bias will compromise the ability of redshifted cm observations to measure the BAO scale \citep{mao2008}. + We ein by reviewing the expected BAO signal and cem PS in Section ??.., We begin by reviewing the expected BAO signal and cm PS in Section \ref{background}. + We describe the observation of the 21ccm 8. including a discussion. of the noise considerations in Section 3..," We describe the observation of the cm PS, including a discussion of the noise considerations in Section \ref{experiment}." + In Section ?? we deseribe our fitting procedure or recovering the BAO scale ancl present our error analysis. xore. concluding in Section. ??..," In Section \ref{fits} we describe our fitting procedure for recovering the BAO scale and present our error analysis, before concluding in Section \ref{summary}." +" To calculate these errors we adopt à set of cosmological parameters similar to those derived from the third vear WALAXP data (?).. namely Q,,,24.04—0.76.h=0.73.050.0.76 and €,=0.042."," To calculate these errors we adopt a set of cosmological parameters similar to those derived from the third year WMAP data \citep{spergel2007}, namely $\Omega_m = 0.24, \Omega_{\Lambda} = 0.76, h = 0.73, \sigma_8 = +0.0.76$ and $\Omega_b = 0.042$." + The sound speed at recombination (s) determines the length seale of the acoustic peaks in both the cosmic microwave background (CALB) anisotropies and the linear matter PS., The sound speed at recombination $(s)$ determines the length scale of the acoustic peaks in both the cosmic microwave background (CMB) anisotropies and the linear matter PS. + We refer to this length as the BAO scale., We refer to this length as the BAO scale. +" The co-moving horizon size at decoupling (7) may be determined from knowledge of Ον, and Q). and an understanding of the physics governing a barvon-photon fluid (2).."," The co-moving horizon size at decoupling $(r)$ may be determined from knowledge of $\Omega_m$ and $\Omega_b$, and an understanding of the physics governing a baryon-photon fluid \citep{page2003}." + 7. caleulate this length scale to be 1464Ls MMpe for the cosmological parameters extracted from the fifth vear WMLADP. cata., \citet{komatsu2008} calculate this length scale to be $146 \pm 1.8$ Mpc for the cosmological parameters extracted from the fifth year WMAP data. + The corresponding angular scale ον=ντο}. is closely related to theposition of the first. acoustic. peak in the CAMB PS. whieh occurs at the scale of the mode which has compressed once at the time of decoupling (sec?)..," The corresponding angular scale $\theta_A = +r/D_A(z_{\rm rec})$ is closely related to theposition of the first acoustic peak in the CMB PS, which occurs at the scale of the mode which has compressed once at the time of decoupling \citep[see][]{page2003}." + Following decoupling the same acoustic scale is imprinted in the matter PS. albeit with a dillerent phase.," Following decoupling the same acoustic scale is imprinted in the matter PS, albeit with a different phase." + This signature is expected to be preserved on large scales where non-linear eravitational effects are small., This signature is expected to be preserved on large scales where non-linear gravitational effects are small. + Pherefore the BAO scale may be used as a standard. ruler to test the geometry of the universe and the role of dark energy., Therefore the BAO scale may be used as a standard ruler to test the geometry of the universe and the role of dark energy. + Neutral hydrogen radiates at ceem due to the hyperfine transition between the singlet and. triplet. ground. states., Neutral hydrogen radiates at cm due to the hyperfine transition between the singlet and triplet ground states. + Assuming a contrast between the kinetic temperature ofthe IGM Zi. and the CMD temperature {ου and ellicient coupling of the spin temperature 7; to Z5. the 00m signal will mirror the underlying density of neutral hydrogen.," Assuming a contrast between the kinetic temperature ofthe IGM $T_k$ and the CMB temperature $T_{\rm CMB}$, and efficient coupling of the spin temperature $T_s$ to $T_k$, the cm signal will mirror the underlying density of neutral hydrogen." + The Lya and X-ray Ες emitted. by the first galaxies. 1s expected. to ensure these conditions hold. during most. of the reionisation era (see.e.g...2)..," The $\alpha$ and X-ray flux emitted by the first galaxies is expected to ensure these conditions hold during most of the reionisation era \citep[see, +e.g.,][]{furlanetto2006}." + X radio interferometer is sensitive to fluctuations in the brightness temperature of neutral eas., A radio interferometer is sensitive to fluctuations in the brightness temperature of neutral gas. + For gas of mean cosmic density the expected. temperature brightness. contrast. in. recishifted ceni emission is where 7 is the optical depth of the neutral gas to 21cm radiation and μι is the mass-weighted neutral fraction of hvdrogen in the IGM., For gas of mean cosmic density the expected temperature brightness contrast in redshifted cm emission is where $\tau$ is the optical depth of the neutral gas to cm radiation and $\bar{x}_{\rm HI}$ is the mass-weighted neutral fraction of hydrogen in the IGM. +" Allowing for fractional ασιαος in the barvonic matter censity AGF). ionisecd fraction 0, 69). ancl peculiar gas velocity δρα)y)=gaat"")locod (where Fo is the peculiar velocity of the the spatial dependence of the brightness temperature Ductuations may be written (es.2) Assuming the peculiar velocity elfect is. described. by. the linear theory result from ?.. 0,UO=fpr90 (note that fo» Lin the highredshift limit) where so=Av denotes the angle between the line of sight ancl the Fourier vector A. the angle dependent 2becm power-spectrum may be written (e.g.2) "," Allowing for fractional fluctuations in the baryonic matter density $\delta(\Vec{x})$, ionised fraction $\delta_x(\Vec{x})$ , and peculiar gas velocity $\delta_v(\Vec{x}) = +\frac{1+z}{H(z)}\frac{dv_r}{dr}(\Vec{x})$ (where $\frac{dv_r}{dr}$ is the peculiar velocity of the, the spatial dependence of the brightness temperature fluctuations may be written \citep[e.g.][]{mao2008} + Assuming the peculiar velocity effect is described by the linear theory result from \citet{kaiser1987}, , $\delta_v(\Vec{k}) = - f \mu^2 \delta (\Vec{k})$ (note that $f \rightarrow +1$ in the highredshift limit) where $\mu = \Vec{k}.\Vec{n}$ denotes the angle between the line of sight and the Fourier vector $\Vec{k}$ , the angle dependent cm power-spectrum may be written \citep[e.g.][]{mao2008} + " +"For n=1. we determine while for apeox. we have Therefore. the upper yy branch remains always positive. while the lower yo branch first remains positive for small 5 and then becomes negative for a greater than a critical 1, given explicitly by This critical g, always exists for any given ὁ because i, remains always greater than ας dictated by equation (91)).","For $\eta=1$, we determine while for $\eta\rightarrow\infty$, we have Therefore, the upper $y_1$ branch remains always positive, while the lower $y_2$ branch first remains positive for small $\eta$ and then becomes negative for $\eta$ greater than a critical $\eta_c$ given explicitly by This critical $\eta_c$ always exists for any given $\delta$ because $\eta_c$ remains always greater than 1 as dictated by equation \ref{spiralmge2etac}) )." + Entirely similar to the aligned m2 cases. the phase relationship between surface mass densities pe and. (60 for the upper gj branch of £5 solution is where the left-hand side corresponds to 5j=1 and the right-hand side corresponds toa5o.," Entirely similar to the aligned $m\ge 2$ cases, the phase relationship between surface mass densities $\mu^g$ and $\mu^s$ for the upper $y_1$ branch of $D_s^2$ solution is where the left-hand side corresponds to $\eta=1$ and the right-hand side corresponds to $\eta\rightarrow\infty$." +" This branchalways has out-of-phase relationship between surface mass densities H"" and (£0 in he range of ασ(1/4.1/2)."," This branchalways has out-of-phase relationship between surface mass densities $\mu^g$ and $\mu^s$ in the range of $\beta\in(-1/4,1/2)$." + Aleanwhile [ου the lower ye branch. the phase relationship between surface mass densities ye’ and pe ids determined by where the left-hand side corresponds to 5j=1 and the right-hand. side corresponds toy=ye where D2=yo 0.," Meanwhile for the lower $y_2$ branch, the phase relationship between surface mass densities $\mu^g$ and $\mu^s$ is determined by where the left-hand side corresponds to $\eta=1$ and the right-hand side corresponds to $\eta=\eta_c$ where $D_s^2=y_2=0$ ." + This branch always has in-phase relationship between, This branch always has in-phase relationship between +Each axis has a drive unit which forms tlic| pivot on one eud of the axis aud a position CLICOCer unit which supports the opposie end.,Each axis has a drive unit which forms the pivot on one end of the axis and a position encoder unit which supports the opposite end. + Actual aliguiment is measured by rasteriug through sources in fight., Actual alignment is measured by rastering through sources in flight. + T16 detector interface bout (DIB) iithe CE yerformus time tageeoine and data foriuting for the N-ray. scieucc data as well as forinatting detector housekeeping data., The detector interface board (DIB) in the CE performs time tagging and data formatting for the X-ray science data as well as formatting detector housekeeping data. + The microprocessor used is an An:dog Device* ADSP2100., The microprocessor used is an Analog Devices ADSP2100. + The DIB receives a fas photon arrival signal from cach «etector WwΠο euables the timing to ~1 mucrosecoud accuracy., The DIB receives a fast photon arrival signal from each detector which enables the timing to $\sim 1$ microsecond accuracy. + A 1 Iz clock (awit1 COYTCSDOrding GPS time tag) is received direcIv from the spacecraft to sviiclirouize the eveut time tageiue clock., A 1 Hz clock (with corresponding GPS time tag) is received directly from the spacecraft to synchronize the event time tagging clock. + Pulse height data or each photon are transmitted froiu the detec‘tor to the DIB upon completion | tl| analog to digital conversiou., Pulse height data for each photon are transmitted from the detector to the DIB upon completion of the analog to digital conversion. +" Ther ""are twos audard telemetry modes: eveut 11 κectral.", There are two standard telemetry modes: event and spectral. + Eveut mode is the “workhorse” telemetry mode for USA: for moderate ount rates. it allows the masimal amorut of information to be preserved on cach roton.," Event mode is the “workhorse” telemetry mode for USA; for moderate count rates, it allows the maximal amount of information to be preserved on each photon." + In event mode. the arrival time and some euerev information is stored for ach photon «etected.," In event mode, the arrival time and some energy information is stored for each photon detected." + There are two submodes of event iode providing 32 ps time xd 16 pulse height channels iu a 12 bi word aud 2 ps time with & pulse height iunels ina 15 bit word respectively., There are two submodes of event mode providing 32 $\mu$ s time and 16 pulse height channels in a 12 bit word and 2 $\mu$ s time with 8 pulse height channels in a 15 bit word respectively. + Data may be output in eveit inodo at either Yor 128 kbps providing maxima couit rates of 3060 or 9910 events per second or 32 ps time or 2118 or 7952 events 1xy second for jes time., Data may be output in event mode at either 40 or 128 kbps providing maximum count rates of 3060 or 9940 events per second for 32 $\mu$ s time or 2448 or 7952 events per second for $\mu$ s time. +" Iu spectral mode. a ""ill resolution enerev spectrum CIS clawjcls) is generated every 10 millisecouds for cach detector."," In spectral mode, a full resolution energy spectrum (48 channels) is generated every 10 milliseconds for each detector." +" The USA experiment also provides space for two ""ride-aloue"" xocessor boards. he RII3000 aud the IDT35081."," The USA experiment also provides space for two “ride-along” processor boards, the RH3000 and the IDT3081." + The RIIS000 board is built around a pair radiatiou iudenued Iuris Seunicouductor version «ft the MIPS R3000 configured as a shadow xür with 2 MD of memory., The RH3000 board is built around a pair radiation hardened Harris Semiconductor version of the MIPS R3000 configured as a shadow pair with 2 MB of memory. + The IDT3081 board incorporates the co IDT3081 processor and 2 MB of DRÀM witrout any specia error correcting mardware., The IDT3081 board incorporates the commercial-off-the-shelf IDT3081 processor and 2 MB of DRAM without any special error correcting hardware. + Both computer boards have access fo the downlink science telemetry stream., Both computer boards have access to the downlink science telemetry stream. + These processors will be used to conduct experiuents in fault-tolerant coluputing. autonomous spacecraft navigation. ak to perform special data analvsis unctionus which are ονομα the scope of the normal scieuce telemetry modes. or which require baudwidths greater than 128 kbps.," These processors will be used to conduct experiments in fault-tolerant computing, autonomous spacecraft navigation, and to perform special data analysis functions which are beyond the scope of the normal science telemetry modes, or which require bandwidths greater than 128 kbps." + The USA instrument has been performing well suce activation Όσσα on 30 April 1999. but the USA iission has not beeu without its difficultics.," The USA instrument has been performing well since activation began on 30 April 1999, but the USA mission has not been without its difficulties." + Approximately, Approximately +"At the outer edges of the solar system, the solar wind pushes up against the interstellar medium.","At the outer edges of the solar system, the solar wind pushes up against the interstellar medium." +" Since the solar wind is moving at supersonic speeds, it forms a shock known as the termination shock."," Since the solar wind is moving at supersonic speeds, it forms a shock known as the termination shock." + The region between the termination shock and the interstellar medium is referred to as the heliosheath., The region between the termination shock and the interstellar medium is referred to as the heliosheath. + Flapping of the heliospheric current sheet produces sectored magnetic fields (Smith2001) that have a significant latitudinal extent., Flapping of the heliospheric current sheet produces sectored magnetic fields \citep{Smith01} that have a significant latitudinal extent. +" There has been research suggesting that the current sheets between the sectored fields found in the heliosheath are compressed to the point that collisionless reconnection begins to occur, resulting in the formation of magnetic islands (Drakeetal.2010;Czechowski2010)."," There has been research suggesting that the current sheets between the sectored fields found in the heliosheath are compressed to the point that collisionless reconnection begins to occur, resulting in the formation of magnetic islands \citep{Drake10,Czechowski10}." +. A turbulent magnetohydrodynamic (MHD) model of the reconnection of the sectored fields has also been proposed (Lazarian&Opher2009) although we will argue later that the data are inconsistent with this hypothesis., A turbulent magnetohydrodynamic (MHD) model of the reconnection of the sectored fields has also been proposed \citep{Lazarian09} although we will argue later that the data are inconsistent with this hypothesis. +" An important question, however, is whether the conventional treatment of collisionless reconnection (Shayetal. is valid in the heliosheath, where it was suggested 2007)that the pick-up ion (PUI) population increases the plasma pressure compared with values at 1 AU (Zank1999;Richardsonetal.2008;Wu 2009)."," An important question, however, is whether the conventional treatment of collisionless reconnection \citep{Shay07} is valid in the heliosheath, where it was suggested that the pick-up ion (PUI) population increases the plasma pressure compared with values at 1 AU \citep{Zank99, Richardson08,Wu09}." +". Although both spacecraft are currently taking data in the heliosheath, the energy range of the detectors does not cover the PUIs, so it is difficult to make a reliable estimate of the value for 8, the ratio of the plasma pressure to the magnetic pressure (Richardson 2008).."," Although both spacecraft are currently taking data in the heliosheath, the energy range of the detectors does not cover the PUIs, so it is difficult to make a reliable estimate of the value for $\beta$, the ratio of the plasma pressure to the magnetic pressure \citep{Richardson08}. ." +" Global MHD simulations suggest, however, that 6 varies from 8 to 0.5 between the termination shock and the interstellar medium with the highest 8 just downstream of the termination shock (Drakeetal. 2010)."," Global MHD simulations suggest, however, that $\beta$ varies from $8$ to $0.5$ between the termination shock and the interstellar medium with the highest $\beta$ just downstream of the termination shock \citep{Drake10}." +". Although this simulation does not include a separate pick-up ion population, it provides a rough estimate for the expected values for f and motivates the range of 8 in our study."," Although this simulation does not include a separate pick-up ion population, it provides a rough estimate for the expected values for $\beta$ and motivates the range of $\beta$ in our study." + In this study we investigate the impact of @ on the dynamics of reconnection and the formation of magnetic islands relevant to the sectored heliosheath., In this study we investigate the impact of $\beta$ on the dynamics of reconnection and the formation of magnetic islands relevant to the sectored heliosheath. +" 'To begin reconnection and island formation a current sheet needs to be compressed to approximately the ion inertial scale d;=c/wpi, where c is the speed of light and wy; is the ion plasma frequency, (Cassaketal.2005;Yamada 2007)."," To begin reconnection and island formation a current sheet needs to be compressed to approximately the ion inertial scale $d_i = c/\omega_{\text{pi}}$, where $c$ is the speed of light and $\omega_{\text{pi}}$ is the ion plasma frequency, \citep{Cassak05,Yamada07}." +. At this point the current sheet becomes unstable to the collisionless tearing mode., At this point the current sheet becomes unstable to the collisionless tearing mode. +" Upstream of the termination shock the heliospheric current sheet has a thickness of around 10,000km (Smith2001) and is predicted to compress to around 2500km just downstream of the shock."," Upstream of the termination shock the heliospheric current sheet has a thickness of around $10,000\text{ km}$ \citep{Smith01} and is predicted to compress to around $2500\text{ km}$ just downstream of the shock." +" In the upstream region the plasma density measured at is around 0.001cmὉ, corresponding to an ion skin depth of around 7,200km."," In the upstream region the plasma density measured at is around $0.001\text{cm}^{-3}$, corresponding to an ion skin depth of around $7,200\text{ km}$." +" In the downstream region the density is compressed to around 0.003cm-?, corresponding to an ion skin depth of around 4200km."," In the downstream region the density is compressed to around $0.003\text{cm}^{-3}$, corresponding to an ion skin depth of around $4200\text{ km}$." +" Thus, the compression of the current sheets across the termination shock should trigger collisionless reconnection in the heliosheath and someand observations support this hypothesis (Opheretal.2011)."," Thus, the compression of the current sheets across the termination shock should trigger collisionless reconnection in the heliosheath and someand observations support this hypothesis \citep{Opher11}." +. In our system we will be examining symmetric current sheets with no guide field (initial out-of-plane magnetic field)., In our system we will be examining symmetric current sheets with no guide field (initial out-of-plane magnetic field). +" In an analytic study Brittnacheretal.(1995) showed that when p;/wo~1, the fastest growing linear mode occurs at kwo70.5, where k is the wavenumber of the tearing mode, wo is the halfwidth of the current sheet, and p; is the ion gyroradius."," In an analytic study \cite{Brittnacher95} showed that when $\rho_i/w_0 \approx 1$, the fastest growing linear mode occurs at $kw_0 \approx 0.5$, where $k$ is the wavenumber of the tearing mode, $w_0$ is the halfwidth of the current sheet, and $\rho_i$ is the ion gyroradius." +" Since p;= νβιάι, where 8; is the plasma beta based on the ion pressure, the current sheet thickness is comparable to that in our simulation."," Since $\rho_i=\sqrt{\beta_i}d_i$ , where $\beta_i$ is the plasma beta based on the ion pressure, the current sheet thickness is comparable to that in our simulation." +ealaxies (seee.g.Weil&ILlernquist1993).,galaxies \citep[see e.g.][]{Weil93}. +. Our work suggests that the group has at least à population of 22 galaxies within a velocity range of 1500 knis ! (seee.g.Ramellaetal.1989). [rom the median of the central elliptical. NGC 4756.," Our work suggests that the group has at least a population of 22 galaxies within a velocity range of 1500 km $^{-1}$ \citep[see +e.g.][]{Ramella89} from the median of the central elliptical, NGC 4756." +" At about 7.5 avemin SW of NGC 4756 a substructure well separated from NGC 4756 is detected. that includes IC 829, AICG 23335. MCG 23336 and AICG 23338. which meets the IHickson criteria for being a compact eroup."," At about 7.5 arcmin SW of NGC 4756 a sub–structure well separated from NGC 4756 is detected, that includes IC 829, MCG –2–33–35, MCG –2–33–36 and MCG –2–33–38, which meets the Hickson criteria for being a compact group." +"sub-structure, The group then [alls within the category of loose groups which could be the birthplace of compact groups (Rood 1994)."," The group then falls within the category of loose groups which could be the birthplace of compact groups \citep{Rood94,Ramel94}." +. At the same time. the [act that the brightest elliptieal (NGC 4756) is unperturbed and quite isolated with respect to the compact group suggests a separate history of these two parts of the svstem.," At the same time, the fact that the brightest elliptical (NGC 4756) is unperturbed and quite isolated with respect to the compact group suggests a separate history of these two parts of the system." + Recently Marcumοἱal.(2004) analyzed a set of 8 extremely isolated E/90 galaxies., Recently \citet{Marcum04} analyzed a set of 8 extremely isolated E/S0 galaxies. + Thev suggest that at least four of their objects are probable fossil eroups., They suggest that at least four of their objects are probable fossil groups. + The colors of (wo of them are quite blue - (B-R)<1 - and one of them KIG 870 posseses a possible double nucleus., The colors of two of them are quite blue - $\leq$ 1 - and one of them KIG 870 posseses a possible double nucleus. + None of our earlv-tvpe galaxies have color ancl structure characteristics similar to these objects., None of our early-type galaxies have color and structure characteristics similar to these objects. +" NGC 4756. with iis normal color and regular structure. suggests either an unperturbed history within a pristine loose group or a very old and ""digested"" merging event."," NGC 4756, with its normal color and regular structure, suggests either an unperturbed history within a pristine loose group or a very old and “digested” merging event." + Indeed. most of the isolated objects of are more similar in structure and color to NGC 4756.," Indeed, most of the isolated objects of \citet{Marcum04} are more similar in structure and color to NGC 4756." + At the present time only inadequate X-ray. data are available and consequently cannot allow a proper and conclusive analvsis of the Xrav. properties of the NGC 4756 group., At the present time only inadequate X-ray data are available and consequently cannot allow a proper and conclusive analysis of the X–ray properties of the NGC 4756 group. + The available Xrav. data would however point to the presence of (wo distinct svstenms al different temperatures. corresponding to the foreground group (softer) and the background cluster (harder).," The available X–ray data would however point to the presence of two distinct systems at different temperatures, corresponding to the foreground group (softer) and the background cluster (harder)." + None of the poor groups observed in X-ravs. like those catalogued by Alulehaey et al. (," None of the poor groups observed in X-rays, like those catalogued by Mulchaey et al. (" +2003) has optical characteristics like those of the NGC 4756 eroup. since,"2003) has optical characteristics like those of the NGC 4756 group, since" +the true anomaly counted positive anticlockwise from the perihelion.,the true anomaly counted positive anticlockwise from the perihelion. +" The Gauss variation equation for the node O is (Bertottietal.2003) = where .1, is the normal component of A."," The Gauss variation equation for the node $\Omega$ is \citep{Ber03} + = where $A_{\nu}$ is the normal component of $\vec{A}$." + It must be recalled that. in order to make meaningful comparisons with the estimated corrections Az to the standard. perihelion rates. they have been obtained by processing the planetary. data in the standard ICRE frame which is à frame with the origin in the (known) solar svstems barvcenter and having the mean ecliptic at J2000 epoch as reference plane with the « axis directed towards the Vernal point (Johnston1999).," It must be recalled that, in order to make meaningful comparisons with the estimated corrections $\Delta\dot\varpi$ to the standard perihelion rates, they have been obtained by processing the planetary data in the standard ICRF frame which is a frame with the origin in the (known) solar system's barycenter and having the mean ecliptic at J2000 epoch as reference plane with the $x$ axis directed towards the Vernal point \citep{Joh99}." +. This is particularly important when (here is some phlivsical feature. like a static body in a given direction as in our case. which breaks the spatial svimmnmelirv: assuming that ay. which is actually a-priori unknown. coincides wilh one οἱ (he frames axes just to simplify the caleulation is. in principle. incorrect.," This is particularly important when there is some physical feature, like a static body in a given direction as in our case, which breaks the spatial symmetry: assuming that $\hat{n}_{\rm X}$, which is actually a-priori unknown, coincides with one of the frame's axes just to simplify the calculation is, in principle, incorrect." +" The analyical calculations lor a non-privileged direction of nx are verycimbersome:: αἱ the end. one is left wilh an expression of (he kind iiA, egqfichere FisoftheformF » in which C; are complicated functions of the semimajor axis v and the eccentricity ο of P. while 7; are trigonometric functionsof the inclination J. the longitude of the ascending node O and the argument of perihelion w of the planet P perturbed by X. whose ecliptic longitude ancl latitude are Ay and oy."," The analytical calculations for a non-privileged direction of $\hat{n}_{\rm X}$ are very; at the end, one is left with an expression of the kind ; where $F$ is of the form _i in which $G_i$ are complicated functions of the semimajor axis $a$ and the eccentricity $e$ of P, while $T_i$ are trigonometric functionsof the inclination $I$, the longitude of the ascending node $\Omega$ and the argument of perihelion $\omega$ of the planet P perturbed by X, whose ecliptic longitude and latitude are $\lambda_{\rm X}$ and $\beta_{\rm X}$." + Releasing such analvtic expressions would be. actually. extremely space-consuming aud of little help: they have to be munerically computed for given. values of a.e.£O.d.," Releasing such analytic expressions would be, actually, extremely space-consuming and of little help: they have to be numerically computed for given values of $a,e,I,\Omega,\omega$." + As a result. by comparing to the estimated correction Ac for a given planet P like Saturn. one has the tidal parameter Κ of X as a function of Ax.o.," As a result, by comparing to the estimated correction $\Delta\dot\varpi$ for a given planet P like Saturn, one has the tidal parameter $\mathcal{K}$ of X as a function of $\lambda_{\rm X},\beta_{\rm X}$." + At this point. it is interesting to note that the form assumed by the External Field (EFE) in the planetary regions of the solar svstem in the recent study by has exactlvthe same functional dependence of (??).. provided that where (DegemanandBroeils1991). Ay=L27x10M ms ? is the characteristic acceleration scale of MOND. and," At this point, it is interesting to note that the form assumed by the External Field (EFE) in the planetary regions of the solar system in the recent study by \citet{Mil09} has exactlythe same functional dependence of , provided that where \citep{Bege} $A_0=1.27\times 10^{-10}$ m $^{-2}$ is the characteristic acceleration scale of MOND, and" +well as the referee whose conunents ercatly improved the per.,well as the referee whose comments greatly improved the paper. +BATSRUS code (Powelletal.19909) and is part of the Space Weatler Modeling Framework (SWALIF) (Tothetal.2005).,BATSRUS code \citep{powell99} and is part of the Space Weather Modeling Framework (SWMF) \citep{toth05}. +. The model solves the set of MIID equations on a non-uniform Cartesian erid and is designed with lughly cficient parallel architecture., The model solves the set of MHD equations on a non-uniform Cartesian grid and is designed with highly efficient parallel architecture. + Tere. we describe the model briefly.," Here, we describe the model briefly." + We refer the reader to the references above for a more detailed description., We refer the reader to the references above for a more detailed description. + The ambicut solar wind conditions iu the model are obtained under the assuuptiou that the source of energv required to power the solar wind ds the change in the polvtropic iudex. 5 im a non-polvtropic medi.," The ambient solar wind conditions in the model are obtained under the assumption that the source of energy required to power the solar wind is the change in the polytropic index, $\gamma$ in a non-polytropic medium." + The nunuencal procedure is as follows., The numerical procedure is as follows. + First. tιο potential maguetic feld is calculated 1sine high 1tsolution SOTO/Michelson DXyppler huager (MDI:Scherreroetal.1995) nmiaeuetograni sYvn0]ifie. niaps (ittp://soistantord.ecda).," First, the potential magnetic field is calculated using high resolution SOHO/Michelson Doppler Imager \citep[MDI;][]{Scherrer95} magnetogram synoptic maps (http://soi.stanford.edu)." +" Secorcl. this poteial field cüstribution is usec to calculate the distribution of the terminal solar wind speed. (ys, as a function of the flux tube expansion factor. fi. based on the Wanug-Shecley- (WSA) model Wang&Shecley1990:AreePizzo 2000).."," Second, this potential field distribution is used to calculate the distribution of the terminal solar wind speed, $u_{wsa}$ as a function of the flux tube expansion factor, $f_s$, based on the Wang-Sheeley-Arge (WSA) model \citep{wangy90,argepizzo00}. ." + Third. the photospheric boundary couditious for 5. aud the terminal speed. tise. are related by tracing the total euerev (Bernoulli Tuteeral) along the flux tubes.," Third, the photospheric boundary conditions for $\gamma$, and the terminal speed, $u_{wsa}$, are related by tracing the total energy (Bernoulli Integral) along the flux tubes." + The spatial distribution of ~ is then specified as a radial function ofthe plotospheric values. aud the MIID equations are solved self-cousisteutlv until a steady-state with a wind solution is obtained.," The spatial distribution of $\gamma$ is then specified as a radial function of the photospheric values, and the MHD equations are solved self-consistently until a steady-state with a wind solution is obtained." +" Figure 5 shows the steady-state values of number density. 7. maenetic field streugth. DB. temperature. T. plasma 2. sound speed. C. and Alfvénn speed. ey respectively, at heieht of r=LIR.."," Figure \ref{fig:f5} shows the steady-state values of number density, $n$, magnetic field strength, $B$, temperature, $T$, plasma $\beta$, sound speed, $C_s$, and Alfvénn speed, $v_A$ respectively, at height of $r=1.1R_\odot$." + Iu order to drive the CATE. we superimpose an uustable. senu-ciceulu flax rope based on the Titov&Deémoulin(1999) model. ou top of the amibicut solution (Boussevetal.20032).," In order to drive the CME, we superimpose an unstable, semi-circular flux rope based on the \cite{titov99} model, on top of the ambient solution \citep{roussev03a}." +.. We match the location and orientation of the dux rope to those of the sourcc active region and its inversion line as they appear iu the magnuetogram data., We match the location and orientation of the flux rope to those of the source active region and its inversion line as they appear in the magnetogram data. + The free energy of the CME is obtained by a prescribed toroidal current: we modifv the magnitude of this current to match the observed CME speed., The free energy of the CME is obtained by a prescribed toroidal current; we modify the magnitude of this current to match the observed CME speed. + We would like to stress that even though the CATE initiation method is not based on actual plotospleric motions. it has been successful in mimicking the CALE conditions ouce it is already propagating aud expanding (Lugazetal.2007:Cohen20082:Manchester 2008).," We would like to stress that even though the CME initiation method is not based on actual photospheric motions, it has been successful in mimicking the CME conditions once it is already propagating and expanding \citep{lugaz07,cohen08a,manchester08}." +. Since we are interested in the development ofthe CAME after it has already. been initiated. this model is appropriate for our study.," Since we are interested in the development of the CME after it has already been initiated, this model is appropriate for our study." + We run the simulation in a Cartesian box of 20/0...«20R..« 20R... with 9 levels of eid refinement around the solar surface.," We run the simulation in a Cartesian box of $20R_\odot\times20R_\odot\times20R_\odot$ , with 9 levels of grid refinement around the solar surface." + The evid size around the active region and up to a height of about 3A. is of the order of 1/50R.., The grid size around the active region and up to a height of about $3R_\odot$ is of the order of $1/50R_\odot$. + The ambient coronal conditions are driven by MDI maguetogram data for Carrington Rotation 2080., The ambient coronal conditions are driven by MDI magnetogram data for Carrington Rotation 2080. + The MIID simulation was performed using the Pleiades cluster at NASA's Advanced Supercomputing (NAS) center., The MHD simulation was performed using the Pleiades cluster at NASA's Advanced Supercomputing (NAS) center. + Prior to a detailed analysis of the magnetic field tlaee-dimenusional evolution. we validate the timine of the simulated CATE by comparing its propagation with STEREO/COR1 observations.," Prior to a detailed analysis of the magnetic field three-dimensional evolution, we validate the timing of the simulated CME by comparing its propagation with STEREO/COR1 observations." + This validation is required for any further assuniptious about the αναο evolution aud its relation to the observed coronal waves., This validation is required for any further assumptions about the dynamic evolution and its relation to the observed coronal waves. + Fortuuatelv. the 13 February 2009 eveut was observed by both STEREO-A aud STEREO-D simultancously. in quadrature.," Fortunately, the 13 February 2009 event was observed by both STEREO-A and STEREO-B simultaneously, in quadrature." + Figure 2. shows a side view of the CME propagation. comparing STEREO-A CORL base differeuce white-light inaeses with svuthetic base differcuce white-light images eenerated from the simulation domain for 5:55. 6:15. and 6:35 UT.," Figure \ref{fig:f2} shows a side view of the CME propagation, comparing STEREO-A COR1 base difference white-light images with synthetic base difference white-light images generated from the simulation domain for 5:55, 6:15, and 6:35 UT." +" We would like to stress that both real aud siauulated data sets have been processed in the same ΠΟΙΟ), and the scale of the images has been choseu so that it provides the vost display."," We would like to stress that both real and simulated data sets have been processed in the same manner, and the scale of the images has been chosen so that it provides the best display." + The couparisou of theπα ο (center coli) with the base difference images (eft column) is used to verity the strucure of the CNDE., The comparison of the simulation (center column) with the base difference images (left column) is used to verify the structure of the CME. + Comparison with the running difference images Gight coluun) is used to verity the lateral extent., Comparison with the running difference images (right column) is used to verify the lateral extent. + We emphlasise that the outer shell of the CALE is a very subtle feature. auc is only really evideut when successive frames are switched back and forth.," We emphasise that the outer shell of the CME is a very subtle feature, and is only really evident when successive frames are switched back and forth." + Thus the reader is cucouraged to examine the CORL running difference movie rdiff.mov). usine the white arrows in the right coluun of Figure 2. as a reference.," Thus the reader is encouraged to examine the COR1 running difference movie ), using the white arrows in the right column of Figure \ref{fig:f2} as a reference." + One can see that the simulated CME frout and the global structure matches well to the observed CALE., One can see that the simulated CME front and the global structure matches well to the observed CME. + Figure 3— compares the simulation results with STEREO-B EUVI data for the period 5:25-6:35 UT., Figure \ref{fig:f3} compares the simulation results with STEREO-B EUVI data for the period 5:25-6:35 UT. +" The left panel of cach pair shows an EUVI base differeuce Πμασο, while the right panel shows base difference mages of the simulated mass deusitv at a height of LR. (about το Main)."," The left panel of each pair shows an EUVI base difference image, while the right panel shows base difference images of the simulated mass density at a height of $1.1R_\odot$ (about 70 Mm)." + We choose this height as it is consistent with calculations of the coronal wave bright frout altitude from EUVI data (Patsourakosctal.2009).. as well as with previous height estimates from SOIIO/EIT. data (81)).," We choose this height as it is consistent with calculations of the coronal wave bright front altitude from EUVI data \citep{Patsourakos09a}, as well as with previous height estimates from SOHO/EIT data \ref{sec:Intro}) )." + We mark the leading edge of the bright frout iu cach base difference EUVLB inage with a dashed white circle., We mark the leading edge of the bright front in each base difference EUVI-B image with a dashed white circle. + We emphasize that this circle has been drawn by eve. and simply iudicates the maxima extent reached by the coronal wave in a eiveu imaec. (," We emphasize that this circle has been drawn by eye, and simply indicates the maximum extent reached by the coronal wave in a given image. (" +The reader is encourage to view the supplemental movies provided with this paper as well:195b_diff.,"The reader is encouraged to view the supplemental movies provided with this paper as well:, )." +mov. densityfrontdif.mov). Figure 3. shows that the expansion of the simulate: wave frout is in a good aereciuent with the observe ouc., Figure \ref{fig:f3} shows that the expansion of the simulated wave front is in a good agreement with the observed one. + Deviations are probably due to the fact that the actual EUVT enmissious are not simply a represcutation of the mass density. but a rather complicated. iuteeratec fuuction of it.," Deviations are probably due to the fact that the actual EUVI emissions are not simply a representation of the mass density, but a rather complicated, integrated function of it." + The simulated bright frout in Figure 3— becomes broader as it expands further from the active region., The simulated bright front in Figure \ref{fig:f3} becomes broader as it expands further from the active region. + This is consistent with observed properties of coronal waves from SOIIO/EIT data (Dereetal.1997:Klassenetal.2000:Podladchikova&Berelunaus 2005)..," This is consistent with observed properties of coronal waves from SOHO/EIT data \citep{Dere97, Klassen00, Podladchikova05a}." +. Areas of decreased ass densitv (corresponding to the core coronal dinuuiues regions) can also be identified iu the simulated data., Areas of decreased mass density (corresponding to the core coronal dimming regions) can also be identified in the simulated data. + We note that both the real aud simulated bright frouts have au increasingly pateliy. diffuse nature as thefront expands away from the active region.," We note that both the real and simulated bright fronts have an increasingly patchy, diffuse nature as thefront expands away from the active region." + We measured theexpansion of the leading edee of the bright front iu ruunius differeuce data from 05:15 - 06:15 UT. which expands with an average velocity of τε 260 kins |.," We measured theexpansion of the leading edge of the bright front in running difference data from 05:45 - 06:15 UT, which expands with an average velocity of $\approx$ 260 $^{-1}$ ." +Figure 9 shows luminosity finelions (hereafter: LE) for clusters outside of the nuclear reeion. in (he F555W filter.,"Figure \ref{fig:lf_object_selection} shows luminosity functions (hereafter: LF) for clusters outside of the nuclear region, in the F555W filter." + The luminosities include our preferred. size-dependent aperture corrections. and have been corrected for extinction in (he Milkv Way but not for extinction in AIS2.," The luminosities include our preferred, size-dependent aperture corrections, and have been corrected for extinction in the Milky Way but not for extinction in M83." + Two different biniings are shown in each panel. variable size bins with equal numbers ol clusters in each bin (as recommended by Maiz Apellaniz Ubeda 2005 and shown with filled circles) ancl approximately equal size bins with variable munbers of clusters in each bin (open circles).," Two different binnings are shown in each panel, variable size bins with equal numbers of clusters in each bin (as recommended by Maiz Apellaniz Ubeda 2005 and shown with filled circles) and approximately equal size bins with variable numbers of clusters in each bin (open circles)." + Variable binning will be our preferred method throughout this paper. and will be discussed in more detail in Section 4.2.," Variable binning will be our preferred method throughout this paper, and will be discussed in more detail in Section 4.2." + The left panel of Figure 9 also shows the unminositv Iunction (in F555W) for clusters in the nuclear starburst region (filled (triangles)., The left panel of Figure \ref{fig:lf_object_selection} also shows the luminosity function (in F555W) for clusters in the nuclear starburst region (filled triangles). +" Each of these luminosity funcüons can be described. to first order. by a single power aw. oCL)xL""."," Each of these luminosity functions can be described, to first order, by a single power law, $\phi(L) \propto L^{\alpha}$." + The best fit value of a is given in each panel lor the variable size bins., The best fit value of $\alpha$ is given in each panel for the variable size bins. + These values are (he same. within the errors.," These values are the same, within the errors." + We find that the exponent a does not change with unminositw. Le.. there is no evidence [or a steepening or [lattening at brighter magnitudes.," We find that the exponent $\alpha$ does not change with luminosity, i.e., there is no evidence for a steepening or flattening at brighter magnitudes." + We also determine a in several otlier wavs from our cluster catalogs: in different filters. by selecting subsamples which have colors in cluster space and by C—D color.," We also determine $\alpha$ in several other ways from our cluster catalogs: in different filters, by selecting subsamples which have colors in cluster space and by $U\!-B\!$ color." + These values for o are compiled in Table 1.. and discussed further in 844.2.," These values for $\alpha$ are compiled in Table \ref{tab:alpha}, and discussed further in 4.2." + We find a power-law index [or the huninositv function of clusters in M83 to be a=—2.04+4 0.08., We find a power-law index for the luminosity function of clusters in M83 to be $\alpha = -2.04 \pm 0.08$ . + This is the mean aud standard: deviation of all a values listed in Table 1. (exelucling the nuclear dataset at the end of the table)., This is the mean and standard deviation of all $\alpha$ values listed in Table \ref{tab:alpha} (excluding the nuclear dataset at the end of the table). + The luminosity function of clusters in the nuclear region have a best fit value of a=—1.9320.12. which is the same as that found for clusters outside of the nuclear region. wilhin the errors.," The luminosity function of clusters in the nuclear region have a best fit value of $\alpha=-1.93\pm 0.12$, which is the same as that found for clusters outside of the nuclear region, within the errors." + llere. we quantilv the sensitivity of the luminosity function of clusters in M82 to different selection techniques. assumptions. and corrections that are tvpically made in the course of the analvsis.," Here, we quantify the sensitivity of the luminosity function of clusters in M83 to different selection techniques, assumptions, and corrections that are typically made in the course of the analysis." + The following items are arranged in (he order in which (hey affect the index a., The following items are arranged in the order in which they affect the power-law index $\alpha$. + We note that (his order may be different. [or other datasets with different characteristics. such as lower photometric accuracy or higherexüncton than found in our WFC3 M82 data.," We note that this order may be different for other datasets with different characteristics, such as lower photometric accuracy or higherextinction than found in our WFC3 M83 data." +For photometric calibration. we establish a system of funt standard stars in the CADIS fields. which are calibrated with respect to spectrophotometric standards in photometric nights (Oke1990).,"For photometric calibration, we establish a system of faint standard stars in the CADIS fields, which are calibrated with respect to spectrophotometric standards in photometric nights \cite{oke}." +.. This Way we have several spectrophotometric standards within each CADIS exposure providing us with independence from photometric conditions for regular imaging., This way we have several spectrophotometric standards within each CADIS exposure providing us with independence from photometric conditions for regular imaging. + CCD images are reduced such that accurate color measurements are ensured even under conditions of changing seeing., CCD images are reduced such that accurate color measurements are ensured even under conditions of changing seeing. + The reduction procedure is outlined in Rósser Melisenheimer (1991)., The reduction procedure is outlined in Rösser Meisenheimer (1991). +" Between all wavebands. the relative calibration is better than for objects of R=22"","," Between all wavebands, the relative calibration is better than for objects of $R=22^m$." + Por CADIS we opted for a classification. scheme. that essentially compares observed colors of each object with a color library of known objects assembled from observed spectra by synthetic photometry performed on our CADIS filter set.," For CADIS we opted for a classification scheme, that essentially compares observed colors of each object with a color library of known objects assembled from observed spectra by synthetic photometry performed on our CADIS filter set." + The spectral libraries used as an input were the Gunn Stryker (1983) catalogue for stars. the galaxy template spectra from Kinney et al. (," The spectral libraries used as an input were the Gunn Stryker (1983) catalogue for stars, the galaxy template spectra from Kinney et al. (" +1996). and the QSO template spectrum of Francis et al. (,"1996), and the QSO template spectrum of Francis et al. (" +1991).,1991). + From this. we generated regular grids of QSO templates ranging in redshift within 0<.| anc having various continuum slopes and emission line equivalent widths.," From this, we generated regular grids of QSO templates ranging in redshift within $04$, yet, since they are believed to be extremely rare and we were not yet able to model their colors well enough." + Objects are classified by locating them in color space and comparing the probability for each class to generate the giver measurement., Objects are classified by locating them in color space and comparing the probability for each class to generate the given measurement. + Given the photometrie error ellipsoid in the n-dimensional color space. each library object can be assignec a probability to cause an observation of the measured colors.," Given the photometric error ellipsoid in the n-dimensional color space, each library object can be assigned a probability to cause an observation of the measured colors." + For a whole class. this probability is assumed to be the average value of the individual class members (Parzen's Kernel estimator. 1963).," For a whole class, this probability is assumed to be the average value of the individual class members (Parzen's Kernel estimator, 1963)." + From these probabilities we can derive the likelihood of each object to belong to the various classes., From these probabilities we can derive the likelihood of each object to belong to the various classes. + Since the galaxy and quasar libraries resemble regular grids in redshift and spectral type. these parameters can also be estimated from the observation.," Since the galaxy and quasar libraries resemble regular grids in redshift and spectral type, these parameters can also be estimated from the observation." + For this purpose. we treat the library as a statistical ensemble generating the measured colors and determine expectation values às well as variances for assessing the quality of the estimate.," For this purpose, we treat the library as a statistical ensemble generating the measured colors and determine expectation values as well as variances for assessing the quality of the estimate." + A detailed discussion of the algorithm and the performance of the classification and redshift estimation will be given in Wolf(1998)., A detailed discussion of the algorithm and the performance of the classification and redshift estimation will be given in Wolf (1998). +ess efficient than ILU. the approximate inner linear solve is less accurate after its fixed ΠΙΟ of iterations.,"less efficient than ILU, the approximate inner linear solve is less accurate after its fixed number of iterations." + Therefore the outer liuear solve needs more iterations o converge to the required aceuracy of 10>., Therefore the outer linear solve needs more iterations to converge to the required accuracy of $10^{-5}$. + The single processor code needs 19 outer linear iterations. whereas the parallel codes need 23 or 21.," The single processor code needs 19 outer linear iterations, whereas the parallel codes need 23 or 24." + Thus the masimally achievable scaling efficiency. is luted to 19/23~0.83., Thus the maximally achievable scaling efficiency is limited to $19/23\approx 0.83$. +" The scaling efficiency. on he SP2 is close to this Πιτ,", The scaling efficiency on the SP2 is close to this limit. + The secoud reason for low scaling efficiency is that we have not optimized the MPI calls iu anv wax., The second reason for low scaling efficiency is that we have not optimized the MPI calls in any way. + The fact that the scaling efficiency. ou the cluster is much etter if onlv one processor per node is used. sugecsts that the MPI calls are a vottleneck.," The fact that the scaling efficiency on the cluster is much better if only one processor per node is used, suggests that the MPI calls are a bottleneck." + Usiug both processors on a node doubles the communication load ou hat node which doubles the waiting time for MPI communication., Using both processors on a node doubles the communication load on that node which doubles the waiting time for MPI communication. + The higher scaling efficicney on the SP2 which has faster switches also suggests that the rus ou the PC cluster are communication limited., The higher scaling efficiency on the SP2 which has faster switches also suggests that the runs on the PC cluster are communication limited. + So far we have been cousideriug only PDEs in a single variable., So far we have been considering only PDEs in a single variable. + Wowever. the definition of the operator S is not restricted to this case.," However, the definition of the operator $\cal S$ is not restricted to this case." + Tn this section we prescut a solution of four coupled nonlinear PDEs., In this section we present a solution of four coupled nonlinear PDEs. + These equations are These equations are aportaut for the binary black hole problem., These equations are These equations are important for the binary black hole problem. + The exact definitions of the various terms can be found in |?]|., The exact definitions of the various terms can be found in \cite{Pfeiffer-Teukolsky-Cook:2001}. + For this paper. oulv the following information is necessary: V? is the Laplace operator on a nonflat manifold. hence Eq.," For this paper, only the following information is necessary: $\tilde\nabla^2$ is the Laplace operator on a nonflat three-dimensional manifold, hence Eq." + is an elliptic equation for c., is an elliptic equation for $\psi$. + Ap is a variant of the vector Laplacian. thus Eq.," $\tildeLapLong$ is a variant of the vector Laplacian, thus Eq." + is an elliptic equation for the vector 1.2.3.," is an elliptic equation for the vector $V^i, +i=1,2,3$ ." + The variables Ai aud A’ are fuuctious of V. so that Eqs., The variables $\tilde A_{ij}$ and $\tilde A^{ij}$ are functions of $V^i$ so that Eqs. + aud have to be solved simultauncously, and have to be solved simultaneously. + The functions A.A and M are given.," The functions $\tilde R$ ,$K$ and $\tilde M^{ij}$ are given." +The above processes all serve to place an upper limit on the [O III] flux emitted by a ealaxvs brightest planetary nebulae.,The above processes all serve to place an upper limit on the [O III] flux emitted by a galaxy's brightest planetary nebulae. + Unfortunately. (here is no equivalent set of conditions which places a lower limit on this quantity.," Unfortunately, there is no equivalent set of conditions which places a lower limit on this quantity." + This leads to a second constraint., This leads to a second constraint. + Observations of planetary nebulae in galaxies wilh well-determined Cepheicl distances vield a value for the PNLF cutoff magnitude of A/*=—4.4740.05 (Ciarclulloetal.2002)., Observations of planetary nebulae in galaxies with well-determined Cepheid distances yield a value for the PNLF cutoff magnitude of $M^* = -4.47 \pm 0.05$ \citep{p12}. +. In other words. planetary nebulae at the bright end of the |O HH] luminosity function emit more than 600£L... of power at 5007À.," In other words, planetary nebulae at the bright end of the [O III] luminosity function emit more than $600 \, L_{\odot}$ of power at 5007." +. Note. however. that this is only a small fraction of the objects total energv: both models and observations indicate that no more than of a central stars total luminosity comes out in this line (e.g..Jacoby1989:Jacohy&CHar-dullo1999:Marigoetal.," Note, however, that this is only a small fraction of the object's total energy: both models and observations indicate that no more than of a central star's total luminosity comes out in this line \citep[\eg][]{p1, jc99, marigo}." + 2004).. Consequently. the post-AGD stars which power a galaxv's brightest planelaries must. at a minimunm. have huminosities in excess of ~6000...," Consequently, the post-AGB stars which power a galaxy's brightest planetaries must, at a minimum, have luminosities in excess of $\sim 6000 L_{\odot}$." + Indeed. in the bulge of M31. 3 out of the 12 planetaries analvzed by Jacoby&Ciardullo(1999) have central star luminosities brighter than 1H.0001...," Indeed, in the bulge of M31, 3 out of the 12 planetaries analyzed by \citet{jc99} have central star luminosities brighter than $14,000 L_{\odot}$." + such high luminosities are a major problem lor PNLE models., Such high luminosities are a major problem for PNLF models. + In. order (ο generate ον0001. of power. a PN central star must have a mass of at least ~0.6... (Vassiliadis 1995)..," In order to generate $\sim 6000 L_{\odot}$ of power, a PN central star must have a mass of at least $\sim 0.6 M_{\odot}$ \citep{vw94, blocker}." + Moreover. as Table 1. suggests. the actual lower mass limit is probably larger.," Moreover, as Table \ref{tab1} suggests, the actual lower mass limit is probably larger." + In Che table. we have listed those SAIC. LMC. and M31 PNs with absolute (OL A5007 magnitudes within 0.5 mag of M*. and with central stars whose properties have been derived via a spectrophotometric analvsis.," In the table, we have listed those SMC, LMC, and M31 PNs with absolute [O III] $\lambda 5007$ magnitudes within 0.5 mag of $M^*$, and with central stars whose properties have been derived via a spectrophotometric analysis." + Except for the SAIC’ PNs. whose core Iuninositües. masses. and M are suppressed by low metallicity (Dopita.Jacoby.&Vassiliaclis1992:Ciardulloetal. 2002).. the Local Group's [O IHI|-bright. planetaries all have cores ereater (han A/~ 0.62AZ..," Except for the SMC PNs, whose core luminosities, masses, and $M^*$ are suppressed by low metallicity \citep{djv92, p12}, the Local Group's [O III]-bright planetaries all have cores greater than $M \sim 0.62 M_{\odot}$ ." + This mass is significantly larger than the 0.564A/. value which is typical for white dwarls in the solar neighborhood (Alacej.Nalezviv., This mass is significantly larger than the $0.56 M_{\odot}$ value which is typical for white dwarfs in the solar neighborhood \citep{madej}. +&Althaus2004).. More importantly. the initial mass-final mass relation [or solar metallicity stars preclicts that the progenitors of 0.62.7. cores should have main-sequence masses close lo ~2.94. (Weidemann2000:Claveretal.2001)..," More importantly, the initial mass-final mass relation for solar metallicity stars predicts that the progenitors of $0.62 M_{\odot}$ cores should have main-sequence masses close to $\sim 2.2 M_{\odot}$ \citep{weidemann, claver}." +" Such high mass objects are not normally associated with earlv-tvpe galaxies. and in M32. which is considered (o be a ""voung elliptical (e.g... 2000).. they. are definitely not present (Brownetal.2000)."," Such high mass objects are not normally associated with early-type galaxies, and in M32, which is considered to be a “young” elliptical \citep[\eg][]{trager}, they are definitely not present \citep{brown}." +. This situation is even worse when one considers the effect of metallicity: if the models of Vassiliadis and Frantsman(1999) are correct. then the main sequence masses of [O IHI|-brightPNs in the metal-rich environments of eiant. ellipticals need to be even greater.," This situation is even worse when one considers the effect of metallicity: if the models of \citet{vw93} and \citet{frantsman} are correct, then the main sequence masses of [O III]-brightPNs in the metal-rich environments of giant ellipticals need to be even greater." +Several lensed QSO radio jets have been imaged on milli-arcsecoud scales with the Very Loug Baseline Aivav (VLBA) and other Very Loug Bascline Interferometer (VLBI) configurations ((Garrett 1991: 1997: 1999: 2001: 2000: 2000:Ixeiiball.Patnaik. 2001:Marlow 2001: 2002).,"Several lensed QSO radio jets have been imaged on milli-arcsecond scales with the Very Long Baseline Array (VLBA) and other Very Long Baseline Interferometer (VLBI) configurations \markcite{1994MNRAS.270..457G,1997MNRAS.289..450K,1999MNRAS.303..727K,2001AJ....122..591R,2000evn..proc...49X,2000A&A...362..845R,2001ApJ...562..649K,2001AJ....121..619M,2002MNRAS.330..205R}( 1994; 1997; 1999; 2001; 2000; 2000;, 2001; 2001; 2002)." + Iu oulv three of these cases is the jet collimated enough aud the resolution high enough that a beud or kink could in priuciple be detected., In only three of these cases is the jet collimated enough and the resolution high enough that a bend or kink could in principle be detected. + The two image gravitational leus DI152|199 was discovered iu the CLASS radio survey aud observations were done on the heck II telescope ((Myers 1999)., The two image gravitational lens B1152+199 was discovered in the CLASS radio survey and follow--up observations were done on the Keck II telescope \markcite{1999AJ....117.2565M}( 1999). + The images are separated by 17.56 and the redshifts of the source aud lens are τν=1.019 and τι=0.139., The images are separated by $1''.56$ and the redshifts of the source and lens are $z_s=1.019$ and $z_l=0.439$. + Subsequently. (2002) observed D11521199 usine the [nibble Space Telescope GIST). the Multi-Elemenut. Racdio-Linked luterferometer Network (ATERLIN) and VLBA.," Subsequently, \markcite{2002MNRAS.330..205R}{ (2002) observed B1152+199 using the Hubble Space Telescope (HST), the Multi-Element Radio-Linked Interferometer Network (MERLIN) and VLBA." + In the IST observations a faint. indistinct leus ealaxy cau © seen along with a fainter object which is iuterpreted as a dwarf galaxy companion.," In the HST observations a faint, indistinct lens galaxy can be seen along with a fainter object which is interpreted as a dwarf galaxy companion." + With VEDI they were able to map the two images of the radio jet ou milliarcsecoud scales., With VLBI they were able to map the two images of the radio jet on milli–arcsecond scales. + They discovered that in image A the jet appears straight while iu nuage D it is bent., They discovered that in image A the jet appears straight while in image B it is bent. + No formal coustraint on the siguificauts of this bend are ooOiven in Rusin (2002) aud further observations may be required to make the detection certain., No formal constraint on the significants of this bend are given in \markcite{2002MNRAS.330..205R}{ (2002) and further observations may be required to make the detection certain. + For the o»urposes of this paper we will take the observations at face value and assume the beud is not au instruuieutal effect., For the purposes of this paper we will take the observations at face value and assume the bend is not an instrumental effect. + Iu section 23.2. lensing explanatious for this bend are investigated., In section \ref{sec:results-b1152+199} lensing explanations for this bend are investigated. + The bend is clearly uot aligned with either the direction to imageo A or to the lens galaxy., The bend is clearly not aligned with either the direction to image A or to the lens galaxy. + Superluiuinal motion is a possible explanation ouly if the jet’s shape can chanuee on a time scale that is simaller than the tine delay between images. Rusin (, Superluminal motion is a possible explanation only if the jet's shape can change on a time scale that is smaller than the time delay between images. \markcite{2002MNRAS.330..205R}{ ( +2002) ft a varicty of zooth models to the macroscopic leus and ect time delavs of I1.1 to 70.6 hus days which making this an unlikely explanation.,2002) fit a variety of smooth models to the macroscopic lens and get time delays of 41.1 to 70.6 $h_{65}^{-1}$ days which making this an unlikely explanation. + They do not attempt to explain the bend with their lens models., They do not attempt to explain the bend with their lens models. + The four inaage lens MG. JOLL0521 was observed with global VLBI by (2000)., The four image lens MG J0414+0534 was observed with global VLBI by \markcite{2000A&A...362..845R}{ (2000). + The jet consists of a two component core and two radio lobes on cither side., The jet consists of a two component core and two radio lobes on either side. + In images A2 aud B all the radio components are nearly collinear while in image Al they are drastically misaligned., In images A2 and B all the radio components are nearly collinear while in image A1 they are drastically misaligned. + Oulv two components are detected in image € so in this case the aliguinent caunot be determined., Only two components are detected in image C so in this case the alignment cannot be determined. + The distortion of image Al could be caused by a substructure near the image or it πο]! be dueto the magnification of a s1all uisaligument iu the other images (see section 3.2.1))., The distortion of image A1 could be caused by a substructure near the image or it might be dueto the magnification of a small misalignment in the other images (see section \ref{sec:with-no-substructure}) ). + The situation will be clarified with further modeling of this particular SOllrce., The situation will be clarified with further modeling of this particular source. + The double quasar Q0957|561 was the first eravitational lens discovered (Walsh.Carswell. 1979) aud has been studied extensively in the past two decades.," The double quasar Q0957+561 was the first gravitational lens discovered \markcite{1979Natur.279..381W}(, 1979) and has been studied extensively in the past two decades." + The VEDI maps of the radio jets appear to show a kink in image A that is not reproduced in image B (ποσα Aé=20 mas. Aa=10 mas with respect to the core) (Garrett 1991: 1999).," The VLBI maps of the radio jets appear to show a kink in image A that is not reproduced in image B (near $\Delta\delta = 20$ mas, $\Delta\alpha = 10$ mas with respect to the core) \markcite{1994MNRAS.270..457G,1999ApJ...520..479B}( 1994; 1999)." + Although in this case the beud is mel less certain than in D1152|199 or ALG JOLLL0551 and we will not try to reproduce it with a leus model here it does sugeest that mulli-arcsecoud kiuks aud beuds are common., Although in this case the bend is much less certain than in B1152+199 or MG J0414+0534– and we will not try to reproduce it with a lens model here – it does suggest that milli-arcsecond kinks and bends are common. + This has very iuportaut consequences m relation to the discussion iu L. because it iuplies that the bend in DI1521199 is not just a rare coincideutal alieumieut of the inge aud a known type of substructure.," This has very important consequences in relation to the discussion in \ref{sec:impl-dark-matt}, because it implies that the bend in B1152+199 is not just a rare coincidental alignment of the image and a known type of substructure." +" The radio jet will be treated as a one dimensional curve ou the sky described by 06,5(5) in the absence of lensing.", The radio jet will be treated as a one dimensional curve on the sky described by $\vec{\theta}_{\rm source}(s)$ in the absence of lensing. +" An image of the jet is described by 6,4448).", An image of the jet is described by $\vec{\theta}_{\rm image}(s)$ . + The curve of the source jet is related to the curve, The curve of the source jet is related to the curve +Salueci (2000) analvzed the rotation curve of 4133's I I disk out to 13 disc scale lengths (16 kpc).,Salucci (2000) analyzed the rotation curve of M33's H I disk out to 13 disc scale lengths (16 kpc). +" From their outermost data points. tan.2:125kms!. which we take as the circular velocity of the dark halo. allowing us to deduce its mass. Mj,225.1x10!M... from the scaling relations in Appendix A. M33 also has a notoriously small upper limit on the mass of its central black hole."," From their outermost data points, $v_{circ} \approx 125 \ \mathrm{km} \ \mathrm{s}^{-1}$, which we take as the circular velocity of the dark halo, allowing us to deduce its mass, $M_{halo}\approx 5.1 \times 10^{11} \ M_{\odot}$, from the scaling relations in Appendix A. M33 also has a notoriously small upper limit on the mass of its central black hole." + Observations from the Space Telescope Imaging Spectrograph (STIS) on the IIubble Space Telescope place an upper limit of My;S1500M. (Ixormendyv et al., Observations from the Space Telescope Imaging Spectrograph (STIS) on the Hubble Space Telescope place an upper limit of $M_{BH} \lesssim 1500 \ M_{\odot}$ (Kormendy et al. + 2001: though see Merritt οἱ al., 2001; though see Merritt et al. + 2001)., 2001). + The masses of the dark halo τμ and black hole Mj; allow us to obtain a constraint on the dark matter interaction from eqn. (2))., The masses of the dark halo $M_{halo}$ and black hole $M_{BH}$ allow us to obtain a constraint on the dark matter interaction from eqn. \ref{Mbh}) ). +" Specificallv. an upper limit on the quantity σι Can be obtained as a function of a ""ELelog = ..((0.051))*. where ps. rs. and ὃς are determined by ρω from the scaling relations. and we have set a=1.1. 1.3. and 1.5 respectively (to obtain the last equality."," Specifically, an upper limit on the quantity $\sigma_1 v_{100}^a$ can be obtained as a function of $a$ : _1 = , where $\rho_s$, $r_s$, and $v_s$ are determined by $M_{halo}$ from the scaling relations, and we have set $\alpha=1.1$, $1.3$, and $1.5$ respectively to obtain the last equality." + The accretion of barvons will increase the black hole mass above our estimate in equ. (2)), The accretion of baryons will increase the black hole mass above our estimate in eqn. \ref{Mbh}) ) + so that equ. (5.1)), so that eqn. \ref{sig33}) ) + is an overestimate and (he constraint could be tighter., is an overestimate and the constraint could be tighter. + It can be argued that constraining the dark matter interaction based on a single spuriously small black hole is unreasonable considering other effects (hat could conspirT to produce a small black hole in the scenario described in §2., It can be argued that constraining the dark matter interaction based on a single spuriously small black hole is unreasonable considering other effects that could conspire to produce a small black hole in the scenario described in 2. +" For example. the black hole in M33 could have been ejected in a merger event. or more importantly, (he value of a in M33's dark halo could have been small."," For example, the black hole in M33 could have been ejected in a merger event, or more importantly, the value of $\alpha$ in M33's dark halo could have been small." + Figure 1. indicates that the black hole mass is extremely sensitive (ο a for a given plivsical cross section for «=0—I., Figure \ref{bhalpha} indicates that the black hole mass is extremely sensitive to $\alpha$ for a given physical cross section for $a=0-1$. + Since the real cosmic variance of à is certainty at least 0.1—0.2 (Subramanian et al., Since the real cosmic variance of $\alpha$ is certainly at least $0.1-0.2$ (Subramanian et al. + 1999). it is plausible (hat a smaller (han average value of a in the post-collapse dark halo of M33 is responsible [or the small black hole in this svstem.," 1999), it is plausible that a smaller than average value of $\alpha$ in the post-collapse dark halo of M33 is responsible for the small black hole in this system." + However. M32 is the best observed local example of a eroup of several bulgeless galaxies (hat lack supermassive black holes comparable to Chose found in bulge svstems (Richstone οἱ al.," However, M33 is the best observed local example of a group of several bulgeless galaxies that lack supermassive black holes comparable to those found in bulge systems (Richstone et al." +" 1998: IxXormendy Gebhardt 2001): NGC 4395 (Sin) May€8x10!M, (Fillipenko IIo 2001). IC 342 (Sed) Mj;<5x10°AL. (Boker οἱ al."," 1998; Kormendy Gebhardt 2001): NGC 4395 (Sm) $M_{BH} \lesssim 8\times 10^4 \ M_{\odot}$ (Fillipenko Ho 2001), IC 342 (Scd) $M_{BH} \lesssim 5\times 10^5 \ M_{\odot}$ (Boker et al." + 1999). NGC 205 (dE5) Δι<9x10M. (Jones et al.," 1999), NGC 205 (dE5) $M_{BH} \lesssim 9\times 10^4 \ M_{\odot}$ (Jones et al." + 1996).It isdoubtful.that cosmic variance ina can account for the small black holes in all of these svstenms., 1996).It isdoubtfulthat cosmic variance in $\alpha$ can account for the small black holes in all of these systems. +"GADGET, and then move a distance along the ray Ar=rh, where η€1 and /gm is the local SPH smoothing length.","GADGET, and then move a distance along the ray $\Delta r=\eta h_{\rm sml}$, where $\eta \leq 1$ and $h_{\rm sml}$ is the local SPH smoothing length." + The process is repeated until a ray is sufficiently far from its origin (=100 kpc)., The process is repeated until a ray is sufficiently far from its origin $\gtrsim 100$ kpc). + The gas properties along a given ray can then be integrated to give the line-of-sight column density and mean metallicity., The gas properties along a given ray can then be integrated to give the line-of-sight column density and mean metallicity. + We test different values of 7 and find that gas properties along a ray converge rapidly and change smoothly for rj20.5 and smaller., We test different values of $\eta$ and find that gas properties along a ray converge rapidly and change smoothly for $\eta=0.5$ and smaller. + We similarly test different numbers of rays and find that the distribution of line-of-sight properties converges for =100 rays., We similarly test different numbers of rays and find that the distribution of line-of-sight properties converges for $\gtrsim 100$ rays. +" Given the local gas properties, we use the GADGET phase equilibrium model of the ISM described in SpringelHernquist(2003) to calculate the local mass fraction in “hot” (diffuse) and “cold” (molecular and HI cloud) phases of dense gas, and assuming pressure equilibrium between the two phases we obtain the density of the local hot and cold phase and the corresponding volume filling factors."," Given the local gas properties, we use the GADGET two-phase equilibrium model of the ISM described in \citet{SH03} to calculate the local mass fraction in “hot” (diffuse) and “cold” (molecular and HI cloud) phases of dense gas, and assuming pressure equilibrium between the two phases we obtain the density of the local hot and cold phase gas and the corresponding volume filling factors." + These values gascorrespond roughly to the fiducial values of McKee&Ostriker (1977)., These values correspond roughly to the fiducial values of \citet{MO77}. +". Using only the hot-phase density allows us to place an effective lower limit on the column density a particular line of as it assumes a ray passes only alongthrough the diffuse ISM, sight,with >90% of the mass of the dense ISM concentrated in cold-phase “clumps.”"," Using only the hot-phase density allows us to place an effective lower limit on the column density along a particular line of sight, as it assumes a ray passes only through the diffuse ISM, with $\gtrsim 90\%$ of the mass of the dense ISM concentrated in cold-phase “clumps.”" +" Given the small volume filling factor (< 0.01) and cross section of such clouds, we expect that the majority of sightlines will pass only through the “hot-phase” medium, with rare outliers dominated by single clouds along the line of sight (covering fraction S; 196)."," Given the small volume filling factor $<0.01$ ) and cross section of such clouds, we expect that the majority of sightlines will pass only through the “hot-phase” medium, with rare outliers dominated by single clouds along the line of sight (covering fraction $\lesssim1\%$ )." +" Using Lpo=eMc?, we model the form of the intrinsic quasar continuum SED Marconietal.(2004), based on optical through hard followingX-ray observations (e.g.,2003;Vignalietal. 2003)."," Using $\Lbol=\dEdt$, we model the form of the intrinsic quasar continuum SED following \citet{Marconi04}, based on optical through hard X-ray observations \citep[e.g.,][]{Elvis94,George98,VB01,Perola02,Telfer02,Ueda03,VBS03}." +". This gives a B-band luminosity log(Lg)=0.80—0.067£+0.017?—0.0023, where £=log(Lyoi/L@)-- 12, and we take Ag=4400À."," This gives a B-band luminosity $\log{(\LB)}=0.80-0.067\mathcal{L}+0.017\mathcal{L}^{2}-0.0023\mathcal{L}^{3}$, where $\mathcal{L} = \log{(\Lbol/L_{\sun})} - 12$ , and we take $\lambda_{B}=4400\,$." + We then use a gas-to-dust ratio to determine the extinction along a given line of sight at this frequency., We then use a gas-to-dust ratio to determine the extinction along a given line of sight at this frequency. +" Observations suggest that the majority of the population of reddened quasars have reddening curves similar to that of the Small Magellenic Cloud (SMC) (Hopkinsetal.2004),, which has a gas-to-dust ratio lower than the Milky Way by approximately the same factor as its metallicity (Bouchetetal.1985)."," Observations suggest that the majority of the population of reddened quasars have reddening curves similar to that of the Small Magellenic Cloud (SMC) \citep{Hopkins04}, which has a gas-to-dust ratio lower than the Milky Way by approximately the same factor as its metallicity \citep{Bouchet85}." +". We consider both a gas-to-dust ratio equal to that of the Milky Way, (An/Nu)uw=8.47x10?cm”, and a gas-to-dust ratio scaled Ag/Nj "," We consider both a gas-to-dust ratio equal to that of the Milky Way, $(A_{B}/N_{H})_{\rm MW}=8.47\times10^{-22}\,{\rm cm^{2}}$, and a gas-to-dust ratio scaled by metallicity, $A_{B}/N_{H} = (Z/0.02)(A_{B}/N_{H})_{\rm MW}$." +"For both cases bywe use the metallicity,SMC-like reddening curve of =(Z/0.02)(Ag/Nu)mw.Pei (1992)..", For both cases we use the SMC-like reddening curve of \citet{Pei92}. . +" We do not perform full radiative transfer calculation but defer this to a future paper,a and therefore do not model scattering or processing of radiation by dust."," We do not perform a full radiative transfer calculation but defer this to a future paper, and therefore do not model scattering or re-processing of radiation by dust." +" Figure | shows the simulation SPH particles at four representative times during the run, with the bolometric luminosity of the supermassive black hole as a function of time below."," Figure \ref{fig:showGADGET} shows the simulation SPH particles at four representative times during the run, with the bolometric luminosity of the supermassive black hole as a function of time below." +" After the first passage (upper left), there is an extended period of strong accretion, but central gas densities are very large and the intrinsic quasar luminosity will be attenuated well below our quasar threshold of Lg;5,>10!!Lo (MgS —23)."," After the first passage (upper left), there is an extended period of strong accretion, but central gas densities are very large and the intrinsic quasar luminosity will be attenuated well below our quasar threshold of $\LBo\geq10^{11}\,L_{\sun}$ $M_{\rm B}\lesssim-23$ )." +" Once the merger begins (upper right), the intrinsic as gas is channeled to the merging cores."," Once the merger begins (upper right), the intrinsic luminosity peaks as gas is channeled to the merging cores." +" However, luminositythis also peaksresults in very large columns which similarly obscure the quasar."," However, this also results in very large columns which similarly obscure the quasar." +" After a short time (lower left), feedback from the quasar clears out the gas in the central regions and the object may be observable as a quasar."," After a short time (lower left), feedback from the quasar clears out the gas in the central regions and the object may be observable as a quasar." +" Shortly after the merger (lower right), gas has been consumed by star formation and accretion or expelled from the center and densities have dropped well below the levels needed to fuel quasar activity."," Shortly after the merger (lower right), gas has been consumed by star formation and accretion or expelled from the center and densities have dropped well below the levels needed to fuel quasar activity." + Figure 2shows the bolometric luminosity of and column densities to the supermassive black hole as a function of, Figure \ref{fig:NH.vs.time} shows the bolometric luminosity of and column densities to the supermassive black hole as a function of +"[rame line-o[-sight. velocity dispersion. 0;,,. a 1"" core radius. and a 100"" cutoff radius.","frame line-of-sight velocity dispersion, $\sigma_{iso}$, a $^{\prime\prime}$ core radius, and a $^{\prime\prime}$ cutoff radius." + We resammple the distorted images with the Subaru pixel scale /pix). coadd them. and convolve with a Gaussian PSF with a FEWILM and acd noise to match the expected noise in (he Subaru GTO observations.," We resample the distorted images with the Subaru pixel scale /pix), coadd them, and convolve with a Gaussian PSF with a FWHM and add noise to match the expected noise in the Subaru GTO observations." + We repeat this procedure for different values of σιω (at a fixed τν=0.3) to generate maps of the weak lensing signal., We repeat this procedure for different values of $\sigma_{iso}$ (at a fixed $z_{lens}=0.3$ ) to generate maps of the weak lensing signal. + We run the Kubo et al. (, We run the Kubo et al. ( +2009) detection method on these images to determine the value of σι where the peak S/N reaches our v=3.7 cluster selection limit.,2009) detection method on these images to determine the value of $\sigma_{iso}$ where the peak S/N reaches our $\nu = 3.7$ cluster selection limit. + In Figure 9.. we plot the detection limit as a function of redshift (£(2)ppt): the solid line represents the p=3.7 cutoff in the lensing peak selection sample.," In Figure \ref{fig:sensitivity.ps}, we plot the detection limit as a function of redshift $L(z) = L(z=0.3) {W_{eff}(z=0.3)/W_{eff}(z)}$ ); the solid line represents the $\nu = 3.7$ cutoff in the lensing peak selection sample." + Our method of caleulating the sensitivity fails at low redshilt z<0.1. because the V.imulation method of IxXhiabanian DellAntonio (2003) underpredicts the significance of ‘lusters that occupy a large angular region.," Our method of calculating the sensitivity fails at low redshift $z<0.1$, because the simulation method of Khiabanian Dell'Antonio (2008) underpredicts the significance of clusters that occupy a large angular region." + However. because none of the GTO2dee? field ]usters have 2<0.2. the comparison of sensilivilies is valid.," However, because none of the $^2$ field clusters have $z<0.2$, the comparison of sensitivities is valid." + There are some fundamental limitations to the accuracy of the ealeulations., There are some fundamental limitations to the accuracy of the calculations. + As a result ol cosmic variance. the actual number and redshift distribution of the background galaxies behind anv cluster may not be well-represented by our model.," As a result of cosmic variance, the actual number and redshift distribution of the background galaxies behind any cluster may not be well-represented by our model." + For clusters near the p=3.7 detection limit. the shear signal is based the shapes of only ~2000 galaxies.," For clusters near the $\nu = 3.7$ detection limit, the shear signal is based the shapes of only $\sim 2000$ galaxies." + At this level. non-uniformities in (he distribution of (he background galaxies are important.," At this level, non-uniformities in the distribution of the background galaxies are important." + Our detection sensitivities should be viewed as averages of the sensitivity across the field rather than the exact sensitivity (to anv one cluster al any. particular position in the field., Our detection sensitivities should be viewed as averages of the sensitivity across the field rather than the exact sensitivity to any one cluster at any particular position in the field. + Although the COSMOS/Subaru field is extremely valuable. it covers <1 square degree ol (he sky.," Although the COSMOS/Subaru field is extremely valuable, it covers $\lesssim 1$ square degree of the sky." + Therefore. any svstematic differences between the properties of the COSMO? field and GTO?2dee? can change the normalization.," Therefore, any systematic differences between the properties of the COSMOS field and $^2$ can change the normalization." + One of the results of the analysis of the DLS (Geller et al. (, One of the results of the analysis of the DLS (Geller et al. ( +2010)) and the GTO2dee? field (this work) is that there are large field-to-field varlalions in (he types and amount of structure present. at all measured redshifts even on degree-sized angular scales.,2010)) and the $^2$ field (this work) is that there are large field-to-field variations in the types and amount of structure present at all measured redshifts even on degree-sized angular scales. + Thus. although the COSMOS field is currently the best field [or calibrating weak lensing detections. larger fields will be necessary.," Thus, although the COSMOS field is currently the best field for calibrating weak lensing detections, larger fields will be necessary." + The effect of these uncertainties is. however. limited.," The effect of these uncertainties is, however, limited." + Because the lensing kernel is so broad. and because the angular diameter distances change very slowly with redshift above 2~1. for the concordance cosmology. problems introduced by cosmic variance are partially mitigated.," Because the lensing kernel is so broad, and because the angular diameter distances change very slowly with redshift above $z\sim 1$ for the concordance cosmology, problems introduced by cosmic variance are partially mitigated." + Typical S/N uncertainties due to backeround galaxy density varialious are on the scales we are interested in. except verv near bright stars or (he cores of rich clusters.," Typical S/N uncertainties due to background galaxy density variations are $\sim 5$ on the scales we are interested in, except very near bright stars or the cores of rich clusters." + In the analvsis of (he incompleteness of weak lensing cluster detection. we take a uncertainty in the sensitivity limit into account when determining which clusters," In the analysis of the incompleteness of weak lensing cluster detection, we take a uncertainty in the sensitivity limit into account when determining which clusters" +represented by error bars in each panel.,represented by error bars in each panel. + The nominal measurement errors from [or MW GCs are comparable to svinbol sizes. and are not shown.," The nominal measurement errors from \cite{pu02} for MW GCs are comparable to symbol sizes, and are not shown." +" The left panels show the Lick CN, and CVs indices plotted against (Fe).", The left panels show the Lick $CN_1$ and $CN_2$ indices plotted against $\langle$ $\rangle$. + On both panels. M 31 and MW GCs occupy approximately the same locus.," On both panels, M 31 and MW GCs occupy approximately the same locus." + There is no compelling evidence lor M 31 GCs having stronger CN indices at fixed (Fe) (fixed |Fe/1I])., There is no compelling evidence for M 31 GCs having stronger CN indices at fixed $\langle$ $\rangle$ (fixed [Fe/H]). + The right panels show CN indices plotted against the |MgFe| index. which is defined as Again. no formal difference is found between the two GC systems in these diagrams.," The right panels show CN indices plotted against the [MgFe]' index, which is defined as Again, no formal difference is found between the two GC systems in these diagrams." + The MW GCs seem to occupy the lower envelope of the distribution of M 31 GCs in the [MgFe]' vs. C.Voplane., The MW GCs seem to occupy the lower envelope of the distribution of M 31 GCs in the [MgFe]' vs. $CN_2$plane. + However. since there are no differences in the (Fe) vs. CNs plane. this mismatch is likely to be due to Mg 5 differences between the two GC svstems in the data by Puzia and collaborators. ancl in their CN strengths.," However, since there are no differences in the $\langle$ $\rangle$ vs. $CN_2$ plane, this mismatch is likely to be due to Mg $b$ differences between the two GC systems in the data by Puzia and collaborators, and in their CN strengths." + The latter suspicion is confirmed by Figure 11.. where Mg 6 and (Fe) from Puziaetal.(2002) and Puziaetal.(2005) are compared.," The latter suspicion is confirmed by Figure \ref{puziamgfe}, where Mg $b$ and $\langle$ $\rangle$ from \cite{pu02} and \cite{pu05} are compared." + The MW data are systematically stronger in Mg 5 for fixed (Fe) than M 31 data. bv about 0.5 A.," The MW data are systematically stronger in Mg $b$ for fixed $\langle$ $\rangle$ than M 31 data, by about 0.5 ${\rm\AA}$." + Following a suggestion by theanonvmots releree. we generated plots similar to Figure 11.. replacing (Fe) by other Fe indices. such as Fed383. Fe4531. Fe5406. and Fe5709. and Mg 5 by Ales. ancl the same result is obtained: MW. clusters are svstematicallv stronger than their M 31 counterparts in Ale indices at [fixed Fe. which suggests that the difference is due to Mg 5 being stronger. and not (Fe) being weaker. in MW clusters.," Following a suggestion by theanonymous referee, we generated plots similar to Figure \ref{puziamgfe}, replacing $\langle$ $\rangle$ by other Fe indices, such as Fe4383, Fe4531, Fe5406, and Fe5709, and Mg $b$ by $_2$, and the same result is obtained: MW clusters are systematically stronger than their M 31 counterparts in Mg indices at fixed Fe, which suggests that the difference is due to Mg $b$ being stronger, and not $\langle$ $\rangle$ being weaker, in MW clusters." + We note that no such difference is found in our data between MW and M 31 (Figure 7)). so we do not understand the origin of this discrepancy in (he data by Puzia and collaborators.," We note that no such difference is found in our data between MW and M 31 (Figure \ref{indc}) ), so we do not understand the origin of this discrepancy in the data by Puzia and collaborators." + Comparing Meg b for MW clusters in common between Puziaetal.(2002) ancl (2007).. we find that indeed the former are on average stronger bv ~0.13 A.," Comparing Mg $b$ for MW clusters in common between \cite{pu02} and \cite{s07}, , we find that indeed the former are on average stronger by $\sim +0.13~{\rm\AA}$ ." + On the other hand. comparing the Puziaetal.(2005) data for M 31 clusters with our own data Lor," On the other hand, comparing the \cite{pu05} data for M 31 clusters with our own data for" +")foranyii Let Since Ζ081= Ej, ΖΥΕΙ= Ej, hborandZ}E}= E%,for any we have = || >1,k >1, N= Thereby, = N= )foranyN Consider the second level extended partial parametric normal form given by Equation ... (5.4).","for any Let Since Z^0_0E^1_1= E^1_1, Z^0_1E^1_1= E^1_2, Z^1_1E^1_1= for any we have = | 1, l, N= Thereby, = N= for any Consider the second level extended partial parametric normal form given by Equation \ref{sec}) )." +" Let 00, For the rest of this paper, we assume that there exists for a is finite."," Let 0, For the rest of this paper, we assume that there exists for a is finite." +" Define a matriz A:= (αμ), :— e; (5."," Define a matrix A:= ), := e_j ^q." +"6) Then, we call a parametric vector field Janon— degeneratemulti— parameternonconservativeperturbationo f thevector fielduv if and rank((A)—r when is transformed into given by Equation (5.4)."," Then, we call a parametric vector field a non-degenerate multi-parameter nonconservative perturbation of the vector field if and (A)= when is transformed into given by Equation \ref{sec}) )." +" When this condition is satisfied, through an invertible linear change of parameters we can transform the vector field into (2) ο ο Mt οm, if and Now we update the grading weight vector )by Therefore, (go, for any"," When this condition is satisfied, through an invertible linear change of parameters we can transform the vector field into = E^1_1+ E^0_k+ E^0_k + E^0_k, if and Now we update the grading weight vector by Therefore, (E^0_k for any" +axis of the galaxy (Schweizer&Seitzer||1988).,axis of the galaxy \citep[][]{Schweizer88}. +". These shells can be seen in the lower left panel of Fig. |,"," These shells can be seen in the lower left panel of Fig. \ref{fig:compare}," + where we present a new deep image of NGC 7600 obtained using the techniques described in[Martínez-Delgado etal.](2010)., where we present a new deep image of NGC 7600 obtained using the techniques described in \cite{MD10}. +. Our new image also reveals a number of fainter features not previously seen., Our new image also reveals a number of fainter features not previously seen. + Appendix A contains full details of these observations., Appendix A contains full details of these observations. +" The complex field of tidal debris in the outer halo of NGC 7600 is better seen in the super-stretched, wide field image in Fig. Bl."," The complex field of tidal debris in the outer halo of NGC 7600 is better seen in the super-stretched, wide field image in Fig. \ref{fig:widefield}." + In this image the inner shell structure visible in Fig., In this image the inner shell structure visible in Fig. +" is saturated, and only two external shells can be discerned, one on either side of the galaxy."," \ref{fig:compare} is saturated, and only two external shells can be discerned, one on either side of the galaxy." +" The bright shell West of the galaxy, labeleda in Fig. Bl,"," The bright shell West of the galaxy, labeled in Fig. \ref{fig:widefield}," + corresponds to the outermost feature visible in Fig. |., corresponds to the outermost feature visible in Fig. \ref{fig:compare}. +" Our deep image reveals two further giant cones of material West of the galaxy, which are not as clearly aligned with the major axis."," Our deep image reveals two further giant cones of material West of the galaxy, which are not as clearly aligned with the major axis." + Fragments of these structures were also reported by , Fragments of these structures were also reported by \citet{Turnbull99}. +Fig., Fig. + B] reveals several features that have not∙∙ been reported so far., \ref{fig:widefield} reveals several features that have not been reported so far. + A diffuse system of debris clouds is visible to the Northeast c in Fig. ϱ))., A diffuse system of debris clouds is visible to the Northeast (labeled in Fig. \ref{fig:widefield}) ). +" It seems to consist of three components, (labeledextending up to 110 kpc from the center of the galaxy."," It seems to consist of three components, extending up to 110 kpc from the center of the galaxy." + A narrow ‘spike’ emerges from the diffuse halo (labeled d)., A narrow `spike' emerges from the diffuse halo (labeled ). +" Finally, we detect a large diffuse stellar cloud (labeled ~9.7’ from the galaxy, corresponding to a projected e)distance of 140 kpc."," Finally, we detect a large diffuse stellar cloud (labeled ) $\sim9.7\arcmin$ from the galaxy, corresponding to a projected distance of 140 kpc." + An extremely faint narrow feature seems to connect this cloud to the main body of NGC 7600., An extremely faint narrow feature seems to connect this cloud to the main body of NGC 7600. +" Together, this diversity of tidal features suggests that NGC 7600 has undergone an active and complex merging history in the recent past."," Together, this diversity of tidal features suggests that NGC 7600 has undergone an active and complex merging history in the recent past." + There is an extremely close correspondence between NGC 7600 and the diffuse structures seen in the Aq-F-2 simulation., There is an extremely close correspondence between NGC 7600 and the diffuse structures seen in the Aq-F-2 simulation. +" Not only are the morphological similarities striking, but the inner shells in the simulation have comparable surface brightness to those of NGC 7600, ~27magarcsecond~?, according to the population synthesis model used by C10."," Not only are the morphological similarities striking, but the inner shells in the simulation have comparable surface brightness to those of NGC 7600, $\sim27\,\mathrm{mag\,arcsecond^{-2}}$, according to the population synthesis model used by C10." + This is particularly remarkable since the model galaxy was in no way constrained to resemble NGC 7600., This is particularly remarkable since the model galaxy was in no way constrained to resemble NGC 7600. + The evolution of Aq-F-2 depicted in the movie highlights several interesting aspects of the formation of systems analogous to NGC 7600 in a CDM cosmogony., The evolution of Aq-F-2 depicted in the movie highlights several interesting aspects of the formation of systems analogous to NGC 7600 in a CDM cosmogony. + The first remarkable feature is the complexity of the shell system itself., The first remarkable feature is the complexity of the shell system itself. +" The merger origin of circumgalactic(1981).. shells was first described in detail by Quinn| who concluded that the shell progenitor must be a cold stellar system on radial orbit, as is approximately the case for the shell progenitora in Aq-F-2. "," The merger origin of circumgalactic shells was first described in detail by \citet{Quinn84}, who concluded that the shell progenitor must be a cold stellar system on a radial orbit, as is approximately the case for the shell progenitor in Aq-F-2. (" +"orbits are perfectly radial to begin with, and, in fact, (Fewour shell progenitor passes pericenter twice before its orbit is aligned and shells are ","Few orbits are perfectly radial to begin with, and, in fact, our shell progenitor passes pericenter twice before its orbit is aligned and shells are produced.)" +The earliest produced.)models of shell galaxies were based on simplifying assumptions and restricted N-body simulations (e.g., The earliest models of shell galaxies were based on simplifying assumptions and restricted N-body simulations \citep[e.g.][]{Dupraz86}. +" In the simplest case, a single instantaneous disruption⋅⋅ event liberates all the stars from the progenitor."," In the simplest case, a single instantaneous disruption event liberates all the stars from the progenitor." +" The outermost shell is formed first, and successive shells are created by phase-wrapping."," The outermost shell is formed first, and successive shells are created by phase-wrapping." +" In our simulation, however, the core of the shell progenitor survives through several pericenters."," In our simulation, however, the core of the shell progenitor survives through several pericenters." +" In the first few passages, the ‘new’ shells appearing are, in fact, the shells of shell systems — one per pericentric passage of the core."," In the first few passages, the `new' shells appearing are, in fact, the shells of shell systems – one per pericentric passage of the core." + Only later do phase-wraps of these multiple shells systems begin to appear., Only later do phase-wraps of these multiple shells systems begin to appear. +" Indeed, the system is even more complex."," Indeed, the system is even more complex." +" In the self-consistent potential of our simulation, energy is exchanged between the shell progenitor, the main halo and the liberated stars."," In the self-consistent potential of our simulation, energy is exchanged between the shell progenitor, the main halo and the liberated stars." + pointed out that interactions between the shell progenitor and its tidal stream (the ‘stalk’ intermittently visible along the shell axis) leads to the decay of the satellite’s orbit independently of dynamical friction against the host (both processes take place here).," \citet{Heisler90} + pointed out that interactions between the shell progenitor and its tidal stream (the `stalk' intermittently visible along the shell axis) leads to the decay of the satellite's orbit independently of dynamical friction against the host (both processes take place here)." + From our simulation it is clear that the orbit of the satellite decays significantly before its final disruption., From our simulation it is clear that the orbit of the satellite decays significantly before its final disruption. + The evolution in the orbit of the shell progenitor gradually changes the alignment of new shells throughout the merger., The evolution in the orbit of the shell progenitor gradually changes the alignment of new shells throughout the merger. + NGC 7600 is highly elliptical and well-aligned with its innermost shells T, NGC 7600 is highly elliptical and well-aligned with its innermost shells \citep{Turnbull99}. +he outer shells visible in Fig., The outer shells visible in Fig. + [3] show⋅⋅ tentative evidence for misalignment., \ref{fig:widefield} show tentative evidence for misalignment. +" In the simulation, the innermost shells (the last to be created) are also aligned with the major axis of the central bulge."," In the simulation, the innermost shells (the last to be created) are also aligned with the major axis of the central bulge." +" The accreted stars in the final system have large velocity dispersions > and exhibit only weak bulk rotation about(c the100kms~*), halo center (Urot»10kms~*)."," The accreted stars in the final system have large velocity dispersions $\sigma>100\mathrm{km\,s^{-1}}$ ), and exhibit only weak bulk rotation about the halo center $v_{rot}\sim10\,\mathrm{km\,s^{-1}}$ )." +" Over the course of the simulation, the morphology of the stellar halo goes through several short-lived transformations."," Over the course of the simulation, the morphology of the stellar halo goes through several short-lived transformations." + Many prominent features are easily disrupted when the central potential is strongly perturbed., Many prominent features are easily disrupted when the central potential is strongly perturbed. + Even the dominant shell system in Aq-F-2 is evolving rapidly., Even the dominant shell system in Aq-F-2 is evolving rapidly. + The first shells created in the merger have already phase-mixed away by z=0., The first shells created in the merger have already phase-mixed away by $z=0$. +" Finally, the shell progenitor in Aq-F-2 is a relatively massive dwarf satellite which enters the main halo along with a number of even smaller galaxies."," Finally, the shell progenitor in Aq-F-2 is a relatively massive dwarf satellite which enters the main halo along with a number of even smaller galaxies." + This ‘correlated infall’ is characteristic of the CDM model (e.g.," This `correlated infall' is characteristic of the CDM model \citep[e.g.][]{Libeskind05,Li08}." +" Not only are individual bright satellites likely toBOOS)... have several luminous companions, but of these groups, large and small, are accreted along filaments of the cosmic web."," Not only are individual bright satellites likely to have several luminous companions, but of these groups, large and small, are accreted along filaments of the cosmic web." + This correlates the directions from which infalling satellites are accreted with the shape οἳof al]the dark matter halo ," This correlates the directions from which infalling satellites are accreted with the shape of the dark matter halo \citep{Lovell11,Vera11}." +Some of the satellites of the shell VVera-Ciroprogenitor are 2011)...already suffering tidal disruption before the system is accreted into the main halo., Some of the satellites of the shell progenitor are already suffering tidal disruption before the system is accreted into the main halo. + The brightest of these creates a perpendicular umbrella feature resembling a shell., The brightest of these creates a perpendicular umbrella feature resembling a shell. + We have presented a new deep image of NGC 7600 revealing new tidal features in its outer regions., We have presented a new deep image of NGC 7600 revealing new tidal features in its outer regions. + The distribution of stellar debris in this image is strikingly similar to that of the Aq-F-2 simulation shown in the movie that accompanies this paper., The distribution of stellar debris in this image is strikingly similar to that of the Aq-F-2 simulation shown in the movie that accompanies this paper. + The simulation suggests a likely scenario for the formation of the observed shell system in NGC 7600 and gives a deeper insight into the violent nature of galaxy assembly inCDM.., The simulation suggests a likely scenario for the formation of the observed shell system in NGC 7600 and gives a deeper insight into the violent nature of galaxy assembly in. +" Our simulation confirms the established hypothesis that shells are created by the disruption of a satellite system on a radial orbit (here the satellite is spheroidal, but disk-like progenitors are also possible)."," Our simulation confirms the established hypothesis that shells are created by the disruption of a satellite system on a radial orbit (here the satellite is spheroidal, but disk-like progenitors are also possible)." +" However, in our simulation, the evolution of the orbit of the main shell progenitor is complex, tidal structures are transient and interact with one another, and shell-like features are"," However, in our simulation, the evolution of the orbit of the main shell progenitor is complex, tidal structures are transient and interact with one another, and shell-like features are" +following iteration series: where in the second terms ou the rielt-haaxc side n2.,following iteration series: where in the second terms on the right-hand side $m>0$. + The solution (9)) of Eq.d 1))is purely formal and docs not eive adequate insight of the behavior of solitonic solutions in birefriugeut mecca., The solution \ref{soliton}) ) of \ref{eq: manakov}) ) is purely formal and does not give adequate insight of the behavior of solitonic solutions in birefringent media. +" Iu order to obtain this insight. it ds convenient to separate the solutions (d4(.ret) aud dole.f) into two parts: Iu this special case. we find that given the coeffücieuts lo,(i, aud D»,14,9 are given by: We firstly analyze the first part the right-hand side of Eq.(13))."," In order to obtain this insight, it is convenient to separate the solutions $u_{1}(x,t)$ and $u_{2}(x,t)$ into two parts: In this special case, we find that given the coefficients $\hat{A}_{2n+1,0}$ and $\hat{B}_{2n+1,0}$ are given by: We firstly analyze the first part the right-hand side of \ref{separ}) )." +" By assuming that yy=A and Byy=B all the other cocficicnts lo,jay and B5,14,9 follow from Eq.(11))."," By assuming that $\hat{A}_{1,0}=A$ and $\hat{B}_{1,0}=B$ all the other coefficients $\hat{A}_{2n+1,0}$ and $\hat{B}_{2n+1,0}$ follow from \ref{recur1}) )." + This implies that Eq.(13)) can be reformulated in the following fori 1011: The first ena on the rigbht-haud side of Eq.(15)) represeuts unperturbed solitons., This implies that \ref{separ}) ) can be reformulated in the following form \cite{Dorren1}: The first term on the right-hand side of \ref{final}) ) represents unperturbed solitons. + The propagation velocity of these solitons is determined by the birefringeuce coefficients 6., The propagation velocity of these solitons is determined by the birefringence coefficients $\delta$. + It follows from Eq.(15)) that the two solitons a6f) aud tty(atSf) propagate with a relative velocity 20600.," It follows from \ref{final}) ) that the two solitons $u_{1}(x,t)$ and $u_{2}(x,t)$ propagate with a relative velocity $2 b \delta$." + This makes that even in au 7ideal situation”. in which the nou-solitouic terms in Eq.(15)) are neelieible an initially localized pulseis still unstable due do the unequal propagation velocity of the solitouic solutions along the priucipalbirefringence axes.," This makes that even in an “ideal situation”, in which the non-solitonic terms in \ref{final}) ) are negligible an initially localized pulse is still unstable due do the unequal propagation velocity of the solitonic solutions along the principal birefringence axes." +these unambiguous results is the combination of exquisite (11ST) observations. extensive near-IR data. and dual-band radio data.,"these unambiguous results is the combination of exquisite (HST) observations, extensive near-IR data, and dual-band radio data." + More recently. Priceefal(2002) presented the s-rav properties and redshilt 0.695+0.005) of020405.. along wilh multi-band eround-based aud LIST optical observations.," More recently, \citet{pkb+02} presented the $\gamma$ -ray properties and redshift $z=0.695\pm 0.005$ ) of, along with multi-band ground-based and HST optical observations." +" The observations between 15 and 65 davs alter (he burst reveal a red bump (wilh a spectrum F,xv 7) brighter than an extrapolation of the early data.", The observations between 15 and 65 days after the burst reveal a red bump (with a spectrum $F_\nu\propto \nu^{-3.9}$ ) brighter than an extrapolation of the early data. + Pricee/αἱ.(2002) interpret (his emission as coming [rom a SN accompanying the burst. but note that the statistical significance of this result depends on the degree of collimation of the GRD ejecta.," \citet{pkb+02} interpret this emission as coming from a SN accompanying the burst, but note that the statistical significance of this result depends on the degree of collimation of the GRB ejecta." + This is because a more collimated outflow results in an earlier steepening of the afterglow lightceurves. and hence a more significant deviation at late time.," This is because a more collimated outflow results in an earlier steepening of the afterglow lightcurves, and hence a more significant deviation at late time." + In this paper we present radio observations of020405.. which point to a uniform density circumburst medium.," In this paper we present radio observations of, which point to a uniform density circumburst medium." + We also show that the radio. optical. ancl X-ray data require an early jet. break. which significantlv strenethens the SN interpretation lor the late-time emission.," We also show that the radio, optical, and X-ray data require an early jet break, which significantly strengthens the SN interpretation for the late-time emission." +. Combining. these two results we conclude that ap xr7 densityB profile. isB not a required signature of a massive stellar progenitor.," Combining these two results we conclude that a $\rho\propto +r^{-2}$ density profile is not a required signature of a massive stellar progenitor." + Very Large Array Inc.)) observations were initiated 1.2 davs after the burst using the standard continuum mode with 2x50 MlIIz contiguous bands., Very Large Array ) observations were initiated 1.2 days after the burst using the standard continuum mode with $2\times 50$ MHz contiguous bands. + A log of all observations is given in Table 1.., A log of all observations is given in Table \ref{tab:rad}. + We used the extra-galactie source 2286 (J13314-305) for [ιν calibration. while the phase was monitored using J1356—343.," We used the extra-galactic source 286 (J1331+305) for flux calibration, while the phase was monitored using $-$ 343." + The data were reduced ancl analvzecl using the Astronomical Imagec» Processing Svstem (Fomalont1981)., The data were reduced and analyzed using the Astronomical Image Processing System \citep{fom81}. +. In Figure 1. we plot the 8.46 1 lighteurve ofGRBO20405.. as well as the radio spectrum between 1.43 and 8.46 Gllz on day 3.3.," In Figure \ref{fig:rad} we plot the 8.46 GHz lightcurve of, as well as the radio spectrum between 1.43 and 8.46 GHz on day 3.3." + The early emission is characterized by(wo important features., The early emission is characterized bytwo important features. +" First. it is brightest (£5,220.5 mJv) during the first observation (/1.2 days). and rapidly faces. Fy,x/1.2-0.1 . between 1.2 and 5r days."," First, it is brightest $F_\nu\approx 0.5$ mJy) during the first observation $t\approx 1.2$ days), and rapidly fades, $F_\nu\propto t^{-1.2\pm +0.4}$ , between $1.2$ and $5$ days." + Second. the spectral index between 1.43 and 3.46 al /223.3 davs is 42—0.3 £0.38. and similarly at /z1.2 davsaq<—0.5 based on the 8.46 and 22.5 GIlz data.," Second, the spectral index between 1.43 and 8.46 at $t\approx 3.3$ days is $\beta_{\rm rad}\approx +-0.3\pm 0.3$ , and similarly at $t\approx 1.2$ days$\beta_{\rm +rad}<-0.5$ based on the 8.46 and 22.5 GHz data." +Photometric variability is a fundamental characteristic of the preauain sequence (PAIS) stars. which manifests as transicut increases in brightucss (outbursts). temporary drops i brightuess (eclipses) iregulu or regular variations for a short or long time scales.,"Photometric variability is a fundamental characteristic of the pre-main sequence (PMS) stars, which manifests as transient increases in brightness (outbursts), temporary drops in brightness (eclipses), irregular or regular variations for a short or long time scales." + The studies of photometric variability give us important information foy the early stages of stellar evolution., The studies of photometric variability give us important information for the early stages of stellar evolution. + Both classes of PMS stars the widespread low-mass (M. < 2M.) T Tug Stars (TTSs) and the more massive Herbie Ac/Be Spy (IAEBESs) show various types of photometric variability (IHerbst et al., Both classes of PMS stars the widespread low-mass $\it M$ $\leq$ $2M_\sun$ ) T Tauri Stars (TTSs) and the more massive Herbig Ae/Be Stars (HAEBESs) show various types of photometric variability (Herbst et al. + 199L. 2007).," 1994, 2007)." + The TTSs can be separated iuto two subclasses: Classical T Tauri stars (CTT) surouuded by au exteuded circumstellar disk and Weak line T Tauri stars (TT) without evidence of disk accretion (Bertout 1989)., The TTSs can be separated into two subclasses: Classical T Tauri stars (CTT) surrounded by an extended circumstellar disk and Weak line T Tauri stars (WTT) without evidence of disk accretion (Bertout 1989). + Some authors (Πατ et al., Some authors (Herbst et al. + 1991) consider appropriate to distinguish a third subclass composed by carly type T Tauri stars (ETTS) with spectral class from IKO to AO., 1994) consider appropriate to distinguish a third subclass composed by early type T Tauri stars (ETTS) with spectral class from K0 to A0. + Most of the stars πι this subelass are actually ILAEDBES. and others are usually considered as CTTS (Ilerbst et al.," Most of the stars in this subclass are actually HAEBES, and others are usually considered as CTTS (Herbst et al." + 1991)., 1994). + According to Herbst et al. (, According to Herbst et al. ( +2007) the high amplitude variability of CTT stars is caused by inagneticallv channeled‘ ‘accretion from the circumstellar‘ clisk outo he star.,2007) the high amplitude variability of CTT stars is caused by magnetically channeled accretion from the circumstellar disk onto the star. + Iu this case the accretion is highly variable in time aud the accretion zones are not uniformly ≺∐↴∖↴↑↥⋅∏⋝∏↑↸∖≼↧∪∐↑∐↸∖↴∖↴↑↸∖↕⋜∐⋅↴∖↴, In this case the accretion is highly variable in time and the accretion zones are not uniformly distributed on the stellar surface. +↿∐⋅↕≯⋜↧↸⊳↸∖∙↽∕∏∐∖↖⇁⋜∐⋅↕⋜↧↕∪∐↴∖↴⋜∐⋅↸∖ nost often nreenlar with auplitudes reachis up to 175 (V) within a few cays., The variations are most often irregular with amplitudes reaching up to $1\fm5$ $V$ ) within a few days. + ↽∕∏∐∖∪↴⋝↴∖↴↸∖↥⋅↖↽↸∖≼⊔⋜∐⋅∶↴⋁↸∖⋜↧⊔↻∐∏≼↧↸∖↖⇁⋜∐⋅↕⋜↧↑↕∪∐↴∖↴↕↕⊔⋝↥⋅↕∶↴⋁∐↑∐↸∖↴∖∷∖↴∎ ⋝↥⋅∐↕∶↴∙⊾↖⇁⋜↧↕∏⋜∏⋝↸∖↕∐↕∪↥⋅⋯⋜↧⊓∪∐↕∪↥⋅↑∐↸∖↸⊳∐⋅↸⊳⋯⊔↴∖↴↑↸∖∐⋜∐⋅↸∖∐↖↽∐⋅∪∐↕⋯∖∐↑∎ and the circumstellar disks., The observed large amplitude variations in brightness bring valuable information for the circumstellar environment and the circumstellar disks. + The large amplitude outbursts of PAIS stars‘ canB be ogrouped] into two main‘ types.YN xuucd after. their respective prototypes: FU. VnOrionis. (FUor: Anmibiartsuniuu 1971) aud EX Lupi (EXor: Herbig 1989).," The large amplitude outbursts of PMS stars can be grouped into two main types, named after their respective prototypes: FU Orionis (FUor; Ambartsumian 1971) and EX Lupi (EXor; Herbig 1989)." + Both types of stars sccm related to low-nass TTS with massive circumstellar disks. aud their," Both types of stars seem related to low-mass TTS with massive circumstellar disks, and their" +nearly color-incdepeucdent partial eclipse (/?=5.57hr) aud the unusually bard X-ray. spectrum of uis source led Whiteetal.(LOST) aud White&Holt(1982) to conclude that the central source is slIrouxcded and partially obscurred by an accretion disk corona. formed from material evaporate ol[D of au X-ray. illuminated disk.,"nearly color-independent partial eclipse $P=5.57\, {\rm hr}$ ) and the unusually hard X-ray spectrum of this source led \citet{White81} and \citet{WhiteHolt} to conclude that the central source is surrounded and partially obscurred by an accretion disk corona, formed from material evaporated off of an X-ray illuminated disk." +" Extensive modeling of the lishteurves by White&Holt(1982).. ΝasoL&Córdova (1982b).. aud Hellier&Mason(1989). constraiued the geoinetri€ parameters of ue system (7=το—825. FRisk—07.3x10Mcin. and Roop""m~93.5—Lx10!em). and suggestec u ep'esence of a pliase-dependent. ve‘ical structure along the edge of the disk."," Extensive modeling of the lightcurves by \citet{WhiteHolt}, \citet{MasonCordovaB}, and \citet{HellierMason} constrained the geometric parameters of the system $i=75-85^\circ$, $R_{\rm disk}=5-7.3 \times 10^{10}\, {\rm cm}$, and $R_{\rm corona}\sim 2.5-4 \times 10^{10}\, {\rm cm}$ ), and suggested the presence of a phase-dependent vertical structure along the edge of the disk." + TIe X-ray spectra obtaiied with previous low-‘esolution instruments have beelex remely difficult to model: the data requi ‘ea complex contiuuuim aud a b'oad Fe line. however bicyack residuals at soft. X-ray. euergles suggest the yresence of additional un'esolved eiission or aSOLyion structure White.Jxalluan.&ÁAugelini1997:P:ulnaretal. 2000).," The X-ray spectra obtained with previous low-resolution instruments have been extremely difficult to model; the data require a complex continuum and a broad Fe line, however broad residuals at soft X-ray energies suggest the presence of additional unresolved emission or absorption structure \citep{White81,WKA,Parmar}." +". With te hieh spectral resolutio iof the HETGCS we a|"" trle to resolve discrete. narrow line eimmission [rou a range of abundant kMs."," With the high spectral resolution of the HETGS we are able to resolve discrete, narrow line emission from a range of abundant ions." + As we describe beOW. detailed analysis of these features and their orital phase variations suggest the presence of plOtoionized material ou the insicle edge oL a bulge located at the point of impact with the accretion stream. aud fIuoresciug material in the inuer disk iluminated by scattered emission [rom the exteucec central corona.," As we describe below, detailed analysis of these features and their orbital phase variations suggest the presence of photoionized material on the inside edge of a bulge located at the point of impact with the accretion stream, and fluorescing material in the inner disk illuminated by scattered emission from the extended central corona." + IU 1822—237 was observed οι 2000 August 23 with the HETGS (Canizares iu the standard. ACIS-S-HETC configuration., 4U $-$ 37 was observed on 2000 August 23 with the HETGS \citep{Canizares} in the standard ACIS-S-HETG configuration. + The observation beean at 16:20:37 UT aud lasted for approximately [0ks covering wo [ull binary pe‘iods.," The observation began at 16:20:37 UT and lasted for approximately $40\, {\rm ks}$ covering two full binary periods." + The source is bright with a pliase-averaged Παν of L8x10Ieros/s/cm?/ o.in the 0.7—I0keV oid.," The source is bright with a phase-averaged flux of $4.8 \times 10^{-10}\, {\rm ergs/s/cm^{2}}$ in the $0.7-10\, {\rm keV}$ band." + Tle zero order image is tlerefore severely piled-up. uakiug it unusable [or spectroscopy.," The zero order image is therefore severely piled-up, making it unusable for spectroscopy." + However. in the combinecl positive aud uegative first order MEG and ΗΕ specra the pliase-aveaged cout rates are only 2.8¢{κ and 2.0ct/s respectivey. and the spectra show no evidence of pile-up p'obleims.," However, in the combined positive and negative first order MEG and HEG spectra the phase-averaged count rates are only $2.8\, {\rm ct/s}$ and $2.0\, {\rm ct/s}$ respectively, and the spectra show no evidence of pile-up problems." + Weised the Chandra Interactive Analysis of Observations software (CLAO to extract the spectra ad generate the aspect-corrected effective area crves., We used the Chandra Interactive Analysis of Observations software (CIAO) to extract the spectra and generate the aspect-corrected effective area curves. + However. due to linitations with the CIAO l.l version that was avallable the time. we were unable to generate tle necessary [files for time itervals within the observation.," However, due to limitations with the CIAO 1.1 version that was available the time, we were unable to generate the necessary files for time intervals within the observation." + Iustead we extraced the spectra for specilic phases usiug custom-bilt. software that was calibrated with the publicly. available Capella d:a Wali 2001).., Instead we extracted the spectra for specific phases using custom-built software that was calibrated with the publicly available Capella data \citep[see][]{Behar}. . + In order to utilize the latest effective area models. all glooil fitting was performed using the CLAO products within ASPEC (version11.0:Arnaucl1," In order to utilize the latest effective area models, all global fitting was performed using the CIAO products within XSPEC \citep[version 11.0:][]{Arnaud}." +996. The depeudent analyses were performed usiug our own software., The phase-dependent analyses were performed using our own software. + For both procedures t1e positive and uegative first order spectra were combinedto maximize the statistical quality of the data., For both procedures the positive and negative first order spectra were combinedto maximize the statistical quality of the data. +allow this statistic to be There therefore exists some room to improve the scoring model. used. by Galaxy Zoo Supernovae (ancl hence. the ellicieney. of the project).,allow this statistic to be There therefore exists some room to improve the scoring model used by Galaxy Zoo Supernovae (and hence the efficiency of the project). + A detailed analysis of the data in Fig., A detailed analysis of the data in Fig. +" 9 shows that reducing the number of classifications needed: before a candidate is considered. classified. (6 3.4)) [rom 20 to 15 (for intermediate scoring events) and from οLO to -S (for low and high scoring events) would reduce the total number of classifications recorded. by 20%. while only moving a handful of candidates («5% )) across the boundaries of S44=1.7 and S,=0.2."," \ref{fig:scoretraj} shows that reducing the number of classifications needed before a candidate is considered classified $\S$ \ref{sec:scoring}) ) from $>20$ to $>15$ (for intermediate scoring events) and from $>10$ to $>8$ (for low and high scoring events) would reduce the total number of classifications recorded by $\sim20 \%$ , while only moving a handful of candidates $<5$ ) across the boundaries of $S_{\mathrm{ave}}=1.7$ and $S_{\mathrm{ave}}=0.2$." + In principle. an analysis of which volunteers consistently ge the classifications correct. (when compared to a professiona astronomer or a spectroscopic classification) could. be usec to weight. cillerent volunteer. responses.," In principle, an analysis of which volunteers consistently get the classifications correct (when compared to a professional astronomer or a spectroscopic classification) could be used to weight different volunteer responses." + For example. an experienced: classifier with a consistent history of correc responses could have a Larger weight than a novice volunteer there is evidence from Fig.," For example, an experienced classifier with a consistent history of correct responses could have a larger weight than a novice volunteer – there is evidence from Fig." + 9 that even good SN candidates can receive the lowest score (many SN trajectories start a an Sj.= 1), \ref{fig:scoretraj} that even good SN candidates can receive the lowest score (many SN trajectories start at an $S_{\mathrm{ave}}=-1$ ). +" Such a feature is not vet. implemented. in Galaxy Zoo Supernovae. but could. be used to arrive at a final S, more quickly."," Such a feature is not yet implemented in Galaxy Zoo Supernovae, but could be used to arrive at a final $S_{\mathrm{ave}}$ more quickly." + Jo date. over 13.000 individuals from the Zooniverse community have visited the Galaxy Zoo Supernovae site and 2.800 have classified one or more SN candidates.," To date, over 13,000 individuals from the Zooniverse community have visited the Galaxy Zoo Supernovae site and 2,800 have classified one or more SN candidates." + This project relies upon the rapid classification of SN candidates ancl although the community is relatively small compared to eg. Galaxy Zoo. a combination of email alerts ancl a committed core of a few hundred: individuals has mace Galaxy Zoo Supernovac a success.," This project relies upon the rapid classification of SN candidates and although the community is relatively small compared to e.g. Galaxy Zoo, a combination of email alerts and a committed core of a few hundred individuals has made Galaxy Zoo Supernovae a success." + An analysis of the fraction. of classifications contributed compared to the average number of classifications per user shows that close to of the classifications in. Galaxy Zoo Supernovae are contributed by less than of the community., An analysis of the fraction of classifications contributed compared to the average number of classifications per user shows that close to of the classifications in Galaxy Zoo Supernovae are contributed by less than of the community. +" In the Galaxy Zoo 2 project (Mastersetal.2010.Lintottetal.inprep.).. close to of the classifications were by individuals whose total classification count was less than 10 galaxies: for Galaxy Zoo Supernovae that. fraction Isater,σα."," In the Galaxy Zoo 2 project \citep[][Lintott et al., in prep.]{2010arXiv1003.0449M}, close to of the classifications were by individuals whose total classification count was less than 10 galaxies; for Galaxy Zoo Supernovae that fraction is." + This paper has introduced. Galaxy. Zoo Supernovae. a new web-based. citizen. science project modelled. after “Galaxy Zoo. that uses members of the public to identify good supernova candidates from wide-field imaging data.," This paper has introduced Galaxy Zoo Supernovae, a new web-based citizen science project modelled after `Galaxy Zoo', that uses members of the public to identify good supernova candidates from wide-field imaging data." +" Using data [rom the Palomar Transient Factory (PPE). we have shown that the citizen scientists are extremely good at identifving real SNe from amongst the thousands of candidates that PLE generates. with only a small ""false negative’ rate at the faintest candidate magnitudes."," Using data from the Palomar Transient Factory (PTF), we have shown that the citizen scientists are extremely good at identifying real SNe from amongst the thousands of candidates that PTF generates, with only a small `false negative' rate at the faintest candidate magnitudes." + Clearly. Galaxy Zoo Supernovae is not restricted to PPE data and can in principle be applied to any future imaging survey. such as SkyMapper (e.g...Welleretal.2007) or Pan-STARRS-1 (e.g..Ixaiser2004)..," Clearly, Galaxy Zoo Supernovae is not restricted to PTF data and can in principle be applied to any future imaging survey, such as SkyMapper \citep[e.g.,][]{2007PASA...24....1K} or Pan-STARRS-1 \citep[e.g.,][]{2004SPIE.5489...11K}." + The candidate upload mechanism is Blexible. and the triplet format (Fig. 1))," The candidate upload mechanism is flexible, and the triplet format (Fig. \ref{fig:egtriplets}) )" + simple. with custom results pages easily produced. for individual surveys.," simple, with custom results pages easily produced for individual surveys." + Perhaps the most exciting aspect for massive future transient surveys such as the Large Svnoptic Survey Telescope (LSST) will be the use of Galaxy Zoo Supernovae classification data to improve the training and accuracy of automated machine-[earning transient classifiers (Starretal.2009).., Perhaps the most exciting aspect for massive future transient surveys such as the Large Synoptic Survey Telescope (LSST) will be the use of Galaxy Zoo Supernovae classification data to improve the training and accuracy of automated machine-learning transient classifiers \citep{2009ASPC..411..493S}. + The underlying concept of Galaxy Zoo Supernovae is easily extended., The underlying concept of Galaxy Zoo Supernovae is easily extended. + For example. there is also no need. to restrict the project. to. single images of new transicnt events.," For example, there is also no need to restrict the project to single images of new transient events." + Multiple images of a potential SN from. dilferent epochs. ie. à candidate history. could. also be uploaded to improve the accuracy of the classifications and thus reduce the possibility of a mis-classification. due to a single poor subtraction.," Multiple images of a potential SN from different epochs, i.e. a candidate history, could also be uploaded to improve the accuracy of the classifications and thus reduce the possibility of a mis-classification due to a single poor subtraction." + Lf this included. data from. before re candidate was first detected. those candidates. with v history of poor subtractions could quite trivially be liminated.," If this included data from before the candidate was first detected, those candidates with a history of poor subtractions could quite trivially be eliminated." +" ""Those asteroids and moving objects which co get uploaded: could also be removed by visually comparing re candidate. position on several epochs.", Those asteroids and moving objects which do get uploaded could also be removed by visually comparing the candidate position on several epochs. + Galaxy Zoo ulupernovae could. also be used to identify new transients trigecred by detections at other wavelengths. for example to uickly: identify optical counterparts to gamma-ray bursts. where previous opticalreference images might not exist and a timely search is critical for follow-up.," Galaxy Zoo Supernovae could also be used to identify new transients triggered by detections at other wavelengths, for example to quickly identify optical counterparts to gamma-ray bursts, where previous opticalreference images might not exist and a timely search is critical for follow-up." +days which is consistent with the dilference in lags between XN-rayv-4.8 Gllz and. X-rav-8.4 Cillz.,days which is consistent with the difference in lags between X-ray-4.8 GHz and X-ray-8.4 GHz. + We split the light curve up into data points surrounding the first Hare at ALJD 53920. which is summarised in table 1.," We split the light curve up into data points surrounding the first flare at MJD 53920, which is summarised in table \ref{lag_table}." + We then calculated the ZDCE to ascertain an accurate measurement of the lag for this Dare only., We then calculated the ZDCF to ascertain an accurate measurement of the lag for this flare $only$. +" We find 0,4= days for X-ray-S8.4 Gllz. and Το=3510 days for X-rav-4.5 CGllz."," We find $\tau_{cent}=14 \pm 11$ days for X-ray-8.4 GHz, and $\tau_{cent}=35 \pm 16$ days for X-ray-4.8 GHz." + Both lag times are below the global lag for the entire light curve., Both lag times are below the global lag for the entire light curve. + We do not. perform this analysis for the second Uare at ALJD 54380 as it was only. sparsely sampled in the radio., We do not perform this analysis for the second flare at MJD 54380 as it was only sparsely sampled in the radio. + The long term X-ray. variability. covering a time-range of about 30. vears. is plotted. in the upper panel of figure 4..," The long term X-ray variability, covering a time-range of about 30 years, is plotted in the upper panel of figure \ref{archiveplot}." + Archival data were searched. for in the literature [rom he instruments Laster (Llalpern&FilippenkoLOS). EXOSAT (Vurner&Pounds19890).. Gunga (Nandra& L994). ASCA using the Tartarus database (Lurneretal.POOL) and NALALNeuton (Dianchietal.2008).," Archival data were searched for in the literature from the instruments $Einstein$ \citep{Einstein_1}, EXOSAT \citep{Turner}, $Ginga$ \citep{Nandra}, ASCA using the Tartarus database \citep{Tartarus} and $XMM-Newton$ \citep{Bianchi_2008}." +. Around ALJD 44400 (~ 1980) a sharp Hare which is brighter han the Wares visible in our dataset was observed., Around MJD 44400 $\sim$ 1980) a sharp flare which is brighter than the flares visible in our dataset was observed. + Since hen the Εικ has been gradually decreasing., Since then the flux has been gradually decreasing. + The long term radio variability at S.A Cllz is plotted in the lower panel of figure 4.., The long term radio variability at 8.4 GHz is plotted in the lower panel of figure \ref{archiveplot}. + Phe Εαν values were taken rom a variety of instruments ancl publications (which are referenced. on the plot)., The flux values were taken from a variety of instruments and publications (which are referenced on the plot). + La order of increasing time the irst point on the plot was taken from Sleeetal.(1994) using the Parkes-Vicbincdilla interferometer (PTL)., In order of increasing time the first point on the plot was taken from \cite{Slee} using the Parkes-Tidbindilla interferometer (PTI). + Then near simultaneous data points were taken with the VLA (Theanetal.2001) and then ATCA (DBransfordοἱal.1998)., Then near simultaneous data points were taken with the VLA \citep{Thean_High_res} and then ATCA \citep{Blanford_ACTA}. +. The Dux from the long baseline array (LBA) observation by Blank.Harnett.&Jones(2005) was the last point plotted ior to the APCA monitoring which is presented. in this APeL., The flux from the long baseline array (LBA) observation by \cite{Blank_LBA} was the last point plotted prior to the ATCA monitoring which is presented in this paper. + When comparing the Lux expected. from. the start of our ATCA monitoring with the LBA data point. the LBA »oint seems too low.," When comparing the flux expected from the start of our ATCA monitoring with the LBA data point, the LBA point seems too low." + The core is un-resolved with all of 1e racio telescopes described above., The core is un-resolved with all of the radio telescopes described above. + Lhe PPL observations 'onstitutes the first data point in figure 4. and the LBA 1e last (before. ATCA monitoring)., The PTI observations constitutes the first data point in figure \ref{archiveplot} and the LBA the last (before ATCA monitoring). + Note. the στidbindilla baseline is part of the LBA network.," Note, the Parkes-Tidbindilla baseline is part of the LBA network." + Blank.—arnett.&Jones(2005)5 comment that in the LBA2 observations. no decrease in Εαν was observed. with respect o baseline length Le it was not resolved: they conclude rom this that the decrease in Hux with respect to the other observations Is accurate.," \cite{Blank_LBA} comment that in the LBA observations, no decrease in flux was observed with respect to baseline length i.e it was not resolved; they conclude from this that the decrease in flux with respect to the other observations is accurate." + However. both the PTL aad the LBA are not sensitive o the same spatial resolutions as the VLA and. ATCA he largest ATCA baseline is Gko and the shortest LBA raseline used. in the archival observation is 113km).," However, both the PTI and the LBA are not sensitive to the same spatial resolutions as the VLA and ATCA (the largest ATCA baseline is 6km and the shortest LBA baseline used in the archival observation is 113km)." + Lt is »ossible that some Lux fon ATCA equivalent baselines) is not accounted for: which could. plausibly give a decrease in lux Le indicating brighter. larger scale structure.," It is possible that some flux (on ATCA equivalent baselines) is not accounted for: which could plausibly give a decrease in flux i.e indicating brighter, larger scale structure." + Phe logical consequence of this is that the PPL data point is also missing some [lux as it samples on a singular baseline of 275km., The logical consequence of this is that the PTI data point is also missing some flux as it samples on a singular baseline of 275km. + We will discuss these measurements within the context of the fundamental plane and attempt to craw some conclusions in section 5.2 A full 12 hour synthesis ATCA observation was performed on 2008 June 29 at S4 and 4.8 Cllz., We will discuss these measurements within the context of the fundamental plane and attempt to draw some conclusions in section 5.2 A full 12 hour synthesis ATCA observation was performed on 2008 June 29 at 8.4 and 4.8 GHz. + The purpose of this observation was to perform a reliable. polarisation calibration to ascertain an accurate measurement of the percentage linear polarised (LP) Εικ from. the source., The purpose of this observation was to perform a reliable polarisation calibration to ascertain an accurate measurement of the percentage linear polarised (LP) flux from the source. + Bower.Falcke.&Mellon(2002) showed that from a sample of 11 LLAGN the mean LP was ον0.2%., \cite{Percent_Flux_LLAGN_Bower} showed that from a sample of 11 LLAGN the mean LP was $\sim 0.2 \%$. + Bignallet from a survey of 22 blazars report a mean LP —3% with a standard. deviation στ1.5., \cite{ATCA_Blazar} from a survey of 22 blazars report a mean LP $\sim 3\%$ with a standard deviation $\sigma=1.5$. + At the time of observation the polarisation of NGC 7213 was «0.14 at 4.8 and 8.4 Gllz respectively. which is more consistent with the reported value of typical LLAGN and. not blazars.," At the time of observation the polarisation of NGC 7213 was $<0.1\%$ at 4.8 and 8.4 GHz respectively, which is more consistent with the reported value of typical LLAGN and not blazars." + The percentage polarisation was caleulated at other epochs. however without a full 12 hour svnthesis parallactic angle calibration the values were often suspect and will not be presented here.," The percentage polarisation was calculated at other epochs, however without a full 12 hour synthesis parallactic angle calibration the values were often suspect and will not be presented here." + We have shown that a weak but statistically significant delay exists between the X-ray and. radio emitting regions. with the radio lageine behind the N-rav.," We have shown that a weak but statistically significant delay exists between the X-ray and radio emitting regions, with the radio lagging behind the X-ray." + A number of models have been proposed to explain and interpret the X-ray to radio lag in both BINRBs and AGN., A number of models have been proposed to explain and interpret the X-ray to radio lag in both BHXRBs and AGN. +" The most notable of these are the ""internal shock model (Blandford1979:Rees1978). and a ‘plasmon model (vanderLaan 1966)."," The most notable of these are the `internal shock model' \citep{Bland_79,Rees} and a `plasmon model' \citep{vanderlaan}." +. We will briefly explore these models and. comment on the relevance - if any - to our data., We will briefly explore these models and comment on the relevance - if any - to our data. + We first consider a plasmon model., We first consider a plasmon model. + After the accretion mechanism(s) have pushed matter into the jet. an acliabatically expanding initially selt-absorbed: svnehrotron emitting plasmon travels at. relativistic speeds. down the path of the jet.," After the accretion mechanism(s) have pushed matter into the jet, an adiabatically expanding initially self-absorbed synchrotron emitting plasmon travels at relativistic speeds down the path of the jet." +" At a given time and frequeney the matter becomes optically thin and is ""detectable"" at that. given frequency (in this case either S.4 and 4.8 2).", At a given time and frequency the matter becomes optically thin and is `detectable' at that given frequency (in this case either 8.4 and 4.8 GHz). + Hf the jet is [ed at à constant mass rate. density and velocity the delay time Lor material to become optically thin will be constant.," If the jet is fed at a constant mass rate, density and velocity the delay time for material to become optically thin will be constant." + Lf these. parameters are not constant the delay between X-ray ancl radio will be variable (e.g. see vanderLaan (1966))) assuming that the clisk and the jet are indeed coupled (ralekeetal.2009)..., If these parameters are not constant the delay between X-ray and radio will be variable (e.g. see \cite{vanderlaan}) ) assuming that the disk and the jet are indeed coupled \citep{SagA_Falcke}. + Note. the higher frequency radio emission (δε Cillz) will become optically thin first. thus acelay from S4 to 4.8 Cllz is always expectec.," Note, the higher frequency radio emission (8.4 GHz) will become optically thin first, thus a delay from 8.4 to 4.8 GHz is always expected." +" Another nioclel for explaining the emission seen in jets is the ""internal shock model (Blandford&Ixonigl1979:Rees 1978)."," Another model for explaining the emission seen in jets is the `internal shock model' \citep{Bland_79,Rees}." +. The svnchrotron lifetime of an emitting region is too short to adequately explain the scales of jets observered in AGN., The synchrotron lifetime of an emitting region is too short to adequately explain the scales of jets observered in AGN. +" These emitting regions - commonly referred to as ""knots! - are often displaced from the central core emission.", These emitting regions - commonly referred to as `knots' - are often displaced from the central core emission. + Localised shocks within these regions are needed to explain the time-scales of variation observed (Rees1978:Felten 1967).," Localised shocks within these regions are needed to explain the time-scales of variation observed \citep{Rees, Felton}. ." +. Jet shock scenarios have also been used. to mocel the common flat spectrum jet observered in DILNIDs and AGN (e.g. see (200931).," Jet shock scenarios have also been used to model the common flat spectrum jet observered in BHXRBs and AGN (e.g. see \cite{Spada,Omar}) )." +stars over the full 5-20 wrange taken with the Infrared Spectrograph URS: Houck et al.,stars over the full 5-20 range taken with the Infrared Spectrograph (IRS; Houck et al. + 2001) aboardSpitzer., 2004) aboard. + We assess the coniplete ice inventory iu quiescent clouds and compare it to observations toward protostars., We assess the complete ice inventory in quiescent clouds and compare it to observations toward protostars. + The background stars discussed here include a source beliud the Serpeus dark cloud. Cly 2. aud two sources behind the Taurus dark cloud. Ehas 13 and Elias 16.," The background stars discussed here include a source behind the Serpens dark cloud, CK 2, and two sources behind the Taurus dark cloud, Elias 13 and Elias 16." +" The observations are part of the ""c2d legacy. program (Evans et 2003).", The observations are part of the “c2d” legacy program (Evans et 2003). + All sources were observed with the short waveleneth. low resolution module (SL: A= 5-11 jou R=A/AA= 61-28). with ou-source integration times of 28 sec per spectral order.," All sources were observed with the short wavelength, low resolution module (SL; $\lambda =$ 5-14 ; $R \equiv \lambda / \Delta \lambda =$ 64-128), with on-source integration times of 28 sec per spectral order." +" CÍK 2 and Elias 13 were also observed with the short waveleneth. hieh resolution module (SIT: A= 10-20juu: R= 600). with integration times of 210 sec and 60 sec per spectra order. respectively,"," CK 2 and Elias 13 were also observed with the short wavelength, high resolution module (SH; $\lambda =$ 10-20; $R = 600$ ), with integration times of 240 sec and 60 sec per spectral order, respectively." + Spectra of Elias 13. Elias 16 απ CIS 2 were part of 000563686 0005637632. arc 01152521.," Spectra of Elias 13, Elias 16 and CK 2 were part of 0005636864, 0005637632, and 0011828224." + The SID spectrum) of Elias1. 16 has heen obliskhed by Berein et ((2005) aud was part of 0003868160., The SH spectrum of Elias 16 has been published by Bergin et (2005) and was part of 0003868160. + The data were reduced using theSpitzer Science. Center (SSC) pipeline. version S11.0.2 (S12 for SIT iu Elias 16) to produce the 2-dimensiona Basic Calibrated Data., The data were reduced using the Science Center (SSC) pipeline version S11.0.2 (S12 for SH in Elias 16) to produce the 2-dimensional Basic Calibrated Data. +" οποιοτήν, customized source extractions were performed. inchiding the subtraction of extended background oenmüssiou."," Subsequently, customized source extractions were performed, including the subtraction of extended background emission." + The spectra were hen defiuged with sincavave fitting routines (Laliuis Boogert 2003)., The spectra were then defringed with sine-wave fitting routines (Lahuis Boogert 2003). + Figure shows theSprtser spectra of the observed ckeround stars. complemented by near-infrared (NTR) xoad baud plotometiy (2ALASS*)).," Figure shows the spectra of the observed background stars, complemented by near-infrared (NIR) broad band photometry )." + In addition. for CTs 2. TRAC (S. T. Megeath. priv.," In addition, for CK 2, IRAC (S. T. Megeath, priv." + comun.), comm.) + aud eround-hased. L/ baud photometry (Chivclisvell IXIooruneof 1986) ave included aud for Elias 16 the 2-5 sspectruni is shown (Whittet ef 11998)., and ground-based $'$ band photometry (Churchwell Koornneef 1986) are included and for Elias 16 the 2-5 spectrum is shown (Whittet et 1998). + Iu order to put the data on au optical depth scale and analyze the ice and dust features. each spectrum is normalized to the spectium of an extincted late-type eiut taken from the ddatabase (Sloan et 22003).," In order to put the data on an optical depth scale and analyze the ice and dust features, each spectrum is normalized to the spectrum of an extincted late-type giant taken from the database (Sloan et 2003)." + A blackbody is used at wavelengths below 2.5 to fit the NIR photometry., A blackbody is used at wavelengths below 2.5 to fit the NIR photometry. + The extinction law used or Serpeus is of the form sly~AP? (Kaas et 22001). that for Taurus has a shallower power aw. Aywhereas~Aob (AWhittet et 11988).," The extinction law used for Serpens is of the form $A_{\lambda} \sim \lambda^{-1.9}$ (Kaas et 2004), whereas that for Taurus has a shallower power law, $A_{\lambda} \sim \lambda^{-1.7}$ (Whittet et 1988)." + Indebetomw ct al. (, Indebetouw et al. ( +2005) fiud a shallower slope on the extinction curve )ovond 6yu.,2005) find a shallower slope on the extinction curve beyond 6. + This flattening is partly due to the silicate and ice features which we account for separately aud the vowerluw is a good approximation to the extinction at onger waveleneths., This flattening is partly due to the silicate and ice features which we account for separately and the powerlaw is a good approximation to the extinction at longer wavelengths. +", ly is taken to be 91 \ Ag (Rieke LLebofskv 1985).", $A_{\rm V}$ is taken to be 9.1 $\times$ $A_{\rm K}$ (Rieke Lebofsky 1985). + Spectral tvpes It IIT. G9 TT. aud Ίο III were adopted for CI 2. Elias 13 aud Elias 16. respectively.," Spectral types K4 III, G9 III, and K3 III were adopted for CK 2, Elias 13 and Elias 16, respectively." + These values are within the rauge of types eiven in Cliar et ((1991) for CIS 2 and close to the K2 III type assigned by Suüth et (01993) for Elias 13 aud 16., These values are within the range of types given in Chiar et (1994) for CK 2 and close to the K2 III type assigned by Smith et (1993) for Elias 13 and 16. + While the selected spectral types eive the best fit (iu removing the photospherie CO aud SiO bands at 5 and 8 yan}). they are uncertain by a few subclasses resulting in an abundance error of on the strong features. especially since the available ddatabase has limited coverage.," While the selected spectral types give the best fit (in removing the photospheric CO and SiO bands at 5 and 8 ), they are uncertain by a few subclasses resulting in an abundance error of on the strong features, especially since the available database has limited coverage." + The 115 pau feature is very strong toward CK 2 aud Elias 16. and weakly detected toward Elias 13.," The 15 $\mu$ m feature is very strong toward CK 2 and Elias 16, and weakly detected toward Elias 13." + The abundance of relative to lis toward CK 2. higher than the ~20% abundance seen toward the Taurus sources.," The abundance of relative to is toward CK 2, higher than the $\sim$ abundance seen toward the Taurus sources." + The derived ccohunn deusitics toward Elias 13 and Elias 16 agree within errors with those obtained from the 125 ffeature CNunuuclin et 22001: Table 1)., The derived column densities toward Elias 13 and Elias 16 agree within errors with those obtained from the 4.25 feature (Nummelin et 2001; Table 1). + The bottom of the 15 ffeature appears single peaked toward all sources (Fig. 3)), The bottom of the 15 feature appears single peaked toward all sources (Fig. \ref{fig:co2}) ) + aud does not show double dips due to crystallization as sole protostars do (Gerakines et 11999. Booeert et 22001).," and does not show double dips due to crystallization as some protostars do (Gerakines et 1999, Boogert et 2004)." + The profile of this baud toward Elias 16 is fitted iu Dergim ct ((2005) with the sui of the polar 77:1)and the apolar 1:1) mustures., The profile of this band toward Elias 16 is fitted in Bergin et (2005) with the sum of the polar 7:1)and the apolar 4:1) mixtures. +" The (IIl290::€O0,—polar. HaoO-rich iuixture accounts for"," The polar, -rich mixture accounts for" +dependence of the dillerence on temperature.,dependence of the difference on temperature. + This ellect is illustrated in Figs 3. and 4..," This effect is illustrated in Figs \ref{hgam_hdel_col} + and \ref{bgam_bdel_c}." +" Phe first of these plots the cilference in 2,47 between the two lines against (2Vo.", The first of these plots the difference in $D_{0.15}$ between the two lines against $(B-V)_0$. + The second of these plots the dillerence in b between the two ines against the parameter e., The second of these plots the difference in $b$ between the two lines against the parameter $c$. +" We have chosen the Ες line as our reference. and we have used the linear fits to calibrate yw values of 2,45 and 6 from L9 to Le and then caleulated weighted: averages."," We have chosen the $\gamma$ line as our reference, and we have used the linear fits to calibrate the values of $D_{0.15}$ and $b$ from $\delta$ to $\gamma$ and then calculated weighted averages." + For the parameter e we found no such rend. and so we simply computed the weighted average of )0 € values for the two lines.," For the parameter $c$ we found no such trend, and so we simply computed the weighted average of the $c$ –values for the two lines." + We have not discovered. a convincing explanation for 10 trends seen., We have not discovered a convincing explanation for the trends seen. + We suspect it is an elect of line blanketing rom weak metal lines. which would explain the temperature lependencee.," We suspect it is an effect of line blanketing from weak metal lines, which would explain the temperature dependence." + However if this is the case one would expect vere to be a correlation between the residual from the fit nd the metallicitv. as estimated from the Ca IL [x line.," However if this is the case one would expect there to be a correlation between the residual from the fit and the metallicity, as estimated from the Ca II K line." + Llowever we found no significant> correlation in a plot of these wo quantities., However we found no significant correlation in a plot of these two quantities. + The Ca LL [x line is the strongest measurable metal [ine over the wavelength. range covered. by the νο spectra. and the only useful indicator of metallicity in spectra of low S/N. such as for the stars in our racial velocity programme.," The Ca II K line is the strongest measurable metal line over the wavelength range covered by the KSK spectra, and the only useful indicator of metallicity in spectra of low S/N, such as for the stars in our radial velocity programme." + With some exceptions (including the A metallic (Am) and peculiar (Ap) stars) the strength. of the Ca IL [x line at constant temperature can be used as a reliable indicator of the metallicity of A-type stars (c.g. Pier 1983. Beers οἱ al.," With some exceptions (including the A metallic (Am) and peculiar (Ap) stars) the strength of the Ca II K line at constant temperature can be used as a reliable indicator of the metallicity of A-type stars (e.g. Pier 1983, Beers et al." + 1992. KSI).," 1992, KSK)." + We measure the EW of the Ca ILE Is [line by münimumX fitting a Gaussian to the eontinuun divided spectrum over the wavelength range given in Table 2., We measure the EW of the Ca II K line by $-\chi^2$ fitting a Gaussian to the continuum divided spectrum over the wavelength range given in Table 2. +" ""Ehis lino is much weaker than the Balmer lines. and. to reduce the error the central waveleneth is fixed at the recshilt determined from the Balmer lines."," This line is much weaker than the Balmer lines, and to reduce the error the central wavelength is fixed at the redshift determined from the Balmer lines." + In 866 we use a plot of EWe versus (DVg to estimate the metallicities of the WSIX stars., In 6 we use a plot of $_{Ca}$ versus $(B-V)_0$ to estimate the metallicities of the KSK stars. + This has two purposes., This has two purposes. + First it allows anomalous highmetallicity halo, First it allows anomalous high–metallicity halo +Observational studies of Galactic open clusters have become a traditional benchmark lo test our comprehension of several aspects of stellar structure ancl evolution (see Chiosi 2007. and references (herein). and also of the formation ancl properties of the Galactic disk (see Moitinho 2010. and references Being the clusters immersed in the Galactic general field. it is widely recognized that. unless a detailed star by star membership analvsis is available (which is the case Lor the vast majority of Galactic clusters. see Carraro et 22008). the interpretation of (heir color-magnitude diagram (CMDs) is seriously complicated by field stars located along the line of sight to the cluster.,"Observational studies of Galactic open clusters have become a traditional benchmark to test our comprehension of several aspects of stellar structure and evolution (see Chiosi 2007, and references therein), and also of the formation and properties of the Galactic disk (see Moitinho 2010, and references Being the clusters immersed in the Galactic general field, it is widely recognized that, unless a detailed star by star membership analysis is available (which is the case for the vast majority of Galactic clusters, see Carraro et 2008), the interpretation of their color-magnitude diagram (CMDs) is seriously complicated by field stars located along the line of sight to the cluster." + Together with variable extinction. field star contamination can produce sequences in the CMD which resemble typical cluster sequences (especially in the case of very. voung clusters). leading to erroneous interpretations.," Together with variable extinction, field star contamination can produce sequences in the CMD which resemble typical cluster sequences (especially in the case of very young clusters), leading to erroneous interpretations." + Unfortunately. the real nature of these field sequences can only be clarified with a difficultposteriori membership analvsis (Villanova et 22005. Moni Didin et This work is part of a series of papers aimed at improving the fhuudamental parameters of poorly studied. Galactic clusters (Seleznev οἱ al.," Unfortunately, the real nature of these field sequences can only be clarified with a difficult membership analysis (Villanova et 2005, Moni Bidin et This work is part of a series of papers aimed at improving the fundamental parameters of poorly studied Galactic clusters (Seleznev et al." + 2010: Carraro Costa 2007. 2009. 2010).," 2010; Carraro Costa 2007, 2009, 2010)." + Here we address (he case of Trumpler 20. whose CMD is obviously dominated by a sienilicant fiekl star population. which has been the cause of past misinterpretations in regards to the cluster itself (Seleznev et 22010: Platais et 22008 - hereafter PlaQs: MeSwain Gies," Here we address the case of Trumpler 20, whose CMD is obviously dominated by a significant field star population, which has been the cause of past misinterpretations in regards to the cluster itself (Seleznev et 2010; Platais et 2008 - hereafter Pla08; McSwain Gies" +cores of the ULICs and the gl stellar cores |. BIls is that their masses and sizes are similar. in adcdition to their densities.,"cores of the ULIGs and the gE stellar cores + BHs is that their masses and sizes are similar, in addition to their densities." +" Tvpical masses for both are several times 10"" M. and typical radii are several hundred: parsees (see Sakomoto et al.", Typical masses for both are several times $^9$ $_{\odot}$ and typical radii are several hundred parsecs (see Sakomoto et al. + 1999 for details of Arp 220. the nearest. ULIC. and Lauer et al.," 1999 for details of Arp 220, the nearest ULIG, and Lauer et al." + 1985 for the core properties of gl cores)., 1985 for the core properties of gE cores). + The BL contribution to the el core masses can be added. in from the correlations of Magorrian ct al., The BH contribution to the gE core masses can be added in from the correlations of Magorrian et al. + 1998 or van der AMarel 1999 which relate the DII mass to the galaxy. mass. in combination with Tables 2 and 3 of Lauer 1985. which relate the core size to the size of the whole galaxy.," 1998 or van der Marel 1999 which relate the BH mass to the galaxy mass, in combination with Tables 2 and 3 of Lauer 1985, which relate the core size to the size of the whole galaxy." + Masses of the stellar cores can be computed directly. from the core sizes. along with the mass-to-light ratio of Pulsugita. Hogan Peebles (1998).," Masses of the stellar cores can be computed directly from the core sizes, along with the mass-to-light ratio of Fukugita, Hogan Peebles (1998)." + jut locally. gl galaxies are much more common than ULIGs.," But locally, gE galaxies are much more common than ULIGs." + The number density of ULICs. with far-infrared luminosities in excess of 107 L. is about Ld10‘Ape? (Saunders ct al., The number density of ULIGs with far-infrared luminosities in excess of $^{12}$ $_{\odot}$ is about $1.1 \times 10^{-7} {\rm Mpc}^{-3}$ (Saunders et al. + 1990)., 1990). + Evpical ULICGs have total A'-band (2.2 pm) absolute magnitudes of Ay=25.4 (Carico et al., Typical ULIGs have total $K$ -band (2.2 $\mu$ m) absolute magnitudes of $M_K = -25.4$ (Carico et al. +" Loss. 1990: here. as throughout this paper we assume an Linstein-de Sitter cosmologv with Jf, = 50 km s1 1). most of whieh comes from pre-existing stews in the progenitor galaxies (the dense cores are optically thick at A-band: CGolcacder et al."," 1988, 1990; here, as throughout this paper we assume an Einstein-de Sitter cosmology with $H_0$ = 50 km $^{-1}$ $^{-1}$ ), most of which comes from pre-existing stars in the progenitor galaxies (the dense cores are optically thick at $K$ -band; Goldader et al." + 1995)., 1995). + Phe number density of normal galaxies with My« 25.11 1.610‘Alpe* (Szokolv et al., The number density of normal galaxies with $M_K < -25.4$ is $1.6 \times 10^{-4} {\rm Mpc}^{-3}$ (Szokoly et al. + 1998). a factor of about 1500 larger than the density of ULICGs.," 1998), a factor of about 1500 larger than the density of ULIGs." + Most of these A -band-buminous normal galaxies are earlv-tvpe galaxies. which have the cores | DIIS discussed in the previous two paragraphs: the contribution of luminous disks. which tend to be blue. to the A-band. luminosity function at the very bright end is small (see c.g. Bineecli. Sandage Tammann 1988 for the optical luminosity function. of the different Llubble types. and Huang et al.," Most of these $K$ -band-luminous normal galaxies are early-type galaxies, which have the cores + BHs discussed in the previous two paragraphs; the contribution of luminous disks, which tend to be blue, to the $K$ -band luminosity function at the very bright end is small (see e.g. Binggeli, Sandage Tammann 1988 for the optical luminosity function of the different Hubble types, and Huang et al." + 1997 for the optical-near-infrared. colors)., 1997 for the optical-near-infrared colors). + Therefore if gl cores were made by ULICGs. the comoving density of ULIGs must have been a factor. 1500 higher in the past than it is today. approximately 10 .," Therefore if gE cores were made by ULIGs, the comoving density of ULIGs must have been a factor 1500 higher in the past than it is today, approximately $^{-4}$ $^{-3}$." + But this is very similar to the comoving density (c.g. Trentham. Blain Goldader 1999) of the SCUBA (=1 η]ν at 850 jin in the observer frame) sources (Snail. Ivison Blain 1997. Bareer et al.," But this is very similar to the comoving density (e.g. Trentham, Blain Goldader 1999) of the SCUBA $>1$ mJy at 850 $\mu$ m in the observer frame) sources (Smail, Ivison Blain 1997, Barger et al." + 1998. Hughes et al.," 1998, Hughes et al." + 1998. Eales et al.," 1998, Eales et al." + 1999). which are presumably high-redshift. objects. and which Darger ct al. (," 1999), which are presumably high-redshift objects, and which Barger et al. (" +1998) argue are ULICGs based on their similar bolometric Iluminosities ancl spectral energy distribution (SEDs).,1998) argue are ULIGs based on their similar bolometric luminosities and spectral energy distribution (SEDs). + Therefore a picture in which SCUDA sources make gl cores and their associated black holes seems very likely not just. based on similarities of their SEDs and Iuminosities to those of local ULICGs but also due to the comoving number density. of local gle cores |. BlIs being similar to that of the high-redshift SCUBA ealaxies., Therefore a picture in which SCUBA sources make gE cores and their associated black holes seems very likely not just based on similarities of their SEDs and luminosities to those of local ULIGs but also due to the comoving number density of local gE cores + BHs being similar to that of the high-redshift SCUBA galaxies. + It is this possibility that we investigate in the rest of this paper., It is this possibility that we investigate in the rest of this paper. + In the previous section we argued that the SCUBA sources are probably the high-redshift) analogues of. Iow-redshift ULIGs. both in terms of their SED and luminosity concordance. and also in terms of the comoving number density concordance between the SCUBA galaxies and the likeliest remnants of the local ULIGs (the gl cores | DIIS).," In the previous section we argued that the SCUBA sources are probably the high-redshift analogues of low-redshift ULIGs, both in terms of their SED and luminosity concordance, and also in terms of the comoving number density concordance between the SCUBA galaxies and the likeliest remnants of the local ULIGs (the gE cores + BHs)." + This SED (Ivison et al., This SED (Ivison et al. + 1998) and luminosity (Darger et al., 1998) and luminosity (Barger et al. + 1999) concordance is observed for individual sources. and is also implied. on statistical grounds.," 1999) concordance is observed for individual sources, and is also implied on statistical grounds." + By this. it is meant that: if the SCUBA sources were. significantly hotter than local ULIGs. then they would. overproduce the far-infrared background: shortward. of about 500. jun measured by Fixsen et al. (," By this it is meant that: if the SCUBA sources were significantly hotter than local ULIGs, then they would overproduce the far-infrared background shortward of about 500 $\mu$ m measured by Fixsen et al. (" +1998) using CODE.,1998) using $COBE$. + If they were signifiantly colder than local ULICGs. they would. severely anderpredict the background at 450 pim: the SCUBA sources are observed to generate at least one-third of the backgroun measured by Fixsen ct al.," If they were signifiantly colder than local ULIGs, they would severely underpredict the background at 450 $\mu$ m: the SCUBA sources are observed to generate at least one-third of the background measured by Fixsen et al." + at 450 jm (Blain et al., at 450 $\mu$ m (Blain et al. + 1999a)., 1999a). + These two statements assume a median source redshift: of approximately 3 (see the radio measurements of Smail e al., These two statements assume a median source redshift of approximately 3 (see the radio measurements of Smail et al. + 2000) and then follow directIv from the result that alios the entire background at 850 pim is generated by the SCUBA sources (Blain et al., 2000) and then follow directly from the result that almost the entire background at 850 $\mu$ m is generated by the SCUBA sources (Blain et al. + 1999b. Barger. Cowie Sanders 1999).," 1999b, Barger, Cowie Sanders 1999)." + Both statements are independent of any specifie model of SCUBA source luminosity and density evolution., Both statements are independent of any specific model of SCUBA source luminosity and density evolution. + Now let us make the following acdcditional assumption. which we will callAT: 3pt 3pt This is an assumption. not an observation. since we have no direct probes of the gas densities in the SCUBA sources.," Now let us make the following additional assumption, which we will call: 3pt 3pt This is an assumption, not an observation, since we have no direct probes of the gas densities in the SCUBA sources." + We only know about CO in two of the SCUBA sorces (Eraver οἱ al., We only know about CO in two of the SCUBA sorces (Frayer et al. + 1998. 1999). and have no measurements at all of high-density. tracers like ICN or CS in these objects.," 1998, 1999), and have no measurements at all of high-density tracers like HCN or CS in these objects." + There are two indirect pieces of evidence supportingAl., There are two indirect pieces of evidence supporting. + Fistlv. LCN has been detected. in. the Cloverleat quasar (Barvainis ct al.," Firstly, HCN has been detected in the Cloverleaf quasar (Barvainis et al." + 1997). a stronely-lensecl infrared quasar which has an SED at far-infrared wavelengths similar to those of the SCUBA sources.," 1997), a strongly-lensed infrared quasar which has an SED at far-infrared wavelengths similar to those of the SCUBA sources." + Secondly. i£ the burst producing the high far-infrarecl luminosity is shortlived (see c.g. Blain et al.," Secondly, if the burst producing the high far-infrared luminosity is shortlived (see e.g. Blain et al." + 1999a). then it is unlikely that it can be maintained in a coherent wav over a galactic scale (in this case. the Large scale over which the luminosity emerges from. requires that the ultimate power source is star. formation)," 1999a), then it is unlikely that it can be maintained in a coherent way over a galactic scale (in this case, the large scale over which the luminosity emerges from requires that the ultimate power source is star formation)." + Vherefore the gas. fuelling the burst. is unlikely to be distributed over the whole galaxy., Therefore the gas fuelling the burst is unlikely to be distributed over the whole galaxy. + Scenarios do exist in which. positive feedback. can happen where explosions in one part of a galaxy can trigger those in another part (c.g. Taniguchi. Trentham Shiova 1998). but these mechanisms are not powerful enough to generate the kinels of Luminosity required here over a whole galaxy.," Scenarios do exist in which positive feedback can happen where explosions in one part of a galaxy can trigger those in another part (e.g. Taniguchi, Trentham Shioya 1998), but these mechanisms are not powerful enough to generate the kinds of luminosity required here over a whole galaxy." + The important point is that if is correct. then the above suspicion of the connection between local ULICs and the SCUBA sources based on the (remnant) number density and SED concordance now becomes a very strong assertion.," The important point is that if is correct, then the above suspicion of the connection between local ULIGs and the SCUBA sources based on the (remnant) number density and SED concordance now becomes a very strong assertion." +complex 3C sources respectively.,complex 3C sources respectively. + Tn this aud other figures we have defined disklike structures (iucliding straight lanes) as simple. and all other dust features Guclidine distorted lanes) as coupler.," In this and other figures we have defined disklike structures (including straight lanes) as simple, and all other dust features (including distorted lanes) as complex." + As we remarked in the previous Section. the simple structures tend to be ound m sources with radio jets.," As we remarked in the previous Section, the simple structures tend to be found in sources with radio jets." + It is well known that jets are more casily detected in weaker radio sources of type FR I aud it is therefore o be expected that dusty disks and lanes are more requently oeseut in the weaker radio sources with jets: any aliguimeut between radio axis aud clust-disks should (e sought there., It is well known that jets are more easily detected in weaker radio sources of type FR I and it is therefore to be expected that dusty disks and lanes are more frequently present in the weaker radio sources with jets; any alignment between radio axis and dust-disks should be sought there. + This is illustrated in Fig. 7..," This is illustrated in Fig. \ref{fig:dpa_p}," + where we ot the aligument angle against radio power., where we plot the alignment angle against radio power. +" Clearly any sources. and actually all of tje weak ones with P99 from Fishers F-distribution).," The difference between the average angles is not significant, but the variance of the distributions is different (confidence level $>99$ from Fisher's F-distribution)." + This of course reflects the fact that all the weak sources are clustered towards ligh alieument angles., This of course reflects the fact that all the weak sources are clustered towards high alignment angles. + As explained in Sect., As explained in Sect. + L1. we caleulated the masses of the dust features in the usual way. following Sadler Gerhard (1985)).," 4.1, we calculated the masses of the dust features in the usual way, following Sadler Gerhard \cite{sadler85}) )." + Iu Fie., In Fig. + 8 we show the derived dust masses agaist the alieuiieut angele., \ref{fig:dpa_m} we show the derived dust masses against the alignment angle. +" No correlation 1s ποστ,", No correlation is seen. + À coufinnation hat he simple sructures have on average lower Masses Is shown in Fie. 9:, A confirmation that the simple structures have on average lower masses is shown in Fig. \ref{fig:mcom_sim}: + the lower masses correspond to the disk aud lane structures., the lower masses correspond to the disk and lane structures. + For the D2 galaxies with simple dust structures we find au average =3.9. with a standard deviation of the mean of 0.20. while complex sructures have au average of 5.0 with standard deviation 0.36.," For the B2 galaxies with simple dust structures we find an average $<\log (M/M{\sun}>=3.9$, with a standard deviation of the mean of 0.20, while complex structures have an average of 5.0 with standard deviation 0.36." + According to Studeuts t-test this difference is significant at the 99.5 level., According to Student's t-test this difference is significant at the 99.5 level. + A stuular differeuce is obtained for the 3C, A similar difference is obtained for the 3C +‘Two dillerent fates of a system starting [from these initial conditions are distinguished: one is characterized. by a libration of Ac around ~250° and the other à circulation of Ac.,"Two different fates of a system starting from these initial conditions are distinguished: one is characterized by a libration of $\Delta\varpi$ around $\sim +250\degr$ and the other a circulation of $\Delta\varpi$." + In the latter case. the eccentricity e» can reach a smaller value (correspondinglv e; a higher value).," In the latter case, the eccentricity $e_2$ can reach a smaller value (correspondingly $e_1$ a higher value)." + These agree pretty well with the directly. numerical integrations., These agree pretty well with the directly numerical integrations. + Such agreements are shown in 66 bv a coniparing plots of the numerical results., Such agreements are shown in 6 by a comparing plots of the numerical results. + 77 shows the velocity of Ac., 7 shows the velocity of $\Delta\varpi$. + Through this figure. we can explain how Ac evolves.," Through this figure, we can explain how $\Delta\varpi$ evolves." + Along the right boundary of the box. the absolute. value of velocity could. be very large. so that Ac increases or decreases quickly.," Along the right boundary of the box, the absolute value of velocity could be very large, so that $\Delta\varpi$ increases or decreases quickly." + Let us write the perturbing part of the Llamiltonian as ff)=ey»Ha ο. where £2). contains the coellicionts Ryjee 20d. sums over nom? in Eq.(3).," Let us write the perturbing part of the Hamiltonian as $H_1= +\sum_{j=0}^{j_{\rm max}} \sum_{k=0}^{k_{\rm max}} R_{j,k} e_1^j +e_2^k$ , where $R_{j,k}$ contains the coefficients $R_{n,j,k,u,l}$ and sums over $n,u,l$ in Eq.(3)." + By careful calculations. we obtain ," By careful calculations, we obtain = e_1^j e_2^k e_1^j e_2^k." +Obviously. when ¢;1. the dominating term on the right hand side has the order ~+.," Obviously, when $e_i \ll 1$, the dominating term on the right hand side has the order $\sim \frac{1}{e_i}$." +" Near the right boundary of the box in 77. we have e,~0.03«1I."," Near the right boundary of the box in 7, we have $e_1 \sim 0.03 \ll 1$." + That's the reason why Ac has a quick change when e; approaches its minimum value as shown in Hb.c. The numerical simulations reveal that the quick varving of Aw in LEb.e is caused by a quick varying of zej when ey»0.," That's the reason why $\Delta\varpi$ has a quick change when $e_1$ approaches its minimum value as shown in 1b,c. The numerical simulations reveal that the quick varying of $\Delta\varpi$ in 1b,c is caused by a quick varying of $\varpi_1$ when $e_1\rightarrow 0$." + In fact. when an orbit is nearly circular (ο~ 0). it would be relatively easy to change its direction (zc). thus 16 two planets could loose the locking of periastrons if they were not in a strong coupling.," In fact, when an orbit is nearly circular $e\sim 0$ ), it would be relatively easy to change its direction $\varpi$ ), thus the two planets could loose the locking of periastrons if they were not in a strong coupling." + On the other hand. whether rev can stronely couple with cach other depends also on row close they can approach cach other. that is. how large jeir eccentricities (especially ο} are.," On the other hand, whether they can strongly couple with each other depends also on how close they can approach each other, that is, how large their eccentricities (especially $e_2$ ) are." + Bearing this in mind we can understand why in casea e» has a higher lower-Iimit iin in cases andο., Bearing this in mind we can understand why in case $e_2$ has a higher lower-limit than in cases and. + Of course. a small es can also cause a quick variation of Ac. but this situation does not happen »ecause the energy. integral prevents e» from approaching very small value.," Of course, a small $e_2$ can also cause a quick variation of $\Delta\varpi$, but this situation does not happen because the energy integral prevents $e_2$ from approaching very small value." + From Fisg.66 and 77. we see cilferent behaviors of Ax (circulation. or libration) have cillerent/ varving directions along the right edge of the box.," From 6 and 7, we see different behaviors of $\Delta\varpi$ (circulation or libration) have different varying directions along the right edge of the box." + By numerically solving the equation dzNzc/edl=0. we find two zero velocity points on the boundary.," By numerically solving the equation $d\Delta\varpi/ dt=0$, we find two zero velocity points on the boundary." + They. define the boundaries of the initial conditions leading to a librating or circulating of A, They define the boundaries of the initial conditions leading to a librating or circulating of $\Delta\varpi$. +" The caleulations show that the apsidal corotation happens if Ax""©(06073307). while if Ax?c(307.1607). Ax circulates."," The calculations show that the apsidal corotation happens if $\Delta\varpi^0\in (160\degr, 330\degr)$, while if $\Delta\varpi^0\in (-30\degr, 160\degr)$, $\Delta\varpi$ circulates." + The case has a Hamiltonian value a little further fron the extremum in 55. so that m(65) has a large amplitucde of libration ancl can not be assumed. as a constant.," The case has a Hamiltonian value a little further from the extremum in 5, so that $\sigma_2 (\theta_2)$ has a large amplitude of libration and can not be assumed as a constant." + As a result. we can not find a corresponcing curve for it in 66.," As a result, we can not find a corresponding curve for it in 6." + However. i£ we draw a series of Hamiltonian contour with cillerent value of o» (adding another dimension to 66). we can also understand its dvnamical evolution.," However, if we draw a series of Hamiltonian contour with different value of $\sigma_2$ (adding another dimension to 6), we can also understand its dynamical evolution." + SS summarizes the initial conditions of the 3s stable examples in the numerical simulations., 8 summarizes the initial conditions of the 38 stable examples in the numerical simulations. + For clarity. we have mapped the svmmetric configurations to one regime according to the symmetry of the Hamiltonian.," For clarity, we have mapped the symmetric configurations to one regime according to the symmetry of the Hamiltonian." + Except the three examples as caseο. all the points for stable svstenis eather along the line of af=3207. anc points for librating and circulating Ac (case and b) are separated. by the CLOted lines of Ac”=160°.330°.," Except the three examples as case, all the points for stable systems gather along the line of $\sigma_2^0=320\degr$, and points for librating and circulating $\Delta\varpi$ (case and ) are separated by the dotted lines of $\Delta\varpi^0=160\degr, 330\degr$." + These agree very. well with the above analvsis with the Llamiltonian., These agree very well with the above analysis with the Hamiltonian. + We have given an estimate of the probability. of Following cdillerent ways as case andc., We have given an estimate of the probability of following different ways as case and. + The analyses here tell that all the initial conditions leading to stable configurations gather in a narrow strip along the line in SS., The analyses here tell that all the initial conditions leading to stable configurations gather in a narrow strip along the line in 8. + That is. for systems having given (is.ci» as in MTable 1. onlv those with ponsinitial conditions2. satisfvingDea 320*seB and ay0|Aw’ü=320°se∣ can surviveH for. long time.," That is, for systems having given $a_{1,2}, e_{1,2}$ as in Table 1, only those with initial conditions satisfying $\sigma_2^0\approx 320\degr$ and $\sigma_1^0+\Delta\varpi^0\approx +320\degr$ can survive for long time." +H We know now the initial conditions determine whether the apsidal corotation happens or not. but whether a system would follow a definite evolution type also depends on the stability of an evolution tvpe.," We know now the initial conditions determine whether the apsidal corotation happens or not, but whether a system would follow a definite evolution type also depends on the stability of an evolution type." + The stabilitv of an orbit in the phase space can be revealed. by its projection on the surface of section., The stability of an orbit in the phase space can be revealed by its projection on the surface of section. + We present in 99 the sections, We present in 9 the sections +between their fuuctioual argumeuts for either of these.,between their functional arguments for either of these. + Fortunately. iuspectiou of the phase augle reveals something iuterestiug.," Fortunately, inspection of the phase angle reveals something interesting." + Using the approximation ii equation (6)). we cau write: from which we define a new variable. If it can be shown that wis uniformly distributed for all distributions of eccentricity. then this would prove that 9 is sinusoidally distributed regardless of the distribution of auy other orbital parameter. given only our assumption of uniform orbital orientation.," Using the approximation in equation \ref{eq:betadef}) ), we can write: from which we define a new variable, If it can be shown that $x$ is uniformly distributed for all distributions of eccentricity, then this would prove that $\beta$ is sinusoidally distributed regardless of the distribution of any other orbital parameter, given only our assumption of uniform orbital orientation." + We do so by considering the characteristic Function of ur. where IE is the expectation value. aud showing that it is equivalent to the characteristic fuuetion of a uniformly distributed variable.," We do so by considering the characteristic function of $x$, where $\mathbb{E}$ is the expectation value, and showing that it is equivalent to the characteristic function of a uniformly distributed variable." + The assumption of uniform orbital orientation vields: so that the characteristic function of becomes: Performing the integral over t. ∖∖↽∐≺↵↕⋅↩⋮∣∣∣↥⊳∖↕∐↩∠↩↥⋅∩↕∐−∩↕⋅≺⇂≺↵↕⋅⊟↩⊳∖⊳∖≺↵⊔∎⋯∐∙⋃∩∐∩↥∎↕∐≺↵↓∎∐⋅⊳∖↕↕⊆↕∐≺," The assumption of uniform orbital orientation yields: so that the characteristic function of $x$ becomes: Performing the integral over $\psi$, where $J_0$ is the zeroth-order Bessel function of the first kind." +⇂⋅∖↾∖⊽≺↵∐≺↵⊸∖↕↥↽≻≺↲↓⋅↥∎∩↥⋅⋯↕∐≺↵↥∐↕≺↵∑∸↥⋅⋜↕↥ over 0 usiug Gegenbauers fiuite integral (see equation 12.1I(1) iu. 2)):, We next perform the integral over $\theta$ using Gegenbauer's finite integral (see equation 12.14(1) in \citet{watson1944treatise}) ): +multiple imaeing (Tole&Wald1998).,multiple imaging \citep{hw98}. + A kev feature of this approach is that it acconunodates lensing from matter along the line of sightpossibly iucludiug the effects frou thousands of galaxiesaud in addition requires no assumptions regarding the Iuninosity-distauce relation (Holz&Wald1995:Bergstrometal.2000).," A key feature of this approach is that it accommodates lensing from matter along the line of sight—possibly including the effects from thousands of galaxies—and in addition requires no assumptions regarding the luminosity-distance relation \citep{hw98,bggm00}." + It 15 to be empluvdzed. however. that the strong lensing results do not depend seuxitivelv ou the details of the methods. with differing analytic aud wuuerical results beiug in good agrecinent (Turner.Ostriker.&Cott1981," It is to be emphasized, however, that the strong lensing results do not depend sensitively on the details of the methods, with differing analytic and numerical results being in good agreement \citep{tog84,hmq99,ms99}." +:ITolz.Miller., In Fig. + 1999).. Tu Fig. d we show the probability of imultiple-nuage of a given source (also referred to as the optical depth to strong lensing. 7) as a function of the source redshift. for a range of cosmologics.," \ref{opt_depth1} we show the probability of multiple-imaging of a given source (also referred to as the optical depth to strong lensing, $\tau$ ) as a function of the source redshift, for a range of cosmologies." + We take a conservative value of the dimensionless lensing efficacy ouwaneter. Fo=0.025 (Turner ct al.," We take a conservative value of the dimensionless lensing efficacy parameter, $F=0.025$ (Turner et al." + 1981)., 1984). + The results are relatively insensitive to details of the mass function. and calculations with a PS distribution (Press&Schechter1971) of galaxy masses yields similar results.," The results are relatively insensitive to details of the mass function, and calculations with a PS distribution \citep{ps74} of galaxy masses yields similar results." + Although aking all of the iuatter in the Universe to be in isothermal spheres is a great oversirplification. it is to © Cluphasized that effective modeling of may strone-eusiug systems is accomplished with isothermal mass distributions (Ikoopiuaus&Fassnacht1999:Witt.Mao.&Weeton2000:Colietal.2001).," Although taking all of the matter in the Universe to be in isothermal spheres is a great oversimplification, it is to be emphasized that effective modeling of many strong-lensing systems is accomplished with isothermal mass distributions \citep{kf99,wmk00,cohn01}." +.2 Althougli NEW xofiles (Navarro.Freuk.&White1996) are expected o be a better approximation to the mass distribution of inassive halos. barvous are expected to isotherinalize he matter distributions for halos of galaxy lass and low Cxochauck&White2001).," Although NFW profiles \citep{nfw96} are expected to be a better approximation to the mass distribution of massive halos, baryons are expected to isothermalize the matter distributions for halos of galaxy mass and below \citep{kochwhite01}." +" Porciani&Madau(2000). have undertaken a study of leusiug in cold dark uatter universes with a PS distribution of galaxy masses, where NEW profiles are utilized. for massive halos (m>35s1015 NEL) and sineular isothermal spherical profiles are used otherwise."," \citet{pm00} have undertaken a study of lensing in cold dark matter universes with a PS distribution of galaxy masses, where NFW profiles are utilized for massive halos $m>3.5\times10^{13}\mbox{ M}_\sun$ ), and singular isothermal spherical profiles are used otherwise." + Our extremely simplified model agrees with their results to within ~20%., Our extremely simplified model agrees with their results to within $\sim20\%$. + Our results are also cousistent with the CLASS data., Our results are also consistent with the CLASS data. +" Data in cosiuology in recent. years has been pointing to a “cosmic concordance model (Balicalletal.1999).. with OQ,=1/3. Q4= 2/3. aud My=70lausecàMpe.H1. and we restrict our attention to this model in what follows."," Data in cosmology in recent years has been pointing to a “cosmic concordance” model \citep{bops99}, with $\Omega_m=1/3$, $\Omega_\Lambda=2/3$ , and $H_0=70\mbox{ +km}\,\mbox{sec}^{-1}\,\mbox{Mpc}^{-1}$, and we restrict our attention to this model in what follows." + The ikelihood results in Fig., The likelihood results in Fig. + 1. imiply that 0.05% of sources at redshift 2=1 would be expected to be multiply imaged on arcsecond scales., \ref{opt_depth1} imply that $0.05\%$ of sources at redshift $z=1$ would be expected to be multiply imaged on arcsecond scales. + At present roughly 100 hish-: SNe wave been observed (nostlv at 2z 0.5). aud thus it is quite unlikely that any of them are multiply aged.," At present roughly $100$ $z$ SNe have been observed (mostly at $z\approx0.5$ ), and thus it is quite unlikely that any of them are multiply imaged." + The situation is more bleak than the uunbers indicate. jowever. as even if oue of the observed high-: SNe happeus o be multiph-iuaged. it is exceedinely uulikelv that we would stumble upon successive Wages.," The situation is more bleak than the numbers indicate, however, as even if one of the observed $z$ SNe happens to be multiply-imaged, it is exceedingly unlikely that we would stumble upon successive images." + The situation is much brighter if SNAP flies., The situation is much brighter if SNAP flies. +" SNAP ""optical? (0.35 1.0 µια) imager would observe 3.800 type Ta SNe per vear. with detailed follow-up (vestframe D-baud photometry and spectra) of a subsample of 2.100 (100 at 2>L2. and all at :zx 1.2)."," SNAP's “optical” $0.35$ $1.0\,\mu\mbox{m}$ ) imager would observe 3,800 type Ia SNe per year, with detailed follow-up (restframe $B$ -band photometry and spectra) of a subsample of 2,400 (100 at $z>1.2$, and all at $z\leq1.2$ )." +" By checking whether prior nuages have appeared nearby (within 15"") when selecting lieh-: SNe for follow-up. SNAP can assure that every multiplv-imased type Ia SN has at least one image with a vedshift aud absolute maeuification determination."," By checking whether prior images have appeared nearby (within $15\arcsec$ ) when selecting $z$ SNe for follow-up, SNAP can assure that every multiply-imaged type Ia SN has at least one image with a redshift and absolute magnification determination." + The ratio of the optical fluxes then allows a determination of the absolute magnification of all other images., The ratio of the optical fluxes then allows a determination of the absolute magnification of all other images. + Couvolviug the optical depth curve of Fig., Convolving the optical depth curve of Fig. + 1. with the expected redshift distribution of SNAP SNe (0lativelw flat. with 1.500 type Ta’s/vear at 12<2<17) vields an expectation of 2 multiply imaged Ia SNe per vear.," \ref{opt_depth1} with the expected redshift distribution of SNAP SNe (relatively flat, with $1,500$ type $/$ year at $1.23% of the Guilonsed) source fx will f observed., Therefore lensed images which have $>3\%$ of the (unlensed) source flux will be observed. + From our simplified SUM calculations. we Bud that of strouely-leuscd eveuts are at least this xisbt.," From our simplified SUM calculations, we find that of strongly-lensed events are at least this bright." + SNAP will sce everv type Ia SN out to redshift 1.5 iu its deep fields. aud will observe the vast majority of strong leusiug eveuts of these sources. thereby uiniizine naeuification bias in the strong lensing sample.," SNAP will see every type Ia SN out to redshift 1.7 in its deep fields, and will observe the vast majority of strong lensing events of these sources, thereby minimizing magnification bias in the strong lensing sample." + SNAP will also see a verv large sample of tvpe II SNe (though only a tiny fraction of these will have detailed ollow-ups)., SNAP will also see a very large sample of type II SNe (though only a tiny fraction of these will have detailed follow-ups). +" While these are significantly dimuuer (peak value 2.3 maguitudes below the Ia peak Gu restframe B- wand). with a dispersion of 1.2 mag (Cillilaud.ποσο,&Phillips 1999))). they also occur at πιο hüeher rates (3 tues more frequent at present day. rising to 510 times nore frequent at redshift 12 (Sullivanctal. 2000)))."," While these are significantly dimmer (peak value 2.3 magnitudes below the Ia peak (in restframe $B$ -band), with a dispersion of 1.3 mag \citep{gnp99}) ), they also occur at much higher rates (3 times more frequent at present day, rising to 5–10 times more frequent at redshift 1–2 \citep{sensm00}) )." + Taking a conservative value of 5 times the Ia rate. we fiud hat SNAP would have 10 multiph-imaged type II SNe iu its sample per ver.," Taking a conservative value of 5 times the Ia rate, we find that SNAP would have 10 multiply-imaged type II SNe in its sample per year." + SNAP will catch the average SN Il eveut oulv 1.5 maguitudes below peak. aud so will uss inaeges demaenified to less than of the uuleused flux.," SNAP will catch the average SN II event only 1.5 magnitudes below peak, and so will miss images demagnified to less than of the unlensed flux." + Convolviug the large iutriusic dispersion in type II peak buiehtucss with the distribution of image pair maguifications (frou our SUM calculations). we find that of multiph-nuaged type IIs will be observable. vielding an expected total of 6 events por vear.," Convolving the large intrinsic dispersion in type II peak brightness with the distribution of image pair magnifications (from our SUM calculations), we find that of multiply-imaged type IIs will be observable, yielding an expected total of 6 events per year." + For these svsteiis. SNAP optical imager light curve will provide a precise determinations of the image time delays. separations. aud relative fluxes," For these systems, SNAP's optical imager light curve will provide a precise determination of the image time delays, separations, and relative fluxes." + As one does not require the standard candle Iuuinosities of leused SNe to do strong-leusius science (see Sec., As one does not require the standard candle luminosities of lensed SNe to do strong-lensing science (see Sec. + P. and 5)). stronely lensed type II svstems are a valuable contribution to the leus datahase.," \ref{S:cosmo} + and\ref{S:hubble}) ), strongly lensed type II systems are a valuable contribution to the lens database." + Combining the rate for SNe Ia aud IL. we couscrvatively estimate that SNAP would detect cight multiph-iaged SNe per vear.," Combining the rate for SNe Ia and II, we conservatively estimate that SNAP would detect eight multiply-imaged SNe per year." + Let us therefore assmue that SNAP will fly. and explore the science that can be done with," Let us therefore assume that SNAP will fly, and explore the science that can be done with" +Lancdstreet (1979) investigated eight helium-strong stars. inding six new magnetic stars.,"Landstreet (1979) investigated eight helium-strong stars, finding six new magnetic stars." + In that. paper. the authors established that. a defining characteristic of the helium-strong stars is the presence of an strong. organized magnetic ielcl.," In that paper, the authors established that a defining characteristic of the helium-strong stars is the presence of an strong, organized magnetic field." +" LR 7355 (11D elisa.2180. the subject of the present. paper. is à bright (V—6."" carly eee star with veh resin’ (320 st. Abt ο al 2002: 270km Glebocki Stawikowski 2000)."," HR 7355 (HD 182180), the subject of the present paper, is a bright (V=6.02) helium-strong early B-type star with high $v \sin i$ (320 km $^{-1}$, Abt et al 2002; 270 km $^{-1}$, Glebocki Stawikowski 2000)." + Originally classified as D51V ον Morris (1961J. Hiltner οἱ al. (," Originally classified as B5IV by Morris (1961), Hiltner et al. (" +1969) re-classified LB. 7355 D2Vn. a classification that. has been used: subsequently.,"1969) re-classified HR 7355 B2Vn, a classification that has been used subsequently." + LR 7355 has also been classified. as a classical Be star (Abt Cardona. 1984) due to observed: emission in. the Lle line of its spectrum., HR 7355 has also been classified as a classical Be star (Abt Cardona 1984) due to observed emission in the $\alpha$ line of its spectrum. + HIPPATRCOS photometry exhibits Pvariability with a period of 0.26 davs (Ixoen Ever 2002)., HIPPARCOS photometry exhibits variability with a period of $\sim$ 0.26 days (Koen Eyer 2002). + Livinius et. al. , Rivinius et al. ( +2008) reported: emission ancl variability. of 1e Ho. profiles. as well as variability of a variety of spectral bsorption lines(i.e. Hle. €. Si).,"2008) reported emission and variability of the $\alpha$ profiles, as well as variability of a variety of spectral absorption lines (i.e. He, C, Si)." + Those authors revisited 1 HIPPATHCOS photometry noting that a period of0.52 days (twice the period. reported: by lxoen Ever (2002)) could. also explain the photometric variation., Those authors revisited the HIPPARCOS photometry noting that a period of 0.52 days (twice the period reported by Koen Eyer (2002)) could also explain the photometric variation. + Ultimately. xwed on the helium variability. the variable Lla emission. and the character of the photometric variation. Rivinius et al. (," Ultimately, based on the helium variability, the variable $\alpha$ emission, and the character of the photometric variation, Rivinius et al. (" +2008) proposed that Εν 7355 hosts à. structured magnetosphere qualitatively similar to that of σ Ori E. With its very rapid. rotation. the establishment of such a magnetosphere around LER 7355 would be of ercat interest.,"2008) proposed that HR 7355 hosts a structured magnetosphere qualitatively similar to that of $\sigma$ Ori E. With its very rapid rotation, the establishment of such a magnetosphere around HR 7355 would be of great interest." + We have therefore undertaken. observations to search for the presence of a magnetic field in this star. and to further explore its spectroscopic and other physical properties.," We have therefore undertaken observations to search for the presence of a magnetic field in this star, and to further explore its spectroscopic and other physical properties." + We obtained S high resolution (11265000). broadband (370-1040 nm) spectra from πο spectropolarimeter ESPaDOns attached to the 3.6-m. Canada-Lrance-Llawaii Telescope. as part of the Alagnetism in. Massive. Stars (MiMeS) Large. Program (Wade ct al.," We obtained 8 high resolution (R=65000) broadband (370-1040 nm) spectra from the spectropolarimeter ESPaDOnS attached to the 3.6-m Canada-France-Hawaii Telescope, as part of the Magnetism in Massive Stars (MiMeS) Large Program (Wade et al." + 2009)., 2009). + The data were obtained over the course of three nights in September 2009., The data were obtained over the course of three nights in September 2009. + Phe log of observations is reported. in Table. 1.., The log of observations is reported in Table \ref{magfield}. + Reduction was performed. at. the. observatory with the Upena pipeline feeding the Libre-IESpUE reduction package (Donati et al., Reduction was performed at the observatory with the Upena pipeline feeding the Libre-ESpRIT reduction package (Donati et al. + 1997). which— vields the Stokes E (intensity) and Stokes V. (circular. polarization) spectrum. as well as. the diagnostic null spectrum (N). which diagnoses any spurious contribution to the polarization measurement.," 1997), which yields the Stokes I (intensity) and Stokes V (circular polarization) spectrum, as well as the diagnostic null spectrum (N), which diagnoses any spurious contribution to the polarization measurement." + Conventionally. four consecutive sub-exposures are combined to produce one MN spectrum.," Conventionally, four consecutive sub-exposures are combined to produce one polarization spectrum." + However. as cach sub-exposure is 1200. seconds in duration (= 0.014 cays). the combination of four sub-exposures into a single spectrum: would. correspond. to a significant fraction (5 or 104) of the rotation period of this star.," However, as each sub-exposure is 1200 seconds in duration (= 0.014 days), the combination of four sub-exposures into a single spectrum would correspond to a significant fraction (5 or ) of the rotation period of this star." + We therefore. processed. the observations. combining only sets of (wo sub-exposures for a total exposure time of 2400 s. Phe consequence of this change will decrease the signal to noise ratio (bv a [factor of ~ V2) of the spectrum. and to lose our ability to diagnose first-order. systematic errors in the time domain.," We therefore processed the observations, combining only sets of two sub-exposures for a total exposure time of 2400 s. The consequence of this change will decrease the signal to noise ratio (by a factor of $\sim \sqrt{2}$ ) of the spectrum, and to lose our ability to diagnose first-order systematic errors in the time domain." + The primary. benefit. however. is to reduce the exposure. time by hall and. to. thereby better resolve the rotational variation of the spectrum and maenetic field.," The primary benefit, however, is to reduce the exposure time by half, and to thereby better resolve the rotational variation of the spectrum and magnetic field." + leginning on July.nei 24. 2008. we conducted three nights (204 data points) of Cousins V. filter photometry of LR 7355. using the 0.9 m. CFIO telescope. operated bv the consortium with a 20482046. CCD detector.," Beginning on July 24, 2008, we conducted three nights (204 data points) of Johnson-Cousins V filter photometry of HR 7355, using the 0.9 m CTIO telescope operated by the consortium with a $2048 \times 2046$ CCD detector." + Variable weather plagued the first. ancl fourth nights of observation: the second. night provided. no data due to weather., Variable weather plagued the first and fourth nights of observation; the second night provided no data due to weather. + A neutral density. filter was employed. to prevent CCD saturation., A neutral density filter was employed to prevent CCD saturation. + The observations were reduced using stancarcd procedures (flat [ielding. zero subtraction. ete)," The observations were reduced using standard procedures (flat fielding, zero subtraction, etc.)" + inIRAF., in. + Aperture photometry was emploved to extract differential photometrie indices for LR. 7355. which were then calibrated against a nearby comparison star. CD-28 15755.," Aperture photometry was employed to extract differential photometric indices for HR 7355, which were then calibrated against a nearby comparison star, CD-28 15755." + We do not emplov a photometric standard. star. since we are primarily interested in changes to the brightness of LR 7355.," We do not employ a photometric standard star, since we are primarily interested in changes to the brightness of HR 7355." + Cosmic rays were removed. using the programCosMIC. a Laplacian edge detection approach described by van Dokkum (2001).," Cosmic rays were removed using the program, a Laplacian edge detection approach described by van Dokkum (2001)." + Accditionally. archival IUIS data were used to help obtain the fundamental parameters of LIU 7355 (see 833).," Additionally, archival IUE data were used to help obtain the fundamental parameters of HR 7355 (see 3)." +" “Phe two IVE eCtra were taken over a Driod of two weeks. one on Aug.""2! En (11 SWP 39549 ) and nuntthe other on Sept. 7. ) 39596 L)."," The two IUE spectra were taken over a period of two weeks, one on Aug. 29, 1990 (H SWP 39549 L) and the other on Sept. 7, 1990 (H SWP 39596 L)." + 30th were taken using the IUIS large aperture., Both observations were taken using the IUE large aperture. + In order to determine the photospheric parameters of llt 7355 we used a comprehensive grid. of metal line blanketed. non-L'TE mocels from PLUSTY (Lanz Llubeny 2007) and also the SYNSPEC line M code.," In order to determine the photospheric parameters of HR 7355 we used a comprehensive grid of metal line blanketed, non-LTE models from TLUSTY (Lanz Hubeny 2007) and also the SYNSPEC line formation code." +" Elective temperatures (Ziaur) from 15000 I to ""ni . n(steps of 1000 Ix) and surface gravities (log g) from 3.0 to -- ""n(steps of 0.25 dex) were considered to model the ical and UV", Effective temperatures $T_{\rm{eff}}$ ) from 15000 K to 22000 K (steps of 1000 K) and surface gravities (log $g$ ) from 3.0 to 4.0 (steps of 0.25 dex) were considered to model the observed optical and UV . +Phase self-calibration (or se/fea/) is an algorithm often used in the calibration of radio astronomical data.,Phase self-calibration (or ) is an algorithm often used in the calibration of radio astronomical data. + It was introduced by Readhead Wilkinson (1978)) and Cotton (1979)). and it has been essential for the success of Very Long Baseline Interferometry (VLBI) imaging.," It was introduced by Readhead Wilkinson \cite{Readhead1978}) ) and Cotton \cite{Cotton1979}) ), and it has been essential for the success of Very Long Baseline Interferometry (VLBI) imaging." + Also. the antenna-based calibrations obtained from the algorithm (Schwab Cotton 1983)) are equivalent to a phase self-calibration.," Also, the antenna-based calibrations obtained from the algorithm (Schwab Cotton \cite{Schwab1983}) ) are equivalent to a phase self-calibration." + The phase selfeal will also be an algorithm widely used with future interferometric instruments. such as the Atacama Large Millimeter Array (ALMA) or the Square Kilometre Array (SKA). now under construction or planned.," The phase selfcal will also be an algorithm widely used with future interferometric instruments, such as the Atacama Large Millimeter Array (ALMA) or the Square Kilometre Array (SKA), now under construction or planned." + Optical interferometric observations (like those in the Very Large Telescope Interferometry. VLTD. will also eventually benefit from some form of selfcal. although closure phases and amplitudes are measured in optical interferometry in à very different way than in radio.," Optical interferometric observations (like those in the Very Large Telescope Interferometry, VLTI) will also eventually benefit from some form of selfcal, although closure phases and amplitudes are measured in optical interferometry in a very different way than in radio." + Thus. the statistical analysis presented here may need some substantial changes to rigorously describe the probability of false detections by optical interferometers.," Thus, the statistical analysis presented here may need some substantial changes to rigorously describe the probability of false detections by optical interferometers." + Given that part of the interferometric observations obtained from all those instruments may come from very faint sources. it is important to take into account the undesired and uncontrollable effects that the instrumentation and/or the calibration and analysis algorithms applied to the data could introduce in the interferometric observations.," Given that part of the interferometric observations obtained from all those instruments may come from very faint sources, it is important to take into account the undesired and uncontrollable effects that the instrumentation and/or the calibration and analysis algorithms applied to the data could introduce in the interferometric observations." + A deep study of all our analysis tools and their effects on noisy data 1s essential for discerning the reliability of detections of very faint sources., A deep study of all our analysis tools and their effects on noisy data is essential for discerning the reliability of detections of very faint sources. + Some discoveries made by pushing the interferometric instruments to their sensitivity limits could turn out to be the result of artifacts produced by the analysis tools., Some discoveries made by pushing the interferometric instruments to their sensitivity limits could turn out to be the result of artifacts produced by the analysis tools. + The main limitations of the phase self-calibration algorithm have been analyzed in many publications (e.g.. Linfield 1986.. Wilkinson et al. 1988)).," The main limitations of the phase self-calibration algorithm have been analyzed in many publications (e.g., Linfield \cite{Linfield1986}, Wilkinson et al. \cite{Wilkinson1988}) )." + It is well known that an unwise use of selfeal can lead to imperfect images. even to the generation of spurious source components. elimination of real components. and deformation of the structure of extended sources.," It is well known that an unwise use of selfcal can lead to imperfect images, even to the generation of spurious source components, elimination of real components, and deformation of the structure of extended sources." + In this paper. we focus on the effects that phase self-calibration produces when applied to pure noise.," In this paper, we focus on the effects that phase self-calibration produces when applied to pure noise." + We show that selfcal can generate a spurious source from pure noise. with a relatively high flux density compared to the rms of the visibility amplitudes.," We show that selfcal can generate a spurious source from pure noise, with a relatively high flux density compared to the rms of the visibility amplitudes." + We analytically and numerically study how the recoverable flux density of such a spurious. source depends on the details of the observations (the sensitivity of the interferometer. the number of antennas. and the averaging time of the selfcal solutions).," We analytically and numerically study how the recoverable flux density of such a spurious source depends on the details of the observations (the sensitivity of the interferometer, the number of antennas, and the averaging time of the selfcal solutions)." + Finally. we study the effects of phase self-calibration applied to the visibilities resulting from observations of real faint sources. instead of pure noise.," Finally, we study the effects of phase self-calibration applied to the visibilities resulting from observations of real faint sources, instead of pure noise." + We present two simple tests that can be applied to real data in order to check whether a given faint source is real or not. and apply these tests to real data. corresponding to VLBI observations of the radio supernova 22004et (Martí-Vidal et al. 2007)).," We present two simple tests that can be applied to real data in order to check whether a given faint source is real or not, and apply these tests to real data, corresponding to VLBI observations of the radio supernova 2004et (Martí–Vidal et al. \cite{MartiVidal2007}) )." + The basics of phase self-calibration can be found in many publications (e.g.. Readhead Wilkinson 1978.. Schwab 1980)).," The basics of phase self-calibration can be found in many publications (e.g., Readhead Wilkinson \cite{Readhead1978}, Schwab \cite{Schwab1980}) )." + Here. we explain the essence of this algorithm in a few lines.," Here, we explain the essence of this algorithm in a few lines." + Let us suppose that we have made an interferometric observation using a set of N antennas., Let us suppose that we have made an interferometric observation using a set of $N$ antennas. + We obtain one visibility. Vij. for each baseline. that is. for each pair of antennas G./).," We obtain one visibility, $V_{ij}$, for each baseline, that is, for each pair of antennas $(i,j)$." +" Let us call ;; the phase of the visibility V;;. Any atmospheric or instrumental effect on the optical path of the signals that arrived to antennas / and / will affect the phase 4j; in the way: where &/"""" represents all the undesired (i.e.. atmospheric and instrumental) contributions to the optical path of the signal received by the antenna / and the contribution to the phase that comes purely from the structured of the observed source. that is.the so calledphase."," Let us call $\phi_{ij}$ the phase of the visibility $V_{ij}$ Any atmospheric or instrumental effect on the optical path of the signals that arrived to antennas $i$ and $j$ will affect the phase $\phi_{ij}$ in the way: where $\phi^{atm}_{l}$ represents all the undesired (i.e., atmospheric and instrumental) contributions to the optical path of the signal received by the antenna $l$ and $\phi^{str}_{ij}$ the contribution to the phase that comes purely from the structure of the observed source, that is,the so called." + It can be easily shown that the quantities known asphases. and defined as (Jennison 1958.. Rogers et al. 1974)):," It can be easily shown that the quantities known as, and defined as (Jennison \cite{Jennison1958}, Rogers et al. \cite{Rogers1974}) ):" +" are independent of 67"".", are independent of $\phi^{atm}_{l}$. + That is. the closure phases Οκ are only defined by the structure of the observed source.," That is, the closure phases $C_{ijk}$ are only defined by the structure of the observed source." + Thus. they are independent of any atmospheric or instrumental contribution that may affect the signals received. by the antennas of the interferometer.," Thus, they are independent of any atmospheric or instrumental contribution that may affect the signals received by the antennas of the interferometer." +"The phase self-calibration algorithm takes advantage of the closure phases toestimate the undesired antenna-dependent contributions 7"".",The phase self-calibration algorithm takes advantage of the closure phases toestimate the undesired antenna-dependent contributions $\phi^{atm}_{l}$ . + In short. the phase," In short, the phase" +"cut-ofÉ radius. r,.","cut-off radius, $r_t$." + Once a mass distribution model is assumed. (he expected Nice can be deduced projecting the 5galaxy cluster spatial mass distribution and taking5 into account a GC formation efficiency.," Once a mass distribution model is assumed, the expected $N_{\rm IGC}$ can be deduced projecting the galaxy cluster spatial mass distribution and taking into account a GC formation efficiency." + The latter is à measure of the fraction of mass converted into GCs., The latter is a measure of the fraction of mass converted into GCs. + MeLaughlin.(1999) defined the GC! lormation efficiency in galaxiesas where Poo. Peas. Ad ως ave the mass densities of GCs. gas. and stars in the galaxy. respectively.," \citet{M99} defined the GC formation efficiency in galaxiesas where $\rho_{\rm GC}$, $\rho_{\rm gas}$, and $\rho_{\rm +stars}$ are the mass densities of GCs, gas, and stars in the galaxy, respectively." + MeLaughlin(1999) found this definition of ec;c to be universal [rom galaxy {ο ealaxy ancl equal to 0.002640.0005., \citet{M99} found this definition of $\epsilon_{GC}$ to be universal from galaxy to galaxy and equal to $0.0026 \pm 0.0005$. +" We will use here a similar definition for the intergalactic medium that. for convenience. we deline in terms of surface density: where Nice is the surface mass density of [GCs and My, is the barvonie surface mass density of the galaxy cluster obtained projecting p(HR)."," We will use here a similar definition for the intergalactic medium that, for convenience, we define in terms of surface density: where $\Sigma_{\rm IGC}$ is the surface mass density of IGCs and $\Sigma_{\rm tot}$ is the baryonic surface mass density of the galaxy cluster obtained projecting $\rho(R)$." + The relation between the barvonic surface mass density and the IGC surface number density is given by where Gi7)ce is the mean mass ofa GC., The relation between the baryonic surface mass density and the IGC surface number density is given by where $\langle m\rangle_{\rm GC}$ is the mean mass of a GC. + Assuming ο=24x10? (MeLaughlin.1999).. the lower panel of Fig.," Assuming $\langle m\rangle_{\rm GC}=2.4\times10^5$ \citep{M99}, the lower panel of Fig." + 4. shows Mooές as a function of 2 for the (hree mass distribution models plotted in the upper panel., \ref{massdis} shows $N_{\rm IGC}/\hat\epsilon_{\rm IGC}$ as a function of $R$ for the three mass distribution models plotted in the upper panel. +" This figure shows that the barvonic mass distribution model required (o. produce an approximately constant. non-null. ος distribution. along Coma (up to Re200"". at least) should be similar to a very extended homogeneous sphere."," This figure shows that the baryonic mass distribution model required to produce an approximately constant, non-null, $N_{\rm IGC}$ distribution along Coma (up to $R\simeq 200 \arcmin$, at least) should be similar to a very extended homogeneous sphere." + The unrealistic nature of this model indicates that a value as low as ?=0.30 for the slope ol the faint end of n(n) is unlikely., The unrealistic nature of this model indicates that a value as low as $\gamma=0.30$ for the slope of the faint end of $n(m)$ is unlikely. + Moreover. it suggests that the IGC surface density. Noo. is actually zero all over Coma. with the probable exception of the surroundings of the central galaxy.," Moreover, it suggests that the IGC surface density, $N_{\rm IGC}$, is actually zero all over Coma, with the probable exception of the surroundings of the central galaxy." + The value of 5 that reduces the mean (Vice) to zero (excluding the central value) can be calculated [rom interpolation in the data listed in Table 3. ancl turns out to bes—0.362: 0.01., The value of $\gamma$ that reduces the mean $\langle N_{\rm IGC}\rangle$ to zero (excluding the central value) can be calculated from interpolation in the data listed in Table \ref{meanIGC} and turns out to be $\gamma=0.36\pm0.01$ . + The former is the slope of n(in) bevond the detection limit of A=23.5 reached by Tyson(1983) and Steidel&Hamilton(1993) and is valid at least down to the /? magnitude, The former is the slope of $n(m)$ beyond the detection limit of $R=23.5$ reached by \citet{T88} and \citet{SH93} and is valid at least down to the $R$ magnitude +"deductions. we get the critical angle @,..;, of the magnetic line at the surface of the dise as follows In the non-rotating black hole ease. @=0. we have aij,=60. which is same as that obtained by Blandford and Payne (1982) for the non-relativistic case.","deductions, we get the critical angle $\alpha_{crit}$ of the magnetic line at the surface of the disc as follows In the non-rotating black hole case, $a=0$, we have $\alpha_{crit}= 60^{\circ}$, which is same as that obtained by Blandford and Payne (1982) for the non-relativistic case." + In Fig., In Fig. + | we depict the relations between the critical angle and radial position of the footpoint of the magnetic line for the rotating black hole with different angular momentum «e., 1 we depict the relations between the critical angle and radial position of the footpoint of the magnetic line for the rotating black hole with different angular momentum $a$. + The configuration and strength of the magnetic field of the dise plays a crucial role on the dynamical properties of the centrifugally driven magnetohydrodynamic flow., The configuration and strength of the magnetic field of the disc plays a crucial role on the dynamical properties of the centrifugally driven magnetohydrodynamic flow. + Assuming that the field configuration above the dise is close to a potential field. the shape of the disc field is determined entirely by the magnetic field D. at the dise surface.," Assuming that the field configuration above the disc is close to a potential field, the shape of the disc field is determined entirely by the magnetic field $B_{z}$ at the disc surface." + The elements of the cold magnetic driven flows behave like beads on the magnetic field lines., The elements of the cold magnetic driven flows behave like beads on the magnetic field lines. + Whether the matter at the dise surface can be flung out mainly depends on the inclination angle of the field line at the dise surface (Blandford and Payne 1982)., Whether the matter at the disc surface can be flung out mainly depends on the inclination angle of the field line at the disc surface (Blandford and Payne 1982). + Blandford and Payne (1982) point out that the flow can be centrifugally driven if the field lines, Blandford and Payne (1982) point out that the flow can be centrifugally driven if the field lines +The observations used were carried out with the detector of theROSAT observatory during two pointed observations in AlavJune and November 1992.,The observations used were carried out with the detector of the observatory during two pointed observations in May-June and November 1992. + The satellite. N-ray telescope (XRT) aud the focal plane detector (PSPC) are described in detail in ΜΕ. (1983) and Pfefferiuann et al. (," The satellite, X-ray telescope (XRT) and the focal plane detector ) are described in detail in Trümmper (1983) and Pfeffermann et al. (" +1986).,1986). + We note that no observations have been performed in the direction of NGC 3109 with theHRI detector ofROSAT., We note that no observations have been performed in the direction of NGC 3109 with the detector of. + The data of the two poiutiues given in Table 1. have been retrieved from the publicROSAT ichive., The data of the two pointings given in Table \ref{tab:pointing} have been retrieved from the public archive. + The data sets from the two observations have been merged to one data set using standard procedures (Ziniieruauu ot al., The data sets from the two observations have been merged to one data set using standard procedures (Zimmermann et al. + 1991)., 1994). + Three detection procedures (local. map. and maxima likelihood) were applied to the merged pointings using conunands (Ziuuunermiuin e al.," Three detection procedures (local, map, and maximum likelihood) were applied to the merged pointings using commands (Zimmermann et al." + 1991)., 1994). + In. the local aud map detection a square shaped detection cell is slid over the nuage., In the local and map detection a square shaped detection cell is slid over the image. + Source counts are determined within the cell. background. counts either from au area surrounding the cell. (local backeround) or from a (smoothed) background tage within the same cell.," Source counts are determined within the cell, background counts either from an area surrounding the cell (local background) or from a (smoothed) background image within the same cell." + Iu the maximaun likelihood detection the distribution of the detected photous above the background is compared in a maximi likelihood ratio test with the analytical poiut-spread function., In the maximum likelihood detection the distribution of the detected photons above the background is compared in a maximum likelihood ratio test with the analytical point-spread function. + The analysis was performed in the five cucrey chamucl ranecs Soft = (chaunel 11-11. 0.1-0.1 keV). Tard = (channel 52-201. 0.5-2.1. keV). Uardl = (channel 52-90. 0.5-0.9 keV) aud Tard? = (channel 91-201. 0.9-2.0 keV) and broad (0.1-2.1 keV).," The analysis was performed in the five energy channel ranges Soft = (channel 11-41, 0.1-0.4 keV), Hard = (channel 52-201, 0.5-2.1 keV), Hard1 = (channel 52-90, 0.5-0.9 keV) and Hard2 = (channel 91-201, 0.9-2.0 keV) and broad (0.1-2.4 keV)." + The five source lists were mereed to one final source list taking detections at off-axis angles x5 iuto account., The five source lists were merged to one final source list taking detections at off-axis angles $\le$ into account. + The maxiumun likelihood. aleorithii was used to determine the final source position. the counts in five energv bands aud the source exteut.," The maximum likelihood algorithm was used to determine the final source position, the counts in five energy bands and the source extent." + A ouc-dimensional energv and position dependent Cassia distribution was applied in order to obtain the source extent., A one-dimensional energy and position dependent Gaussian distribution was applied in order to obtain the source extent. + The source extent (Lut) is given as the Gaussian OCtauss ILuduess ratios ZZRIL and ΠΠ were caleulated from the counts in the bands as “RL=(IIS)/(Il|5) and JIR2=(II2ΠΠ|II), The source extent $Ext$ ) is given as the Gaussian $\sigma_{\rm Gauss}$ Hardness ratios $H\!R1$ and $H\!R2$ were calculated from the counts in the bands as $H\!R1=(H-S)/(H+S)$ and $H\!R2=(H2-H1)/(H1+H2)$. + The existence Bikelibood ratio and the extent likelihood rafio was calculated according to Cash (1979) and Cruddace et al. (, The existence likelihood ratio and the extent likelihood ratio was calculated according to Cash (1979) and Cruddace et al. ( +1988).,1988). + We selected for our final source catalog ouly detecions with au existence likelihood ratio10. which is equal to a probability of existence7).," We selected for our final source catalog only detections with an existence likelihood ratio, which is equal to a probability of existence." + We give the value for the extent oulv in case the exteut likelihood ratio is 20., We give the value for the extent only in case the extent likelihood ratio is . +" A 90% source error radius was caleulated. adding quadratically a svsteiatic error of 5"" ((cf."," A $90\%$ source error radius was calculated, adding quadratically a systematic error of $5$ (cf." + Ister 1993)., Kürrster 1993). + The positional error derived for large off-axis aueles nay be somewhat unuderestinated due to the asviuuetry of the poiut-spread-fuuctiou., The positional error derived for large off-axis angles may be somewhat underestimated due to the asymmetry of the point-spread-function. + But the positional error should not be larger than οντήν, But the positional error should not be larger than $\sim$. + We finally screened the catalog of sources by displaying the positions of these sources on the hard. soft. and broad bandROSATPSPC image.," We finally screened the catalog of sources by displaying the positions of these sources on the hard, soft, and broad band image." + We could confirm 91 of the detected sources., We could confirm 91 of the detected sources. + This screened catalog of poiutlike and moderately extended sources is giveu iu Table 6., This screened catalog of pointlike and moderately extended sources is given in Table 6. + We eive iu the first colum of the catalog for cach confirmed source the sequence ΠΕ and iu the second column the source umber (from the catalog of uuscreenued detectious)., We give in the first column of the catalog for each confirmed source the sequence number and in the second column the source number (from the catalog of unscreened detections). + We always refer to the source ο in the text., We always refer to the source number in the text. + Iu Fig., In Fig. + 1 we show theROSAT image of the NGC 3109 field in the hard baud (0.5 2.0 keV)., \ref{ps:figros} we show the image of the NGC 3109 field in the hard band (0.5 – 2.0 keV). + We note that the dwarf spheroidal galaxy Autila which is ~1.°22 tto thesouth of NGC 3109 is outside of the observed field, We note that the dwarf spheroidal galaxy Antila which is $\sim$ to thesouth of NGC 3109 is outside of the observed field +According to the standard. gravitational instability picture present-day cosmic structures have evolved. from. tiny initial Wuctuations in the mass density Ποια that) obey Gaussian statistics.,According to the standard gravitational instability picture present-day cosmic structures have evolved from tiny initial fluctuations in the mass density field that obey Gaussian statistics. + However. departures from. Caussianity inevitably arise at some level during the inflationary epoch.," However, departures from Gaussianity inevitably arise at some level during the inflationary epoch." + “Phe various mechanisms that produce primordial non-CGaussianitv during inflation have been thoroughly investigated. by ? (ancl references therein)., The various mechanisms that produce primordial non-Gaussianity during inflation have been thoroughly investigated by \cite{bartolo04} (and references therein). +" A convenient wav of modeling non-Ciaussianity is to include cquadratic correction in the Dardeen's gauge-invariant potential d: where dj, represents a Gaussian random field and the imensionless parameter [κι quantifies the amplitude of the corrections to the curvature perturbations.", A convenient way of modeling non-Gaussianity is to include quadratic correction in the Bardeen's gauge-invariant potential $\Phi$ : where $\Phi_{\rm L}$ represents a Gaussian random field and the dimensionless parameter $f_{\rm{\rm NL}}$ quantifies the amplitude of the corrections to the curvature perturbations. + The above definition in which the term κι(Pp) is small guarantees that ==0.," The above definition in which the term $-f_{\rm{\rm NL}}\,\langle\Phi_{\rm L}^2\rangle$ is small guarantees that $<\Phi>=<\Phi_{\rm L}>=0$." + Although the quadratic model uantifies the level of primordial non-Gaussianity predicted bv a large number of scenarios for the generation of the initial seeds for structure formation (including standard single-lield. ancl multi-fielel inflation. the curvaton ancl the inhomogeneous reheating scenarios). one should keep in mind that there are dillerent wavs for a density Ποιά to be non-Gaussian (NG) and that different observational tests capable of going bevond. second order statistics should. be used to fully characterize the nature of non-Caussianity.," Although the quadratic model quantifies the level of primordial non-Gaussianity predicted by a large number of scenarios for the generation of the initial seeds for structure formation (including standard single-field and multi-field inflation, the curvaton and the inhomogeneous reheating scenarios), one should keep in mind that there are different ways for a density field to be non-Gaussian (NG) and that different observational tests capable of going beyond second order statistics should be used to fully characterize the nature of non-Gaussianity." + ‘To date. the strongest observational constraint lor NG models are. provided by the recent analysis of the WALAP D-vear temperature Iluctuation maps (?) according to which 9«(νι<11 at the 95% confidence level in the local model.," To date, the strongest observational constraint for NG models are provided by the recent analysis of the WMAP 5-year temperature fluctuation maps \citep{komatsu08} according to which $-9 < f_{\rm NL} +< 111$ at the 95 confidence level in the local model." + Phe Large scale structure (LSS) provides alternative observational constraints which are. in principle. more stringent than the cosmic microwave background (CAIB) since they carry information on the 3D. primordial Iuctuation fields. rather than on a 2D temperature map.," The large scale structure (LSS) provides alternative observational constraints which are, in principle, more stringent than the cosmic microwave background (CMB) since they carry information on the 3D primordial fluctuation fields, rather than on a 2D temperature map." + Moreover. i£ the level of primordial non-CGaussianity depends on scale then CMD and LSS provide independent constraints since they probe dillerent scales.," Moreover, if the level of primordial non-Gaussianity depends on scale then CMB and LSS provide independent constraints since they probe different scales." + For this reason. the WMLATDP 5-vear limits on [κι need not to apply on the smaller scales probed by the LSS andthe NC models that we consider in," For this reason, the WMAP 5-year limits on $f_{\rm{\rm NL}}$ need not to apply on the smaller scales probed by the LSS andthe NG models that we consider in" +estimated GRB values.,estimated GRB values. + The second caveat is the ionization correction. which is more difficult to deal with. as the ionization state of the diffuse IGM is not directly observed and is à matter of ongoing debate 2007).," The second caveat is the ionization correction, which is more difficult to deal with, as the ionization state of the diffuse IGM is not directly observed and is a matter of ongoing debate ." +. The above estimates are all based on the photo-ionization cross section of a neutral absorber., The above estimates are all based on the photo-ionization cross section of a neutral absorber. + An ionized absorber would have a somewhat lower cross seclion al eenergies. and therefore a larger column density would be required to produce the same 7.," An ionized absorber would have a somewhat lower cross section at energies, and therefore a larger column density would be required to produce the same $\tau$." + Caleulating cross sections for different ionization states and different metallicities in the IGAI is bevond the scope of this paper., Calculating cross sections for different ionization states and different metallicities in the IGM is beyond the scope of this paper. + HLowever. in Fig.," However, in Fig." + 7 we plot separately (he contributions to the photo-onization cross section of HH and He. and that ofthe metals with solar composition.," \ref{fig:cs} we plot separately the contributions to the photo-ionization cross section of H and He, and that of the metals with solar composition." + It can be seen that the metals are dominated by II and He below the O edge at 0.54 keV where (hey overtake (he IE and Ile contribution., It can be seen that the metals are dominated by H and He below the O edge at 0.54 keV where they overtake the H and He contribution. + For redshifted absorption itis thus (he metal contribution that mostly determines 7(0.5 keV) unless the metallicity is radically sub-solar., For redshifted absorption it is thus the metal contribution that mostly determines $\tau$ (0.5 keV) unless the metallicity is radically sub-solar. + The pure metal contribution can also be thought of as an upper limit to the cross section for ionized plasma in which IL and Ile are totallv ionized (although in reality the metal contribution also somewhat decreaseswith ionization)., The pure metal contribution can also be thought of as an upper limit to the cross section for ionized plasma in which H and He are totally ionized (although in reality the metal contribution also somewhat decreaseswith ionization). + A 2—1 absorber in which II and Ie are totally transparent. (ionized) would still retain more than of its opacity at 0.5 keV (observed) mostly due to C and O. and that fraction of course needs to be further scaled with the metallicity.," A $z = 1$ absorber in which H and He are totally transparent (ionized) would still retain more than of its opacity at 0.5 keV (observed) mostly due to C and O, and that fraction of course needs to be further scaled with the metallicity." + To summarize (his section. the mean high-: opacity for the diffuse IGAL within the standard cosmological model can explain tlie soft oopacity measured [rom spectra of hieh z GRBs (and quasars) as long as the gas is not too highlv ionized. and as long as the metallicity is à reasonable fraction of the solar value and does not decrease too quickly with redshift.," To summarize this section, the mean $z$ opacity for the diffuse IGM within the standard cosmological model can explain the soft opacity measured from spectra of high $z$ GRBs (and quasars) as long as the gas is not too highly ionized, and as long as the metallicity is a reasonable fraction of the solar value and does not decrease too quickly with redshift." + The low ionization is possible since the (truly diffuse IGM suffered less gravitational collapse than the denser line absorbing IGM svstenis that have been heated to ~109 KIN2001).. The metallicity of 0.2 0.4 solar required to explain the absorption is actually lower than the Fe abundance observed in the hot eas of galaxy. clusters up (o 2=1.32008).. but slightly higher (han (hat implied by supernova rates (Graur et al.," The low ionization is possible since the truly diffuse IGM suffered less gravitational collapse than the denser line absorbing IGM systems that have been heated to $\sim 10^6$ K. The metallicity of 0.2 – 0.4 solar required to explain the absorption is actually lower than the Fe abundance observed in the hot gas of galaxy clusters up to $z = 1.3$, but slightly higher than that implied by supernova rates (Graur et al." + 2011) andthe abundances observed in IGM filaments towards nearby 2<0.4 metal absorbers2003)., 2011) andthe abundances observed in IGM filaments towards nearby $z < 0.4$ metal absorbers. +. Recall that most of the IGM column is accumulated up to z=1—2 (Eq. 2..," Recall that most of the IGM column is accumulated up to $z = 1 - 2$ (Eq. \ref{tau}," + Fig. 10)).," Fig. \ref{fig:igm}) )," + so even a sharp drop in metallicity bevond those redshilts does not change our conclusions., so even a sharp drop in metallicity beyond those redshifts does not change our conclusions. + In fact. the mean metallicity in damped Lyman-o (DLA) absorbers up to z«4 is also consistent wil (hese values.," In fact, the mean metallicity in damped $\alpha$ (DLA) absorbers up to $z < 4$ is also consistent with these values." + although the scatter in metallicity in DLAs 2010).. and in ealaxy clusters 2007).. al any given z is quite large.," although the scatter in metallicity in DLAs , and in galaxy clusters , at any given $z$ is quite large." +The statistical. equilibrium equations. (SEE). and. the radiative transfer coefficients for a two-level atom with HFS. in the spherical statistical tensor representation can be found in LLO4.,"The statistical equilibrium equations (SEE), and the radiative transfer coefficients for a two-level atom with HFS, in the spherical statistical tensor representation can be found in LL04." +" Here we write only the expression of the emission coefficient (in the absence of magnetic fields) with 450.1.2.3 (corresponding respectively to the Stokes parameters 7.Q.U. and V). N the number density of atoms. A(x,J,-αι) the Einstein. coefficient. for spontaneous emission. Th.Q) a geometrical tensor (see Sect."," Here we write only the expression of the emission coefficient (in the absence of magnetic fields) with $j\!=\!0,1,2,3$ (corresponding respectively to the Stokes parameters $I,Q,U,$ and $V$ ), $\mathcal{N}$ the number density of atoms, $A(\alpha_{u}J_{u} \to \alpha_{\ell} J_{\ell})$ the Einstein coefficient for spontaneous emission, ${\mathcal{T}}_{Q}^{K}(j,\mathbf{\Omega})$ a geometrical tensor (see Sect." + 5.11 of LLO4). and d the profile of the line.," 5.11 of LL04), and $\Phi$ the profile of the line." + The indices { and uv have the usual meaning of lower and upper (level). respectively.," The indices $\ell$ and $u$ have the usual meaning of lower and upper (level), respectively." + It is important to recall that Eq. (5)).," It is important to recall that Eq. \ref{eq:epsilon}) )," +" and the SEE needed to find the spherical statistical tensors p""CE,FL)) two-levelare valid under thea"," and the SEE needed to find the spherical statistical tensors $\rho^K_Q(F_u,F_u^{\prime})$ are valid under the." +pproximation. For a atom with HFS. this approximation requires that the incident radiation field should be flat (1.e.. independent of frequency) across a spectral interval Av larger than the frequency intervals among the HFS levels. and larger than the inverse lifetimes of the same levels.," For a two-level atom with HFS, this approximation requires that the incident radiation field should be flat (i.e., independent of frequency) across a spectral interval $\Delta\nu$ larger than the frequency intervals among the HFS levels, and larger than the inverse lifetimes of the same levels." + Given the small frequency separation between the various HFS levels (see Fig. 2)).," Given the small frequency separation between the various HFS levels (see Fig. \ref{fig:hfs-comp}) )," + this appears to be a good approximation for the Sc line under investigation., this appears to be a good approximation for the Sc line under investigation. + Scandium has only one stable isotope (?Sc). of nuclear spin 12 7/2.," Scandium has only one stable isotope $^{45}$ Sc), of nuclear spin $I=7/2$ ." + The Sc line at 4247 originates from the transition between the levels 3445 Ds (lower level) and 3d4p! D; (upper level).," The Sc line at 4247 originates from the transition between the levels $3d4s\, ^1$ $_2$ (lower level) and $3d4p\, ^1$ $_2$ (upper level)." + The Einstein coefficient for spontaneous emission is A=1.29x108 s! (Ralchenkoetal...2008).," The Einstein coefficient for spontaneous emission is $A=1.29 \times +10^{8}$ $^{-1}$ \citep[][]{Ral08}." +. Because of HFS. each J-level splits into 5 F-levels. and the spectral line under investigation consists of 13 HFS components (see the upper panel of Fig. 2).," Because of HFS, each $J$ -level splits into 5 $F$ -levels, and the spectral line under investigation consists of 13 HFS components (see the upper panel of Fig. \ref{fig:hfs-comp}) )." + We use the energies of the J-levels provided by Ralchenkoetal.(2008).. while we calculate the energies of the various HFS levels by applying Eq. (1) ).," We use the energies of the $J$ -levels provided by \citet{Ral08}, while we calculate the energies of the various HFS levels by applying Eq. \ref{eq:hfs-energy}) )," + using the values of the magnetic dipole and of the electric quadrupole HFS constants listed in Table 1.., using the values of the magnetic dipole and of the electric quadrupole HFS constants listed in Table \ref{Tab:const}. + The laboratory positions and the relative strengths of the various HFS components are shown in the lower panel of Fig. 2.., The laboratory positions and the relative strengths of the various HFS components are shown in the lower panel of Fig. \ref{fig:hfs-comp}. + Despite the simplicity of the atomic model considered (two-level atom). because of the high values of the quantum numbers involved. the SEE form a set of3200 equations in 3200 unknowns (the various spherical statistical tensors MDΔΙΑ.FP) of the upper and lower levels).," Despite the simplicity of the atomic model considered (two-level atom), because of the high values of the quantum numbers involved, the SEE form a set of 3200 equations in 3200 unknowns (the various spherical statistical tensors $^{\alpha J I}\rho^K_Q(Ff,F^{\prime}f^{\prime})$ of the upper and lower levels)." + To reduce the amount of numerical calculations involved in the solution of this set of equations. we limit ourselves to considering only the spherical statistical tensors with K€2. thus reducing the SEE to a set of 278 equations.," To reduce the amount of numerical calculations involved in the solution of this set of equations, we limit ourselves to considering only the spherical statistical tensors with $K \le 2$, thus reducing the SEE to a set of 278 equations." + Because of the low value of the anisotropy factor that we assume for the radiation field (see following subsection). thestatistical tensorsof higher rank are found to be almost two orders of magnitude smaller. so that," Because of the low value of the anisotropy factor that we assume for the radiation field (see following subsection), thestatistical tensorsof higher rank are found to be almost two orders of magnitude smaller, so that" +SNRs.,SNRs. +" Even if Emax 1s an order of magnitude smaller owing to the lifetime of the secondary shocks, the maximum energy of 10 TeV is still large enough to account for the TeV gamma-ray emission from middle-aged SNRs (Abdo et al."," Even if $E_{\rm max}$ is an order of magnitude smaller owing to the lifetime of the secondary shocks, the maximum energy of 10 TeV is still large enough to account for the TeV gamma-ray emission from middle-aged SNRs (Abdo et al." + 2009a; 2009b; 2010c; 2010d; Aharonian et al., 2009a; 2009b; 2010c; 2010d; Aharonian et al. + 2002; 2008b; Buckley et al., 2002; 2008b; Buckley et al. + 1998)., 1998). +" Since the Mach numbers of the secondary shocks are small, the injection rate of particles into the acceleration process in the secondary shocks would be much smaller than that in the shock."," Since the Mach numbers of the secondary shocks are small, the injection rate of particles into the acceleration process in the secondary shocks would be much smaller than that in the primary shock." +" However, particles by the primary shock can besuprathermal advected downstreamgenerated and re-accelerated to higher energies at the secondary shocks."," However, suprathermal particles generated by the primary shock can be advected downstream and re-accelerated to higher energies at the secondary shocks." +" As shown in Fig. 2,,"," As shown in Fig. \ref{f2}," +" the total surface area of the secondary shocks is comparable to that of the primary shock, suggesting that most advected particles meet the secondary shocks."," the total surface area of the secondary shocks is comparable to that of the primary shock, suggesting that most advected particles meet the secondary shocks." +" If the volume filling factor of the clouds is much larger than that realized in our simulations, the total surface area of the secondary shocks would be much larger."," If the volume filling factor of the clouds is much larger than that realized in our simulations, the total surface area of the secondary shocks would be much larger." + In that case the suprathermal particles can be successively accelerated by multiple secondary shocks., In that case the suprathermal particles can be successively accelerated by multiple secondary shocks. +" Given the particle momentum accelerated at the primary shock as No(p)«p?spectrumexp(-p/ pw), where pp,:10 GeV is the break momentum due to the wave damping, the spectrum re-accelerated n times by the secondary shocks becomes (Melrose Pope 1993): where is the generalized hypergeometric function written using the Pochhammer symbol [(g).=g(g+1)...(g-k—-1),(g)o l]a2s-2,b-2s-l,d-([(s-D/(s-2)H."," Given the particle momentum spectrum accelerated at the primary shock as $N_{0}(p)\propto p^{-2}\,\exp(-p/p_{\rm br})$ , where $p_{\rm br} \simeq 10$ GeV is the break momentum due to the wave damping, the spectrum re-accelerated $n$ times by the secondary shocks becomes (Melrose Pope 1993): where is the generalized hypergeometric function written using the Pochhammer symbol $(g)_k=g(g+1)...(g+k-1),\,(g)_0=1$ ], $a=s-2$, $b=s-1$, $d=\{(s-1)/(s+2)\}^{1/3}$." + Here we have assumed that the injection at the secondary shocks is inefficient owing to their small Mach number., Here we have assumed that the injection at the secondary shocks is inefficient owing to their small Mach number. + Note that eq. (6)), Note that eq. \ref{bpl}) ) +" is valid for ρή>my.","29) ${\rm{St}}_L$ is the Stokes number for the largest particle $r_L = (3m_L/4\pi\rho_s)^{1/3}$, $H=c_g/\Omega$ is the scale height of the gas, $\gamma$ is the adiabatic index of the gas, and in this expression it is assumed that the sticking coefficient $S = 1$, and that $m_L>>m_0$." + The above equation is similar to the formula lor grain growth proposed by to [actors of order unity.," The above equation is similar to the formula for grain growth proposed by \citet{ste97} + to factors of order unity." + Finally. we point out that the Garand model for particle growth is restricted to the value g=11/6 in order (to preserve its completely analvtieal nature.," Finally, we point out that the Garaud model for particle growth is restricted to the value $q = 11/6$ in order to preserve its completely analytical nature." + As a means ol a fair comparison. we chose to compare the Garaud model to our explicit case (Eq.," As a means of a fair comparison, we chose to compare the Garaud model to our explicit case (Eq." + 28) for reasons explained below., 28) for reasons explained below. +" In the limit of my,22my and q=11/6. Eq. ("," In the limit of $m_L >> m_0$ and $q=11/6$, Eq. (" +28) becomes We present the results of our comparison in Figure 5 lor (he same initial conditions as described at the beginning of 3.2 (upper curves).,28) becomes We present the results of our comparison in Figure 5 for the same initial conditions as described at the beginning of 3.2 (upper curves). + We find quite generally Chat our explicit calculation (Es., We find quite generally that our explicit calculation (Eqs. + 28 and 30) leads (o a faster growth rate than what is predicted [rom the, 28 and 30) leads to a faster growth rate than what is predicted from the +At high redshifts z>2 most of the baryons in the Universe rest in the intergalactic medium (IGM) and can be uniquely described as gas at still low-density contrast 6x10.,At high redshifts $z \ge 2$ most of the baryons in the Universe rest in the intergalactic medium (IGM) and can be uniquely described as gas at still low-density contrast $\delta \le 10$. + It is almost identically distributed as the underlying dark matter and is highly ionized by the UV background radiation (T.<10° K).," It is almost identically distributed as the underlying dark matter and is highly ionized by the UV background radiation $T < +10^5$ K)." + The subsequent evolution changes that picture., The subsequent evolution changes that picture. + At redshift =0. only a fraction of =30% of the IGM is still existing under conditions comparable with those at z>2 (?)..," At redshift $z \approx 0$, only a fraction of $\approx 30\%$ of the IGM is still existing under conditions comparable with those at $z>2$ \citep{Stocke04}." + During the evolution toward low redshifts. the mean-scale streaming motions could have led to shock-confined filaments containing gas at much higher temperatures.," During the evolution toward low redshifts, the mean-scale streaming motions could have led to shock-confined filaments containing gas at much higher temperatures." + Numerical simulations by ? suggest that approximately 30 to 50 of the cosmic baryons at ς=O are in the form of the intergalactic medium with a temperature ofK. which is called warm-hot intergalactic medium (WHIM).," Numerical simulations by \citet{CenOstriker99} suggest that approximately 30 to 50 of the cosmic baryons at $z=0$ are in the form of the intergalactic medium with a temperature of, which is called warm-hot intergalactic medium (WHIM)." + Further numerical simulations (e.g...??) with different numerical schemes and. resolutions also consistently support this picture.," Further numerical simulations \citep[e.g.,][]{Dave01,Dolag06} with different numerical schemes and resolutions also consistently support this picture." + These numerical predictions have initiated much observational effort in order to reveal the existence of the WHIM., These numerical predictions have initiated much observational effort in order to reveal the existence of the WHIM. + Owing to the high degree of tonization. the observational signature of the WHIM is very weak. in particular with respect to neutral hydrogen.," Owing to the high degree of ionization, the observational signature of the WHIM is very weak, in particular with respect to neutral hydrogen." + Therefore. the detection of highly ionized metal lines is much more promising.," Therefore, the detection of highly ionized metal lines is much more promising." + Observationally. the WHIM was first proposed through its metal absorption features in the spectra of bright quasars and blazers (22222)..," Observationally, the WHIM was first proposed through its metal absorption features in the spectra of bright quasars and blazers \citep{Hellsten98,Perna98,Fang00,Cen01,Fang01}." + After the first detection of absorption lines in the spectra of a bright quasar by ? and ?.. a number of detections were reported through absorption features ofOviOvi.vim. and ions (????).. but they are considered to be rather tentative.," After the first detection of absorption lines in the spectra of a bright quasar by \citet{Tripp00} and \citet{Tripp01}, a number of detections were reported through absorption features of, and ions \citep{Nicastro02,Fang02,Mathur03,Fujimoto04}, but they are considered to be rather tentative." + A detection with sufficiently high signal-to-noise ratio is reported by ??..," A detection with sufficiently high signal-to-noise ratio is reported by \citet{Nicastro05b,Nicastro05a}." + They found absorption signatures of the WHIM at two redshifts in the spectra of the blazar Mrk421 during its two outburst phases., They found absorption signatures of the WHIM at two redshifts in the spectra of the blazar Mrk421 during its two outburst phases. + Future proposed missions such as are expected to detect numerous WHIM absorbers., Future proposed missions such as are expected to detect numerous WHIM absorbers. + Detection of WHIM absorption in the spectra of afterglows of gamma-ray bursts (GRBs) were also proposed by 9? using dedicated missions such as and were considered more recently by ? for the prospects opened by the recently proposed satellite missions and, Detection of WHIM absorption in the spectra of afterglows of gamma-ray bursts (GRBs) were also proposed by \citet{Elvis04} using dedicated missions such as and were considered more recently by \citet{Branchini09} for the prospects opened by the recently proposed satellite missions and. +XENIA.. ? investigated the feasibility of these detections in a realistic manner based on cosmological hydrodynamic simulations., \citet{Kawahara06} investigated the feasibility of these detections in a realistic manner based on cosmological hydrodynamic simulations. + Additionally. several tentative detections of the WHIM through its metal line emission are claimed by ? and ὁ with the satellite.," Additionally, several tentative detections of the WHIM through its metal line emission are claimed by \citet{Kaastra03} and \citet{Finoguenov03} with the satellite." + However. these detections are not significant enough to exclude the possibility that the observed emission lines are of Galactic origin because of the limited energy resolution (=80 eV) of the current X-ray detectors. ?.. ?..," However, these detections are not significant enough to exclude the possibility that the observed emission lines are of Galactic origin because of the limited energy resolution $\simeq 80$ eV) of the current X-ray detectors. \citet{Yoshikawa03}, \citet{Yoshikawa04}," + and ?. showed that future X-ray missions equipped with a high-energy resolution spectrograph such as (Diffuse Interealactic Oxygen Surveyor) and (Missing Baryon Explorer) can convincingly detect the line emisslol of the WHIM., and \citet{Fang05} showed that future X-ray missions equipped with a high-energy resolution spectrograph such as (Diffuse Intergalactic Oxygen Surveyor) and (Missing Baryon Explorer) can convincingly detect the line emission of the WHIM. + A comprehensive review is given by ?.., A comprehensive review is given by \citet{ProchaskaTumlinson08}. + It is still an open question. how much the WHIM contributes to the anisotropies of the cosmic microwave background radiation. via the Sunyaev-Zeldovich effect (SZ-effect)., It is still an open question how much the WHIM contributes to the anisotropies of the cosmic microwave background radiation via the Sunyaev-Zeldovich effect (SZ-effect). +" Although the density contrast of the WHIM is moderate (6« 100). its temperature is high (10° K «T. 10"" κι. and it is supposed to make a significant contribution to the cosmic baryon budget of =?50%."," Although the density contrast of the WHIM is moderate $\delta < 100$ ), its temperature is high $10^5$ K $< T <$ $10^7$ K), and it is supposed to make a significant contribution to the cosmic baryon budget of $\approx 50 +\%$." + Estimates provided by ?.. ?.. and ? indicate on a non-negligible contribution. which under certain conditions might be even comparable with the overall SZ contribution of clusters of galaxies.," Estimates provided by \citet{Atrio06}, \citet{Atrio08}, and \citet{GenovaSantos09} indicate on a non-negligible contribution, which under certain conditions might be even comparable with the overall SZ contribution of clusters of galaxies." + Thus the SZ effect could serve as an additional detection channel for the WHIM., Thus the SZ effect could serve as an additional detection channel for the WHIM. + However. the strength of a thermal SZ effect is still a matter of debate because the results obtained by numerical simulations are much less pronounced.," However, the strength of a thermal SZ effect is still a matter of debate because the results obtained by numerical simulations are much less pronounced." + Therefore. it is of principal importance to investigate the detailed thermodynamic state and the internal kinematics of the structures which may hide a large fractioi of cosmic baryons.," Therefore, it is of principal importance to investigate the detailed thermodynamic state and the internal kinematics of the structures which may hide a large fraction of cosmic baryons." + The detailed physics of the WHIM is highly demanding for computational astrophysics. however.," The detailed physics of the WHIM is highly demanding for computational astrophysics, however." + The treatment of low-density regions in great detail is difficult., The treatment of low-density regions in great detail is difficult. + Compared with the numerical handling of high-density matter distributions where adaptive techniques can be applied. for low-density regions. necessary higher overall particle and/or grid number is unavoidable for an appropriate description.," Compared with the numerical handling of high-density matter distributions where adaptive techniques can be applied, for low-density regions, necessary higher overall particle and/or grid number is unavoidable for an appropriate description." + In. addition. higher resolution calls fora more detailed consideration of local physics. e.g.. star formation. feedback. contamination by heavy elements. etc.," In addition, higher resolution calls fora more detailed consideration of local physics, e.g., star formation, feedback, contamination by heavy elements, etc." + Altogether the computational effort, Altogether the computational effort +]t has been almost oue decade since the first atinospheric measurement of a hot Jupiter (Charbonueauetal.2002) aud vet this class of exotic exoplanet still provides us with many uivsteries waiting to be solved.,It has been almost one decade since the first atmospheric measurement of a hot Jupiter \citep{Charbonneau2002} and yet this class of exotic exoplanet still provides us with many mysteries waiting to be solved. + These include the culprit responsible for the stratospheric temperature, These include the culprit responsible for the stratospheric temperature +In order to understand the formation of giant planets. and hence. the formation of planetary svstems. we must be able to determine (he interior structure and. composition of giant planets.,"In order to understand the formation of giant planets, and hence, the formation of planetary systems, we must be able to determine the interior structure and composition of giant planets." + Jupiter and Saturn. our solar svstenrs gas giants. combine to make up of the planetary mass of our solar svstem.," Jupiter and Saturn, our solar system's gas giants, combine to make up of the planetary mass of our solar system." + Interestingly. knowledge of only a few kev quantities allows us to gain important insieht into their interior structure.," Interestingly, knowledge of only a few key quantities allows us to gain important insight into their interior structure." + The equation of state of hvdrogen. together wil measurements of the mass. radius. aud oblateness of Jupiter and Saturn is sufficient (o show that these planets are hydrogen-helium rich objects with a composition similar to that of the Sun (Demarcus1958).," The equation of state of hydrogen, together with measurements of the mass, radius, and oblateness of Jupiter and Saturn is sufficient to show that these planets are hydrogen-helium rich objects with a composition similar to that of the Sun \citep{Demarcus58}." +. Furthermore. estimates of the transport coellicients of dense metallic hydrogen ancl the observation that Jupiter emits more infrared radiation than it absorbs from the Sun (Low1966).. is sufficient to show Chat gas eijant planet interiors are warm. fluid. and convective. not cold and solid (Hubbard.1963).," Furthermore, estimates of the transport coefficients of dense metallic hydrogen and the observation that Jupiter emits more infrared radiation than it absorbs from the Sun \citep{Low66}, is sufficient to show that gas giant planet interiors are warm, fluid, and convective, not cold and solid \citep{Hubbard68}." +. I1 has also been clear for some time that the composition of Jupiter aud Saturn is not exactly like (hat of the Sun.these planets are enhanced in “heavy elements” (atoms more massive than helium). compared to the Sun (Podolak&Cameron1974).," It has also been clear for some time that the composition of Jupiter and Saturn is not exactly like that of the Sun—these planets are enhanced in “heavy elements” (atoms more massive than helium), compared to the Sun \citep{Podolak74}." +. An understanding of how these planets attained these heavy elements. ancl (heir relative ratios. can give us a wealth ol information on planetary formation aud the state of the solar nebula.," An understanding of how these planets attained these heavy elements, and their relative ratios, can give us a wealth of information on planetary formation and the state of the solar nebula." +ABBA (sco c.g. Cuby ot al.2,"ABBA (see e.g. Cuby et al.," +0034... Leomoince-Busscrolle et al., Lemoine-Busserolle et al. + 2003) Spectroscopic data where reduced using IRAF xocedures and couforming to the ISAAC Data Reduction Guide 1.57., 2003) Spectroscopic data where reduced using IRAF procedures and conforming to the ISAAC Data Reduction Guide 1.5. + The first skv-subtraction was performed wv subtracting one frame from the other in cach AB oür., The first sky-subtraction was performed by subtracting one frame from the other in each AB pair. + After removing the 50 Iz pickup that occured diving the last nieht and flat-ficldine these frames. we waveleugth-calibrated the two-dimensional spectra using he atlas of ΟΠ lines (Rousselot et al..," After removing the 50 Hz pickup that occured during the last night and flat-fielding these frames, we wavelength-calibrated the two-dimensional spectra using the atlas of OH lines (Rousselot et al.," + 2000)., 2000). + Finally. we combined cach A-B and B-A frames after suitable shifts aud extracted the onc-dimceusional spectrum.," Finally, we combined each A-B and B-A frames after suitable shifts and extracted the one-dimensional spectrum." + We used the observed tellure standards to flux-calibrate ancl correct for telluric features iu the individual spectra. fitting the hot (O aud B) stars with a blackbody curve.," We used the observed telluric standards to flux-calibrate and correct for telluric features in the individual spectra, fitting the hot (O and B) stars with a blackbody curve." +" Table 1 sumnnanzes the photometric data obtained on object #22582. computed within a 1.5"" aperture on secing matched images."," Table \ref{tab_phot} summarizes the photometric data obtained on object 2582, computed within a $1.5''$ aperture on seeing matched images." + This source is unresolved. aud it is not detected ou the WEPC2/TIST nuage Girrueyzc 23.8 /aresce? and Reryoy:7 27.3. 26 on. LIST pixels).," This source is unresolved, and it is not detected on the WFPC2/HST image $\mu_{F702W} \ge$ 23.8 $^2$ and $R_{F702W} \ge$ 27.3, $\sigma$ on 4 HST pixels)." + It is undetected in V aud Π and oulv mareinally detected iu I., It is undetected in $V$ and $R$ and only marginally detected in $I$. + This object would have ecu selected from our optical data. since if is only mareiually detected in the I band.," This object would have been selected from our optical data, since it is only marginally detected in the I band." +" The spectroscopic observations revealed the presence of3 cluission lines in 2 overlapping regions of the ./ Da :1.285-1.315 pov and 1.335-1.395 pini. observed with exposure times of 10.8 and 18.9 ksec respectively,"," The spectroscopic observations revealed the presence of3 emission lines in 2 overlapping regions of the $J$ band: 1.285-1.345 $\mu m$ and 1.335-1.395 $\mu m$, observed with exposure times of 10.8 and 18.9 ksec respectively." + These lines were identified as aad aat wavelengths corresponding to au average redshift of >=1.676 for this IR-sclected source., These lines were identified as and at wavelengths corresponding to an average redshift of $z=1.676$ for this IR-selected source. + The corresponding 2D and extracted spectra are shown in Fig. 2.., The corresponding 2D and extracted spectra are shown in Fig. \ref{2582_spectrum}. + As scen ou the 2D spectra. the “trace” ofthe spectrmm docs no ollow a detector line.," As seen on the 2D spectrum, the “trace” of the spectrum does not follow a detector line." + Extraction (with iraf task apall) was oue bv shifting the fitted “trace” of the spectrum of the xiehter star used for slit aliguement outo the position of he ine of #22582., Extraction (with iraf task apall) was done by shifting the fitted “trace” of the spectrum of the brighter star used for slit alignement onto the position of the line of 2582. + The observed line fluxes are eiven in Table 2.., The observed line fluxes are given in Table \ref{tab_2582}. + Because of the excellent secine couditious auk he slit width. we cau sately cousider that the bulk of the flux from this unresolved source was included in the slit.," Because of the excellent seeing conditions and the slit width, we can safely consider that the bulk of the flux from this unresolved source was included in the slit." + The lines ave not resolved as compared to the imstriunenta xofile measured using the OIL sky lines., The lines are not resolved as compared to the instrumental profile measured using the OH sky lines. + Thus. the line-ofsight velocity dispersion σ should be smaller than 20-30 sus. From simple SED fit bbelow) and adopting “concordance” cosuological parameters’.. the apparent 7 org/instruments/isaagdenitude translates to an absolute D-baud iaguitude," Thus, the line-of-sight velocity dispersion $\sigma$ should be smaller than 20-30 km/s. From simple SED fit below) and adopting “concordance” cosmological , the apparent $J$ magnitude translates to an absolute $B$ -band magnitude" +The probability (hat the net shear in the full multiple-deflection calculation exceeds the shear due to the single closest lens ranges from (lens halos with small physical extents. s*=50h! kpe) to (lens halos with large physical extents. s*=200h! kpc).,"The probability that the net shear in the full multiple-deflection calculation exceeds the shear due to the single closest lens ranges from (lens halos with small physical extents, $s^\ast = 50h^{-1}$ kpc) to (lens halos with large physical extents, $s^\ast = 200h^{-1}$ kpc)." + Figure 10 shows that the net shear due to all foreground lenses is also generally larger than the shear induced by the strongest individual weak lens in the full. multiple-defleetion calculation.," Figure 10 shows that the net shear due to all foreground lenses is also generally larger than the shear induced by the strongest individual weak lens in the full, multiple-deflection calculation." + As in Figure 9. (he ratio of the shears. μαιμιαν. is weakly-cdepencdent upon the specifies of the lens halo parameters.," As in Figure 9, the ratio of the shears, $\gamma_{\rm net} / \gamma_{\rm max}$, is weakly-dependent upon the specifics of the lens halo parameters." + The probability that the net shear in (he full multiple-deflection calculation exceeds the shear due to the single strongest weak lens ranges from (lens halos with small physical extents. s*=50h! kpe) to (lens halos with large physical extents. s*=200! kpc).," The probability that the net shear in the full multiple-deflection calculation exceeds the shear due to the single strongest weak lens ranges from (lens halos with small physical extents, $s^\ast = 50h^{-1}$ kpc) to (lens halos with large physical extents, $s^\ast = 200^{-1}$ kpc)." + Figures 9 ancl 10. then. show that for anv given distant source ealaxv. (he net shear (hat its image experiences due to all foreground. lenses exceeds. the shear due solely to the closest lens. as well as the shear due solely to the strongest individual weak lens.," Figures 9 and 10, then, show that for any given distant source galaxy, the net shear that its image experiences due to all foreground lenses exceeds the shear due solely to the closest lens, as well as the shear due solely to the strongest individual weak lens." + It may seem somewhat counter-intuitive (hat the net shear experienced by the images of distant source galaxies in (he multiple-deflection calculations generally exceeds the shear due to a naive single-defllection calculation., It may seem somewhat counter-intuitive that the net shear experienced by the images of distant source galaxies in the multiple-deflection calculations generally exceeds the shear due to a naive single-deflection calculation. + That is. al first glance one mieht expect that multiple weak galaxv-galaxy lensing deflections should. on average. cancel each other.," That is, at first glance one might expect that multiple weak galaxy-galaxy lensing deflections should, on average, cancel each other." + For a given source (his would. indeed. be the case if all the foreground lenses were located at precisely (he same angular separation from the source. had identical gravitational potentials. and had identical redshilts. τι.," For a given source this would, indeed, be the case if all the foreground lenses were located at precisely the same angular separation from the source, had identical gravitational potentials, and had identical redshifts, $z_l$." + Such an idealized situation is. of course. not the case in the real universe.," Such an idealized situation is, of course, not the case in the real universe." + That is. we cannot think in terms of a single lens plane for the ealaxy-galaxy lensing problem. and to a certain extent the solution has to be understood numerically.," That is, we cannot think in terms of a single lens plane for the galaxy-galaxy lensing problem, and to a certain extent the solution has to be understood numerically." + This is due to the [act that (here are a wide range of lens-source separations. (he lenses have a wide range of gravitational potentials. ancl (he lenses are distributed broadly in redshilt.," This is due to the fact that there are a wide range of lens-source separations, the lenses have a wide range of gravitational potentials, and the lenses are distributed broadly in redshift." + These. in combination. result in increased shear in the multiple-deflection calculation for ealaxv lensing. much as the non-uniformities in the mass distribution along the line of sight eive rise (o a net “cosmic shear (see. e.g.. reviews by Dartelmann Schneider 2001: van Waerbeke Mellier 2003: Refregier 2003: Munshi et 22008).," These, in combination, result in increased shear in the multiple-deflection calculation for galaxy-galaxy lensing, much as the non-uniformities in the mass distribution along the line of sight give rise to a net “cosmic shear” (see, e.g., reviews by Bartelmann Schneider 2001; van Waerbeke Mellier 2003; Refregier 2003; Munshi et 2008)." + That is. like galaxv-galaxy lensing. cosmic shear is inherently a multiple-deflecon problem in which the deflections do not simply cancel.," That is, like galaxy-galaxy lensing, cosmic shear is inherently a multiple-deflection problem in which the deflections do not simply cancel." + A detailed investigation of how the shear experienced by a given source galaxy is affected: as one successively adds in more and more weak galaxy lenses will be presented in Howell Brainerd (2010)., A detailed investigation of how the shear experienced by a given source galaxy is affected as one successively adds in more and more weak galaxy lenses will be presented in Howell Brainerd (2010). + The last question of this section. the effect of multiple dellections on the mean tangential shear about the lens centers. is addressed in Figure 11.," The last question of this section, the effect of multiple deflections on the mean tangential shear about the lens centers, is addressed in Figure 11." + In Figures 9 and 10. we have computed quantities (uel shear. shear due to the closest weak lens. and shear due to the strongest individual weak lens) (hat cannot. in practice. be measured in an observational data set.," In Figures 9 and 10, we have computed quantities (net shear, shear due to the closest weak lens, and shear due to the strongest individual weak lens) that cannot, in practice, be measured in an observational data set." + That is. without precise knowledge of the intrinsic shape of a source galaxy. (he. angular," That is, without precise knowledge of the intrinsic shape of a source galaxy, the angular" +for 9 of the 16 GRB hosts in their sample.,for 9 of the 16 GRB hosts in their sample. + Finally. the Savaglio et ((2009) comparison includes several host ealaxies of CRBs that they classify as short-«duratiou (GRB 051221. GRB 050116: although see Soderberg et 22007) as well as the unusual GRB 060505. a burst whose plienomenological classification remains unclear (c.g. Fryubo et 22006). Levesque Iewlev. 2007. Ofek et 22007. MeDreeu et 22008. Thonne et 22008).," Finally, the Savaglio et (2009) comparison includes several host galaxies of GRBs that they classify as short-duration (GRB 051221, GRB 050416; although see Soderberg et 2007) as well as the unusual GRB 060505, a burst whose phenomenological classification remains unclear (e.g. Fynbo et 2006b, Levesque Kewley 2007, Ofek et 2007, McBreen et 2008, Thönne et 2008)." + Short-duration CRBs are thought to be plenomenologically distinct. from LORBs (c.g. Berger 2010 aud references therein). and should be considered separately iu such studies.," Short-duration GRBs are thought to be phenomenologically distinct from LGRBs (e.g. Berger 2010 and references therein), and should be considered separately in such studies." + Most recentlv. Tan et ((2010) compared theALZ relation for SDSS galaxies from Liang et ((2007) to a small sample of 5 LORB host galaxies.," Most recently, Han et (2010) compared the relation for SDSS galaxies from Liang et (2007) to a small sample of 5 LGRB host galaxies." + While the sample size is nallo and the comparison sample redshift is Inhomoecnous with the LGORB host redshifts. the LGRD host galaxies are found to cousisteutlv lie below theAZ relation for SDSS egalaxics.," While the sample size is small, and the comparison sample redshift is inhomogenous with the LGRB host redshifts, the LGRB host galaxies are found to consistently lie below the relation for SDSS galaxies." + Iu Figure Lowe plot theALZ velation for our sample of 2«1 LORB host galaxies., In Figure 1 we plot the relation for our sample of $z < 1$ LGRB host galaxies. + We find that these two paralucters have a stroug and statistically significant positive correlation (Pearsou's kr = 0.80. p = 0.001).," We find that these two parameters have a strong and statistically significant positive correlation (Pearson's $r$ = 0.80, $p$ = 0.001)." + This is a sijenificaut deviation from the results of Savaelio et ((2009). who find noA-Z relation for their sample of GRB host galaxies.," This is a significant deviation from the results of Savaglio et (2009), who find no relation for their sample of GRB host galaxies." + We postulate that this is primarily due to differences im uactallicity determinations., We postulate that this is primarily due to differences in metallicity determinations. + While our stellar masses derived for these host galaxies are in agreement with the stellar masses of Savaglio et ((2009). our metallicities are largely based on late-tinme spectroscopic observations from our ougong host galaxy survey. and the LGRD host data plotted in Figure 1 are based on inetallicitics that were determined usine the Wobuluicky Isewleyv (2001) Ros calibration.," While our stellar masses derived for these host galaxies are in agreement with the stellar masses of Savaglio et (2009), our metallicities are largely based on late-time spectroscopic observations from our ongoing host galaxy survey, and the LGRB host data plotted in Figure 1 are based on metallicities that were determined using the Kobulnicky Kewley (2004) $_{23}$ calibration." + We have also compared our LORB host ealaxy data to two star-forming ealaxy samples: yalacics: For the nearby (2< 0.3) LGRD host ealaxies. we adopt data from 753.000 star-forming SDSS ealaxies as a coniparison sample.," We have also compared our LGRB host galaxy data to two star-forming galaxy samples: : For the nearby $z < 0.3$ ) LGRB host galaxies, we adopt data from $\sim$ 53,000 star-forming SDSS galaxies as a comparison sample." + The data plotted iu Figure 1l are taken from Table 3 of Tremonti ct ((2001). and. has been biuned by mass im increments of ~0.1 dex.," The data plotted in Figure 1 are taken from Table 3 of Tremonti et (2004), and has been binned by mass in increments of $\sim$ 0.1 dex." + The Tremonti et (2001) metallicities have been converted iuto the Bos metallicity calibration of Iwobulnicky Iewlev (2001). using the conversion cocficicnts elven in Table 3 of Iwewley Ellison (2008).," The Tremonti et (2004) metallicities have been converted into the $_{23}$ metallicity calibration of Kobulnicky Kewley (2004), using the conversion coefficients given in Table 3 of Kewley Ellison (2008)." + In additiou. the Tremonti et ((2001) stellar lnasses were derived using spectral iudices. and Zahid et ((2010) find that these masses differ frou masses determined using thePhere code bv a coustaut offset. attributable to the differeut IMEs aud techuiques (spectral vs. photometric) used in the two methods.," In addition, the Tremonti et (2004) stellar masses were derived using spectral indices, and Zahid et (2010) find that these masses differ from masses determined using the code by a constant offset, attributable to the different IMFs and techniques (spectral vs. photometric) used in the two methods." + As a result. we have decremented the Tremouti et ((2001) stellar masses by the recommended offset of 0.17 dex to bring them iuto agreement with the stellar uiass determinations of the code: for more discussion see Zahid et ((2010).," As a result, we have decremented the Tremonti et (2004) stellar masses by the recommended offset of 0.17 dex to bring them into agreement with the stellar mass determinations of the code; for more discussion see Zahid et (2010)." + The sample covers a redshift range of 0.005«20.25. with a median redshift of Dodd.yalarics:," The sample covers a redshift range of $0.005 < z < 0.25$, with a median redshift of $z \sim 0.1$.:" + For the intermeciate-redshift (0.3—2 <1) LGRD host galaxies. we compare our results to stellar mmass-binued data for 1.330 cussion line galaxies from the Deep Extragalactic Evolutionary Probe 2 (DEEP2) survey.," For the intermediate-redshift $0.3 < z < 1$ ) LGRB host galaxies, we compare our results to stellar mass-binned data for 1,330 emission line galaxies from the Deep Extragalactic Evolutionary Probe 2 (DEEP2) survey." + The stellar masses anc metallicities for these galaxies were determined by Zahid et ((2010). using thePhere stcllay wiass code and the Woluluiicky Ixexvley (2001) Roy metallicity diagnostic (it is worth noting that the metallicities are based on equivalent width data rather than fluxes. which could iutroduce a systematic error of up to ~O.5dex: see Zahid et 22010).," The stellar masses and metallicities for these galaxies were determined by Zahid et (2010), using the stellar mass code and the Kobulnicky Kewley (2004) $_{23}$ metallicity diagnostic (it is worth noting that the metallicities are based on equivalent width data rather than fluxes, which could introduce a systematic error of up to $\sim$ 0.5dex; see Zahid et 2010)." + The data cover a redshift range from 0.75<+0.82., The data cover a redshift range from $0.75 < z < 0.82$. + From this couparison. we find that most of the LCRD hosts iu our sample fall below the staudardZ relation for star-forming galaxies at simular redshifts. with cifferences ranging frou 0.05 to 0.75 dex across a fixed stellar masses.," From this comparison, we find that most of the LGRB hosts in our sample fall below the standard relation for star-forming galaxies at similar redshifts, with differences ranging from $-0.05$ to $-0.75$ dex across a fixed stellar masses." + We do note that. for the hieh-metallicity hosts of GRB 050826 and CRB 020819. the measured metallicities agree with the SDSS aud DEEP2Al-Z velatious to within the svstematic errors.," We do note that, for the high-metallicity hosts of GRB 050826 and GRB 020819, the measured metallicities agree with the SDSS and DEEP2 relations to within the systematic errors." + Across the whole sample we find an average offset from the eeneral star-forming galaxy populations of 0.1240.18 dex in metallicity ΟΕ 0.17 dex for the +-0.3 sample. 38+ 0.2 dex for the 0.38«2<1 sample).," Across the whole sample we find an average offset from the general star-forming galaxy populations of $-0.42 \pm 0.18$ dex in metallicity $-0.45 \pm$ 0.17 dex for the $z < 0.3$ sample, $-0.38 \pm$ 0.2 dex for the $0.3 < z < 1$ sample)." + We mast also consider the sclection effects inherent im such a study., We must also consider the selection effects inherent in such a study. + Host galaxy surveys are typically limited to LORBs with well-detected optical afterglows that cau be confidently associated with a host., Host galaxy surveys are typically limited to LGRBs with well-detected optical afterglows that can be confidently associated with a host. +" As a result. these surveys are limited in thei abilitv to sample ""dark? LORBs: Fyubo ct ((2009) estimate an overall dark Durst fraction of - based on their survev of 77 Swift LGRDs."," As a result, these surveys are limited in their ability to sample “dark"" LGRBs; Fynbo et (2009) estimate an overall dark burst fraction of - based on their survey of 77 Swift LGRBs." + The primary cause of the dark LCRD phenomenon remains uukuown: however. recent evidence has supported the effects of dust extinction. ij particular dust that is primarily present in the cireunburst caviroument (Perley et 22009).," The primary cause of the dark LGRB phenomenon remains unknown; however, recent evidence has supported the effects of dust extinction, in particular dust that is primarily present in the circumburst environment (Perley et 2009)." + Levesque et ((2010b) sugeest that this circumburst extinction could iu turu be connected to high metallicity., Levesque et (2010b) suggest that this circumburst extinction could in turn be connected to high metallicity. + A connection between dark LORBs aud higher-metallicity host cuviromments is also discussed iu Fyubo ot ((2009) aud Ciraliun et (2000)., A connection between dark LGRBs and higher-metallicity host environments is also discussed in Fynbo et (2009) and Graham et (2009). + Tf the dark. burst phenomenon is correlated with higher-auctallicity host environments. aud our sample is biased against the hosts ofdark LORBs. it is therefore possible that the apparent divergence of LGRDs from the eeneralAZ relation ouly holds true for the most nearby lowerauass sample.," If the dark burst phenomenon is correlated with higher-metallicity host environments, and our sample is biased against the hosts of dark LGRBs, it is therefore possible that the apparent divergence of LGRBs from the general relation only holds true for the most nearby lower-mass sample." + Future inclusion of additional dark burst host environnieuts would help to further clarify the true nature of this observed LGRB host offset., Future inclusion of additional dark burst host environments would help to further clarify the true nature of this observed LGRB host offset. +" Finally, in Figure 1 we compare theAZ relation determined for our intermeciate-redshift LORB hosts to binned data from the Erb et ((2006)ALZ relation for a sample of 87 ultraviolet-sclected star-formine galaxies at 2z2."," Finally, in Figure 1 we compare the relation determined for our intermediate-redshift LGRB hosts to binned data from the Erb et (2006) relation for a sample of 87 ultraviolet-selected star-forming galaxies at $z \gtrsim 2$." + The metallicities for this sample. originally derived using the |NIYAG5s8 L/To diagnostic from Pettiui Pagel (2001). have been converted to the Iobuluickv Rewley (2001) calibration according to the coefficients in Table 3 of Iewlev Ellison (2008): the masses are iu agreement with the code deteriunation aud do not require the offset decrement applied to the SDSS siuuple.," The metallicities for this sample, originally derived using the $\lambda$ $\alpha$ diagnostic from Pettini Pagel (2004), have been converted to the Kobulnicky Kewley (2004) calibration according to the coefficients in Table 3 of Kewley Ellison (2008); the masses are in agreement with the code determination and do not require the offset decrement applied to the SDSS sample." + Exb et ((2006) find that their +—2 sample is offset from the localAZ relation by —0.3 dex: we fud a sxidler average offset of ~0.16 dex between the Exh ot ((2006) sample aud the Zahid et ((2010) DEEP2 siuuple., Erb et (2006) find that their $z \sim 2$ sample is offset from the local relation by $\sim$ 0.3 dex; we find a smaller average offset of $\sim0.16$ dex between the Erb et (2006) sample and the Zahid et (2010) DEEP2 sample. + This is ~0.2 dex less than the average offset that we measure for our LOGRB host sample at 0.3<2«I., This is $\sim$ 0.2 dex less than the average offset that we measure for our LGRB host sample at $0.3 < z < 1$. + From this we cau conclude thatthe low-metallicity offset seen here for LGRD host ealaxies is smaller. though still preseut. when compared to star-forming galaxies at 2~ 2.Future observations of LGRB host galaxies," From this we can conclude thatthe low-metallicity offset seen here for LGRB host galaxies is smaller, though still present, when compared to star-forming galaxies at $z \sim 2$ .Future observations of LGRB host galaxies" +all of these corrections are The SDSS (??) has imaged ~104 deg? in u. g. r. i. and z.,"all of these corrections are The SDSS \citep{stoughton/etal:2002,abazajian/etal:2003} has imaged $\sim 10^4$ $^2$ in $u$, $g$, $r$, $i$, and $z$." + From this sample. spectroscopic LRG targets are efficiently selected using two color/maegnitude cuts (?)..," From this sample, spectroscopic LRG targets are efficiently selected using two color/magnitude cuts \citep{eisenstein/etal:2001}." + The tiling algorithm ensures nearly complete samples (2).., The tiling algorithm ensures nearly complete samples \citep{blanton/etal:2003}. +" ILowever. spectroscopic fiber collisions prohibit simultaneous spectroscopy for objects separated by <55"". leaving ~7% of targeted objects without redshifts (?).."," However, spectroscopic fiber collisions prohibit simultaneous spectroscopy for objects separated by $<55''$ , leaving $\sim 7\%$ of targeted objects without redshifts \citep{masjedi/etal:2006}." + Overlapping plates on ~1/3 of the survey. area. mitigate (his problem ancl permit us to calibrate this effect in our analvsis. as detailed below.," Overlapping plates on $\sim 1/3$ of the survey area mitigate this problem and permit us to calibrate this effect in our analysis, as detailed below." + The ‘photometric sample’ as referred. to below consists of objects [rom the imaging sample that were (Largeted as LRGs according to (he color/magnitude cults laid out in ?. but lack spectra., The `photometric sample' as referred to below consists of objects from the imaging sample that were targeted as LRGs according to the color/magnitude cuts laid out in \citet{eisenstein/etal:2001} but lack spectra. +" The ‘spectroscopic sample consists of objects from (he imaging sample (hal were targeted as LRGs aud subsequently The goal of (his analysis is to measure the group multiplicity function For the spectroscopic LRG sample with —23.207/7"", Combining equations (2) and (5). we can express D, as follows."," Suppose that a combination of studying the light curve and identifying the lensed source has allowed us to either measure the Einstein angle or to place a strong upper limit: $\theta_E\geq \theta_E^{lim}.$ Combining equations (2) and (5), we can express $D_L$ as follows." +of all channels.,of all channels. + The further reduction applied (in part on several occasions) the following tasks: correlated noise removal on the full array: correlated noise removal on groups sharing the same amplifier box and the same wiring: baseline subtraction: despiking: flagging of data outside suitable telescope scanning velocity and/or acceleration limits: flagging of bad channels., The further reduction applied (in part on several occasions) the following tasks: correlated noise removal on the full array; correlated noise removal on groups sharing the same amplifier box and the same wiring; baseline subtraction; despiking; flagging of data outside suitable telescope scanning velocity and/or acceleration limits; flagging of bad channels. + Each reduced scan (1.e. raster pattern) was then gridded into a weighted intensity map and a corresponding weight map., Each reduced scan (i.e. raster pattern) was then gridded into a weighted intensity map and a corresponding weight map. + The weights of the data points contributing to a certain pixel of the intensity map were determined as 1/o7 where c denotes the rms of the reduced time series of the corresponding channel and subsean., The weights of the data points contributing to a certain pixel of the intensity map were determined as $1/\sigma^2$ where $\sigma$ denotes the rms of the reduced time series of the corresponding channel and subscan. + Individual maps were then coadded. again noise-weighted. to build the final intensity map and the corresponding weight map. which in turn allows to retrieve the rms for each pixel and to construct a signal-to-noise (S/N) map.," Individual maps were then coadded, again noise-weighted, to build the final intensity map and the corresponding weight map, which in turn allows to retrieve the rms for each pixel and to construct a signal-to-noise (S/N) map." + The deseribed data reduction is affected by the presence of astronomical signals in the time series. which leads to a flux loss due the subtraction of correlated noise.," The described data reduction is affected by the presence of astronomical signals in the time series, which leads to a flux loss due the subtraction of correlated noise." + In case of strong sources this is manifestly revealed by the appearance of areas of negative fluxes adjacent to the sources., In case of strong sources this is manifestly revealed by the appearance of areas of negative fluxes adjacent to the sources. + Moreover. the source emission wrongly contributes to the determination of the rms and weights.," Moreover, the source emission wrongly contributes to the determination of the rms and weights." + To minimise these effects we applied an iterative approach by subsequently improving a model of the flux distribution of the astronomical source., To minimise these effects we applied an iterative approach by subsequently improving a model of the flux distribution of the astronomical source. +" In a first step a map was produced by a ""blind"" execution of the reduction as described above.", In a first step a map was produced by a “blind” execution of the reduction as described above. + A first source model was constructed from the resulting map by extracting all pixels above a given S/N threshold (typically 3) and setting the remaining pixels to zero., A first source model was constructed from the resulting map by extracting all pixels above a given S/N threshold (typically 3) and setting the remaining pixels to zero. + This model was converted to a time series for each channel and subtracted from the databefore any baseline subtraction. despiking and correlated noise suppression.," This model was converted to a time series for each channel and subtracted from the databefore any baseline subtraction, despiking and correlated noise suppression." + After the weight determination and before the map was built. the model was re-introduced into the time stream.," After the weight determination and before the map was built, the model was re-introduced into the time stream." + The resulting map was used to extract a new source model., The resulting map was used to extract a new source model. + In subsequent iterations this process is repeated until the measured flux distribution converges., In subsequent iterations this process is repeated until the measured flux distribution converges. + As a result. most of the faint extended emission should be recovered in the reduction.," As a result, most of the faint extended emission should be recovered in the reduction." + The 20°«20° image of the south-west region of the SMC that was obtained. is presented in Fig. ..," The $\times$ 20' image of the south-west region of the SMC that was obtained, is presented in Fig. \ref{fig1}." + It is the first sub- map of a large region in the Small Magellanic Cloud., It is the first sub-millimeter map of a large region in the Small Magellanic Cloud. + This south-west region of the SMC has had most of its known molecular clouds mapped at a 437 resolution and at hight sensitivity in the CO (J21-0) line with SEST (??)..," This south-west region of the SMC has had most of its known molecular clouds mapped at a 43"" resolution and at hight sensitivity in the CO (J=1-0) line with SEST \citep{RLB93,RLB+93}." + All the GMCs observed in CO lines with SEST (shown as contours in Fig. 1)), All the GMCs observed in CO lines with SEST (shown as contours in Fig. \ref{fig1}) ) +" are detected with the present LABOCA observation,", are detected with the present LABOCA observation. + There is also extended emission well outside observed CO peaks., There is also extended emission well outside observed CO peaks. + If the 870m emission originates from dust. this result shows that there is much more dense gas than what is traced by current CO observations.," If the $\mu$ m emission originates from dust, this result shows that there is much more dense gas than what is traced by current CO observations." + Comparing with the MIPS 1604m map of the same region. we see that the spatial distribution of the 8704 emission is well correlated with the one observed in the far-infrared.," Comparing with the MIPS $\mu$ m map of the same region, we see that the spatial distribution of the $\mu$ m emission is well correlated with the one observed in the far-infrared." + A short analysis of the dust emission outside the observed CO is presented in Appendix AppendixB:., A short analysis of the dust emission outside the observed CO is presented in Appendix \ref{appendb}. +. The present paper compares the 870jm and CO data and is therefore restricted to the regions where CO has been observed and detected., The present paper compares the $\mu$ m and CO data and is therefore restricted to the regions where CO has been observed and detected. + The entities for which we deduce nasses m the following and that are refered to as “clouds” are the densest parts of the molecular clouds. associated with CO emission.," The entities for which we deduce masses in the following and that are refered to as ""clouds"" are the densest parts of the molecular clouds, associated with CO emission." + For comparison. we complement these data with the SIMBA observations at 1.2 mm previously studied (?) and with Spitzer MIPS observations at 160j:m in the same region from the combined S*MC and SAGE-SMC surveys (??)..," For comparison, we complement these data with the SIMBA observations at 1.2 mm previously studied \citep{Bot:2007yq} and with Spitzer MIPS observations at $\mu$ m in the same region from the combined $^3$ MC and SAGE-SMC surveys \citep{Bolatto:2007rc, Gordon:2009lq}." + Furthermore. in order to estimate the contribution of free-free emission to the observed millimeter emission. we also use radio ATCA maps at 8.6. 4.8 GHz that were obtained from J. Dickel phys.unm.edu/~johnd/).," Furthermore, in order to estimate the contribution of free-free emission to the observed millimeter emission, we also use radio ATCA maps at 8.6, 4.8 GHz that were obtained from J. Dickel $\sim$ johnd/)." + To estimate the LABOCA. SIMBA. MIPS and radio fluxes in à way that is comparable to CO. we do the following.," To estimate the LABOCA, SIMBA, MIPS and radio fluxes in a way that is comparable to CO, we do the following." + All maps are convolved to the 43° CO(1-0) resolution and projected on the same sampling grid.," All maps are convolved to the 43"" CO(1-0) resolution and projected on the same sampling grid." + Because we are interested in comparing the LABOCA. SIMBA. MIPS and CO fluxes. it is important to remove the extended emission in all maps in order to compare emission in the region detected with all tracers (the peaks of the GMCs).," Because we are interested in comparing the LABOCA, SIMBA, MIPS and CO fluxes, it is important to remove the extended emission in all maps in order to compare emission in the region detected with all tracers (the peaks of the GMCs)." + To do so. we begin by masking the region where CO is detected and fitin each map (LABOCA. radio. SIMBA. MIPS) a 2D plane to the emission outside the CO detected region.," To do so, we begin by masking the region where CO is detected and fit in each map (LABOCA, radio, SIMBA, MIPS) a 2D plane to the emission outside the CO detected region." + The fitted plane is then removed from the maps (in units of surface brightness) to leave only the peak of emission where CO was observed., The fitted plane is then removed from the maps (in units of surface brightness) to leave only the peak of emission where CO was observed. + The integrated fluxes are then computed in a region above a defined We threshold., The integrated fluxes are then computed in a region above a defined $W_{CO}$ threshold. + This threshold is defined individually for each cloud so that the area of the cloud we sample is similar to the one that was used to determine the virial masses and CO luminosities of the clouds (?).., This threshold is defined individually for each cloud so that the area of the cloud we sample is similar to the one that was used to determine the virial masses and CO luminosities of the clouds \citep{RLB+93}. + This method enables us to analyze the emisstor coming from the dust associated with the CO emission only., This method enables us to analyze the emission coming from the dust associated with the CO emission only. + It attempts to filter extended envelopes around the clouds — uncertainties on this filtering process will be discussed in section 4.1]. — as well as possible emission associated withHr., It attempts to filter extended envelopes around the clouds – uncertainties on this filtering process will be discussed in section \ref{sec:geom} – as well as possible emission associated with. + Using an map of the Small Magellanie Cloud (?).. we estimated that the remaining column densities associated to the peaks of the molecular clouds we study. after filtering. are less than a few percent of the total hydrogen column densities as determined from the dust millimeter emission.," Using an map of the Small Magellanic Cloud \citep{SSD+99}, we estimated that the remaining column densities associated to the peaks of the molecular clouds we study, after filtering, are less than a few percent of the total hydrogen column densities as determined from the dust millimeter emission." + The fluxes obtained are summarized in Tab., The fluxes obtained are summarized in Tab. + | and are used to build the spectral energy distribution for each cloud (c.f Fig. 25., \ref{tab1} and are used to build the spectral energy distribution for each cloud (c.f Fig. \ref{fig2}) ). + At long wavelength like 870gm. the broad-band flux densities determined from the maps may contain. non-negligible contributions by thermal free-free continuum emission and CO line emission.," At long wavelength like $\mu$ m, the broad-band flux densities determined from the maps may contain non-negligible contributions by thermal free-free continuum emission and CO line emission." + In ?.. estimates of the free-free emission and of the CO line at 1.2mm were found to be negligible contributions to the measured fluxes.," In \citet{Bot:2007yq}, estimates of the free-free emission and of the CO line at 1.2mm were found to be negligible contributions to the measured fluxes." + Even if we expect this to be the case at, Even if we expect this to be the case at +"Before we can start computing the xy?-functions for our joint lensing reconstruction, we have to address two issues concerning the resolution of our reconstruction grid.","Before we can start computing the $\chi^{2}$ -functions for our joint lensing reconstruction, we have to address two issues concerning the resolution of our reconstruction grid." + The first is related to the weak-lensing regime., The first is related to the weak-lensing regime. +" If we want to average over at least ten galaxies per pixel, the typical background-galaxy density in the field of a cluster would not allow a higher resolution than ~10x pixels, which is of course way too coarse to see any cluster substructures."," If we want to average over at least ten galaxies per pixel, the typical background-galaxy density in the field of a cluster would not allow a higher resolution than $\sim10\times10$ pixels, which is of course way too coarse to see any cluster substructures." +" In addition, pixels of a homogeneous grid can occur which contain fewer than 10 or even no galaxies because of the inhomogeneous, random galaxy distribution."," In addition, pixels of a homogeneous grid can occur which contain fewer than 10 or even no galaxies because of the inhomogeneous, random galaxy distribution." +" We solve these problems by an adaptive averaging procedure, in which we average galaxy ellipticities within circles around each pixel centre."," We solve these problems by an adaptive averaging procedure, in which we average galaxy ellipticities within circles around each pixel centre." + Their radii are stepwise increased until each circle contains the desired number of galaxies., Their radii are stepwise increased until each circle contains the desired number of galaxies. +" Different pixels will need different radii, depending on the local galaxy density in that area of the field."," Different pixels will need different radii, depending on the local galaxy density in that area of the field." +" On a fine grid, galaxies shared by neighbouring pixels will of course cause these pixels to be correlated (see Fig[T))."," On a fine grid, galaxies shared by neighbouring pixels will of course cause these pixels to be correlated (see \ref{overlap}) )." +" The second issue concerns the strong-lensing regime, in particular the arc positions."," The second issue concerns the strong-lensing regime, in particular the arc positions." +" Since strong lensing is confined to much smaller scales than weak lensing, essential positional information is lost if the strong-lensing constraints are incorporated at the same resolution as weak lensing."," Since strong lensing is confined to much smaller scales than weak lensing, essential positional information is lost if the strong-lensing constraints are incorporated at the same resolution as weak lensing." + This requires us to refine the grid near cluster centres until it is capable of resolving the exact arc positions (see Fig. [2))., This requires us to refine the grid near cluster centres until it is capable of resolving the exact arc positions (see Fig. \ref{refinedgrid}) ). + The most important ingredient of our cluster reconstruction is the X function (Eq. [10)), The most important ingredient of our cluster reconstruction is the $\chi^{2}$ -function (Eq. \ref{chi2}) ) + that we need to minimise., that we need to minimise. + Consider first the weak-lensing term., Consider first the weak-lensing term. +" As discussed before, the lensing grid pixels are correlated because of the adaptive-averaging procedure, and the expectation value of the ellipticity is the reduced shear rather than the shear."," As discussed before, the weak-lensing grid pixels are correlated because of the adaptive-averaging procedure, and the expectation value of the ellipticity is the reduced shear rather than the shear." +" Thus we find, for Ig]<1, where (2) represents the results of the averaging process for each pixel."," Thus we find, for $|g|\leq 1$, where $\left\langle\varepsilon\right\rangle$ represents the results of the averaging process for each pixel." + We are using Einstein's sum convention here and below., We are using Einstein's sum convention here and below. + The case |g|>1 is not relevant in our reconstruction because it only affects at most very few pixels on the reconstruction, The case $|g|>1$ is not relevant in our reconstruction because it only affects at most very few pixels on the reconstruction +"One method for determining the number of hydrogen atoms in a galaxy is to assume that the mass of gas in the galaxy is some fraction of its stellar mass: where =+ος is the gas fractionfzas(z) givenMegas/(Mgasin ?,, and weMu) have neglected(1+zo the possible contribution of helium to the gas mass of a galaxy.","One method for determining the number of hydrogen atoms in a galaxy is to assume that the mass of gas in the galaxy is some fraction of its stellar mass: where $f_{\rm gas}(z) = M_{\rm gas}/(M_{\rm gas}+M_{\ast}) \propto (1+z)^{0.9}$ is the gas fraction givenin \citet{pap10}, and we have neglected the possible contribution of helium to the gas mass of a galaxy." +" Substituting Equation (1) into Equation (10)) and approximating V(z)/W(0)~psrn(z)/psrn(0), we get: where psen(z) isthe cosmic SFR (CSFR) given (12)by log(Ógern(z))=—2.06+3.39log(12) for z«1.3 and PsrFR(Z)~const. for 1.3€z«4.0 "," Substituting Equation \ref{eqn:nhpap}) ) into Equation \ref{eqn:galfluxgeneral}) ) and approximating $\Psi(z)/\Psi(0) \sim \dot{\rho}_{\rm SFR}(z)/\dot{\rho}_{\rm SFR}(0)$, we get: where $\dot{\rho}_{\rm SFR}(z)$ isthe cosmic SFR (CSFR) given by $\log(\dot{\rho}_{\rm SFR}(z)) = -2.06 +3.39\log(1+z)$ for $z < 1.3$ and $\dot{\rho}_{\rm SFR}(z) \sim \mbox{const.}$ for $1.3 \leq z \leq 4.0$ \citep{ly10}." +"To get the total contribution to the (?)..EGB, we convolve with the comoving number density of star-forming galaxies per stellar mass interval as a function of redshift and integrate: where ®(z,M’)=d?N/dM'dVeom is the Schecter function for stellar mass with parameters as determined in ?,, M’ is given by M,=10”’Mo5, and we take M!min..,—8.0 and M/,,,max=12.0."," To get the total contribution to the EGB, we convolve with the comoving number density of star-forming galaxies per stellar mass interval as a function of redshift and integrate: where $\Phi(z,M') = d^2N/dM'dV_{\rm com}$ is the Schecter function for stellar mass with parameters as determined in \citet{els08}, $M'$ is given by $M_{\ast} = 10^{M'}M_{\odot}$, and we take $M'_{\rm min} = 8.0$ and $M'_{\rm max} = 12.0$." +" Alternatively, we can determine the spectrum of a galaxy by assuming that the luminosity of the galaxy is proportional to some power of its SFR (???):: ΤριοςV."," Alternatively, we can determine the spectrum of a galaxy by assuming that the luminosity of the galaxy is proportional to some power of its SFR \citep{fie10, mak10,M31lat10}: $L_{\rm ph} \propto \Psi^{\alpha}$ ." +" Since =Nu and (qu(E))«V (as demonstrated Lgsin Section(E)(qu(£)) ??)), where A and «are the best-fit parameters of the above power law determined from observations of star-forming galaxies in the Local Group and their SFRs (see Section ??))."," Since $L_{\rm ph}(E) = \leftN_{\rm H}$ and $\left \propto \Psi$ (as demonstrated in Section \ref{subsubsection:schecter}) ), where $A$ and $\alpha$ are the best-fit parameters of the above power law determined from observations of star-forming galaxies in the Local Group and their SFRs (see Section \ref{subsubsec:inputIR}) )." +" Assuming the ? initial mass function, the SFR of a galaxy is related to its total infrared luminosity, Lin; (?).."," Assuming the \citet{cha03} initial mass function, the SFR of a galaxy is related to its total infrared luminosity, $L_{\rm IR}$, \citep{hop10}." +" The photon flux for a galaxy at redshift z Then, the total contribution to the EGB is found by convolving the galaxy photon flux with an infrared luminosity function, 6(z,Lx)=d?N/dLyRdVeom and integrating over infrared luminosity and redshift: where we take [ΠΠήν=101015 and LiR;max=1015 Lo."," The photon flux for a galaxy at redshift $z$ Then, the total contribution to the EGB is found by convolving the galaxy photon flux with an infrared luminosity function, $\Phi(z,L_{\rm IR}) = d^2N/dL_{\rm IR}dV_{\rm com}$ and integrating over infrared luminosity and redshift: where we take $L_{\rm IR,min} = 10^{10}L_{\odot}$ and $L_{\rm IR,max} = 10^{15}L_{\odot}$ ." + ofcon, Another alternative is to relate the cosmic density of hydrogen in star-forming galaxies to the cosmic star formation rate. +ditions®.," Given that stars are formed in giant molecular clouds (GMCs), it is reasonable to assume where $\dot{\rho}_{\rm SFR}$ is the cosmic star formation rate density (see Section \ref{subsubsection:schecter}) ), $\rho_{\rm H_2}$ is the cosmic molecular hydrogen density in star-forming galaxies, and $\xi({\rm H_2})$ is the star formation “efficiency"" (SFE) of molecular hydrogen \citep{big08,gne09,bau10}." +. , \citet{ler08} measure the SFE to be $\sim (5.25 \pm 2.5)\times 10^{-10} {\rm yr^{-1}}$ and to be roughly constant over a wide range of. +"We can relate the density of atomic hydrogen to the density ofmolecular hydrogen through the average mass ratio of atomic and molecular hydrogen (R=(Mum in star-forming galaxies, pyr~pg,."," We can relate the density of atomic hydrogen to the density ofmolecular hydrogen through the average mass ratio of atomic and molecular hydrogen $\mathcal{R} = \left$ ) in star-forming galaxies, $\rho_{\rm HI} \sim \mathcal{R}\rho_{\rm H_2}$." +" The average mass /Mng,))ratio of atomic and molecular hydrogen can be found by integrating radial profiles of the gas surface densities of star-forming galaxies found in ?,, resulting in R~ 0.9."," The average mass ratio of atomic and molecular hydrogen can be found by integrating radial profiles of the gas surface densities of star-forming galaxies found in \citet{ler08}, resulting in $\mathcal{R}\sim 0.9$ ." +" Note that in so doing, we only integrate the profiles out to the optical radius since recent surveys indicate that star formation is extremely inefficient beyond this radius (?) low..."," Note that in so doing, we only integrate the profiles out to the optical radius since recent surveys indicate that star formation is extremely inefficient beyond this radius \citep{big10} ." +" Thus, with appropriate modifications to Equation [I0], we find the flux from a particular"," Thus, with appropriate modifications to Equation \ref{eqn:galfluxgeneral}, , we find the flux from a particular" +"With A,=1.281 HAT-P-13b has a large radius given its mass and age.",With $R_\mathrm{p}=1.281$ HAT-P-13b has a large radius given its mass and age. + This implies it possesses an interior energy source. like nany other Hot Jupiter planets.," This implies it possesses an interior energy source, like many other Hot Jupiter planets." + Given its eccentric orbit. this energy source could have a strong contribution due to tidal heating.," Given its eccentric orbit, this energy source could have a strong contribution due to tidal heating." + Based on our analysis of &» and our interior models we found that the adiabatic transition is between 3 and bbar., Based on our analysis of $k_2$ and our interior models we found that the adiabatic transition is between 3 and bar. + We ran atmosphere models to estimate what values of the intrinsic temperature (734) these would correspond to., We ran atmosphere models to estimate what values of the intrinsic temperature $T_\mathrm{int}$ ) these would correspond to. + At the adiabatic transitions of 3 and bbar we found Τη=750 and KK. respectively.," At the adiabatic transitions of 3 and bar we found $T_\mathrm{int}=750$ and K, respectively." + This also gives us the intrinsic luminosity Lin., This also gives us the intrinsic luminosity $L_\mathrm{int}$. +" Assuming Lin, is provided only by tidal heating. we estimated Q with the following relation (?) This gives us a lower limit on the Q value of HAT-P-13b since tidal heating might not be the only interior energy source."," Assuming $L_\mathrm{int}$ is provided only by tidal heating, we estimated $Q$ with the following relation \citep{Milleretal09} + This gives us a lower limit on the $Q$ value of HAT-P-13b since tidal heating might not be the only interior energy source." + There could be other effects contributing to Zi. for instance Ohnmtic dissipation (?)..," There could be other effects contributing to $L_\mathrm{int}$, for instance Ohmic dissipation \citep{BatyginStevenson10}." + Our estimates of the lower limit on Q for the different eccentricity measurements are displayed in. Tab. Ι.., Our estimates of the lower limit on $Q$ for the different eccentricity measurements are displayed in Tab. \ref{tab:Qs}. + For comparison. Jupiter's Qvalue has been calculated to be between 10° and 10° (2)..," For comparison, Jupiter's $Q$value has been calculated to be between $10^5$ and $10^6$ \citep{GoldreichSoter66}." + In addition to an allowed &»-interval. ? also provided a set of possible interior models of HAT-P-13b that give κ. values within the given interval.," In addition to an allowed $k_2$ -interval, \citet{Batyginetal09} also provided a set of possible interior models of HAT-P-13b that give $k_2$ values within the given interval." + These models range 1n core mass from 0 toME., These models range in core mass from 0 to. +. However. for the given BBL-interval we find a maximum possible core mass that is significantly smaller (=87 ME).," However, for the given BBL-interval we find a maximum possible core mass that is significantly smaller $\approx87$ )." + This difference is a result of different model assumptions., This difference is a result of different model assumptions. + The models of αἱ have cores with constant densities of eg/cm? (Batygin. comm.)). resembling water cores.," The models of \citet{Batyginetal09} all have cores with constant densities of $^3$ (Batygin, ), resembling water cores." + In contrast. the models presented in this work were calculated using a compressible rock EOS (?).. increasing the densities in the cores up to gg/cm?.," In contrast, the models presented in this work were calculated using a compressible rock EOS \citep{HubbardMarley89}, increasing the densities in the cores up to $^3$." + As a consequence of the lower and constant core densities in the BBL models. a core of a specific mass requires a larger radius thàn à core of the same mass in our models.," As a consequence of the lower and constant core densities in the BBL models, a core of a specific mass requires a larger radius than a core of the same mass in our models." + This results in a greater Love number than our models with the same core mass., This results in a greater Love number than our models with the same core mass. + That is why our models need smaller core masses in order to fall in the allowed &»-interval., That is why our models need smaller core masses in order to fall in the allowed $k_2$ -interval. + Models of HAT-P-I13b in this work with à core mass of would have a smaller κ. than the lower &»-boundary of the BBL-interval., Models of HAT-P-13b in this work with a core mass of would have a smaller $k_2$ than the lower $k_2$ -boundary of the BBL-interval. + Hence. the different maximum core masses in this work and in ? arise from the different core EOS used.," Hence, the different maximum core masses in this work and in \citet{Batyginetal09} arise from the different core EOS used." + This shows the major influence of the EOS., This shows the major influence of the EOS. + In our example here. the different core EOS cause an uncertainty of about in the maximum possible core mass.," In our example here, the different core EOS cause an uncertainty of about in the maximum possible core mass." + As mentioned before (see 3.2))4 the eccentricity is crucial for determining an allowed &;-interval., As mentioned before (see \ref{subsec:e}) ) the eccentricity is crucial for determining an allowed $k_2$ -interval. + We used the results from BBL to obtain a from another eccentricity measurement (?).., We used the results from BBL to obtain a from another eccentricity measurement \citep{Winnetal10}. + Our new interval. ranging from 0.265 to 0.379 1s significantly smaller than the one previously used by BBL (0.116«&»0.425).," Our new interval, ranging from 0.265 to 0.379 is significantly smaller than the one previously used by BBL $0.116 < k_2 < +0.425$ )." +" This allowed for à more precise estimate of a maximum possible core mass (Ma,«27 ME)).", This allowed for a more precise estimate of a maximum possible core mass $M_\mathrm{core}<27$ ). + It of course has to be kept in mind that the ultimate significance of this new eccentricity value (and deduced κ.) is unclear., It of course has to be kept in mind that the ultimate significance of this new eccentricity value (and deduced $k_2$ ) is unclear. + Other effects like the stellar jitter produce a large uncertainty on the eccentricity measurement of the inner planet. as recently pointed out by ?..," Other effects like the stellar jitter produce a large uncertainty on the eccentricity measurement of the inner planet, as recently pointed out by \citet{PayneFord11}." + One way to help to constrain the eccentricity would be a detection of the occultation (secondary eclipse) of the planet (for instance. with Spitcer)).," One way to help to constrain the eccentricity would be a detection of the occultation (secondary eclipse) of the planet (for instance, with )." + The timing of the occultation can be used to place a strong constraint on ecosc. where e is the orbital eccentricity and w is the longitude of periastron (2)..," The timing of the occultation can be used to place a strong constraint on $e\cos\omega$, where $e$ is the orbital eccentricity and $\omega$ is the longitude of periastron \citep{Charbonneauetal05}." + Observations to determine ecos« for HAT-P-13b are currently being made (Harrington Hardy. conun.)).," Observations to determine $e\cos\omega$ for HAT-P-13b are currently being made (Harrington Hardy, )." + In this work. we presented new interior models of the transiting Hot Jupiter HAT-P-13b. with the aim of showing to what extent interior. models of extrasolar giant planets can be constrained by using the tidal Love number &» 1n addition to the known observables mass and radius.," In this work, we presented new interior models of the transiting Hot Jupiter HAT-P-13b with the aim of showing to what extent interior models of extrasolar giant planets can be constrained by using the tidal Love number $k_2$ in addition to the known observables mass and radius." + We also varied the envelope temperature and metallicity in order to demonstrate the uncertainties imposed on the inferred interior models., We also varied the envelope temperature and metallicity in order to demonstrate the uncertainties imposed on the inferred interior models. + One mainresult of our work Is that based on the Love number &» one cannot draw a conclusion on the precise core mass of the planet., One mainresult of our work is that based on the Love number $k_2$ one cannot draw a conclusion on the precise core mass of the planet. + Only a core mass can be inferred which is given by adiabatic zero-envelope-metallicity models., Only a core mass can be inferred which is given by adiabatic zero-envelope-metallicity models. + Taking into account the allowed ko interval (0.116. and |O HI] ABOOT can be easily observed. ancl measured to substantial redshifts.," If the relation is tight, it provides a mechanism for studying the evolution of the relationship between black hole and galaxy formation processes, as the emission lines, $\beta$ and [O III] $\lambda$ 5007 can be easily observed and measured to substantial redshifts." + An initial attempt to compare (his relationship between low and high redshift sample using data from the literature has been published by Shieldsetal. (2002).., An initial attempt to compare this relationship between low and high redshift sample using data from the literature has been published by \citet{shieldsetal02}. . +" This paper reports on an investigation of the M, vs [O HI] FWIIM relation for AGN from a large. homogeneousdata set. the Sloan Digital 5kv Survey (SDSS) Early Data Release"," This paper reports on an investigation of the ${\rm M_{\bullet}}$ vs [O III] FWHM relation for AGN from a large, homogeneousdata set, the Sloan Digital Sky Survey (SDSS) Early Data Release" +Following Keenan ct al. (,Following Keenan et al. ( +2007). we categorise emission-line ratios as three tvpes. namelv: (i) branching ratios (i.e. where the transitions arise [rom a common upper level). which are predicted to be constant under normal plasma conditions. (,"2007), we categorise emission-line ratios as three types, namely: (i) branching ratios (i.e. where the transitions arise from a common upper level), which are predicted to be constant under normal plasma conditions. (" +"An exception is where there is significant opacity. which does not apply to the lines considered. here): (ii) ratios which are predicted to be relatively insensitive to variations in T. and N, over the range of plasma porameters of interest: (ii) ratios which are predicted. to be strongly. N, sensitive. and hence potentially provide. useful. electron density. cliagnostics.","An exception is where there is significant opacity, which does not apply to the lines considered here); (ii) ratios which are predicted to be relatively insensitive to variations in $_{e}$ and $_{e}$ over the range of plasma parameters of interest; (iii) ratios which are predicted to be strongly $_{e}$ --sensitive, and hence potentially provide useful electron density diagnostics." + Clearly. raios which fall into categories (i) or (ii) are the most uselu for identifving and assessing the importance of blends. as weIL as investigating possible errors or problems with the adoped atomic data. as one does not need to reliably. know 1e plasma electron temperature and. density o calculate a ine ratio for comparison with the observed value.," Clearly, ratios which fall into categories (i) or (ii) are the most useful for identifying and assessing the importance of blends, as well as investigating possible errors or problems with the adopted atomic data, as one does not need to reliably know the plasma electron temperature and density to calculate a line ratio for comparison with the observed value." + In Tabes 5 and 6 we therefore list. the observed ine ratios for 1ο SERTLS89 and SERTS95 active regions. respectively (àong with the associated le errors). which fall into category (i) or (ii). along with theoretical values both rom the present calculations and the database. which emplovs the atomic data of Del Zanna et al. (," In Tables 5 and 6 we therefore list the observed line ratios for the SERTS–89 and SERTS–95 active regions, respectively (along with the associated $\sigma$ errors), which fall into category (i) or (ii), along with theoretical values both from the present calculations and the database, which employs the atomic data of Del Zanna et al. (" +2004).,2004). + Once again. following Ixeenan et al. (," Once again, following Keenan et al. (" +2007). for category (ii) ratios we have defined “relatively insensitive as being hose which are predicted to vary by. less than E20 per cent when the electron. density is changed by a [actor of 2 (io. £0.83 dex).,"2007), for category (ii) ratios we have defined `relatively insensitive' as being those which are predicted to vary by less than $\pm$ 20 per cent when the electron density is changed by a factor of 2 (i.e. $\pm$ 0.3 dex)." + As noted by Keenan et al.," As noted by Keenan et al.," + most of the electron densities derived for the SERTS89 and SERLS95, most of the electron densities derived for the SERTS–89 and SERTS–95 +"Figure 8 shows the S/N for the detection of the O; feature in our super-Earth prototype, for observation of all the primary transits available on average over the 5 year mission time, with stellar noise only (left) and all the above and zodiacal noises (right).","Figure \ref{f:O3-primary} shows the S/N for the detection of the $_3$ feature in our super-Earth prototype, for observation of all the primary transits available on average over the 5 year mission time, with stellar noise only (left) and all the above and zodiacal noises (right)." +" As seen above for the NIR spectroscopy, habitable planets can be characterized only around low mass stars."," As seen above for the NIR spectroscopy, habitable planets can be characterized only around low mass stars." +" Additionally, because the O; feature is difficult to detect, we calculate this and all subsequent plots for this species at ppc (value derived from occurring statistics for transiting habitable planets, see Section 6))."," Additionally, because the $_3$ feature is difficult to detect, we calculate this and all subsequent plots for this species at pc (value derived from occurring statistics for transiting habitable planets, see Section \ref{s:stats}) )." + It can be seen that the ozone feature will be detectable in transmission only for warm habitable planets around the lowest mass M dwarves., It can be seen that the ozone feature will be detectable in transmission only for warm habitable planets around the lowest mass M dwarves. + It should be noted that the chosen value for µ mmol!) implies an atmosphere dominated by water- corresponding to a super-Earth with a sufficient water reservoir near the inner edge of the habitable zone.," It should be noted that the chosen value for $\mu$ $^{-1}$ ) implies an atmosphere dominated by water-vapor, corresponding to a super-Earth with a sufficient water reservoir near the inner edge of the habitable zone." + O3 detection as well as its interpretation in terms of biosignature are problematic within a H5O-rich atmosphere:, $_3$ detection as well as its interpretation in terms of biosignature are problematic within a $_2$ O-rich atmosphere: +Magnetic fields are observed in almost all. astronomical objects. they permeate planets and stars as well as galaxies and clusters.," Magnetic fields are observed in almost all astronomical objects, they permeate planets and stars as well as galaxies and clusters." + Most. if not all. of the interstellar and intergalactic plasma appears to be magnetized and the magnetic fields contribute significantly to physical processes.," Most, if not all, of the interstellar and intergalactic plasma appears to be magnetized and the magnetic fields contribute significantly to physical processes." + Examples include the formation of stars (?).. the anisotropy of transport processes (thermal conduction or plasma resistivity. see e.g. ?)). the angular momentum transport in. aceretion dises or the propagation of cosmic ray populations (?)..," Examples include the formation of stars \citep{2009RMxAC..36..128P}, the anisotropy of transport processes (thermal conduction or plasma resistivity, see e.g. \citet{2001ApJ...562L.129N}) ), the angular momentum transport in accretion discs or the propagation of cosmic ray populations \citep{2007ARNPS..57..285S}." + Although magnetic fields are ubiquitous in the cosmos. we often cannot treat them properly in astrophysical situations due to. the lack of knowledge of their properties.," Although magnetic fields are ubiquitous in the cosmos, we often cannot treat them properly in astrophysical situations due to the lack of knowledge of their properties." + Cosmic magnetic fields are difficult to observe and their distribution. evolution and origins are far from being perfectly understood.," Cosmic magnetic fields are difficult to observe and their distribution, evolution and origins are far from being perfectly understood." + We have three main sources of information: the Zeeman effect. synchrotron radiation and Faraday rotation.," We have three main sources of information: the Zeeman effect, synchrotron radiation and Faraday rotation." + The Zeeman effect is extremely difficult to detect. because other line shifting effects. such as thermal Doppler-broadening. are usually stronger.," The Zeeman effect is extremely difficult to detect, because other line shifting effects, such as thermal Doppler-broadening, are usually stronger." + We obtain a great deal of information from synchrotron radiation but only regarding the magnetic field component perpendicular to the line of sight., We obtain a great deal of information from synchrotron radiation but only regarding the magnetic field component perpendicular to the line of sight. + In order to get a picture of the 3D magnetic field. one needs another source of information.," In order to get a picture of the 3D magnetic field, one needs another source of information." + This leads us to Faraday rotation. the change of the polarisation-plane of long wavelength radiation due to a magnetic field along the line of sight.," This leads us to Faraday rotation, the change of the polarisation-plane of long wavelength radiation due to a magnetic field along the line of sight." + Faraday rotation provides a powerful tool. but is also difficult to observe. to evaluate. and to interpret due to the involved line of sight projection.," Faraday rotation provides a powerful tool, but is also difficult to observe, to evaluate, and to interpret due to the involved line of sight projection." + This projection ts one of the main obstacles to understand the 3D properties of magnetic fields., This projection is one of the main obstacles to understand the 3D properties of magnetic fields. + One important property of cosmic magnetic fields that we do not know much about is magnetic helicity., One important property of cosmic magnetic fields that we do not know much about is magnetic helicity. + It is defined as the integral over a Volume V with surface OV on which n-B=0: where A refers to the vector potential from electrodynamics with B=VxA., It is defined as the integral over a Volume $V$ with surface $\partial V$ on which $\fe{n} \cdot \fe{B}=0$; where $\fe{A}$ refers to the vector potential from electrodynamics with $\fe{B}=\nabla \times \fe{A}$. + Helicity is à measure for the “spiral quality of a magnetic field., Helicity is a measure for the “spiral quality” of a magnetic field. + It quantifies how much the magnetic field lines are sheared and twisted and counts the number of spirals the field lines exhibit within a given volume., It quantifies how much the magnetic field lines are sheared and twisted and counts the number of spirals the field lines exhibit within a given volume. + Particularly turbulent magnetic fields should show considerable helicity., Particularly turbulent magnetic fields should show considerable helicity. + The relevance of helicity has increased since its inclusion as an essential element in the magnetic dynamo theory. which tries to explain the sustainement of magnetic fields on large scales over cosmic timescales (see???)..," The relevance of helicity has increased since its inclusion as an essential element in the magnetic dynamo theory, which tries to explain the sustainement of magnetic fields on large scales over cosmic timescales \citep[see][]{2002BASI...30..715S,2005PhR...417....1B,2005AN....326..400B}." +" The possible operation of a large scale dynamo for instance is directly connected to the generation of helicity in turbulent environments (see2?2)., a process which. until now. could not be verified through observation,"," The possible operation of a large scale dynamo for instance is directly connected to the generation of helicity in turbulent environments \citep[see][]{2006A&A...448L..33S,2009PPCF...51l4043B,2007PPCF...49..447S}, a process which, until now, could not be verified through observation." + This study is particularly concerned with the question of how to extract knowledge regarding turbulent magnetic helicity spectra from the statistical information found in radio-observational data involving polarisation and Faraday rotation measurements., This study is particularly concerned with the question of how to extract knowledge regarding turbulent magnetic helicity spectra from the statistical information found in radio-observational data involving polarisation and Faraday rotation measurements. + It was highly motivated by the studies of ?.., It was highly motivated by the studies of \citet{2010JETPL..90..637V}. + Information on magnetic fields can be imprinted onto radio data by two of the processes already mentioned above: androtation., Information on magnetic fields can be imprinted onto radio data by two of the processes already mentioned above: and. +.. Yet information is not only contained in their mean values but also in higher order correlation and eross-correlation. functions., Yet information is not only contained in their mean values but also in higher order correlation and cross-correlation functions. + We therefore investigate a set of suitable radio observables for their cross-correlations. to see how these are connected to the statistical properties of the magnetic fields to be examined.," We therefore investigate a set of suitable radio observables for their cross-correlations, to see how these are connected to the statistical properties of the magnetic fields to be examined." + This idea goes back to previous works by 22222??.. ," This idea goes back to previous works by \citet{1982ApJ...261..310S,1983ApJ...271L..49S,1989AJ.....98..244E,1989AJ.....98..256E,2003A&A...401..835E,2006PhRvD..73f3507K,2009MNRAS.398.1970W}. ." +The set of radio observables we investigate contains the total intensity /(x). the polarised intensity P(x) and the Faraday depth (x).," The set of radio observables we investigate contains the total intensity $I(\fe{x})$, the polarised intensity $P(\fe{x})$ and the Faraday depth $\phi(\fe{x})$." + We work out all correlation functions between them in a general framework., We work out all correlation functions between them in a general framework. + We restrict ourselves to fourth order in the magnetic field strength and as far as possible we do all calculations analytically., We restrict ourselves to fourth order in the magnetic field strength and as far as possible we do all calculations analytically. + The aim is to find a direct relation to statistical properties of the magnetic fields. such as their power spectra.," The aim is to find a direct relation to statistical properties of the magnetic fields, such as their power spectra." + —The intensity /(x) and the polarised intensity P(x) are connected to the synchrotron emission within a magnetized volume., The intensity $I(\fe{x})$ and the polarised intensity $P(\fe{x})$ are connected to the synchrotron emission within a magnetized volume. + We assume them to be taken at sufficiently high frequencies and. therefore. free of Faraday rotation.," We assume them to be taken at sufficiently high frequencies and, therefore, free of Faraday rotation." + The Faraday depth @(x) is measured via the Faraday rotation of a polarized background source at a different frequency seen through the same volume., The Faraday depth $\phi(\fe{x})$ is measured via the Faraday rotation of a polarized background source at a different frequency seen through the same volume. + The observational situation 15 visualized in Fig. (1))., The observational situation is visualized in Fig. \ref{obsreg}) ). + With regard to these observable quantities. we can successfully establish all correlation functions in the form ofanalytical relations to the magnetic field power and helicity spectra implementing Gaussian field statistics for simplicity.," With regard to these observable quantities, we can successfully establish all correlation functions in the form ofanalytical relations to the magnetic field power and helicity spectra implementing Gaussian field statistics for simplicity." +through an intermediate rauge. the Fe II inflow velocity becomes apparcutly smaller. while the |O IH] outflow velocity becomes apparcutly larger.,"through an intermediate range, the Fe II inflow velocity becomes apparently smaller, while the [O III] outflow velocity becomes apparently larger." + Within the intermediate range. objects show neither motion strougly aud cluster around the origin.," Within the intermediate range, objects show neither motion strongly and cluster around the origin." + If oricutation were the onlv factor. then properties of the objects near the origin should be intermediate between the two tails.," If orientation were the only factor, then properties of the objects near the origin should be intermediate between the two tails." + Furthermore. relationships among those properties should behave Ina wav that tracks the relatiouships between the wo tails.," Furthermore, relationships among those properties should behave in a way that tracks the relationships between the two tails." + The oricutation-ouly livpothlesis is disprove by feure 2. which shows the huuinosity at A5100 slotted against the PWOAL of IL) for the objects hat have no siguificaut offset velocity iu either Fe Ἡ or |O IIIJ.," The orientation-only hypothesis is disproven by figure 2, which shows the luminosity at $\lambda$ 5100 plotted against the FWHM of $\beta$ for the objects that have no significant offset velocity in either Fe II or [O III]." + While the edge-on objects have lower uuinositv aud larger lie width than the pole-on objects. the putative— intermediate objects show he opposite trend higher huuinosity objects rave larger Hue width.," While the edge-on objects have lower luminosity and larger line width than the pole-on objects, the putative intermediate objects show the opposite trend – higher luminosity objects have larger line width." + The correlation cocficicut or these 1081 objects closest to the origin is 135. indicating a probability of less than 10. οἳ i0 correlation.," The correlation coefficient for these 1081 objects closest to the origin is 0.35, indicating a probability of less than $^{-7}$ of no correlation." + Thus. our couclusion is that this ⋅ ⋅⋅ ⋅ ∐↸∖↴⋝∪↕∪⋯∖⊓⋅∐⊳↕∏∐∐∐∪↴∖↴↕↑↖↽∙↕↴∐⊳↸∖↥⋅↑⋜⊔∐↑↕↸∖↴∖↴↕∐↑∐∖↴∖↴↸∖ Eddington⋅↜ ratio⋅ objects. that are pole-ou aud the Hel Eddington ratio objects that are edec-on.," Thus, our conclusion is that this intermediate subset represents a mix of the low Eddington ratio objects that are pole-on and the high Eddington ratio objects that are edge-on." + The uest step is to divide the intermediate subset into those objects that represent. the pole-on counterparts of the edge-on. low Eddington ratio objects and those that represeut the edge-on counterparts of the pole-on. high Eddington ratio objects.," The next step is to divide the intermediate subset into those objects that represent the pole-on counterparts of the edge-on, low Eddington ratio objects and those that represent the edge-on counterparts of the pole-on, high Eddington ratio objects." + To do this. note that the solid angle over which objects appear pole-on is aller than that over which they appear edge-on.," To do this, note that the solid angle over which objects appear pole-on is smaller than that over which they appear edge-on." + Counting objects in the two tails of igure 1 aud asstmingthat these tails represent objects that ave within 30 deerees of the preferred onrieutation. we calculate that approximately half of the intermediate objects should be the edgc-on counterparts of the objects that show large [O III] outflows aud half should be the pole-on counterparts of the objects that show large Fe 11 inflows.," Counting objects in the two tails of figure 1 and assuming that these tails represent objects that are within 30 degrees of the preferred orientation, we calculate that approximately half of the intermediate objects should be the edge-on counterparts of the objects that show large [O III] outflows and half should be the pole-on counterparts of the objects that show large Fe II inflows." + Because our interpretation of figure 2 ix that the correlation seen between Lsiyy and ΕΠΑΕ IL/ is due to the mix of objects with two different sets of plivsical parameters. we divide the distiibutiou of objects iu figure 2 with a line perpendicular to the best fit line (the bisector of the two dashed lines shown). at a point that divides the distribution into two approximately equal subsets;," Because our interpretation of figure 2 is that the correlation seen between $_{5100}$ and FWHM $\beta$ is due to the mix of objects with two different sets of physical parameters, we divide the distribution of objects in figure 2 with a line perpendicular to the best fit line (the bisector of the two dashed lines shown), at a point that divides the distribution into two approximately equal subsets." + We choose to label the upper right cud of the distribution as the low-Eddington pole-ou objects because if the two parts of theiutermediate objects were assigned in the opposite seuse. they would appear to ect brighter when they were viewed edec-on than when they were viewed pole-on.," We choose to label the upper right end of the distribution as the low-Eddington pole-on objects because if the two parts of the intermediate objects were assigned in the opposite sense, they would appear to get brighter when they were viewed edge-on than when they were viewed pole-on." + Towever. both the division and the assiguinent are speculative and based somewhat on a preconception about the structure aud kinematics of the objects in the saiiple.," However, both the division and the assignment are speculative and based somewhat on a preconception about the structure and kinematics of the objects in the sample." + Table ↽⋅1 gives median.⋅ erties⋅⋟ for the jour. subsets., Table 1 gives median properties for the four subsets. + All the propertiespro are calculated from data in Table 2 in IInetal.(2008)., All the properties are calculated from data in Table 2 in \citet{hu08}. +". Note that the lack hole masses are calculated using the values of oy, rather than FWIIAL Το. and that the Eddington ratios are calculated using VALS yy as ↕∐↑↸∖↥⋅↕⊔↸∖≼∐⋜↧↑↸∖↴∖↴∏↴⋝↴∖↴↸∖↑↥⋅↸∖↻↥⋅↸∖"," Note that the black hole masses are calculated using the values of $\sigma_{H\beta}$ rather than FWHM $\beta$, and that the Eddington ratios are calculated using $\lambda$ $_{5100}$ as the bolometric luminosity." +↴∖↴↸∖∐↑↴∖↴⋜↧∐∐↘∪↕↑∐↸∖↕∪↖↖⇁. ⋅⋅ ⇁⋅⋅⋅ characteristic. values for the subsets are in the range of only a few percent. though it should ve noted that the range of auv property within a subset is huge. as can be που in figure 2.," Uncertainties in these characteristic values for the subsets are in the range of only a few percent, though it should be noted that the range of any property within a subset is large, as can be seen in figure 2." + While some quantitative conclusions are drawn (low about the behavior of properties within and between subsets we caution that (a) the subsets are drawn frou a pareut sample that has oen chosen in a way that undoubtedly skews some of these statistics aud (b) our definitions of the subsets and how they are associated is arbitrary. though we believe that it all creates a consistent picture.," While some quantitative conclusions are drawn below about the behavior of properties within and between subsets, we caution that (a) the subsets are drawn from a parent sample that has been chosen in a way that undoubtedly skews some of these statistics and (b) our definitions of the subsets and how they are associated is arbitrary, though we believe that it all creates a consistent picture." + Note particularly that the eutire sample is assuined to be the sum of two separable populations. aud this is unlikely to be the case.," Note particularly that the entire sample is assumed to be the sum of two separable populations, and this is unlikely to be the case." + In reality. it is doubtful that a sharp transition exists between objects that show an Fe II inflow if they are seen edge-on aud those that show an {O TH) outflow if they are seen pole-on.," In reality, it is doubtful that a sharp transition exists between objects that show an Fe II inflow if they are seen edge-on and those that show an [O III] outflow if they are seen pole-on." + Also. our classification ofobjects as either edge-on or pole-on certainly weakens the apparent effects.," Also, our classification of objects as either edge-on or pole-on certainly weakens the apparent effects." + The behavior of luminosity and broad line width is particularly inportant as these observables are used to derive black hole mass aud Eddingtou ratio., The behavior of luminosity and broad line width is particularly important as these observables are used to derive black hole mass and Eddington ratio. + Both of these behave propertiesqualitatively as expected eiveu the results of previous studies of, Both of these properties behave qualitatively as expected given the results of previous studies of +velocity effect should vanish).,velocity effect should vanish). + It may be expected. that because the ΠΠ regions are created inside large overdeusities at hieh redshift. patchy models are more Gaussian on the whole.," It may be expected, that because the HII regions are created inside large overdensities at high redshift, patchy models are more Gaussian on the whole." + The main problem with this notion is that in anv patchy model with a comoving bubble size comparable to ours this effect will suffer from “washing out” by the primordial CMD., The main problem with this notion is that in any patchy model with a comoving bubble size comparable to ours this effect will suffer from “washing out” by the primordial CMB. + On scales where Doppler induced fluctuations become larger thu the primordial CMD. the impact of patchiness amouuts only to a fraction of the total sigual in Model D. in Model €. the rest being attributed to scatterings owing to density modulatious alone.," On scales where Doppler induced fluctuations become larger than the primordial CMB, the impact of patchiness amounts only to a fraction of the total signal in Model B, in Model C), the rest being attributed to scatterings owing to density modulations alone." + Also. the majority of non Gaussian contributions comes from clusters aud filaments at 5«3. compare Figure 5..," Also, the majority of non Gaussian contributions comes from clusters and filaments at $z < 3$, compare Figure \ref{3epochs-histo}." +" We computed the kurtosis zz 5) of thermal SZ ""cleaned imaps (ic. primorcial CXMB|Doppler) that were filtered with a Caussian i|] Fourier space. approximately cutting out ~coutanuuation— by the primordial ΟΠΣ— anisotropies— below 72«3500. and beam sincaring at scales of 7&9000 comparable to the augular resolution of ACT. (similar to the window function proposed by IIuffeubereer&Seljak 2001))."," We computed the kurtosis _4 - 3 of thermal SZ “cleaned” maps (i.e. primordial CMB+Doppler) that were filtered with a Gaussian in Fourier space, approximately cutting out “contamination” by the primordial CMB anisotropies below $l\simeq +3500$, and beam smearing at scales of $l\simeq 9000$ comparable to the angular resolution of ACT (similar to the window function proposed by \citealt{Huffenberger:2004gm}) )." + Using this method. we do not find a statistically sjenificaut difference between patchy aud homogeneous models of reionization.," Using this method, we do not find a statistically significant difference between patchy and homogeneous models of reionization." + Cosmidc imicrowave backeround iueasurenients lave been and will likely remain the most precise tools for the measurement of cosmological paraueters., Cosmic microwave background measurements have been and will likely remain the most precise tools for the measurement of cosmological parameters. + The best constraints will come frou a combination of CNID temperature aud polarization power spectra which encapsulate all the relevaut information iu the sv maps., The best constraints will come from a combination of CMB temperature and polarization power spectra which encapsulate all the relevant information in the sky maps. + The aim is to make the data cosmic variance limited to ax hieli as possible multipole numbers., The aim is to make the data cosmic variance limited to as high as possible multipole numbers. + WMATP is cosinic variance linited up to 7&500.," WMAP is cosmic variance limited up to $l \simeq +500$." + The Plauck satellite should achieve cosumüc variance liuitation out to /=2500 for its temperature power spectruni measurement., The Planck satellite should achieve cosmic variance limitation out to $l=2500$ for its temperature power spectrum measurement. + Heuce. Planck will reach iuto the regnunue where the secondary anisotropies become inuportant.," Hence, Planck will reach into the regime where the secondary anisotropies become important." + To avoid biases in paramcter estination.," To avoid biases in parameter estimation," +"It should be noted that the minima Tig for which ietallicitv effects are uceligible tends to increase with eravity,",It should be noted that the minimum $T_{\rm eff}$ for which metallicity effects are negligible tends to increase with gravity. +" For instance. at logy=0.5. the effects of [ML/TI] in A ave indeed ήπιο for TugZ3700 KE. while at logg=2.5 they are ouly negligible for Tag< LoOOTNIs. This is due to the fact that at temperatures close to where the molecules dissociate. the effect of metallicity is rather large. as the pressure im the line forming regions increases with lower |M/II| due to the overall lower opacities,"," For instance, at $\log g=0.5$, the effects of $\MoH$ in $V-K$ are indeed minor for $T_{\rm eff} \ga 3700$ K, while at $\log g=2.5$ they are only negligible for $T_{\rm eff} \ga 4000$ K. This is due to the fact that at temperatures close to where the molecules dissociate, the effect of metallicity is rather large, as the pressure in the line forming regions increases with lower $\MoH$ due to the overall lower opacities." + This causes a shift in the chemical equilibria iu the line forming regions. Which is more pronounced at higher gravities Gvhere the relative changes iu the pressure are higher) than at low οταντος where less molecules form (for given temperature and metallicity).," This causes a shift in the chemical equilibria in the line forming regions, which is more pronounced at higher gravities (where the relative changes in the pressure are higher) than at low gravities where less molecules form (for given temperature and metallicity)." + A ctailed comparison of svuthetic photometric colors with observations idu the Tig color planes can be made in a straightforward wav if svuthetic colors are provided in the form of Zig logg color relatious. with eravitics at different temperatures specified according to areprescutative Li logg relation.," A detailed comparison of synthetic photometric colors with observations in the $T_{\rm eff}$ –color planes can be made in a straightforward way if synthetic colors are provided in the form of $T_{\rm eff}$ $\log g$ –color relations, with gravities at different temperatures specified according to a representative $T_{\rm eff}$ $\log g$ relation." + Such au approach was adopted in Paper I to make a comparison of svuthetic aud observed colors at Solar metallicity., Such an approach was adopted in Paper I to make a comparison of synthetic and observed colors at Solar metallicity. + In this work we cluploy the saine strategy to compare photometric colors of late-type giauts at 3ub-Solar moetallicities., In this work we employ the same strategy to compare photometric colors of late-type giants at sub-Solar metallicities. + Since a homogeneous set of Tig logg relations suitable for use with late-type eiauts at sub-Solar moetallicities is not readily available in the literature. we focus im this Section on the derivation of new empirical Tey logg scales. at |M/H|=0.5.LO.L5.2.0.," Since a homogeneous set of $T_{\rm eff}$ $\log g$ relations suitable for use with late-type giants at sub-Solar metallicities is not readily available in the literature, we focus in this Section on the derivation of new empirical $T_{\rm eff}$ $\log g$ scales, at $\MoH=-0.5, -1.0, -1.5, -2.0$." + For this purpose we eniploy. a sample of late-type giauts iu Galactic elobular clusters (CCC's). with their effective temperatures aud eravities collected from the literature.," For this purpose we employ a sample of late-type giants in Galactic globular clusters (GGCs), with their effective temperatures and gravities collected from the literature." + The choice of CGC ejauts is based on several considerations., The choice of GGC giants is based on several considerations. + First. GGCs are ecnerally well observed. with precise atmospheric parameters of individual stars available over a wide ranec of effective temperatures and eravities.," First, GGCs are generally well observed, with precise atmospheric parameters of individual stars available over a wide range of effective temperatures and gravities." + Second. CCs span a wide metallicity range. which is crucial for the derivation of Tig logg relations at differcut |MJTI].," Second, GGCs span a wide metallicity range, which is crucial for the derivation of $T_{\rm eff}$ $\log g$ relations at different $\MoH$." + Finally. they are of similar age which implies a similarity in the atmospheric parameters of individual stars in clusters of similar inctallicity.," Finally, they are of similar age which implies a similarity in the atmospheric parameters of individual stars in clusters of similar metallicity." + This allows binning of stars frou different clusters into eroups according to their metallicities. to increase the muuber of individual stars available in a given metallicity eroup.," This allows binning of stars from different clusters into groups according to their metallicities, to increase the number of individual stars available in a given metallicity group." + Ideally. the new τω logg relatious should be derived musing a salple of late-tvpe giants with their effective teniperatures and eravities mnieasured usine direct methods. e.g.àY effective teniperatures obtained via the interferometric measurements of stellar radii aud eravities from parallaxes (i.c.. evolutionary eravities. see Sect.," Ideally, the new $T_{\rm eff}$ $\log g$ relations should be derived using a sample of late-type giants with their effective temperatures and gravities measured using direct methods, e.g., effective temperatures obtained via the interferometric measurements of stellar radii, and gravities from parallaxes (i.e., `evolutionary' gravities, see Sect." + L1.2 below)., \ref{GGCloggs} below). + Uufortuuatelv. direct measurements of atinosphierie parameters are currently available ouly for the nearby giauts. the majority of which have metallicities close to Solar.," Unfortunately, direct measurements of atmospheric parameters are currently available only for the nearby giants, the majority of which have metallicities close to Solar." + Needless to sav. late-type eiauts iu the GaCs are not accessible. due to the large distances involved.," Needless to say, late-type giants in the GGCs are not accessible, due to the large distances involved." + For this reason. our new relations derived im this Section are based on spectroscopic effective temperatures and eravitics of CCC elants Gu combination with Tig ," For this reason, our new relations derived in this Section are based on spectroscopic effective temperatures and gravities of GGC giants (in combination with $T_{\rm eff}$ " +H [4134+117 has four lensed images of a radio-quiet quasar at redshift 2.560 that are in the shape of a cloverleaf(Magainetal.1988).,H 1413+117 has four lensed images of a radio-quiet quasar at redshift 2.560 that are in the shape of a cloverleaf\citep{magain88}. + The optical emission from the four lensed images is so strong that attempts to measure the redshift of the lens have not been successful., The optical emission from the four lensed images is so strong that attempts to measure the redshift of the lens have not been successful. + The total magnification of the background quasar is estimated to be — 110 (Kayseretal.1990)., The total magnification of the background quasar is estimated to be $\sim$ 10 \citep{kayser90}. +. The system has a plethora of molecular emission and absorption detections: for example. CO (3-2: Barvainisetal.190. 4-3. 5-4. 7-6: Barvainisetal.1997. and 5-6. 8-7. 9-8: Bradfordetal.2009). HCN (1-0: Solomonetal. 2003)) and CN (3—2: Riecherset 2007).," The system has a plethora of molecular emission and absorption detections; for example, CO (3–2; \citealt{barvainis94}, 4–3, 5–4, 7–6; \citealt{barvainis97} and 5–6, 8–7, 9–8; \citealt{bradford09}) ), HCN (1–0; \citealt{soloman03}) ) and CN (3–2; \citealt{riechers07}) )." + The quasar is also ultra-luminous in the sub-mm and has an estimated dust mass of ~44 1107M. (Barvainis&Ivison 2002).," The quasar is also ultra-luminous in the sub-mm and has an estimated dust mass of $\sim$ $\times$ $^{8}\,M_{\odot}$ \citep{barvainis02}." +. Previous observations searching for maser activity failed to detect any water maser emission from this quasar down toan unlensed isotropic luminosity limit of 4600 £L... with a IO spectral resolution (Wilneretal.1999).," Previous observations searching for maser activity failed to detect any water maser emission from this quasar down toan unlensed isotropic luminosity limit of 4600 $L_{\odot}$, with a 10 $^{-1}$ spectral resolution \citep{wilner99}." +. MS cBSS8 is a star-forming Lyman break galaxy at redshift 2.727 which is gravitationally lensed by the massive cluster MS 1512436 at redshift 0.37 (Yeeetal.1996)., MS $-$ cB58 is a star-forming Lyman break galaxy at redshift 2.727 which is gravitationally lensed by the massive cluster MS 1512+36 at redshift 0.37 \citep{yee96}. +.. The galaxy is lensed into a gravitational are by the cluster and is estimated to have a high total magnification of 7 550 (Seitzetal.1998)., The galaxy is lensed into a gravitational arc by the cluster and is estimated to have a high total magnification of $\ga$ 50 \citep{seitz98}. +. CO (3-2) has been detected from the galaxy (Bakeretal.2004)... which along with the large potential maser magnification led to MS cB58 being included in our sample.," CO (3–2) has been detected from the galaxy \citep{baker04}, which along with the large potential maser magnification led to MS $-$ cB58 being included in our sample." + SMM 71635946612 is composed of three lensed images of a pairof merging galaxies at redshift 2.516., SMM J16359+6612 is composed of three lensed images of a pair of merging galaxies at redshift 2.516. + The lens is the massive cluster A2218 at redshift 0.18. and provides a total magnification of ~ 445 (Kneibetal.2004..," The lens is the massive cluster A2218 at redshift 0.18, and provides a total magnification of $\sim$ 45 \citep{kneib04}." +" The merging lensed galaxies show strong sub-mm emission (Kneibetal.2004) and a number of CO detections (transitions 3-3, 4—3. 5-4. 6-5. 7-6: e.g. Weietal.2005:Kneibetal. 20053)."," The merging lensed galaxies show strong sub-mm emission \citep{kneib04} and a number of CO detections (transitions 3–2, 4–3, 5–4, 6–5, 7–6; e.g., \citealt{weiss05b,kneib05}) )." + SMM 11635946612 was recently observed for water maser emission with the EVLA by Edmondsetal.(2009) and Wage&Momjian(2009)., SMM J16359+6612 was recently observed for water maser emission with the EVLA by \citet{edmonds09} and \citet{wagg09}. +. However. no water vapour was detected down to an unlensed luminosity of ~ 55400L. within a IOKkmss. + channel.," However, no water vapour was detected down to an unlensed luminosity of $\sim$ $L_{\odot}$ within a 10 $^{-1}$ channel." + In this section. our observations with the Effelsberg 100 m radio telescope and subsequent follow-up observations with the EVLA of tentative water maser detections are presented.," In this section, our observations with the Effelsberg 100 m radio telescope and subsequent follow-up observations with the EVLA of tentative water maser detections are presented." + The spectroscopic observations with the Effelsberg 100 m radio telescope were carried out with the 5 em dual-polarization HEMT receiver at the primary focus., The spectroscopic observations with the Effelsberg 100 m radio telescope were carried out with the 5 cm dual-polarization HEMT receiver at the primary focus. + This receiver is sensitive between 5.75 and 6.75 GHz. which for the detection of 22.2 GHz water masers corresponds to a redshift range of 2.29 to 2.87.," This receiver is sensitive between 5.75 and 6.75 GHz, which for the detection of 22.2 GHz water masers corresponds to a redshift range of 2.29 to 2.87." + The primary beam of the telescope at these frequencies has a FWHM of ~120 aresec. which is easily large enough to encompass the angular extent of the gravitationally lensed images.," The primary beam of the telescope at these frequencies has a FWHM of $\sim$ 120 arcsec, which is easily large enough to encompass the angular extent of the gravitationally lensed images." + The data were taken using the position-switching mode where a 2.5 min on-source scan was immediately followed by a 2.5 min off-source scan., The data were taken using the position-switching mode where a 2.5 min on-source scan was immediately followed by a 2.5 min off-source scan. + This off-source scan was subtracted from the on-source scan to remove the contribution of the sky background and the instrument from the on-source measurements., This off-source scan was subtracted from the on-source scan to remove the contribution of the sky background and the instrument from the on-source measurements. + Observations of standard flux-density calibrators were also taken to determine the antenna gain 2295: Ottetal.1994))., Observations of standard flux-density calibrators were also taken to determine the antenna gain 295; \citealt{ott94}) ). + The spectra were formed using the 163384-channel Fast Fourier Transform Spectrometer (FFTS: Kleinetal.2006))., The spectra were formed using the 384-channel Fast Fourier Transform Spectrometer (FFTS; \citealt{klein06}) ). + Both the 20 and 100 MHz bandwidths that are available with the FFTS were used during these observations., Both the 20 and 100 MHz bandwidths that are available with the FFTS were used during these observations. + A summary of the integration times. observing dates and bandwidths used for each lens system is given in Table I..," A summary of the integration times, observing dates and bandwidths used for each lens system is given in Table \ref{obs-log}." + The spectra were analysed using the package within GILDAS., The spectra were analysed using the package within . + Each scan was inspected for any strong gain variations or radio frequency interference (RFI). with any spurious scans or frequency ranges flagged.," Each scan was inspected for any strong gain variations or radio frequency interference (RFI), with any spurious scans or frequency ranges flagged." + The scans were then averaged to form a spectrum of the lens system for each observing epoch., The scans were then averaged to form a spectrum of the lens system for each observing epoch. + A low-order polynomial was then fitted to the spectrum to subtract any continuum emission from the lensed images., A low-order polynomial was then fitted to the spectrum to subtract any continuum emission from the lensed images. + For those lens systems that were observed on more than one occasion. an average spectrum weighted by the integration times was also produced.," For those lens systems that were observed on more than one occasion, an average spectrum weighted by the integration times was also produced." + We smoothed the spectra using Hanning smoothing to a spectral resolution of IO kmss! +., We smoothed the spectra using Hanning smoothing to a spectral resolution of 10 $^{-1}$ $^{-1}$. + Where we found a possible water maser line. a Gaussian line protile was fitted to the unsmoothed spectrum to determine the FWHM. the integrated line flux. the line peak flux density and the line velocity.," Where we found a possible water maser line, a Gaussian line profile was fitted to the unsmoothed spectrum to determine the FWHM, the integrated line flux, the line peak flux density and the line velocity." + Our spectroscopic observations found tentative detections of water maser lines from the gravitational lens system IRAS 1021444724 (see Section 4+— for details)., Our spectroscopic observations found tentative detections of water maser lines from the gravitational lens system IRAS 10214+4724 (see Section \ref{results} for details). + To confirm. these detections independently. we carried out interferometric spectroscopic observations with the EVLA.," To confirm these detections independently, we carried out interferometric spectroscopic observations with the EVLA." + These observations would also spatially match any water maser emission with the lens system., These observations would also spatially match any water maser emission with the lens system. + This is the same strategy that was used to confirm the detection of a water maser from the lensed quasar MG J04144-0534 (Impellizzerietal. 2008)., This is the same strategy that was used to confirm the detection of a water maser from the lensed quasar MG J0414+0534 \citep{impellizzeri08}. + IRAS 1021444724 was observed at a central frequency of 6.7675 GHz with the EVLA on 2008 May 30 and 31 using 15 antennas that had recently been upgraded with the new C-band receivers., IRAS 10214+4724 was observed at a central frequency of 6.7675 GHz with the EVLA on 2008 May 30 and 31 using 15 antennas that had recently been upgraded with the new C-band receivers. + The data were taken through a total bandwidth of 6.25 MHz and split into 64 channels., The data were taken through a total bandwidth of 6.25 MHz and split into 64 channels. + This gave a spectral coverage of 277 1 and a spectral resolution of 4.3 ! per channel., This gave a spectral coverage of 277 $^{-1}$ and a spectral resolution of 4.3 $^{-1}$ per channel. + IRAS. 1021444724 was known to be a weak radio source (Lawrenceetal.1993).. therefore the observations were phase-referenced by observing the calibrator JJ09584-474 every ~ [15 minutes to determine the phase and amplitude solutions.," IRAS 10214+4724 was known to be a weak radio source \citep{lawrence93}, therefore the observations were phase-referenced by observing the calibrator J0958+474 every $\sim$ 15 minutes to determine the phase and amplitude solutions." + Observations of another nearby continuum. source. 1310334412. were also taken throughout the run to verify the calibration process.," Observations of another nearby continuum source, J1033+412, were also taken throughout the run to verify the calibration process." + The flux-density calibration was determined with 1147 and 2286 assuming 6.7 GHz flux-densities of 5.858 and 6.051 Jy. respectively.," The flux-density calibration was determined with 147 and 286 assuming 6.7 GHz flux-densities of 5.858 and 6.051 Jy, respectively." + IRAS 1021444724 was observed for ~ 8.5 h in total., IRAS 10214+4724 was observed for $\sim$ 8.5 h in total. + The data were reduced in the standard way using CASA., The data were reduced in the standard way using . + A data cube was created using all of the channels. except for the first and last five channels.," A data cube was created using all of the channels, except for the first and last five channels." + The noise per channel was 0.57 mJy beam+ and the noise in the resulting continuum map was 78 jiJy, The noise per channel was 0.57 mJy $^{-1}$ and the noise in the resulting continuum map was 78$\mu$ Jy $^{-1}$ . + We now present a brief description of the radio spectra obtained, We now present a brief description of the radio spectra obtained +samples stars down to V~21.,samples stars down to $V \simeq 21$. +" In the very central region of the cluster (r<12”), the CMD shows the presence of a well defined population of massive MS stars together with a population of low mass PMS objects."," In the very central region of the cluster $r<12\arcsec$ ), the CMD shows the presence of a well defined population of massive MS stars together with a population of low mass PMS objects." +" Apparently only few MS stars are detected in the cluster center at magnitudes fainter than V~19.5, while in the external regions 120"") stars with masses down to ~1M, are detected both in the MS and PMS regions."," Apparently only few MS stars are detected in the cluster center at magnitudes fainter than $V \simeq 19.5$, while in the external regions $18\arcsec - 120\arcsec$ ) stars with masses down to $\sim +1$ $_{\odot}$ are detected both in the MS and PMS regions." +" By using archival WFPC2 observations in the F656N band combined with the WFPC2 broad-band SB04 were able to identify objects with excess Haphotometry, emission, which is a signature of the PMS phase."," By using archival WFPC2 observations in the F656N band combined with the WFPC2 broad-band photometry, SB04 were able to identify objects with excess $\alpha$ emission, which is a signature of the PMS phase." +" While the majority of these objects on their CMD occupies a region consistent with very young PMS isochrones (1 Myr), some stars fall near the ZAMS (see their Figure 7)."," While the majority of these objects on their CMD occupies a region consistent with very young PMS isochrones (1 Myr), some stars fall near the ZAMS (see their Figure 7)." +" SB04 speculate on a possible spread in age of the cluster stars, but they warn that it is difficult to reach a firm conclusion because of the decreasing completeness and photometric accuracy of their photometry at fainter magnitudes (V 19)."," SB04 speculate on a possible spread in age of the cluster stars, but they warn that it is difficult to reach a firm conclusion because of the decreasing completeness and photometric accuracy of their photometry at fainter magnitudes $V>19$ )." + A careful examination and comparison of the recent studies on 33603 mentioned above shows that they do not exclude the possible presence of multiple star formation episodes in the recent cluster history and even of a population of low mass MS stars., A careful examination and comparison of the recent studies on 3603 mentioned above shows that they do not exclude the possible presence of multiple star formation episodes in the recent cluster history and even of a population of low mass MS stars. +" However, this scenario necessarily lacks a clear observational confirmation, since field contamination remains a crucial point in the study of stellar populations in 33603."," However, this scenario necessarily lacks a clear observational confirmation, since field contamination remains a crucial point in the study of stellar populations in 3603." +" An efficient way to overcome these obstacles, when observations exist that are separated by a sufficiently large temporal baseline (> 10yr), is the use of proper motions to separate cluster stars from foreground and background objects."," An efficient way to overcome these obstacles, when observations exist that are separated by a sufficiently large temporal baseline $\geq 10 yr$ ), is the use of proper motions to separate cluster stars from foreground and background objects." +" As mentioned in refsec,rr, ,thepropermotionsstudy forthecoreregiono fN Beibilyntheresettiod eem bine M. ionepochs 2Myrand4—5Myrold,res pectively."," As mentioned in \\ref{sec_err}, the proper motions study for the core region of NGC 3603 by \cite{roc10} showed signatures of at least two star formation epochs in the cluster, 1-2 Myr and 4-5 Myr old, respectively." +"Moreover,theCM up fromthe fieldstars, revealsthe presenceo f alowmassMS."," Moreover, the CMD as cleaned-up from the field stars, reveals the presence of a low mass MS." +T Dascleaned ," The authors conclude that the latter is likely a population of objects not belonging to the cluster, that the proper motion technique failed to identify." +hal buajaspon h , We will offer later in our paper new observational evidence supporting the hypothesis that an old stellar population belonging to the cluster is present in the region of the CMD occupied by the candidate low MS stars identified by \cite{roc10}. +"As an alternative and independent method to the star formation history in 33603, we have decided to investigatetake full advantage of our new deep F656N band exposures to search for objects with excess Ha emission, since this feature is a good indicator of the PMS stage and therefore of recent star formation."," As an alternative and independent method to investigate the star formation history in 3603, we have decided to take full advantage of our new deep $F656N$ band exposures to search for objects with excess $\alpha$ emission, since this feature is a good indicator of the PMS stage and therefore of recent star formation." +" By looking at the spatial distribution and age of all the objects with Ha excess emission, we will be able to better understand their cluster membership."," By looking at the spatial distribution and age of all the objects with $\alpha$ excess emission, we will be able to better understand their cluster membership." + The presence of a Ha emission line j4 À) in young stellar objects is strongnormally interpreted (EWas a signature210 of the mass accretion process onto the surface of the object that requires the presence of an inner disk (seeFeigelson therein)..," The presence of a strong $\alpha$ emission line $_{H\alpha} +\gtrsim$ 10 ) in young stellar objects is normally interpreted as a signature of the mass accretion process onto the surface of the object that requires the presence of an inner disk \citep[see][and reference +therein]{fei99,Whi03}." +" The traditional approach to search photometrically for Ha emitters is based on the use of the R-band magnitude as a measure of the level of the photospheric continuum near the Ha line, so that stars with strong Ha emission will have a large Κ--Ho color."," The traditional approach to search photometrically for $\alpha$ emitters is based on the use of the R-band magnitude as a measure of the level of the photospheric continuum near the $\alpha$ line, so that stars with strong $\alpha$ emission will have a large $R-H\alpha$ color." +" However, as discussed in De (2010a),, since the R band is over an order of magnitude wider than the Ha filter, the R-Ha color does not provide an accurate measurement of the stellar continuum level inside the Ho band."," However, as discussed in \citet{DeM10}, since the R band is over an order of magnitude wider than the $\alpha$ filter, the $\alpha$ color does not provide an accurate measurement of the stellar continuum level inside the $\alpha$ band." +" Thus, while helpful to identify PMS stars, the R—Ha color does not provide an absolute measure of the Ha luminosity nor of the Ha equivalent width."," Thus, while helpful to identify PMS stars, the $R-H\alpha$ color does not provide an absolute measure of the $\alpha$ luminosity nor of the $\alpha$ equivalent width." +" This additional information can be derived using measurements in the neighboring V and I bands, as recently shown by(2010a)."," This additional information can be derived using measurements in the neighboring V and I bands, as recently shown by." +. This method allows us to reliably identify PMS objects actively undergoing mass accretion GC3603byr&uildess al, This method allows us to reliably identify PMS objects actively undergoing mass accretion regardless of their age. +" (3Oik Oosho amat —1 broad-band photometry with narrow-band Ha imaging to heautidestifiycálldéatsr exaoss ie anidno fadajausitlatixelongingtot Ho luminosity and mass accretion rate (seeDeMarchietal.2010a,formore details)."," Briefly, the method combines V and I broad-band photometry with narrow-band $\alpha$ imaging to identify all stars with excess $\alpha$ emission and to measure their $\alpha$ luminosity and mass accretion rate \citep[see][for more +details]{DeM10}." + We followed this approach to select bona-fide PMS stars in the field of 33603., We followed this approach to select bona-fide PMS stars in the field of 3603. + Figure 4. shows the V—Ha vs. V—1 diagram for the stars in our catalogue., Figure \ref{fig_hasele} shows the $V-H\alpha$ vs. $V-I$ diagram for the stars in our catalogue. +" We use the median V— dereddened color of stars with small («0.05 mmag) photometricHo uncertainties in each of the three V, I and Ha bands, as a function of V— to define the reference template with respect to which the I,excess Ho emission is identified (dashed line in 4))."," We use the median $V-H\alpha$ dereddened color of stars with small $<0.05$ mag) photometric uncertainties in each of the three V, I and $\alpha$ bands, as a function of $V-I$, to define the reference template with respect to which the excess $\alpha$ emission is identified (dashed line in Figure \ref{fig_hasele}) )." +" We selected a first sample of stars with excess Ho Figureemission by considering all those with a color at least 5c above that of the reference line, where σ here is the uncertainty on the V—Ho color of the star."," We selected a first sample of stars with excess $\alpha$ emission by considering all those with a $V-H\alpha$ color at least $5\,\sigma$ above that of the reference line, where $\sigma$ here is the uncertainty on the $V-H\alpha$ color of the star." + Then we calculated the equivalent width of the Ha emission line x.) from the measured color excess using Equation 4 of DeMarchietal.(2010a)., Then we calculated the equivalent width of the $\alpha$ emission line $_{H\alpha}$ ) from the measured color excess using Equation 4 of \citet{DeM10}. +". We finally considered as bona-fide PMS stars those objects with EWg, >10 (White&2003) and V—I>0; this allows us to clean our sample from possible contaminants, such as older stars with chromospheric activity and Ae/Be stars, respectively (seeScholzetal.2007)."," We finally considered as bona-fide PMS stars those objects with $_{H\alpha}>$ 10 \citep{Whi03} and $V-I>0$; this allows us to clean our sample from possible contaminants, such as older stars with chromospheric activity and Ae/Be stars, respectively \citep[see][]{sch07}." +". With this approach, we selected first sample of ~800 objects with Ha excess emission."," With this approach, we selected a first sample of $\sim 800$ objects with $\alpha$ excess emission." +" Througha a visual inspection of the images, we noticed that some of these objects, although well detected both in the V and I bands, are located along filaments of gas and dust clearly visible in the Ha image (see panel in Figure 1))."," Through a visual inspection of the images, we noticed that some of these objects, although well detected both in the V and I bands, are located along filaments of gas and dust clearly visible in the $\alpha$ image (see right panel in Figure \ref{fig_ha}) )." +" It is crucial to consider that, if the rightcentroid of a star falls on top of a filament that is only partially included in the annulus that our photometry routines use for background subtraction (from 4 to 7 pixel radius),"," It is crucial to consider that, if the centroid of a star falls on top of a filament that is only partially included in the annulus that our photometry routines use for background subtraction (from 4 to 7 pixel radius)," + N(NH2D))=25x107 im the western cloud. in the main cloud the column density is slightly lower. in the range 1-8x107-.. reaching its maximum value of 8x10 cclose to the peak position of BIMA 4 (see Fig. 2 .,"$N$ $\simeq25\times10^{14}$ in the western cloud, in the main cloud the column density is slightly lower, in the range $1$ $\times10^{14}$, reaching its maximum value of $8\times10^{14}$ close to the peak position of BIMA 4 (see Fig. \ref{fnh2dpar}" +bb)., b). + The uncertainty of the ccolumn density is - 25-35&., The uncertainty of the column density is $\sim$ 25–35. +. In order to properly estimate the deuterium fractionation. defined as Diya.= NONH:D)/N(NH3. we made the VVLA images using the same we range as the PdBI data (5-50 £1). estimating the column densities for both aand ffor the same angular scales.," In order to properly estimate the deuterium fractionation, defined as $D_{\mathrm{frac}}=N$ $/N$ ), we made the VLA images using the same $uv$ range as the PdBI data (5–50 $k\lambda$ ), estimating the column densities for both and for the same angular scales." + Finally. we convolved the παπα eemission to a circular beam of 7” (the major axis of the bbeam).," Finally, we convolved the and emission to a circular beam of $7''$ (the major axis of the beam)." + In Fig., In Fig. + 3. we present the spectra obtained at the eemission peak of each condensation wwestern cloud. BIMA 2-S. dust ridge core. BIMA 3. and BIMA 4) together with the hyperfine fit obtained toward these positions.," \ref{fdfrac} we present the spectra obtained at the emission peak of each condensation western cloud, BIMA 2-S, dust ridge core, BIMA 3, and BIMA 4) together with the hyperfine fit obtained toward these positions." + In Table | we list the excitation temperature.Του. the rotational temperature.7)... the παπα ccolumn densities. Dye. and the rratio for each core and a few YSOs.," In Table \ref{tdfrac} we list the excitation temperature, the rotational temperature, the and column densities, $D_{\mathrm{frac}}$, and the ratio for each core and a few YSOs." + Toward the YSOs BIMA | and IRS 5. we report. on upper limits. with DiamD.d. andwecannotdramanyconclusion forthebehaviorof im the protostellar phase.," Toward the YSOs BIMA 1 and IRS 5, we report on upper limits, with $<0.1$, and we cannot draw any conclusion for the behavior of in the protostellar phase." + More interestingly. in the western cloud us ~0.8. which is the highest value of iin the region and among the highest reported in the literature (e.g..Crapsietal.2007:Pillai2007;Fontant2008).," More interestingly, in the western cloud is $\sim0.8$, which is the highest value of in the region and among the highest reported in the literature \citep[\eg][]{crapsi2007,pillai2007,fontani2008}." +" In the main cloud. ppresents significant variations among the different cores. with ddecreasing from the northwest (Dj4,20.5 in BIMA 2-S and the dust ridge core) to the southeast (Dr420.1 in BIMA 3 and BIMA 4)."," In the main cloud, presents significant variations among the different cores, with decreasing from the northwest $\simeq$ 0.5 in BIMA 2-S and the dust ridge core) to the southeast $\simeq$ 0.1 in BIMA 3 and BIMA 4)." + This suggests a chemical differentiation along the main cloud., This suggests a chemical differentiation along the main cloud. + Our high angular resolution study of the ttoward the massive star-forming region 220293+3952 reveals strong eemission toward starless cores. whereas us not (or marginally) detected in cores containing YSOs. which suggests that the production of lis more effective in the pre-protostellar phase than in the protostellar phase.," Our high angular resolution study of the toward the massive star-forming region 20293+3952 reveals strong emission toward starless cores, whereas is not (or marginally) detected in cores containing YSOs, which suggests that the production of is more effective in the pre-protostellar phase than in the protostellar phase." + Palauetal.(2007) notice that the starless cores in this region seem to be predominant on the southeri side of the main cloud and in the western cloud. while the northern side of the main cloud harbors all the YSOs known n the region. suggestive of the dense gas in the main cloud berπα progressively more evolved as it moves from south to north.," \citet{palau2007} notice that the starless cores in this region seem to be predominant on the southern side of the main cloud and in the western cloud, while the northern side of the main cloud harbors all the YSOs known in the region, suggestive of the dense gas in the main cloud being progressively more evolved as it moves from south to north." + It addition. chemical differentiation among pre-protostellar anc protostellar cores was also found by Palauetal.(2007) using the rratio. Which was high for pre-protstellar cores and low 1 protostellar cores (see col.," In addition, chemical differentiation among pre-protostellar and protostellar cores was also found by \citet{palau2007} using the ratio, which was high for pre-protstellar cores and low in protostellar cores (see col." + 9 of Table 1))., 9 of Table \ref{tdfrac}) ). +" Thus. for this region. the behavior ofDj... measured fromNH?D//NHs.. is similar to the behavior of rratio. suggesting that both ratios can be used to distinguish between pre-protostellar and protostellar cores and that both ratios could be related with the evolutionary stage of the dense gas,"," Thus, for this region, the behavior of, measured from, is similar to the behavior of ratio, suggesting that both ratios can be used to distinguish between pre-protostellar and protostellar cores and that both ratios could be related with the evolutionary stage of the dense gas." + A possible interpretation of the differences in sseen in the pre-protostellar cores of region could be that they are in different evolutionary stages., A possible interpretation of the differences in seen in the pre-protostellar cores of region could be that they are in different evolutionary stages. + According to the study of Crapsietal.(2005).. there is an increasing trend for aas the starless core approaches the onset of gravitational collapse (from 0.03-0.1 in the youngest cores to 0.1—0.4 toward the most evolved cores).," According to the study of \citet{crapsi2005}, there is an increasing trend for as the starless core approaches the onset of gravitational collapse (from 0.03–0.1 in the youngest cores to 0.1–0.4 toward the most evolved cores)." + This would indicate that the western cloud is the most evolved pre-protostellar core and that BIMA 3 and BIMA 4 are less evolved., This would indicate that the western cloud is the most evolved pre-protostellar core and that BIMA 3 and BIMA 4 are less evolved. + However. in regions of massive star formation. typically associated with clustered environments. other factors. like temperature. UV radiation. and/or molecular outflows. can play important roles in altering," However, in regions of massive star formation, typically associated with clustered environments, other factors, like temperature, UV radiation, and/or molecular outflows, can play important roles in altering" +"sources, molecular outflows, and H2O masers in previous works indicate on-going star formation.","sources, molecular outflows, and $H_{2}O$ masers in previous works indicate on-going star formation." + The distance to the Sun estimated for these H II regions is in the range dg=1.0- 2.3 kpc (Georgelin 1975).., The distance to the Sun estimated for these H II regions is in the range $d_{\odot}=1.0$ $2.3$ kpc \citep{Georgelin75}. . + Most works use dg=1.8 kpc for this group of nebulosities., Most works use $d_{\odot}=1.8$ kpc for this group of nebulosities. +" Within uncertainties, Sh2-231, Sh2-232, Sh2-233 and Sh2-235 have comparable CO radial velocities (Blitz,Fich&Stark 1982)."," Within uncertainties, Sh2-231, Sh2-232, Sh2-233 and Sh2-235 have comparable CO radial velocities \citep{Blitz82}." +. This indicates that we are dealing with a large HII-molecular complex with components located essentially at the same distance from the Sun., This indicates that we are dealing with a large HII-molecular complex with components located essentially at the same distance from the Sun. + Sh2-235 is the most prominent H II region in this group., Sh2-235 is the most prominent H II region in this group. + It is a diffuse optical H II region excited by a star of spectral type O9.5 V (BD+35°1201)., It is a diffuse optical H II region excited by a star of spectral type O9.5 V $+35^{\circ}1201$ ). +" Allenetal.(2005) identify two clusters associated with the Sh2-235 H II region, Sh2-235 Cluster and KKC 11."," \citet{Allen05} identify two clusters associated with the Sh2-235 H II region, Sh2-235 Cluster and KKC 11." +" Kumar,Keto&Clerkin(2006) add to these objects the cluster Sh2-235 East2.", \citet{Kumar06} add to these objects the cluster Sh2-235 East2. + Kirsanovaetal.(2008) conclude that these objects are still embedded in dense clumps of the parental molecular cloud G174+2.5., \citet{Kirsanova08} conclude that these objects are still embedded in dense clumps of the parental molecular cloud $G174+2.5$. +" They also argue that the Sh2-235 Cluster and Sh2-235 E2 probably started the primordial gas expulsion, but KKC 11 isless evolved."," They also argue that the Sh2-235 Cluster and Sh2-235 E2 probably started the primordial gas expulsion, but KKC 11 isless evolved." + South-west of the Sh2-235 are four small nebulae named, South-west of the Sh2-235 are four small nebulae named +on (imescales as short as one week 2009).,on timescales as short as one week . +. Our observations were designed to probe whether such activitv is present in the diffuse debris disk orbiting a much. older niin sequence star., Our observations were designed to probe whether such activity is present in the diffuse debris disk orbiting a much older main sequence star. + To accomplish these aims. we made observations using all three Spitzer instruments relspitObs)).," To accomplish these aims, we made observations using all three Spitzer instruments \\ref{spitObs}) )." + The location of the emitting material in relation (ο the three radial velocity (RV) planets is also of considerable interest in understanding (he origin of the dust which might lie either interior to. in-between or exterior to the planets.," The location of the emitting material in relation to the three radial velocity (RV) planets is also of considerable interest in understanding the origin of the dust which might lie either interior to, in-between or exterior to the planets." + To investigate this question we mace mid-IHR. images with the Michelle micl-IR. camera on the 32n Gemini telescope and looked for extended nea-Il emission with the 85-1 baseline Ixeck Interlerometer releround))., To investigate this question we made mid-IR images with the Michelle mid-IR camera on the 8-m Gemini telescope and looked for extended near-IR emission with the 85-m baseline Keck Interferometer \\ref{ground}) ). + Alter a discussion of the entire set of observations. we describe our results in ancl cliscuss their implications in relcliscuss..," After a discussion of the entire set of observations, we describe our results in \\ref{results} and discuss their implications in \\ref{discuss}." + Observations were made of ILDGO830 using all three Spitzer instruments (Table 1)) the ILAC MIPS cameras ancl the IRS spectrograph2004)., Observations were made of HD69830 using all three Spitzer instruments (Table \ref{ObsLog}) ) — the IRAC MIPS cameras and the IRS spectrograph. +. In addition to discovery data obtained wilh MIPS and URS in 2004. the two photometric insirumen(s were used al one epoch in 2007 while the IRS spectrometer was used on 5 occasions at low resolution and 6 occasions at high resolution to look for small variations in the emission Iron small dust erains responsible lor the excess from (his source.," In addition to discovery data obtained with MIPS and IRS in 2004, the two photometric instruments were used at one epoch in 2007 while the IRS spectrometer was used on 5 occasions at low resolution and 6 occasions at high resolution to look for small variations in the emission from small dust grains responsible for the excess from this source." + In the case of the IRS observations. a nearby star HLD68146 (FTV) which is known to have no long wavelength excess was used as a relerence star for both flat fielding and bad pixel monitoring.," In the case of the IRS observations, a nearby star HD68146 (F7V) which is known to have no long wavelength excess was used as a reference star for both flat fielding and bad pixel monitoring." + I addition. the IIS peak-up array was used to obtain 22 jou photometry along with each IRS spectrum.," In addition, the IRS peak-up array was used to obtain 22 $\mu$ m photometry along with each IRS spectrum." + We have used the IRS peak-up photometry to look lor temporal variations and in (he absence of any variability. we averaged the IRS spectral data to obtain the best spectrum of the excess for comparison with dust moclels.," We have used the IRS peak-up photometry to look for temporal variations and in the absence of any variability, we averaged the IRS spectral data to obtain the best spectrum of the excess for comparison with dust models." + We also examined (he spectral data for evidence for temporal variations., We also examined the spectral data for evidence for temporal variations. +"dependence in the calculation of the cluster magnetic field strength, ","dependence in the calculation of the cluster magnetic field strength, $B(M_v)$." +"Also, the model used in CBS06 is in our B(M,).analysis, since we are enforcing the known relation to slightly lower cluster masses."," Also, the model used in CBS06 is in our analysis, since we are enforcing the known relation to slightly lower cluster masses." +" However, this relation is not observationally verified at lower masses, and we can allow their model choice when restricting ourselves to the mass ranges they consider."," However, this relation is not observationally verified at lower masses, and we can allow their model choice when restricting ourselves to the mass ranges they consider." + We use these contours to guide our selection of models for further study., We use these contours to guide our selection of models for further study. + We wish to adequately sample the space of allowable models and explore the limits allowed by observational constraints., We wish to adequately sample the space of allowable models and explore the limits allowed by observational constraints. + We also wish to explore the effects of holding one parameter constant and varying the others to their extreme allowed values., We also wish to explore the effects of holding one parameter constant and varying the others to their extreme allowed values. +" To aid analysis, we collect our choices into six model groups, enumerated in2."," To aid analysis, we collect our choices into six model groups, enumerated in." +. In this table we list the values chosen for a particular parameter set and a unique designation for that set used in further plots., In this table we list the values chosen for a particular parameter set and a unique designation for that set used in further plots. +" In Model Group 1 we set a to 0.0, fix c—0.7, and vary the magnetic field parameters as widely as possible from a minimum of (B)=0.2 to 3.1µία."," In Model Group 1 we set $a$ to $0.0$, fix $c=0.7$, and vary the magnetic field parameters as widely as possible from a minimum of $\aveb=0.2$ to $3.1~\mg$." +" We also vary the scaling parameter associated with the magnetic field, b."," We also vary the scaling parameter associated with the magnetic field, $b$ ." +" Each (B)is coupled with a unique 6, except for (B)=1.5wG, where we examine b=0.8 and b=1.1, which are the minimum and maximum allowed values for this particular configuration."," Each $\aveb$is coupled with a unique $b$, except for $\aveb=1.5 \mg$, where we examine $b=0.8$ and $b=1.1$, which are the minimum and maximum allowed values for this particular configuration." +" We explore the opposite behavior in Model Set 2 by fixing the magnetic field parameters to (B)=2.0wG and simple linear scaling b=1.0 while having no explicit M, dependence and studying the maximum and minimum allowed values for turbulent pressure scaling, c."," We explore the opposite behavior in Model Set 2 by fixing the magnetic field parameters to $\aveb=2.0 \mg$ and simple linear scaling $b=1.0$ while having no explicit $M_v$ dependence and studying the maximum and minimum allowed values for turbulent pressure scaling, $c$." + We chose this value of the magnetic, We chose this value of the magnetic +Changes in the spectral resolution are unavoidable in slit-spectrographs such as the HDS. but should be largely absent in fiber-fed spectrographs.,"Changes in the spectral resolution are unavoidable in slit-spectrographs such as the HDS, but should be largely absent in fiber-fed spectrographs." + However. the intrinsic variations due to the Rossiter-MeLauglin effect will be present in all transmission spectroscopy observations.," However, the intrinsic variations due to the Rossiter-McLauglin effect will be present in all transmission spectroscopy observations." + To avoid the consequences of line shape changes the flux first should be integrated over the total width of the line before it can be compared between spectra. meaning that A in equation | should be large enough.," To avoid the consequences of line shape changes the flux first should be integrated over the total width of the line before it can be compared between spectra, meaning that $\Delta \lambda$ in equation 1 should be large enough." + We therefore do our analysis with a minimum width of 0.75A., We therefore do our analysis with a minimum width of 0.75. +. Most likely. the non-linearity of the pixels in the HDS CCD is causing the effect seen in the top panel of Fig. 3..," Most likely, the non-linearity of the pixels in the HDS CCD is causing the effect seen in the top panel of Fig. \ref{other}." + Since it was not possible to directly measure the non-linearity of the CCD. we corrected for it in an empirical way. by performing a least-squares fit to the correlation between line depth and count level.," Since it was not possible to directly measure the non-linearity of the CCD, we corrected for it in an empirical way, by performing a least-squares fit to the correlation between line depth and count level." + For the weighted mean of the 59 strong comparison lines. the reduced chi-squared drops from y7/v26.11 to y7/v=1.05 after this correction.," For the weighted mean of the 59 strong comparison lines, the reduced chi-squared drops from $\chi^2/\nu$ =6.11 to $\chi^2/\nu$ =1.05 after this correction." + The bottom panel of Fig., The bottom panel of Fig. + 3 shows the remaining residuals., \ref{other} shows the remaining residuals. + Although there is some correlated variation still visible. it averages out over the transit.," Although there is some correlated variation still visible, it averages out over the transit." + Since we integrate over the total extent of the lines. we do not expect variations in the seeing to affect our results.," Since we integrate over the total extent of the lines, we do not expect variations in the seeing to affect our results." + Nevertheless. since the seeing influences how much flux of the star enters the slit. the seeing is anti-correlated with the count level in the spectra.," Nevertheless, since the seeing influences how much flux of the star enters the slit, the seeing is anti-correlated with the count level in the spectra." + Therefore. a correlation between the seeing and the average line strength is also present.," Therefore, a correlation between the seeing and the average line strength is also present." + However. the resulting reduced chi-squared is y/v22.90. significantly higher than that resulting from the continuum count level. indicating that changes in seeing are not the underlying cause of the line variations.," However, the resulting reduced chi-squared is $\chi^2/\nu$ =2.90, significantly higher than that resulting from the continuum count level, indicating that changes in seeing are not the underlying cause of the line variations." + In à similar manner as for the weighted mean of the reference lines. the correlation between line depth and continuum count level was removed for the DD doublet.," In a similar manner as for the weighted mean of the reference lines, the correlation between line depth and continuum count level was removed for the D doublet." + We subsequently determined the depth of the transit for the three DD passbands separately., We subsequently determined the depth of the transit for the three D passbands separately. + A least-squares fit was performed on the data using as a model a scaled version of the HST light curve as presented by Brown et al. (, A least-squares fit was performed on the data using as a model a scaled version of the HST light curve as presented by Brown et al. ( +2001).,2001). + The best fitting model is subsequently removed from the data. revealing low-level variations due to changing telluric contaminations most evident at the end of the night.," The best fitting model is subsequently removed from the data, revealing low-level variations due to changing telluric contaminations most evident at the end of the night." + This tellure. residual was found to scale with the airmass and with the strength of some strong telluric lines in the red part of the spectrum (as shown in Fig. 2))., This telluric residual was found to scale with the airmass and with the strength of some strong telluric lines in the red part of the spectrum (as shown in Fig. \ref{circum}) ). + A linear fit was performed between the average strength of the strong telluric lines and the NaDD residuals to remove the telluric contribution., A linear fit was performed between the average strength of the strong telluric lines and the D residuals to remove the telluric contribution. + Note that the fitting of the continuum count level. transit signal. and tellurte contamination was performed in a iterative way. but the solutions did not significantly change after the first round.," Note that the fitting of the continuum count level, transit signal, and telluric contamination was performed in a iterative way, but the solutions did not significantly change after the first round." + In. addition. a consistency check was performed to see whether our telluric line contamination removal was reasonable.," In addition, a consistency check was performed to see whether our telluric line contamination removal was reasonable." + Many telluric lines are present around the DD doublet. in both the line and reference bands.," Many telluric lines are present around the D doublet, in both the line and reference bands." + We used the tellurie line list of Lundstrom (1991) to construct a synthetic telluric spectrum., We used the telluric line list of Lundstrom (1991) to construct a synthetic telluric spectrum. + We then constructed a reference spectrum from the average of all exposures which was subsequently removed from the 30 frames., We then constructed a reference spectrum from the average of all exposures which was subsequently removed from the 30 frames. + Although the absolute telluric contamination is now lost. all information on the change in telluric contamination becomes clearly visible in this way.," Although the absolute telluric contamination is now lost, all information on the change in telluric contamination becomes clearly visible in this way." + The synthetic telluric spectrum was then fitted to these frames. ane the change in telluric contribution in the various spectral bands determined.," The synthetic telluric spectrum was then fitted to these frames, and the change in telluric contribution in the various spectral bands determined." + This gives very similar results as the methoc described above., This gives very similar results as the method described above. + We use the former method in our final analysis since the contribution of tellurie. sodium relative to that of water and oxygen undergoes seasonal variations. but withir one night is expected to vary following the other tellurie lines.," We use the former method in our final analysis since the contribution of telluric sodium relative to that of water and oxygen undergoes seasonal variations, but within one night is expected to vary following the other telluric lines." + Note that NAROS used the spectrum of the rapidly rotating BS star HD42545 to remove the telluric contamination arounc the DD doublet. however the sodium absoption towards this star is dominated by interstellar contributions (although this is unlikely to have influenced their results).," Note that NAR05 used the spectrum of the rapidly rotating B5 star HD42545 to remove the telluric contamination around the D doublet, however the sodium absoption towards this star is dominated by interstellar contributions (although this is unlikely to have influenced their results)." + We measured the depth of the NaDD features in the transmission spectrum within three spectral passbands centered on the two stellar lines. with widths of0.75A..L5ÁÀ.. and 3.," We measured the depth of the D features in the transmission spectrum within three spectral passbands centered on the two stellar lines, with widths of, and ." +0A.. The results are presented in Fig. 4.., The results are presented in Fig. \ref{res1}. . + The sodium absorption due to the planets. atmosphere is detected at >So. at a level of 0.0564£0.007% (2x3À band).0.0T0L0.011% (2X1.SA — band). andO.1354£0.017% (2x0.75A band).," The sodium absorption due to the planet's atmosphere is detected at $>$$\sigma$, at a level of $\pm$ $\times$ $ $ band), $\pm$ $\times$ $ $ band), and $\pm$ $\times$ $ $ band)." +T hequoteduncertaintie sare lo error intervals as determined from the SNR in the spectra using chi-square analysis., The quoted uncertainties are $\sigma$ error intervals as determined from the SNR in the spectra using chi-square analysis. + The resulting reduced chi-squares values. y/v. are 47/28=1.63. 31/28=1.10. and 45/28=1.75 respectively. and indicate that the residual noise levels are 10-30% higher than expected from Poisson statistics.," The resulting reduced chi-squares values, $\chi^2/\nu$, are 47/28=1.63, 31/28=1.10, and 45/28=1.75 respectively, and indicate that the residual noise levels are $-$ higher than expected from Poisson statistics." + A way to take this residual noise into account in the error budget is to scale the error bars up such that y7/v=1., A way to take this residual noise into account in the error budget is to scale the error bars up such that $\chi^2/\nu$ =1. + This would increase the uncertainties by 10-30%... resulting in conservative estimates of the significance of the sodium detection of -ὂσ in each individual passband.," This would increase the uncertainties by $-$, resulting in conservative estimates of the significance of the sodium detection of $\sim$ $\sigma$ in each individual passband." + A crucial part of our data analysis is the empirical correction for the correlation of line depth with the continuum count level in the spectra. attributed to non-linearity effects in the CCD.," A crucial part of our data analysis is the empirical correction for the correlation of line depth with the continuum count level in the spectra, attributed to non-linearity effects in the CCD." + To assess the robustness of our result we performed a slightly different empirical correction by directly correlating the weighted mean-strength of the 59 reference lines with that of the NaDD lines., To assess the robustness of our result we performed a slightly different empirical correction by directly correlating the weighted mean-strength of the 59 reference lines with that of the D lines. + Depending on the passband. this alternative analysis results in a transit depth 20-30% lower than determined above. also with higher y/v values.," Depending on the passband, this alternative analysis results in a transit depth $-$ lower than determined above, also with higher $\chi^2/\nu$ values." + Since this would still be ~S5cr detections. it further supports the detection.," Since this would still be $\sim$ $\sigma$ detections, it further supports the detection." + Since the first method gives significantly less noisy results. we believe that method it is more reliable.," Since the first method gives significantly less noisy results, we believe that method it is more reliable." + In our analysis we do not take into account the variation in radial velocity of the planet (and its atmospheric. absorption) relative to that of the star., In our analysis we do not take into account the variation in radial velocity of the planet (and its atmospheric absorption) relative to that of the star. + During the transit. the radial velocity of the planet variesfrom about —14 to +14 km sec!.," During the transit, the radial velocity of the planet variesfrom about $-$ 14 to +14 km $^{-1}$ ." + For a Lorentzian shaped planetary absorption profile with a width comparable to that of the star (see below). the strength of the," For a Lorentzian shaped planetary absorption profile with a width comparable to that of the star (see below), the strength of the" +considered disk flaring which can increase the cross section area for stellar X-rays considerably.,considered disk flaring which can increase the cross section area for stellar X-rays considerably. + Numerical simulations indeed show order-of-magnitude variations as a result of varying disk flaring for otherwise constant stellar and disk parameters (Schisanoetal.2009)., Numerical simulations indeed show order-of-magnitude variations as a result of varying disk flaring for otherwise constant stellar and disk parameters \citep{schisano09}. + Another factor is the spectral energy. distribution of the ionizing and heating X-ray source., Another factor is the spectral energy distribution of the ionizing and heating X-ray source. + Agal accurate measurement of the irradiating spectrum is not possible although the intrinsic. stellar. ray spectrum ca be reconstructed from observations.," Again, accurate measurement of the irradiating spectrum is not possible although the intrinsic stellar X-ray spectrum can be reconstructed from observations." + X-ray spectral hardess indeed significantly influences |[Net]] emission. from disks in numerical studies (Schisanoetal.. 2009)., X-ray spectral hardness indeed significantly influences ] emission from disks in numerical studies \citep{schisano09}. +. Further factors that have not been considered in this study include disκ gaps and holes (although we showed that our sample of traisition disks behaves similar to optically thick disks without jets). grain structure and size distribution. the degree of dust settling. or accretion from the environment onto the disk.," Further factors that have not been considered in this study include disk gaps and holes (although we showed that our sample of transition disks behaves similar to optically thick disks without jets), grain structure and size distribution, the degree of dust settling, or accretion from the environment onto the disk." + Most significantly. unrecognized Jets may contribute to some enhancement of u]] emission. as is clearly evident from the subsample with known jets.," Most significantly, unrecognized jets may contribute to some enhancement of ] emission, as is clearly evident from the subsample with known jets." + Most of these additional features require further observational study. and some may remain inaccessible.," Most of these additional features require further observational study, and some may remain inaccessible." + We have studied u]| emission from a large sample of disk-surrounded pre-niam sequence stars. most of them showing optically thick disks (1.e.. Class II sources). but some of them additionally ejecting Jets. and others showing signatures. of transition disks.," We have studied ] emission from a large sample of disk-surrounded pre-main sequence stars, most of them showing optically thick disks (i.e., Class II sources), but some of them additionally ejecting jets, and others showing signatures of transition disks." + We have been interested primarily in locating the [Neu]] emission source. but also in finding clues about the ionization. and excitation mechanism itself.," We have been interested primarily in locating the ] emission source, but also in finding clues about the ionization and excitation mechanism itself." + To this end. we have studied correlations between the observed [Net]] line Juminosity and stellar and circumstellar properties such as the stellar X-ray luminosity. the accretion rate. the mass loss rate. and the luminosity in the [ΟΠ] 26300 line.," To this end, we have studied correlations between the observed ] line luminosity and stellar and circumstellar properties such as the stellar X-ray luminosity, the accretion rate, the mass loss rate, and the luminosity in the ] $\lambda$ 6300 line." + Our principal findings can be summarized as follows:, Our principal findings can be summarized as follows: +(FOCCD).,(50CCD). + The 50CCD is an uuvigueted aperture with a field of view of 527. aud a focal plate scale of ..0507 1., The 50CCD is an unvigneted aperture with a field of view of $\times$ and a focal plate scale of .0507 $^{-1}$. + In this setting no filter is used aud tle shape of the baudpass is governed by the detector Gvhich has a sensitivity from ~20000 to 103300 À)) and by the reflectivity of the optics., In this setting no filter is used and the shape of the bandpass is governed by the detector (which has a sensitivity from $\sim$ 000 to 300 ) and by the reflectivity of the optics. + The ceutral wavelength of the 50CCD is5850À.. and the bandpass is LEOA.," The central wavelength of the 50CCD is, and the bandpass is 4410." +. The FWHAL of the PSF is close to 2 pixels at 50000 and the encircled euergv radius is 3 pixels (Leithereretal.2001)., The FWHM of the PSF is close to 2 pixels at 000 and the encircled energy radius is 3 pixels \citep{Letal:01}. +. The observations were made with the CCD detector using a eain of Le per analoe-to-digital couverter unit., The observations were made with the CCD detector using a gain of 1 $e^-$ per analog-to-digital converter unit. + All the exposures were split into two equal components to allow cosmic-ray rejection., All the exposures were split into two equal components to allow cosmic-ray rejection. + Table 1 gives in column (1) the object name according to the SAIP nomenclature when available. iu colunus (2) and (3) the sky coordinates. iu column {1} the nebular diameters measured with respect to the intensity coutour of the outer most structure in the 5007 line. in column (5) the total integration time. and in cobuun (6) whether or not the central star was detected in the images.," Table 1 gives in column (1) the object name according to the SMP nomenclature when available, in columns (2) and (3) the sky coordinates, in column (4) the nebular diameters measured with respect to the intensity contour of the outer most structure in the 5007 line, in column (5) the total integration time, and in column (6) whether or not the central star was detected in the images." + The photometric technique has already been described in detail iu Villaveretal.(2003)., The photometric technique has already been described in detail in \cite{Vss:03}. +. Tn sunu. we have applied aperture photometry using the PHOT task.," In summary, we have applied aperture photometry using the PHOT task." + Given the spatially resolved nature of the nebula we measure the flux within a circular aperture with a radius of 2 pixels centered ou the star. and subtract the nebular emission by estimating the median nebular flix iu an annulus with a width of 1 or 2 pixels adjacent to the stellar aperture.," Given the spatially resolved nature of the nebula we measure the flux within a circular aperture with a radius of 2 pixels centered on the star, and subtract the nebular emission by estimating the median nebular flux in an annulus with a width of 1 or 2 pixels adjacent to the stellar aperture." + The nebular emission within this aperture can be highly inhomogeucous and strong variations from the median of the nebular ux are reflected in the large standard deviation., The nebular emission within this aperture can be highly inhomogeneous and strong variations from the median of the nebular flux are reflected in the large standard deviation. + These uncertainties are propagated iuto the errors of the measured maeuitudes., These uncertainties are propagated into the errors of the measured magnitudes. + The internal consistency. of the procedure. which is accurate at the level. has been tested in previous papers by performune aperture photometry ou nebular subtracted images built by co-adding 2D monochromatic images taken from the STIS spectroscopy.," The internal consistency of the procedure, which is accurate at the level, has been tested in previous papers by performing aperture photometry on nebular subtracted images built by co-adding 2D monochromatic images taken from the STIS spectroscopy." + The instrimucutal inaguitudes are eiven in the svstem by using the zero-poiut calibration aud aperture corrections prescuted in Brownetal.(2002)., The instrumental magnitudes are given in the system by using the zero-point calibration and aperture corrections presented in \cite{Betal:02}. +. The STIS charge trauster efficiency (CTE) correction was applied in this version of the pipeline (see Shawotal. 2006)) but it has been shown only to have au effect less than 0.01 maes (BRejkubactal.2000). for stars in the center of the field., The STIS charge transfer efficiency (CTE) correction was applied in this version of the pipeline (see \citealt{Shaw:06}) ) but it has been shown only to have an effect less than 0.01 mags \citep{Retal:00} for stars in the center of the field. +" The stellar extinction correction has been estimated from the nebular Balmer decrement.ο, aud the relation ο=—1.11Epy (Seaton1979).. where Ep,ντ is the color excess."," The stellar extinction correction has been estimated from the nebular Balmer decrement, and the relation $c~=~1.41~E_{B-V}$ \citep{Sea:79}, where $_{B-V}$ is the color excess." + Ultimately this approach relies ou the lack of strong spatial variations in the extinction within the nebula caused by internal absorption by dust., Ultimately this approach relies on the lack of strong spatial variations in the extinction within the nebula caused by internal absorption by dust. + Significant spatial variations in the ratio within the nebulae have not been found for auv of the heavily reddened objects iu our sample. confirnmune the validity of this approach.," Significant spatial variations in the ratio within the nebulae have not been found for any of the heavily reddened objects in our sample, confirming the validity of this approach." +" The extinction coustauts have been taken frou except for J 5. MG 16 and MO 33 where the extinction could not be determined because the intensity of the line was bleuded with the 0515, 6583 line ciission in the slitless spectra."," The extinction constants have been taken from \citep{Shaw:06} except for J 5, MG 16 and MO 33 where the extinction could not be determined because the intensity of the line was blended with the 6548, 6583 line emission in the slitless spectra." + The extinction constants for J 5. MG 16. aud MO 33 are not available in the literature aud therefore we have assumed," The extinction constants for J 5, MG 16, and MO 33 are not available in the literature and therefore we have assumed" +the free energy in differential rotation.,the free energy in differential rotation. + In (he opposite extreme case (hat angular momentum is conserved during the contraction phase. J = const. which is equivalent (o no dissipation into magnetoacoustic flux. we have alter contraction. but before final spin-dowu: We have again assumed that T/Ww and Wo both scale as 21.," In the opposite extreme case that angular momentum is conserved during the contraction phase, J = const, which is equivalent to no dissipation into magnetoacoustic flux, we have after contraction, but before final spin-down: We have again assumed that $\tw$ and $W$ both scale as $R^{-1}$." + In this case. a maximal amount of the excess binding energy is converted to rotational energy alter contraction.," In this case, a maximal amount of the excess binding energy is converted to rotational energy after contraction." + This condition of constant angular momentum is commonly assumed. in contraction of isolated neutron stars (Villainetal.2004:Ott2006).. but is unlikely to apply to real rotating magnetic PNS still buried within the collapse ambiance unless they are rotating very slowly.," This condition of constant angular momentum is commonly assumed in contraction of isolated neutron stars \citep{vil04,ott06}, but is unlikely to apply to real rotating magnetic PNS still buried within the collapse ambiance unless they are rotating very slowly." + If the PNS evolves by shedding magnetoacoustic energy at roughly constant T/|W) then and These expressions again assume (hat the contraction is homologous so (hat the change in radius is an appropriate measure of (he change in binding energy., If the PNS evolves by shedding magnetoacoustic energy at roughly constant $\tw$ then and These expressions again assume that the contraction is homologous so that the change in radius is an appropriate measure of the change in binding energy. + One example of such possible behavior would be if (he PNS were born or quickly evolved to a condition of mareinal stability to a secular bar mode and (hen contraction occurs along the locus of secular bar instability with T//W~0.14., One example of such possible behavior would be if the PNS were born or quickly evolved to a condition of marginal stability to a secular bar mode and then contraction occurs along the locus of secular bar instability with $\tw \sim 0.14$. + Another example would be contraction alonge the locus near the lower threshold for exciting NANI. as illustrated in Fig.," Another example would be contraction along the locus near the lower threshold for exciting NAXI, as illustrated in Fig." + I., 1. + The amount of energy that could be dumped from the rotation to magnetoacoustic enerev during the contraction is (hus a rather sensitive function of how the dissipation affects the angular momentum., The amount of energy that could be dumped from the rotation to magnetoacoustic energy during the contraction is thus a rather sensitive function of how the dissipation affects the angular momentum. + In the extreme case of conserved angular momentimn. if the contraction were quasihomologous so that T7W did scale closely as Rt. then Eqn.," In the extreme case of conserved angular momentum, if the contraction were quasi–homologous so that $\tw$ did scale closely as $R^{-1}$, then Eqn." +" 6 suggests that a fraction. (05,/P0,(D.Wu) of the final binding energy. something of order 25 times the initial rotational energy. could be invested in rotational energy and then liberated in spin down magnetoacoustic power."," \ref{jconst} suggests that a fraction $(R_{pns}/R_{ns})(T_{pns}/|W_{pns}|)$ of the final binding energy, something of order 25 times the initial rotational energy, could be invested in rotational energy and then liberated in spin down magnetoacoustic power." + This rotational energy must be limited since. as we argue here. no contracting configuration can penetrate into the lorbidden zone αἱ T/|W=0.14.," This rotational energy must be limited since, as we argue here, no contracting configuration can penetrate into the forbidden zone at $\tw \gtrsim 0.14$." + As an example. if we assume that the PNS is born with T/W|~0.03 and contracts along a locus of J = const (uppermost thin line in Fig.," As an example, if we assume that the PNS is born with $\tw \sim 0.08$ and contracts along a locus of J = const (uppermost thin line in Fig." + 1) with negligible production, 1) with negligible production +Erupting objects with luminosities between those of novae and supernovae (SNe) are being discovered at an accelerated. rate (c.g. Ixulkarni et al.,"Erupting objects with luminosities between those of novae and supernovae (SNe) are being discovered at an accelerated rate (e.g., Kulkarni et al." + 2007a.b: Berger et al.," 2007a,b; Berger et al." + 2000: Smith et al., 2009; Smith et al. + 2000. 2011: IWasliwal ct al.," 2009, 2011; Kasliwal et al." + 2010a: Mason ct al., 2010a; Mason et al. + 2010: Pastorello ct al., 2010; Pastorello et al. + 2010)., 2010). + Phere is not vet an accepted: term for these ἵνρο of objects., There is not yet an accepted term for these type of objects. + We will refer to them as Intermediate Luminosity Optical ‘Transients (LOTs)., We will refer to them as Intermediate Luminosity Optical Transients (ILOTs). + Another popular name for these objects is luminous rec novae. (Ixulkarni et al., Another popular name for these objects is luminous red novae (Kulkarni et al. + 2007a.b). although using this nomenclature may be confusing. as these transients are most probably. not any kind. of novae.," 2007a,b), although using this nomenclature may be confusing, as these transients are most probably not any kind of novae." + While the nature of these eruptions is poorly understood. there are several dillerent proposed. explanations in the literature (see Washi. Frankowski Soker 2010. hereafter IXESI10. for further discussion).," While the nature of these eruptions is poorly understood, there are several different proposed explanations in the literature (see Kashi, Frankowski Soker 2010, hereafter KFS10, for further discussion)." + IKESIO noticed that when rescaling the time axis for the V-band light curves of ILOTTs and major Luminous Blue Variable (LBV) eruptions. which at first seemed unconnected. the shape becomes similar for à decline in more than 3 magnitudes.," KFS10 noticed that when rescaling the time axis for the V-band light curves of ILOTs and major Luminous Blue Variable (LBV) eruptions, which at first seemed unconnected, the shape becomes similar for a decline in more than $3$ magnitudes." + INESIO suggested that these transients may have a similar powering mechanism mass accretion onto a main sequence (AIS) star in a binary system., KFS10 suggested that these transients may have a similar powering mechanism – mass accretion onto a main sequence (MS) star in a binary system. + WKWESLO also showed that the light. curves are different than the light curves of novae and SNe (type la and LL)., KFS10 also showed that the light curves are different than the light curves of novae and SNe (type Ia and II). + However. the unique shape of the light curve of ILO'Ts is not vet understood.," However, the unique shape of the light curve of ILOTs is not yet understood." + ὃν major LBV cruptions’ we refer to cruptions in which the luminosity rapicly (Sb month) increases by a [few magnitudes. as opposed. to less dramatic cruptions. such as 5 Dor phases. weak eruptions in which the luminosity is changed by 0.5 magnitude in the V-band. or slow raises in magnitude.," By `major LBV eruptions' we refer to eruptions in which the luminosity rapidly $\lesssim 1$ month) increases by a few magnitudes, as opposed to less dramatic eruptions, such as S Dor phases, weak eruptions in which the luminosity is changed by $\lesssim 0.5$ magnitude in the V-band, or slow raises in magnitude." + All these processes are most probably internally related to the LDVs and are not to accretion. processes which we cliscuss here., All these processes are most probably internally related to the LBVs and are not to accretion processes which we discuss here. + Our proposed. model of an eccentric binary interaction for ILO'Es is directly based on the mereehurst model for VS38 Mon (Soker Tylenda 2003. 2006. 2007: Tvlena Soker 2006). in which a ~0.3M. star that merged. with an ~NM. star created the outburst.," Our proposed model of an eccentric binary interaction for ILOTs is directly based on the mergeburst model for V838 Mon (Soker Tylenda 2003, 2006, 2007; Tylena Soker 2006), in which a $\sim 0.3~\rm{M_{\odot}}$ star that merged with an $\sim 8~\rm{M_{\odot}}$ star created the outburst." + Indirectly. the binary model for ILOEs is supported by the similarities between ILOTS and LBVs (IXESIO). such as the massive binary system a Car.," Indirectly, the binary model for ILOTs is supported by the similarities between ILOTS and LBVs (KFS10), such as the massive binary system $\eta$ Car." + Damineli (1996) ancl Frew (2004: updated by Smith Frew 2011) noted that the beginning of the nineteenth century major cruptions of 5 Car occurred. near periastron passages of the binary svstem., Damineli (1996) and Frew (2004; updated by Smith Frew 2011) noted that the beginning of the nineteenth century major eruptions of $\eta$ Car occurred near periastron passages of the binary system. + A (quantitative model for the periastron triggering of the η Car nineteenth century major eruptions. including mass loss and mass transfer (aceretion) was recently conducted. bv Kashi Soker (2010).," A quantitative model for the periastron triggering of the $\eta$ Car nineteenth century major eruptions, including mass loss and mass transfer (accretion) was recently conducted by Kashi Soker (2010)." + Washi (2010) further argued that the eruptions of the LBV P Cyeni in the seventeenth century were also trigeered by a periastron passages of an invisible companion., Kashi (2010) further argued that the eruptions of the LBV P Cygni in the seventeenth century were also triggered by a periastron passages of an invisible companion. + The process of accretion onto a MS star was proposed in the past as an explanation for several clillerent tvpes of objects. e.g.. symbiotic stars (Ixenvon Webbink 1984).," The process of accretion onto a MS star was proposed in the past as an explanation for several different types of objects, e.g., symbiotic stars (Kenyon Webbink 1984)." + Ixenvon Gallagher (1985) suggested that epochs of rapid mass exchange can account for the variability of some massive stars although we note that a Car and. other, Kenyon Gallagher (1985) suggested that epochs of rapid mass exchange can account for the variability of some massive stars although we note that $\eta$ Car and other +exolic stellar populations or a chumpy interstellar medium (Ouchietal.]xobavashietal. 2010).,"exotic stellar populations or a clumpy interstellar medium \citep{ouchi+08, mao+07, kobayashi+10}." +. We illustrate the problem in Figure 6.., We illustrate the problem in Figure \ref{ew_3part}. + The left panel of the figure shows the LAE equivalent width measurements as a function of (continuum subtracted) Lya Iuninosity. Lor both the present sample and the sample of objects Found byGr07.," The left panel of the figure shows the LAE equivalent width measurements as a function of (continuum subtracted) $\alpha$ luminosity, for both the present sample and the sample of objects found by." +. The ligure displavs no evidence for a shift in (he equivalent width distribution as a Iunction of Iuminosit., The figure displays no evidence for a shift in the equivalent width distribution as a function of luminosity. +" A 2samiple Anderson-Darling test (Scholz&Stephens1987). which compares the equivalent widths of bright (L>3κ10"" eres 1) and faint (1.252κ107 3 \times 10^{42}$ ergs $^{-1}$ ) and faint $1.25 \times 10^{42} < L < 3 \times 10^{42}$ ergs $^{-1}$ ) LAEs confirms that there is no significant difference between the two samples. + Moreover. if we apply the non-parametric rank-order Efron&Petrosian(1992) test to the data. we find no reason (o reject the hypothesis that equivalent width and Lya Iuminosity are statistically independent quantiles.," Moreover, if we apply the non-parametric rank-order \citet{efron} test to the data, we find no reason to reject the hypothesis that equivalent width and $\alpha$ luminosity are statistically independent quantities." + In contrast. the middle panel of Figure G displays the distribution of Lya equivalent widths as a [function of continuum magnitude.," In contrast, the middle panel of Figure \ref{ew_3part} displays the distribution of $\alpha$ equivalent widths as a function of continuum magnitude." + The difference between the (wo diagrams is striking., The difference between the two diagrams is striking. + While the lack of low equivalent-width sources with faint continuum magnitudes is simply a selection effect (the Lya emission-line is (oo [αμ to be seen). the absence of hieh equivalent-width. bright continuum objects is real.," While the lack of low equivalent-width sources with faint continuum magnitudes is simply a selection effect (the $\alpha$ emission-line is too faint to be seen), the absence of high equivalent-width, bright continuum objects is real." + If we apply the non-parametric rank-order statistic described by Efron&Petrosian(1992) to our truncated dataset. (hen we find that the null hypothesis of independence between equivalent width and continuum magnitude is excluded at the 5o level (for the Gr07 sample) ancl the τσ level (for our new z=3.1 dataset).," If we apply the non-parametric rank-order statistic described by \citet{efron} to our truncated dataset, then we find that the null hypothesis of independence between equivalent width and continuum magnitude is excluded at the $5 \sigma$ level (for the Gr07 sample) and the $7 \sigma$ level (for our new $z = 3.1$ dataset)." + In other words. equivalent width shows no correlation when plotted against line brightness. but a clear anti-correlation when compared to continuum brightness.," In other words, equivalent width shows no correlation when plotted against line brightness, but a clear anti-correlation when compared to continuum brightness." + The explanation for these seeminely contradictory results probably lies in (he [act that equivalent width is a derived quantity formed from (wo photometric measurements. me for theemission line. and one for the continuum.," The explanation for these seemingly contradictory results probably lies in the fact that equivalent width is a derived quantity formed from two photometric measurements, one for theemission line, and one for the continuum." + Consequently. the points displaved in the first (wo panels of Figure G possess correlated. errors.," Consequently, the points displayed in the first two panels of Figure \ref{ew_3part} possess correlated errors." + In. the left-hand. ciagran. enussion-line strength and equivalent width are positively correlated. so photometric errors will preferentially scatter objects into the high-Iuminositv. hieh-equivalent width region of the diagram.," In the left-hand diagram, emission-line strength and equivalent width are positively correlated, so photometric errors will preferentially scatter objects into the high-luminosity, high-equivalent width region of the diagram." + Conversely. in (he middle panel. continuum strength aud equivalent width are negalivelv correlated. so errors in the abscissa will move objects away [rom this portion of 1 figure.," Conversely, in the middle panel, continuum strength and equivalent width are negatively correlated, so errors in the abscissa will move objects away from this portion of the figure." + When this dichotomy is coupled with the heteroskedastic nature of the dataset the largest uncertainties are associated with the objects having the faintest continuum magnitudes and therefore the highest equivalent widths — the result can be an apparent correlation in one figure. and a lack of correlation in another.," When this dichotomy is coupled with the heteroskedastic nature of the dataset – the largest uncertainties are associated with the objects having the faintest continuum magnitudes and therefore the highest equivalent widths – the result can be an apparent correlation in one figure, and a lack of correlation in another." + The best wav to investigate the systematics of equivalent width is to plot the two independent quantities in the relation line strength and continuum strength against one another., The best way to investigate the systematics of equivalent width is to plot the two independent quantities in the relation – line strength and continuum strength – against one another. + This is done in the right-hand. panel of Figure 6.., This is done in the right-hand panel of Figure \ref{ew_3part}. . + Ilere. there is no evidence of," Here, there is no evidence of" +Following Marko and Siggia [?].. we limit our study to the long DNA.,"Following Marko and Siggia \cite{Marko}, we limit our study to the long DNA." +" In this case. because of the presence of exp(—E/"",,L) factor. the term which corresponds to the ground state eigenvalue of LL"" is much greater than other terms in (he expansion of the partition funcüon."," In this case, because of the presence of $\exp(-\mathcal{E}_{n,\,k,\,0}^{\,R}\,L) $ factor, the term which corresponds to the ground state eigenvalue of $H_0^{\,R}$ is much greater than other terms in the expansion of the partition function." + Therelore. the partition function can be approximated only by the eround state term where all other terms can be neglected.," Therefore, the partition function can be approximated only by the ground state term where all other terms can be neglected." + If we denote the difference between the ground state and the first excited state eigenvalues by AE! then the long DNA limit corresponds to the condition AE’L>1., If we denote the difference between the ground state and the first excited state eigenvalues by $\Delta\mathcal{E}^{R}$ then the long DNA limit corresponds to the condition $\Delta\mathcal{E}^{R}L\gg 1$. + We will discuss in the next section (hat this condition is indeed satisfied in the stretching experiments., We will discuss in the next section that this condition is indeed satisfied in the stretching experiments. + The operator J is the Hamiltonian of a top in a uniform external field. and its ground state is unique.," The operator $H_0^{\,R}$ is the Hamiltonian of a top in a uniform external field, and its ground state is unique." +" Thus the ground state of If must be a simultaneous eigenvector of J, and J.. with eigenvalues im=&0 [?].."," Thus the ground state of $H_0^{\,R}$ must be a simultaneous eigenvector of $J_3$ and $J_z$, with eigenvalues $m=k=0$ \cite{Marko}. ." +" We denote the ground state and its eigenvalue by |0.0.0) and £j,1, respectively."," We denote the ground state and its eigenvalue by $|0,0,0\rangle $ and $\mathcal{E}_{0,\,0,\,0}^{\,R}$ respectively." + Therefore. αἱlong DNA limit we obtain and Since the ground state is not degenerate. Gy=[0] and one can write Z ?!can be written as ZO expand. (z) in powers of A. - equation (56)). we have," Therefore, atlong DNA limit we obtain and Since the ground state is not degenerate, $ G_0=\{0\}$ and one can write where Therefore, $Z^{\,(2)}$ can be written as We expand $\langle z\rangle $ in powers of $\lambda $, From equation \ref{z2}) ), we have" + Therefore. αἱlong DNA limit we obtain and Since the ground state is not degenerate. Gy=[0] and one can write Z ?!can be written as ZO expand. (z) in powers of A. - equation (56)). we have ," Therefore, atlong DNA limit we obtain and Since the ground state is not degenerate, $ G_0=\{0\}$ and one can write where Therefore, $Z^{\,(2)}$ can be written as We expand $\langle z\rangle $ in powers of $\lambda $, From equation \ref{z2}) ), we have" + Therefore. αἱlong DNA limit we obtain and Since the ground state is not degenerate. Gy=[0] and one can write Z ?!can be written as ZO expand. (z) in powers of A. - equation (56)). we have ;," Therefore, atlong DNA limit we obtain and Since the ground state is not degenerate, $ G_0=\{0\}$ and one can write where Therefore, $Z^{\,(2)}$ can be written as We expand $\langle z\rangle $ in powers of $\lambda $, From equation \ref{z2}) ), we have" + Therefore. αἱlong DNA limit we obtain and Since the ground state is not degenerate. Gy=[0] and one can write Z ?!can be written as ZO expand. (z) in powers of A. - equation (56)). we have ;U," Therefore, atlong DNA limit we obtain and Since the ground state is not degenerate, $ G_0=\{0\}$ and one can write where Therefore, $Z^{\,(2)}$ can be written as We expand $\langle z\rangle $ in powers of $\lambda $, From equation \ref{z2}) ), we have" + Therefore. αἱlong DNA limit we obtain and Since the ground state is not degenerate. Gy=[0] and one can write Z ?!can be written as ZO expand. (z) in powers of A. - equation (56)). we have ;U)," Therefore, atlong DNA limit we obtain and Since the ground state is not degenerate, $ G_0=\{0\}$ and one can write where Therefore, $Z^{\,(2)}$ can be written as We expand $\langle z\rangle $ in powers of $\lambda $, From equation \ref{z2}) ), we have" +ones.,ones. + Lf instead this was he case. we are left with two possibilities: The same issues apply also to the original formulation of the so called. scenario (Heppenheimer&Porco 1977).. also based on the presence of the nebular gas but locating the capture events during the phase of rapid. eas accretion and mass growth of the giant Recently. the plausibility. of gas-basecd scenarios has been put on jeopardy.," If instead this was the case, we are left with two possibilities: The same issues apply also to the original formulation of the so called scenario \citep{hep77}, also based on the presence of the nebular gas but locating the capture events during the phase of rapid gas accretion and mass growth of the giant Recently, the plausibility of gas-based scenarios has been put on jeopardy." + The comparative study performed by Jewitt&Sheppard(2005) pointed out that the giant planets possess similar abundances of irregular satellites. once their apparent magnitudes are scaled and corrected to match the same geocentrie distance.," The comparative study performed by \cite{jes05} pointed out that the giant planets possess similar abundances of irregular satellites, once their apparent magnitudes are scaled and corrected to match the same geocentric distance." + Due to the dillerent formation histories of gas and ice giants. the gas-based scenarios cannot supply a convincing explanation to this The (Comesetal.2005:Morbidelliοἱ2005:Tsiganisetal.2005). instead: undermines the physical relevance of the gas-basecl scenarios.," Due to the different formation histories of gas and ice giants, the gas-based scenarios cannot supply a convincing explanation to this The \citep{gom05,mor05,tsi05} instead undermines the physical relevance of the gas-based scenarios." + Formulated to explain the present orbital structure of the outer Solar System. it postulates that the giant planets formed. (or migrated. due to the interaction with the nebular eas) in a more compact configuration than the current one.," Formulated to explain the present orbital structure of the outer Solar System, it postulates that the giant planets formed (or migrated due to the interaction with the nebular gas) in a more compact configuration than the current one." + Suceessively. due to their mutual gravitational interactions. the giant planets evolved. through a phase of dynamical rearrangement. in," Successively, due to their mutual gravitational interactions, the giant planets evolved through a phase of dynamical rearrangement in" +"angle, prompt gamma-ray luminosity distribution and spectral shape, without requiring any luminosity evolution (see 2.3 and 3.2).","angle, prompt gamma-ray luminosity distribution and spectral shape, without requiring any luminosity evolution (see 2.3 and 3.2)." + The corresponding redshift distribution (see Fig., The corresponding redshift distribution (see Fig. +" 5) implies that at this bright limit the adopted model predicts about 6 GRBs per year, while only one GRB at z=6 has been identified in two years of operation."," 5) implies that at this bright limit the adopted model predicts about $6$ GRBs per year, while only one GRB at $z\ga 6$ has been identified in two years of operation." +" As a matter of fact, only for about half of the bursts an optical afterglow has been observed, and for only 30 per cent it has been possible to infer a redshift estimate."," As a matter of fact, only for about half of the bursts an optical afterglow has been observed, and for only $30$ per cent it has been possible to infer a redshift estimate." + It is therefore quite reasonable to guess that this fraction could be about 10 per cent for bursts at z=6 (see Fiore et al., It is therefore quite reasonable to guess that this fraction could be about $10$ per cent for bursts at $z\ga 6$ (see Fiore et al. + 2007)., 2007). + Recently Salvaterra Chincarini (2007) obtained a good formal fit to the SWIFT counts down to S&0.4 ph s! οι”. adopting as free parameters the count normalization and the GRB LF (two further parameters).," Recently Salvaterra Chincarini (2007) obtained a good formal fit to the counts down to $S\approx 0.4$ ph $^{-1}$ $^{-2}$, adopting as free parameters the count normalization and the GRB LF (two further parameters)." +" They considered the case of low metallicity environment by adopting a kinematical model and predict the occurrence of only 1 GRB yr! for theSWIFT bright flux limit (1 ph s! cm""?).", They considered the case of low metallicity environment by adopting a kinematical model and predict the occurrence of only 1 GRB $^{-1}$ for the bright flux limit $1$ ph $^{-1}$ $^{-2}$ ). + Their result imply a redshift determination efficiency for GRBs greater than 50 per cent., Their result imply a redshift determination efficiency for GRBs greater than $50$ per cent. +" It is worth noticing that reaching completeness down to 0.1 ph! s! cm? would significantly increase the number of detected GRBs and in turn allow to explore the Universe during the recombination epoch, z>8, with good statistical significance."," It is worth noticing that reaching completeness down to $0.1$ $^{-1}$ $^{-1}$ $^{-2}$ would significantly increase the number of detected GRBs and in turn allow to explore the Universe during the recombination epoch, $z \ga 8$, with good statistical significance." +" further decrease in the flux limit to 0.01 ph! s! cm~?, would Ainstead only increase the GRB sample by factor of 2; at this flux limit practically all GRBs would be detecteda (see Figs."," A further decrease in the flux limit to $0.01$ $^{-1}$ $^{-1}$ $^{-2}$, would instead only increase the GRB sample by a factor of $2$; at this flux limit practically all GRBs would be detected (see Figs." + 5 and 6)., 5 and 6). + In order to account for the trend of GRBs to be at substantial redshift Firmani et al. (, In order to account for the trend of GRBs to be at substantial redshift Firmani et al. ( +2005) proposed that the GRB LF is evolving.,2005) proposed that the GRB LF is evolving. + Daigne et al. (, Daigne et al. ( +2006) tested the hypothesis of an increasing efficiency of GRB production by massive stars with increasing redshift.,2006) tested the hypothesis of an increasing efficiency of GRB production by massive stars with increasing redshift. + Detailed redshift distributions of GRBs will discriminate among these different possibilities., Detailed redshift distributions of GRBs will discriminate among these different possibilities. +" We can conclude that the hypothesis that metal-poor, rapidly rotating massive stars are the GRB progenitors (Woosley Heger 2006; Yoon et al."," We can conclude that the hypothesis that metal-poor, rapidly rotating massive stars are the GRB progenitors (Woosley Heger 2006; Yoon et al." + 2006) is consistent with the observedSWIFT counts., 2006) is consistent with the observed counts. + Clearly determinations of GRB redshifts will be extremely informative on the progenitor and galaxy formation models., Clearly determinations of GRB redshifts will be extremely informative on the progenitor and galaxy formation models. +" We stress that the adopted galaxy formation scenario exploits quite a standard IMF, independent of the gas metallicity."," We stress that the adopted galaxy formation scenario exploits quite a standard IMF, independent of the gas metallicity." +" As a matter of fact, we showed that the cold star forming gas is rapidly (t«107 yr) enriched to the possible threshold around 3—5x10-34 Za, below which the IMF might be strongly biased toward high mass stars (see Bromm et al."," As a matter of fact, we showed that the cold star forming gas is rapidly $t\ll 10^7$ yr) enriched to the possible threshold around $3-5 \times 10^{-4}\, Z_{\odot}$ , below which the IMF might be strongly biased toward high mass stars (see Bromm et al." + 2001; Schneider et al., 2001; Schneider et al. + 2006)., 2006). + Therefore the possible contribution of pop III stars with IMF strongly biased toward high masses is not considered here., Therefore the possible contribution of pop III stars with IMF strongly biased toward high masses is not considered here. +" However, Bromm Loeb (2006) showed that at 2&10 the contribution of pop III to cosmic SFR could be of order of 1/10 of the overall SFR, becoming dominant at z=15; the GRB rate from pop III massive stars would grow correspondingly."," However, Bromm Loeb (2006) showed that at $z\approx 10$ the contribution of pop III to cosmic SFR could be of order of 1/10 of the overall SFR, becoming dominant at $z\ga 15$; the GRB rate from pop III massive stars would grow correspondingly." +" Though the idea that GRBs are preferentially located in metal poor environments is attractive, nevertheless observational estimates of the metal content of host galaxies are still controversial."," Though the idea that GRBs are preferentially located in metal poor environments is attractive, nevertheless observational estimates of the metal content of host galaxies are still controversial." + While most of the results suggest that at high-z GRB hosts exhibit metallicity Ζ<0.1—0.3Ze (Prochaska et al.," While most of the results suggest that at $z$ GRB hosts exhibit metallicity $Z\la 0.1-0.3\, +Z_{\odot}$ (Prochaska et al." +" 2007, Price et al."," 2007, Price et al." +" 2007), there are claims of higher metal content (see Savaglio et al."," 2007), there are claims of higher metal content (see Savaglio et al." + 2003)., 2003). +" Once a metal poor (Z~0.1 Ze) collapsar model is assumed, our galaxy formation scenario predicts that GRB hosts are very young, with age less than 5x107 yr, independently of the halo mass."," Once a metal poor $Z\sim 0.1\, Z_{\odot}$ ) collapsar model is assumed, our galaxy formation scenario predicts that GRB hosts are very young, with age less than $5 \times 10^{7}$ yr, independently of the halo mass." +" This young age directly mirrors the predicted short timescale, lai&5x10° yr, of chemical enrichment of the cold gas, independently of mass."," This young age directly mirrors the predicted short timescale, $t_{\rm crit}\approx 5\times +10^{7}$ yr, of chemical enrichment of the cold gas, independently of mass." +" Such independence makes the GRB rate at high-z a good tracer of the virialization rate of relatively small galaxy halos, Mu~4 is inferred. which is consistent with the broad pulse profile in the observed lighteurves.," A pseudo redshift $z\sim 4$ is inferred, which is consistent with the broad pulse profile in the observed lightcurves." + This burst likely belongs to Case (IIT) discussed above., This burst likely belongs to Case (III) discussed above. +" If the cutoff feature is real and is indeed due to pair attenuation. the requirement that 77.,,, should be smaller than 77‘ ,.demands P<6."," If the cutoff feature is real and is indeed due to pair attenuation, the requirement that $E_{\gamma_l,th}^{\rm o}$ should be smaller than $E_{\gamma,c}^{\rm o}$ demands $\Gamma \leq 6$." +" Using 18). 199), and 200), with 7)=0.67. one can estimate r>LO! em. which is consistent with the conclusion drawn from analyzing the Swift X-ray data (Kumar et al."," Using \ref{opt3}) ), \ref{A3}) ), and \ref{rad}) ), with $\beta_1=0.67$, one can estimate $r \geq 10^{16}$ cm, which is consistent with the conclusion drawn from analyzing the Swift X-ray data (Kumar et al." + 2007)., 2007). + Since the quality of the data is poor. we look forward to the high quality data retrieved by GLAST to finally pin down r in the We thank the anonymous referee for important remarks and Olivier Godet.Kohta Murase. Enrico Ramirez-Ruiz for helpful discussion/comments.," Since the quality of the data is poor, we look forward to the high quality data retrieved by GLAST to finally pin down $r$ in the We thank the anonymous referee for important remarks and Olivier Godet,Kohta Murase, Enrico Ramirez-Ruiz for helpful discussion/comments." + This work is supported by NASA under grants NNGO6GH62G. NNX07AJ66G and NNX07AJ64G.," This work is supported by NASA under grants NNG06GH62G, NNX07AJ66G and NNX07AJ64G." +"energy derivative term in equation (8)) or the equivalent term in equation (6)); and (2) the fact that equation (12)) is manifestly non-conservative for neutrino, and consequently lepton, number when integrated over mass.","energy derivative term in equation \ref{eq:boltzlag}) ) or the equivalent term in equation \ref{eq:boltzeulov/ccon}) ); and (2) the fact that equation \ref{eq:lagnoc}) ) is manifestly non-conservative for neutrino, and consequently lepton, number when integrated over mass." +" In the neutrino opaque regions, the energy-derivative term is responsible for promoting neutrinos in energy as they are compressed, as expected for a relativistic Fermi gas and first noted by (1972) and Arnett(1977)."," In the neutrino opaque regions, the energy-derivative term is responsible for promoting neutrinos in energy as they are compressed, as expected for a relativistic Fermi gas and first noted by \citet{Cast72} and \citet{Arne77}." +". There are five extant codes that can compute the spectral neutrino radiation hydrodynamics for core-collapse simulations in 2D or 3D. These codes are (in alphabeticalsupernova order by name): the FAU-NCSU-Oak Ridge 2D/3D code ((S. W. Bruenn et al.,"," There are five extant codes that can compute the spectral neutrino radiation hydrodynamics for core-collapse supernova simulations in 2D or 3D. These codes are (in alphabetical order by name): the FAU-NCSU-Oak Ridge 2D/3D code (S. W. Bruenn et al.," +" in preparation), the Stony Brook 2D code citepSwMy09,SwMy05,, the MPA-Garching 2D code citepRaJa02,BuRaJa06,, the Arizona-Caltech-Hebrew University-Princeton 2D code citepLiBuWa04,BuLiDe07,, and the Kyoto-Tokyo 2D/3D ccode (Suwaetal.2010)."," in preparation), the Stony Brook 2D code \\citep{SwMy09,SwMy05}, the MPA-Garching 2D code \\citep{RaJa02,BuRaJa06}, the Arizona-Caltech-Hebrew University-Princeton 2D code \\citep{LiBuWa04,BuLiDe07}, and the Kyoto-Tokyo 2D/3D code \citep{SuKoTa10}." +". Of the multi-D codes, aand include a spherically-symmetric, post-Newtonian GR approximation, while the others are strictly Newtonian in their gravitation, hydrodynamics, and neutrino transport."," Of the multi-D codes, and include a spherically-symmetric, post-Newtonian GR approximation, while the others are strictly Newtonian in their gravitation, hydrodynamics, and neutrino transport." +" Mülleretal.(2010) have updated tto include general relativity in the transport and hydrodynamics using the conformally flat approximation.CHIMERA,"," \citet{MuJaDi10} have updated to include general relativity in the transport and hydrodynamics using the conformally flat approximation.," +",V2D,, and ttransport neutrinos by the flux-limited diffusion method (FLD).", and transport neutrinos by the flux-limited diffusion method (FLD). +" aalso has a non-moment, multi-angle (Sy) mode."," also has a non-moment, multi-angle $S_N$ ) mode." +" uuses the variable Eddington tensor (VET) method with a closure computed using a spherically averaged, model Boltzmann equation."," uses the variable Eddington tensor (VET) method with a closure computed using a spherically averaged, model Boltzmann equation." +" The ccode uses the Isotropic Diffusion Source Approximation (IDSA;Liebendórferetal.2009), which divides the neutrinos into “trapped’ and “‘free-streaming” neutrinos, with a diffusion source to connect them."," The code uses the Isotropic Diffusion Source Approximation \citep[IDSA;][]{LiWhFi09}, which divides the neutrinos into “trapped' and “free-streaming” neutrinos, with a diffusion source to connect them." +" Of these codes, only iis capable of solving the full space-neutrino energy-species coupling of the neutrino transport that the core-collapse supernova problem requires, while all other codes break at least one of that coupling to reduce computational costs and simplify aspectcode development.CHIMERA,"," Of these codes, only is capable of solving the full space-neutrino energy-species coupling of the neutrino transport that the core-collapse supernova problem requires, while all other codes break at least one aspect of that coupling to reduce computational costs and simplify code development.," +",VERTEX,, and bbreak the non-radial (lateral, or angular) spatial coupling through the “ray-by-ray” (RbR) approximation, and bbreaks the coupling between energy groups and neutrino species."," and break the non-radial (lateral, or angular) spatial coupling through the “ray-by-ray” (RbR) approximation, and breaks the coupling between energy groups and neutrino species." +" In the RbR approximation, the neutrino transport is computed as a number of independent, spherically symmetric problems, referred to as ""rays,"" which allows for the reuse of existing ID neutrino transport codes. ("," In the RbR approximation, the neutrino transport is computed as a number of independent, spherically symmetric problems, referred to as “rays,” which allows for the reuse of existing 1D neutrino transport codes. (" +See Figure 9 for a schematic illustration of the RbR approximation.),See Figure \ref{fig:rbr} for a schematic illustration of the RbR approximation.) +" RbR methods exhibit good parallel scaling for large numbers of independent radial rays, which can be evolved without communication while the neutrino transport."," RbR methods exhibit good parallel scaling for large numbers of independent radial rays, which can be evolved without communication while computing the neutrino transport." +" Typically, in RbR codes, the computingneutrinos in opaque regions are advected laterally with the fluid motions and contribute to the pressure."," Typically, in RbR codes, the neutrinos in opaque regions are advected laterally with the fluid motions and contribute to the pressure." + The independence of the rays artificially sharpens, The independence of the rays artificially sharpens +The He? kinematics exhibit an ordered velocity gradient of more than over the NIFS field of view.,The 2 kinematics exhibit an ordered velocity gradient of more than over the NIFS field of view. + The line width mostly lies in the range FWHM. but rises to a peak of FWHM in the nuclear spaxel and a ridge of elevated velocity dispersion FWHM) runs from there through the middle of the south-eastern clump.," The line width mostly lies in the range FWHM, but rises to a peak of FWHM in the nuclear spaxel and a ridge of elevated velocity dispersion FWHM) runs from there through the middle of the south-eastern clump." + A second ridge of elevated FWHM lies in the lower right of Fig. |..," A second ridge of elevated FWHM lies in the lower right of Fig. \ref{fig:2AH2}," + bu lies near the edge of the detected emission and is likely to be of lower statistical significance. although hints of a similar feature are apparent in the observations of Hatch et al. (," but lies near the edge of the detected emission and is likely to be of lower statistical significance, although hints of a similar feature are apparent in the observations of Hatch et al. (" +2007).,2007). + In Fig., In Fig. + 3 we show an H2 rotation curve and a position-velocity diagram along the major axis of the H2? emission., \ref{fig:2AH2kinemcut} we show an 2 rotation curve and a position-velocity diagram along the major axis of the 2 emission. + There is a close morphological and kinematic correspondence between this ΠΟ emission and the double-peaked bar of emission seen in the IFS data of Hatch et al. (, There is a close morphological and kinematic correspondence between this 2 emission and the double-peaked bar of emission seen in the IFS data of Hatch et al. ( +2007) at lower spatial resolution.,2007) at lower spatial resolution. + Similarly. there is also close agreement between he global He? kinematies and those of the CO emission: in single-dish observations of CO(2-1) emission Edge (2001) measured a inewidth of FWHM. offset by from an assumed zeropoint redshift of 720.0338. which translates to in our assumed frame (220.0349) ie. the of the rotation curve in Fig. 3..," Similarly, there is also close agreement between the global 2 kinematics and those of the CO emission: in single-dish observations of CO(2-1) emission Edge (2001) measured a linewidth of FWHM, offset by from an assumed zeropoint redshift of z=0.0338, which translates to in our assumed frame (z=0.0349) i.e. the mid-point of the rotation curve in Fig. \ref{fig:2AH2kinemcut}." + Interferometry by Edge Frayer (2003) demonstrated that the CO(CI-0) emission arises from both the BCG and the companion galaxy. with the bulk of the emission residing in the former a mass of 1.210 of cool molecular gas on a spatial scale —<3.5kpe.," Interferometry by Edge Frayer (2003) demonstrated that the CO(1-0) emission arises from both the BCG and the companion galaxy, with the bulk of the emission residing in the former – a mass of $1.2 \times 10^{9}$ of cool molecular gas on a spatial scale $<3.5$." +. Given the close spatio- correspondence. it is reasonable to assume that theHa.. H2? and CO emission are all tracing the same gas system.," Given the close spatio-kinematic correspondence, it is reasonable to assume that the, 2 and CO emission are all tracing the same gas system." + In Fig., In Fig. + 4. we compare the He? v=1-0 Scl) line profile integrated over the NIFS aperture with the single dish CO¢l—0) profile from Edge (2001)., \ref{fig:2AH2COcomp} we compare the 2 v=1-0 S(1) line profile integrated over the NIFS aperture with the single dish CO(1--0) profile from Edge (2001). + Whilst there are some differences in detail — such as the strong narrow ΠΟ feature from. the north-western clump at += the two lines span the same overall range in velocity. although proportionally more CO emission arises at larger velocities.," Whilst there are some differences in detail – such as the strong narrow 2 feature from the north-western clump at – the two lines span the same overall range in velocity, although proportionally more CO emission arises at larger velocities." + The latter may originate from diffuse emission within the BCG. possibly in the form of a jet- outflow. as discussed further in section 4.2.," The latter may originate from diffuse emission within the BCG, possibly in the form of a jet-driven outflow, as discussed further in section 4.2." + Indeed. the spatially-unresolved. compact CO(1—0) emission found by Edge Frayer (2003). which is likely to correspond directly to the Π.Ο we see with NIFS. accounts for only 60 per cent of the integrated single-dish line intensity measured by Edge (2001) within the IRAM beam.," Indeed, the spatially-unresolved, compact CO(1–0) emission found by Edge Frayer (2003), which is likely to correspond directly to the 2 we see with NIFS, accounts for only 60 per cent of the integrated single-dish line intensity measured by Edge (2001) within the IRAM beam." + There may. however. be some contribution to the single-dish flux from the BCG’s companion galaxy.," There may, however, be some contribution to the single-dish flux from the BCG's companion galaxy." + stamp plots of the H22 line profiles on a grid of cells arranged according to position in the NIFS field are shown in Fig. 5.., Postage-stamp plots of the 2 line profiles on a grid of cells arranged according to position in the NIFS field are shown in Fig. \ref{fig:2AH2profs}. + Wilman et al. (, Wilman et al. ( +2009) demonstrated that the [ine ratio serves as a good discriminant between H»2 emission excited by star formation (for which Πο v-1-0 — 0.2) and the non-photoionization processes advocated by Ferland et al. (,2009) demonstrated that the line ratio serves as a good discriminant between 2 emission excited by star formation (for which 2 v=1-0 $\sim 0.2$ ) and the non-photoionization processes advocated by Ferland et al. ( +2009) (for which H22 vz1-0 ~ 1).,2009) (for which 2 v=1-0 $\sim 1$ ). + In the long-slit spectrum of Edge et al. (, In the long-slit spectrum of Edge et al. ( +2002) we measured ΠΟ vz1-0 S(3)/Paa=00.79.,2002) we measured 2 v=1-0 0.79. + lies just blueward of the spectral coverage of these NIFS data. so we focus instead on at (rest) which is within the spectral range.," lies just blueward of the spectral coverage of these NIFS data, so we focus instead on at (rest) which is within the spectral range." + The line is not detected. anywhere in the field of view. with a 3a upper limit of Brz//H»2 v=1-0 Sel) «(0.10 for the integrated. spectrum.," The line is not detected anywhere in the field of view, with a $3\sigma$ upper limit of 2 v=1-0 S(1) $<0.10$ for the integrated spectrum." +" This limit is consistent with the values of Br5//H»2 v=l-0 S¢lj=0.039 and 0.078. for the ""extra heat’ and “cosmic ray” cases. respectively. calculated by Ferland et al. ("," This limit is consistent with the values of 2 v=1-0 S(1)=0.039 and 0.078 for the `extra heat' and `cosmic ray' cases, respectively, calculated by Ferland et al. (" +2009).,2009). + Fig., Fig. + 6 shows spectra within the NIFS 3 arcsec aperture and for the 0.2(0.3 aresec region of nuclear emission indicated in Fig. |.., \ref{fig:2AH2spec} shows spectra within the NIFS $3 \times 3$ arcsec aperture and for the $0.2 \times 0.3$ arcsec region of nuclear emission indicated in Fig. \ref{fig:2AH2}. + There is no discernible difference in the emission line ratios of the two spectra. suggesting that the excitation source is spatially distributed rather than nucleated.," There is no discernible difference in the emission line ratios of the two spectra, suggesting that the excitation source is spatially distributed rather than nucleated." + When combined with the flux ratio of He? vz1-0 /Paa=00.53 from Edge et al. (, When combined with the flux ratio of 2 v=1-0 0.53 from Edge et al. ( +2002) we infer 0.053.,2002) we infer $<0.053$. + FEhisissignif icantlybelowlhecaseDrecombinationvealucofü.0: The expected," This is significantly below the case B recombination value of 0.083, but closer to the values of 0.058 and 0.064 expected for the `extra heat' and `cosmic ray' filament excitation models." + //H22 v=l-0 Sel) ratio for star-forming regions is typically much higher., The expected 2 v=1-0 S(1) ratio for star-forming regions is typically much higher. + For example. in Moorwood Oliva (1988). 7 of out 8 galactic nuclei optically-classitied as pure HII systems have //H2? vz1-0 Stl) 23: in composite and Seyfert nuclei. the ratio is of order unity.," For example, in Moorwood Oliva (1988), 7 of out 8 galactic nuclei optically-classified as pure HII systems have 2 v=1-0 S(1) $ \geq 3$; in composite and Seyfert nuclei, the ratio is of order unity." + Our limit is well below this range implying that the excitation of H»2 emission in 2A 0335+096 cannot be dominated by star formation., Our limit is well below this range implying that the excitation of 2 emission in 2A 0335+096 cannot be dominated by star formation. + In any case. the star formation rate inferred from the mid-infrared emission in 2A 0335-096 by ODea et al. (," In any case, the star formation rate inferred from the mid-infrared emission in 2A 0335+096 by O'Dea et al. (" +2008) is just for the entire galaxy. compared to ~~15 for the systems in the Wilman et al. (,"2008) is just for the entire galaxy, compared to $\sim 15$ for the systems in the Wilman et al. (" +2009) sample.,2009) sample. + The 3c upper limit on the equivalent width of is0., The $3\sigma$ upper limit on the equivalent width of is. +8À.. With reference to the evolutionary models shown in Davies et al. (, With reference to the evolutionary models shown in Davies et al. ( +2006) (their Fig.,2006) (their Fig. + 8) the latter would imply an absence of star formation for at least the pastMyr.. if considered as a monolithie stellar population.," 8) the latter would imply an absence of star formation for at least the past, if considered as a monolithic stellar population." + The measured equivalent width of the CO(2.0) bandhead at (rest) is9.9À: although this figure is below the expected for most stellar populations more than old (Fig.," The measured equivalent width of the CO(2,0) bandhead at (rest) is; although this figure is below the expected for most stellar populations more than old (Fig." + 6 of Davies et al., 6 of Davies et al. + 2006). it is likely to lie within the bounds of the systematic uncertainties arising from. for example. the form of the initial mass function in these environments.," 2006), it is likely to lie within the bounds of the systematic uncertainties arising from, for example, the form of the initial mass function in these environments." + Modest dilution from non-stellar sources of continuum emission remains another possibility., Modest dilution from non-stellar sources of continuum emission remains another possibility. + Although we do not detect emission within the NIFS aperture. emission is present in this region in the IFU observations of Hatch et al. (," Although we do not detect emission within the NIFS aperture, emission is present in this region in the IFU observations of Hatch et al. (" +2007) and in the long-slit spectrum of Donahue et al. (,2007) and in the long-slit spectrum of Donahue et al. ( +2007).,2007). + From these works we estimate an flux within the 3.3 arcsec NIFS aperture of 5.10.P equating to an luminosity of 1.4101," From these works we estimate an flux within the $3 \times 3$ arcsec NIFS aperture of $5 \times 10^{-15}$, equating to an luminosity of $1.4 \times 10^{40}$." + Using the Kennicutt (1998) Ha--star formation rate relation. this would translate to a star formation rate of if all the were due to star formation.," Using the Kennicutt (1998) –star formation rate relation, this would translate to a star formation rate of if all the were due to star formation." + Corrections for Galactic and intrinsic dust extinction (each. approximately | magnitude: Donahue et al., Corrections for Galactic and intrinsic dust extinction (each approximately 1 magnitude; Donahue et al. + 2007) would boost the estimates by a factor of 6., 2007) would boost the estimates by a factor of 6. + As noted by Donahue et al. (, As noted by Donahue et al. ( +2007). the extinction-corrected star formation rate for the entire galaxy inferred from the emission is 15-20 and that inferred from the excess UV emission is of a similar order of magnitude.,"2007), the extinction-corrected star formation rate for the entire galaxy inferred from the emission is 15–20 and that inferred from the excess UV emission is of a similar order of magnitude." + These estimates would be compatible with the mid-infrared estimate of (ODea et al., These estimates would be compatible with the mid-infrared estimate of (O'Dea et al. + 2008) if only 1O per cent of the emission were due to star formation., 2008) if only 10 per cent of the emission were due to star formation. + For comparison. a fit —by Donahue et al. (," For comparison, a fit by Donahue et al. (" +2011) to the mid-infrared emission features with an HIT region photodissociation region model yielded a star formation rate of1.,2011) to the mid-infrared emission features with an HII region photodissociation region model yielded a star formation rate of. + The low level of ongoing circumnuclear star formation corroborates the findings of Romanishin Hintzen (1988)., The low level of ongoing circumnuclear star formation corroborates the findings of Romanishin Hintzen (1988). + Their analysis of the B-I colour gradient of the BCG showed that star formation is occurring at radiiKpe.. as evidenced by a plateau in B-I bluer than in non-cooling flow BCGs: the colour reddens at smaller radii. suggesting a decline in the star formation rate or dust extinction.," Their analysis of the B–I colour gradient of the BCG showed that star formation is occurring at radii, as evidenced by a plateau in B–I bluer than in non-cooling flow BCGs; the colour reddens at smaller radii, suggesting a decline in the star formation rate or dust extinction." + The latter explanation is ruled out by our, The latter explanation is ruled out by our +importantly. this observation is confirmed by the theoretical study of Chabrier et al. (,"importantly, this observation is confirmed by the theoretical study of Chabrier et al. (" +2007). who have recently modified stellar evolution codes to include the effects of stellar activity.,"2007), who have recently modified stellar evolution codes to include the effects of stellar activity." + These authors also report systematic differences between the properties of active and inactive stars in similar amount and trend as those found from eclipsing binary studies., These authors also report systematic differences between the properties of active and inactive stars in similar amount and trend as those found from eclipsing binary studies. + With improved. statistics with respect to Stauffer Hartmann (1986) and the context provided by the new evidence discussed above. we analyse the existence of differences between active and inactive stars of spectral types late-K and M. In the present study we use luminosities directly determined from accurate trigonometric parallaxes and carry out a thorough analysis of possible biases. such as the effect of pre-main sequence (PMS) and binary stars.," With improved statistics with respect to Stauffer Hartmann (1986) and the context provided by the new evidence discussed above, we analyse the existence of differences between active and inactive stars of spectral types late-K and M. In the present study we use luminosities directly determined from accurate trigonometric parallaxes and carry out a thorough analysis of possible biases, such as the effect of pre-main sequence (PMS) and binary stars." + Also. we interpret the results in physical terms. 1.e.. effective temperature rald radius variations.," Also, we interpret the results in physical terms, i.e., effective temperature and radius variations." + If active stars were indeed cooler and larger than their inactive counterparts. while keeping similar luminosities. this should be observable in single field stars (in addition to close binaries) thus generalizing the proposed stellar activity scenario to all low-mass stars.," If active stars were indeed cooler and larger than their inactive counterparts, while keeping similar luminosities, this should be observable in single field stars (in addition to close binaries) thus generalizing the proposed stellar activity scenario to all low-mass stars." + The sample used to test this hypothesis is composed of selected late-K and M dwarfs from the Palomar/Michigan State University survey of nearby stars (hereafter PMSU; Reid et al., The sample used to test this hypothesis is composed of selected late-K and M dwarfs from the Palomar/Michigan State University survey of nearby stars (hereafter PMSU; Reid et al. + 1995: Hawley et al., 1995; Hawley et al. + 1996)., 1996). + This catalog lists the position. My. distance. TIO. CaH and CaOH spectral indices. Πα equivalent width and proper motions for each of the 1966 stars that it contains.," This catalog lists the position, $M_{\rm V}$, distance, TiO, CaH and CaOH spectral indices, $\alpha$ equivalent width and proper motions for each of the 1966 stars that it contains." + The distances listed are averaged combinations of Hipparcos trigonometric parallaxes and spectrophotometric determinations., The distances listed are averaged combinations of Hipparcos trigonometric parallaxes and spectrophotometric determinations. + Because of our working hypothesis of the Tr dependence on activity. only objects with direct trigonometric parallaxes are useful to our study because spectroscopic and photometric parallaxes could be biased by activity.," Because of our working hypothesis of the $T_{\rm eff}$ dependence on activity, only objects with direct trigonometric parallaxes are useful to our study because spectroscopic and photometric parallaxes could be biased by activity." + The restriction of trigonometric parallaxes reduces the number of stars in the working sample to 746. with 1.3 <4 58.0 pe and 6.65 «My 16.0 mag.," The restriction of trigonometric parallaxes reduces the number of stars in the working sample to 746, with 1.3 $ directions with left aud right states listed in Table 1 as test RJla.," A computational volume $64\times 1\times 1$ units was used, with fixed value boundaries in the $x$ direction, and periodic boundaries in the $y$ and $z$ directions with left and right states listed in Table \ref{tabshocktubes} as test RJ1a." + As Dai&Woodward(1991). show. the soution consists of a rieht come fast shock with Mach uuuber 6.5L. a left eoiug fast shock with Mach umber 2.51. a slow shock. a slow rarefaction. aud a cofact cliscoutinuity.," As \cite{1994JCoPh.111..354D} show, the solution consists of a right going fast shock with Mach number 6.54, a left going fast shock with Mach number 2.54, a slow shock, a slow rarefaction, and a contact discontinuity." + Phiurbas shows a V+B error of a few parts iu 104 in the region Ixiug between the two fast shocks., Phurbas shows a $\nabla \cdot \mathbf{B}$ error of a few parts in $10^4$ in the region lying between the two fast shocks. + As an example of idlidinieusional snooth flow with bulk motions. we demonstrate the performance of Phnurbas on threc-dineusional Ixeblviu-IHehuhloltz," As an example of multidimensional smooth flow with bulk motions, we demonstrate the performance of Phurbas on three-dimensional Kelvin-Helmholtz" +for at least some post-starburst galaxies.,for at least some post-starburst galaxies. + Therefore. it: is necessary to examine whether the radio emission is due to star formation.," Therefore, it is necessary to examine whether the radio emission is due to star formation." + AGN radio emission can be distinguished in two ways (seeMushotzky.2004.forareview)..., AGN radio emission can be distinguished in two ways \citep[see][for a review]{mushotzky04}. + First. multiple radio emission components such as lobes or jets are signatures of AGN activity (Fanaroll&Bülev1974:HeviglioLHelfand 2006).," First, multiple radio emission components such as lobes or jets are signatures of AGN activity \citep{fanaroff74,reviglio06}." +. In our sample. we find extended: multiple emission regions that are not matched to the optical light distribution in SDSS.J094818.6|023004. SDSSJIGOSOSOS.7|394755. and SDSSJ161910.4]064223. as well as the uncertain case SDSSJ1543224)331018 (see Figure 1)).," In our sample, we find extended multiple emission regions that are not matched to the optical light distribution in SDSSJ094818.6+023004, SDSSJ16080808.7+394755, and SDSSJ161910.4+064223 as well as the uncertain case SDSSJ154322.4+331018 (see Figure \ref{fig:match}) )." + Second. the racio luminosities of these galaxies can be used to identify raclio-emitting AGNs.," Second, the radio luminosities of these galaxies can be used to identify radio-emitting AGNs." + The radio-to-optical flux ratio or racdio Iuminosity. itself can be used statistically to recognise radio emission from ACN activity (e.g.Iveziéοἱal.2002:Bestetal.200 5).," The radio-to-optical flux ratio or radio luminosity itself can be used statistically to recognise radio emission from AGN activity \citep[e.g.][]{ivezic02,best05}." + But with the small number of objects in our sample. it is not safe to use the radio-to-optical [ux ratio to distinguish radio emission from AGN anc [rom star formation.," But with the small number of objects in our sample, it is not safe to use the radio-to-optical flux ratio to distinguish radio emission from AGN and from star formation." + Moreover. the boundary of the Lux ratio between the two emission sources is not sharp (c.g.&Lelfancl 20060).," Moreover, the boundary of the flux ratio between the two emission sources is not sharp \citep[e.g.][]{reviglio06}." + Ifo we assume that the radio emission is duc entirely to ongoing star formation (e.g.Coto3004). we can convert the observed. radio Luminosity to the expected current star formation rate (SER) following the conversion given by Reclely.&Condon (2001): assuming the Salpeter initial mass function 1955) with a mass range from 0.1 to LOO AL. (seeBell03:Hopkinsetal.2003.fordillerent. conversions)...," If we assume that the radio emission is due entirely to ongoing star formation \citep[e.g.][]{goto04}, we can convert the observed radio luminosity to the expected current star formation rate (SFR) following the conversion given by \citet{yun01}: assuming the Salpeter initial mass function \citep{salpeter55} with a mass range from 0.1 to 100 ${\rm M_{\odot}}$ \citep[see][for different conversions]{bell03,hopkins03}. ." + The coellicient in this equation has a statistical scatter of about (Yun.Heddyv.&Condon2001)., The coefficient in this equation has a statistical scatter of about \citep{yun01}. +. When we adopt the Chabrier (Chabrier2003) initial mass function. the difference in the estimated SEI with these two initial mass functions 1s logSPIsoοσοIonas~0.186 Bardellietal.2009).," When we adopt the Chabrier \citep{chabrier03} initial mass function, the difference in the estimated SFRs with these two initial mass functions is ${\rm log_{10} SFR_{Salpeter} - log_{10} SFR_{Chabrier}} \sim 0.186$ \citep{bardelli09}." +". For our twelve radio post-starburst ealaxies. racio luminosities are estimated for three dilferent spectral indices (a=1.0.1) (Longue&Westpfahl.1995) or a power-law energy. distribution. ἐνx9""."," For our twelve radio post-starburst galaxies, radio luminosities are estimated for three different spectral indices $\alpha = -1, 0, 1$ \citep{tongue95} for a power-law energy distribution $F_{\nu} \propto \nu^{\alpha}$." + The radio luminosity Lieu; ranges from about 10SWLiz5L to 10777WVLz as presented in Table 2..," The radio luminosity $L_{1.4 GHz}$ ranges from about $10^{21.8} {\rm W ~ Hz^{-1}}$ to $10^{25.2} {\rm W ~ Hz^{-1}}$ , as presented in Table \ref{tab:radio_mass}." + For the galaxies which have no detectable radio counterparts. we use the racio Εαν upper limit of 1 my at 1.4 112.," For the galaxies which have no detectable radio counterparts, we use the radio flux upper limit of 1 mJy at 1.4 GHz." + Figure 5. shows the resulting predicted. 9015 as a function of stellar mass., Figure \ref{fig:radio_sfr} shows the resulting predicted SFRs as a function of stellar mass. + All galaxies with detected. racio emission. except SDSSJOS2254.8|192128 would have SER nIOAM.vr assuming. the radio. emissions is. due entirely. to ongoing star formation., All galaxies with detected radio emission except SDSSJ082254.8+192128 would have SFR $> 10 M_{\odot} ~ {\rm yr^{-1}}$ assuming the radio emission is due entirely to ongoing star formation. + This level of hidden star formation seems highly unlikely given the absence of strong emission lines such as OL] and Ha. as we now show.," This level of hidden star formation seems highly unlikely given the absence of strong emission lines such as [OII] and $\alpha$, as we now show." + We estimate the expected. unextinetecl Luminosity ane equivalent width of the OL11]A3727 emission line from the SER upper limit derived: earlier. assuming that the racio emission is [rom current star formation.," We estimate the expected unextincted luminosity and equivalent width of the $\lambda$ 3727 emission line from the SFR upper limit derived earlier, assuming that the radio emission is from current star formation." + Using the conversion from SER. to OL] luminosity from Lopkinsetal.(2003). we derive the expected equivalent. width where 2. is the continuum at 3727A.," Using the conversion from SFR to [OII] luminosity from \citet{hopkins03}, we derive the expected equivalent width where $P_{c}$ is the continuum at ${\rm \AA}$." + For SDSSJOS2254.8|192128. which has the lowest expected SPR ~4M.ve among the radio sources. we [ind an equivalent width of about 260A. which is much larger than the observational limit of EW(OL]) = 0.63 citepgoto07..," For SDSSJ082254.8+192128, which has the lowest expected SFR $\sim 4 M_{\odot} ~ {\rm yr^{-1}}$ among the radio sources, we find an equivalent width of about 260, which is much larger than the observational limit of EW([OII]) $=$ 0.63 \\citep{goto07}." + This constraint on the equivalent width is not allectedl by dust. extinction. which allects continuum and line emission. equally.," This constraint on the equivalent width is not affected by dust extinction, which affects continuum and line emission equally." + It is a reasonable assumption that both emission lines and the blue stellar continuum originate from the same stellar population in the case of the highly obscured intensive star forming galaxies which we consider here., It is a reasonable assumption that both emission lines and the blue stellar continuum originate from the same stellar population in the case of the highly obscured intensive star forming galaxies which we consider here. + Lt is unlikely that selective high dust extinction of the emission line (lux can explain the absence of emission lines with this large expected equivalent. width., It is unlikely that selective high dust extinction of the emission line flux can explain the absence of emission lines with this large expected equivalent width. + We also examine the optical depth for dustextinction (Tee) which is applied to the voung stellar population in the VESPA analysis CLojeiroetal.2007)., We also examine the optical depth for dustextinction $\tau_{BC}$ ) which is applied to the young stellar population in the VESPA analysis \citep{tojeiro07}. +. Although zge: might be less reliable than the constraint with ENgs. the distribution of zge: should. be at least consistent with the constraint from the expected EW.," Although $\tau_{BC}$ might be less reliable than the constraint with ${\rm EW}_{\rm line}$, the distribution of $\tau_{BC}$ should be at least consistent with the constraint from the expected EW." + Figure 5. shows that zge: is low for sources of high radio Iuminosity., Figure \ref{fig:radio_sfr} shows that $\tau_{BC}$ is low for sources of high radio luminosity. + This trend. is opposite to what would be needed to explain the absence of OLI] emission if the radio emission is due to star formation., This trend is opposite to what would be needed to explain the absence of [OII] emission if the radio emission is due to star formation. + We thus conclude that the radio emission in these twelve ealaxies is dominated by AGN activity., We thus conclude that the radio emission in these twelve galaxies is dominated by AGN activity. + Radio luminosity has been commonly used as a tracer of mechanical energv input by. racio-mode AGN feedback., Radio luminosity has been commonly used as a tracer of mechanical energy input by radio-mode AGN feedback. + A simple scaling relation. albeit with non-negligible scatter. between radio luminosity and. mechanical power has been suegeested (c.g.Birzanctal.2004).," A simple scaling relation, albeit with non-negligible scatter, between radio luminosity and mechanical power has been suggested \citep[e.g.][]{birzan04}." +.. Adopting the scaling relationship from Birzanοἱal.(2008) we estimate the mechanical power Lien from raclio-mode AGN activity [rom the measured. ἐν. for the twelve objects which are matehed to radio sources.," Adopting the scaling relationship from \citet{birzan08} + we estimate the mechanical power $L_{mech}$ from radio-mode AGN activity from the measured $L_{1.4 GHz}$ for the twelve objects which are matched to radio sources." + The mechanical power in radio-emitting samples ranges from 1.2«1075 to Ls.10!erg/s. as shown in Figure 6..," The mechanical power in radio-emitting samples ranges from $1.2 \times 10^{43}$ to $1.8 \times 10^{44} ~ {\rm erg / s}$, as shown in Figure \ref{fig:radio_mass}." + Interestingly. the mechanical energy is higher for objects of higher galaxy stellar mass. in agreement with Bestctal. (2005).. who show that luminous radio sources are more likely to be hosted by more massive galaxies.," Interestingly, the mechanical energy is higher for objects of higher galaxy stellar mass, in agreement with \citet{best05}, who show that luminous radio sources are more likely to be hosted by more massive galaxies." + Although our sample is radio Ilux-limited. the absence of Luminous racio sources for low-mass galaxies is not due to selection effects. as the distribution of the radio luminosity upper limits for objects without radio counterparts shows in Figure 5..," Although our sample is radio flux-limited, the absence of luminous radio sources for low-mass galaxies is not due to selection effects, as the distribution of the radio luminosity upper limits for objects without radio counterparts shows in Figure \ref{fig:radio_sfr}." + Phis trend is not surprising because massive galaxies host massive central black holes. which can produce radio jets with a large amount of mechanical power (secMeier2003:Bestet.al. discussion)..," This trend is not surprising because massive galaxies host massive central black holes, which can produce radio jets with a large amount of mechanical power \citep[see][for a discussion] +{meier03,best05,bardelli10}. ." + It also suggests that the mechanicalpower is correlated with the old stellar population. which dominates the stellar mass.," It also suggests that the mechanicalpower is correlated with the old stellar population, which dominates the stellar mass." + In contrast. no correlation of recently. formed. stellar mass with mechanical power output 1s apparent. as," In contrast, no correlation of recently formed stellar mass with mechanical power output is apparent, as" +"We conclude that jet ejection leads to enhanced |Neu]] emission, although we cannot demonstrate whether |[Net]] emission forms in shocks close to the star. or in absorbing accretion flows toward the star as the increased mass loss rates of jet engines also implies higher accretion rates. and therefore more massive accretion flows close to the stellar X-ray source.","We conclude that jet ejection leads to enhanced ] emission, although we cannot demonstrate whether ] emission forms in shocks close to the star, or in absorbing accretion flows toward the star as the increased mass loss rates of jet engines also implies higher accretion rates, and therefore more massive accretion flows close to the stellar X-ray source." + We still do find indications that the production of [Net] emission weakly scales with the X-ray luminosity., We still do find indications that the production of ] emission weakly scales with the X-ray luminosity. + This finding supports previous theoretical models of X-ray irradiated and ionized stellar environments although irradiated. winds. accretion flows and jets should also be considered as targets. apart from the so far favored disk surface layers.," This finding supports previous theoretical models of X-ray irradiated and ionized stellar environments although irradiated winds, accretion flows and jets should also be considered as targets, apart from the so far favored disk surface layers." + The correlation found between [Net]] emission from jet-driving CTTS and Lx suggests an important role of stellar short-wavelength radiation in exciting this line in the jet/outflow gas at least relatively close to the stars themselves., The correlation found between ] emission from jet-driving CTTS and $L_{\rm X}$ suggests an important role of stellar short-wavelength radiation in exciting this line in the jet/outflow gas at least relatively close to the stars themselves. + There is obvious need for deeper studies to disentangle the various possible origins of emission., There is obvious need for deeper studies to disentangle the various possible origins of ] emission. + The beam ts large and potentially includes both unresolved outflow and disk contributions., The beam is large and potentially includes both unresolved outflow and disk contributions. + Narrow slit observation using high resolving power. possibly stepped across the source for integral field spectroscopy. could uncover disk line profiles (symmetric. centered at stellar velocity. disk-like velocity range if bound or blue-shifted if photoevaporating) separately from outflow signatures (asymmetric lines. blue-shifted or red-shifted. with high velocities) at larger distances from the star.," Narrow slit observation using high resolving power, possibly stepped across the source for integral field spectroscopy, could uncover disk line profiles (symmetric, centered at stellar velocity, disk-like velocity range if bound or blue-shifted if photoevaporating) separately from outflow signatures (asymmetric lines, blue-shifted or red-shifted, with high velocities) at larger distances from the star." + Such observations have now provided first interesting results (vanBoekel 2009)..," Such observations have now provided first interesting results \citep{boekel09, najita09, pascucci09}. ." +uniform density sphere and the angular momentum is @=4/sini with i the angle of inclination to the line of sight.,"uniform density sphere and the angular momentum is $\omega = {\cal G}/ +\sin i$ with $i$ the angle of inclination to the line of sight." +" Assuming values representative of these clumps and sini=1, this becomes: Across all the clumps the average values of Brot are: (Brot)=(0.014+0.003) and (0.013+0.004) for aand rrespectively."," Assuming values representative of these clumps and $\sin i =1$, this becomes: Across all the clumps the average values of $\beta_\mathrm{rot}$ are: $\langle \beta_\mathrm{rot} \rangle = (0.014 \pm 0.003)$ and $(0.013 +\pm 0.004)$ for and respectively." + At most the rotational energy is just six per cent for the ssample and 14 per cent for oof the gravitational energy in the clumps., At most the rotational energy is just six per cent for the sample and 14 per cent for of the gravitational energy in the clumps. + reffig:betacomparisonshowsthedistributionof Brot for the two clump populations., \\ref{fig:beta_comparison} shows the distribution of $\beta_\mathrm{rot}$ for the two clump populations. +" There is a strong preference for low ratios, with the fraction of clumps rapidly falling off as βιοι increases."," There is a strong preference for low ratios, with the fraction of clumps rapidly falling off as $\beta_\mathrm{rot}$ increases." +" Additionally, both populations closely match each other and the ratios found by etal] while |GBF93] distribution is wider, spreading to higher |Caselli(2002),,values."," Additionally, both populations closely match each other and the ratios found by \citet{caselli02}, while the \citetalias{goodman93} distribution is wider, spreading to higher values." + K-S teststhe could not confirm, K-S tests could not confirm +imiting the total list of z3.0 detections to those which could be point-like.,limiting the total list of $>3.0\sigma$ detections to those which could be point-like. + We adopted the slightly more stringent imits of 0.6S) = (16.7 \pm 1.7) (S/1\,{\rm{mJy}})^{-0.80 \pm 0.07}$ $^{-2}$." + pt must be emphasized tha of the data in this diagram.5 only our 43-Cllz 1point aux contours. plus the ΑΛΛΟ source. count. represent: clirec observations at 43. CGllz.," It must be emphasized that of the data in this diagram, only our 43-GHz point and contours plus the WMAP source count represent direct observations at 43 GHz." + The other direct! observationa result in the diagram is the representation of the 20-Cillz souce count from the AVPOG survey., The other direct observational result in the diagram is the representation of the 20-GHz souce count from the AT20G survey. + All other data are inferred or projected from 31 Cllz. 43 Gllz or 95 Cillz.," All other data are inferred or projected from 31 GHz, 43 GHz or 95 GHz." + Phere is no scaling of any result in the diagram., There is no scaling of any result in the diagram. + 1l., 1. + This 43-Cllz survev (VLA. D-arrav) reaches approximately 7 mv over an area of 0.5deg?.. with a primary beam of 1.0 aremin FWILIM. and ai circular synthesized. beam of 2.3 aresce FWA," This 43-GHz survey (VLA D-array) reaches approximately 7 mJy over an area of 0.5, with a primary beam of 1.0 arcmin FWHM and a circular synthesized beam of 2.3 arcsec FWHM." + Done in snapshot mode to follow the ‘wicde-shallow’ dictum. it found. many apparent sources. most of which on inspection proved to be at the junction of response lines.," Done in snapshot mode to follow the `wide-shallow' dictum, it found many apparent sources, most of which on inspection proved to be at the junction of response lines." +Most. can be eliminated on this basis. and on the basis that they are extended. to,"Most can be eliminated on this basis, and on the basis that they are extended to" +predict pu using Eq. (19).,predict $T_{\rm eff}^{\rm jump}$ using Eq. \ref{eq_jump1}) ). + Later ou this will be used as a tool to connect two fitting formulac for the two ranges in Diy at either side of the bistability jump (see Sect. 5))., Later on this will be used as a tool to connect two fitting formulae for the two ranges in $\teff$ at either side of the bi-stability jump (see Sect. \ref{s_recipe}) ). + Figure 2 shows that at effective temperatures Digg< 22 HOO K. AL initially decreases.," Figure \ref{f_massloss} shows that at effective temperatures $\teff \le$ 22 500 K, $\dot{M}$ initially decreases." + This is similar to the AT behaviour in the Τμ range between 50 000 aud 27 50 Ix. For some series (dependent ou the adopted L./À.) the mass loss decreases uutil our calculations cud at Tig = 12 500., This is similar to the $\dot{M}$ behaviour in the $\teff$ range between 50 000 and 27 500 K. For some series (dependent on the adopted $L_*/M_*$ ) the mass loss decreases until our calculations end at $\teff$ = 12 500. + For other series of L. and AL... the initial clecrease suddenulv switches to anotherwercese.," For other series of $L_*$ and $M_*$, the initial decrease suddenly switches to another." + Vink. et al. (, Vink et al. ( +1999) already anticipated that somewhere. at lower τω. a recombination would occur from Fe to simular to the recombination from Fe to at ~ 25 000 Ix. Lamers et al. (,"1999) already anticipated that somewhere, at lower $\teff$, a recombination would occur from Fe to similar to the recombination from Fe to at $\sim$ 25 000 K. Lamers et al. (" +1995) already. mentioned the possible existence of such a second bi-stabilitv πο around == 10 000 I& from their determumatious of οςfece. but +ιο observational evideuce or this second jump is still quite meagre.,"1995) already mentioned the possible existence of such a second bi-stability jump around = 10 000 K from their determinations of $\ratio$, but the observational evidence for this second jump is still quite meagre." + To understand the characteristics of the “second” bi-stability jump as a function of ciffereut stellar parameters (AL. and £..). we have also studied the models around this secoud jump iu some more cetail.," To understand the characteristics of the “second” bi-stability jump as a function of different stellar parameters $M_*$ and $L_*$ ), we have also studied the models around this second jump in some more detail." + Since our model exid is terminated at 12 500 Ix. it is not possible to determine the maxi M of he second bistability Jump ina cousistent way. simular to hat of the first jump ciseussed in Sect. 3.2..," Since our model grid is terminated at 12 500 K, it is not possible to determine the maximum $\dot{M}$ of the second bi-stability jump in a consistent way, similar to that of the first jump discussed in Sect. \ref{s_jump}." + Thus. it is not yosstble to determine the exac VAize of the second jump in AL.," Thus, it is not possible to determine the exact size of the second jump in $\dot{M}$." + Neither is it possible to derive an accurate equation for the position of the second bi-stability jump in Tig (as was done in Eq., Neither is it possible to derive an accurate equation for the position of the second bi-stability jump in $\teff$ (as was done in Eq. + or the first jmp around 25 O00 I., \ref{eq_jump1} for the first jump around 25 000 K). +" Still. i js useful to determine a rough relationship between the position of the secoix ΠΠ)] in Zig and the average log «p> by investigating for cach model at which temperature the mass-loss rate still decreases aud for which models Hyproaching the second bi-tabilitv jump. the mass loss AA mncereases,"," Still, it is useful to determine a rough relationship between the position of the second jump in $\teff$ and the average log $<\rho>$ by investigating for each model at which temperature the mass-loss rate still decreases and for which models approaching the second bi-stability jump, the mass loss again increases." + The relation found between the temperature of the second. bistability jump and log «p> is determined by eve and is roughly eiven by: where TI? is in EIS. From the quantities £. aud AL it is again possible to estimate log «pb2 using Eq. (5)), The relation found between the temperature of the second bi-stability jump and log $<\rho>$ is determined by eye and is roughly given by: where $T^{\rm jump2}$ is in kK. From the quantities $L_*$ and $M_*$ it is again possible to estimate log $<\rho>$ using Eq. \ref{eq_gamma1}) ) + aud then to roughlv predict 779912. απο Eq. (61)., and then to roughly predict $T^{\rm jump2}$ using Eq. \ref{eq_jump2}) ). + This formmla will be used for our mass-loss recipe at the low temperature side (see Sect. 5))., This formula will be used for our mass-loss recipe at the low temperature side (see Sect. \ref{s_recipe}) ). + Iu this section. we present values for the wind efficiency number 4 for the differeut. CL...M.) series.," In this section, we present values for the wind efficiency number $\eta$ for the different $(L_*,M_*)$ series." + jj (sometimes called the wind performance number) describes the fraction of the Iuonuentuini of the radiation that is trausterred to the ious in the wincl: Figure 5 shows the behaviour of ;j as a function of Tig for the complete C»exid of models., $\eta$ (sometimes called the wind performance number) describes the fraction of the momentum of the radiation that is transferred to the ions in the wind: Figure \ref{f_eta} shows the behaviour of $\eta$ as a function of $\teff$ for the complete grid of models. + FigureOo 5 demonstrates thatTig., Figure \ref{f_eta} demonstrates that. + The figure shows that when a star evolves rediwards at constaut huninosity (from high to low temperature) the moment cficieney jj initially decreases until the star approaches the brstabilitv Jump around 25 000 IX. where the wind cfficienev. suddenlydereeses bv a factor of two to three.," The figure shows that when a star evolves redwards at constant luminosity (from high to low temperature) the momentum efficiency $\eta$ initially decreases until the star approaches the bi-stability jump around 25 000 K, where the wind efficiency suddenly by a factor of two to three." + Subsequeuth below about 22 500 IW. 4 decreases again and mi some cases (again dependent ou L and M.) it eventually junips again at the second bi-stability jump.," Subsequently, below about 22 500 K, $\eta$ decreases again and in some cases (again dependent on $L_*$ and $M_*$ ) it eventually jumps again at the second bi-stability jump." + This overall behaviour of jg is similar to that of AM as shown in Fig. 2.., This overall behaviour of $\eta$ is similar to that of $\dot{M}$ as shown in Fig. \ref{f_massloss}. + Tn some of the panels of Fig. 5..," In some of the panels of Fig. \ref{f_eta}," +" 1.0. iu those cases where LfAL, is large. 4 exceeds the single scattering limit."," i.e. in those cases where $L_*/M_*$ is large, $\eta$ exceeds the single scattering limit." + This occurs at Tig& 40 000 TS and log (£./£..)2 6., This occurs at $\teff \ga$ 40 000 K and log $L_*/\lsun) \ga$ 6. + It sugeests that already for high luminosity OB stars stellar winds cannot be treated in thescattering formalis., It suggests that already for high luminosity OB stars stellar winds cannot be treated in the formalism. + The sinele-scattering limit which is definitely iuvalid for the optically thick winds of Wolt-Ravet type stars. is often asstuned to be valid for the winds of “normal” supereiauts.," The single-scattering limit which is definitely invalid for the optically thick winds of Wolf-Rayet type stars, is often assumed to be valid for the winds of “normal” supergiants." +" Tere. however. we come to the conclusion that due toscattering. i already exceeds unity for luminous. but ""nonual"" OD superegiauts. in case loe(L/L.)2 6."," Here, however, we come to the conclusion that due to, $\eta$ already exceeds unity for luminous, but “normal” OB supergiants, in case $L/\lsun) \ga$ 6." + This was already suggested w Lamers Leitherer (1993) on the basis of observations., This was already suggested by Lamers Leitherer (1993) on the basis of observations. + Puls et al , Puls et al. ( +ο996) proposed that the reason for the systematic discrepancy between the observe πο. rates and recent standard radiation driven wiud models (Pauldrach et al.,1996) proposed that the reason for the systematic discrepancy between the observed mass-loss rates and recent standard radiation driven wind models (Pauldrach et al. + 1991) was caused bv an inadequate treatiucun of iuulti-liue. effects iun these wind uodels., 1994) was caused by an inadequate treatment of multi-line effects in these wind models. + To conipare our lew dnass-loss predictions with the most sophisticated prior investigations. it is usofu to brietiy discuss the most mniportaut assumptions tha are niade iu inodelliue the wind dynamics of OB-type stars.," To compare our new mass-loss predictions with the most sophisticated prior investigations, it is useful to briefly discuss the most important assumptions that are made in modelling the wind dynamics of OB-type stars." + The felowing our basic choices must be iade:, The following four basic choices must be made: +from tιο SANs and ZCZÜT ire in better agreement at Do0. rowever. the SAMs underestimate the stellar mass In cenral galaxies in prescut-dav halos more massive than 10525.IND...,"from the SAMs and ZCZ07 are in better agreement at $z \sim 0$, however, the SAMs underestimate the stellar mass in central galaxies in present-day halos more massive than $\sim 10^{12} \Msunh$." + Note that for halos larger than this characeristic mass. ACN feedback starts to plaving au Πιηροτα! role (see c.e.. Stringeretal.2008)). sugeesting its effect might be overestimated within these models. resultiie in over-quenuching stellar mass erowth.," Note that for halos larger than this characteristic mass, AGN feedback starts to playing an important role (see e.g., \citealt{Stringer09}) ), suggesting its effect might be overestimated within these models, resulting in over-quenching stellar mass growth." + When looking at the fraction of stellar nass in prescut-av central galaxies that is already im place at +—1. there is a factor of two disagreement between the SAM and the ZCZO7 results.," When looking at the fraction of stellar mass in present-day central galaxies that is already in place at $z \sim 1$, there is a factor of two disagreement between the SAMs and the ZCZ07 results." +" For example. ZCZüT obtain that about 30% of the stars in laos of ~3«Lol?hINT. are formed by 2~1l. while the SAMs predict about ο,"," For example, ZCZ07 obtain that about $30\%$ of the stars in halos of $\sim 3 +\times 10^{12} \Msunh$ are formed by $z \sim 1$, while the SAMs predict about $60\%$." + The discrepancy is siguificantg even when conservatively accounting for a possible uuerestimation of the DEEP? stellar masses., The discrepancy is significant even when conservatively accounting for a possible underestimation of the DEEP2 stellar masses. + Note also hat these «Mferenees are already preseut at higher redshifts. as we find that the ratio of stellar mass in central galaxies at +~2 in the MPA SAM is comparable to he one predicted by ZCZüT at 2~d.," Note also that these differences are already present at higher redshifts, as we find that the ratio of stellar mass in central galaxies at $z \sim 2$ in the MPA SAM is comparable to the one predicted by ZCZ07 at $z \sim 1$." + Our results are d1 agreement with previous works that studied SAAD predictions. wuch found an excess of stars already in place by :—1 (e.g. Crotonetal.2006:Itzbichler&White 2007)).," Our results are in agreement with previous works that studied SAM predictions, which found an excess of stars already in place by $z \sim 1$ (e.g., \citealt{Croton06, Kitzbichler07}) )." + Those. however. were focused on iiteerated properties ae uot explicitly asa function of halo mass as we show here.," Those, however, were focused on integrated properties and not explicitly as a function of halo mass as we show here." + The SAAL precicons for the total amount of stars acquired through 1uereiue on top of that already in place at 2~ Lare. a fist order. iu good agreement with ZCZÜT results.," The SAM predictions for the total amount of stars acquired through merging on top of that already in place at $z \sim 1$ are, at first order, in good agreement with ZCZ07 results." + However. the individual contributions to the central galaxies stellar mass from mergers of sinaller ceutrals aud satelite mereers are markedly different.," However, the individual contributions to the central galaxies stellar mass from mergers of smaller centrals and satellite mergers are markedly different." + Iu ZCZOT the significaut mereer contribution arises frou. the smaller central progenitors., In ZCZ07 the significant merger contribution arises from the smaller central progenitors. +" Iu coitrast, the SAAIs predict a large coutribution fron neretys of satellites."," In contrast, the SAMs predict a large contribution from mergers of satellites." + It is the partial cancellation of these op»osing differences that leads to a reasonable agreciieut o ‘the total merger contribution., It is the partial cancellation of these opposing differences that leads to a reasonable agreement of the total merger contribution. + As a whole. the SAMs and the ZCZUÜUT results lead to a similar behavjor oft1ο star formation contribution with halo mass.," As a whole, the SAMs and the ZCZ07 results lead to a similar behavior of the star formation contribution with halo mass." + Whie the comparison between he ZCZUT observational results— aud the SANs predictions is informative. there ATC ποιο siniplified assinptious in the ormer.," While the comparison between the ZCZ07 observational results and the SAMs predictions is informative, there are some simplified assumptions in the former." + ZCZüT apply the iethoc as a proof of concept and point out hat there is room for inprovenient with more SOoüsticated applications., ZCZ07 apply the method as a proof of concept and point out that there is room for improvement with more sophisticated applications. + With the SAAIs. we are ale to examune different working assunptious ciuaploved bv ZCZÜüT and euide these efforts.," With the SAMs, we are able to examine different working assumptions employed by ZCZ07 and guide these efforts." + For instance. o luk ealaxics at two epochs. ZCZÜT use hne aver:e relationship beWCCLL the prescut-day halo lnass and the mass of the mad progenitor at ;~1. ucelectiie the individual scatter aποιος halos.," For instance, to link galaxies at two epochs, ZCZ07 use the average relationship between the present-day halo mass and the mass of the main progenitor at $z \sim1$, neglecting the individual scatter among halos." + We tes the validity of this assunition. using the full asscidv information available iji the SAMs. finding that it results in neelieible differences.," We test the validity of this assumption, using the full assembly information available in the SAMs, finding that it results in negligible differences." + Ou the other haud. sole of the assumptions mace bv ZCZOT to cstimate the overall coitributiou frou nüergers and star formation can certainv be improved.," On the other hand, some of the assumptions made by ZCZ07 to estimate the overall contribution from mergers and star formation can certainly be improved." + Iu particulary. the original ZC'ZÜT estimation does not take iuto account the smooth accretion of dark matter particles to the final halo mass.," In particular, the original ZCZ07 estimation does not take into account the smooth accretion of dark matter particles to the final halo mass." + Iu he Milemuita Simulation the smooth accretion since Dol accounts for about ~30% of the final halo nase., In the Millennium Simulation the smooth accretion since $z \sim1$ accounts for about $\sim 30\%$ of the final halo mass. + It is ciffieult. however. to estimate the coutrinition of stellar nass from verv small halos. below the resolution of current ununuerical simulations.," It is difficult, however, to estimate the contribution of stellar mass from very small halos, below the resolution of current numerical simulations." + If smooth accretion is as sjenificaut in the real 1universe. it will certainly be needed o be included iu such approximations.," If smooth accretion is as significant in the real universe, it will certainly be needed to be included in such approximations." + More realistic SFE depeudence on halo mass can also be implemented o improve the estimation inethod., More realistic SFE dependence on halo mass can also be implemented to improve the estimation method. + Conroy Wechsler (2009) preseut related caleulatious or the evolution of stellar masses aud star formation., Conroy Wechsler (2009) present related calculations for the evolution of stellar masses and star formation. + They use abundance matching to monotonically lus ealaxies to halos., They use abundance matching to monotonically link galaxies to halos. + They predict simular. but more dramatic treuds than both the SAMs aud the ZCZUT approaci," They predict similar, but more dramatic trends than both the SAMs and the ZCZ07 approach." + For instance. they sugecst that ealaxics in lower amass halos (~103145FAL.3 exmv them stellar ass pirely by star formation. while essentially all of the ass is alreacky in place by 2~1 du preseut-dav halos o 108TALL.," For instance, they suggest that galaxies in lower mass halos $\sim 10^{11}\Msunh$ ) grow their stellar mass purely by star formation, while essentially all of the mass is already in place by $z \sim 1$ in present-day halos of $10^{13} +\Msunh$." + The results support a picture in which stellar mass erows onlv via star formation. sugecsting that the stellar mass frou simaller progenitors does not merge iuto the central galaxy. but remains as satellites or diffuse light.," Their results support a picture in which stellar mass grows only via star formation, suggesting that the stellar mass from smaller progenitors does not merge into the central galaxy, but remains as satellites or diffuse light." + Additiolal studies are needed o fully clarify their differences with the results prescuted here and in ZCZOT., Additional studies are needed to fully clarify their differences with the results presented here and in ZCZ07. + Recew]v. Neisteimctal.(2011a)— has critically studied tj0 assumptions iade in the abundance matching imetrodo using SAM catalogs and found important differences. jucicatiue that environnieutal processes av be importuit.," Recently, \citet{Neistein10} has critically studied the assumptions made in the abundance matching method using SAM catalogs and found important differences, indicating that environmental processes may be important." + We have demonstrated that p1enoimenoloegical methods such as ZCZÜUT are powoerfii for studyiug ealaxv formation and evolution., We have demonstrated that phenomenological methods such as ZCZ07 are powerful for studying galaxy formation and evolution. + TheΝο provide key constraints for theoretical models. suclas tιο SANIs. as a function of halo uass," They provide key constraints for theoretical models, such as the SAMs, as a function of halo mass." + By highlighting remaining shorteomius of galaxy oruatiou models. they can guide to nuproviug theoretical predictions at hieji redshift and merease our understanding of the complex picture of galaxy formation and evolujon.," By highlighting remaining shortcoming of galaxy formation models, they can guide to improving theoretical predictions at high redshift and increase our understanding of the complex picture of galaxy formation and evolution." + At the same time. while ZCZÜT is useful as a proo: of concept. fiture work. should use more sophisticaed methods applied to better data. and the SAMS can SCrve an importai role in developing and testing suc1 methods.," At the same time, while ZCZ07 is useful as a proof of concept, future work should use more sophisticated methods applied to better data, and the SAMs can serve an important role in developing and testing such methods." + Future work will aso explore the role of cuvirouuent iu the buildup of stellar mass witli ithe host halos., Future work will also explore the role of environment in the buildup of stellar mass within the host halos. +" O1e of the main assumptions im tιο current TOD framework is that the galaxy coutent in lalos «epeuds ouly on the halo nass, and is iudependent of the large-scale euvironneut where the halo is located."," One of the main assumptions in the current HOD framework is that the galaxy content in halos depends only on the halo mass, and is independent of the large-scale environment where the halo is located." + Receut theoretical ποιος have shown: that the clustering properies of dark matter alos depend ou the large-scale enviroment (the so-called lialo asseniblv bias: Cao.Sprireel&White2005:WechslerMo 2007)).," Recent theoretical studies have shown that the clustering properties of dark matter halos depend on the large-scale environment (the so-called halo assembly bias; \citealt{Gao05,Wechsler06,Croton07,Jing07}) )." + This euvironmental effect unight also πηρα ealaxy xoperties and galaxy clustering (Ziuetal.2006:Zuetal. 2008)).," This environmental effect might also impact galaxy properties and galaxy clustering \citealt{Zhu06, Zu08}) )." + Usine tιο SAMs. we may be able to test the effect of large-scae environment ou stellar mass assenmiblv and galaxy evoution (c.f. IIovle.Jimenez&Verde 20113).," Using the SAMs, we may be able to test the effect of large-scale environment on stellar mass assembly and galaxy evolution (c.f., \citealt{Hoyle11}) )." + Moreover. we could use SAM results to incorporate enviromental effects to ple1onienoloeical methods such as ZCZOT. dncreasing the coustraimiugs power of galaxy clustering data on galaxw formation models.," Moreover, we could use SAM results to incorporate environmental effects to phenomenological methods such as ZCZ07, increasing the constraining power of galaxy clustering data on galaxy formation models." + We thauk Cabriclla De Lucia and Cerard Lemsou for providing substantial help with using the Milleuuiuuu Databases., We thank Gabriella De Lucia and Gerard Lemson for providing substantial help with using the Millennium Databases. + This work has been supported by NSF, This work has been supported by NSF +and one needs to understand the relation between the potential from mass aud those from mass tracers.,and one needs to understand the relation between the potential from mass and those from mass tracers. + Iu this section we assume that each and every PSB dark halo coutains one galaxy. aud compare the potential calculated from their umber deusifv or halo lass density with that from CDM particles in the siniulatio-," In this section we assume that each and every PSB dark halo contains one galaxy, and compare the potential calculated from their number density or halo mass density with that from CDM particles in the simulation." + Iu Figure 3 we compare the potential frou galaxy uunuber deusitv (y-axis) with the correct potential from CDAL particles., In Figure 3 we compare the potential from galaxy number density $y$ -axis) with the correct potential from CDM particles. + Dark halos more massive than 2.9«10HAZ.fh ave used for the mmuber density calculation., Dark halos more massive than $2.9\times 10^{11}M_{\odot}/h$ are used for the number density calculation. +" Their mean separation is 10) tMipe. which is equal that of the SDSS galaxies brighter than M,=19.55logh (Choi et al."," Their mean separation is $4.6 h^{-1}$ Mpc, which is equal to that of the SDSS galaxies brighter than $M_r=-19.5+5{\rm log}h$ (Choi et al." + 2007)., 2007). + The correlation coefücieut between the two poteutial fields is fairly high (7=0.988)., The correlation coefficient between the two potential fields is fairly high $r=0.988$ ). +" At Φον,=0 the potential from the galaxy πο density has a dispersion of 0.20 times the RAIS potential value.", At $\Phi_{DM}=0$ the potential from the galaxy number density has a dispersion of 0.20 times the RMS potential value. + Figure [| compares between the magnitudes of the raccless shear tensor Tj;=ΟΦV2. estimated Youn latter density. halo umber density.sop and halo mass density fields.," Figure 4 compares between the magnitudes of the traceless shear tensor $T_{ij} = \partial_i\partial_j \Phi - {1\over 3}\delta^K_{ij}\nabla^2\Phi$, estimated from matter density, halo number density, and halo mass density fields." + Top panel shows that the corresponudeuce vetween the shear fields from the galaxy προ deusity and iatter density is not so good., Top panel shows that the correspondence between the shear fields from the galaxy number density and matter density is not so good. +" The correlation cocfücieut is only 0.858. and the dispersion of the shear uaenitude obtained from galaxy umber deusity is 0.17 ines the RMS shear maguitude at [T]par/(T|54,)?=2 "," The correlation coefficient is only 0.858, and the dispersion of the shear magnitude obtained from galaxy number density is 0.47 times the RMS shear magnitude at $|T|_{DM}/\langle|T|^2_{DM}\rangle^{1/2}=2$ ." +Accuracy du potential and shear can be ereatlh iuproved if the halo mass is used to weigh galaxies aud the halo mass density field. instead of the απο deusitv field. is uxed to caleulate the potential.," Accuracy in potential and shear can be greatly improved if the halo mass is used to weigh galaxies and the halo mass density field, instead of the number density field, is used to calculate the potential." + The secoud aud third panels of Figure 1 demonstrate such improvement when the halo mass threshold is set to 2.9«101AZ./ and 1.0«1OPAL/h. respectively.," The second and third panels of Figure 4 demonstrate such improvement when the halo mass threshold is set to $2.9\times 10^{11}M_{\odot}/h$ and $1.0\times 10^{12}M_{\odot}/h$, respectively." +" The latter objects corresponds to the SDSS galaxies brighter than M,~20.1| Slogh. close to that of the AZ. galaxies (Choi et al."," The latter objects corresponds to the SDSS galaxies brighter than $M_r\approx-20.4+5{\rm log}h$ , close to that of the $M_*$ galaxies (Choi et al." + 2007). in the sense that their mean separations (G.6h. ΛΠΟ ave the same.," 2007), in the sense that their mean separations $6.6 h^{-1}$ Mpc) are the same." + In the middle panel. at Thor(Tlpar’?=2. the dispersion iu is oulv 0.17 times the RAIS shear inagnitude. an |T|improvementpy by alinost a factor 3.," In the middle panel, at $|T|_{DM}/\langle|T|_{DM}\rangle^{1/2}=2$, the dispersion in $|T|_{DH}$ is only 0.17 times the RMS shear magnitude, an improvement by almost a factor 3." + The correlation drops as the halo mass threshold increases. but it still remains quite good for massive dark lalos with AL>1.0«10AL./h.," The correlation drops as the halo mass threshold increases, but it still remains quite good for massive dark halos with $M>1.0\times 10^{12}M_{\odot}/h$." + Figure 5 shows how the correlation changes as a function of the halo mass threshold., Figure 5 shows how the correlation changes as a function of the halo mass threshold. + The solid line is the case when the halo mass deusitv field is used. aud the dashed line is for the halo umber cdeusity.," The solid line is the case when the halo mass density field is used, and the dashed line is for the halo number density." + The correlation drops rapidly as the threshold increases above 107775. TAL., The correlation drops rapidly as the threshold increases above $10^{13}h^{-1}$ $_{\odot}$. + We conclude that the gravitational x»teutial can be estimated quite accurately by using the observed galaxy distribution. but accuracy can be ercatly nuproved if the total mass associated with the dark halo us Galaxy svsteni is used to weiel: galaxies in the shear chsor calculation.," We conclude that the gravitational potential can be estimated quite accurately by using the observed galaxy distribution, but accuracy can be greatly improved if the total mass associated with the dark halo plus galaxy system is used to weigh galaxies in the shear tensor calculation." + When one chooses to use the mass feld instead of he number density field. one needs to adopt a halo nass estimator.," When one chooses to use the mass field instead of the number density field, one needs to adopt a halo mass estimator." + We sugeest to use the red-baud optica uunmnostw together with the morphology-depeuden nass-to-light ratios to estimate the relative mass of ealaxies., We suggest to use the red-band optical luminosity together with the morphology-dependent mass-to-light ratios to estimate the relative mass of galaxies. + An example of using r-band bIuniuositv as the nass estimator for dark halo plus galaxy systems. can o» found iu Park Choi (2009). where the methoc ined out to work quite well iu the seuse that galaxy properties show interesting dependence on local aud elobal cuviromments at plysically meanuinefiul scales.," An example of using $r$ -band luminosity as the mass estimator for dark halo plus galaxy systems, can be found in Park Choi (2009), where the method turned out to work quite well in the sense that galaxy properties show interesting dependence on local and global environments at physically meaningful scales." + Note that we dout need to know the absolute value of halo mass if parseuueters are normalized by their RAIS values as we do here., Note that we don't need to know the absolute value of halo mass if parameters are normalized by their RMS values as we do here. + Using aux halo mass estimator monotonically proportional to the actual halo mass will inprove the accuracy of the resulting potential field., Using any halo mass estimator monotonically proportional to the actual halo mass will improve the accuracy of the resulting potential field. + When galaxy distance is obtained from redshift. the ealaxy distribution becomes biased in such a way that clusters and groups are stretched. fllamcuts appear more pronunent bv broadenius the interior but compressing the exterior. and voids look elongated along the line of sight (Ikaiser 1987).," When galaxy distance is obtained from redshift, the galaxy distribution becomes biased in such a way that clusters and groups are stretched, filaments appear more prominent by broadening the interior but compressing the exterior, and voids look elongated along the line of sight (Kaiser 1987)." + These redshift space distortion effects eenerate error when the eravitational poteutial is estimated directly frou the salaxyw distribution in redshift space., These redshift space distortion effects generate error when the gravitational potential is estimated directly from the galaxy distribution in redshift space. + We will show here that this crror can be imost entirely removed by making a linear correction to 16 redshift space distribution of galaxies., We will show here that this error can be almost entirely removed by making a linear correction to the redshift space distribution of galaxies. + We calculate the peculiar velocities of dark halos from je dark halo παοί deusity or mass density in redshift PAmace using Equation (11)., We calculate the peculiar velocities of dark halos from the dark halo number density or mass density in redshift space using Equation (11). + They are compared with the rue peculiar velocities in Figure 6., They are compared with the true peculiar velocities in Figure 6. + The upper panel shows the «-component of the peculiar velocity at cach αςalaxy location calculated from halo nuuber deusity. aud 1ο bottom one shows that from halo mass density.," The upper panel shows the $x$ -component of the peculiar velocity at each galaxy location calculated from halo number density, and the bottom one shows that from halo mass density." + It can vc seen that the relation is a little tighter in the second Case., It can be seen that the relation is a little tighter in the second case. + The top pancl of Figure 7 shows the correlation vetween the shear inagnitudes estimated from hal πιον density and from matter deusitv., The top panel of Figure 7 shows the correlation between the shear magnitudes estimated from halo number density and from matter density. + The correlation vecolucs stronger when the halo mass density is usec, The correlation becomes stronger when the halo mass density is used + (2~2. ju. ina AsLOO san zzd 2<10. 20.5. pau (<0.1 ju) ," $z\sim2$ $\mu$ $\lambda \gs 400$ $\mu$ $z\gs 1$ $z \ls +10$ $z\gs 0.5$ $\mu$ $\ls 0.1$ $\mu$ " +L&pl The condensation rank associates any topological space with a unique ordinal number.,18pt The condensation rank associates any topological space with a unique ordinal number. + In this we prove that the condensation rank of any infinite dimensional injective Banach space is paperequal to or greater than the first uncountable ordinal number.K, In this paper we prove that the condensation rank of any infinite dimensional injective Banach space is equal to or greater than the first uncountable ordinal number.: +"eywords, CCondensation rank: Injective Banach space: Borel derivative.", Condensation rank; Injective Banach space; Borel derivative. + Primary 46D25: 021010: 54À05 Secondary 28À05, Primary 46B25; 03E10; 54A05 Secondary 28A05. + Topological derivative has been used as a tool for the understaucding of topological spaces ancl classification of Danach spaces. see 4.2.3.17].. for some recent and relevant results see [r.8.9.I8]..," Topological derivative has been used as a tool for the understanding of topological spaces and classification of Banach spaces, see \cite{BessegaPel,baker,bakerTop,PelchSemadani}, for some recent and relevant results see \cite{Galego11AMS,Galego09AMS,GalegoFun,Samuel09}." + Topological derivative is a Borel derivative that it derives the limit point derived set of a set., Topological derivative is a Borel derivative that it derives the limit point derived set of a set. + In (his paper we define a Borel derivative that it derives the condensation derived set of a set and call condensation derivative., In this paper we define a Borel derivative that it derives the condensation derived set of a set and call condensation derivative. + Indeed. one generally expects to have the iterative condensation derived sets of anv given set converged much faster than that of the corresponding iterative limit point derived sets of the given set.," Indeed, one generally expects to have the iterative condensation derived sets of any given set converged much faster than that of the corresponding iterative limit point derived sets of the given set." + One. however. should notice that the limit point rank of the real line and also the infinite dimensional Banach space FN) is both the first uncountable number Q. In other words. the limit point rank can nol distinguish between the real line and /4:0.CN). This is. of course. different from condensation rank: CRGR)=1 while CR(S(N))= This is our fundamental Alsojustification for clefining condensation derivative and ils associated rank.," One, however, should notice that the limit point rank of the real line and also the infinite dimensional Banach space $l_\infty(\NZ)$ is both the first uncountable number $\Omega.$ In other words, the limit point rank can not distinguish between the real line and $l_\infty(\NZ).$ This is, of course, different from condensation rank; $CR(R)=1$ while $CR(l_\infty(\NZ))=\Omega.$ This is our fundamental justification for defining condensation derivative and its associated rank." + This paper indeed raises (he possibility ol using condensation derivative. and its generalized derivatives associated with arbitrary infinite cardinal numbers. as à tool for better understanding and the classification of classical Danach spaces.," This paper indeed also raises the possibility of using condensation derivative, and its generalized derivatives associated with arbitrary infinite cardinal numbers, as a tool for better understanding and the classification of classical Banach spaces." + A second motivation for defining condensation derivative and its rank is [or its application in obtaiming a measure theoretical version of Aleksandrovs Theorem. see |11.12]..," A second motivation for defining condensation derivative and its rank is for its application in obtaining a measure theoretical version of Aleksandrov's Theorem, see \cite{mg,mgph}." + In 1916. P. $. Aleksandrov proved that any uncountable Borel set in a separable complete metric space contains a nonempty perlect subset.," In 1916, P. S. Aleksandrov proved that any uncountable Borel set in a separable complete metric space contains a nonempty perfect subset." + One vear later. M. Ya.," One year later, M. Ya." + Suslin introduced. the class of analvtie sets for which Aleksandrov's Theorem was readily extended (ο this class of sels. see e.g. |1.IH.16]..," Suslin introduced the class of analytic sets for which Aleksandrov's Theorem was readily extended to this class of sets, see e.g. \cite{bbt,Ku68,P}." + Since then. perfect sets in complete separable metric spaces have been studied extensively.," Since then, perfect sets in complete separable metric spaces have been studied extensively." + One. however. might not find many results in general Hausdorff topological spaces because (here are not enough tools to construct Cantor and perfect sets from application of Aleksandrov and Cantor's ideas.," One, however, might not find many results in general Hausdorff topological spaces because there are not enough tools to construct Cantor and perfect sets from application of Aleksandrov and Cantor's ideas." + In order to make such construction possible we have recently defined the condensation derivative. see ΕΠ].," In order to make such construction possible we have recently defined the condensation derivative, see \cite{mg}." + The condensation derivative is a Borel derivative which is measure-preserving on closed. but not. F5. subsets ol anv non-atomie regular Borel measure space.," The condensation derivative is a Borel derivative which is measure-preserving on closed, but not $F_\sigma$, subsets of any non-atomic regular Borel measure space." +" A ""sufficient number of iterations of the condensation derivative function composed on a suitable set. approaches a perfect. set: sufficient number here refers (ο a sufficient large ordinal number.", A “sufficient” number of iterations of the condensation derivative function composed on a suitable set approaches a perfect set; a sufficient number here refers to a sufficient large ordinal number. + The necessary number of ilerations depends on (he initial set aud the topological property of the whole space., The necessary number of iterations depends on the initial set and the topological property of the whole space. + This, This +later (his. In Leonardetal.(2007).. a parametric convergence reconstruction is performed (o reconstruct A1689 cluster (from HIST ACS space-based data). which is one of the biggest and most massive known galaxy clusters.,"later this In \cite{flexion:leonard07}, a parametric convergence reconstruction is performed to reconstruct A1689 cluster (from HST ACS space-based data), which is one of the biggest and most massive known galaxy clusters." +" The galaxy density is important (n,=15 gal/arcmin?) because of the magnification effect.", The galaxy density is important $n_g = 75$ $^2$ ) because of the magnification effect. + The measurements were carried out on stacked images. which resulted in better shape measurement accuracy (07.=0.029 1).," The measurements were carried out on stacked images, which resulted in better shape measurement accuracy $\sigma_e^{\mathcal{F}}=0.029$ $^{-1}$ )." + In this study. the galaxv-galaxy flexion signal has been used to show that foreground galaxies are well-fittecd by a singular isolhermal sphere with a characteristic dispersion σι...," In this study, the galaxy-galaxy flexion signal has been used to show that foreground galaxies are well-fitted by a singular isothermal sphere with a characteristic dispersion $\sigma_v$." + Then. for each confirmed [oreground galaxy. the dispersion σε; is estimated from their flexion effect on background ealaxies.," Then, for each confirmed foreground galaxy, the dispersion $\sigma_{v,i}$ is estimated from their flexion effect on background galaxies." + Therefore. the mass reconstruction is modeled as (he sum of the fits obtained [or each loreeround galaxy.," Therefore, the mass reconstruction is modeled as the sum of the fits obtained for each foreground galaxy." + This method is rather reliable because it depends on the visible distribution of the cluster., This method is rather reliable because it depends on the visible distribution of the cluster. + Then. it offers a wav to include the flexion. measurements in the reconstruction method.," Then, it offers a way to include the flexion measurements in the reconstruction method." + However. the measure of the dispersion σε; lor each foreground ealaxy remains very noisy and (he reconstruction lakes no account for the possible presence of dark haloes in the cluster.," However, the measure of the dispersion $\sigma_{v,i}$ for each foreground galaxy remains very noisy and the reconstruction takes no account for the possible presence of dark haloes in the cluster." + The ain of this paper is to compare the ability of shear and flexion to reconstruct convergence maps., The aim of this paper is to compare the ability of shear and flexion to reconstruct convergence maps. + A comparison between shear and flexion. taking into account the noise contributions. has been carried out.," A comparison between shear and flexion, taking into account the noise contributions, has been carried out." + Using noise simulations. we have shown that flexion becomes more interesting than shear on scales smaller than the scale containing one galaxy (pixel scale).," Using noise simulations, we have shown that flexion becomes more interesting than shear on scales smaller than the scale containing one galaxy (pixel scale)." + Consequently. the flexion measurements should not be used alone to reconstruct a binned convergence map because the [lexion is dominating on scales bevoud the pixel scale.," Consequently, the flexion measurements should not be used alone to reconstruct a binned convergence map because the flexion is dominating on scales beyond the pixel scale." + The literature contains several papers that trv (o use flexion to reconstruct convergence map but. their resulis are not convincing.," The literature contains several papers that try to use flexion to reconstruct convergence map but, their results are not convincing." + Nonetheless. flexion. has already. been detected: and can still be used to measure the statistical properties of substructures in dark matter halos on very small scales 2009).," Nonetheless, flexion has already been detected and can still be used to measure the statistical properties of substructures in dark matter halos on very small scales \citep{flexion:bacon09}." +. Concerning convergence map reconstruction. it is now clear (hat flexion should not be," Concerning convergence map reconstruction, it is now clear that flexion should not be" +"In this paper we have addressed two issues of great interest to current research in Cosmology, in particular in connection with the forthcoming generation of large galaxy redshift surveys.","In this paper we have addressed two issues of great interest to current research in Cosmology, in particular in connection with the forthcoming generation of large galaxy redshift surveys." + The first issue is physical - the callibration of the BAO using the sound horizon in the CMB., The first issue is physical - the callibration of the BAO using the sound horizon in the CMB. + The second issue is statistical - a comparison of parameter fitting using Fisher matrix and Monte Carlo techniques., The second issue is statistical - a comparison of parameter fitting using Fisher matrix and Monte Carlo techniques. + We examined if the degeneracy between geometrical (Alcock-Paczynski) and dynamical (redshift space) distortions in the pattern of the galaxy distribution could be lifted., We examined if the degeneracy between geometrical (Alcock-Paczynski) and dynamical (redshift space) distortions in the pattern of the galaxy distribution could be lifted. +" The key point here is to use the BAO in the pattern of the galaxy distribution as a feature of known physical size, the sound horizon rs~150Mpc."," The key point here is to use the BAO in the pattern of the galaxy distribution as a feature of known physical size, the sound horizon $r_{\rm s} \approx 150 {\rm Mpc}$." +" We have shown, using a toy model, that this indeed can be callibrated using the equivalent feature in the CMB."," We have shown, using a toy model, that this indeed can be callibrated using the equivalent feature in the CMB." +" By adding a prior onto the sound horizon of —1% we have shown, using a Fisher matrix analysis, error ellipses for line of sight and tangential distortion parameters shrink by for a 20(h~*Gpc)? ‘DESpec/BigBOSS’-like survey with shot noise."," By adding a prior onto the sound horizon of $\sim 1 \%$ we have shown, using a Fisher matrix analysis, error ellipses for line of sight and tangential distortion parameters shrink by for a $20(h^{-1} {\rm Gpc})^3$ `DESpec/BigBOSS'-like survey with shot noise." +" This improvement is even more marked in smaller surveys, for 1(h~*Gpc)? the improvement is nearly a factor of 10."," This improvement is even more marked in smaller surveys, for $1(h^{-1} {\rm Gpc})^3$ the improvement is nearly a factor of 10." + When our model for the power spectrum becomes more complicated (using CAMB) and we use the same Gaussian prior of ~1% on the sound horizon the improvement of the ellipse is by a factor of 2.5., When our model for the power spectrum becomes more complicated (using CAMB) and we use the same Gaussian prior of $\sim 1 \%$ on the sound horizon the improvement of the ellipse is by a factor of $2.5$. +" When we start to include real data (from WMAP), which contains more information than just the sound horizon scale, then the improvement of the error ellipse is by a factor of 21."," When we start to include real data (from WMAP), which contains more information than just the sound horizon scale, then the improvement of the error ellipse is by a factor of $21$." + On the statistical side we have carried out a Monte Carlo Nested Sampling analysis on our parameter space., On the statistical side we have carried out a Monte Carlo Nested Sampling analysis on our parameter space. + We find that Monte Carlo and Fisher methods can agree reasonably well for large volume (~20(h~*Gpc)*) surveys with parameter constraints being nearly symetric and likelihood contours agreeing to within a factor of two., We find that Monte Carlo and Fisher methods can agree reasonably well for large volume $\sim 20(h^{-1} {\rm Gpc})^3$ ) surveys with parameter constraints being nearly symetric and likelihood contours agreeing to within a factor of two. +" However, for smaller volume surveys the difference between constraints from the two methods can be greater with the areas of likelihood contours differing by more than a factor of four."," However, for smaller volume surveys the difference between constraints from the two methods can be greater with the areas of likelihood contours differing by more than a factor of four." + The Nested Sampling analysis demonstrates that in general the likelihood distributions in the parameter space our toy model can be non-Gaussian., The Nested Sampling analysis demonstrates that in general the likelihood distributions in the parameter space our toy model can be non-Gaussian. +" This undermines a central assumption in the Fisher matrix analysis, where errors are Gaussian by construction."," This undermines a central assumption in the Fisher matrix analysis, where errors are Gaussian by construction." +" All the likelihood distributions are strongly skewed, with the exception of that around 8."," All the likelihood distributions are strongly skewed, with the exception of that around $\beta$." +" This likelihood falls off more steeply than a Gaussian, having kurtosis."," This likelihood falls off more steeply than a Gaussian, having kurtosis." + In this example better knowledge of r; does not help to improve constraints on f., In this example better knowledge of $r_s$ does not help to improve constraints on $\beta$. + The Fisher constraints on the amplitude of the power spectrum for a 1(h~'Gpc)* survey demonstrate the unphysicality of the Fisher formalism., The Fisher constraints on the amplitude of the power spectrum for a $1 (h^{-1} {\rm Gpc})^3$ survey demonstrate the unphysicality of the Fisher formalism. + Allowed within the 68% confidence limits are negative and zero values for A*., Allowed within the $68 \%$ confidence limits are negative and zero values for $A^*$. + Clearly in this case the Fisher information can only provide us with an upper limit., Clearly in this case the Fisher information can only provide us with an upper limit. + The Monte Carlo analysis, The Monte Carlo analysis +secenarios of BH-galaxy coevolution.,cenarios of BH-galaxy coevolution. +of Martell et al. (,"of Martell et al. ," +2008c).. which found a carbon depletion rate of 20—30 dex + for globulu chisters with metallicities between 2.0 and 2.5., which found a carbon depletion rate of $20-30$ dex $^{-1}$ for globular clusters with metallicities between $-2.0$ and $-2.5$. +" We do not see stroug star-to-star variations in CN or CID baud streneth iu NGC 5166. but we do fiud hat a suni of two Ciaussians represeuts the generalized ustoera of CN band streneth better than a sinele Gaussian curve,"," We do not see strong star-to-star variations in CN or CH band strength in NGC 5466, but we do find that a sum of two Gaussians represents the generalized histogram of CN band strength better than a single Gaussian curve." + This suggests that the underlying $(3839) distribution is likely to consist of two eroups hat are distinct but not widely separated., This suggests that the underlying $S(3839)$ distribution is likely to consist of two groups that are distinct but not widely separated. + There is a very weak anticorrelation between CN aud CIT baud iudices. nmt it is muted even compared to simularly metal-poor clusters.," There is a very weak anticorrelation between CN and CH band indices, but it is muted even compared to similarly metal-poor clusters." + It may be that NGC 5166 experienced. weaker mumordal eurichiment than other Galactic elobular clusters. and even other low-nctallicity elobular clusters.," It may be that NGC 5466 experienced weaker primordial enrichment than other Galactic globular clusters, and even other low-metallicity globular clusters." + It would be interesting to investigate whether theoretical scenarios for primordial eurichiueut of elobulu clusters predict varving eurichiueut efficiencies for particularly: low-metallicity or low-mass clusters., It would be interesting to investigate whether theoretical scenarios for primordial enrichment of globular clusters predict varying enrichment efficiencies for particularly low-metallicity or low-mass clusters. + Although the initial abundances in NGC 5166 may exhibit less of a range than abundances i typical elobular clusters. the stellar evolution-driven abundance changes match well with what is expected from the literature.," Although the initial abundances in NGC 5466 may exhibit less of a range than abundances in typical globular clusters, the stellar evolution-driven abundance changes match well with what is expected from the literature." + Surface carbon depletion. a result of slow circulation of immaterial between the photosphere aud the hydrogeu-buruiug shell in bright red elauts. beeins near the “bump iu the ROB huninosity function aud proceeds at a rate consistent with the observatious of Martell et al.," Surface carbon depletion, a result of slow circulation of material between the photosphere and the hydrogen-burning shell in bright red giants, begins near the “bump” in the RGB luminosity function and proceeds at a rate consistent with the observations of Martell et al." + aud the predictions of Denisseukov VaudeuDerG(2003).. The data set preseuted here is particularly well suited to the study of deep mixing iu the red eiauts in NGC 5166. suce the data extends to quite faint maguitudes.," and the predictions of Denissenkov VandenBerG. The data set presented here is particularly well suited to the study of deep mixing in the red giants in NGC 5466, since the data extends to quite faint magnitudes." + This is made possible by the multiplexing ability of VIRUS-P as an inteeral field spectrograph., This is made possible by the multiplexing ability of VIRUS-P as an integral field spectrograph. + We also show that VIRUS-P can be used to get velocities for stars to better than 17 if good template matching is donec., We also show that VIRUS-P can be used to get velocities for stars to better than 17 if good template matching is done. + The future VIRUS inustrmuent on the ΠουΕαν Telescope will have conrparable spectral resolution., The future VIRUS instrument on the Hobby-Eberly Telescope will have comparable spectral resolution. +" Iowever. mstead of a suele spectrograph it will have more than 100 IFU spectrographs. aud the fiber size ou the sky will shrink from L.1 to 1.5""."," However, instead of a single spectrograph it will have more than 100 IFU spectrographs, and the fiber size on the sky will shrink from $4.1\arcsec$ to $1.5\arcsec$." + This will make VIRUS a very capable iustruinent for observing larger. more crowded elobular clusters.," This will make VIRUS a very capable instrument for observing larger, more crowded globular clusters." + Support for RAV. was provided by the National Science Foundation through AST-0619128. which funds the McDonald Observatory REU program.," Support for R.W. was provided by the National Science Foundation through AST-0649128, which funds the McDonald Observatory REU program." + Support for S.L.M. aud C.ILS. was provided by the NSF eraut. AST-0£06958., Support for S.L.M. and G.H.S. was provided by the NSF grant AST-0406988. + The authors recognize aud acknowledge the very sjenificaut cultural role aud reverence that the sunuuit of Mauna Kea has always lad within the indigenous Hawaiian comunity., The authors recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. + We are most fortunate to have the opportunity to conduct observations from this mountain., We are most fortunate to have the opportunity to conduct observations from this mountain. +"Averaging this result over the binary’s period, expanding up to O(e’) and taking the projection on the secondary’s orbital plane yields: The change in the magnitude of the eccentricity is the projection of e on the x axis.","Averaging this result over the binary's period, expanding up to $\mathcal{O}(e')$ and taking the projection on the secondary's orbital plane yields: The change in the magnitude of the eccentricity is the projection of $\mathbf{\dot{\bar{e}}}$ on the $x$ axis." +" To zero order in eccentricity this change is: This contribution is zero for i=0,7/2."," To zero order in eccentricity this change is: This contribution is zero for $i=0,\pi/2$." +" Up to O(é) the change is: precession of the argument of periapsis retains me the term: Comparing and to we find, similarly to GS, eq.(44)that the eccentricityeq.(46) evolves eq.(64)like: We recover the result of ? that circular orbits remain circular."," Up to $\mathcal{O}(\bar{e})$ the change is: Averaging over the precession of the argument of periapsis retains only the term: Comparing and to we find, similarly to GS, that the eccentricity evolves like: We recover the result of \cite{byorp_1999kw4} that circular orbits remain circular." +" Àn interesting result is that both the semi-major axis evolution and eccentricity evolution are independent of the asteroid's albedo and thermal conductivity, in the two extreme regimes of high and low thermal conductivities."," An interesting result is that both the semi-major axis evolution and eccentricity evolution are independent of the asteroid's albedo and thermal conductivity, in the two extreme regimes of high and low thermal conductivities." + Our calculations were tested on the binary asteroid 1999KW4 which is the best modeled binary., Our calculations were tested on the binary asteroid 1999KW4 which is the best modeled binary. + Figure 5 shows our calculated change in the semi-major axis and in the inclination of the binary., Figure \ref{fig:1999kw4} shows our calculated change in the semi-major axis and in the inclination of the binary. +" Our calculations show that the secondary is currently drifting away from the primary at a rate of about à—7 cm/year, which is in an agreement to within 596 with the result of ?.."," Our calculations show that the secondary is currently drifting away from the primary at a rate of about $\dot{a}=7\; \text{cm}/\text{year}$ , which is in an agreement to within $5\%$ with the result of \cite{byorp_1999kw4}." +" Due to the similarity between YORP and BYORP, the statistics found in are similar for BYORP."," Due to the similarity between YORP and BYORP, the statistics found in are similar for BYORP." + We preformed calculations on the 2500 randomly constructed asteroids., We preformed calculations on the 2500 randomly constructed asteroids. + The stability of di(i—0)/dt with respect to a change in the inclination determines the stability of the rest of the equilibrium points., The stability of $di(i=0)/dt$ with respect to a change in the inclination determines the stability of the rest of the equilibrium points. + The correlation that was found between the sign of 5(e=0) and the stability at e=0 also holds for the sign of à(i=0) and the stability at i=0., The correlation that was found between the sign of $\dot{s}(\epsilon=0)$ and the stability at $\epsilon=0$ also holds for the sign of $\dot{a}(i=0)$ and the stability at $i=0$. +" For randomly shaped asteroids, there is an equal likelihood for 4=0 to be a stable point or an unstable point and 7396 were either Type I or Type II (with equal likelihood)."," For randomly shaped asteroids, there is an equal likelihood for $i=0$ to be a stable point or an unstable point and $73\%$ were either Type I or Type II (with equal likelihood)." + Our calculations also show that 2 out of the 18 real asteroids are not Type I or II., Our calculations also show that 2 out of the 18 real asteroids are not Type I or II. +" Of the remaining 16 asteroids, 6 were Type I and 10 were Type II, which is consistent with our random asteroids."," Of the remaining 16 asteroids, 6 were Type I and 10 were Type II, which is consistent with our random asteroids." +" Unlike YORP, the timescale for reaching the stable point can be longer than the lifetime of the system, so not every binary will reach it."," Unlike YORP, the timescale for reaching the stable point can be longer than the lifetime of the system, so not every binary will reach it." +" In order for the system to reach its stable point, the difference between the starting inclinationand the inclination at the stable point needs to be Aizs6-1 "," In order for the system to reach its stable point, the difference between the starting inclinationand the inclination at the stable point needs to be $\Delta i\approx \beta^{-1}$ " +The existence of active galactic nuclei has long been taken as evidence for the existence of massive black holes. in 1e centres of some galaxies (Lynden-Bell 1969).,The existence of active galactic nuclei has long been taken as evidence for the existence of massive black holes in the centres of some galaxies (Lynden-Bell 1969). + However. -- tis only relatively recently. that high spatial resolution gauclies of the kinematies of galactic nuclei have revealed that essentially all galaxies harbour large central masses sce Ho (1999) for a review of the evidence].," However, it is only relatively recently that high spatial resolution studies of the kinematics of galactic nuclei have revealed that essentially all galaxies harbour large central masses [see Ho (1999) for a review of the evidence]." + The existence of these observations also means that there are now enough data to study the demographics of massive black holes. in order to seek clues to their origins.," The existence of these observations also means that there are now enough data to study the demographics of massive black holes, in order to seek clues to their origins." + The first significant discovery in this regard is that there is à correlation between the mass of the black hole. AMpg. and the mass of the host. galaxys spheroidal component. ALon.," The first significant discovery in this regard is that there is a correlation between the mass of the black hole, $M_{\rm BH}$, and the mass of the host galaxy's spheroidal component, $M_{\rm sph}$." + Although there is a variety of possible biasses in measuring this correlation. it seems broadly to be the case that there is a linear relationship. such that AlbyO.005AZun CMagorrian et 11998).," Although there is a variety of possible biasses in measuring this correlation, it seems broadly to be the case that there is a linear relationship, such that $M_{\rm BH} +\sim 0.005 M_{\rm sph}$ (Magorrian et 1998)." + Although this correlation is reasonably strong. there is still considerable scatter in the relation. such that jore Ls more than a factor of ten variation in the inferred. value of Alpy for galaxies of given spheroicl mass (Magorrian et 11998).," Although this correlation is reasonably strong, there is still considerable scatter in the relation, such that there is more than a factor of ten variation in the inferred value of $M_{\rm BH}$ for galaxies of given spheroid mass (Magorrian et 1998)." + Some of this scatter can probably be attributed to the uncertainties in calculating black hole masses [rom relatively poor kinematic data ancl simplified dynamical models (van der Marel L997)., Some of this scatter can probably be attributed to the uncertainties in calculating black hole masses from relatively poor kinematic data and simplified dynamical models (van der Marel 1997). + Llowever. there are also astrophysical reasons why one might expect significant dispersion in this relation.," However, there are also astrophysical reasons why one might expect significant dispersion in this relation." + bor example. consider the simplest possible scenario in which galaxies form and evolve in near isolation.," For example, consider the simplest possible scenario in which galaxies form and evolve in near isolation." + Η the central black holes in these galaxies accrete mass fairlv steadily from their hosts. then the mass of a black hole simply reflects the age of its host.," If the central black holes in these galaxies accrete mass fairly steadily from their hosts, then the mass of a black hole simply reflects the age of its host." + Under the eurrentIv-Favoured. hierarchical paradigm for ealaxy formation. in which larger galaxies are formed from he merging of smaller galaxies (White Rees 1978). the simple linear correlation between galaxy mass and black hole miss is reaclily explained.," Under the currently-favoured hierarchical paradigm for galaxy formation, in which larger galaxies are formed from the merging of smaller galaxies (White Rees 1978), the simple linear correlation between galaxy mass and black hole mass is readily explained." + Each time two galaxies merge to orm a larger svstem. their black holes rapidly spiral to the centre of the new galaxy. due to dynamical friction.," Each time two galaxies merge to form a larger system, their black holes rapidly spiral to the centre of the new galaxy due to dynamical friction." + The lack holes then merge. creating a proportionatelv-Iarger slack hole.," The black holes then merge, creating a proportionately-larger black hole." + Llowever. a galaxy formed. by this process of repeated mergers cannot be characterized by a single age. so he above explanation for the scatter in black hole masses must be modificd somewhat.," However, a galaxy formed by this process of repeated mergers cannot be characterized by a single age, so the above explanation for the scatter in black hole masses must be modified somewhat." + One measure of such a galaxys age is the time since it last underwent a major merger. and Waullmann LHlaehnelt. (2000) have shown that. this timescale is a key factor in explaining the scatter in black hole masses.," One measure of such a galaxy's age is the time since it last underwent a major merger, and Kauffmann Haehnelt (2000) have shown that this timescale is a key factor in explaining the scatter in black hole masses." + Lf the last merger happened long ago. then it will have occurred. between relatively unevolved. galaxies in which there would have been a [large amount of cold eas.," If the last merger happened long ago, then it will have occurred between relatively unevolved galaxies in which there would have been a large amount of cold gas." + Lf the black hole aceretes some fixed fraction of this gas. then," If the black hole accretes some fixed fraction of this gas, then" +case can be approximated Rieger.Bosch-Ramon.(2007))) here D is the magnetic field and p the mass density of the jet.,case can be approximated \cite{rieger07}) ) where the Alfven $V_A$ ) is given by here $B$ is the magnetic field and $\rho$ the mass density of the jet. ++ Hence the turbulent acceleration. timescale(£iu)Gfd will. be For shear acceleration to be dominant over turbulent acceleration. f;taiibdFoo., Hence the turbulent acceleration $t_{acc}^{(t)}$ ) will be For shear acceleration to be dominant over turbulent acceleration $t_{acc}^{(s)}1$ for magnetized particles) and $\gamma(\gg 1)$ is the Lorentz factor of the electron scattered." + Since the magnetic field at the jet boundary of MINNS0L is parallel to the jet axis (or toroidal)CXaron(1999):Pushkareyetal.(2005):Gabuzda (1999))). we consider 72Ayfe.," Since the magnetic field at the jet boundary of MKN501 is parallel to the jet axis (or \cite{aaron99,pushkarev05,gabuzda99}) ), we consider $\tau\simeq\lambda_\parallel/c$." +" Also if we consider where ALD is the cillerence between the bulk Lorentz factor at the jet spine and the jet boundary ancl Ar is the thickness of the shear [aver. then the condition for shear acceleration to be dominant over turbulent acceleration will be If we consider the mass densitv of the jet is dominated. by cold protons and if the number of protons are equal to the number of non-thermal electrons. then the jet mass density can be written in terms of equipartition magnetic (121) as and (10)) will be where à is the observed. photon spectral index. my is the proton mass and 5,54 is the Lorentz factor of electron responsible for the minimum observed. photon [requenevy Minin "," Also if we consider where $\Delta \Gamma$ is the difference between the bulk Lorentz factor at the jet spine and the jet boundary and $\Delta r$ is the thickness of the shear layer, then the condition for shear acceleration to be dominant over turbulent acceleration will be If we consider the mass density of the jet is dominated by cold protons and if the number of protons are equal to the number of non-thermal electrons, then the jet mass density can be written in terms of equipartition magnetic $B_{eq}$ ) as and \ref{eq:shthick1}) ) will be where $\alpha$ is the observed photon spectral index, $m_p$ is the proton mass and $\gamma_{min}$ is the Lorentz factor of electron responsible for the minimum observed photon frequency $\nu_{min}$ ." +"Lhe equipartition magnetic field can be expressed in terms of observed. quantities as where P(5,;,) is the flux at the minimum. observed frequeney Min. d is the luminosity distance. V is the volume of the emission region. and er is Thomson cross section."," The equipartition magnetic field can be expressed in terms of observed quantities as where $F(\nu_{min})$ is the flux at the minimum observed frequency $\nu_{min}$, $d_L$ is the luminosity distance, $V$ is the volume of the emission region and $\sigma_T$ is Thomson cross section." +. Hence. for] .P(r)-2.<> Landa2-0.7. shear acceleration. will dominate the particle spectrum at the jet boundary of AUNN501 if the thickness of the shear laver Where 2 is the radius of the spherical region considered. (," Hence, for $\Gamma(r)^2\gg1$ and $\alpha\simeq 0.7$, shear acceleration will dominate the particle spectrum at the jet boundary of MKN501 if the thickness of the shear layer Where $R$ is the radius of the spherical region considered. (" +We assume 1037//z as minimum observed. frequency and the flux at 10Z/z.: is obtained. [rom the Hux at. 1.6644: considering the same spectral index.,We assume $10 MHz$ as minimum observed frequency and the flux at $10 MHz$ is obtained from the flux at $1.6 GHz$ considering the same spectral index. + The flux at. 1.6674: and /? in (14)) are obtained from a region around LRA 10mes and declination LOmes from Fig. of Cirolettietal.(2004)))., The flux at $1.6 GHz$ and $R$ in \ref{eq:shthick3}) ) are obtained from a region around R.A $10\;mas$ and declination $-10\;mas$ from $7$ of \cite{giroletti04}) ). +" The corresponding equipartition magnetic field D, for P=5is L2«loτά.", The corresponding equipartition magnetic field $B_{eq}$ for $\Gamma=5$ is $1.2\times 10^{-3} G$. + The electrons accelerated by shear acceleration cool via svnchrotron radiation., The electrons accelerated by shear acceleration cool via synchrotron radiation. + Phe cooling time for svnchrotron loss is given by Using (5)) and (15)). we find and since £44loop shear acceleration. dominates over svnchrotron cooling.," The cooling time for synchrotron loss is given by Using \ref{eq:shacc}) ) and \ref{eq:syncool}) ), we find and since $t_{acc}^{(s)}\ll t_{cool}$, shear acceleration dominates over synchrotron cooling." + It can be noted. that (16)) is independent of the electron energy and hence the maximum energy of the electron will be decided by the loss processes other than svachrotron loss (whieh are not considered in this simplistic treatment)., It can be noted that \ref{eq:acccool}) ) is independent of the electron energy and hence the maximum energy of the electron will be decided by the loss processes other than synchrotron loss (which are not considered in this simplistic treatment). + If we maintain the general form of mean scattering time 7=z. then for shear acceleration to dominate over turbulent acceleration the thickness of the shear laver (Ar) should be Lt can be noted that (10)) is equal to (17)) if we set in the latter£=1 and z=gry/c.," If we maintain the general form of mean scattering time $\tau=\tau_0p^\xi$, then for shear acceleration to dominate over turbulent acceleration the thickness of the shear layer $\Delta r$ ) should be It can be noted that \ref{eq:shthick1}) ) is equal to \ref{eq:shthickgen}) ) if we set in the latter $\xi=1$ and $\tau_0 p^\xi = \eta r_g/c$." +" ""articles accelerated at the shear laver of the jet boundary. diffuse into the jet. medium before getting cooled oll via svnchrotron radiation."," Particles accelerated at the shear layer of the jet boundary, diffuse into the jet medium before getting cooled off via synchrotron radiation." + As the magnetic field at the jet »»undary is parallel to the jetaxis (or Aaron (1999))). the radial diffusion of the electron into thejet medium is determined by cross Ποιά cilfusion.," As the magnetic field at the jet boundary is parallel to the jetaxis (or \cite{aaron99,pushkarev05,gabuzda99}) ), the radial diffusion of the electron into the jet medium is determined by cross field diffusion." + The cross field. dillusion coellicient can »' approximated as (Axford(1965):Jokipii(1987):Achter- (1994))) Where ον1) is the scaling factor determining the field," The cross field diffusion coefficient can be approximated as \cite{axford65, jokipii87, abraham94}) ) Where $\eta(>1)$ is the scaling factor determining the field" +a source of macerraiuties for some clement measurements (o.@.. Vladilo 19Os: Touetal.20011). while the Ilinüted redshift coverage with the known DLAs may not be adequate for detecting the preseuce of evolution.,"a source of uncertainties for some element measurements (e.g., Vladilo 1998; \cite{hou01}) ), while the limited redshift coverage with the known DLAs may not be adequate for detecting the presence of evolution." + As first pointed out by Boissé e al. (, As first pointed out by Boissé et al. ( +1998). DLAs with lüeh Nut and lieh metallicity mieht be mussine from the data asa consequence of dust extinction which would imply a biased deernnation of evolution.,"1998), DLAs with high ${ N_{\rm HI}}$ and high metallicity might be missing from the data as a consequence of dust extinction which would imply a biased determination of evolution." + For the a elements. dust-corrected daa show mule chhancement or near soli values for most observevb clements in contrast to the metallicity patern of moetal-poor Galactic stars (c.@.. Vladilo19951: Peπαetal.2 00)}).," For the $\alpha-$ elements, dust-corrected data show mild enhancement or near solar values for most observed elements in contrast to the metallicity pattern of metal-poor Galactic stars (e.g., \cite{vla98}; \cite{pet00}) )." + This nüeht imply a different SF history than ha of the Milkv. Wav. although Prochaska et al. (," This might imply a different SF history than that of the Milky Way, although Prochaska et al. (" +2000) ound au agreement beween the propertics of the Calactic tick disk aud the DLAs.,2000) found an agreement between the properties of the Galactic thick disk and the DLAs. +" Iu Πο», where galaxies are formed by agerceationOO of siualler subsructures. Mcrecrs andl coutiuuous easOUM intall play au important role. contributing to regulate the star formation (SE: Tissera 20003) aud chemical histories (c.m. Coractid. 2000)) of the ealactic objects."," In HCSs, where galaxies are formed by aggregation of smaller substructures, mergers and continuous gas infall play an important role, contributing to regulate the star formation (SF; \cite{tis00}) ) and chemical histories (e.g., \cite{cor00}) ) of the galactic objects." + As sugeested by IEvehuelt et al. (, As suggested by Haehnelt et al. ( +1998). froii a kinemiatical study of nunericeal simulations. DLAs could be the xoesenitor substructures of tocav Galaxies tha merece to Ότι Galactic objects ina uerarchical clustering scenario.,"1998) from a kinematical study of numerical simulations, DLAs could be the progenitor substructures of today galaxies that merge to form galactic objects in a hierarchical clustering scenario." + The variety of morphological types together with the act that they tend to be chemically voung sccm to support this hy]othiesis., The variety of morphological types together with the fact that they tend to be chemically young seem to support this hypothesis. + With the aim at uuderstaudiug he possible link between he structure in a IICS aud the iine of DLAs. in this letter. we assess the chemical xoperties of torav-galaxy building blocks as a function of the redshift.," With the aim at understanding the possible link between the structure in a HCS and the nature of DLAs, in this letter, we assess the chemical properties of today-galaxy building blocks as a function of the redshift." + For this purpose. we focus our study on he analysis of tje unmweiehted mean metallicities of the jeutral hydrogen as a function of : since they are more sensitive to the xoperties of the individual objecs.," For this purpose, we focus our study on the analysis of the unweighted mean metallicities of the neutral hydrogen as a function of $z$ since they are more sensitive to the properties of the individual objects." + We also couuneut on the massaweighted mean metallicities hat are related o the chemical conteut of the Universe., We also comment on the mass-weighted mean metallicities that are related to the chemical content of the Universe. + We use livdrodyiαλασα cosmological models that treat the ο evohtion of both: barvous aud dark matter in a selt-consisteut way. providing a welbdeseribed history of formation. aud inchide star formation and chemical evolution.," We use hydrodynamical cosmological models that treat the non-linear evolution of both baryons and dark matter in a self-consistent way, providing a well-described history of formation, and include star formation and chemical evolution." + Resuts of the simulations are compared with available observational data on chemical abundauces of DLAs., Results of the simulations are compared with available observational data on chemical abundances of DLAs. + We discss nuaplicatious for galaxy formation., We discuss implications for galaxy formation. + Qur Lydrocyiunical chemical simulations follow the joint evolution. of the dark matter and barvous within a cosmological context (Tisseraetal. 1997)) iucludius SF aud chemical evolution., Our hydrodynamical chemical simulations follow the joint evolution of the dark matter and baryons within a cosmological context \cite{tis97}) ) including SF and chemical evolution. + Stars are formed from cold and dense gas in a convergent flow according to the Sclauidt law., Stars are formed from cold and dense gas in a convergent flow according to the Schmidt law. + Cascous particles are eradually transformed into stars in different SF episodes., Gaseous particles are gradually transformed into stars in different SF episodes. + The contribution of type I (SNT) and type ID (SNII) superuovas frou each of these SF episodes to the chemical curichuenut of the eas compement are taken iuto account according to stellar evolution models aud metallicity eurichiueut vields., The contribution of type I (SNI) and type II (SNII) supernovas from each of these SF episodes to the chemical enrichment of the gas component are taken into account according to stellar evolution models and metallicity enrichment yields. + Chemical elements generated in a given particle are distributed amoung eas particles within its neielhibornug area. weighting each contribution with a kernel function that depends on the distance (i.c.. by using the smooth particle hydrodvuaunics technique).," Chemical elements generated in a given particle are distributed among gas particles within its neighboring area, weighting each contribution with a kernel function that depends on the distance (i.e., by using the smooth particle hydrodynamics technique)." + We adopt thi| vields given by Woosley Weaver (1995) for SNII aud those eiven by Thieleniann. Nomoto Hashimoto (1993) for SNL," We adopt the yields given by Woosley Weaver (1995) for SNII and those given by Thielemann, Nomoto Hashimoto (1993) for SNI." + A time delav of 105 vrs Is assunied for duarv star systems to explode as SNI., A time delay of $10^8$ yrs is assumed for binary star systems to explode as SNI. +" We adop a fixed Salpeter huütial Mass. Euuctiou. with lower auk uppY onaass cut-offs of 0.1AL: and 120M. respectively,"," We adopt a fixed Salpeter Initial Mass Function with lower and upper mass cut-offs of $0.1 \ {\rm M_{\sun}}$ and $120\ {\rm M_{\sun}}$, respectively." + Iu lis work the effects of cuerey injection into the interstellar iiediunmi due to supernova explosions have not becn included., In this work the effects of energy injection into the interstellar medium due to supernova explosions have not been included. + For a detailed discussion of the chemical nodel see Mosconi et al. (, For a detailed discussion of the chemical model see Mosconi et al. ( +2000).,2000). + We analyze cosmological simulations of a typical LO Alpe cube volume το]xeseuted by 61 equal mass particles (Ον=0.1)., We analyze cosmological simulations of a typical 10 Mpc cube volume represented by $64^3$ equal mass particles $\Omega_b=0.1$ ). + Initial couditious are consisteut with a Staucdarcd Cold Dirk Matter Universe (JF=50lousIMpe ) with cluster amudanee normalization. σος=0.67.," Initial conditions are consistent with a Standard Cold Dark Matter Universe $H=50\ {\rm km \ s^{-1}Mpc^{-1}}$ ) with cluster abundance normalization, $\sigma_8=0.67$." + We have run a se of three sinulatious with different realizations of the power sjoectrun. estimating averaged results over them.," We have run a set of three simulations with different realizations of the power spectrum, estimating averaged results over them." + The SN piruneters adopted iu these simulations correspond to those eiviug the best agreocmen with observatious of ealaxies at 2=0 (Mosconictal.20003) and the [D/Fo] abuudauce pattern in the Milky Way (Coraetal. 20003)., The SN parameters adopted in these simulations correspond to those giving the best agreement with observations of galaxies at $z=0$ \cite{mos00}) ) and the [O/Fe] abundance pattern in the Milky Way \cite{cor00}) ). + We identified galactic objects at them virial radius at different stages of evolution of the simulated voluue., We identified galactic objects at their virial radius at different stages of evolution of the simulated volume. + Galactic objects are formed by a ark matter halo aud à barvonic component in the form of σας and stars., Galactic objects are formed by a dark matter halo and a baryonic component in the form of gas and stars. + To diminish iumuuerical resolution problems. we analyze ealactic objects with more than 2XO barvonic articles within their virial radius aud in the range 0.25<2<22.35.," To diminish numerical resolution problems, we analyze galactic objects with more than 200 baryonic particles within their virial radius and in the range $0.25 < z < 2.35$." + Consequently. the analyzed objects have virial velocities within z100250kansf.," Consequently, the analyzed objects have virial velocities within $\approx 100-250 \ {\rm km \ s^{-1}}$." + We study a total wmuber of 380 galactic ob;jects satisfvine the a)ove coucitions which are all considered as possible absorbers., We study a total number of 380 galactic objects satisfying the above conditions which are all considered as possible absorbers. + It is likely twt DLAs observations map the chemical properties of the eascous disks not expected to be good tracers o| the metal content at the centra regions (e.g. Jimenezetal—1999: Somervilleοἳal. 2001:: Savaglio 2000)).," It is likely that DLAs observations map the chemical properties of the gaseous disks not expected to be good tracers of the metal content at the central regions (e.g., \cite{jim99}; \cite{som01}; \cite{sav00}) )." + ence. in order to carry out a suitable conrparisou beween the simulated galactic objects and DLAs observations. we use a Monte Carlo technique to simulate liue-oSsights (LOS) and estimate the chemical properties of the neutral lyvdrogen component with Nuyp>2s1o?atoms/cm2 (Wolfeetal. 1986)) along the LOS.," Hence, in order to carry out a suitable comparison between the simulated galactic objects and DLAs observations, we use a Monte Carlo technique to simulate line-of-sights (LOS) and estimate the chemical properties of the neutral hydrogen component with ${ N_{\rm HI}> 2 \times 10^{20} {\rm atoms/cm^{-2}}}$ \cite{wol86}) ) along the LOS." + We assu16 that he hydrogenOo mass i a oOgas particle rendus neutral if uo SF activity has ever occured within that particle., We assume that the hydrogen mass in a gas particle remains neutral if no SF activity has ever occured within that particle. + As a combied result of ανασα evolution. mergers aud interactions. he SF rate history of each galactic object can be described a sa coutribution of au ambicut SF rate and a series of staiM ποιο Tissera 2000)).," As a combined result of dynamical evolution, mergers and interactions, the SF rate history of each galactic object can be described as a contribution of an ambient SF rate and a series of starbursts (e.g., \cite{tis00}) )." + The timings between starbursts are not ad hoc. but eiveu naturally by the evolution ofthe ob:jects iu the IICS adopted.," The timings between starbursts are not ad hoc, but given naturally by the evolution of the objects in the HCS adopted." + Thus. we have a cousisteut description of the chemical eurichlieut of the stellar populatious aud gaseous component due to the fact that the different ejecta times of SNI and SNIT cau," Thus, we have a consistent description of the chemical enrichment of the stellar populations and gaseous component due to the fact that the different ejecta times of SNI and SNII can" + , +the P-values are shown in Table 2..,the $P$ -values are shown in Table \ref{table: KS tests}. + Unsurprisingly. there is very strong evidence that the IG. and SG/LINISIU subsets are drawn from. dilferent. parent. populations in panel (i) of Figure 1: apart from a handful. of sources. RCs are ound on the upper sequence. and SGs/LINERs on the lower sequence.," Unsurprisingly, there is very strong evidence that the RG and SG/LINER subsets are drawn from different parent populations in panel (i) of Figure \ref{fig:plot1}; apart from a handful of sources, RGs are found on the upper sequence, and SGs/LINERs on the lower sequence." + Though the bimodality is not as pronounced. in he other two cases. the /-values are still highlv signilicant.," Though the bimodality is not as pronounced in the other two cases, the $P$ -values are still highly significant." + The very small 2-values are mainly clue to the dillerences in (A): there is no significant evidence from one-dimensional WKS tests that the loe(A) distributions of the RGs and SCGs/LINERSs are drawn from clillerent arent populations (but note that an intrinsic dependence on A could exist given he upper A limits for some of the FR. 1 Cis)., The very small $P$ -values are mainly due to the differences in $R$ ): there is no significant evidence from one-dimensional KS tests that the $\lambda$ ) distributions of the RGs and SGs/LINERs are drawn from different parent populations (but note that an intrinsic dependence on $\lambda$ could exist given the upper $\lambda$ limits for some of the FR I RGs). + One can also model the dependence of loe(?) on log(A) w fitting a linear function (in log-log space) to each of the iG and SG/ALINELB subsets in all three xinels of Figure 1 or 6«log(A)«|2., One can also model the dependence of $R$ ) on $\lambda$ ) by fitting a linear function (in log-log space) to each of the RG and SG/LINER subsets in all three panels of Figure \ref{fig:plot1} for $-6 < \log({\lambda}) < -2$. + Standard linear reeression was found ο give similar fit cocllicients (within the uncertainties) to hose obtained from the tas kin the package. which takes into account claa with limits using he method. of Schmitt(1985).," Standard linear regression was found to give similar fit coefficients (within the uncertainties) to those obtained from the task in the package, which takes into account data with limits using the method of \citet[][]{schmitt85}." +.. The slopes of the various ines range [roni ~0.6 to OA. broaclv consistent. with equation 6...," The slopes of the various lines range from $\sim$$-0.6$ to $-0.4$, broadly consistent with equation \ref{eqn_merloni4}." + The average vertical ollsets between the lines are about 2.6 dex (panel i). 2.1 dex (panel ii) ancl 1.5 dex panel iii).," The average vertical offsets between the lines are about 2.6 dex (panel i), 2.1 dex (panel ii) and 1.5 dex (panel iii)." + Lastlv. we also fitted. Linear functions (again in log-og space) through the combined. distribution of Πας and SCs/LINERs with G«log(À)2 in cach panel of Figure 1..," Lastly, we also fitted linear functions (again in log-log space) through the combined distribution of RGs and SGs/LINERs with $-6 < \log(\lambda) < -2$ in each panel of Figure \ref{fig:plot1}." + The fits from standard. linear regression are loe(R)=0.71los(A)|L.l (panel i). los(/)0.69log(A)|0.05 (panel ii). and log(/7)=—0.61log(A)2.05 (panel ii).," The fits from standard linear regression are $\log(R) = -0.71 \log(\lambda) + 1.1$ (panel i), $\log(R) = -0.69 \log(\lambda) + 0.05$ (panel ii), and $\log(R)= -0.61 \log(\lambda) - 2.95$ (panel iii)." + Again. similar coellicients. are. found if the cata with limits are treated. more rigorously.," Again, similar coefficients are found if the data with limits are treated more rigorously." + Stacked! histograms of the radio loudness residuals (ic. the vertical ollscts [rom the line of best fit) are shown in Figure 2.., Stacked histograms of the radio loudness residuals (i.e. the vertical offsets from the line of best fit) are shown in Figure \ref{fig:plot2}. + The residuals for the RCs and SCGs/LINERs overlap only slightly in panel (i)., The residuals for the RGs and SGs/LINERs overlap only slightly in panel (i). + For the unbinned data. the dillerence between the median residual of the lc subset. and the meclian residual of the SCLINER. subset is 2.5r dex: the range covered by both subsets together is 56 dex.," For the unbinned data, the difference between the median residual of the RG subset and the median residual of the SG/LINER subset is 2.5 dex; the range covered by both subsets together is 5.6 dex." + For the core radio powers (panel ii). the dillerence. between the meclians: has decreased to 2.0 dex and the range to 4.5 dex.," For the core radio powers (panel ii), the difference between the medians has decreased to 2.0 dex and the range to 4.5 dex." + The implementation of the mass correction (panel iii) further reduces the dillerence between the medians (to 1.7 dex). as well as the range (to 4.1 dex).," The implementation of the mass correction (panel iii) further reduces the difference between the medians (to 1.7 dex), as well as the range (to 4.1 dex)." + In the third case. the standard deviation of the unbinned distribution is 1.0 dex.," In the third case, the standard deviation of the unbinned distribution is 1.0 dex." + Despite the changes in the histogram properties. there is no evidence from one-dimensional WS tests (on the unbinned data) that," Despite the changes in the histogram properties, there is no evidence from one-dimensional KS tests (on the unbinned data) that" +holds for the classical instability. strip).,holds for the classical instability strip). + 5) The blue edge for any given mode the Fundamental) is not shifted. significantly by increasing Z. thile | roc ecloo 1 ∖∖↓⊔↓⊲∣↓⊔↓⊔⇂⊔↳⊔↓⊳∖⊳∖↓⊔⊔⊔⇂↓⊔⇂∖∖↸⋯⇂⊳ΠΕΡ.," 5) The blue edge for any given mode the fundamental) is not shifted significantly by increasing Z, while the red edge is shifted red-ward." + ≼∩↾∐↥⋖⊾↓∢⋟∖∖⋎−↓⇂⇂↓↕↓↕↓↕⋖≱≻↕∙∖⇁∢⊾⊔∠⇂∪⇂∎↿↓∐⋅⊲↓⊔⊳∖↿⋜↧∣⋡∐⊀↓↿∙∖⇁∐���⋏∙≟⋖⋅↓⋅⊲↓⊳∖ populated by the highest number of excited modes., 6) The low-luminosity end of the instability finger is populated by the highest number of excited modes. + 7) Unstable modes. with L/ÀAJ=3.5 are. primarily strange mocles., 7) Unstable modes with $L/M\geq3.5$ are primarily strange modes. + ae . . ↓⊲↓⋏∙≟⊔↓⋅⋖⋅⇀↗≻↓≻↓⋅⋖⋅⊳∖⋖⊾⊔⇂⊳∖⋜⋯⋜↧∐∢⊾↓⋅⊔⋜⊔↓∖⇁⋖⋅∖⇁↓⋖⊾∖∖⋎∪⇂∣⇂↥⋖⊾⊳∖⋜⋯↓⋖⊾↓⋅∢⊾⊳∖⊔↓↿⊳∖. ⋅ ∣⋡⇂⇂⇂⊳∣⋡⋖⋅≼⇍⋜↧⇂⇂≻⋖⋅↕↿⊲↓⊔≼⇍↓⋯⇂⋖⋅⊳∖⋜↧∐↿↓⊔⋅∢⊾⇀∖≼⋰↓∩⋅∠⇂⊔↓⋯⇂⋖⋅⊳∖⊔↓≻↿∪∕⋅⋅∶↓∪⋡⋠⊔ rellects the extent and mocde-density of the instability region more ellectivelv.," Figure \ref{Z-modes} presents an alternative view of the same results but, because it includes all the excited modes up to $k=10$, it reflects the extent and mode-density of the instability region more effectively." + Many. of these features were already well known from previous studies, Many of these features were already well known from previous studies +Observational and theoretical studies of galaxy rotation curves (Rubin&Ford 1970).. /wolocitv dispersions of elliptical galaxies (Faber&Jackson 1976).. barvou fraction in clusters (Cloweetal.2006:Masseyetal. 2007).. gravitational lensing. structure formation. CAIB power spectrun etc.,"Observational and theoretical studies of galaxy rotation curves \citep{rubin70}, velocity dispersions of elliptical galaxies \citep{faber76}, baryon fraction in clusters \citep{clowe06,mass07}, gravitational lensing, structure formation, CMB power spectrum etc." + indicate that a sienificant fraction of the mass of the Universe has no clectromaguctic interaction (Bertonectal.2005)., indicate that a significant fraction of the mass of the Universe has no electromagnetic interaction \citep{bertone05}. +.. At ealactic scale. the main evidence for the existence of such eravitating matter with verv high mass to lieht ratio comes from observations of ealaxy rotation curves.," At galactic scale, the main evidence for the existence of such gravitating matter with very high mass to light ratio comes from observations of galaxy rotation curves." + The gravitational potential derived. from the observed rotation curve can uot be explained ouly by the visible niass with auv reasonable mass to light ratio (RubinSpanoetal. 2008).," The gravitational potential derived from the observed rotation curve can not be explained only by the visible mass with any reasonable mass to light ratio \citep{rubin70,rubin80,sofue96,sofue01,spano08}." +.. Though there are modified theories of the eravitation aud other sugeestions (Mileroii1983:Sanders1997:Brownstein&Moffat2006) to explain this anomaly. the dark matter concept is widely accepted to be a simpler explanation of these observations.," Though there are modified theories of the gravitation and other suggestions \citep{milgrom83,beken84,sand86,fahr90,sanders97,brown06} to explain this anomaly, the dark matter concept is widely accepted to be a simpler explanation of these observations." + Though observations of galaxy rotation curves established. the existence of the dark matter at galactic scale. there is no ecucral agreemieut on the nature aud various properties (like mass distribution) of this major constituent of the Universe (Navarroetal.1996:deBlols2005).," Though observations of galaxy rotation curves established the existence of the dark matter at galactic scale, there is no general agreement on the nature and various properties (like mass distribution) of this major constituent of the Universe \citep{nfw96,blok05}." +. Poteutially. ealaxv rotation curves can also shed light ou some aspects of the dark matter properties aud thus help us in deriving a better understanding of the nature of the dark matter.," Potentially, galaxy rotation curves can also shed light on some aspects of the dark matter properties and thus help us in deriving a better understanding of the nature of the dark matter." +" One such key aspect is the density profile or the mass distribution of the dark matter at galactic scale,", One such key aspect is the density profile or the mass distribution of the dark matter at galactic scale. + Ou the theoretical front. there are various lass distribution models of the dark matter halo.," On the theoretical front, there are various mass distribution models of the dark matter halo." + The isothermal profile. the Navarro-Freuk-White (NEW) profile aud some variant of these two profiles are used extensively in both theoretical aud observational studies.," The isothermal profile, the Navarro-Frenk-White (NFW) profile and some variant of these two profiles are used extensively in both theoretical and observational studies." + Au almost flat observed rotation curve outside the core of a galaxy led to the davk matter halo model with 1/7? isothermal deusity profile1995)., An almost flat observed rotation curve outside the core of a galaxy led to the dark matter halo model with $1/r^2$ isothermal density profile. +. The deusitv at the centre is nof fuite iu this model., The density at the centre is not finite in this model. + However. it is possible to impose appropriate boundary conditions to derive a non-sneulu solution with density ονο=porZ/602|00602). where py ds the central deusitv and or. ds the vcore radius.," However, it is possible to impose appropriate boundary conditions to derive a non-singular solution with density $\rho(r)_{NIS} = \rho_0r_c^2/(r_c^2+r^2)$, where $\rho_0$ is the central density and $r_c$ is the “core radius”." + At Luge radius. this profile will be similar to 1/77 singular isothermal profile.," At large radius, this profile will be similar to $1/r^2$ singular isothermal profile." + A cut-off radius Γρ is also required to be imposed to keep the total mass of the halo finite., A cut-off radius $r_{max}$ is also required to be imposed to keep the total mass of the halo finite. + However. the non-iugular isothermal profile was not very successful in explaining the observed rotation curves.," However, the non-singular isothermal profile was not very successful in explaining the observed rotation curves." +" A significant progress in the field was the iutroductiou of an alternative deusitv profile. the NEW deusity profile. p(r)gw=porn)]. where p. aud (rp, are the characteristicv densityfrin. and| characteristic radius respectively (Navarroctal.1996.1997:Jing2000)."," A significant progress in the field was the introduction of an alternative density profile, the NFW density profile, $\rho(r)_{NFW} = \rho_0r_c^3/[r(r_c+r)^2]$, where $\rho_c$ and $r_c$ are the characteristic density and characteristic radius respectively \citep{nfw96,nfw97,jing00}." +. The NFW> profile has been quite successful iu explaining the observed rotation curves for many ealaxies., The NFW profile has been quite successful in explaining the observed rotation curves for many galaxies. + Over the time. a class of variaut of the isothermal aud the NEW profiles are also introduced to fine tune the agreement of theory. aud observations (Burkert1995:Zhao1996:Fukushiee&Makino2001).," Over the time, a class of variant of the isothermal and the NFW profiles are also introduced to fine tune the agreement of theory and observations \citep{burk95,zhao96,fuku01}." +. All these density profiles are of more or less similar micrit. as far as explaining the rotation curve is concerned.," All these density profiles are of more or less similar merit, as far as explaining the rotation curve is concerned." + However. detailed analvsis shows that the NEW. profile has a number of problems.," However, detailed analysis shows that the NFW profile has a number of problems." + For cxaunple. observations of ealaxies and clusters sugeest a central flat density core (deBlok2007:I&uziodeNaravetal.2008).. whereas. in NEW profile. dark matter density has a ceutral cusp with a logarithuuc slope ~1.," For example, observations of galaxies and clusters suggest a central flat density core \citep{blok07,kdn08}, whereas, in NFW profile, dark matter density has a central cusp with a logarithmic slope $\approx -1$." + Nunerical simulations show that the presence of baryon can change the mass distribution significantly (EbZantetal.20014:Shlos-nan2010.andreferences therein)... aud for isothermal cusp. nmünor merecr and dynamical fiction may lead o a shallower ceutral deusitv slope (Romano-Diazct 2008).," Numerical simulations show that the presence of baryon can change the mass distribution significantly \citep[][and references therein]{ez04,sm10}, and for isothermal cusp, minor merger and dynamical friction may lead to a shallower central density slope \citep{rd08}." +. The NEW profile also secmis not to fit the observed rotation curves of the dark matter dominated ow surface brightucss galaxies aud low mass dwuf ealaxies (deBlok2002.2005).," The NFW profile also seems not to fit the observed rotation curves of the dark matter dominated low surface brightness galaxies and low mass dwarf galaxies \citep{blok02,blok05}." +. À inore serious issue with the NEW profile is that the profile is derived by fittine analytical function to the density distribution derived from ποσα. simulation of structure formation with dark matter., A more serious issue with the NFW profile is that the profile is derived by fitting analytical function to the density distribution derived from numerical simulation of structure formation with dark matter. + This. in a sense. lacks a proper physical understanding.," This, in a sense, lacks a proper physical understanding." + Though some physical insight, Though some physical insight +and spectroscopic classification (Gallego et al. 1996)3.,and spectroscopic classification (Gallego et al. \cite{Gal96}) ). + The averaged colours of each IIubble type are listed in Table l. jointly with the mean colours caleulated by Fukugita et al. (19953).," The averaged colours of each Hubble type are listed in Table 4, jointly with the mean colours calculated by Fukugita et al. \cite{Fuk95}) )." + The vertical ticks iu these diagrams show Fukueita et al. (19953) , The vertical ticks in these diagrams show Fukugita et al. \cite{Fuk95}) ) +colours and averaged colours for cach spectroscopic typo., colours and averaged colours for each spectroscopic type. + Overall. eulv-tvpe spirals show a bluer colour thau those of Fukugita et al. (1995)).," Overall, early-type spirals show a bluer colour than those of Fukugita et al. \cite{Fuk95}) )," + probably related to the presence of the star-forming process., probably related to the presence of the star-forming process. + On the other hand. regulars and BC'Ds do show redder Br colours than Fukueita’s sample: this could be a selection effect. even that very blue objects would not show up at the original objective-prisin plates as they were taken in the IIo region.," On the other hand, irregulars and BCDs do show redder $B-r$ colours than Fukugita's sample; this could be a selection effect, given that very blue objects would not show up at the original objective-prism plates as they were taken in the $\alpha$ region." + Although the spectroscopic histograms show a great dispersion we observe that SBN galaxies are redder thaw other types., Although the spectroscopic histograms show a great dispersion we observe that SBN galaxies are redder than other types. + The —bluest objects appear to be BCDs aud DIITIIIs., The bluest objects appear to be BCDs and DHIIHs. + These two facts could )o explaine in two different wavs: SBNs could be αΠςcted by larger dust reddening or the starburst could be more relevant in BCD and DIT ealaxies. making them bluer.," These two facts could be explained in two different ways: SBNs could be affected by larger dust reddening or the starburst could be more relevant in BCD and DHIIH galaxies, making them bluer." + In fact. Gallego et al. (1997))," In fact, Gallego et al. \cite{Gal97}) )" + showed that the mean 2.V. colour excess for SBN galaxies is 0.2 hieher than for ealaxies., showed that the mean $B-V$ colour excess for SBN galaxies is $^m$ higher than for galaxies. + Both kind of data are mixed iu Figure L., Both kind of data are mixed in Figure \ref{fig4}. + SBN galaxies dominate the spiral zone (from T21 -Sa- to T=6 -Sc-). adding a great colour dispersion to our sauple.," SBN galaxies dominate the spiral zone (from T=1 -Sa- to T=6 -Sc-), adding a great colour dispersion to our sample." + There are also 7 very blue objects. all of them late-type spirals (Se1) or Airegulus.," There are also 7 very blue objects, all of them late-type spirals (Sc+) or irregulars." +" some of these objects are low metallicity galaxies. for exeuuple UC'M220111610 (Br),y= 0.15. inetalliitv Z; /7) or UCMO019|0017 (Br)y 0:33. metallicity Z; /20)."," some of these objects are low metallicity galaxies, for example UCM2304+1640 $(B-r)_{ef}$ $-$ 0.18, metallicity ${Z_{\sun}}/{7}$ ) or UCM0049+0017 $(B-r)_{ef}$ $-$ 0.33, metallicity ${Z_{\sun}}/{20}$ )." + The Bor histogram for the whole sample is plotted in Figure 5.., The $B-r$ histogram for the whole sample is plotted in Figure \ref{fig5}. + The averaged effective. colour of the UCM saluple is 0.23250.H1., The averaged effective colour of the UCM sample is $0.73\pm0.41$. + The distribution is rather flat. beimg dominated by galaxies with a colour correspouding Oa tvpical spiral.," The distribution is rather flat, being dominated by galaxies with a colour corresponding to a typical spiral." + Iu Figure 6 we plot the B absolute magnitude My versus the effective colour (2rep., In Figure \ref{fig6} we plot the $B$ absolute magnitude $M_B$ versus the effective colour $(B-r)_{ef}$. + Labels correspond to spectroscopic type of each object., Labels correspond to the spectroscopic type of each object. + An extinction vector of 0.L magnitudes in the Bland has been drawn., An extinction vector of 0.4 magnitudes in the $B$ band has been drawn. + SBN ealaxies are located iu the most bpuuiuous aud reddest part of the plot. joiutlv with Sy2 galaxies.," SBN galaxies are located in the most luminous and reddest part of the plot, jointly with Sy2 galaxies." + Iu the other haud. BCDs appear to. be the bluest and faintest objects in our suuple.," In the other hand, BCDs appear to be the bluest and faintest objects in our sample." + UCAL objects: are compared with a nonual sample of galaxies frou the literature in Figure 7: we have selected comuuon galaxies in the Nearby Universe from the NGC. IC and Alek catalogs extracted from the NED database?.," UCM objects are compared with a normal sample of galaxies from the literature in Figure \ref{fig7}; we have selected common galaxies in the Nearby Universe from the NGC, IC and Mrk catalogs extracted from the NED database." +. The BCD data have been extracted from Doublier ct al. (1997))., The BCD data have been extracted from Doublier et al. \cite{Dou97}) ). + Both sets of reference data are liehteued., Both sets of reference data are drawn lightened. + Iu the top panel we have compared our colours with those of spirals., In the top panel we have compared our colours with those of spirals. + As expected. most of the UCAL sample is located in the region where normal spiral galaxies are found in this colouranaenuitude diagram: some of our galaxies have similar colours to those of earbv-tvpe ealaxies though this could be due to internal reddeniug.," As expected, most of the UCM sample is located in the region where normal spiral galaxies are found in this colour-magnitude diagram; some of our galaxies have similar colours to those of early-type galaxies though this could be due to internal reddening." +" The BCD galaxies in our sample seem to be about 0.7"" brighter aud 0.2"" bluer than the Doublier et al. (1997])", The BCD galaxies in our sample seem to be about $^m$ brighter and $^m$ bluer than the Doublier et al. \cite{Dou97}) ) + sample., sample. +where the Àj; are evaluated with vw at the inner boundary. butotherwise with £ and r al the outer shock.,"where the $\lambda _{\pm i}$ are evaluated with $u$ at the inner boundary, butotherwise with $L$ and $r$ at the outer shock." + Now eliminating ο between equations D3 and D5 gives (he dispersion relation: where For 1<3<1.5.94 Oas ης4 0. and as 5—1 for fixed r./r;.," Now eliminating $B_+/B_-$ between equations B3 and B5 gives the dispersion relation: where For $1<\gamma <1.5$,$\beta\rightarrow 0$ as $r_i/r_s\rightarrow 0$ , and as $\gamma\rightarrow 1$ for fixed $r_s/r_i$ ." +The photosvuthesis-sustainiue TZ around Gl 581 is defined as the spatial domain of all distances A from the ceutral star where the biological productivity is ercater han zero. i... Tn our iodel. bioogical productivity is considered o be solely a function of the surface temperature and the COs partial oessure du the atmosphere.,"The photosynthesis-sustaining HZ around Gl 581 is defined as the spatial domain of all distances $R$ from the central star where the biological productivity is greater than zero, i.e., In our model, biological productivity is considered to be solely a function of the surface temperature and the $_2$ partial pressure in the atmosphere." +" Our »uwanieterization vields zero productivity for VC or Tug lü07C or Poo,x105 bar (Francketal. 2000a)."," Our parameterization yields zero productivity for $T_{\mathrm{surf}} \leq 0^{\circ}$ C or $T_{\mathrm{surf}} +\geq 100^{\circ}$ C or $P_{\mathrm{CO}_2}\leq 10^{-5}$ bar \citep{franck00a}." +. The inner aud outer boundaries of the IZ do not depend on the detailed paraimcterization of he biological prodictivity within the temperature aud oessure tolerance window., The inner and outer boundaries of the pHZ do not depend on the detailed parameterization of the biological productivity within the temperature and pressure tolerance window. + Parameterized convection models are the simplest mocels or investicating the thermal evolution of terrestrial aue sand satellites., Parameterized convection models are the simplest models for investigating the thermal evolution of terrestrial planets and satellites. + They have heen successfully applied o the evolution of Mercry. Venus. Earth. Mars aud he àoon (Stevensonetal.1983:Sleep20001.," They have been successfully applied to the evolution of Mercury, Venus, Earth, Mars, and the Moon \citep{stevenson83,sleep00}." + Franck&Bounama(1995) studiedt16 thermal aud volatile ustorv of Earth aud Venus iu f1ο framework of comparative auetologv., \cite{franck95} studied the thermal and volatile history of Earth and Venus in the framework of comparative planetology. + The internal structure of massive terrestrial anets with one to teu Ear liiuasses has been ivesieated w Valenciaetal.(2006) o obtain scaling laws for total radius. mautle thickness. core size. aud average density as a function of mass.," The internal structure of massive terrestrial planets with one to ten Earth masses has been investigated by \cite{valencia06} to obtain scaling laws for total radius, mantle thickness, core size, and average density as a function of mass." + Similar scaling laws were foiud for differeu conrpositions., Similar scaling laws were found for different compositions. + We will use these scaling laws for the mmass-depencdent properties of super-Earths and also the mass-incdependcut material properties eiven by Franck.&Bounama (1995)., We will use these scaling laws for the mass-dependent properties of super-Earths and also the mass-independent material properties given by \cite{franck95}. +. The thermal history aud future of a super-Eartl has to be determined to calculate the spreading rate for solving key Eq. (2))., The thermal history and future of a super-Earth has to be determined to calculate the spreading rate for solving key Eq. \ref{gfr}) ). + À paraincterized model of whole mautle convection including the volatile exchange between the laute and surface reservoirs (Franck&Bounama1995:Francd19908) is applied.," A parameterized model of whole mantle convection including the volatile exchange between the mantle and surface reservoirs \citep{franck95,franck98} is applied." + The kev equations used in our preseit study are m accord with our previous work focused on C Sate and Cl 581d: see vouBloletal.€2007).. for details," The key equations used in our present study are in accord with our previous work focused on Gl 581c and Gl 581d; see \cite{vonbloh07}, for details." +" A kev clement is the computation of the areal spreading rate S: note that S$ is a function of the average lautο temperature Z,,. the surface temperature Diag. the heat flow from the mantle 4,,. and the area of ocean basins Ay (Turcotte&Schubert2002)."," A key element is the computation of the areal spreading rate $S$; note that $S$ is a function of the average mantle temperature $T_m$, the surface temperature $T_{\mathrm{surf}}$, the heat flow from the mantle $q_m$, and the area of ocean basins $A_0$ \citep{turcotte02}." +. It is eiven as where s is the thermal diffusivity and & the thermal conductivity., It is given as where $\kappa$ is the thermal diffusivity and $k$ the thermal conductivity. +" To calculate the spreading rate. the thermal evolution of the mantle has be to computed: where pis the density. eis the specific heat at coustaut xessure. £ ijs the enerev production rate bv decay of radiosgenic heat sources in the mautle per unit voluue. aud A, aud &, ave the outer and immer radii of the uautle. respectively,"," To calculate the spreading rate, the thermal evolution of the mantle has be to computed: where $\rho$ is the density, $c$ is the specific heat at constant pressure, $E$ is the energy production rate by decay of radiogenic heat sources in the mantle per unit volume, and $R_m$ and $R_c$ are the outer and inner radii of the mantle, respectively." +" To calculate the thermal evolution or a plauct with several Earth masses. ie. 2.1 and 13 AL, as pursued for C1 581e in our present study. the planetary xuaueters have to be adjusted."," To calculate the thermal evolution for a planet with several Earth masses, i.e., 3.1 and 4.3 $M_\oplus$ as pursued for Gl 581g in our present study, the planetary parameters have to be adjusted." +" Thus we asstuc where HR, is the planctary radius. sceValenciaetal. (2006)."," Thus we assume where $R_p$ is the planetary radius, see\cite{valencia06}." +.. The total radius. mantle thickness. core size. and average deusity are all functions of mass. with the subscript denoting Earth values.," The total radius, mantle thickness, core size, and average density are all functions of mass, with the subscript $\oplus$ denoting Earth values." + The exponent of 0.27 has been oltained for super-Earths., The exponent of $0.27$ has been obtained for super-Earths. + The values of I. Rin. Rh... as wel as the other planetary properties are scaled accordingly.," The values of $R_p$, $R_m$, $R_c$, as well as the other planetary properties are scaled accordingly." +" It iieans that R,. Ry, awl AR. dmnerease bv a factor of 1.36 for AL=3.142). and 1.18 for M=L2,."," It means that $R_p$, $R_m$ and $R_c$ increase by a factor of 1.36 for $M = 3.1 M_\oplus$ and 1.48 for $M = 4.3 M_\oplus$." + Table 1 gives a suuuuary of the size paramcters for the iodels of the planets with 3.1 and L5 AL): see the stidv ly vouDlohetal.(2007) for additional information.," Table \ref{param} gives a summary of the size parameters for the models of the planets with 3.1 and 4.3 $M_\oplus$; see the study by \cite{vonbloh07} + for additional information." + The values for an Earth-size planet are inchded for comparisoi., The values for an Earth-size planet are included for comparison. + The onset of plate tectonics on lnassive terrestrial planets is a topic of controversy., The onset of plate tectonics on massive terrestrial planets is a topic of controversy. + While ONeill&Lenardic(2007). stated that there might be in an episodic or stagnant lid regime. Valencia&O'Connell(2009) proposed that a anore nassive planet is likely ο convect in a plate ectonic reelme sinülar to Earth.," While \cite{oneill07} stated that there might be in an episodic or stagnant lid regime, \cite{valencia09} proposed that a more massive planet is likely to convect in a plate tectonic regime similar to Earth." + Thus. the more massive the plauet is. the higher the Ravleigh number that controls convecjon. the thinner he top boundary laver (lithosphere). axd the higher the convective velocities.," Thus, the more massive the planet is, the higher the Rayleigh number that controls convection, the thinner the top boundary layer (lithosphere), and the higher the convective velocities." + In the framework. of our model. a dlate-tectomie-driven carhou evele is cousidered necessary or carbon-based life.," In the framework of our model, a plate-tectonic-driven carbon cycle is considered necessary for carbon-based life." +" This approach follows the previous work by vouDlohetal. (2007).. who gave a detailed discussion of the equations and parameters used iu their study for the super-Earths with 5 aud δ AZ).. identified as Gl 581c aud Cl 581d. respectively,"," This approach follows the previous work by \cite{vonbloh07}, , who gave a detailed discussion of the equations and parameters used in their study for the super-Earths with 5 and 8 $M_\oplus$ , identified as Gl 581c and Gl 581d, respectively." +that the percentage of cIusters possessing radio halos should be greater than. T0.,that the percentage of clusters possessing radio halos should be greater than $70\%$. + This is inconsistent with the observations in which only ~ of these massive clusters possess radio halos., This is inconsistent with the observations in which only $\sim$ of these massive clusters possess radio halos. + According to these results. the secondary electrons do not seem to be the dominant origin of the radio halos.," According to these results, the secondary electrons do not seem to be the dominant origin of the radio halos." + On the other hand. if radio halos were transient. phenomena associated with a single acceleration event. such as a major merger shock. they would have lifetimes ~0.1 Gyr.," On the other hand, if radio halos were transient phenomena associated with a single acceleration event, such as a major merger shock, they would have lifetimes $\sim 0.1$ Gyr." + Because of the short lifetimes of the sources. radio halos would be hardly observable even in (he massive clusters.," Because of the short lifetimes of the sources, radio halos would be hardly observable even in the massive clusters." + The observed percentage is (hus loo high to explain in the hierarchical clustering formation model., The observed percentage $\sim$ is thus too high to explain in the hierarchical clustering formation model. + According to the results presented in $ ??.. the lifetimes of radio halos may be ~ Gvr.," According to the results presented in $\S$ \ref{seccom}, the lifetimes of radio halos may be $\sim$ Gyr." + As mentioned in 5$ ??.. relativistic electrons in ICM lose energy on the time seale of order LO” vears because of the inverse Compton and svuchrotron losses.," As mentioned in $\S$ \ref{secint}, relativistic electrons in ICM lose energy on the time scale of order $\sim10^{8}$ years because of the inverse Compton and synchrotron losses." + This indicates that a significant level of re-acceleration is necessary (0 support the relativistie electrons against radiative losses and (o maintain radio halos to last for & Gyr 2003)..," This indicates that a significant level of re-acceleration is necessary to support the relativistic electrons against radiative losses and to maintain radio halos to last for $\sim$ Gyr \citep{bru01,kuo03}. ." + As discussed in ??.. the percentage of radio halos [or Ly>LOY erg bo c385. is more robust.," As discussed in \ref{seccom}, the percentage of radio halos for $L_{\mathrm{X}} > 10^{45}$ erg $^{-1}$, $\sim$, is more robust." +" We here investigate the effects of the lifetime of the radio halos. the dividing mass. and the threshold mass ratio A,, on our results."," We here investigate the effects of the lifetime of the radio halos, the dividing mass, and the threshold mass ratio $\triangle_m$ on our results." + Only the ACDAM model is considered., Only the $\Lambda$ CDM model is considered. + First. the lifetimes of radio halos can affect the ratios of the radio halos.," First, the lifetimes of radio halos can affect the ratios of the radio halos." + The percentage ol radio halos with {μι=1 Gyr is ~21% and seems to be lower than the observationa results. ~38%... as shown in Table 1..," The percentage of radio halos with $t_{\mathrm{rh}}=1$ Gyr is $\sim 21\%$ and seems to be lower than the observational results, $\sim$, as shown in Table \ref{tbl}." + However. we note that the lifetime of the radio halo is of ~ Gyr and could be slightly longer or shorter than 1 Gyr and the difference of the asstumecl lifetime could affect the predicted percentage of the radio halo.," However, we note that the lifetime of the radio halo is of $\sim$ Gyr and could be slightly longer or shorter than 1 Gyr and the difference of the assumed lifetime could affect the predicted percentage of the radio halo." +" For example. if a longer lifetime for the radio halo. /4,=1.5 Gyr. is assumed. then the percentage of the radio halo would become ~:32% and would be in agreement with the observationa. results."," For example, if a longer lifetime for the radio halo, $t_{\mathrm{rh}}=1.5$ Gyr, is assumed, then the percentage of the radio halo would become $\sim +32\%$ and would be in agreement with the observational results." + Second. the dividing mass at AJ=LOPAL. may be lower than the realistic mass corresponding to Ly=LO” erg !|.," Second, the dividing mass at $M = 10^{15} M_{\odot}$ may be lower than the realistic mass corresponding to $L_{\mathrm{X}} = +10^{45}$ erg $^{-1}$." + For example. the A773 cluster with LycLOLx10% erg + has mass in the range 1.252.08 xlOPAL. (Govonietal.2001).," For example, the A773 cluster with $L_{\mathrm{X}} \sim 1.01 \times 10^{45}$ erg $^{-1}$ has mass in the range 1.25–2.08 $\times 10^{15} M_{\odot}$ \citep{gov01}." +. In Table 3.. we show the percentages corresponding to different dividing masses.," In Table \ref{tb3}, we show the percentages corresponding to different dividing masses." +" Obviously. the results with fg,=1 Gyr are improved but those with {μμ= cosmological (ime are worse if a higher and more realistic dividing mass is taken."," Obviously, the results with $t_{\mathrm{rh}}=1$ Gyr are improved but those with $t_{\mathrm{rh}}=$ cosmological time are worse if a higher and more realistic dividing mass is taken." +" Third. different threshold A,, also affect our results."," Third, different threshold $\triangle_{\mathrm{m}}$ also affect our results." +" The results with different. A,, are shown in Table 4..", The results with different $\triangle_{\mathrm{m}}$ are shown in Table \ref{tb4}. +" The values of A,, strongly affect. the results for /,4—1 ανν and /4,= cosmological time.", The values of $\triangle_{\mathrm{m}}$ strongly affect the results for $t_{\mathrm{rh}}=1$ Gyr and $t_{\mathrm{rh}}=$ cosmological time. +" For A,=0.7. the results with {μι= cosmological time sees {ο be close to the observational results:this implies that the radio halos would only be generated in the mergers with (wo nearly equal-mass progenitors if the secondary. electrons were the dominant origin for forming radio halos."," For $\triangle_{\mathrm{m}}=0.7$, the results with $t_{\mathrm{rh}}=$ cosmological time seems to be close to the observational results;this implies that the radio halos would only be generated in the mergers with two nearly equal-mass progenitors if the secondary electrons were the dominant origin for forming radio halos." +" For A,,= 0.5."," For $\triangle_{\mathrm{m}}=0.5$ ," +"small clataset is to fix O| O,,—1. ie. we can impose the flatness condition measured by WALAP (ο=1.02+.02 with Llubble kev project. fy prior. Freedman et al 2001. Spergel et al 2003).","small dataset is to fix $\Omega_\Lambda + \Omega_m$ =1, i.e. we can impose the flatness condition measured by WMAP $\Omega_{\rm tot}=1.02\pm.02$ with Hubble key project $H_0$ prior, Freedman et al 2001, Spergel et al 2003)." + With this condition. we can again make shear correlation function predictions. then obtain X7 fits to the data for various values of ax and £24. incrementing in units of 0.05 and 0.05 respectively.," With this condition, we can again make shear correlation function predictions, then obtain $\chi^2$ fits to the data for various values of $\sigma_8$ and $\Omega_\Lambda$, incrementing in units of 0.05 and 0.05 respectively." + We marginalise over Lo and zuedina as before., We marginalise over $H_0$ and $z_{\rm median}$ as before. + The results are shown in Figure 4. for the cases where we exclude and include the unknown redshift sample fixed al 20.95 0.05.," The results are shown in Figure 4, for the cases where we exclude and include the unknown redshift sample fixed at $z=0.95\pm0.05$ ." +" LIere we find that the constraints on ον or O,, are substantially improved over the case where we do not prescribe [atness.", Here we find that the constraints on $\Omega_\Lambda$ or $\Omega_m$ are substantially improved over the case where we do not prescribe flatness. +" In the case where we exclude the unknown recdshift galaxies. we find a weak constraint Oy>10.167,Dg) or Oy>1(0.25.Pe)"," In the case where we exclude the unknown redshift galaxies, we find a weak constraint $\Omega_\Lambda>1-0.16\sigma_8^{-1.95} (1\sigma)$ or $\Omega_\Lambda>1-0.25\sigma_8^{-1.76} (2\sigma)$." + [f we then force a prior ox—0.540.04. we obtain OX=0.91a at the 2e level. consistent with standard ACDAL as defined above.," If we then force a prior $\sigma_8=0.84\pm0.04$, we obtain $\Omega_\Lambda=0.91^{+.09}_{-0.27}$ at the $2\sigma$ level, consistent with standard $\Lambda$ CDM as defined above." + Again. these results oller a low normalisation of the matter power spectrum: for Oy=0.7. we require ax«0.72 at the lo level.," Again, these results offer a low normalisation of the matter power spectrum; for $\Omega_\Lambda=0.7$, we require $\sigma_8<0.72$ at the $1\sigma$ level." + As discussed in the previous section. this result. is dominated by the fact that our two fields. are devoid of significant large-scale structure: further fields will require measurement. before cosmological implications can be conclusively drawn.," As discussed in the previous section, this result is dominated by the fact that our two fields are devoid of significant large-scale structure; further fields will require measurement before cosmological implications can be conclusively drawn." + 1£ we now include galaxies with unknown redshift. we lind a best-fit constraint O421.O.15te40.04).," If we now include galaxies with unknown redshift, we find a best-fit constraint $\Omega_\Lambda=1-0.15(\sigma_8\pm0.04)^{-1.5}, +\sigma_8<0.72 (1\sigma)$ ." + In the case where we impose a prior ex=0.84+ 0.04. we obtain Oy=0.83nla).," In the case where we impose a prior $\sigma_8=0.84\pm0.04$ , we obtain $\Omega_\Lambda=0.83^{+0.06}_{-0.11} +(2\sigma)$." + This. and the constraint clirectly from our contours 4<0.76(10) is in accord with 10 concordance ACDAL model: only the power spectrum normalisation is outside the range expected.," This, and the constraint directly from our contours $\Omega_\Lambda<0.76 (1\sigma)$ is in accord with the concordance $\Lambda$ CDM model; only the power spectrum normalisation is outside the range expected." + Despite the limitations due to the size of our dataset. dese constraints are already. impressive. and. demonstrate re power of using 3-D information.," Despite the limitations due to the size of our dataset, these constraints are already impressive, and demonstrate the power of using 3-D information." + Figure 4 compares the accuracies of the 2D analysis of Brown et al (2003. dashed ines) for only the CDES and SLL fields with the current 32D analysis (solid lines): clearly one gains very significantly from he inclusion of the redshift information. bv a factor of 72 everywhere in uncertainty (bevond ex7 0.4).," Figure 4 compares the accuracies of the 2D analysis of Brown et al (2003, dashed lines) for only the CDFS and S11 fields with the current 3-D analysis (solid lines); clearly one gains very significantly from the inclusion of the redshift information, by a factor of $>2$ everywhere in uncertainty (beyond $\sigma_8>0.4$ )." + This holds out he promise of very precise measurements of cosmological xwameters with future 3-D lensing surveys., This holds out the promise of very precise measurements of cosmological parameters with future 3-D lensing surveys. + In this paper. we have explored the evolution. of. large-scale structure for redshifts ο«1.," In this paper, we have explored the evolution of large-scale structure for redshifts $z<1$." + This has been achieved using weak gravitational lensing together with photomoetric recishifts for a set of galaxies. both measured upon two fields from the COABO-17 survey (Wolf et al 2001).," This has been achieved using weak gravitational lensing together with photometric redshifts for a set of galaxies, both measured upon two fields from the COMBO-17 survey (Wolf et al 2001)." + We have described. the construction of theoretical models of evolving matter power spectra. both in ternis of phenomenology of the growth of structure. and. in erms of characterisation of this erowth with cosmological xuwameters.," We have described the construction of theoretical models of evolving matter power spectra, both in terms of phenomenology of the growth of structure, and in terms of characterisation of this growth with cosmological parameters." + We have then shown how to calculate the shear »ower spectrum from this matter power spectrum. ancl vice versa.," We have then shown how to calculate the shear power spectrum from this matter power spectrum, and vice versa." + In particular. we have discussed the importance of the Cross powerspectrum for shears between redshift shells. and jwe related phenomenological models for evolution between he matter and shear cross power spectra.," In particular, we have discussed the importance of the cross powerspectrum for shears between redshift shells, and have related phenomenological models for evolution between the matter and shear cross power spectra." +time.,time. + Iu this section. we refer to the basic object ina cell as a “particle”. bearing m munud that it may describe individual galaxies or virtalized subclusters.," In this section, we refer to the basic object in a cell as a “particle”, bearing in mind that it may describe individual galaxies or virialized subclusters." +" The potential energy in the cell cau be separated iuto a local aud backeround component such that where ®joeq, is the potential cucrey that arises from pairs where both members of the pair are within the cell and Pharckeround IX the poteutial energy that results from pairs that have one member in the cell and the other member outside the cell.", The potential energy in the cell can be separated into a local and background component such that where $\Phi_\mathrm{local}$ is the potential energy that arises from pairs where both members of the pair are within the cell and $\Phi_\mathrm{background}$ is the potential energy that results from pairs that have one member in the cell and the other member outside the cell. + The local poteutial enerev iu the cell comes from. siunuuius up the potential euergv of all pais within the cell such that where G is the eravitational constant. i is the mass of a galaxy. rj; is the distance between particle ; aud particle j and the sim is taken over all possible pairs of galaxies within the cell.," The local potential energy in the cell comes from summing up the potential energy of all pairs within the cell such that where $G$ is the gravitational constant, $m$ is the mass of a galaxy, $r_{ij}$ is the distance between particle $i$ and particle $j$ and the sum is taken over all possible pairs of galaxies within the cell." + Here κ) describes the potential of particles that are exteuded sources aud is a modification to the potential used. to describe poiut masses., Here $\kappa(r)$ describes the potential of particles that are extended sources and is a modification to the potential used to describe point masses. + It is related to Q(Ge/24) through equation and is usually of order unity for particles that are simall compared to the cell size., It is related to $\zeta(\epsilon/R_1)$ through equation and is usually of order unity for particles that are small compared to the cell size. + We can write the local potential iu terms of the average Inverse separation of ealaxy pairs so that where the NCN|1)/2 factor is the number of unique pairs in a cell with NV particles., We can write the local potential in terms of the average inverse separation of galaxy pairs so that where the $N(N-1)/2$ factor is the number of unique pairs in a cell with $N$ particles. + Tere (1/75 is the average Inverse pairwise separation of all galaxy pairs in the cell., Here $\langle 1/r\rangle$ is the average inverse pairwise separation of all galaxy pairs in the cell. + Iu an expanding universe. the expansionof the uuiverse exactly cancels the simoothed background terii iu the potential (Saslaw&Fang1996) so we cau ignore the backerouud term for cells that are larger than the scale at which the two-point correlation fuuction € is negligible.," In an expanding universe, the expansionof the universe exactly cancels the smoothed background term in the potential \citep{1996ApJ...460...16S} so we can ignore the background term for cells that are larger than the scale at which the two-point correlation function $\xi_2$ is negligible." + At these scales. the potential energy is extensive since the expansion ofthe universe cancels out the background terim," At these scales, the potential energy is extensive since the expansion of the universe cancels out the background term." + For simaller cells. Saslaw&Fang(1996) sugeest that exteusivitv is also a good approximation iu the regime where £2& Lso that the correlation energy within a cellis much greater than the correlation cucrey between cells.," For smaller cells, \citet{1996ApJ...460...16S} suggest that extensivity is also a good approximation in the regime where $\xi_2 \gtrsim 1$ so that the correlation energy within a cell is much greater than the correlation energy between cells." + This approximation holds because the form of the partition function is independent of scale., This approximation holds because the form of the partition function is independent of scale. +" The scale dependence is provided by the clustering parameter b which is related to the two-point correlation function «ο through (Sashuv&Fang1996) For these reasons. the potential energv in a cell is approximately exteusive regardless of its radius. aud the local potential dj, is à good approximation for the correlation potential energv."," The scale dependence is provided by the clustering parameter $b$ which is related to the two-point correlation function $\xi_2$ through \citep{1996ApJ...460...16S} + For these reasons, the potential energy in a cell is approximately extensive regardless of its radius, and the local potential $\Phi_\mathrm{local}$ is a good approximation for the correlation potential energy." + This also lots us use RW iustead of Ry in the scaling factors A and « For au individual cell. the potential energy. VW. is thus and using equation(2). we can write the scaled potential euergy as where we have used the scaling factor A given by equation because we are dealing with the detailed configuration of the galaxies iu the cell.," This also lets us use $R$ instead of $R_1$ in the scaling factors $A$ and $a$ For an individual cell, the potential energy, $W$, is thus and using equation, we can write the scaled potential energy as where we have used the scaling factor $A$ given by equation because we are dealing with the detailed configuration of the galaxies in the cell." + Hore. the Gin? factors cancel aud VW. is determined oulv by I. R aud te)fr).," Here, the $Gm^2$ factors cancel and $W_*$ is determined only by $N$, $R$ and $\langle \kappa(r)/r\rangle$." + For a homogeneous cell. the average inverse separation of all pairs of particles scaled to the cell radius is We can then write where 4 is a form factor that describes the shape of a cluster of ealaxies through its coufleuration aud the size and mass of cach particles individual halo iu comparison to a homogeneous cell.," For a homogeneous cell, the average inverse separation of all pairs of particles scaled to the cell radius is We can then write where $\eta$ is a form factor that describes the shape of a cluster of galaxies through its configuration and the size and mass of each particle's individual halo in comparison to a homogeneous cell." + This gives where This is defined ouly for cells with VW&2 because i ds not meauimgful where NV=0 or IN=1 since there are uo other particles in the cell to form a cluster., This gives where This is defined only for cells with $N\geq 2$ because $\eta$ is not meaningful where $N = 0$ or $N = 1$ since there are no other particles in the cell to form a cluster. + The kinetic energy of a cell is defined as This depends ou οἳ which depends ou the units used to describe time., The kinetic energy of a cell is defined as This depends on $v^2$ which depends on the units used to describe time. + A suitable choice for the time unit is a represcutative dynamical time for the cluster. given by For e eiven in teris of the dvuaimical time. the kinetic enerev is therefore and from equation we ect We can write the velocity as so that (c 2ois the meau-squared velocity.. eiven. in. units- of cell radii per dvianuical time.," A suitable choice for the time unit is a representative dynamical time for the cluster, given by For $v$ given in terms of the dynamical time, the kinetic energy is therefore and from equation we get We can write the velocity as so that $\upsilon^2$ is the mean-squared velocity, given in units of cell radii per dynamical time." + In terms of c. we ect," In terms of $\upsilon$ , we get" +The case with random longitudes generates too low open flux at solar maxima.,The case with random longitudes generates too low open flux at solar maxima. + The rms difference between the results from CJSS10 is 1.19x10 Wb when c=0 (the purely random case) compared to 1.09x10/4 Wb when c=0.15., The rms difference between the results from CJSS10 is $1.19 \times 10^{14}$ Wb when $c=0$ (the purely random case) compared to $1.09 \times 10^{14}$ Wb when $\mathrm{c}=0.15$. +" When we consider only the cycle maximum values of the open flux for each cycle, the difference is greater, with the rms deviation falling from 1.93x10'* Wb for c=0 to 1.00x1014 Wb for c=0.15."," When we consider only the cycle maximum values of the open flux for each cycle, the difference is greater, with the rms deviation falling from $1.93 \times 10^{14}$ Wb for $c=0$ to $1.00 \times 10^{14}$ Wb for $c=0.15$." + Next we compare our simulations during 1913 — 1986 (cycles 12-21) based on Rg and Rz with the results from CJSS10 and with the observed data., Next we compare our simulations during 1913 – 1986 (cycles 12–21) based on $R_G$ and $R_Z$ with the results from CJSS10 and with the observed data. + Note that all results shown are based on averages over 20 sets of random realizations of the semi-synthetic sunspot records., Note that all results shown are based on averages over 20 sets of random realizations of the semi-synthetic sunspot records. +" We first set the radial diffusivity to η,=0.", We first set the radial diffusivity to $\eta_r=0$. +" Figure 3((a) compares the time evolution of total flux from CJSS10 with the models based on Rg and Rz, respectively."," Figure \ref{fig:1913_1986}( (a) compares the time evolution of total flux from CJSS10 with the models based on $R_G$ and $R_Z$, respectively." + The three curves almost overlap., The three curves almost overlap. +" For the period from the early 1970s onwards, the direct magnetic measurements from the Mount Wilson and Wilcox observatories are also shown."," For the period from the early 1970s onwards, the direct magnetic measurements from the Mount Wilson and Wilcox observatories are also shown." + Figure 3((c) shows the evolution of the polar field for both hemispheres., Figure \ref{fig:1913_1986}( (c) shows the evolution of the polar field for both hemispheres. +" Since the input of the BMRs emergences is randomly distributed on the two hemispheres, our reconstructed north and south polar fields are similar."," Since the input of the BMRs emergences is randomly distributed on the two hemispheres, our reconstructed north and south polar fields are similar." + The reversal times (indicated by cyan vertical lines) are similar to those given by ?.., The reversal times (indicated by cyan vertical lines) are similar to those given by \citet{Makarov03}. + The largest differences between the models occur in cycle 19., The largest differences between the models occur in cycle 19. + Figure 3((d) shows the evolution of the modeled open flux in comparison with that inferred from the geomagnetic aa index (?).., Figure \ref{fig:1913_1986}( (d) shows the evolution of the modeled open flux in comparison with that inferred from the geomagnetic $aa$ index \citep{Lockwood09b}. . +" For the whole time period, the rms difference between the inferred values from the aa index and CJSS10, Rz and Rg are 0.99, 0.92, 0.96 x10! Wb, respectively, corresponding to about of the average value of 6.92 x10! Wb of the ? data."," For the whole time period, the rms difference between the inferred values from the $aa$ index and CJSS10, $R_Z$ and $R_G$ are 0.99, 0.92, 0.96 $\times 10^{14}$ Wb, respectively, corresponding to about of the average value of 6.92 $\times10^{14}$ Wb of the \citet{Lockwood09b} data." + The time-latitude plot of the longitudinal averaged signed photospheric field (magnetic butterfly diagram) during this time period is shown in Figure 3((b) for the reconstruction based on Rz., The time-latitude plot of the longitudinal averaged signed photospheric field (magnetic butterfly diagram) during this time period is shown in Figure \ref{fig:1913_1986}( (b) for the reconstruction based on $R_Z$. +" As found in previous studies, the latitude separation of the two polarities leads to a net flux when azimuthally averaged."," As found in previous studies, the latitude separation of the two polarities leads to a net flux when azimuthally averaged." + The advection of this flux to the poles reverses the polar fields each cycle., The advection of this flux to the poles reverses the polar fields each cycle. + The regular polar field reversals and the anti-phase between the polar field and the low latitude field are well reproduced., The regular polar field reversals and the anti-phase between the polar field and the low latitude field are well reproduced. +" These results show that our SFTM with sources based on the sunspot numbers Rz or Rg is consistent with the reconstruction of CJSS10, which used the recorded properties of the actually sunspot groups, and also compares well with the observed photospheric and the heliospheric magnetic field."," These results show that our SFTM with sources based on the sunspot numbers $R_Z$ or $R_G$ is consistent with the reconstruction of CJSS10, which used the recorded properties of the actually sunspot groups, and also compares well with the observed photospheric and the heliospheric magnetic field." + Because the sunspot number data are less reliable before 1849 (??) we have chosen to use a non-vanishing value for the radial diffusivity η».," Because the sunspot number data are less reliable before 1849 \citep{Vaquero07, Svalgaard10} we have chosen to use a non-vanishing value for the radial diffusivity $\eta_r$." +" This was found to be necessary because when 7,=0 is used, the e-folding decay time due to 7 alone is approximately 4000 years."," This was found to be necessary because when $\eta_r=0$ is used, the e-folding decay time due to $\eta_{H}$ alone is approximately 4000 years." +" This timescale was obtained numerically, and is considerably longer than the simple estimate ARS/η because the meridional flow tends to keep the magnetic field at the two poles separated."," This timescale was obtained numerically, and is considerably longer than the simple estimate $\pi R_{\sun}^2/\eta$ because the meridional flow tends to keep the magnetic field at the two poles separated." + The long e-folding time means that the field at any given time is affected by errors in the sunspot numbers at all previous times., The long e-folding time means that the field at any given time is affected by errors in the sunspot numbers at all previous times. + This is very undesirable because noisy data at the beginning of the dataset then contribute for the entire period covered by the simulations without significant damping., This is very undesirable because noisy data at the beginning of the dataset then contribute for the entire period covered by the simulations without significant damping. +" Introducing a weak radial diffusivity η,=25 km?s~! (which leads to a decay time about 20 yr, as found by ?,, ?)) is aimed at keeping 7, small while still being able to sensibly use the early data."," Introducing a weak radial diffusivity $\eta_r=25$ $^2$ $^{-1}$ (which leads to a decay time about 20 yr, as found by \citeauthor{Baumann06}, \citeyear{Baumann06}) ) is aimed at keeping $\eta_r$ small while still being able to sensibly use the early data." + Figure 3((e) shows the polar field evolution with the weak radial diffusion included., Figure \ref{fig:1913_1986}( (e) shows the polar field evolution with the weak radial diffusion included. +" Compared to Figure 3((c), the largest differences are on the order of20%."," Compared to Figure \ref{fig:1913_1986}( (c), the largest differences are on the order of." +. The time evolution of the corresponding open fluxes is shown in Figure 3((f)., The time evolution of the corresponding open fluxes is shown in Figure \ref{fig:1913_1986}( (f). +" During the minimum phases of some cycles, the model is now closer to the data inferred from the aa index (e.g. Rg model around 1955 and Rz model around 1976), while other deviate more strongly (e.g., Rz model around 1924 and 1936)."," During the minimum phases of some cycles, the model is now closer to the data inferred from the $aa$ index (e.g. $R_G$ model around 1955 and $R_Z$ model around 1976), while other deviate more strongly (e.g., $R_Z$ model around 1924 and 1936)." +" For the whole time period, the rms deviations for the models based on Rz and Rg are 0.93 and 0.96 in 1014 Wb, respectively."," For the whole time period, the rms deviations for the models based on $R_Z$ and $R_G$ are 0.93 and 0.96 in $10^{14}$ Wb, respectively." + CJSS10 found a strong correlation between the polar field of cycle n and the strength of the subsequent cycle n+1., CJSS10 found a strong correlation between the polar field of cycle $n$ and the strength of the subsequent cycle $n+1$. +" Without radial diffusion, the correlation coefficients are 0.80 and 0.52 for the Rz and Rg, cases respectively."," Without radial diffusion, the correlation coefficients are 0.80 and 0.52 for the $R_Z$ and $R_G$, cases respectively." +" In our case with a sample size of 7, a significance level of p= 0.05 corresponds to r= 0.74."," In our case with a sample size of 7, a significance level of $p=$ 0.05 corresponds to $r=$ 0.74." +" For all cases, there is no correlation between the polar field around the activity minimum of cycle n and the strength of the same cycle."," For all cases, there is no correlation between the polar field around the activity minimum of cycle $n$ and the strength of the same cycle." + The introduction of radial diffusivity and the corresponding decay of the polar field decreases the correlation between the polar field and its subsequent cycle strength and somewhat increases the correlation between the polar field of cycle n and the strength of the same cycle., The introduction of radial diffusivity and the corresponding decay of the polar field decreases the correlation between the polar field and its subsequent cycle strength and somewhat increases the correlation between the polar field of cycle $n$ and the strength of the same cycle. + All these correlation coefficients do not exceed the level required for significance at the p=0.05 level., All these correlation coefficients do not exceed the level required for significance at the $p=0.05$ level. + We conclude that the SFTM with input data based on sunspot numbers effectively describes the solar magnetic field since 1913., We conclude that the SFTM with input data based on sunspot numbers effectively describes the solar magnetic field since 1913. +" Although the introduction of a non-vanishing radial diffusivityleads to some possibly undesired decay of the polar field, it decreases the error caused by the noisy early sunspot numbers."," Although the introduction of a non-vanishing radial diffusivityleads to some possibly undesired decay of the polar field, it decreases the error caused by the noisy early sunspot numbers." + The photospheric and the heliospheric field are reasonably well reproduced., The photospheric and the heliospheric field are reasonably well reproduced. +" In the next section, we present the results back to 1700."," In the next section, we present the results back to 1700." +With a sample as large as the CJF. jet astrophysics (Lorentz factors. acceleration. propagation) is clearly addressed in important ways. through studying both morphologies and velocities.,"With a sample as large as the CJF, jet astrophysics (Lorentz factors, acceleration, propagation) is clearly addressed in important ways, through studying both morphologies and velocities." + The completed CJF allows an investigation of the dependence of jet properties on a range of source parameters including host object type. luminosity. and redshift.," The completed CJF allows an investigation of the dependence of jet properties on a range of source parameters including host object type, luminosity, and redshift." + Extensive VLBI surveys in the past have provided a morphological classification of compact radio sources (e.g.. Wilkinson 1995 and references therein) and motion studies have yielded apparent velocity and Lorentz factor statistics that can be compared to other indicators of relativistic motion (e.g.. Ghisellini et al.," Extensive VLBI surveys in the past have provided a morphological classification of compact radio sources (e.g., Wilkinson 1995 and references therein) and motion studies have yielded apparent velocity and Lorentz factor statistics that can be compared to other indicators of relativistic motion (e.g., Ghisellini et al." + 1993; Vermeulen Cohen 1994. Vermeulen 1995: Jorstad et al.," 1993; Vermeulen Cohen 1994, Vermeulen 1995; Jorstad et al." + 2001: Kellermann et al., 2001; Kellermann et al. + 2004: Cohen et al., 2004; Cohen et al. + 2006)., 2006). + Several projects have been conducted to investigate the pe-scale structures of samples of AGN using the VLBA. e.g.. by Fomalont et al. (," Several projects have been conducted to investigate the pc-scale structures of samples of AGN using the VLBA, e.g., by Fomalont et al. (" +2000). Jorstad et al. (,"2000), Jorstad et al. (" +2001). Kellermann et al. (,"2001), Kellermann et al. (" +2004). and Piner et al. (,"2004), and Piner et al. (" +2004).,2004). + The CJF survey integrates several VLBI surveys conducted from Caltech and Jodrell Bank into a complete flux-density limited sample., The CJF survey integrates several VLBI surveys conducted from Caltech and Jodrell Bank into a complete flux-density limited sample. + For all the CJ surveys. sources were selected from the region of sky bounded by declination > 35° anc Galactic latitude |b]>10° based on the 6 em MPI-NRAO 5 GHz surveys (e.g.. Kühhr et al..," For all the CJ surveys, sources were selected from the region of sky bounded by declination $>$ $^{\circ}$ and Galactic latitude $|b|>10^{\circ}$ based on the 6 cm MPI-NRAO 5 GHz surveys (e.g., Kühhr et al.," + 1981)., 1981). +" The original sample (""Pearson-Readhead"". PR sample. Pearson Readheac 1981). is a complete sample of 65 sources with flux density Sscu, 21.3 Jy. many of which were imaged with VLBI at 5 GHz and 1.6 GHz (Pearson Readhead 1981. 1988: Polatidis et al."," The original sample (“Pearson-Readhead”, PR sample, Pearson Readhead 1981), is a complete sample of 65 sources with flux density $S_{5 \rm GHz}\geq$ 1.3 Jy, many of which were imaged with VLBI at 5 GHz and 1.6 GHz (Pearson Readhead 1981, 1988; Polatidis et al." + 1995)., 1995). +" The CJI extended the PR sample down to Ssou,= 0.7 Jy (total of 200 sources) (Polatidis et al.", The CJ1 extended the PR sample down to $S_{5 \rm GHz}\geq$ 0.7 Jy (total of 200 sources) (Polatidis et al. + 1995; Thakkar et al., 1995; Thakkar et al. + 1995; Xu et al., 1995; Xu et al. + 1995)., 1995). +" For CJ2 the limit is Ssou,> 0.35 Jy with the restriction that the sources should have a flat spectrum (v>—0.5) resulting in a total of 193 sources (Taylor et al.", For CJ2 the limit is $S_{5 \rm GHz}\geq$ 0.35 Jy with the restriction that the sources should have a flat spectrum $\alpha>-0.5$ ) resulting in a total of 193 sources (Taylor et al. + 1994: Henstock et al., 1994; Henstock et al. + 1995)., 1995). + The CJF. defined by Taylor et al. (," The CJF, defined by Taylor et al. (" +"1996). is a complete flux-limited VLBI sample of 293 flat-spectrum radio sources. drawn from the 6 em and 20 em Green Bank Surveys (Gregory Condon 1991: White Becker 1992) with selection criteria as follows: $(6 em)> 350 mJy.à$,2—0.5. 0(B1950.0)235*. and |b!|>10°.","1996), is a complete flux-limited VLBI sample of 293 flat-spectrum radio sources, drawn from the 6 cm and 20 cm Green Bank Surveys (Gregory Condon 1991; White Becker 1992) with selection criteria as follows: $S$ (6 $\ge$ $350$ mJy, $\delta $ $\ge $ $^{\circ }$, and $^{\circ}$." + Although the CJF survey is based on surveys made at different epochs it can be regarded as a statistically complete survey (see Taylor et al., Although the CJF survey is based on surveys made at different epochs it can be regarded as a statistically complete survey (see Taylor et al. + 1996. Kühhr et al.," 1996, Kühhr et al." + Optical identifications have been made for 97 of the CJF sample and redshifts obtained for 94 of the objects (Stickel Kühhr 1994: Stickel et al., Optical identifications have been made for 97 of the CJF sample and redshifts obtained for 94 of the objects (Stickel Kühhr 1994; Stickel et al. + 1994; Xu et al., 1994; Xu et al. + 1994; Vermeulen Taylor 1995: Vermeulen et al., 1994; Vermeulen Taylor 1995; Vermeulen et al. + 1996. Vérron-Cetty Vérron 2003).," 1996, Vérron-Cetty Vérron 2003)." + All redshifts now available for CJF are tabulated in Britzen et al., All redshifts now available for CJF are tabulated in Britzen et al. + 2007a. with comments for values not previously The composition of the CJF is 67 quasars. 18 radio galaxies. 11 BL Lae objects. and 3 still unclassified objects.," 2007a, with comments for values not previously The composition of the CJF is 67 quasars, 18 radio galaxies, 11 BL Lac objects, and 3 still unclassified objects." + Between 5 and 10 of the sources (Pearson et al., Between 5 and 10 of the sources (Pearson et al. + 1998) in the CJ samples are (Wilkinson 1995)., 1998) in the CJ samples are (Wilkinson 1995). + An overview summarizing existing investigations of first- and second-epoch observations of subsamples of the CJF with references is given in Pearson et al. (, An overview summarizing existing investigations of first- and second-epoch observations of subsamples of the CJF with references is given in Pearson et al. ( +1998).,1998). + Preliminary results for selected samples of CJF sources have already been published in Vermeulen (1995).," Preliminary results for selected samples of CJF sources have already been published in Vermeulen (1995)," +"[—e""f. may be decomposed as Πο = uus Bo) using the set of spin spherical harmonics «Σμίθ.0). complex-valued functions on the sphere.","$f \rightarrow e^{is\psi}f$, may be decomposed as ) = _s _s ) using the set of spin spherical harmonics ${}_s Y_{l m}(\theta,\phi)$, complex-valued functions on the sphere." + Standard scalar spherical harmonics are represented by s=0: from these we obtain the spin harmonies using spin-raising and lowering operators?)., Standard scalar spherical harmonics are represented by $s=0$; from these we obtain the spin harmonics using spin-raising and lowering operators. +. The decomposition depends on the orthogonality. aud completeness relationships For a band-limited funetion with «άν40 only for /xL. the brute force computation of the transform requires O(L!) operations: roughly. there are ~L? terms in the sum [for each of the ~L? points on the sphere required to Nvquist sample the function.," The decomposition depends on the orthogonality and completeness relationships For a band-limited function with ${}_s a_{lm} \neq 0$ only for $l \leq L$, the brute force computation of the transform requires ${\cal O}(L^4)$ operations: roughly, there are $\sim L^2$ terms in the sum for each of the $\sim L^2$ points on the sphere required to Nyquist sample the function." + In this work. we describe a “fast” translorm. which perlorms the analvsis and svuthesis for spin-s funelions in Q(L) operations on an equiangular grid.," In this work, we describe a “fast” transform, which performs the analysis and synthesis for $s$ functions in ${\cal O}(L^3)$ operations on an equiangular grid." + several methods exist for spin transforms on the sphere. but our method offers some advantages.," Several methods exist for spin transforms on the sphere, but our method offers some advantages." + The algoritm for à scalar spherical harmonic transform scales very. well. as O(L?log?L). and relates the required Legendre (transform to a [ast Fourier transform (FFT) on a specifie equiangular grid.," The algorithm for a scalar spherical harmonic transform scales very well, as ${\cal O}(L^2 \log^2 L)$, and relates the required Legendre transform to a fast Fourier transform (FFT) on a specific equiangular grid." + used (hat method and further relations between (he scalar harmonics and the 5=#2 harmonics. implementing spin transforms at (he same scaling.," used that method and further relations between the scalar harmonics and the $s=\pm 2$ harmonics, implementing spin transforms at the same scaling." + The difficultv with these methods is that they require a large amount of memory (o store precomputed special functions., The difficulty with these methods is that they require a large amount of memory to store precomputed special functions. + These preconputecd functions require OCL) operations and storage. and so spoil (he efficiency. for computing a smele transform. but need to be computed only once. in principle.," These precomputed functions require ${\cal O}(L^3)$ operations and storage, and so spoil the efficiency for computing a single transform, but need to be computed only once, in principle." +In earlier work (Robertson Leiter 9005. hereafter 1102} we extended analyses of magnetic propeller effects (Campana ct al.,"In earlier work (Robertson Leiter 2002, hereafter RL02) we extended analyses of magnetic propeller effects (Campana et al." + 1998. Zhang. Yu Zhang 1998) of neutron stars (NS) in low mass x-ray binarics (LAINDB) to the domain of GDBIIC.," 1998, Zhang, Yu Zhang 1998) of neutron stars (NS) in low mass x-ray binaries (LMXB) to the domain of GBHC." + From the luminosities at the low/high spectral state transitions. accurate rates of spin were found for NS and accurate quiescent Iuminosities were calculated for NS and GBC.," From the luminosities at the low/high spectral state transitions, accurate rates of spin were found for NS and accurate quiescent luminosities were calculated for NS and GBHC." +" The NS magnetic moments were found to be consistent: with. ~LO ""m7€. magnetic ⋠⋅fields. in.. good agreement with those others have found(e.g. Dhattacharya 1995) from spin-clown rates for similarly spinning 200 - ) Hz millisecond. pulsars."," The NS magnetic moments were found to be consistent with $\sim 10^{8 - 9}$ G magnetic fields, in good agreement with those others have found (e.g. Bhattacharya 1995) from spin-down rates for similarly spinning 200 - 600 Hz millisecond pulsars." + GBILC spins were found to be typically Viz., GBHC spins were found to be typically 10 - 50 Hz. +" Their magnetic moments of ~107"" gauss cn’ are ~200 times larger than those of ‘atoll’ class NS(e.g. Burderi et al.", Their magnetic moments of $\sim 10^{29}$ gauss $^3$ are $\sim 200$ times larger than those of `atoll' class NS (e.g. Burderi et al. + 2002. DiSalvo Bureleri 2003).," 2002, DiSalvo Burderi 2003)." +" The implied: magnetic fields of GBIIC are in good agreement with fields of ~ 107€ that have been found at the base of thejets ofGRS 1915|105 ""halrabarti(Ciliozzi. Bodo Chisellini 1999. “- Rao € 2001) and in the accretion disk of Cyvenus N-1 (Cinedin et al."," The implied magnetic fields of GBHC are in good agreement with fields of $\sim 10^8$ G that have been found at the base of the jets of GRS 1915+105 (Gliozzi, Bodo Ghisellini 1999, Vadawale, Rao Chakrabarti 2001) and in the accretion disk of Cygnus X-1 (Gnedin et al." + 2003)., 2003). + At accretion disk inner radii corresponding to the low/high spectral state switch. the magnetic fields of both catoll/ class NS. and ΟΡΙΟ are 75-10 G. which may account for some of their strong similarities(c.g. u et al.," At accretion disk inner radii corresponding to the low/high spectral state switch, the magnetic fields of both `atoll' class NS and GBHC are $\sim 5\times10^7$ G, which may account for some of their strong similarities (e.g. Yu et al." + 2003. Efanaka Shibazaki 1996. van der Ixlis 1994," 2003, Tanaka Shibazaki 1996, van der Klis 1994)." + In later work (Leiter Robertson 2003. Robertson Leiter 2003. hereafter. RLO3) we have cescribed how the Einstein field equations of General Relativity. applied. to compact plasmas with equipartition magnetic fields permit the existence. of magnetic. eternally collapsing objects (MECO) that can have lifetimes in excess of a Hubble time.," In later work (Leiter Robertson 2003, Robertson Leiter 2003, hereafter RL03) we have described how the Einstein field equations of General Relativity applied to compact plasmas with equipartition magnetic fields permit the existence of magnetic, eternally collapsing objects (MECO) that can have lifetimes in excess of a Hubble time." +" These highly redshifted. faintly (as distantly observed. in quiescence) radiating objects can produce ""ultrasoft! thermal peaks and the magnetic propeller cllects found in RLO2."," These highly redshifted, faintly (as distantly observed in quiescence) radiating objects can produce `ultrasoft' thermal spectral peaks and the magnetic propeller effects found in RL02." + spectralHere we examine the accretion disk - magnetosphere interaction and show how the magnetosphere can drive jets., Here we examine the accretion disk - magnetosphere interaction and show how the magnetosphere can drive jets. + Our model should be applicable for any jet producing objects with sullicienthy large magnetic moments. whether T-Tauri stars or NS. or €DIC and active ealactic nuclei (AGN) modeled as MECO.," Our model should be applicable for any jet producing objects with sufficiently large magnetic moments, whether T-Tauri stars or NS, or GBHC and active galactic nuclei (AGN) modeled as MECO." + In this context. the scaling of the magnetic moments of MECO with mass will be an important consideration.," In this context, the scaling of the magnetic moments of MECO with mass will be an important consideration." + As shown in RLOS. the MECO is dominated," As shown in RL03, the MECO is dominated" + , +"follows. We adopt Ti, =26-50 IN (Chinietal.1997:Johnstone 2003).. and X. [IPC] L4x10 ! derived from the comparison of the estimated IICO — column density and the CASO column density (Chinietal.1997) ","follows, We adopt $T_{\rm{ex}}$ =26-50 K \citep{chi97, joh03}, , and $X$ $^{13}$ $^{+}$ ] $\sim$ $\times$ $^{-10}$ derived from the comparison of the estimated $^{13}$ $^{+}$ column density and the $^{18}$ O column density \citep{chi97} ." +Figure ?? shows NALA velocity channel maps in the HPCO (1-0) emission at avelocity interval of 0.26 kins+., Figure \ref{H13_ch} shows NMA velocity channel maps in the $^{13}$ $^{+}$ (1-0) emission at avelocity interval of 0.26 $\rm{km~s^{-1}}$. + The blue-shifted emission. Viag —9.3-9.8 kins ! is seen at the part of the 3 mim dust peak.," The blue-shifted emission, $V_{\rm{LSR}}$ =9.3-9.8 km $^{-1}$ , is seen at the south-western part of the 3 mm dust peak." + Close to the systemic velocity of Vis 10.6 kin 1 the peak position of the blue-shifted enmission shilts [rom south-west to west.," Close to the systemic velocity of $V_{\rm{LSR}}$ =10.6 km $^{-1}$, the peak position of the blue-shifted emission shifts from south-west to west." + The red-shifted emission. Via 10.8-11.5 km |. is seen at the northern part of the 3 mm dust peak.," The red-shifted emission, $V_{\rm{LSR}}$ =10.8-11.5 km $^{-1}$, is seen at the northern part of the 3 mm dust peak." + This velocity gradient along the major axis of the clisk-like envelope implies the rotational motion., This velocity gradient along the major axis of the disk-like envelope implies the rotational motion. + We also note the velocity gradient along the minor axis. i.e. the strong blue-shifted component in the velocity range of Vig 10.2-10.4 kins J| is located at the western part of the protostar. while there appears weak red-shifted extension in the velocity range of Vis 10.6-11.3 km | at the eastern side of the protostar.," We also note the velocity gradient along the minor axis, i.e. the strong blue-shifted component in the velocity range of $V_{\rm{LSR}}$ =10.2-10.4 km $^{-1}$ is located at the western part of the protostar, while there appears weak red-shifted extension in the velocity range of $V_{\rm{LSR}}$ =10.6-11.3 km $^{-1}$ at the eastern side of the protostar." + The fan-shaped structure in the total integrated intensity map of Fieure??) is also confirmed in the velocity. channel maps in the range of Viag = 10.2 -10.4 and 10.8-11.3 kms |., The fan-shaped structure in the total integrated intensity map of $b$ is also confirmed in the velocity channel maps in the range of $V_{\rm{LSR}}$ = 10.2 -10.4 and 10.8-11.3 km $^{-1}$. +" We have also detected a weak 3.3 mm continuum source at 3.8 σ level toward ~ 40"" northeast of MAIS 7 (see Figure οσα: herea fleriecalllhiscomponent M MST—N E).", We have also detected a weak 3.3 mm continuum source at 3.8 $\sigma$ level toward $\sim$ $''$ northeast of MMS 7 (see Figure \ref{cont}$ $a$; hereafter we call this component MMS 7-NE). +"Dhepeakpositionandthe 0535"" 28.5. Dec= -05703'41.1"" (J2000) and 6.81 mJv. respectively. [rom the 2-dimensional Gaussian fitting to the image."," The peak position and the total 3.3 mm flux of this source are estimated to be RA= $^h$ $^m$ $^s$, Dec= $^{\circ}$ $\arcmin$ $\arcsec$ (J2000) and 6.81 mJy, respectively, from the 2-dimensional Gaussian fitting to the image." + This source is also seen as a point source in (he Ixs image. and San and 244m sources taken with theSPITZER/IRAC (see Figure 3).," This source is also seen as a point source in the K's image, and $\mu$ m and $\mu$ m sources taken with the (see Figure 3)." + This source was alsodetected to be a very compact 350 jun dust component byLis et al. (, This source was alsodetected to be a very compact 350 $\mu$ m dust component byLis et al. ( +1983) with CSO. which locates al the southeast of CSO11. although they did not identilv this object.,"1988) with CSO, which locates at the southeast of CSO11, although they did not identify this object." +" The 3.3 mnm continuum flix corresponds to 0.040.830 M..."" 7=0-1.Tag20Is "," The 3.3 mm continuum flux corresponds to 0.04-0.30 $_{\odot}$ $\beta=0-1,~T_{\rm{dust}}~=~20~\rm{K}$ " +The RM values obtained are displayed in Fig. 10..,The RM values obtained are displayed in Fig. \ref{fig:rm}. +" The RM of the core varied from ~—500rad/m? to ~+30rad/n?, then gradually changed back to a negative value of ~—141rad/m?."," The RM of the core varied from $\sim -500 \textrm{\,rad/m}^2$ to $\sim+30 \textrm{\,rad/m}^2$, then gradually changed back to a negative value of $\sim-141 \textrm{\,rad/m}^2$." +" The RM of the jet also exhibited variations, although less pronounced."," The RM of the jet also exhibited variations, although less pronounced." +" Despite the relatively large measurement errors, it appears as if the RM of the core and the jet vary in unison."," Despite the relatively large measurement errors, it appears as if the RM of the core and the jet vary in unison." +" Temporal variability of the RM has been reported for only a few AGNs and on timescales of typically 1 - 3 years: (??),, (?,andreferencestherein) and (?).."," Temporal variability of the RM has been reported for only a few AGNs and on timescales of typically 1 - 3 years: \citep{asada_rm,zavala_rm}, \citep[][and references therein]{zavala_rm} and \citep{gomez_rm}." +" The Faraday screen responsible for the rotation of the EVPA in these sources is understood to be source intrinsic, i.e., either circumnuclear (related to the narrow line region or the torus surrounding the AGN), or internal, meaning that it is physically associated with the jet (e.g.,relatedtoasheatharoundthejet, ?).."," The Faraday screen responsible for the rotation of the EVPA in these sources is understood to be source intrinsic, i.e., either circumnuclear (related to the narrow line region or the torus surrounding the AGN), or internal, meaning that it is physically associated with the jet \citep[e.g., related to a sheath around the jet,][]{inoue_rm}." +" According to ? (and references therein), the internal Faraday rotation causes depolarization in the source."," According to \cite{gomez_rm} (and references therein), the internal Faraday rotation causes depolarization in the source." +" Thus, when the rotation reaches an angle of ~45°, the fractional polarization decreases by a factor of two."," Thus, when the rotation reaches an angle of $\sim 45^\circ$, the fractional polarization decreases by a factor of two." +" This effect is not seen for J1128+592 in our data, therefore an external Faraday screen is more plausible."," This effect is not seen for J1128+592 in our data, therefore an external Faraday screen is more plausible." +" From Fig. 10,,"," From Fig. \ref{fig:rm}," +" it is obvious that the apparent variation in the RM of core and jet exhibit similar trends, despite their projected linear distance of >5 ppc."," it is obvious that the apparent variation in the RM of core and jet exhibit similar trends, despite their projected linear distance of $\geq 5$ pc." + This suggests that the core and jet are both covered by the same Faraday screen., This suggests that the core and jet are both covered by the same Faraday screen. +" The relative offsets between the RM of the jet and core, and the slightly more pronounced variability in the RM of the core component is indicative of a second Faraday screen, which covers only the core region but not the jet."," The relative offsets between the RM of the jet and core, and the slightly more pronounced variability in the RM of the core component is indicative of a second Faraday screen, which covers only the core region but not the jet." +" We tried to decompose the RM into two Faraday screens, one that is common to both core and jet, and causes a similar variability trend throughout our six VLBA epochs (ARM~150rad/m? on a timescale of 5 to 6 months), and a second component, which only affects the core-region of the VLBI structure."," We tried to decompose the RM into two Faraday screens, one that is common to both core and jet, and causes a similar variability trend throughout our six VLBA epochs $\Delta \textrm{RM} \sim 150 \textrm{\,rad/m}^2$ on a timescale of 5 to 6 months), and a second component, which only affects the core-region of the VLBI structure." + This latter Faraday screen causes an RM variation in the core-region of ARM«x300rad/m? on shorter timescales of 1.5 months.," This latter Faraday screen causes an RM variation in the core-region of $\Delta \textrm{RM}\leq 300 \textrm{\,rad/m}^2$ on shorter timescales of 1.5 months." +" At this point, it is obvious that this decomposition is affected by the relatively large measurement uncertainties and should be confirmed by future more finely (in time and frequency) sampled measurements."," At this point, it is obvious that this decomposition is affected by the relatively large measurement uncertainties and should be confirmed by future more finely (in time and frequency) sampled measurements." + We may hypothesize that the screen affecting both components identically could be the same local screen that is responsible for the IDV and the annual modulation., We may hypothesize that the screen affecting both components identically could be the same local screen that is responsible for the IDV and the annual modulation. +" In this case, the observed systematic variation in the RM could be caused by: (i) variations in the parallel component of the interstellar magnetic field Bj, (ii) variation in the electron density n, in the local screen, or (iii) a variation in the path length, i.e., the thickness of the screen with respect to its projection on the ecliptic (orbital plane), or of course, a combination of these three effects."," In this case, the observed systematic variation in the RM could be caused by: (i) variations in the parallel component of the interstellar magnetic field $B_\parallel$, (ii) variation in the electron density $n_e$ in the local screen, or (iii) a variation in the path length, i.e., the thickness of the screen with respect to its projection on the ecliptic (orbital plane), or of course, a combination of these three effects." +" If we attribute most of the observed systematic RM variability to a screen in the nearby galactic ISM, changes in the magnetic field and/or the electron density over spatial scales of shorter than 2 AU (or timescales of a few weeks) would indicate the presence of MHD-turbulence in the ISM."," If we attribute most of the observed systematic RM variability to a screen in the nearby galactic ISM, changes in the magnetic field and/or the electron density over spatial scales of shorter than 2 AU (or timescales of a few weeks) would indicate the presence of MHD-turbulence in the ISM." +" On the other hand, if the magnetic field is homogeneous on scales and frozen in, it will not vary strongly (with neither time nor on AU-size scales)."," On the other hand, if the magnetic field is homogeneous on AU-scales and frozen in, it will not vary strongly (with neither time nor on AU-size scales)." +" The projection angle of the magnetic field (Bj~Bosin(9)), could however in principle vary if the screen is very close, because the Earth orbits the Sun."," The projection angle of the magnetic field $B_\parallel \sim B_0 \sin(\phi)$ ), could however in principle vary if the screen is very close, because the Earth orbits the Sun." +" For a presumed screen distance of ~37 ppc, one expects variations in the projection angle of no more than ~arcsin(2AU/37pc)107? °, which is far too small to cause any significant variation in the RM."," For a presumed screen distance of $\sim 37$ pc, one expects variations in the projection angle of no more than $\sim \arcsin (2 \textrm{AU} / 37 \textrm{pc}) \sim 10^{-5~}~^\circ$ , which is far too small to cause any significant variation in the RM." + It is also difficult to explain a fractional RM variation of A RM ~ 150 rad/m? solely by changes in the path length., It is also difficult to explain a fractional RM variation of $\Delta$ RM $\sim$ 150 $^2$ solely by changes in the path length. +" This points towards a combination of time-variable path length, electron density, and perhaps even magnetic field, in such a way that it would explain the observed systematic RM changes, as illustrated by the 3D-diagram in Fig. 11.."," This points towards a combination of time-variable path length, electron density, and perhaps even magnetic field, in such a way that it would explain the observed systematic RM changes, as illustrated by the 3D-diagram in Fig. \ref{fig:vel}." + We note that this time dependence would be the natural consequence of a refractive lens moving through the line of sight., We note that this time dependence would be the natural consequence of a refractive lens moving through the line of sight. +" These lenses are used to explain the so-called ""extreme scattering events” in some IDV sources (???) and cause systematic intensity variations on timescales of months."," These lenses are used to explain the so-called “extreme scattering events” in some IDV sources \citep{ese_model, ese_model2, ese_model3} + and cause systematic intensity variations on timescales of months." +" ? discuss the geometrical effects of such a lens and mention the possibility of RM variations, which, in their case, were not however detected."," \cite{ese_model} discuss the geometrical effects of such a lens and mention the possibility of RM variations, which, in their case, were not however detected." +" Since the frequency-dependent ""bending"" of the rays by the plasma lens leads to caustics and differential amplification of the (polarized) substructure of the source, it is possible that such a lens also introduces apparent RM variations."," Since the frequency-dependent “bending” of the rays by the plasma lens leads to caustics and differential amplification of the (polarized) substructure of the source, it is possible that such a lens also introduces apparent RM variations." +" The discussion of this possibility, however, is beyond the scope of this paper and deserves a future, more thorough elaboration."," The discussion of this possibility, however, is beyond the scope of this paper and deserves a future, more thorough elaboration." +" The variation in the line-of-sight ""thickness"" of the screen (or the related emission measure, which is ~f neds) should also produce variation in the scattering measure (the line-of- integrated rms electron density) and the related variability index."," The variation in the line-of-sight “thickness” of the screen (or the related emission measure, which is $\sim \int n_e ds$ ) should also produce variation in the scattering measure (the line-of-sight integrated rms electron density) and the related variability index." +" However, the limited accuracy of the variability-index measurements illustrates these variations only very marginally"," However, the limited accuracy of the variability-index measurements illustrates these variations only very marginally" +(sce their figure 2a).,(see their figure 2a). + They plotted. the (two. extremes. of optical depth that can cause a double-peaked. profile to be observed. and. found that they. produce an increase of peak separation of only < 0.1 +.," They plotted the two extremes of optical depth that can cause a double-peaked profile to be observed, and found that they produce an increase of peak separation of only $\leq$ 0.1 $^{-1}$." + Likewise. we find [roni our model that an increase of ~2 in optical depth results in an increase of peak separation of only 70.2 kins+ (c£.," Likewise, we find from our model that an increase of $\sim$ 2 in optical depth results in an increase of peak separation of only $\sim$ 0.2 $^{-1}$ (c.f." + figures 12 and 13 of Ward-Thompson Buckley 2001)., figures 12 and 13 of Ward-Thompson Buckley 2001). + These two numbers can be compared to the dillerences of order ~12 1 caused by increasing. turbulence. as seen in oqFigure I.," These two numbers can be compared to the differences of order $\sim$ 1--2 $^{-1}$ caused by increasing turbulence, as seen in Figure 1." + Thus it can be seen that variations in optical depth will only introduce a small scatter in the observed. peak separation. which is dominated by variations in levels of turbulence.," Thus it can be seen that variations in optical depth will only introduce a small scatter in the observed peak separation, which is dominated by variations in levels of turbulence." + llence we see that the relative evel of turbulence in protostellar envelopes can be estimated. from the relative separation of the two peaks of the classic double-peaked asvmmetrie infall profile., Hence we see that the relative level of turbulence in protostellar envelopes can be estimated from the relative separation of the two peaks of the classic double-peaked asymmetric infall profile. + No other xuameter has such a large ellect on the separation of the two peaks (\Ward-Thompson Buckley 2001)., No other parameter has such a large effect on the separation of the two peaks (Ward-Thompson Buckley 2001). + Even hough the profiles in Figure 1 are calculated. for the specific parameters. Listed above. the same cllect of increasing peak separation with increasing turbulence was seen in al models.," Even though the profiles in Figure 1 are calculated for the specific parameters listed above, the same effect of increasing peak separation with increasing turbulence was seen in all models." + We now use this diagnostic to estimate the relative levels of turbulence in the envelopes of protostars., We now use this diagnostic to estimate the relative levels of turbulence in the envelopes of protostars. + The majority of the data we use are taken from the literature. but data for two accitional sources were obtained.," The majority of the data we use are taken from the literature, but data for two additional sources were obtained." +" L1489 was observed at a position of RA. (1950) = 04 OL” 40.67. Dec. (1950) = | 26° 10’ 49"" and L1448N was observed al à position of R.A. (1950) = 03"" 22"" 318. Dec. (1950) = |30 34' 45""."," L1489 was observed at a position of R.A. (1950) = $^h$ $^m$ $^s$, Dec. (1950) = $+$ $^\circ$ $^\prime$ $^{\prime\prime}$ and L1448N was observed at a position of R.A. (1950) = $^h$ $^m$ $^s$, Dec. (1950) = $+$ $^\circ$ $^\prime$ $^{\prime\prime}$." + Phese observations were carried out at the James Clerk Maxwell Telescope. C(JOCMT) on 2001 August ) using the receiver RxA2 (Davies et al.," These observations were carried out at the James Clerk Maxwell Telescope (JCMT) on 2001 August 10, using the receiver RxA2 (Davies et al." + 1992). with the Dieital Autocorrelation Spectrometer (DAS) backend.," 1992), with the Digital Autocorrelation Spectrometer (DAS) backend." + The DAS was configured with the optimum frequeney resolution of 95kIIz per channel. equivalent to 0.1 .," The DAS was configured with the optimum frequency resolution of 95kHz per channel, equivalent to $\sim 0.1$ $^{-1}$." + This Lope:is very similar to the resolution o£ the literature data that we usce., This is very similar to the resolution of the literature data that we use. + The observations were mace using [requeney switching mocde (Matthews 1996)., The observations were made using frequency switching mode (Matthews 1996). + ALL data reducjon was carried out using the package (Pacman 1990)., All data reduction was carried out using the package (Padman 1990). + ligure 2 shows a tvpical resu0 for one of the +2) spectra., Figure 2 shows a typical result for one of the $^+$ $\rightarrow$ 2) spectra. + We see the two peaks of the line profile. separated hy an absorption dip. and the characteristic infall asymmetric proile.," We see the two peaks of the line profile, separated by an absorption dip, and the characteristic infall asymmetric profile." + From such a spectrum the positions of the red. am blue peaks can be, From such a spectrum the positions of the red and blue peaks can be +Among the chemically peculiar (CP) stars of the upper main sequence. the Lle\In stars constitute some of the objects most intensively studied with a wide range of optical and ultraviolet spectra (summarised by Wahleren 2004)).,"Among the chemically peculiar (CP) stars of the upper main sequence, the HgMn stars constitute some of the objects most intensively studied with a wide range of optical and ultraviolet spectra (summarised by \citealt{wal04}) )." + Phe reasons for this include that: many of these stars are extremely slow rotators. making details of their line profiles easily. studied. for isotopic anomalies. for example: they are not allectecd by strong magnetic fields. which simplifies theoretical considerations: and there are many of these stars bright enough to study with the highest spectral resolutions available.," The reasons for this include that: many of these stars are extremely slow rotators, making details of their line profiles easily studied for isotopic anomalies, for example; they are not affected by strong magnetic fields, which simplifies theoretical considerations; and there are many of these stars bright enough to study with the highest spectral resolutions available." + Most. often these stars have »oen studied individually. but a few studies have considered single elements among a set of stars to determine the overall ohaviour of abundances and isotope distributions as a function of physical variables such as ((for example. Smith1993.1994.1996.1997:&daj 2000)).," Most often these stars have been studied individually, but a few studies have considered single elements among a set of stars to determine the overall behaviour of abundances and isotope distributions as a function of physical variables such as (for example, \citealt{s93,s94,s96,s97,sd93,wl99,db2000}) )." + LIere. we report an analysis of strong unblended ines of the rare noble eas xenon (atomic number 54: cosmic on the scale where 12.00)) with a view to determining its abundance in a sample of llgMn stars.," Here, we report an analysis of strong unblended lines of the rare noble gas xenon (atomic number 54; cosmic on the scale where ) with a view to determining its abundance in a sample of HgMn stars." + As will be shown. Xe is found in nearly all llgMn stars ancl exhibits abundance excesses of 3 dex or more.," As will be shown, Xe is found in nearly all HgMn stars and exhibits abundance excesses of 3 dex or more." + Previous observations of lin the spectra of Le\In stars are scanty. although it was originally reported as a possible identification in 3 Cen A by Jidelman(1962) and a probable identification was reported by Andersen.Jaschek&Cowley(1984). in the He-weak Bp star 66000 which seems to be closely related to the HgMn stars.," Previous observations of in the spectra of HgMn stars are scanty, although it was originally reported as a possible identification in 3 Cen A by \citet{bid62} and a probable identification was reported by \citet*{andersen_etal84} in the He-weak Bp star 6000 which seems to be closely related to the HgMn stars." + More recently. wwas identified in HI 7361 by Adelman(1992): 46 al by Sadakaneetal. (2001): οπο by Rvabchikova&Smirnov (1988): 33 Com by Xdelman.Philip&Adelman(1996):: 112 Her bv livabchikova.Zakharova&Acelman(1996).," More recently, was identified in HR 7361 by \citet{adel92}; 46 Aql by \citet*{sada-etal01}; ; $\kappa$ Cnc by \citet{rs88}; 33 Gem by \citet*{adel-etal96}; 112 Her by \citet*{ryab-etal96}." +. This sparseness may be attributable to the past tendeney to observe these stars mainly in the blue photographie region. where [lines are relatively weak.," This sparseness may be attributable to the past tendency to observe these stars mainly in the blue photographic region, where lines are relatively weak." + For example. Guthrie.(1985) explored Cowlev's Dominion Astrophysical Observatory 4 spectrograms of several HgMn stars but. did. not reportNei.," For example, \citet{guth85} + explored Cowley's Dominion Astrophysical Observatory $^{-1}$ spectrograms of several HgMn stars but did not report." + In this work. the strong lines of απο were A5292.22 ancl A4844.33.. supplemented. by. the weaker A4603.03. visible in most of the programme stars.," In this work, the strong lines of used were $\lambda$ 5292.22 and $\lambda$ 4844.33, supplemented by the weaker $\lambda$ 4603.03 visible in most of the programme stars." + The list of stars analysed for this study is from the paper of Smith&Dworetsky(1993) who originally listed 26 stars., The list of stars analysed for this study is from the paper of \citet{sd93} who originally listed 26 stars. + In Table 1.. two stars are omitted that are not Lle\In stars. 36 Lyn (a magnetic Ap star) and LR 6000. a hot analogue of the LeAIn stars.," In Table \ref{sample}, two stars are omitted that are not HgMn stars, 36 Lyn (a magnetic Ap star) and HR 6000, a hot analogue of the HgMn stars." +Pwo other stars were also omitted. 4 ,"Two other stars were also omitted, $\varphi$ " +through two main observational evidences: (1) the presence of very Lixich stars amone (GC populatious aud (2) the lack of Na auti-correlation (or ο correlation). with the second gencration stars also showing a rather ligh Li content.,"through two main observational evidences: (1) the presence of very Li-rich stars among GC populations and (2) the lack of $-$ Na anti-correlation (or $-$ O correlation), with the second generation stars also showing a rather high Li content." + In a recent work. we focused on ~90 TO stars belonging to the metal-rich GC 1 Tuc: in this case. likely because of the ligh metallicity. a large star-to-star scatter in Li abundances erases aly Na auticorrelation. while Li aud O appear to be only weakly positively correlated (D'Orazi ct al.," In a recent work, we focused on $\sim$ 90 TO stars belonging to the metal-rich GC 47 Tuc: in this case, likely because of the high metallicity, a large star-to-star scatter in Li abundances erases any $-$ Na anticorrelation, while Li and O appear to be only weakly positively correlated (D'Orazi et al." + 2010)., 2010). + The cluster seeumis to display a different behaviour from NGC 6752 aud NCC 6397: for the first one. Pasquini et al. (," The cluster seems to display a different behaviour from NGC 6752 and NGC 6397: for the first one, Pasquini et al. (" +2005) detected a significant Na auticorrelation (and also O correlation aud N anticorrelation).,2005) detected a significant $-$ Na anticorrelation (and also $-$ O correlation and $-$ N anticorrelation). + Coucerning the secoud cluster. the situation seenis more conrplex since Lind et al. (," Concerning the second cluster, the situation seems more complex since Lind et al. (" +2009) detected a quite constant value in Li abuudauces. with oulv three stars (out of 100) driving a lint of Na auticorrelation.,"2009) detected a quite constant value in Li abundances, with only three stars (out of 100) driving a hint of $-$ Na anticorrelation." + Enlaveine the sample of sinmmltaucous determinations of Li and p-capture elements iu CCs is hence of paramount iuportance: m this Letter we preseut Li results on the iutermiediateauetallicity ([Fe/TI|2-1.18:: Carretta et 22009a) cluster NGC 6121 (MI). by analyzing the same suuple of a hundred red giant brauch (ROB) stars studied bv. Marina et 2005].," Enlarging the sample of simultaneous determinations of Li and $p$ -capture elements in GCs is hence of paramount importance: in this Letter we present Li results on the intermediate-metallicity ([Fe/H]=-1.18; Carretta et 2009a) cluster NGC 6121 (M4), by analyzing the same sample of a hundred red giant branch (RGB) stars studied by Marino et (2008)." + As found by Marino and coworkers. ALL hosts two distinct populations of stars. mainly characterized by a clifferent sodiuu conuteut (i.c. the Na-vich aud Na-poor groups). auc defining different sequences on the magnitude diagram C versus (€ B).," As found by Marino and coworkers, M4 hosts two distinct populations of stars, mainly characterized by a different sodium content (i.e., the Na-rich and Na-poor groups), and defining different sequences on the $-$ magnitude diagram $U$ versus $U-B$ )." + We derived Li abundances for the stars »longiue to the two eroups. aud located both below aud above the RGB buup lunuinositv: this evolutionary stage avs a fundamental role in this context.," We derived Li abundances for the stars belonging to the two groups, and located both below and above the RGB bump luminosity; this evolutionary stage plays a fundamental role in this context." + Theoretical models (hen 1967). coufirmmed bv ervatious of ficld stars bv Cratton et al. (," Theoretical models (Iben 1967), confirmed by observations of field stars by Gratton et al. (" +2000). xediet a depletion iu Li due to the first dredge-up (1DUDP) of a factor of ~ 20 at the base of the SB euch.,"2000), predict a depletion in Li due to the first dredge-up (1DUP) of a factor of $\sim$ 20 at the base of the SGB branch." + On the lower RGB. below the bui Iunuinosity. he molecular weight eradieut associated with the IT innudauce Jump acts as a barrier that prevents further (xtra musing (Charbouncl et al.," On the lower RGB, below the bump luminosity, the molecular weight gradient associated with the H abundance jump acts as a barrier that prevents further extra mixing (Charbonnel et al." + 1991): then the Li abundance remains constant until the ROB bump is reached., 1994); then the Li abundance remains constant until the RGB bump is reached. + At this stage. the II shell reaches and cancels this discontinuity aud non-standard mixing processes (unonu-convective oxtramixing. see. e.g. Charbonnel Zahl 2007) cause the total destruction of the remainiug Li.," At this stage, the H shell reaches and cancels this discontinuity and non-standard mixing processes (non-convective extramixing, see, e.g., Charbonnel Zahn 2007) cause the total destruction of the remaining Li." + Our sample consists of LOL ROB stars. whose spectra were acquired with FLAMES on VLT/UT2 (Pasquini et al.," Our sample consists of 104 RGB stars, whose spectra were acquired with FLAMES on VLT/UT2 (Pasquini et al." + 2002) with the fbher link to the ligh-resolution spectrograph UVES (RI~ 10.000).," 2002) with the fiber link to the high-resolution spectrograph UVES $R\sim40,000$ )." + A detailed description of observations. target properties. aud data reduction and derivation of atmospheric parameters is provided in [Ίο et al. (," A detailed description of observations, target properties, and data reduction and derivation of atmospheric parameters is provided in Marino et al. (" +2008).,2008). + Adopting Ikurucz (1993) model atmospheres and using the ROSA abundance code (Catton. 1988). we derived Li abunudauces by menus of a spectral svuthesis of the Li resonance doublet at 6708A.," Adopting Kurucz (1993) model atmospheres and using the ROSA abundance code (Gratton, 1988), we derived Li abundances by means of a spectral synthesis of the Li resonance doublet at 6708." +. We changed the CN values for the two differeut eroups of Na-rich aud Na-poor stars (threshold value at [Na/Fe|=0.2 dex) in order to optimize the svuthesis best fit aud to account for the CN cuhancement iu the Na-rich population (see Alarino ct al., We changed the CN values for the two different groups of Na-rich and Na-poor stars (threshold value at [Na/Fe]=0.2 dex) in order to optimize the synthesis best fit and to account for the CN enhancement in the Na-rich population (see Marino et al. + 2008)., 2008). + Abundances for along with stellar parameters aud metallicity are the ones presented in Marino et al. (, Abundances for along with stellar parameters and metallicity are the ones presented in Marino et al. ( +2008).,2008). + Concerning Li abundance. error estimates have been computed in the same fashion as described in D'Orazi et al. (," Concerning Li abundance, error estimates have been computed in the same fashion as described in D'Orazi et al. (" +2010). taking into account both stellar parameter and best-fit uncertainties: for errors in Na Giuternal aud systematic). we refer the reader to Miro et al. (,"2010), taking into account both stellar parameter and best-fit uncertainties; for errors in Na (internal and systematic), we refer the reader to Marino et al. (" +2008).,2008). + Stellar parameters and abundances are given in Table 1 (completely available in electronic version through CDS)., Stellar parameters and abundances are given in Table \ref{t:tab1} (completely available in electronic version through CDS). + Tn Figure 1.. we show the Li abundances as a function of the absolute magnitude A for all our sample stars: as expected. Li disappears above the bump lhuuinositv (Ay 000.10. Ferraro et al.," In Figure \ref{f:limag}, we show the Li abundances as a function of the absolute magnitude $M_{\rm V}$ for all our sample stars: as expected, Li disappears above the bump luminosity $M_{\rm V}$ $-$ $\pm$ 0.10; Ferraro et al." + 1999)., 1999). + If we focus ou the region below the bump level (at the left side of the dashed line iu Figure 1)). there is no systematic difference in Li abuudances between Na-rich (filled squares) and Na-poor stars (o1upty svinbols).," If we focus on the region below the bump level (at the left side of the dashed line in Figure \ref{f:limag}) ), there is no systematic difference in Li abundances between Na-rich (filled squares) and Na-poor stars (empty symbols)." + However. when we look at the diagram as a whole we can see a differeut drop in the Li content with magnitude for the wo populations.," However, when we look at the diagram as a whole we can see a different drop in the Li content with magnitude for the two populations." +" Specifically, while Li secus to lave a geutle decrease with luminosity for the Na-poor stars. he Na-vich group presents a very abrupt decline. ie. at the πλ huninosity Li suddenly disappears."," Specifically, while Li seems to have a gentle decrease with luminosity for the Na-poor stars, the Na-rich group presents a very abrupt decline, i.e., at the bump luminosity Li suddenly disappears." + This act. which reflects different timescales for mixing aud renee for Lidepletion®.. suggests a structural differeuce οποσα Na-rich aud Na-poor stars: however. uo current heoretical model predicts such a behavior aud we cannot provide a satisfactory explanation to date.," This fact, which reflects different timescales for mixing and hence for Li, suggests a structural difference between Na-rich and Na-poor stars; however, no current theoretical model predicts such a behavior and we cannot provide a satisfactory explanation to date." + Iu this contest. we mention that the so-called “thermohaline uixius has been proposed responsible for uou-canonical wining acting at the RGB bump (sec. e.g.. Egeletou et al.," In this context, we mention that the so-called “thermohaline mixing"" has been proposed responsible for non-canonical mixing acting at the RGB bump (see, e.g., Eggleton et al." + 2007: Charbounel Zahn 2007)., 2007; Charbonnel Zahn 2007). + Egeletou aud coworkers suggested that the molecular weight inversion created. by the Πο Πορ) Πο reaction could be the cause of such a musing: why Na-vich aud Na-poor stars should be differeutially affected by this kind of mixing is not obvious and our result could be the input for further theoretical aud observational iuvestigatious in this direction., Eggleton and coworkers suggested that the molecular weight inversion created by the $^3$ $^3$ $p$ $^4$ He reaction could be the cause of such a mixing: why Na-rich and Na-poor stars should be differentially affected by this kind of mixing is not obvious and our result could be the input for further theoretical and observational investigations in this direction. + By considering oulv the stars fünter than the buup huuinositvy. we show Li abundances as a functiou of Na in Figure 2: ax one can sec. there is no Na auti-correlation. with second ecneration stars 0.2 dex) sharing the same Li content of the primordial population.," By considering only the stars fainter than the bump luminosity, we show Li abundances as a function of Na in Figure \ref{f:lina}: as one can see, there is no $-$ Na anti-correlation, with second generation stars $>$ 0.2 dex) sharing the same Li content of the primordial population." + As an example. we show iu Figue 23 the spectra. around the Li regiou. for the two most extreme cases in Na abuudauces.," As an example, we show in Figure \ref{f:spec} the spectra, around the Li region, for the two most extreme cases in Na abundances." +" The two stars. with 0.02 aud [Na/Fe|210.13. respectively, show identical Li features (uote that the stars have very sila parameters. and the same line y.reneth reflects the same Li abundance)."," The two stars, with $-$ 0.02 and [Na/Fe]=+0.43, respectively, show identical Li features (note that the stars have very similar parameters, and the same line strength reflects the same Li abundance)." + The average Li abundances are loga( Liy=1.336£0.023 (ius 0.062) anc logo(Li) 1.987z50.038. Gus 0.136). respectively for," The average Li abundances are $\log{n{\rm (Li)}}$ $\pm$ 0.023 (rms 0.062) and $\log{n{\rm (Li)}}$ $\pm$ 0.038 (rms 0.136), respectively for" +witattehara.gsu.eddu In order (o avoid excessive photon collisions. the highlv. variable TeV emission from blazars has been interpreted in terms of inverse Compton radiation emerging from ultrarelativistic jets with bulk Lorentz factors. D15—LOO (e.g.. INyawczvnski. Coppi Aharonian 2002: Piner Edwards 2004: Ghisellini. Taveechio Clhiaberge 2004).,"du} In order to avoid excessive photon–photon collisions, the highly variable TeV emission from blazars has been interpreted in terms of inverse Compton radiation emerging from ultrarelativistic jets with bulk Lorentz factors, $\Gamma \sim 15-100$ (e.g., Krawczynski, Coppi Aharonian 2002; Piner Edwards 2004; Ghisellini, Tavecchio Chiaberge 2004)." + Earlier. very high values of P (~ 100) were inferred from the intraday radio variability (IDV) which is a common feature of blazars (Wagner Witzel 1995: Kraus et 22003).," Earlier, very high values of $\Gamma$ $\sim 100$ ) were inferred from the intraday radio variability (IDV) which is a common feature of blazars (Wagner Witzel 1995; Kraus et 2003)." + It now appears that the bulk of this IDV may arise from interstellar scintillations (e.g.. INedziora-Cihiudezer et 22001: Bienall et 22003).," It now appears that the bulk of this IDV may arise from interstellar scintillations (e.g., Kedziora-Chudczer et 2001; Bignall et 2003)." + Nonetheless. (he required microarcsecond angular sizes of the scintillating components would still need Po30. and probably substantially larger. in order to reconcile apparent brightness temperatures. Ty~LOM tly (Dlandford 2002: Rickett et 22002) with the canonical limit of Ty< 10151 needed to avoid the inverse Compton cabastrophe (e.g.. Ixellernann Pantiny-Toth 1969).," Nonetheless, the required microarcsecond angular sizes of the scintillating components would still need $\Gamma > 30$, and probably substantially larger, in order to reconcile apparent brightness temperatures, $T_B \sim 10^{13-14}$ K (Blandford 2002; Rickett et 2002) with the canonical limit of $T_B < 10^{12}$ K needed to avoid the inverse Compton catastrophe (e.g., Kellermann Pauliny-Toth 1969)." + Direct evidence for high values of T5 comes from the VSOP survey (IIoriuchi et 22004)., Direct evidence for high values of $T_B$ comes from the VSOP survey (Horiuchi et 2004). + Standard models for gamma-ray bursts also invoke bulk ultrarelativistic jet flows with P100—1000 (e.g.. Sari. Piran IHHalpern 1999: Mésszárros 2002).," Standard models for gamma-ray bursts also invoke bulk ultrarelativistic jet flows with $\Gamma \sim 100-1000$ (e.g., Sari, Piran Halpern 1999; Mésszárros 2002)." + In contrast. (he only. direct probe of extragalactie jet motion. namely the radio knots detected by Very Long Baseline Interferometry (WLBI). reveal typical proper motions corresponding lo apparent speeds. Capp=c3;55. OL 106 or less (Jorstad οἱ 22001: Cohen οἱ 22003: Giovannini 2003).," In contrast, the only direct probe of extragalactic jet motion, namely the radio knots detected by Very Long Baseline Interferometry (VLBI), reveal typical proper motions corresponding to apparent speeds, $v_{app} \equiv c\beta_{app}$, of $c$ or less (Jorstad et 2001; Cohen et 2003; Giovannini 2003)." + Recent measurements have shown that roughly one-third to one-half of the VLBI components measured in TeV blazars are found to be subluminal or even essentially stationary (Piner Edwards 2004; Girolettii et 22004)., Recent measurements have shown that roughly one-third to one-half of the VLBI components measured in TeV blazars are found to be subluminal or even essentially stationary (Piner Edwards 2004; Giroletti et 2004). + As emphasized by Piner Edwards (2004). the apparent lack of relativistically moving shocks (hat are assumed to be responsible," As emphasized by Piner Edwards (2004), the apparent lack of relativistically moving shocks that are assumed to be responsible" +the line of sight than 0.3.,the line of sight than $-$ 0.3. + It is this new. more-complicated situation which motivates us to reconsider the distance to 0.3 (aud by extension aand 20) iu the light of previous work by Corbel et al. (," It is this new, more-complicated situation which motivates us to reconsider the distance to $-$ 0.3 (and by extension and ) in the light of previous work by Corbel et al. (" +1997) and Blu et al. (,1997) and Blum et al. ( +2001) as well as new observations.,2001) as well as new observations. + Iu this paper. we present newer. higher velocity -resolution CO spectroscopy towards aand its associated radio nebula0.3.. and also towards 2 (out of 3) ofthe brightest iregious of W31.," In this paper, we present newer, higher velocity -resolution $CO$ spectroscopy towards and its associated radio nebula, and also towards 2 (out of 3) of the brightest regions of W31." + We also preseut the ΑΠ. absorption sSpectruni originally mentioned iu C'orbe et al. (, We also present the $NH_3$ absorption spectrum originally mentioned in Corbel et al. ( +1997).,1997). + We then add. hieher-resolution. infrare spectroscopic observations of the LBV star at the ceuter of 0.3., We then add higher-resolution infrared spectroscopic observations of the LBV star at the center of $-$ 0.3. + Iu Section 2. we present the observations auc cata reduction as well as the iain results from our observations.," In Section 2, we present the observations and data reduction as well as the main results from our observations." + In Section 3. we use these data to derive a robust distance estimate for aand0:3.," In Section 3, we use these data to derive a robust distance estimate for and." +.. We then discuss du some detail the nupliceatious of this distance for aad20. as well as the structure of W31 as a whole.," We then discuss in some detail the implications of this distance for and, as well as the structure of W31 as a whole." + Finally. iu Section 1 sve preseut our conclusions.," Finally, in Section 4 we present our conclusions." + Following the work by Corbel et al. (, Following the work by Corbel et al. ( +1997). we obtained rew anillimeter observations with the 15 m Swedish-ESO Subuullimeter Telescope (SEST) at La Silla. Chile. ou 1998 Aueust 27 and 1999 March 2.,"1997), we obtained new millimeter observations with the 15 m Swedish-ESO Submillimeter Telescope (SEST) at La Silla, Chile, on 1998 August 27 and 1999 March 2." + We took spectra at i6 position of LBV 1806-20. (same as in Corbel et al., We took spectra at the position of LBV 1806-20 (same as in Corbel et al. + 1997) at the transitious “CO(J=10) and PCO(J210j Or a total inteeratiou ine of 5 minutes cach (Fig., 1997) at the transitions $^{12}$ CO(J=1–0) and $^{13}$ CO(J=1–0) for a total integration time of 5 minutes each (Fig. +a. 2)., 2). +- As ιο fullewidth at παπια (FWOAD beannidth of 16 SEST is aat ~ 115 CIIz. the spectra toward aalso iuclude the region of 20.," As the full-width at half-maximum (FWHM) beamwidth of the SEST is at $\sim$ 115 GHz, the spectra toward also include the region of ." + Additionally. at 2CO(J=L0) we made spectral observations towardstwo," Additionally, at $^{12}$ CO(J=1–0) we made spectral observations towardstwo" +If ADAFs are present in the DL Lac objects. there is a maximal jet power for a given black hole mass due to an upper limit on the accretion rate inj for an ADAF Y11995).,"If ADAFs are present in the BL Lac objects, there is a maximal jet power for a given black hole mass due to an upper limit on the accretion rate $\dot{m}_{\rm crit}$ for an ADAF \citep{ny95}." +. Compared with the standard disk ease. ADAFs have much stronger magnetic field strength (Livio.Ogilivie.&Pringle1999;ArmitageNatarajan1999).," Compared with the standard disk case, ADAFs have much stronger magnetic field strength \citep{l99,an99}." +. We found in Fig., We found in Fig. + that the power of jets in all sources is less than 0.01.μμ., \ref{fig2} that the power of jets in all sources is less than $0.01~L_{\rm Edd}$. + The power of the jets in most sources Can be explained by the Dlandford-Znajek mechanism if an ADAF is surrounding a rapiclly spinning black hole at an accretion rate i=0.01. while six sources with jel power hieher (han the maximal jet power in (he case of e=0.95.," The power of the jets in most sources can be explained by the Blandford-Znajek mechanism if an ADAF is surrounding a rapidly spinning black hole at an accretion rate $\dot{m}=0.01$, while six sources with jet power higher than the maximal jet power in the case of $a=0.95$." + The jets in (hese six sources may be powered by the Blandford-Pavne mechanism from the ADAFs (e.g. ADIOS proposed by Blanclord Begelmann 1999)., The jets in these six sources may be powered by the Blandford-Payne mechanism from the ADAFs (e.g. ADIOS proposed by Blandford Begelmann 1999). + Another possibility may be that the critical accretion rate Ment Is higher (han 0.01., Another possibility may be that the critical accretion rate $\dot{m}_{\rm crit}$ is higher than $0.01$. + If the critical accretion rate is 0.1. (he power of jets in all sources can be explained in the lrame of the Dlandford-Znajek mechanism for ADAFs surrounding rapidly spinning black holes.," If the critical accretion rate is $0.1$, the power of jets in all sources can be explained in the frame of the Blandford-Znajek mechanism for ADAFs surrounding rapidly spinning black holes." + For given black hole mass. (here is an upper limit on the optical continuum emission [from an ADAF (Cao2002a).," For given black hole mass, there is an upper limit on the optical continuum emission from an ADAF \citep{cao02a}." +. As the radiative efficienev of ADAF is verv low. even the maximal optical continuum luminosity of an ADAF is much fainter than the standard accretion disk at the same accretion rate.," As the radiative efficiency of ADAF is very low, even the maximal optical continuum luminosity of an ADAF is much fainter than the standard accretion disk at the same accretion rate." + We test ADAF scenario in Fig. 6..," We test ADAF scenario in Fig. \ref{fig3}," + and found that the pure ADAF model is unable to produce sulficient optical ionizing emission derived from U]-line enussion for all sources (see the dash-dotted line in Fig., and found that the pure ADAF model is unable to produce sufficient optical ionizing emission derived from -line emission for all sources (see the dash-dotted line in Fig. + 3)., 3). + The optical continuum emission from three sources 08258+493. 0851+202. and 2240—260 can be explained as emission from standard disks accreting al n=0.01 to 0.1 respectively. which is consistent with the fact (hat milly the jets in these three sources nay. be produced by the Blandlord-Pavne mechanism for standard disks (see Fig. 1)).," The optical continuum emission from three sources $0828+493$, $0851+202$, and $2240-260$ can be explained as emission from standard disks accreting at $\dot{m}=0.01$ to $0.1$ respectively, which is consistent with the fact that only the jets in these three sources may be produced by the Blandford-Payne mechanism for standard disks (see Fig. \ref{fig1}) )." + For the remainder. we propose their optical continuum emission to be produced by the ADAF--SD svstems.," For the remainder, we propose their optical continuum emission to be produced by the $+$ SD systems." + The optical continuum Iuminositv. of the ADAF+SD svstem is available as a funetion of black hole mass m. while the accretion rate mi and (he transition radius rq are specilied.," The optical continuum luminosity of the $+$ SD system is available as a function of black hole mass $m$, while the accretion rate $\dot m$ and the transition radius $r_{\rm tr}$ are specified." + Such calculations presented in Fie., Such calculations presented in Fig. + 6 show that the optical ionizing continuum emission from these DL Lac objects can be explained bv ve ADAF+SD model. if 7j are in the range of 40 to 150 for i=0.01.," \ref{fig3} show that the optical ionizing continuum emission from these BL Lac objects can be explained by the $+$ SD model, if $r_{\rm tr}$ are in the range of $40$ to $150$ for $\dot{m}=0.01$." + We also calculate je Cases of dx=O.L. though it is still unclear whether an ADAF ean exist in the inner region of the disk for such a high acceretion rate.," We also calculate the cases of $\dot{m}=0.1$, though it is still unclear whether an ADAF can exist in the inner region of the disk for such a high accretion rate." + We find (that the transition radii are in the range of 100—400 [or i»=0.1., We find that the transition radii are in the range of $100-400$ for $\dot{m}=0.1$. + The jets in these DL Lac objects may be accelerated. by either the Blandlord-Znajek mechanism or the Blandlord-Pavne mechanism (or by both two mechanisms) from the inner ADAF region. while the optical ionizing continuum emission is mainlv from the outer standard disk region.," The jets in these BL Lac objects may be accelerated by either the Blandford-Znajek mechanism or the Blandford-Payne mechanism (or by both two mechanisms) from the inner ADAF region, while the optical ionizing continuum emission is mainly from the outer standard disk region." + For adiabatie inflow-outfllow solutions (ADIOSs) (Dlandford&Begelman1999).. the accretion rate of the disk is a [function of radius r instead of a constant accretion rate along r for à pure ADAF.," For adiabatic inflow-outflow solutions (ADIOSs) \citep{bb99}, the accretion rate of the disk is a function of radius $r$ instead of a constant accretion rate along $r$ for a pure ADAF." + The ADIOS is described bv the similar equations for an ADAF. while a," The ADIOS is described by the similar equations for an ADAF, while a" +We would like to thank the referee for the constructive comments and for the help in improving the presentation of this work.,We would like to thank the referee for the constructive comments and for the help in improving the presentation of this work. + This work is supported by the National Science Foundation (grants 10673034 and 10621303) and National Basic Research Program (973 programs 2007CB815404 and 2009CB824800) of China., This work is supported by the National Science Foundation (grants 10673034 and 10621303) and National Basic Research Program (973 programs 2007CB815404 and 2009CB824800) of China. + DX is at the Dark Cosmology Centre funded by Danish National Research Foundation., DX is at the Dark Cosmology Centre funded by Danish National Research Foundation. + YZF is also supported by Danish National Research Foundation and by Chinese Academy of Sciences., YZF is also supported by Danish National Research Foundation and by Chinese Academy of Sciences. +energy is advected in towards the BLD) and quasi-ractial (i... the [low is geometrically thick. having roughly a spherical structure).,"energy is advected in towards the BH) and quasi-radial (i.e., the flow is geometrically thick, having roughly a spherical structure)." + Our first goal in the present work is to obtain estimations for jet-related quantities. in particular the mass loading. power and Lorentz [factor of the jet. when the DIL rotational energy is transferred. to the disc inside the ergosphere. and then to compare them with those derived from the Blandford-Znajek mechanism.," Our first goal in the present work is to obtain estimations for jet-related quantities, in particular the mass loading, power and Lorentz factor of the jet, when the BH rotational energy is transferred to the disc inside the ergosphere, and then to compare them with those derived from the Blandford-Znajek mechanism." + In the limit of the spin-down power regime. the model proposed. here can be regarded as a variant of the Blandford-Znajek mechanism. where the DII rotational energy. is transferred. to the disc inside the ergosphere rather than transported: to remote astrophysical loads.," In the limit of the spin-down power regime, the model proposed here can be regarded as a variant of the Blandford-Znajek mechanism, where the BH rotational energy is transferred to the disc inside the ergosphere rather than transported to remote astrophysical loads." +" Our second. goal is to determine. the upper limit of the spin parameter attained by a stationary Were BLE when both jet formation and. Bll-cise magnetic connection are considered ancl to investigate how the value of the mass accretion rate can influence the departure of the DII spin parameter from its theoretical maximum limit of (01,—1.", Our second goal is to determine the upper limit of the spin parameter attained by a stationary Kerr BH when both jet formation and BH-disc magnetic connection are considered and to investigate how the value of the mass accretion rate can influence the departure of the BH spin parameter from its theoretical maximum limit of $a_* = 1$. + In Section 2.. we describe the assumptions of the node.," In Section \ref{sec:assumptions}, we describe the assumptions of the model." + In Section 3.. we derive the mass low rate into the jets.," In Section \ref{sec:qjet}, we derive the mass flow rate into the jets." + Using the eeneral-relativistic conservation laws for matter in the accretion disc (Section 4)). we derive the launching power of the jets (Section 5)) and the angular momentunm removed by the jets (Section 6)).," Using the general-relativistic conservation laws for matter in the accretion disc (Section \ref{sec:conserv}) ), we derive the launching power of the jets (Section \ref{sec:jetspower}) ) and the angular momentum removed by the jets (Section \ref{sec:angmom}) )." + In Section 7.. we caleulate the elficicney of launching the jets and show that when the BL aceretes at low rates. the spin-down of the DII is an cllicient mechanism to launch the jets via the aceretion disc.," In Section \ref{sec:efficiency}, we calculate the efficiency of launching the jets and show that when the BH accretes at low rates, the spin-down of the BH is an efficient mechanism to launch the jets via the accretion disc." + 1n Section S.. we study the spin evolution of the BLL and discuss conditions of DII stationary states for given mass accretion rates.," In Section \ref{sec:evolution}, we study the spin evolution of the BH and discuss conditions of BH stationary states for given mass accretion rates." + In Section 9.. we refer to the long lifetime ofan AGN from the 111 spin-down power as a particular relevance of the proposed. model to the observational data.," In Section \ref{sec:relevance}, we refer to the long lifetime of an AGN from the BH spin-down power as a particular relevance of the proposed model to the observational data." + In Section 10.. we present a summary of the key points. as well as our conclusions. and suggest further work to be done.," In Section \ref{sec:summary}, we present a summary of the key points, as well as our conclusions, and suggest further work to be done." +and on the mask usec in the reduction.,and on the mask used in the reduction. + It may be computed. with the orbital elements. when several measurements are available. but. for a single measurement. it. results in. an error of ⋅⋅0.3 kms L. to a rough estimation.," It may be computed with the orbital elements when several measurements are available, but, for a single measurement, it results in an error of 0.3 km $^{-1}$, to a rough estimation." +. In addition to the observations performed. with and withsoprnn. we still obtained 3 measurements from two other telescopes: the Euler telescope with the spectrovelocimeter. in La Silla. and the 1m telescope of the Simeis Observatory in Crimea.," In addition to the observations performed with and with, we still obtained 3 measurements from two other telescopes: the Euler telescope with the spectrovelocimeter, in La Silla, and the 1 m telescope of the Simeis Observatory in Crimea." + Finally. 2275 measurements were obtained for the 66 stars that were selected as variable or probably variable.," Finally, 2275 measurements were obtained for the 66 stars that were selected as variable or probably variable." + The measurements are gatherecl in one plain text file. with one header record. preceding the RW of each star.," The measurements are gathered in one plain text file, with one header record preceding the RV of each star." + Each header contains: Some headers are presented in Table 1.., Each header contains: Some headers are presented in Table \ref{tab:header}. + The headers are followed with the measurement records (Table 2)). which consist oft Some of the header cata are included in Table 3.. where the statistical indicators of variability are also presented.," The headers are followed with the measurement records (Table \ref{tab:mesRV}) ), which consist of: Some of the header data are included in Table \ref{tab:Vmoy}, where the statistical indicators of variability are also presented." + The caleulation of the orbital elements of the SB2 systems requires One to answer the preliminary question: what can we do when the RY of the components are close to the svstemic velocity. anc when only one RV is obtained from the CCE since only one dip is visible?," The calculation of the orbital elements of the SB2 systems requires one to answer the preliminary question: what can we do when the RV of the components are close to the systemic velocity, and when only one RV is obtained from the CCF since only one dip is visible?" + X solution is to fit the ος with two Gaussian curves. assuming the widths and the depth ratio of the CCE components from the observations where they are well separated (Duquennoy1987).," A solution is to fit the CCF with two Gaussian curves, assuming the widths and the depth ratio of the CCF components from the observations where they are well separated \citep{Duquennoy87}." +. However. the RY then obtained are not very reliable in practice.," However, the RV then obtained are not very reliable in practice." + Our idea is then to keep the blended measurements as they are. and to use a simple model to express them as a function of the RY of the components: the orbital elements are then cerived from all the measurements.," Our idea is then to keep the blended measurements as they are, and to use a simple model to express them as a function of the RV of the components; the orbital elements are then derived from all the measurements." + When € is the relative contribution of the primary velocity. 14. to the measured.velocity. Vo. we have the relation: where 15 is the RY of the secondary. component.," When $C$ is the relative contribution of the primary velocity, $V_1$, to the measuredvelocity, $V_0$, we have the relation: where $V_2$ is the RV of the secondary component." + The radial velocities obtained with ancl with are derived. by fitting the CCE with a background. level minus a normal distribution (Barannectal.1979)., The radial velocities obtained with and with are derived by fitting the CCF with a background level minus a normal distribution \citep{Baranne79}. +. When the standard deviations and the depths of the CCE of the components are fixed. Cis a function of AV=[|yVS.," When the standard deviations and the depths of the CCF of the components are fixed, $C$ is a function of $\Delta V_R=|V_1 - V_2|$." + in order to see the shape of that function. we consider a simple example hereafter: the same standard. deviation. mee ue. is assumed. for both correlation dips. and we apply several depth ratios. αοαι.," In order to see the shape of that function, we consider a simple example hereafter: the same standard deviation, $\sigma_{CCF}$ , is assumed for both correlation dips, and we apply several depth ratios, $d_2/d_1$." + We calculate the sum of two normal distributions and the position of the blend. Vo. is derived by fitting to the sum a single normal distribution.," We calculate the sum of two normal distributions and the position of the blend, $V_0$ , is derived by fitting to the sum a single normal distribution." + The value of C'is then derived by inverting equation 1.., The value of $C$ is then derived by inverting equation \ref{eq:V0}. + Phese operations are repeated for several separations between the centers of the two correlation dips. as long as the blended distribution exhibits a sole minimum.," These operations are repeated for several separations between the centers of the two correlation dips, as long as the blended distribution exhibits a sole minimum." + The results are represented in Fig. 1.., The results are represented in Fig. \ref{fig:C_V2}. +" Each line corresponds to a fixed depth ratio. which is οαι=(1L COSCO). where C00) is thevalue ofC when the components’ velocities are nearly the same (ποσα,"," Each line corresponds to a fixed depth ratio, which is $d_2/d_1= (1-C(0))/C(0)$ , where $C(0)$ is thevalue of$C$ when the components' velocities are nearly the same (“nearly”," +"Recently. a ""σα clownsizine” hypothesis (Navakshin2010a) for planet formation was acdvancecl (seealsoBoleyal.2010:Navakshin 2010c.b).","Recently, a “tidal downsizing” hypothesis \citep{Nayakshin10c} for planet formation was advanced \citep[see + also][]{BoleyEtal10,Nayakshin10a,Nayakshin10b}." +. Planets. both rocky and eas giants. are built in this hypothesis very carly on. while the gascous disc is still comparable in mass with the star.," Planets, both rocky and gas giants, are built in this hypothesis very early on, while the gaseous disc is still comparable in mass with the star." + In brick the disc is expected to fragment on gaseous clumps with mass 10 Jupiter masses at LOO AU scales. where radiative cooling is sullicientlv fast.," In brief, the disc is expected to fragment on gaseous clumps with mass $\sim 10$ Jupiter masses at $\sim 100$ AU scales, where radiative cooling is sufficiently fast." + The gas clumps then contract due to radiative cooling., The gas clumps then contract due to radiative cooling. + The contraction. process niv be protracted enough (Navakshin20100). to allow the dust to sediment inside the embryos to make terrestrial planet cores (asproposed.byBoss1998.earlier)..," The contraction process may be protracted enough \citep{Nayakshin10a} to allow the dust to sediment inside the embryos to make terrestrial planet cores \citep[as proposed + by][earlier]{Boss98}." + Finally. embrvos (gas clumps) migrate closer to the star. where heir gaseous envelopes are tidally ancl possibly irracliatively disrupted. leaving behind either rocky cores of terrestrial planets or more massive eas giants.," Finally, embryos (gas clumps) migrate closer to the star, where their gaseous envelopes are tidally and possibly irradiatively disrupted, leaving behind either rocky cores of terrestrial planets or more massive gas giants." + Numerical simulations of massive gas dises by e.g. Vorobvov.&Basu(2006):3olevοἱal.(2010) appear o support the embryo migration part of the hypothesis. while the recent simulation by Cha&Navakshin(2010) ias actually resulted. in a “super-Earth™ solid core being delivered. from ~100 AU to ~S AU.," Numerical simulations of massive gas discs by e.g., \cite{VB06,BoleyEtal10} + appear to support the embryo migration part of the hypothesis, while the recent simulation by \cite{ChaNayakshin10} has actually resulted in a “super-Earth” solid core being delivered from $\sim 100$ AU to $\sim 8 $ AU." + Nevertheless. the numerical simulations of this kind. are in their infancy. and it also remains unclear how robust the results are given that the embryo evolution strongly. depends. on assumed. dust Opacity ancl othe parameters of the problem.," Nevertheless, the numerical simulations of this kind are in their infancy, and it also remains unclear how robust the results are given that the embryo evolution strongly depends on assumed dust opacity and other parameters of the problem." + A supplementary way to test à hypothesis is to consider its least model dependent: predicictions and contrast then to observations., A supplementary way to test a hypothesis is to consider its least model dependent predictions and contrast them to observations. + In this paper we make one such comparison by considering he spins of the planets at birth in the context of the tidal downsizing scheme., In this paper we make one such comparison by considering the spins of the planets at birth in the context of the tidal downsizing scheme. + We point out that gas clumps born in the disc Ivv fragmentation are usually found to rotate in prograde direction with the spin tightly aligned to that of the parent clisc., We point out that gas clumps born in the disc by fragmentation are usually found to rotate in prograde direction with the spin tightly aligned to that of the parent disc. + We show below that rotation of the giant embrvos endows both rocky anc giant planets born inside the embryos with prograde rotation at high. potentially near break-up. rates.," We show below that rotation of the giant embryos endows both rocky and giant planets born inside the embryos with prograde rotation at high, potentially near break-up, rates." + The offsets of planets direction of spin from the disc rotatior iin this scenario is due to embryo-embryo interactions., The offsets of planet's direction of spin from the disc rotation in this scenario is due to embryo-embryo interactions. + We also note that rapid rotation of the inner zones of the emvos implies that rocky planets born there bv AESeravitationa instability may not form single but be in binaries or even multiples., We also note that rapid rotation of the inner zones of the embryos implies that rocky planets born there by gravitational instability may not form single but be in binaries or even multiples. + These predictions are consistent with the observations of the Solar Sysem planets rotation pattern. e.e.. relatively rapid and mainly prograde.," These predictions are consistent with the observations of the Solar System planets rotation pattern, e.g., relatively rapid and mainly prograde." + We also note that the Earth and the Moon would have to be born inside the same giant planet embryo i ‘the tidal downsizing hypothesis is correct., We also note that the Earth and the Moon would have to be born inside the same giant planet embryo if the tidal downsizing hypothesis is correct. + We conclue the paper by noting that despite these encouraging results. there is a whole list of observations (sce 822 compled partly. due to the anonymous referee of this paper) that the tidal downsizing hypothesis needs to be further tested uON.," We conclude the paper by noting that despite these encouraging results, there is a whole list of observations (see \ref{sec:other} compiled partly due to the anonymous referee of this paper) that the tidal downsizing hypothesis needs to be further tested upon." +from these objects for population ages z150.200 Myr) and taking into account three processes: (a) dust forms in the expanding ejecta with a vicld per SNL of 0.5424... CTodini Ferrara 2001: Nozawa et al.,from these objects for population ages $>150-200$ Myr) and taking into account three processes: (a) dust forms in the expanding ejecta with a yield per SNII of $0.54 M_\odot$ (Todini Ferrara 2001; Nozawa et al. + 2003: Bianchi Schneider 2007). (b) SNIL clestrov dust in the ISAL they shock to velocities >100 km {with an ellicienev of 0.12 (Melxee 989) and (ο) a homogeneous mixture of gas and. clust is assimilated into star formation (astration).," 2003; Bianchi Schneider 2007), (b) SNII destroy dust in the ISM they shock to velocities $> 100 $ km $^{-1}$, with an efficiency of 0.12 (McKee 1989), and (c) a homogeneous mixture of gas and dust is assimilated into star formation (astration)." + Once the dust mass is calculated for each galaxv in the simulation. we ranslate this into a value of οV) using the appropriate SN dust extinction. curve given. by Bianchi Schneider (2007) as explained in Daval ct al. (," Once the dust mass is calculated for each galaxy in the simulation, we translate this into a value of $E(B-V)$ using the appropriate SN dust extinction curve given by Bianchi Schneider (2007) as explained in Dayal et al. (" +2010).,2010). + Phe resulting values of £(2V2 for galaxies at 27 are shown in Fig., The resulting values of $E(B-V)$ for galaxies at $z\approx 7$ are shown in Fig. + 3 as à function of the stellar mass.," \ref{ebmv} + as a function of the stellar mass." + Many. galaxies. especially he smallest ones. are almost cust-free. and. none of them. shows a dust reddening value larger than £(BV)=0.009.," Many galaxies, especially the smallest ones, are almost dust-free, and none of them shows a dust reddening value larger than $E(B-V)=0.009$." + This evidence allows us to safely neglect the effects of dust on the UV LE., This evidence allows us to safely neglect the effects of dust on the UV LF. + In addition to predicting the elobal evolution of the LE. a major strength of our study is that it makes possible to extract the physical. properties of the high-: galaxies which are a part of the faint-encl of the LE.," In addition to predicting the global evolution of the LF, a major strength of our study is that it makes possible to extract the physical properties of the $z$ galaxies which are a part of the faint-end of the LF." + We start by concentrating on the stellar ages. reported in Fig.," We start by concentrating on the stellar ages, reported in Fig." + 4 as à function of the UV. magnitude. from. which the following main conclusions can be drawn.," \ref{fig:age} as a function of the UV magnitude, from which the following main conclusions can be drawn." + On average. fainter (and less massive) objects tend to be vounger at all recdshifts. with typical ages for observable objects in the range 200-300 Myr αἲ 2—5ands0-130 MIve at 2=7S. with the caveat that a considerable age spread exists at all luminosities.," On average, fainter (and less massive) objects tend to be younger at all redshifts, with typical ages for observable objects in the range 200-300 Myr at $z=5$ and 80-130 Myr at $z=7-8$, with the caveat that a considerable age spread exists at all luminosities." + These ages imply that these galaxies started to form stars as early as 2=0.4. clearly suggesting that their UV light might have inlluenced the cosmic reionization history.," These ages imply that these galaxies started to form stars as early as $z=9.4$, clearly suggesting that their UV light might have influenced the cosmic reionization history." + From a cilferent perspective. we note that stellar ages of ~100150 Mr are expected Lor galaxies at the sensitivity limit of WEC3 forz-7S in agreement with the observational estimates obtained by Labbé et al. (," From a different perspective, we note that stellar ages of $\sim 100-150$ Myr are expected for galaxies at the sensitivity limit of WFC3 for $z=7-8$, in agreement with the observational estimates obtained by Labbé et al. (" +2010a) ancl Finkelstein ct al. (,2010a) and Finkelstein et al. ( +2010).,2010). + A second important Κον ohvsical parameter of pristine galaxies is their stellar and. οιvs metallicity., A second important key physical parameter of pristine galaxies is their stellar and gas metallicity. + In the following we will only discuss the scHlar metallicity. keeping in mined that the (wo closely match. each other.," In the following we will only discuss the stellar metallicity, keeping in mind that the two closely match each other." + Somewhat surprisingly (but πο unexpectedly) even the faintest galaxies appear to be alreacy enriched to remarkable levels: at the JWST sensitivity threshold. we find Z0.0.7. at all redshifts: galaxies identified ον HST (ALiy< 15) systematically show metallicities in excess of Z=1/10Z. evenat 2:=7SN.," Somewhat surprisingly (but not unexpectedly) even the faintest galaxies appear to be already enriched to remarkable levels: at the JWST sensitivity threshold, we find $Z > 0.03 Z_\odot$ at all redshifts; galaxies identified by HST $M_{UV} < -18$ ) systematically show metallicities in excess of $Z=1/10 Z_\odot$ even at $z=7-8$." + Phus we come to the interesting conclusion that even at these carly epochs. the self-enrichment. due to the metals produced. following the first star formation episodes is able to increase the metal abundances of such small objects to levels comparable to their. present-davy counterparts (e.g. the Alagellanic Clouds).," Thus we come to the interesting conclusion that even at these early epochs, the self-enrichment, due to the metals produced, following the first star formation episodes is able to increase the metal abundances of such small objects to levels comparable to their present-day counterparts (e.g. the Magellanic Clouds)." +" In. addition. such high mean metallicites could. in. principle preclude the formation of Pop LLL stars according to the critical metallicity scenario (Schneider ct al 2002. 2003: Schneider Omulai 2010) which predicts Ζει=10.""tZ. as the upper limit for the formation of Pop LL stars."," In addition, such high mean metallicites could in principle preclude the formation of Pop III stars according to the critical metallicity scenario (Schneider et al 2002, 2003; Schneider Omukai 2010) which predicts $Z_{cr}=10^{-5\pm 1} Z_\odot$ as the upper limit for the formation of Pop III stars." + However. as we will discuss in more detail later. inside these carly structures. small pocket of (quasi) pristine gas may survive in which a relatively tiny amount of Pop HE stars continue to form as pointed out by TESO7 and Jimenez Laiman (2006).," However, as we will discuss in more detail later, inside these early structures, small pocket of (quasi) pristine gas may survive in which a relatively tiny amount of Pop III stars continue to form as pointed out by TFS07 and Jimenez Haiman (2006)." + In brief. the scenario leads to the concept of a “Pop wave. Le. the physical phenomenon by which in each ealaxy the formation of stars below the critical metallicity is progressively segregated towards the external regions of the galaxy. where almost unpollutecl regions are still present.," In brief, the scenario leads to the concept of a ""PopIII wave"", i.e. the physical phenomenon by which in each galaxy the formation of stars below the critical metallicity is progressively segregated towards the external regions of the galaxy, where almost unpolluted regions are still present." + Until this process comes to an end. (νου metal pockets produced: around the first stars forming regions reach a considerable volume filling [actor in the svsteni) Poplll ancl Popll formation modes coexist in the same galaxy.," Until this process comes to an end (when metal pockets produced around the first stars forming regions reach a considerable volume filling factor in the system), PopIII and PopII formation modes coexist in the same galaxy." + One mieht naively think that this process can take longer in large ealaxies than in small ones. but it is (roughly) true only Oo zero-th order approximation. as in lower mass galaxies 10 efficiency. of star formation is also depressed and the unount of time required. once scaled by the barvonie mass of je svstenm. is not dramatically different from that of larger uNslenms.," One might naively think that this process can take longer in large galaxies than in small ones, but it is (roughly) true only to zero-th order approximation, as in lower mass galaxies the efficiency of star formation is also depressed and the amount of time required, once scaled by the baryonic mass of the system, is not dramatically different from that of larger systems." + ‘Taken together. Fig.," Taken together, Fig." +" 4 and 5. provide a first. guess of 16 properties of a typical high-z galaxy with given absolute ""V magnitude Mrs.", \ref{fig:age} and \ref{fig:metal} provide a first guess of the properties of a typical $z$ galaxy with given absolute UV magnitude $M_{UV}$. + This can be useful when comparing 16 observed. photometric data with synthetic SEDs., This can be useful when comparing the observed photometric data with synthetic SEDs. + Fig., Fig. + 6 shows the relation between the SER. and stellar mass of galaxies at 2.=7., \ref{fig:schaerer} shows the relation between the SFR and stellar mass of galaxies at $z=7$. + Simulated objects follow an almost linear relation with significant spread. ic. an almost constant specific star. formation rate.," Simulated objects follow an almost linear relation with significant spread, i.e. an almost constant specific star formation rate." + This trend. closely matches the one found in the analysis of stacked. SEDs of ΝΕΟΣ z-dropout by Labbe et al. (, This trend closely matches the one found in the analysis of stacked SEDs of WFC3 $z$ -dropout by Labbé et al. ( +20100). although a single object analysis reveals large errors in the determination of both the stellar mass and. the SER for these objects (Gonzalez et al.,"2010b), although a single object analysis reveals large errors in the determination of both the stellar mass and the SFR for these objects (Gonzalez et al." + 2010)., 2010). + We note that simulated galaxies tend to have a slightly higher SER. (for a fixed stellar mass) than expected. by the extrapolation of the relation to. smaller objects., We note that simulated galaxies tend to have a slightly higher SFR (for a fixed stellar mass) than expected by the extrapolation of the relation to smaller objects. + However. in a re-analysis of the observed. 2=7 sample including the effect of nebular continuum and line emission along with that of dust absorption. Schaerer cle Barros (2010) find smaller stellar masses anc larger SER with respect to previous works.," However, in a re-analysis of the observed $z=7$ sample including the effect of nebular continuum and line emission along with that of dust absorption, Schaerer de Barros (2010) find smaller stellar masses and larger SFR with respect to previous works." + Our simulated. galaxies lie somewhat in between these two observational estimates., Our simulated galaxies lie somewhat in between these two observational estimates. + Fie., Fig. + 7 shows the evolution of the galaxy properties as à function of redshift for galaxies with cillerent stellar masses., \ref{fig:prop_mass} shows the evolution of the galaxy properties as a function of redshift for galaxies with different stellar masses. + The mean age of stellar population for all galaxies in the simulation is found to decrease with redshift x(1|z)2 however. the age spread increases for less massive galaxies at any redshift.," The mean age of stellar population for all galaxies in the simulation is found to decrease with redshift $\propto (1+z)^{-2}$; however, the age spread increases for less massive galaxies at any redshift." +" Phe average stellar metallicity is also growing with time for AJ,>10'M... but show a much Latter (almost constant) evolution in the smallest objects. leveling at about 1/25 Z. for the tiniest star-forming galaxies."," The average stellar metallicity is also growing with time for $M_*>10^7 M_\odot$, but show a much flatter (almost constant) evolution in the smallest objects, leveling at about 1/25 $Z_\odot$ for the tiniest star-forming galaxies." +" However. even or dwarf galaxies with Al,z10734. one can find individual objects enriched. up to 1/10 of solar metallicity already ab o2=10."," However, even for dwarf galaxies with $M_* \approx 10^5 M_\odot$ one can find individual objects enriched up to $1/10$ of solar metallicity already at $z=10$." + This mass-dependent metallicity evolution is mwobably caused by the cillerent ability to retain metals deposited by supernova explosions of the massive and dwarf »opulations., This mass-dependent metallicity evolution is probably caused by the different ability to retain metals deposited by supernova explosions of the massive and dwarf populations. + As the potential wells of the latter one are shallower. metals escape easily into the intergalactic medium hus setting an upper limit to the amount of metals than can ος kept in their main body (Mac Low Ferrara 1999).," As the potential wells of the latter one are shallower, metals escape easily into the intergalactic medium thus setting an upper limit to the amount of metals than can be kept in their main body (Mac Low Ferrara 1999)." +" An obvious implication is that IGM metals preferentially come rom small and common objects. thus resulting in a more io0mogeneous enrichment (Ferrara, Pettini Shchekinov 2000: Macau. Ferrara Rees 2001)."," An obvious implication is that IGM metals preferentially come from small and common objects, thus resulting in a more homogeneous enrichment (Ferrara, Pettini Shchekinov 2000; Madau, Ferrara Rees 2001)." +radius. the expansion is typically for No — 3 and for N = 3/2.,"radius, the expansion is typically for $N$ = 3 and for $N$ = 3/2." + The dependence of D ou N can be understood in termsof the compressibility y=90logp/op = NCLLN)p. which is larger for NV = 3 than for Vo — 3/2.," The dependence of $D$ on $N$ can be understood in termsof the compressibility $\chi \, = \, +\partial \log \rho/\partial p$ = $N/(1 + N)/p$, which is larger for $N$ = 3 than for $N$ = 3/2." + The larger the compressibility. the larger the deformation.," The larger the compressibility, the larger the deformation." + Tn order to visualize the deformation of the secondary conrpared to the spherical case. Fig.," In order to visualize the deformation of the secondary compared to the spherical case, Fig." + 2. displavs lines of constant density for No = 3 and N = 3/2., \ref{fig3} displays lines of constant density for $N$ = 3 and $N$ = 3/2. + Au inspection of Fig., An inspection of Fig. + 2. shows that the largest departure from spherical svuuuetrv is observed in the outermost lavers of the polytropic star. whereas the ceutral regions are only slightly affected.," \ref{fig3} shows that the largest departure from spherical symmetry is observed in the outermost layers of the polytropic star, whereas the central regions are only slightly affected." + The results displaved in Table 1 are in excellent agreement with the work of Uryu Enguchi (1999). based on a different ummerical method.," The results displayed in Table 1 are in excellent agreement with the work of Uryu Eriguchi (1999), based on a different numerical method." + Iudeed. for N — 3/2 they found distortion effects of ~ for 0.1 «oq xol.," Indeed, for $N$ = 3/2 they found distortion effects of $\sim$ for 0.1 $\le \, q \, \le $ 1." + Thew however did not analyse the case No — 3., They however did not analyse the case $N$ = 3. + A comparison of the nunerical ratio Re/A. where A is the orbital separation. aud the ratio given within the Roche model according to Egeleton (1983) shows simall differences (less than 254)). i agreement with the results of Rezzolla ct al. (," A comparison of the numerical ratio $R_{\rm f}/A$, where $A$ is the orbital separation, and the ratio given within the Roche model according to Eggleton (1983) shows small differences (less than ), in agreement with the results of Rezzolla et al. (" +2001) and confirming indeed that the Roche potential is a good approximation in the present case (the so-called. first assuuption. sce 81).,"2001) and confirming indeed that the Roche potential is a good approximation in the present case (the so-called first assumption, see 1)." + Tn order to analyse the consequences of the distortion effects found in the previous section on period and lass transfer rate mo CV systems. we follow the secular evolution of the secondary using the same models aud input plysics as described iu Ίου Baraffe (1999) aud Baraffe Πο (2000).," In order to analyse the consequences of the distortion effects found in the previous section on period and mass transfer rate in CV systems, we follow the secular evolution of the secondary using the same models and input physics as described in Kolb Baraffe (1999) and Baraffe Kolb (2000)." + We focus on systems below the 2-3 h period gap aud specifically on the miuiuuuu period discrepancybetween observations and models., We focus on systems below the 2-3 h period gap and specifically on the minimum period discrepancybetween observations and models. + Although distortion effects seen to be more importaut for systems above the period gap (P>3 h) (see Tah. 1))," Although distortion effects seem to be more important for systems above the period gap $P > 3$ h) (see Tab. \ref{tab1}) )," + their consequences are difficult to quantify given the large uncertaiuties of evolutionary. models describing such systems. stich as the magnetic braking law aud the resulting mass trauster rate. the evolutionary stage of the secoudary at onset of mass transfer or the mixing Ieneth parameter.," their consequences are difficult to quantify given the large uncertainties of evolutionary models describing such systems, such as the magnetic braking law and the resulting mass transfer rate, the evolutionary stage of the secondary at onset of mass transfer or the mixing length parameter." + Below the period gap. such uncertainties are fortunately considerably reduced (see Daraffe Που 2000: IKolb et al.," Below the period gap, such uncertainties are fortunately considerably reduced (see Baraffe Kolb 2000; Kolb et al." + 2001 for details)., 2001 for details). + Iu the following. we ouly consider the effects of distortion ou the geometry of he system.," In the following, we only consider the effects of distortion on the geometry of the system." + The orbital propertics. e.g. the orbital period aud separation. and the mass transfer rate will be iudeed affected by the larecr effective radius of the donor. estunated in 82. compared to the uucistorted case.," The orbital properties, e.g. the orbital period and separation, and the mass transfer rate will be indeed affected by the larger effective radius of the donor, estimated in 2, compared to the undistorted case." + However. for the moment. we ignore the rotational and tidal effects on the thermal structure of the star. assuining that its immer structure is unaffected and determined by the uuperturbed stellar structure equations iu spherical svunnetry.," However, for the moment, we ignore the rotational and tidal effects on the thermal structure of the star, assuming that its inner structure is unaffected and determined by the unperturbed stellar structure equations in spherical symmetry." + A rough estimate of the thermal effects on he secondarvs properties resulting frou its expansion is derived in the nex section (83.2)., A rough estimate of the thermal effects on the secondary's properties resulting from its expansion is derived in the next section 3.2). + We analyse an evolutionary sequence with au initial donor nias of 0.21 AZ... a primary mass of 0.6 AL... and eravitational radiation (CR) as angular moment loss mechanism (see [Kolb Baratte 1999).," We analyse an evolutionary sequence with an initial donor mass of 0.21 $\msol$, a primary mass of 0.6 $\msol$, and gravitational radiation (GR) as angular momentum loss mechanism (see Kolb Baraffe 1999)." + Frou the radius Ry obtained from integration of the standard stellar structure equations. and the mass ratio q. which varies along the sequence of evolution. the effective radius is derived according to Tab. 1..," From the radius $R_2$ obtained from integration of the standard stellar structure equations, and the mass ratio $q$, which varies along the sequence of evolution, the effective radius is derived according to Tab. \ref{tab1}." + The mass transfer rate is then calculated as a function of the cifference between effective donor radius aud Roche radius. following Ritter (1985).," The mass transfer rate is then calculated as a function of the difference between effective donor radius and Roche radius, following Ritter (1988)." + The comparison between sequences without distortion (solid line) and. with distortion (dashed. line) is shown in the orbital period - effective tenmiperature diaegrai (Fig. D)., The comparison between sequences without distortion (solid line) and with distortion (dashed line) is shown in the orbital period - effective temperature diagram (Fig. \ref{fig4}) ). +" Although reducing the discrepancy with the observed D. distortion effects provide an nmerease of he minimi period P544, of oulv ~ (or 1-5 min). conipared to the uudistorted case."," Although reducing the discrepancy with the observed $P_{\rm min}$, distortion effects provide an increase of the minimum period $P_{\rm turn}$ of only $\sim$ (or $\sim$ 4-5 min), compared to the undistorted case." + This is slightlv less hau what is naivelv expected fromthe period - radius relation Pox(R3My 3, This is slightly less than what is naively expected fromthe period - radius relation $P \propto (R_2^3/M_2)^{1/2}$ . + An increase of the radius winGC. as expected frou distortion effects near the uiiminmnn period (see Tab. 1)).," An increase of the radius by $\sim$, as expected from distortion effects near the minimum period (see Tab. \ref{tab1}) )," + should indeed vield ~ increase of P., should indeed yield $\sim$ increase of $P$. + The snaller effect. found ou P stes roni the dependence of augular monmoenutun loss driven by CGR on the secoudary radius Jes:halxPSOmt ," The smaller effect found on $P$ stems from the dependence of angular momentum loss driven by GR on the secondary radius $\dot J_{\rm GR}/J\, \propto \, P^{-8/3} \, \propto \, R_2^{-4}$." +Consequently. the larger radius in he distorted sequence inplies a decrease of Joy. and thus a smaller mass transfer rate —Mo.," Consequently, the larger radius in the distorted sequence implies a decrease of $\dot J_{\rm GR}$, and thus a smaller mass transfer rate $-\dot M_2$." +" As shown below Pu, depends ou the ratio ro—ἐκται of the secondarvs IxelviuΠοιο time fup aud the mass transfer time fa;=Ας Ma)."," As shown below $P_{\rm turn}$ depends on the ratio $\tau=t_{\rm KH}/t_M$ of the secondary's Kelvin–Helmholtz time $t_{\rm KH}$ and the mass transfer time $t_M = +M_2/(-\dot M_2)$ ." + The decrease of AL thus vields a decrease of 7. nuplving less departure from thermal equilibrium auc thus a smaller Jaan ," The decrease of $-\dot M_2$ thus yields a decrease of $\tau$ , implying less departure from thermal equilibrium and thus a smaller $P_{\rm turn}$ ." +BecauseJan depends explicitly on the mass of the primary. Pau does also depend on it. but ouly weakly.," Because$\dot J_{\rm GR}$ depends explicitly on the mass of the primary, $P_{\rm turn}$ does also depend on it, but only weakly," +"being the smaller distance modulus, providing photometry up to 0.3 magnitudes brighter.","being the smaller distance modulus, providing photometry up to 0.3 magnitudes brighter." +" Considering that subgroup Ic is, at most, as reddened as the ONC by interstellar extinction, we expect that the isochrone shown in also applies to the CMD of subgroup Ic."," Considering that subgroup Ic is, at most, as reddened as the ONC by interstellar extinction, we expect that the isochrone shown in also applies to the CMD of subgroup Ic." +" Thus, we still expect to find in each neighborhood the two main populations discussed above, the least reddened containing both ONC and subgroup Ic members, together with foreground field stars."," Thus, we still expect to find in each neighborhood the two main populations discussed above, the least reddened containing both ONC and subgroup Ic members, together with foreground field stars." +" Therefore, the presence of spurious sources belonging to the Ic subgroup should not affect our computation of the OMC-1 extinction map."," Therefore, the presence of spurious sources belonging to the Ic subgroup should not affect our computation of the OMC-1 extinction map." +" In deriving the OMC-1 extinction map, we model the background sample with the reddened galactic model but neglect any contamination by extragalactic sources."," In deriving the OMC-1 extinction map, we model the background sample with the reddened galactic model but neglect any contamination by extragalactic sources." + We now address the reliability of this assumption., We now address the reliability of this assumption. +" To compute the extragalactic counts model reddened by the OMC-1, we use a deep NIR catalog of galaxies based on SOFI observations in an area of 340 arcmin’, centered on the coordinates RA=3""32’28” and DEC=—27°48’27” (kindly provided by T. communication))."," To compute the extragalactic counts model reddened by the OMC-1, we use a deep NIR catalog of galaxies based on SOFI observations in an area of 340 ${\rm arcmin}^2$, centered on the coordinates $3^h 32^{\prime} 28^{\prime\prime}$ and $-27^{\circ} 48^{\prime} 27^{\prime\prime}$ (kindly provided by T. )." +" At these coordinates, the interstellar galactic extinction is particularly low (SFD98 extinction map provides Ay~ 0.02), entirely negligible compared to the extinction provided by the OMC-1."," At these coordinates, the interstellar galactic extinction is particularly low (SFD98 extinction map provides $A_V\sim 0.02$ ), entirely negligible compared to the extinction provided by the OMC-1." +" Thus, assuming that the distribution of galaxies beyond the OMC-1 is well reproduced by the SOFI catalog, we randomly and uniformly spread the sample of galaxies over the field."," Thus, assuming that the distribution of galaxies beyond the OMC-1 is well reproduced by the SOFI catalog, we randomly and uniformly spread the sample of galaxies over the field." +" Then, assuming that the main source of extinction is provided by the OMC-1, we add the proper amount of extinction based on our map, converting from visible to the infrared wavelengths via the extinction curve given by Cardellietal.(1989): We repeat this procedure 1,000 times, and we average the sample of 1,000 extragalactic CMDs, in order to minimize Statistical fluctuations."," Then, assuming that the main source of extinction is provided by the OMC-1, we add the proper amount of extinction based on our map, converting from visible to the infrared wavelengths via the extinction curve given by \citet{Cardelli00}: We repeat this procedure 1,000 times, and we average the sample of 1,000 extragalactic CMDs, in order to minimize statistical fluctuations." + We find that the reddened extragalactic population accounts for just ~1% of the observed background sample in down to H~17., We find that the reddened extragalactic population accounts for just $\sim$ of the observed background sample in down to $\sim$ 17. +" This is roughly the same fraction of galaxies found by Riccietal.(2008) in their analysis of the deep ACS images of the Orion Nebula, and confirms our hypothesis of negligible extragalactic contamination."," This is roughly the same fraction of galaxies found by \citet{Ricci2008} in their analysis of the deep ACS images of the Orion Nebula, and confirms our hypothesis of negligible extragalactic contamination." +" We also remark that we removed all the galaxies resolved by ACS from the analyzed sample, thus further minimizing the incidence of extragalactic sources."," We also remark that we removed all the galaxies resolved by ACS from the analyzed sample, thus further minimizing the incidence of extragalactic sources." + It is known that most of the extinction toward the Trapezium cluster arises at the interface between the M42 HII region and the neutral diffuse matter (seeO'Dellandreferences therein)., It is known that most of the extinction toward the Trapezium cluster arises at the interface between the M42 HII region and the neutral diffuse matter \citep[see][and references therein]{ODell2009}. +" As indicated by O'Dell&Yusef-Zadeh (2000)., internal extinction may also play a role."," As indicated by \citet{odell2000}, internal extinction may also play a role." +" Aiming at mapping the extinction provided by the diffuse matter in front of the OMC-1 (the Orion Nebula hhereafter), we focus now our attention on the sample of stars which are candidate members of the ONC."," Aiming at mapping the extinction provided by the diffuse matter in front of the OMC-1 (the Orion Nebula hereafter), we focus now our attention on the sample of stars which are candidate members of the ONC." +" ΑΙ these sources have been detected in theJ,, --bands."," All these sources have been detected in the, -bands." + We face now a different set of problems., We face now a different set of problems. +" Whereas one can safely assume that the 2 Myr isochrone provides a relatively accurate locus for the dereddened stellar photospheres, one has to consider the spurious presence of circumstellar matter, disks"," Whereas one can safely assume that the 2 Myr isochrone provides a relatively accurate locus for the dereddened stellar photospheres, one has to consider the spurious presence of circumstellar matter, disks" +frequency within ancl between IF. bands.,frequency within and between IF bands. + SeCealibration with a point source model was used to optimize the phases of the phase refereuc'e calibrator. aud then these phases were applied to the Cassini visibilities.," Self-calibration with a point source model was used to optimize the phases of the phase reference calibrator, and then these phases were applied to the Cassini visibilities." + No self-calibratiou was apσος to the Cassini data., No self-calibration was applied to the Cassini data. + At this state images were mace of both the pliase refereuce source aud Cassini., At this state images were made of both the phase reference source and Cassini. + The piase reference source. by self-calibration. was always located at its sky position.," The phase reference source, by self-calibration, was always located at it's sky position." + We usec Lthe phase calibrator image to verily that a j»oint source model was adequate., We used the phase calibrator image to verify that a point source model was adequate. + ΤΙe location ol the peak signal iu the Cassini uünage was 1jeasured with the AIPS task maxfit and used to shift the image to place Cassini at (or very near ile phase center., The location of the peak signal in the Cassini image was measured with the AIPS task maxfit and used to shift the image to place Cassini at (or very near) the phase center. + Two-dimeusioual quadratic fits to ile peaks iu images of Cassini provide positio|is relative to the nominal phase center with formal errors Uuder 0.02 mas in both coordinates. [ar smaller than our systematic errors.," Two-dimensional quadratic fits to the peaks in images of Cassini provide positions relative to the nominal phase center with formal errors under 0.02 mas in both coordinates, far smaller than our systematic errors." + Tje post-slit baseline phases were examined to verify hat the removal of the position offset hac centered the Cassii signal at theprioir position., The post-shift baseline phases were examined to verify that the removal of the position offset had centered the Cassini signal at the position. + Figu‘es L amd show {1e uushiltecd images of Cassin for all eieht epochs., Figures \ref{fig4} and \ref{fig5} show the unshifted images of Cassini for all eight epochs. + The irst [our epochs. in Figure L. all have large osels [i‘ol the phase center.," The first four epochs, in Figure \ref{fig4}, all have large offsets from the phase center." + This was caused by a oue-second error iu the time sec: when calculatiig the spacecralt position during co‘relation. the resilt of ignoriug a leap secoLd.," This was caused by a one-second error in the time used when calculating the spacecraft position during correlation, the result of ignoring a leap second." + This error was ciscove‘eck in 2008 March. but re-correlation with a cor'ected correlator model was not xpssible because the raw cata recordings were no ouger available.," This error was discovered in 2008 March, but re-correlation with a corrected correlator model was not possible because the raw data recordings were no longer available." + The total delays were unaíected by this offset., The total delays were unaffected by this offset. + The ast [our epochs. in Figure 5.. 5row much simatlle“position ollsets alter the eap second error was fouid and correctect.," The last four epochs, in Figure \ref{fig5}, show much smaller position offsets after the leap second error was found and corrected." + The position ol the peak Cassini signal was measured with respect to its image pliase center. which in tura cle;»euded ou the assumed position of the phase reference source and the geometric moclel.," The position of the peak Cassini signal was measured with respect to its image phase center, which in turn depended on the assumed position of the phase reference source and the geometric model." + Thus. any error in the pliase reference source position produces a correspoucding error in the position of Cassiii.," Thus, any error in the phase reference source position produces a corresponding error in the position of Cassini." + We used the best availablepriori positions lor our pliase relereuce sources curing data analysis. but improved positions have recently become available as part of the ICRE2 catalog (Feyeta.2009).," We used the best available positions for our phase reference sources during data analysis, but improved positions have recently become available as part of the ICRF2 catalog \citep{Fey09}." +. Table 3 shows the ICRE2 position of our primary phase reference sources., Table \ref{tab3} shows the ICRF2 position of our primary phase reference sources. + The maximuui dilfereuce betwee Lourpriori relereuce souce positious aud the ICRE2 positions is 0.16 mas (for JOO3T--LEEE iu right ascension): all other p«sition differences are less than 0.1 mas., The maximum difference between our reference source positions and the ICRF2 positions is 0.16 mas (for J0931+1414 in right ascension); all other position differences are less than 0.1 mas. + Note. however. that the ICRF2 position errors vary by mo'e ian au order of maguitude between sources.," Note, however, that the ICRF2 position errors vary by more than an order of magnitude between sources." + Future observatious will coutinue to improve the less accurate source positions., Future observations will continue to improve the less accurate source positions. +known but less well studied intrahour variables.,known but less well studied intrahour variables. + Note that all are located in regions where multiple clouds are found and (he probability of cloud interactions is high., Note that all are located in regions where multiple clouds are found and the probability of cloud interactions is high. + The differential velocities in these regions are also significant (10 km ! and even as high as 45 km ! )., The differential velocities in these regions are also significant $>$ 10 km $^{-1}$ and even as high as $\sim$ 45 km $^{-1}$ ). + The location of the scintillation sight lines is quite suggestive. but a more stringent test of the connection between scintillation screens and the warm LISM clouds can be achieved using the recently determined velocity vectors of the LISM clouds.," The location of the scintillation sight lines is quite suggestive, but a more stringent test of the connection between scintillation screens and the warm LISM clouds can be achieved using the recently determined velocity vectors of the LISM clouds." + The transverse velocity can now be calculated. and directly. compared to the (transverse [low measured toward local scintillation screens., The transverse velocity can now be calculated and directly compared to the transverse flow measured toward local scintillation screens. + Without a velocity vector. the only observable velocity is the radial component.," Without a velocity vector, the only observable velocity is the radial component." + The velocity components of LISM clouds located along or near the three scintillation sieht lines studied in (his work are listed in Table 1.., The velocity components of LISM clouds located along or near the three scintillation sight lines studied in this work are listed in Table \ref{tab:lismvecs}. + The comparison of scintillation (ranusverse velocities with the transverse velocities of nearby warm LISM clouds is the subject of the following sections., The comparison of scintillation transverse velocities with the transverse velocities of nearby warm LISM clouds is the subject of the following sections. + Observers have characterized the scintillation in fIux density by forming its auto-correlation function and defining a time scale as the time lag where the correlation [alls to half of its (noise-corrected) value at zero lag., Observers have characterized the scintillation in flux density by forming its auto-correlation function and defining a time scale as the time lag where the correlation falls to half of its (noise-corrected) value at zero lag. + When this time scale is plotted against day of vear. an annual variation can be seen for the HIV sources. see Figures 3- 5..," When this time scale is plotted against day of year, an annual variation can be seen for the IHV sources, see Figures \ref{fig:1257}- \ref{fig:1819}." + The HIV itself and the annual variation of ils lime scale are produced by the Earth's motion relative to the scintillation pattern of focused ancl delocusecl waves produced by (he turbulent plasma., The IHV itself and the annual variation of its time scale are produced by the Earth's motion relative to the scintillation pattern of focused and defocused waves produced by the turbulent plasma. + The lime scale for interstellar scintillation. /;4.. is determined by the characteristic spatial scale of the ISS diffraction pattern divided by the fransverse velocity of the Earth relative to the pattern.," The time scale for interstellar scintillation, $t_{\rm iss}$, is determined by the characteristic spatial scale of the ISS diffraction pattern divided by the transverse velocity of the Earth relative to the pattern." +" Two processes cause an annual varlalion i/i, lhe changing velocitv of the Earth relative to the interstellar plasma and the possibility that the diffraction pattern is nol statistically circular but is characterized bv an ellipse with axial ratio “1. geometric mean spatial scale sy... and orientation angle of (he major axis θ with respect to East (through North)."," Two processes cause an annual variation in $t_{\rm iss}$ – the changing velocity of the Earth relative to the interstellar plasma and the possibility that the diffraction pattern is not statistically circular but is characterized by an ellipse with axial ratio $A$, geometric mean spatial scale $s_{\rm iss}$, and orientation angle of the major axis $\theta_{A}$ with respect to East (through North)." + The noncircular diffraction pattern could be produced either by an anisotropic source structure or by anisotropic scattering., The noncircular diffraction pattern could be produced either by an anisotropic source structure or by anisotropic scattering. + Thus both the effective pattern scale aud velocity vary. as the Earth orbits the Sun., Thus both the effective pattern scale and velocity vary as the Earth orbits the Sun. + The algebraic details are as follows., The algebraic details are as follows. + If Vi: is the velocity of (he Earth relative to the Sun on a given dav ancl Vion is (he (unknown) velocity of the interstellar plasma relative to the Sun. we write RA and DEC components of the Earth's transverse velocity relative to the interstellar plasma (and to the scintillation pattern) as:," If $\vec{V}_{\rm E}$ is the velocity of the Earth relative to the Sun on a given day and $\vec{V}_{\rm ism}$ is the (unknown) velocity of the interstellar plasma relative to the Sun, we write RA and DEC components of the Earth's transverse velocity relative to the interstellar plasma (and to the scintillation pattern) as:" +tlt angle appears to be smooth and. continuous over the beat evele.,tilt angle appears to be smooth and continuous over the beat cycle. + Possible recent changes in the structure of the inner lavers of the disk have been also discussed by Oosterbroek et al. (, Possible recent changes in the structure of the inner layers of the disk have been also discussed by Oosterbroek et al. ( +2001). who detected: a rapid spin down in Her X- following an anomalous low state.,"2001), who detected a rapid spin down in Her X-1 following an anomalous low state." + Εις spin down was no accompanied bv a significant simultaneous change in the mass accretion rate (Oosterbroek et al., This spin down was not accompanied by a significant simultaneous change in the mass accretion rate (Oosterbroek et al. + 2001)., 2001). + Instead. 1 was more plausibly associated with changes in the structure of the outer magnetosphere of the neutron star and/or in the inner disk lavers.," Instead, it was more plausibly associated with changes in the structure of the outer magnetosphere of the neutron star and/or in the inner disk layers." + These observations impose importan constraints on any theory modeling the accretion torques and phenomena related. to the inner edge of the disk. in Ler X-1., These observations impose important constraints on any theory modeling the accretion torques and phenomena related to the inner edge of the disk in Her X-1. + The strong emission line at 6.4 keV is detected in all observations. with larger broadening and normalization during the main-on.," The strong emission line at $\sim 6.4$ keV is detected in all observations, with larger broadening and normalization during the main-on." + Past reports of Fe features in the spectra of Her. N-1 include an exposure (Indo et al., Past reports of Fe features in the spectra of Her X-1 include an exposure (Endo et al. + 2000) and a set of 63. observations analvzed by Leahy e al. (, 2000) and a set of 63 observations analyzed by Leahy et al. ( +2001).,2001). + The good. coverage of the beat period allowec Leahy et al. (, The good coverage of the beat period allowed Leahy et al. ( +2001) to undertake a svstematic study of the line variation along the precession cevcle.,2001) to undertake a systematic study of the line variation along the precession cycle. + They. Lounc a broad feature near ~6.5 keV. with the EW varving considerably between main on. short on and low state.," They found a broad feature near $\sim 6.5$ keV, with the EW varying considerably between main on, short on and low state." + The mean values for cach state are 0.48 keV. 0.66 keV. anc ~1.31 keV. respectively.," The mean values for each state are 0.48 keV, 0.66 keV, and $\sim 1.37$ keV, respectively." + Similar correlations are not eviden in the data. where instead an additional Fe XXVI line. possibly a coronal signature. is detected during the low states (sce 6.4)).," Similar correlations are not evident in the data, where instead an additional Fe XXVI line, possibly a coronal signature, is detected during the low states (see \ref{7keV}) )." + Nevertheless. we find evidence lor a significant variation of the line energy over the 35 day period: the Fe line emission originates in near neutral Fe (Fe XIV or colder) in the low and short-on state observations. whereas in the main-on the observed Fe Ίνα centroid energies (6.6520.1 keV and 6.5040.02 keV as measured using PN at Φος=0.02 and 0.17) correspond to Fe NX-Fe ΣΙ (Palmeri et al.," Nevertheless, we find evidence for a significant variation of the line energy over the 35 day period: the Fe line emission originates in near neutral Fe (Fe XIV or colder) in the low and short-on state observations, whereas in the main-on the observed Fe $\alpha$ centroid energies $6.65 \pm 0.1$ keV and $6.50 \pm 0.02$ keV as measured using PN at $\Phi_{35}=0.02$ and 0.17) correspond to Fe XX-Fe XXI (Palmeri et al." + 2003)., 2003). + Phe line centroids observed using the EPIC PN deviate by do from the 6.40 keV neutral value., The line centroids observed using the EPIC PN deviate by $4 \sigma$ from the 6.40 keV neutral value. + This has been already noticed by 102. who suggested three possible explanations for both the line broadening and the centroid displacement: In addition to these possibilities. we also notice that the region responsible for the Fe Ίνα line emission is likely to be different. for lines observed at. dillerent beat. phases.," This has been already noticed by R02, who suggested three possible explanations for both the line broadening and the centroid displacement: In addition to these possibilities, we also notice that the region responsible for the Fe $\alpha$ line emission is likely to be different for lines observed at different beat phases." + The Fe lines have cillerent energies. Dux. and broadening in the main-on compared to the low state.," The Fe lines have different energies, flux, and broadening in the main-on compared to the low state." + While data taken during the main on clearly suggest a correlation between the fluorescent Fe Ixo line and the soft X-ray emission. the sume is not explicitly evident in data taken during the low state.," While data taken during the main on clearly suggest a correlation between the fluorescent Fe $\alpha$ line and the soft X-ray emission, the same is not explicitly evident in data taken during the low state." + At such phases. instead. the line is a [actor 5 weaker ancl is clearly modulated with the orbital period.," At such phases, instead, the line is a factor $>5$ weaker and is clearly modulated with the orbital period." + The correlation between the UV and the neutral be Ix point to a common origin with the fast rise UVWI emission., The correlation between the UV and the neutral Fe K point to a common origin with the fast rise UVW1 emission. + Still. it is hard to distinguish the contributions from the companion and the disk to the Fe Ix line emission.," Still, it is hard to distinguish the contributions from the companion and the disk to the Fe K line emission." + A large contribution from the companion would explain why the Fe Ix line is so strong in the low state of Her N-1 compared to other aceretion disk sources: in Her N-1 the companion is much larger (2.3 A.) than for other LAINBs., A large contribution from the companion would explain why the Fe K line is so strong in the low state of Her X-1 compared to other accretion disk sources: in Her X-1 the companion is much larger (2.3 ) than for other LMXBs. + However. due to the fast rise of the Fe Ix Dux with the orbital phase. the disk origin scenario is still strong.," However, due to the fast rise of the Fe K flux with the orbital phase, the disk origin scenario is still strong." + A possible contribution to the Fe Ίνα emission. may arise from relatively cold material in an accretion cisk wind. such as commonly observed in cataclysmic variables (see e.g. Drew LOOT).," A possible contribution to the Fe $\alpha$ emission may arise from relatively cold material in an accretion disk wind, such as commonly observed in cataclysmic variables (see e.g. Drew 1997)." + Although no consensus has been reached in he case of low-mass X-ray. binaries. in the case of Hor X- evidence of outllowing gas. possibly a wind or material ablated from LZ Her. has been reported by Anderson et al. (," Although no consensus has been reached in the case of low-mass X-ray binaries, in the case of Her X-1 evidence of outflowing gas, possibly a wind or material ablated from HZ Her, has been reported by Anderson et al. (" +1996) and Boroson et al. (,1996) and Boroson et al. ( +2001).,2001). + UV lines observed with the FOS and STIS spectrographs on the »ersist. even in the middle of the eclipse. when the X-ray yeatec atmosphere of the normal star and the accretion disk should be entirely. hidden from view.," UV lines observed with the FOS and STIS spectrographs on the persist even in the middle of the eclipse, when the X-ray heated atmosphere of the normal star and the accretion disk should be entirely hidden from view." + The velocities inferred rom the broadening of the N V lines are not constant over a time scale of ~1 vr. while a comparison between observations taken at Onnery —0.10. 0.21 and 0.29 show hey are stable over the orbital phase.," The velocities inferred from the broadening of the N V lines are not constant over a time scale of $\sim 1$ yr, while a comparison between observations taken at $\phi_{binary}$ =0.10, 0.21 and 0.29 show they are stable over the orbital phase." + Between these phases. he velocity of the neutron star is expected to change by z60 km/s. In this respect we note that the Fe Ίνα line was not been detected by during the micelle of the eclipse. and the upper limit on the line [ux is 19 or less of hat measured outside the eclipse.," Between these phases, the velocity of the neutron star is expected to change by $\approx +60$ km/s. In this respect we note that the Fe $\alpha$ line was not been detected by during the middle of the eclipse, and the upper limit on the line flux is $\sim10$ or less of that measured outside the eclipse." + This in turn sets an upper imit on a potential contribution to the emission of this line » a wind or some sort of circumstellar material., This in turn sets an upper limit on a potential contribution to the emission of this line by a wind or some sort of circumstellar material. + Phere is no Doppler signature of a wind in the LIZIG spectrum of the Le Wl Hine CJimenez-Garate et al., There is no Doppler signature of a wind in the HETG spectrum of the Fe K line (Jimenez-Garate et al. + 2003). and the wind would 1tve to be enclosed by the Roche lobe due to the absence of Ie Ix in eclipse.," 2003), and the wind would have to be enclosed by the Roche lobe due to the absence of Fe K in eclipse." + On the other hand. taken as a body the data reported rere sugeest a complex origin for the overall emission of the ke Ίνα line.," On the other hand, taken as a body the data reported here suggest a complex origin for the overall emission of the Fe $\alpha$ line." + To our knowledge. a complex. of lines which include all ionization states from be NVIIE to NNIV. be Ixo has not been observed in any astrophysical source.," To our knowledge, a complex of lines which include all ionization states from Fe XVIII to XXIV Fe $\alpha$ has not been observed in any astrophysical source." + Γι may still indicate an outflow of relatively cold gas or some, This may still indicate an outflow of relatively cold gas or some +way. but iu lis case the dots represcut the distribution of the poiut« iu he best-fitting simulation that realius a bound core to the present dax.,"way, but in this case the dots represent the distribution of the points in the best-fitting simulation that retains a bound core to the present day." + The boldface dots are the particles that remain bound to Serayo. while the ordinary dots are particles tat were already inbound at that time.," The boldface dots are the particles that remain bound to Sgr, while the ordinary dots are particles that were already unbound at that time." + Note the remarkade similarity with the distribution of the OIIS clusters., Note the remarkable similarity with the distribution of the OHS clusters. +" In particular. the correlation between the particles that have flown in the Ser Stream iu rece times (less than 3 Cor ago) and the ΟΠΣ clusters with [AV.|«601ans latany D, is quite striking."," In particular, the correlation between the particles that have flown in the Sgr Stream in recent times (less than 3 Gyr ago) and the OHS clusters with $|\Delta V_r| < 60\kms$ atany $D_{orb}$ is quite striking." +" We define Np, as the umber of svuthetic or rea clusters having —GOluus|5)= 1630125). PONp.45».=10)110(121). aud Είδοςc11)= 35(28). where the result iu brackets refers to thehigher velocity dispersion model.," For comparison, for a model with $\sigma=110\kms$ (or $\sigma=150\kms$ ) and $V_r=0\kms$, the statistics are as follows: $F(N_{D<6} \ge 5) = 463 (425)$ , $F(N_{D<12} \ge 10) = +140 (121)$, and $F(N_{D<18} \ge 14) = 35 (28)$ , where the result in brackets refers to thehigher velocity dispersion model." + According to these tests using “hbootstrapped” raudon data sets; the observed phase-space clumpingis lighly uulikely to have occurred by chance. in agrecment with our previous test.," According to these tests using “bootstrapped” random data sets, the observed phase-space clumpingis highly unlikely to have occurred by chance, in agreement with our previous test." + The fact that the observed structure has a slightly lower, The fact that the observed structure has a slightly lower +"the flare luminosity should he iL,2LOMeres| (soo Eq. 7)).",the flare luminosity should be $\nu L_\nu\gtrsim10^{46}{\rm erg~s^{-1}}$ (see Eq. \ref{eq:Lmin}) ). + It is obvious from Fig. ," It is obvious from Fig. \ref{fig1}," +or frou comparing Eqs. (5)), or from comparing Eqs. \ref{eq:n_phot_flares}) ) +" aud (18)). that for e./ep~1l the observed uunuber density. of sufficiently: bright sources is much xnaller than the deusitv of active flares required to account for the ΠΟ fux. unless €,./e,,l1."," and \ref{eq:hXLF}) ), that for $\epsilon_e/\epsilon_B\sim1$ the observed number density of sufficiently bright sources is much smaller than the density of active flares required to account for the UHECR flux, unless $\epsilon_e/\epsilon_p\ll1$." +" For vl,molülerss| the uuniber density of active flares js lute to <10HAIpe7. whieh implies based ou Eq. (5))"," For $\nu L_\nu\gtrsim10^{47}{\rm +erg~s^{-1}}$ the number density of active flares is limited to $<10^{-14}{\rm Mpc}^{-3}$, which implies based on Eq. \ref{eq:n_phot_flares}) )" + tha eye.2AOL. aud eQL=A(vLo)teu/e.)zjUAeres 1.," that $\epsilon_p/\epsilon_e\gtrsim10^3(\nu L_\nu)_{47}^{-1}$, and $\epsilon_p L=\Lambda(\nu L_\nu)(\epsilon_p/\epsilon_e) +\gtrsim10^{51}\Lambda_1{\rm erg~s^{-1}}$ ." +" For vL,~l0Merest, the uumuber density of sources appears to be cousisteut with the required muuber density of active flares im Eq. (5))"," For $\nu +L_\nu\sim10^{46}{\rm erg~s^{-1}}$, the number density of sources appears to be consistent with the required number density of active flares in Eq. \ref{eq:n_phot_flares}) )" +" for efe,~OL.", for $\epsilon_e/\epsilon_p\sim0.1$. + However. the X-ray sources identified could be candidate UITECT sources oulv if they are transient. and only a simall fraction of the sources observed are variable.," However, the X-ray sources identified could be candidate UHECR sources only if they are transient, and only a small fraction of the sources observed are variable." + Crupoeetal.(2001). examined 113 bright ROSAT AGN ou a tine scale of ~6 vrs. and found that only 3 showed a factor of LO variation over this time scale (all others varied by a factor less than 3).," \citet{Grupe01} + examined 113 bright ROSAT AGN on a time scale of $\sim6$ yrs, and found that only 3 showed a factor of $10$ variation over this time scale (all others varied by a factor less than 3)." + Similarly. Winter et al. (," Similarly, Winter et al. (" +2008) compared audNRT observations of l7 sources aud fouud fractional variations of onlv a few teus of percent OVOT ~[00 days (see their Table 12). sugeesting that venis.—BY of all hard N-rav sources have a lifetime of--=10 ,"2008) compared and observations of 17 sources and found fractional variations of only a few tens of percent over $\sim 100$ days (see their Table 12), suggesting that $\lesssim 3\%$ of all hard X-ray sources have a lifetime of $\lesssim 10$ years." +This nuüplies that the ummber density of SOUECOS variable on ~5 miu (the typical iuteeration time in the analysis of Cape et al., This implies that the number density of X-ray sources variable on $\sim5$ min (the typical integration time in the analysis of Grupe et al. + 2001 is ~300 8) to ~10 vr time scale is Comparing with Eq. (5)).," 2001 is $\sim300$ s) to $\sim10$ yr time scale is Comparing with Eq. \ref{eq:n_phot_flares}) )," +" this that UIIECR flares must satisfv νε>500 and coustraintimpliese,L=;IUobtainedAeyesd for (v£,jig=1."," this implies that UHECR flares must satisfy $\epsilon_p/\epsilon_e>500$ and $\epsilon_p +L\gtrsim10^{50}\Lambda_1{\rm erg~s^{-1}}$ for $(\nu L_\nu)_{46}=1$." + A similar ls Usus EGRET’s LF., A similar constraint is obtained using EGRET's LF. +" The requirement lde,L—21000Nopes1 nay be avoided if the magnetic fie ene density is mich higher than the electron cuerey deusitv. εερ«1l."," The requirement $\epsilon_p L\gtrsim10^{50}\Lambda_1{\rm erg~s^{-1}}$ may be avoided if the magnetic field energy density is much higher than the electron energy density, $\epsilon_e/\epsilon_B\ll1$." + For ε10 ?. the minima flare huninosity is (Eq. 7))," For $\epsilon_e/\epsilon_B<10^{-2}$ , the minimum flare luminosity is (Eq. \ref{eq:Lmin}) )" +" vL,< and the required umuber density of active N-rayv flares iu Eq. (5))"," $\nu L_\nu<10^{44}{\rm erg~s^{-1}}$ , and the required number density of active X-ray flares in Eq. \ref{eq:n_phot_flares}) )" + is consistent with the umber deusity of variable N-vay sources in Eq. (19)), is consistent with the number density of variable X-ray sources in Eq. \ref{eq:hXLFvar}) ) +" for efe,~ l.", for $\epsilon_e/\epsilon_p\sim1$ . +" The gamma-ray hnuuiuositv is suppressed νεερ with eL,<οσον1. a range in which the uumber density of sources is poorly coustraimed by EGRET."," The gamma-ray luminosity is suppressed by $\epsilon_e/\epsilon_B$ with $\nu L_\nu<10^{42}{\rm erg~s^{-1}}$, a range in which the number density of sources is poorly constrained by EGRET." + Next. we consider the ερO.1 regime.," Next, we consider the $\epsilon_e/\epsilon_B\sim 0.1$ regime." +" Here the jiumuuu fare luminosity is vl,~LdPeres| and the required nunber deusity of active X-ray flares is consistent with the number density of variable N-rav sources for e./e,«10? and with EGRET’s LF for ἐν)€p«103 (uoo Fie. 13)."," Here the minimum flare luminosity is $\nu L_\nu\sim10^{45}{\rm +erg~s^{-1}}$ and the required number density of active X-ray flares is consistent with the number density of variable X-ray sources for $\epsilon_e/\epsilon_p<10^{-2}$ and with EGRET's LF for $\epsilon_e/\epsilon_p<10^{-3}$ (see Fig. \ref{fig1}) )." + As mentioned in 2.. IC enission may be shifted above the observable range (70.1 Te in electroiiagneticallv-dominated outfiows.," As mentioned in \ref{sec:flares}, IC emission may be shifted above the observable range $>0.1$ TeV) in electromagnetically-dominated outflows." +" For €feg~V)Ul aud efe,<10? we eet eyfep>10. which iuplies that the outflow can uot be clectromaguetically doninated."," For $\epsilon_e/\epsilon_B\sim 0.1$ and $\epsilon_e/\epsilon_p<10^{-2}$ we get $\epsilon_p/\epsilon_B>10$, which implies that the outflow can not be electromagnetically dominated." +" This. iu turn. nuplies that the flares should be acconrpanied by observable eamuna-ray enission. aud heuce that efe,<10 nist be satisfied."," This, in turn, implies that the flares should be accompanied by observable gamma-ray emission, and hence that $\epsilon_e/\epsilon_p<10^{-3}$ must be satisfied." +" The preceding that for a flare duration in the range discussionlla=At10 Προςvr. the requirement eyloL=>LP?AcresD quay he avoided= oulv for €,./ep< 2or efe,«105."," The preceding discussion implies that for a flare duration in the range $1{\rm hr}\lesssim\Delta t\lesssim10$ yr, the requirement $\epsilon_p L\gtrsim10^{50}\Lambda_1{\rm erg~s^{-1}}$ may be avoided only for $\epsilon_e/\epsilon_B<10^{-2}$ or $\epsilon_e/\epsilon_p<10^{-3}$." + These constraints are likely to iuprove iu the near future with new 5-1ay data from the recently lanuchedGLAST satellite?.. aud with proposed N-ray telescopes such asEXIST., These constraints are likely to improve in the near future with new $\gamma$ -ray data from the recently launched and with proposed X-ray telescopes such as. + Next. we cousicder ie case of fares with At<>10 vr.," Next, we consider the case of flares with $\Delta t\gg10$ yr." + Since there is little information on source variability ou such time scales. all observed sources are flare candidates.," Since there is little information on source variability on such time scales, all observed sources are flare candidates." +" For Ate""Ape10ου vr. ie active flare number density is >LO5 (soe Eq. 3)."," For $\Delta t\gtrsim 100$ yr, the active flare number density is $>10^{-9}{\rm Mpc}^{-3}$ (see Eq. \ref{eq:n_lim}) )." + At this density. the N-rav LE. requires (see Fig. 1))," At this density, the X-ray LF requires (see Fig. \ref{fig1}) )" +" au Xarav flux pL,οergs1. which implies rough Eq."," an X-ray flux $\nu L_\nu<10^{45}{\rm erg~s^{-1}}$ , which implies through Eq." + 7 that εερ<0.1., \ref{eq:Lmin} that $\epsilon_e/\epsilon_B<0.1$. +" The EGRET LF requires either e;/e,«105 or that the IC eunuicravy cluission be shifted outside the observable range. which uav be possible for fares that are clectromaguetically ominated."," The EGRET LF requires either $\epsilon_e/\epsilon_p<10^{-3}$ or that the IC gamma-ray emission be shifted outside the observable range, which may be possible for flares that are electromagnetically dominated." + There is one important caveat to the above coustraints., There is one important caveat to the above constraints. + The required muuber density of sources is low. XO.1Gpe7. so that that no source is expected to be detected within a distance of ~1 Gpc. which is the GZEK horizon of particles with E~107 eV. This iuples that snapshot surveys can uot provide useful 'onstraimts ou the local (2—0) umber density of high flares.," The required number density of sources is low, $\lesssim 0.1{\rm Gpc^{-3}}$ , so that that no source is expected to be detected within a distance of $\sim1$ Gpc, which is the GZK horizon of particles with $E\sim10^{19}$ eV. This implies that snapshot surveys can not provide useful constraints on the local $z\sim 0$ ) number density of high luminosity flares." + For this reason. the 2~0 LEs shown ..in Fie.," For this reason, the $z\sim 0$ LFs shown in Fig." +" El are not measured directly at hieli Iuninosities. vL,>σοκ+) "," \ref{fig1} are not measured directly at high luminosities, $\nu +L_\nu>10^{45.5}{\rm erg~s^{-1}}$." +Rather. the muuber deusitv of bright sources is measured at a higher redshift aud the local number deusitv is interred from the evolution of the LF with : as measured at lower values of vi.," Rather, the number density of bright sources is measured at a higher redshift and the local number density is inferred from the evolution of the LF with $z$ as measured at lower values of $\nu L_\nu$." +" For example. the nuuber deusitv of soft N-rav sources witli pL,Weres tis measured to be ~5«10.HAIpe.? at z~l1 aud inferred (but not measured) to be much lower than ~LODMpe? at 2~0. based on the LE evolution measured at lower rL, (sec.e.g.Figure5ofIIasiugeretal. 2005)."," For example, the number density of soft X-ray sources with $\nu L_\nu>10^{46}{\rm erg~s^{-1}}$ is measured to be $\sim 5\times10^{-11}{\rm Mpc}^{-3}$ at $z\sim1$ and inferred (but not measured) to be much lower than $\sim10^{-12}{\rm Mpc}^{-3}$ at $z\sim +0$, based on the LF evolution measured at lower $\nu L_\nu$ \citep[see, e.g. Figure 5 of][]{Hasinger05}." +. Loung-teriu monitoring surveys offer nich better prospects for constrainiug the source population than suapshot survevs., Long-term monitoring surveys offer much better prospects for constraining the source population than snapshot surveys. + For example. if the flare duration is a few davs. then a survey that lasts for a vear can put constraints that are ~100 times better than a snapshot survey.," For example, if the flare duration is a few days, then a survey that lasts for a year can put constraints that are $\sim 100$ times better than a snapshot survey." + Upcoming survevs. such as Pau ive expected to provide relevant data soon. and planned surveys such as will provide better constraining power m the future.," Upcoming surveys, such as Pan are expected to provide relevant data soon, and planned surveys such as will provide better constraining power in the future." +" We can not exclude the possibility that the number deusity of flaring somrees with iL,>10cres+ does not decrease towards z~0 as fast as the nunber density of lower rL, sources. and remains at a level of ~5«10.MAtpe% whieh is mareinally consistent with that required for the local production rate per nuit volume of UITECTRs."," We can not exclude the possibility that the number density of flaring sources with $\nu L_\nu>10^{46}{\rm erg~s^{-1}}$ does not decrease towards $z\sim 0$ as fast as the number density of lower $\nu L_\nu$ sources, and remains at a level of $\sim 5\times10^{-11}{\rm +Mpc}^{-3}$, which is marginally consistent with that required for the local production rate per unit volume of UHECRs." +" However. such a scenario is nunatural since it requirestwo colucideuces: the fares ust become a dominant source of οποιον output onlv at pL, l0Éoes+ (or else they would modify the observed LF evolution at lower pjL,).aud exist oulvat 2~0 (or else we would observe them at z 0.5)."," However, such a scenario is unnatural since it requirestwo coincidences: the flares must become a dominant source of energy output only at $\nu +L_\nu>10^{46}{\rm erg~s^{-1}}$ (or else they would modify the observed LF evolution at lower $\nu L_\nu$ ),and exist onlyat $z\sim 0$ (or else we would observe them at $z\gtrsim 0.5$ )." + Tt is difficult to rule out a scenario in which the UITEC'R flares involve “clectromaguetically-dark” or protou only” flares.," It is difficult to rule out a scenario in which the UHECR flares involve ""electromagnetically-dark"" or ""proton only"" flares." + Althouehthere is currently no evidence or physical reasoning to motivate the consideration of a new class of hidden sources. we nevertheless discuss its," Althoughthere is currently no evidence or physical reasoning to motivate the consideration of a new class of hidden sources, we nevertheless discuss its" +Takahara Kusunose. 2001) or a particle injection (e.g. in a relativistic shock) lasting for πέος.,"Takahara Kusunose, 2001) or a particle injection (e.g. in a relativistic shock) lasting for $R/c$." + However the similarity of these two timescales also puts in evidence the inconsistency of the assumed model., However the similarity of these two timescales also puts in evidence the inconsistency of the assumed model. + More precisely if the typical cooling timescale for the particle radiating the bulk of the emission is of the order of the light crossing time. the assumption of steady state for deriving the particle distribution cannot be satisfied.," More precisely if the typical cooling timescale for the particle radiating the bulk of the emission is of the order of the light crossing time, the assumption of steady state for deriving the particle distribution cannot be satisfied." + In such a situation therefore we have to consider a different scenario., In such a situation therefore we have to consider a different scenario. + In this respect two observational facts should be taken into account for the modeling of the emission., In this respect two observational facts should be taken into account for the modeling of the emission. + The variability characterizing blazars in general. and low power BL Laces in particular. indicates that the deposition of energy Is not continuous. but rather suggests a finite time of injection for each typical flare.," The variability characterizing blazars in general, and low power BL Lacs in particular, indicates that the deposition of energy is not continuous, but rather suggests a finite time of injection for each typical flare." + Furthermore the symmetry of the raise and decay of flux in the light curves during flaring episodes. together with the absence of a plateau at constant flux. also," Furthermore the symmetry of the raise and decay of flux in the light curves during flaring episodes, together with the absence of a plateau at constant flux, also" +for sueh highlyoO obscured. sources.,for such highly obscured sources. + Dased on these. ancl assuminge Ecdcdiugtone accretion. we estimate black hole masses of x 105M..," Based on these, and assuming Eddington accretion, we estimate black hole masses of $\sim$ $\times$ $10^8$." +. This is supported by the empirical relation between radio Iuminosity. A/py and accretion rate (Lacyetal.2001). which leads to (Mg) ~ x LO again assuming Eddington accretion.," This is supported by the empirical relation between radio luminosity, $M_{\rm{BH}}$ and accretion rate \citep{lacy01}, which leads to $\langle M_{\rm{BH}}\rangle$ $\sim$ $\times$ $10^8$ $_{\odot}$ again assuming Eddington accretion." + Our sources do nol represent a complete census of massive black holes αἱ 2 2 22. and are likely to experience further growth between then and z ~ 00.," Our sources do not represent a complete census of massive black holes at $z$ $\sim$ 2, and are likely to experience further growth between then and $z$ $\sim$ 0." + With (his in mind. can we reconcile such massive black holes at 2 222 with the space density of massive black holes today?," With this in mind, can we reconcile such massive black holes at $z$ $\sim$ 2 with the space density of massive black holes today?" + The density of our τος 22 heavily obscured radio-Ioud sources is 72733 x 10* 7 , The density of our $z$ $\sim$ 2 heavily obscured radio-loud sources is $\sim$ $\times$ $10^{-7}$ $^{-3}$. +Lauerοἱal.(2007). estimate the space density of black holes with Mp 7 x 105 ((ivpical of our sources) is 233. x LO! ? locally., \citet{lauer07} estimate the space density of black holes with $M_{\rm{BH}}$ $\ge$ $\times$ $10^8$ (typical of our sources) is $\sim$ $\times$ $10^{-4}$ $^{-3}$ locally. + This generous gap between the space densities implies we are not overproducing black holes at z e 22., This generous gap between the space densities implies we are not overproducing black holes at $z$ $\sim$ 2. + Our study lor the first time directly demonstrates (he existence of deep silicate absorption (Tozc 66) radio-Ioud sources at z 22., Our study for the first time directly demonstrates the existence of deep silicate absorption $\tau_{9.7}$ $\sim$ 6) radio-loud sources at $z$ $\sim$ 2. + This is in strong contrast with z z 11 racdio-Ioud populations where none have τοσο 1 (HEaasetal.2005;Ogleetal.2006).," This is in strong contrast with $z$ $\ls$ 1 radio-loud populations where none have $\tau_{9.7}$ $>$ 1 \citep{haas05,ogle06}." + Dhehighobscurationsofoursources. LRbrightandred(& 22). However.highradiofliuresarenolparlofourselec," The high obscurations of our sources is largely a selection bias, as our sample was selected to be mid-IR bright and red 2)." +"tion, andhencethedOY radio-loud [ractionofourhigh— T 10922 sources is a real effect."," However, and hence the radio-loud fraction of our $\tau$ $z$ $\sim$ 2 sources is a real effect." + This implies a direct or indirect coupling between the racio source and surrounding ISM., This implies a direct or indirect coupling between the radio source and surrounding ISM. + Weecimanοἱal.(2006). present a z e 22 saniple similar (o ours. but including a radio selection.," \citet{weedman06} present a $z$ $\sim$ 2 sample similar to ours, but including a radio selection." + A quick analvsis of their sample vields two sources that are both radio-Ioud. and have 797 ; 11. furthersupportingloourresulls.," A quick analysis of their sample yields two sources that are both radio-loud, and have $\tau_{9.7}$ $>$ 1, further supporting to our results." +" The much greater Z4,,445/L1jg ratios of our sources relative to local radio-Ioud sources imply we are observing these sources in the brief window between (he birth of the radio source and belore feedback effects have shed the dustv. envelope and halted the starburst and/or black hole aceretion.", The much greater $L_{14\mu\rm{m}}/L_{1.4\rm{GHz}}$ ratios of our sources relative to local radio-loud sources imply we are observing these sources in the brief window between the birth of the radio source and before feedback effects have shed the dusty envelope and halted the starburst and/or black hole accretion. + Willottetal.(2002) arene that the IR-brightness is anti-correlatecd with the age of the radio source consistent with a radio source-clriven [eedback. scenario., \citet{willott02} argue that the IR-brightness is anti-correlated with the age of the radio source consistent with a radio source-driven feedback scenario. + Given the age of MIPSI5880 (z10* vvis). its radio jets are not necessarily powerful enough to accomplish this.," Given the age of MIPS15880 $\gs$ $10^7$ yrs), its radio jets are not necessarily powerful enough to accomplish this." + But this may be a function of radio luminosity., But this may be a function of radio luminosity. + MIC1138-262. à 2 22.2 radio galaxy more than two orders of magnitude more racdio-Inninous than our sources. does show powerlul outflows. which are probably driven by lateral shocks from the radio jets (Nesvadhaetal.2006)..," MRC1138-262, a $z$ 2.2 radio galaxy more than two orders of magnitude more radio-luminous than our sources, does show powerful outflows, which are probably driven by lateral shocks from the radio jets \citep{outflows_rl}." +. A mid-IR. study of a sample of z ~ 22 radio galaxies. covering a range of radio Iuminosities. would therefore provide very useful constraints on radio jet/ISM interactions al the epoch when radio galaxies are in the process of shedding their dust envelopes.," A mid-IR study of a sample of $z$ $\sim$ 2 radio galaxies, covering a range of radio luminosities, would therefore provide very useful constraints on radio jet/ISM interactions at the epoch when radio galaxies are in the process of shedding their dusty envelopes." + The decade of the seveuties opens with a world of caution., The decade of the seventies opens with a world of caution. + Reviving a poit made by Pauli. a paper by Zumino [35].. suggests that the quantization of GR may be problematic and τσ! make seuse only by viewing GR as the low energy lit of a more ecneral theory.," Reviving a point made by Pauli, a paper by Zumino \cite{zumino}, suggests that the quantization of GR may be problematic and might make sense only by viewing GR as the low energy limit of a more general theory." + Using the technology developed by DeWitt aud Feviuman for gravity. tΠου and Veltman decide to study the renorinalizabilitv of GR.," Using the technology developed by DeWitt and Feynman for gravity, t'Hooft and Veltman decide to study the renormalizability of GR." + Almost as a wari. up exercise. they consider the renormalization of Yang-Mills theory. and find that the theory is renormalizable result that has won then this year Nobel prize [36]..," Almost as a warm up exercise, they consider the renormalization of Yang-Mills theory, and find that the theory is renormalizable – result that has won them this year Nobel prize \cite{t'Hooft71}." + Iu a seuse. oue can say that the first plivsical result of the research In quanti eravitv is the proof that Yaug-Mills theory is renormalizable.," In a sense, one can say that the first physical result of the research in quantum gravity is the proof that Yang-Mills theory is renormalizable." + David Finkelstein writes his inspiring “spacetime code” series of papers Gvhich. amoug others ideas. discuss quantum groups).," David Finkelstein writes his inspiring “spacetime code"" series of papers \cite{Finkelstein} (which, among others ideas, discuss quantum groups)." + Following the program. tΠου fiuds evidence of unareuonualizable divergeuces in GR with matter fields.," Following the program, t'Hooft finds evidence of un-renormalizable divergences in GR with matter fields." + Shortly after. t'ITooft aud. Veltiiau. as well as Deser and Van Nieiveuhuizen. coufina the evidence [38]..," Shortly after, t'Hooft and Veltman, as well as Deser and Van Nieuwenhuizen, confirm the evidence \cite{thooft73}." + IHaskiug announces thederivation of black hole radiation [39].., Hawking announces thederivation of black hole radiation \cite{hawking74}. . + A GQuacroscopically), A (macroscopically) +where are (he astrometric ancl velocity semi-amplitudes [ον (hie two cases. and where designate (he period P and phase o. respectively.,"where are the astrometric and velocity semi-amplitudes for the two cases, and where designate the period $P$ and phase $\phi$, respectively." + One (hen goes on to combine information about (he strs mass and (for astrometry) its distance. to infer the planet mass m (astrometry) or msim? (RV). where 7 is the inclination.," One then goes on to combine information about the star's mass and (for astrometry) its distance, to infer the planet mass $m$ (astrometry) or $m\sin i$ (RV), where $i$ is the inclination." + In the astrometric case. there are of course two such equations. one for each direction in the plane of the sky. whose ratio gives cos/. ancl so permit one to break (he misin/ degeneracy Chat plagues the intrinsically 1-dimensional RV measurement.," In the astrometric case, there are of course two such equations, one for each direction in the plane of the sky, whose ratio gives $\cos i$, and so permit one to break the $m\sin i$ degeneracy that plagues the intrinsically 1-dimensional RV measurement." + Because the form of equation (1)) is essentially identical in (he (wo cases. it is generally assumed (hat (he error properties. i.e.. the relation between the measurement errors ancl the derived-parameter errors. is also the same.," Because the form of equation \ref{eqn:basicform}) ) is essentially identical in the two cases, it is generally assumed that the error properties, i.e., the relation between the measurement errors and the derived-parameter errors, is also the same." + Of course. it is well known that the parameter errors have a different dependence on semimajor axis d. svstem distance D. ete.," Of course, it is well known that the parameter errors have a different dependence on semimajor axis $a$, system distance $D$, etc." +" Most notably. with other parameters held fixed. astrometric sensitivity increases linearly with e whereas RV sensitivitv declines as à.7,"," Most notably, with other parameters held fixed, astrometric sensitivity increases linearly with $a$ whereas RV sensitivity declines as $a^{-1/2}$." + But here I am referring to something else., But here I am referring to something else. + The differences just mentioned all impact the final result because (μον chanee the characteristic signal-to-noise ratio of the experiment. where Nis the number of measurements and σ is the error in each measurement (assumed. Lor simplicity to be all the same).," The differences just mentioned all impact the final result because they change the characteristic signal-to-noise ratio of the experiment, where $N$ is the number of measurements and $\sigma$ is the error in each measurement (assumed for simplicity to be all the same)." + Here I will show that the astrometric aud RV measurements have substantially different error properties even when SNR is identical., Here I will show that the astrometric and RV measurements have substantially different error properties even when SNR is identical. + ] will work within the famework of the minimum variance bound (ATVB). also frequently called the Fisher-matrix approximation.," I will work within the framework of the minimum variance bound (MVB), also frequently called the Fisher-matrix approximation." + As the same approximation will be applied to both techniques. (his will allow me to hiehleht the dillerence between them.," As the same approximation will be applied to both techniques, this will allow me to highlight the difference between them." + Of course. if equation (1)) really did fully represent both techniques. there could not be any difference in their error properties.," Of course, if equation \ref{eqn:basicform}) ) really did fully represent both techniques, there could not be any difference in their error properties." + ILowever. the (rue functional forms of the source motions are actually," However, the true functional forms of the source motions are actually" +flux deusitv is also Is-corrected to the rest frame of the source at 5 GIIz (see Fig.,flux density is also K-corrected to the rest frame of the source at 5 GHz (see Fig. + 3)., 3). + In Fie., In Fig. + Lae plot the relation )etween the apparent nüsalieumieut. APA and the ratio of the extended radio flux at 5 GIIz iu the rest frame of he source to the broad-line flux., 4 we plot the relation between the apparent misalignment $\Delta$ PA and the ratio of the extended radio flux at 5 GHz in the rest frame of the source to the broad-line flux. + A weak correlation at 90 or cent sienificance shows that a trend for sources with üeher ratios have larger wisaliguiaenut APA., A weak correlation at 90 per cent significance shows that a trend for sources with higher ratios have larger misalignment $\Delta$ PA. + Tn preseut sample. there are two TeV οταν sources: AfknlI21 (1101|381) and MXxub5O1 (1652|398).," In present sample, there are two TeV $\gamma$ -ray sources: Mkn421 (1101+384) and Mkn501 (1652+398)." + We know that the three TeV οταν objects are quite different from other οταν sources (Coppi Aharonian 1999a.b).," We know that the three TeV $\gamma$ -ray objects are quite different from other $\gamma$ -ray sources (Coppi Aharonian 1999a,b)." + Ouly Alkul21 is listed in the third EGRET catalog (Iartinan et al., Only Mkn421 is listed in the third EGRET catalog (Hartman et al. + 1999)., 1999). + However. we caunot fud obvious differeut behaviours for these two TeV οταν objects from the remains in the sample (see Fies.," However, we cannot find obvious different behaviours for these two TeV $\gamma$ -ray objects from the remains in the sample (see Figs." + 2 1. labeled by large squares}.," 2 $-$ 4, labeled by large squares)." +beginnings by the model causes wavelength dependence of the ellipticity maximum. a blue B8—{ο dip. and an SB bump. overlapping with the bar bump and largest in. B.,"beginnings by the model causes wavelength dependence of the ellipticity maximum, a blue $B\,$ $\,I_{\rm \scriptstyle C}$ dip, and an SB bump, overlapping with the bar bump and largest in $B$." +" The spiral structure forms a blue pseudo-ring (axb x16""7x12""). which produces an SB bump and a B /c dip."," The spiral structure forms a blue pseudo-ring $a\,$$\times$$\,b\,$$\approx$$16\arcsec$$\times$$12\arcsec$ ), which produces an SB bump and a $B\,$ $\,I_{\rm \scriptstyle C}$ dip." + The ellipticity profile shows a maximum around «=14”. accompanied by an SB bump. and an almost constant PA.," The ellipticity profile shows a maximum around $a\,$$=$$\,14\arcsec$, accompanied by an SB bump, and an almost constant PA." +" The behaviour of the profiles there is not typical — in the inner partit is dominated by an inner pseudo-ring (ab z13""x7""). and in the region of the outer part it is due to a bar-like structure pw). ref354GC7469bi"," The behaviour of the profiles there is not typical – in the inner partit is dominated by an inner pseudo-ring $a\,$$\times$$\,b\,$$\approx$$13\arcsec$$\times$$7\arcsec$ ), and in the region of the outer part it is due to a bar-like structure \\ref{35_NGC7469bi_Ew}) )." +Thisisbestillustratedinle by a double- ellipticity maximum and a corresponding weak double structure of the SB. bump., This is best illustrated in $I_{\rm \scriptstyle C}$ by a double-peaked ellipticity maximum and a corresponding weak double structure of the SB bump. + Given the small deprojected ellipticity of 0.12. the bar-like structure 1s most probably an oval/lens.," Given the small deprojected ellipticity of 0.12, the bar-like structure is most probably an oval/lens." + Márquez&Moles(1994) suggested the bump is due to a lens but based mainly on the fact that they could not find a reasonable fit by a bar., \citet{MM_94} suggested the bump is due to a lens but based mainly on the fact that they could not find a reasonable fit by a bar. + The wavelength dependence of the ellipticity maximum is caused by the inner pseudo-ring and the spiral structure., The wavelength dependence of the ellipticity maximum is caused by the inner pseudo-ring and the spiral structure. + The variations in the PA profile are related to the spiral structure., The variations in the PA profile are related to the spiral structure. + The inner 7” of the profiles are influenced by underlying features., The inner $7\arcsec$ of the profiles are influenced by underlying features. + Ciroretal.(2005) associated them with a dwarf galaxy remnant and star formation regions: a faint spiral structure could be traced in their residual images., \citet{CAM_05} associated them with a dwarf galaxy remnant and star formation regions; a faint spiral structure could be traced in their residual images. + 77603 and the galaxy about I’ to the SE are an example of an anomalous redshift association (Arp 1971).., 7603 and the galaxy about $1\arcmin$ to the SE are an example of an anomalous redshift association \citep{A_71}. . + 77603 is disturbed and shows evidence of tidal interaction (see ).., 7603 is disturbed and shows evidence of tidal interaction \citep[see][and references therein]{LG_04}. . +the differeut evolutionary histories of Jupiter and Saturn.,the different evolutionary histories of Jupiter and Saturn. +" Saturu's greater distance from the Sun would cause the incident solar flux to be a factor of (αγας} less at Saturn than at Jupiter. where e; aud es are the semi-major axes of Jupicr and Saturn respectively,"," Saturn's greater distance from the Sun would cause the incident solar flux to be a factor of $(a_{\rm J}/a_{\rm S})^2$ less at Saturn than at Jupiter, where $a_{\rm J}$ and $a_{\rm S}$ are the semi-major axes of Jupiter and Saturn respectively." + Even in the compact configuration proposed iu the Nice model. the difference im incident flux would be (5.15AU/s.18AT)?=O.LL implying that the incident flux would have been more thin twice as strong at Jupiters location than SaWas waar," Even in the compact configuration proposed in the Nice model, the difference in incident flux would be $(5.45\ {\rm AU}/8.18\ {\rm AU})^2 = 0.44$, implying that the incident flux would have been more than twice as strong at Jupiter's location than Saturn's \citep{tsiganis05,morbidelli05}." + The greater amount of incident flux at Jupiter would have caused there to be a ereater amount of photoevaporative nass loss iu the Jovian system., The greater amount of incident flux at Jupiter would have caused there to be a greater amount of photoevaporative mass loss in the Jovian system. + Furthermore. the increased rate of yhotocvaporation would have caused the Jovian subuebula to be more drastically truucatec than he Saturnian subnebula eiven he sale solar unmdnositv.," Furthermore, the increased rate of photoevaporation would have caused the Jovian subnebula to be more drastically truncated than the Saturnian subnebula given the same solar luminosity." + We describe our disk inodel as well as our nodels for ἀπ from the solar rebula απο jiofoevaporation d Section 2.., We describe our disk model as well as our models for infall from the solar nebula and photoevaporation in Section \ref{sec:disk}. + The results of our snnulations are preseuted im Section 3.. with he results from) our steadyv-tate disk models resented ii Section 3.1. aud the results frou our nue-dependent. decaviug disk model iu Section 3.2..," The results of our simulations are presented in Section \ref{sec:results}, with the results from our steady-state disk models presented in Section \ref{subsec:steady} and the results from our time-dependent, decaying disk model in Section \ref{subsec:decay}." + Iu. Section 3 we preseut a SULA aud discussion of our results., In Section \ref{sec:results} we present a summary and discussion of our results. + Qur disk meocel is an extension of au earlier Xiotoevaporative viscous disk model that was oxeviouslv applied to the evolution of the solar rebula €2).., Our disk model is an extension of an earlier photoevaporative viscous disk model that was previously applied to the evolution of the solar nebula \citep{mitchell10}. + Besides its application to circiuuplauearv rebulae. the current amodel differs frou the xevious imnodel i that it inelucdes iufall from he solar nebula.," Besides its application to circumplanetary nebulae, the current model differs from the previous model in that it includes infall from the solar nebula." + The details of the iufall wil ο diseussed iu Section 2.1.., The details of the infall will be discussed in Section \ref{subsec:infall}. + It is this iufall that allows for steady-state solutions., It is this infall that allows for steady-state solutions. + Our model uses the common o-viscosity prescription with a viscosity that is proportional to +., Our model uses the common $\alpha$ -viscosity prescription with a viscosity that is proportional to $r$. + where vy and Ry ave scalines for viscosity aud radius., where $\nu_0$ and $R_0$ are scalings for viscosity and radius. + This assumption has been used in the past by mnany authors (273...," This assumption has been used in the past by many authors \citep{clarke07,hartmann98b}." +" The linear dependence of viscosity on radius m our model implics that the temperature profile is proportional to 9,", The linear dependence of viscosity on radius in our model implies that the temperature profile is proportional to $r^{-1/2}$. + The iidplaue disk temperature. Zi. Is used m order to determine the viscosity constaut 19.," The midplane disk temperature, $T_{\rm disk}$, is used in order to determine the viscosity constant $\nu_0$." + where Àds the Doltzmaun coustaut aud Gr) is the mean molecular weight., where $k$ is the Boltzmann constant and $\muh$ is the mean molecular weight. + We lave scaled the iidplaue temperature profiles in our models such that iu the Jovian system the temperature has been set to zx250lI at 1)Ry., We have scaled the midplane temperature profiles in our models such that in the Jovian system the temperature has been set to $\approx 250\ {\rm K}$ at $10\ R_{\rm J}$. + This is consistent with the slow-inflow. ow-opacitv circun-Jovian accretion disk model investigated by (7)..," This is consistent with the slow-inflow, low-opacity circum-Jovian accretion disk model investigated by \citep{canup02}." + For the Saturnia svstenm the radial temperature profiles ln our nodels have been set to zz100I& at 20Rs. the approximate location of Titan.," For the Saturnian system, the radial temperature profiles in our models have been set to $\approx 100\ {\rm K}$ at $20\ R_{\rm S}$, the approximate location of Titan." + Mos models of circtuuplanetary disks eimiplov a value of a that is generally smaller than that used in circumstellar cask models (2).., Most models of circumplanetary disks employ a value of $\alpha$ that is generally smaller than that used in circumstellar disk models \citep{canup09}. +" The simulations preseuted in this work consider à values in the range of lOτα with our reference models having a value of à=10.3,"," The simulations presented in this work consider $\alpha$ values in the range of $10^{-2}-10^{-4}$, with our reference models having a value of $\alpha = 10^{-3}$." + Tustead of usine r aud X: the radius aud mass surface deusitv of the gas. it is useful ο describe the system im terms the variables / and yg: the specific angular monieutun aud torque.," Instead of using $r$ and $\Sigma$; the radius and mass surface density of the gas, it is useful to describe the system in terms the variables $h$ and $g$; the specific angular momentum and torque." + This is a good choice of variables to make when the viscosity Is xoportional to r as df allows us to transforni the viscous disk equation into a sinple. linear differceutial equaion With a constant cocfiicient (?)..," This is a good choice of variables to make when the viscosity is proportional to $r$ as it allows us to transform the viscous disk equation into a simple, linear differential equation with a constant coefficient \citep{hartmann98a}." + where G is the gravitational constant and © is he Ieplemian orbital velocity., where $G$ is the gravitational constant and $\Omega$ is the Keplerian orbital velocity. + The relationship vetween g and X in Equ. (5)), The relationship between $g$ and $\Sigma$ in Eqn. \ref{eqn:g}) ) + implies that the nass surface densitv is inversely proportional to he viscosity., implies that the mass surface density is inversely proportional to the viscosity. + Thus. Xxà.|l," Thus, $\Sigma\propto \alpha^{-1}$." +" By substituting iu the functional formi of viscosity. the continuity equation for radial mass rausport can be written as where Af, is the mass of the planet."," By substituting in the functional form of viscosity, the continuity equation for radial mass transport can be written as where $M_{\rm p}$ is the mass of the planet." + As we are interested in the addition of material to the disk. a source terii must be added outo the," As we are interested in the addition of material to the disk, a source term must be added onto the" +"other hand, there is no bump emerging from the essentially gaussian (observed) PMDFs of 11039, 22516, and 77762 (Figs.","other hand, there is no bump emerging from the essentially gaussian (observed) PMDFs of 1039, 2516, and 7762 (Figs." + 5 and 6))., \ref{fig5} and \ref{fig6}) ). +" In addition, it is interesting to note that the bump in the central region of 22682 appears almost identically in PMDFs built with independent data sets."," In addition, it is interesting to note that the bump in the central region of 2682 appears almost identically in PMDFs built with independent data sets." + Another issue is to what degree incompleteness in crowded regions - and the more difficult measurement of PM components for faint stars - affect the PMDFs., Another issue is to what degree incompleteness in crowded regions - and the more difficult measurement of PM components for faint stars - affect the PMDFs. +" Additionally, could the bump be related to incompleteness?"," Additionally, could the bump be related to incompleteness?" +" We use 22477, the most distant and populous OC of our sample (thus, the most prone to suffering from incompleteness) to examine this point (App. B1))."," We use 2477, the most distant and populous OC of our sample (thus, the most prone to suffering from incompleteness) to examine this point (App. \ref{dMagBump}) )." +" Since our analysis depends on the number of member stars (especially at the central region), we selected J—12.5 as the boundary between bright and faint stars."," Since our analysis depends on the number of member stars (especially at the central region), we selected $J=12.5$ as the boundary between bright and faint stars." +" At the distance of 22477, this boundary corresponds to a stellar mass of m£7:1.6Mo."," At the distance of 2477, this boundary corresponds to a stellar mass of $m\approx1.6\,\ms$." +" The bright and faint deconvolved PMDFs built for the central region are similar (Fig. B3)),"," The bright and faint deconvolved PMDFs built for the central region are similar (Fig. \ref{fig11}) )," + consistently presenting the high-velocity bump at jiz12masyr~!.," consistently presenting the high-velocity bump at $\bar\mu\approx12\,\mas$." + The only significant difference is that the faint (less massive) star PMDF is shifted ~1.3masyr towards high values of ji with respect to that of the bright! stars., The only significant difference is that the faint (less massive) star PMDF is shifted $\sim1.3\mas$ towards high values of $\bar\mu$ with respect to that of the bright stars. + A similar shift occurs for the bright and faint star PMDFs in the outer region (without the bump)., A similar shift occurs for the bright and faint star PMDFs in the outer region (without the bump). +" Although relatively small, the shift Ajzz1.3masyr!8kms~’ between the bright and faint PMDFs might suggest slightly different kinematics for stars in different mass ranges."," Although relatively small, the shift $\Delta\bar\mu\approx1.3\,\mas\approx8\,\kms$ between the bright and faint PMDFs might suggest slightly different kinematics for stars in different mass ranges." + This experiment also suggests that incompleteness and PM. measurements of faint stars - at least to the level available in UCACS - are not critical for the PMDFs., This experiment also suggests that incompleteness and PM measurements of faint stars - at least to the level available in UCAC3 - are not critical for the PMDFs. +" Additionally, one might ask whether the bump may come from residual, i.e. unaccounted for field contamination."," Additionally, one might ask whether the bump may come from residual, i.e. unaccounted for field contamination." +" It is true that, given the statistical way wedecontaminate the clusters (Sect. 3)),"," It is true that, given the statistical way we the clusters (Sect. \ref{trgt}) )," + some field-star contribution might persist in the subtracted PMDFs., some field-star contribution might persist in the subtracted PMDFs. +" However, both 22477 and 22782 are located in the third Galactic quadrant and at high Galactic latitudes, which by itself minimises contamination (as can also be seen in Figs."," However, both 2477 and 2782 are located in the third Galactic quadrant and at high Galactic latitudes, which by itself minimises contamination (as can also be seen in Figs." + Bl and B2))., \ref{fig9} and \ref{fig10}) ). +" Thus, any residual contamination should be minimum, which would contradict the fraction of stars composing the bump, ~40% in the central region of 22477 and &7% in 22682."," Thus, any residual contamination should be minimum, which would contradict the fraction of stars composing the bump, $\approx40\%$ in the central region of 2477 and $\approx7\%$ in 2682." +" The above arguments suggest that the bump is related to a cluster kinematic property, but we cannot definitely rule out the possibility that it might be an artefact of the RL deconvolution, and/or some residual contamination by stars with peculiar PM components."," The above arguments suggest that the bump is related to a cluster kinematic property, but we cannot definitely rule out the possibility that it might be an artefact of the RL deconvolution, and/or some residual contamination by stars with peculiar PM components." + There is no direct interpretation for the additional bump seen in the deconvolved PMDFs of 22477 and NGC22682., There is no direct interpretation for the additional bump seen in the deconvolved PMDFs of 2477 and 2682. +" Assuming that it is physical, one possibility is that the double peak may arise from a merger of two clusters (as suggested by the referee, Thijs Kouwenhoven)."," Assuming that it is physical, one possibility is that the double peak may arise from a merger of two clusters (as suggested by the referee, Thijs Kouwenhoven)." +" In this sense, deOliveira,Bica&Dottori(2000) carried out N-body simulations of cluster encounters, studying long-term structural changes up to ~1 GGyr."," In this sense, \citet{OBD2000} carried out N-body simulations of cluster encounters, studying long-term structural changes up to $\sim1$ Gyr." +" They found that the clusters may coalesce at such ages, but until then, the presence of the two clusters can still be traced by means isophotal distortions and ellipticity variations, as observed in model and actual clusters (e.g. deOliveiraetal. 2000))."," They found that the clusters may coalesce at such ages, but until then, the presence of the two clusters can still be traced by means isophotal distortions and ellipticity variations, as observed in model and actual clusters (e.g. \citealt{ODBD2000}) )." +" In this scenario, internal differences in kinematics might persist too, producing different signatures in the deconvolved PMDFs."," In this scenario, internal differences in kinematics might persist too, producing different signatures in the deconvolved PMDFs." +" Alternatively, the high-average velocity component may be related to mass segregation, in which a fraction of the stars collectively migrate along the radial direction (over a time-scale of a relaxation time) within a star cluster."," Alternatively, the high-average velocity component may be related to mass segregation, in which a fraction of the stars collectively migrate along the radial direction (over a time-scale of a relaxation time) within a star cluster." +" In the cases dealt with here, it occurs only in the two most populous OCs, 22477 and 22682."," In the cases dealt with here, it occurs only in the two most populous OCs, 2477 and 2682." +" Maybe it cannot be detected (by the present approach) in the other OCs because they are less populated (i.e., possibly the same reason why it is seen in the outer parts of 22682 with the optical data, but not with UCAC3)."," Maybe it cannot be detected (by the present approach) in the other OCs because they are less populated (i.e., possibly the same reason why it is seen in the outer parts of 2682 with the optical data, but not with UCAC3)." +" Finally, working with histograms and a different PM-data set, Bica&Bon- raised the possibility that the high-velocity component in 22682 might be related to the presence of binaries."," Finally, working with histograms and a different PM-data set, \citet{M67} raised the possibility that the high-velocity component in 2682 might be related to the presence of binaries." +" However, given the findings of Kouwenhoven&deGrijs (2008), this possibility seems the least probable."," However, given the findings of \citet{KG2008}, this possibility seems the least probable." +" In any case, a definitive solution for the bump nature would require detailed simulations of the internal cluster dynamics (including cluster merger, mass segregation, and binarity), a task that is beyond the scope of the present paper."," In any case, a definitive solution for the bump nature would require detailed simulations of the internal cluster dynamics (including cluster merger, mass segregation, and binarity), a task that is beyond the scope of the present paper." +" The velocity dispersions derived from the deconvolved PMDFs (Table 2)) of 11039 and 22516 (and, to a lesser degree, 22682), are consistent with those of (approximately virialized) OCs of ~10?ms."," The velocity dispersions derived from the deconvolved PMDFs (Table \ref{tab2}) ) of 1039 and 2516 (and, to a lesser degree, 2682), are consistent with those of (approximately virialized) OCs of $\sim10^3$." +". On the other hand, those of 22516 and 22477 appear to be excessively high for OCs of a similar mass scale."," On the other hand, those of 2516 and 2477 appear to be excessively high for OCs of a similar mass scale." +" However, such large dispersion values can be partly explained by an observational limitation related to distance, since both OCs are the most distant of the sample."," However, such large dispersion values can be partly explained by an observational limitation related to distance, since both OCs are the most distant of the sample." +" For a limited observational time-base, the PM determination for"," For a limited observational time-base, the PM determination for" +of our sources which were taken for identification purposes: they are consistent with ΑΕ ἵνρο stars.,of our sources which were taken for identification purposes: they are consistent with A/F type stars. + Although our spectra are not high resolution. our model fits indicate that all sources have metallicities which are less than Solar (for most sources at the 3e. confidence level).," Although our spectra are not high resolution, our model fits indicate that all sources have metallicities which are less than Solar (for most sources at the $\sigma$ confidence level)." + Higher resolution spectra with good signal-to-noise are necessary to determine their metal content with higher confidence., Higher resolution spectra with good signal-to-noise are necessary to determine their metal content with higher confidence. + In section 3. we noted that the vast majority of our sources are located. at distances greater than 3 kpe. with some being over 20 kpe distant. (if we have detected either the fundamental or first over-tone mode).," In section \ref{distance} we noted that the vast majority of our sources are located at distances greater than 3 kpc, with some being over 20 kpc distant (if we have detected either the fundamental or first over-tone mode)." + Similarly. many are at a height of 1 kpe or more from the Galactic plane. with several being at least 10 kpe from the plane.," Similarly, many are at a height of 1 kpc or more from the Galactic plane, with several being at least 10 kpc from the plane." + Some of our sources are therefore at the remote edge of our Galaxy., Some of our sources are therefore at the remote edge of our Galaxy. + SX Phe stars have been found at both large distances and well into the Galactic plane (eg Berstein. Ixnezek Olfutt 1995: Jeon. Ixim and Nemec 2010).," SX Phe stars have been found at both large distances and well into the Galactic plane (eg Berstein, Knezek Offutt 1995; Jeon, Kim and Nemec 2010)." + They are therefore. in principal. potential tracers of Galactic structure such as streams or the remnants of mergers.," They are therefore, in principal, potential tracers of Galactic structure such as streams or the remnants of mergers." + We note that 1356 and 1359 lic around ~6 from the large globular cluster M3 (which is 10.4 kpe from the Sun) which places them at a distance of ~2 kpe from AIS., We note that J1356 and J1359 lie around $\sim6^{\circ}$ from the large globular cluster M3 (which is 10.4 kpc from the Sun) which places them at a distance of $\sim$ 2 kpc from M3. + Although tidal tails have been detected. at distances of several kpe from globular clusters (eg Oclenkirchen οἱ al 2003). no tidal tails have been detected. from M3. (Jordi Crebel 2010).," Although tidal tails have been detected at distances of several kpc from globular clusters (eg Odenkirchen et al 2003), no tidal tails have been detected from M3 (Jordi Grebel 2010)." + he other source of particular note. is J0305 which is located in the direction of the Galactic anti-center and at a distance of 30kpc (implying a Calactocentric distance of 38 kpc) and a height of 21 kpe below the Galactic plane., The other source of particular note is J0305 which is located in the direction of the Galactic anti-center and at a distance of 30kpc (implying a Galactocentric distance of 38 kpc) and a height of 21 kpc below the Galactic plane. + Recent work shows that the stellar density of the Galaxy decreases sharply at Galactocentric distances greater than 25 kpe (eg Watkins et al 2009. Sesar et al. 2010) which max indicate that 0305 is associated with a sub-structure of the halo.," Recent work shows that the stellar density of the Galaxy decreases sharply at Galactocentric distances greater than 25 kpc (eg Watkins et al 2009, Sesar et al, 2010) which may indicate that J0305 is associated with a sub-structure of the halo." + Alternatively it may be in the process of being ejected from our Galaxy., Alternatively it may be in the process of being ejected from our Galaxy. + A more detailed: radial velocity study is required to answer this question., A more detailed radial velocity study is required to answer this question. + SX Phe stars have been identified in globular clusters and nearby dwarl galaxies (eg Olech ct al 2005. Poretti οἱ al 2008).," SX Phe stars have been identified in globular clusters and nearby dwarf galaxies (eg Olech et al 2005, Poretti et al 2008)." + Based on the number of blue stellar pulsators which we have identified in our survey. we now make an estimate of the total number of SX Phe stars which are present in our Galaxy.," Based on the number of blue stellar pulsators which we have identified in our survey, we now make an estimate of the total number of SX Phe stars which are present in our Galaxy." + Since our survey is biased towards low Galactic ields. hiehhy redcdened: (but. intrinsically blue) pulsators could be confused. with apparently much τοσο sources making potential contamination a significant. concern.," Since our survey is biased towards low Galactic fields, highly reddened (but intrinsically blue) pulsators could be confused with apparently much redder sources making potential contamination a significant concern." + For his reason. we therefore base our simulation on those fields or which the total extinction is less than «τν 0.45.," For this reason, we therefore base our simulation on those fields for which the total extinction is less than $A_{V}$ =0.45." + A total of 35 fields had a column density less than our limit which corresponds to an area of LO square degrees., A total of 35 fields had a column density less than our limit which corresponds to an area of 10 square degrees. + We find eleven due pulsators in these fields (these are Hageged in the last column of Table 1)., We find eleven blue pulsators in these fields (these are flagged in the last column of Table 1). + Low resolution spectroscopic data exist. for. seven of hese eleven pulsators and a spectroscopic analysis indicates hey have a metal content consistent with that of SX Phe stars., Low resolution spectroscopic data exist for seven of these eleven pulsators and a spectroscopic analysis indicates they have a metal content consistent with that of SX Phe stars. + Llere we assume that all eleven. pulsators at. high Galactic latitudes are SN Phe stars., Here we assume that all eleven pulsators at high Galactic latitudes are SX Phe stars. + We use a simulation of he Galactic populations found in the fields to extrapolate he number of SX Phe stars founc in the whole Galaxy., We use a simulation of the Galactic populations found in the fields to extrapolate the number of SX Phe stars found in the whole Galaxy. + Our simulation uses a moclifiecl version of a mocel originally, Our simulation uses a modified version of a model originally +"ep=DBo/B,, is the ratio of the magnitude of the large-scale magnetic field aligned with the shock normal, Bo, to the amplitude of the postshock wave field that interacts with low energy particles, B,.","$\epsilon_B = B_0/B_{\perp}$, is the ratio of the magnitude of the large-scale magnetic field aligned with the shock normal, $B_0$, to the amplitude of the postshock wave field that interacts with low energy particles, $B_{\perp}$." +" This is an adjustable parameter, although, as discussed in (1997)... it is confined theoretically and experimentally to values, eg~0.3."," This is an adjustable parameter, although, as discussed in \cite{malkov97}, it is confined theoretically and experimentally to values, $\epsilon_B \sim 0.3$." +" The method of solving the NLDSA problem based on the Monte Carlo particle transport, developed by Ellison and co-workers and later adapted for modeling magnetic field amplification in shocks by Vladimirov (hereafter EV), makes the following physical assumptions: The problem of NLDSA is thus stated as that of finding a steady state particle distribution function in a system where a supersonic motion exists at an infinite boundary, and the flow is subsonic at the opposite boundary."," The method of solving the NLDSA problem based on the Monte Carlo particle transport, developed by Ellison and co-workers and later adapted for modeling magnetic field amplification in shocks by Vladimirov (hereafter EV), makes the following physical assumptions: The problem of NLDSA is thus stated as that of finding a steady state particle distribution function in a system where a supersonic motion exists at an infinite boundary, and the flow is subsonic at the opposite boundary." +" The distribution function F(zr,p) in this case retains"," The distribution function $F(x, {\bf p})$ in this case retains" +The enignmatic radio-quiet central compact. objects discovered in supernova remnants (SNRs) have challenged conventional thoughts that most voung neutron stars (NdSs) evolve inamnmeanmner similar to Crab-like pulsars(seePavlov.Sanwal.&Teter2004;IXaspi.Roberts.llarding2006.[orrecent reviews).,"The enigmatic radio-quiet central compact objects discovered in supernova remnants (SNRs) have challenged conventional thoughts that most young neutron stars (NSs) evolve in a manner similar to Crab-like pulsars\citep[see][for recent reviews]{pav04,kas06}." +. The X-ray source LE 161348—5055 (hereinalter 11613). the prototvpe of the growing raclio-quiel objects in SNRs. was first detected with as a faint. unresolved source located near the center of (he SNR. RCW 103 with an age of~2000 vr (Nugent1954). and distance of 3.3 kpc (Caswellet 1975).," The X-ray source 1E $-$ 5055 (hereinafter 1E1613), the prototype of the growing radio-quiet objects in SNRs, was first detected with as a faint, unresolved source located near the center of the SNR RCW 103 \citep{tuo80} with an age of$\sim 2000$ yr \citep{nug84} and distance of $\sim 3.3$ kpc \citep{cas75}." +". From X-ray observations withτρ. GotthelfPetre.&Ibwang(1997). found a compact X-ray source inside RCW 103 with the X-ray luminosity Ly~10""! ! and the black-body temperature about 0.6 keV. Further observation of 11916019. together with archived and cata showecl that this source manifestecl an order-of magnitude decrease in luminosity over four vears (Gotthelf.Petre.&Vasisht1999).. suggesting that this object may be an accreting source rather a cooling NS."," From X-ray observations with, \citet{got97} found a compact X-ray source inside RCW 103 with the X-ray luminosity $L_{\rm X}\sim 10^{34}$ $^{-1}$ and the black-body temperature about 0.6 keV. Further observation of 1E1613, together with archived and data showed that this source manifested an order-of magnitude decrease in luminosity over four years \citep{got99}, suggesting that this object may be an accreting source rather a cooling NS." + Bul no X-ray pulsations. radio or optical counter part were detected.," But no X-ray pulsations, radio or optical counter part were detected." + From observations and archival data.," From observations and archival data," +if we split our sample according to à galaxv's concentration. the ratio Poy{συ which we use as a proxy for distinguishing cisk-dominated (60/425 <2.6) and bulec-dominated ( Royfuy 2.6) galaxies (asine.g.Waullmannetal.2003).,"if we split our sample according to a galaxy's concentration, the ratio $R_{90}/R_{50}$, which we use as a proxy for distinguishing disk-dominated $R_{90}/R_{50}$ $<$ 2.6) and bulge-dominated ( $R_{90}/R_{50}$ $>$ 2.6) galaxies \citep[as in e.g.][]{Kauffmann2003}." +. This cut. vields 54 (133) low (high) concentration galaxies., This cut yields 54 (133) low (high) concentration galaxies. + We [find that this split. produces. two nearly. identical distributions. both contributing nearly equally to the total integrated mass density.," We find that this split produces two nearly identical distributions, both contributing nearly equally to the total integrated mass density." + For the GASS stellar. mass range. disk-dominated galaxies do not account [or the majority of the gas content of galaxies.," For the GASS stellar mass range, disk-dominated galaxies do not account for the majority of the gas content of galaxies." + Instead. appears to be evenly. distributed across a range of galaxy |vpes.," Instead, appears to be evenly distributed across a range of galaxy types." + From our derived SER. density function. we measure a partial SER. density. of (8.5+0.5)10 M. Alpe? | which is 4744% of the total SER. density (Salimοἱal.2007:Wederet2007). and consistent with the results in those papers measured over the CLASS stellar mass range.," From our derived SFR density function we measure a partial SFR density of $8.5\pm0.5) \times10^{-3}$ $_\odot$ $^{-3}$ $^{-1}$ which is $\pm$ of the total SFR density \citep{Salim2007, Wyder2007} and consistent with the results in those papers measured over the GASS stellar mass range." + Interestingly this suggests that CLASS galaxies account [or nearly the same fraction of the total SEL. density as they do in ccontent., Interestingly this suggests that GASS galaxies account for nearly the same fraction of the total SFR density as they do in content. +" We can also calculate an integrated volume-averaged SEI and implied gas consumption timescale which we determine to be 2.9.101 vp+ (timescale = 3.4404 Cir) for CLASS galaxies (AL,>107 3).", We can also calculate an integrated volume-averaged SFE and implied gas consumption timescale which we determine to be $2.9\times10^{-10}$ $^{-1}$ (timescale = $\pm$ 0.4 Gyr) for GASS galaxies $M_\star > 10^{10}$ ). +" Because we have measurements of the total aand SER density. we can calculate a SEL for lower mass galaxies (AL,«LOM )). which we find to be 2.1.102° + (timescale = £6£0.5 Gr)."," Because we have measurements of the total and SFR density, we can calculate a SFE for lower mass galaxies $M_\star < 10^{10}$ ), which we find to be $2.1\times10^{-10}$ $^{-1}$ (timescale = $\pm$ 0.5 Gyr)." + The volume-averaged SEE appears to be relatively constant across the full galaxy population., The volume-averaged SFE appears to be relatively constant across the full galaxy population. +" Although our results suggest that the average SEE is similar above and below 1017|AZ... it o.is possible. that it. only changes significantly.-- above the transition.. mass at AZ,~3.⋅I0LoAM..."," Although our results suggest that the average SFE is similar above and below $10^{10}$, it is possible that it only changes significantly above the transition mass at $M_\star \sim 3\times 10^{10}$." + We show in Figure Ὁ how the volume-averaged mass. SER and SEE density functions vary with δν.," We show in Figure \ref{Fig:SFEdist} how the volume-averaged mass, SFR and SFE density functions vary with $_\star$." +" Quantities are. plotted. per. M, bin on the left. and as a cumulative quantity on the right."," Quantities are plotted per $_\star$ bin on the left, and as a cumulative quantity on the right." + In the bottom panels. we see that the trend in gas consumption remains quite Hat across all stellar masses. remaining constant up to our highest stellar mass bin. though with increasing scatter.," In the bottom panels, we see that the trend in gas consumption remains quite flat across all stellar masses, remaining constant up to our highest stellar mass bin, though with increasing scatter." + ‘To explore this further. in Fig 6. and 7. we compare the elobal scaling relationsof aand SEE and find that they each paint a very. clillercnt picture.," To explore this further, in Fig \ref{Fig:sfe_all} and \ref{Fig:sfe_all_obs} we compare the global scaling relationsof and SFE and find that they each paint a very different picture." + In the left panel of cach pair of figures we plot the binned specific star formation rate (VS HR/XAL)asa function of stellar mass. mass surface density. concentration and color(AL... pa. Roufdtsu. anc NUV-r).," In the left panel of each pair of figures we plot the binned specific star formation rate $\Sigma SFR/\Sigma M_\star$ ) as a function of stellar mass, mass surface density, concentration and color, $\mu_\star$ , $R_{90}/R_{50}$, and NUV-r)." + In all cases. is steadily declining. twpically by a factor of 10-30 across the range of the CLASS sample.," In all cases, is steadily declining, typically by a factor of 10-30 across the range of the GASS sample." + In the right panels we show the average SFE (ShR/MAgg. where nnon-detections are given zero mumass).," In the right panels we show the average SFE $\Sigma SFR/\Sigma M_{HI}$, where non-detections are given zero mass)." + Phe average SEI is nearly Lat. stracddling 3100 1 . Corresponding. to a gas depletion. timescale. of ⋅⋅3 Gyr.," The average SFE is nearly flat, straddling $\sim 3 \times 10^{-9}$ $^{-1}$ , corresponding to a gas depletion timescale of 3 Gyr." + Although in certain cases a small upwards or downweud trend is suggested. these deviations are not statistically. significant.," Although in certain cases a small upwards or downward trend is suggested, these deviations are not statistically significant." + Values for these quantities are given in Tables 1 and 2.., Values for these quantities are given in Tables \ref{Tab:SSFR} and \ref{Tab:SFE}. + We have chosen to plot bin-averaged quantities where the numerator and denominator are summed separately in order to simplify the treatment of non-detections., We have chosen to plot bin-averaged quantities where the numerator and denominator are summed separately in order to simplify the treatment of non-detections. +" We have checked that this trend is also apparent for mean or median SPERM, and SFE measured. for individual galaxies. the distribution of which is discussed in the next section."," We have checked that this trend is also apparent for mean or median $SFR/M_\star$ and SFE measured for individual galaxies, the distribution of which is discussed in the next section." + ‘This result is remarkable for two cdillerent reasons., This result is remarkable for two different reasons. +" The first is that the timescale for gas consumption is nearly constant while the galaxys specific star formation rate or ""building timescale” is strongly dependent on stellar mass ancl correlated quantities.", The first is that the timescale for gas consumption is nearly constant while the galaxy's specific star formation rate or “building timescale” is strongly dependent on stellar mass and correlated quantities. + The second remarkable aspect is that the global avcrage SEE that we measure for the CASS sample is very close to that observed locally for molecular gas in disks (e.g.Leroyetal.2008.usingtheΕΝsurvey.Walterct 2008)..," The second remarkable aspect is that the global average SFE that we measure for the GASS sample is very close to that observed locally for molecular gas in disks \citep[e.g.][using the THINGS survey, Walter et al. 2008]{Leroy2008}." + ‘This suggests that the entire reservoir is being converted into stars at the same rate as the molecular gas., This suggests that the entire reservoir is being converted into stars at the same rate as the molecular gas. + It would appear to argue against a “bottleneck” in the Dow. of gas onto galaxies occurring. on average. at the interface between the atomic ancl molecular phase.," It would appear to argue against a “bottleneck” in the flow of gas onto galaxies occurring, on average, at the interface between the atomic and molecular phase." + Instead. it would. appear that the gas-limiting step occurs prior to the phase: that quenching of the detectable cold gas is not responsible for regulating the star formation history of galaxies., Instead it would appear that the gas-limiting step occurs prior to the phase; that quenching of the detectable cold gas is not responsible for regulating the star formation history of galaxies. + We consider this result. and its relation to previous work. in the next section.," We consider this result, and its relation to previous work, in the next section." + We first start out by asking whether a constant volume-averaged SEE is surprising. particularly for galaxies in the GASS mass range?," We first start out by asking whether a constant volume-averaged SFE is surprising, particularly for galaxies in the GASS mass range?" + While the global. Schmidt. law suggests à star formation clliciency that rises with gas surface densitv or varies inversely. with dvnamical or [ree-fall timescale (IXennicutt.1998).. more recent. compilations of star formation laws (e.g..Leroyetal.2008) consider fixed giant molecular cloud star-forming elliciencies (with a varving atomic-to-molecular ratio) and. pressure regulation of the SPE and/or atomic-molecular ratio.," While the global Schmidt law suggests a star formation efficiency that rises with gas surface density or varies inversely with dynamical or free-fall timescale \citep{Kennicutt1998}, more recent compilations of star formation laws \citep[e.g.,][]{Leroy2008} consider fixed giant molecular cloud star-forming efficiencies (with a varying atomic-to-molecular ratio) and pressure regulation of the SFE and/or atomic-molecular ratio." + Because we measure neither the size of the gaseous ancl star-forming disk. nor the molecular phase. it is not easy to connect. our global results to these theoretical predictions.," Because we measure neither the size of the gaseous and star-forming disk, nor the molecular phase, it is not easy to connect our global results to these theoretical predictions." + Global galaxy-averaged (quantities sample a range of eas surface densities. timescales ancl conditions within the LISAL," Global galaxy-averaged quantities sample a range of gas surface densities, timescales and conditions within the ISM." + Additionally. our mean SFEs combine measurements from galaxies with range of morphological tvpes. environments and presumably ark halo masses and spin parameters.," Additionally, our mean SFEs combine measurements from galaxies with range of morphological types, environments and presumably dark halo masses and spin parameters." + Lt is a considerable worctical challenge to interpret this result on its own., It is a considerable theoretical challenge to interpret this result on its own. + Observationallv. low elliciencies have been measured for low-mass galaxies (Gehaetal.2006).. LSB galaxies etal.2008:Wer 2009). and. DLAs (Wolfe&Chen 2006).," Observationally, low efficiencies have been measured for low-mass galaxies \citep{Geha2006}, LSB galaxies \citep{Boissier2008, Wyder2009}, and DLAs \citep{Wolfe2006}." +. Conversely high elliciencies have been measured in starburst galaxies (e.g.Lehnert&Leckman1996:Ixenni-cutt1998). and in galaxies undergoing interactions (Youngetal.1986:Solomon&SageLOSS) and/or some form. of environmental disturbance (e.g. stripping) (Roseetal.2009: 2004)..," Conversely high efficiencies have been measured in starburst galaxies \citep[e.g.][]{Lehnert1996,Kennicutt1998} and in galaxies undergoing interactions \citep{Young1986, Solomon1988} and/or some form of environmental disturbance (e.g. stripping) \citep{Rose2009,KK04}. ." + However. measurements ofnormal star-forming galaxies (e.g.Wennicutt1998) show that galaxiesfollow the global Schmidt. law. implving— a slowly varving SEE over the range of gas surface densities typically probed.," However, measurements ofnormal star-forming galaxies \citep[e.g.][]{Kennicutt1998} show that galaxiesfollow the global Schmidt law, implying a slowly varying SFE over the range of gas surface densities typically probed." + Youngetal.(1986) ancl Devereux&Young(1991) noted a [lat SEI across the Hubble. sequence using, \citet{Young1986} and \citet{Devereux1991} noted a flat SFE across the Hubble sequence using +" 1.5150 kpe). have similar half light radii (50=rySLOO pe) and are among the faintest objects (vith OSARXo 540) detectable in the SDSS at that distance(2?).," They are all very distant from the MW $D > 150$ kpc), have similar half light radii $50 \lesssim r_{h} \lesssim 100$ pc) and are among the faintest objects (with $-4.0 \lesssim M_{V} \lesssim -5.0$ ) detectable in the SDSS at that distance." +. Based ou spectroscopic results. CVu II appears to be dark matter dominated with a M/Li=360|I and is metal poor. with ([Fe/II =—2.19(?).," Based on spectroscopic results, CVn II appears to be dark matter dominated with a $M/L_{V}=360^{+380}_{-180}$ and is metal poor, with $\langle$ $\rangle=-2.19$." +. On the other haud. neither Leo V nor Pisces IT have robust mass estimates. although the kincmatic study of suggests that Leo V miehlt be dark matter dominated.," On the other hand, neither Leo V nor Pisces II have robust mass estimates, although the kinematic study of suggests that Leo V might be dark matter dominated." + Leo V bemus several hints that it aight have been idally stripped. including a spectroscopic [Fe/TII] that is hieher than MW satellites of simular huuinositv. aud nore compatible with brighter objects.," Leo V bears several hints that it might have been tidally stripped, including a spectroscopic [Fe/H] that is higher than MW satellites of similar luminosity, and more compatible with brighter objects." + Leo V also shows siens of being disturbed. with au apparently extended due horizoutal brauch distribution anc kincmatic ΠΟΡΟΣ nore then 10 half light radi away from the satellite center(2).," Leo V also shows signs of being disturbed, with an apparently extended blue horizontal branch distribution and kinematic members more then 10 half light radii away from the satellite center." +. There have also been sugeestious hat Leo V aud the nearby satellite Leo IV are counected oa stellar bridge’. and share a conumuon origin115]leoivleov.," There have also been suggestions that Leo V and the nearby satellite Leo IV are connected by a `stellar bridge', and share a common origin." +. Pisces II has iad no published spectroscopic follow up to date., Pisces II has had no published spectroscopic follow up to date. + Thei stellar populations. based on earlier work.," Their stellar populations, based on earlier work," +We consider a very luminous star blowing a dense wind and a particular shell within that wind.,We consider a very luminous star blowing a dense wind and a particular shell within that wind. + It is accelerated rapidly to the terminal velocity. perhaps several thousand km s!.," It is accelerated rapidly to the terminal velocity, perhaps several thousand km $^{-1}$." + When close to the terminal velocity that expanding shell is effectively detached from the star and thereafter continues to expand with its centre following a straight-line trajectory. the velocity vector of which is equal to the velocity vector of the source at the time of detachment.," When close to the terminal velocity that expanding shell is effectively detached from the star and thereafter continues to expand with its centre following a straight-line trajectory, the velocity vector of which is equal to the velocity vector of the source at the time of detachment." + If the very luminous source is à member of a binary system. the trajectory of the centre of a shell of wind does not deviate as the star continues in its closed orbit.," If the very luminous source is a member of a binary system, the trajectory of the centre of a shell of wind does not deviate as the star continues in its closed orbit." + Thus if emission lines are formed in the shell after the time of detachment. the mean Doppler shift of the shell spectrum will reflect the velocity vector of the source at the time of detachment rather than at the time of formation of the emission lines.," Thus if emission lines are formed in the shell after the time of detachment, the mean Doppler shift of the shell spectrum will reflect the velocity vector of the source at the time of detachment rather than at the time of formation of the emission lines." + If any given shell glows for a time lasting a significant fraction of the binary orbit. at any one moment the centre of any emission line will reflect the velocity of the source. but delayed and averaged over part of the orbit.," If any given shell glows for a time lasting a significant fraction of the binary orbit, at any one moment the centre of any emission line will reflect the velocity of the source, but delayed and averaged over part of the orbit." + The centre of an emission line formed in the wind will (for an approximately circular orbit seen approximately edge on) execute a sinusoidal oscillation with a velocity amplitude smaller than that of a line formed in the atmosphere co-moving with the star., The centre of an emission line formed in the wind will (for an approximately circular orbit seen approximately edge on) execute a sinusoidal oscillation with a velocity amplitude smaller than that of a line formed in the atmosphere co-moving with the star. + This scenario is speculative. but might be relevant to binary systems containing Wolf-Rayet stars or objects with at least some of their observational characteristics.," This scenario is speculative, but might be relevant to binary systems containing Wolf-Rayet stars or objects with at least some of their observational characteristics." + One such object is the Galactic microquasar SS 433. and in this note I suggest that the emission spectrum associated with the wind from the accretion disk exhibits just this behaviour.," One such object is the Galactic microquasar SS 433, and in this note I suggest that the emission spectrum associated with the wind from the accretion disk exhibits just this behaviour." + SS 433 is very luminous and famous for its continual ejection of plasma 1n two opposite Jets at approximately one quarter the speed of light., SS 433 is very luminous and famous for its continual ejection of plasma in two opposite jets at approximately one quarter the speed of light. + The system is a 13-day binary ( probably powered by supereritcal accretion by the compact member from its companion). and the orbital speed of the compact object is fairly well established as ~ 175 km s.," The system is a 13-day binary ( probably powered by supercritcal accretion by the compact member from its companion), and the orbital speed of the compact object is fairly well established as $\sim$ 175 km $^{-1}$." + Despite the fame of the emission lines from the relativistic Jets. the so-called stationary emission lines are much more intense. in particular the brilliant He line.," Despite the fame of the emission lines from the relativistic jets, the so-called stationary emission lines are much more intense, in particular the brilliant $\alpha$ line." + Most aspects of the system are reviewed in Fabrika (2004)., Most aspects of the system are reviewed in Fabrika (2004). + The stationary lines in fact are not quite stationary. rather they exhibit sinusoidal Doppler shifts with a [3-day period: the oscillation of HB and He I stationary emission lines first demonstrated that SS 433 is a binary (Crampton. Cowley Hutchings 1980).," The stationary lines in fact are not quite stationary, rather they exhibit sinusoidal Doppler shifts with a 13-day period; the oscillation of $\beta$ and He I stationary emission lines first demonstrated that SS 433 is a binary (Crampton, Cowley Hutchings 1980)." + The velocity amplitudes of the Balmer series and He I lines. when treated as though they come from a single source. are very roughly 70 km s' and do not provide a direet measure of the orbital speeds of either the compact object or its companion. because they are redshifted most when the compact object is very close to eclipse by the companion (orbital phase 0). rather than a quarter of a period earlier when the compact object is receding fastest from us (orbital phase 0.75); see for example Crampto Hutchings (1981) and Gies et al (2002).," The velocity amplitudes of the Balmer series and He I lines, when treated as though they come from a single source, are very roughly 70 km $^{-1}$ and do not provide a direct measure of the orbital speeds of either the compact object or its companion, because they are redshifted most when the compact object is very close to eclipse by the companion (orbital phase 0), rather than a quarter of a period earlier when the compact object is receding fastest from us (orbital phase 0.75); see for example Crampton Hutchings (1981) and Gies et al (2002)." + This phasing of the emission lines relative to the photometric ephemeris naturally suggests that the Balmer and He I emission lines are formed i an aceretion stream passing from the donor to the companion., This phasing of the emission lines relative to the photometric ephemeris naturally suggests that the Balmer and He I emission lines are formed in an accretion stream passing from the donor to the companion. + However. Gies et al (2002). evidently influenced by the extreme brilliance of the stationary Ha. proposes that these emissio lines are formed in the wind from the aceretion disk. but at distances comparable to or greater than the dimensions of the binary system.," However, Gies et al (2002), evidently influenced by the extreme brilliance of the stationary $\alpha$, proposes that these emission lines are formed in the wind from the accretion disk, but at distances comparable to or greater than the dimensions of the binary system." + In that paper it is suggested that interference with the wind from the disk by the companion. or indeed by a wind from the companion. creates a void in the disk wind.," In that paper it is suggested that interference with the wind from the disk by the companion, or indeed by a wind from the companion, creates a void in the disk wind." + This void would enfeeble the blue part of the spectrum when the companion is between us and the compact object (and conversely enfeeble the red half a period later)., This void would enfeeble the blue part of the spectrum when the companion is between us and the compact object (and conversely enfeeble the red half a period later). + The origins of the stationary emission lines were later clarified by analysis of the stationary He line. in terms of a superposition of several Gaussian profiles (Blundell. Bowler Schmidtobreick 2008). exploiting a remarkable sequence of spectra taken nightly over several orbits (see Schmidtobreick Blundell] 2006).," The origins of the stationary emission lines were later clarified by analysis of the stationary $\alpha$ line, in terms of a superposition of several Gaussian profiles (Blundell, Bowler Schmidtobreick 2008), exploiting a remarkable sequence of spectra taken nightly over several orbits (see Schmidtobreick Blundell 2006)." + The spectra used in Blundell. Bowler Schmidtobreick (2008) are displayed as a montage in Fig.2 of Schmidtobreick Blundell (2006).," The spectra used in Blundell, Bowler Schmidtobreick (2008) are displayed as a montage in Fig.2 of Schmidtobreick Blundell (2006)." + That data set extends from JD 2453245 until JD 245332]. and in Blundell. Bowler Schmidtobreick (2008) the spectra were analysed up to JD +274. after which there was something of a hiatus. followed by an optical outburst and a radio flare (Blundell. Schmidtobreick Trushkin 2011).," That data set extends from JD 2453245 until JD 2453321, and in Blundell, Bowler Schmidtobreick (2008) the spectra were analysed up to JD +274, after which there was something of a hiatus, followed by an optical outburst and a radio flare (Blundell, Schmidtobreick Trushkin 2011)." + Up to JD +274. most Πα spectra were adequately fitted," Up to JD +274, most $\alpha$ spectra were adequately fitted" +Figure 5 shows these dispersions as a function of the corresponding instrumental magnitude for different Saturation typically sets in brightward of ~—13.5 (marked by the left blue vertical line).,Figure \ref{fig:res} shows these dispersions as a function of the corresponding instrumental magnitude for different Saturation typically sets in brightward of $\sim$$-$ 13.5 (marked by the left blue vertical line). +" For well-exposed stars (typically between magnitude —13.5 and —12.5, but we include fainter stars for F225W and F275W filters to improve the statistics), the 68.27* percentile levels of the positional rms are marked by red horizontal lines."," For well-exposed stars (typically between magnitude $-$ 13.5 and $-$ 12.5, but we include fainter stars for F225W and F275W filters to improve the statistics), the $^{\rm th}$ percentile levels of the positional rms are marked by red horizontal lines." +" The corresponding 1-D values are displayed at the top of each panel, in units of both pixels and mas."," The corresponding 1-D values are displayed at the top of each panel, in units of both pixels and mas." + The best results are obtained for redder filters., The best results are obtained for redder filters. + Here we used all the images listed in Table 1 (two to four different epochs for each filter) to compute positional rms., Here we used all the images listed in Table \ref{tab1} (two to four different epochs for each filter) to compute positional rms. +" We will see in the next section that, by selecting only images within the same epoch, positional dispersions are even smaller."," We will see in the next section that, by selecting only images within the same epoch, positional dispersions are even smaller." + We noted that very blue and very red stars behave differently with respect to our GD correction when observed through the bluest filters (Kozhurina-Platais et ((2011) see a similar effect)., We noted that very blue and very red stars behave differently with respect to our GD correction when observed through the bluest filters (Kozhurina-Platais et (2011) see a similar effect). + This is probably due to a chromatic effect induced by fused-silica CCD windows within the optical, This is probably due to a chromatic effect induced by fused-silica CCD windows within the optical +Tlence. one can find (he age of the large-scale jet in 3C 273 by substituting into equation 14 the head velocity Speaq=O.837/cos8 (equation 8 for 2=101 and a=0.8) and separation of the jet head from the core dy.)=60 Κρο to obtain {μαι~3.8x101cotà vrs.,"Hence, one can find the age of the large-scale jet in 3C 273 by substituting into equation 14 the head velocity $\beta_{\rm head} = 0.837 / \cos \theta$ (equation 8 for $R = 10^4$ and $\alpha = 0.8$ ) and separation of the jet head from the core $d_{\rm proj} = 60$ kpc, to obtain $t_{\rm jet} \sim 3.8 \times 10^4 \, \cot \theta$ yrs." + For 0=10° it is ligo2.1xLO? vis. and for 0=30° one obtains fj~0.7xLO? vrs.," For $\theta = 10^{\circ}$ it is $t_{\rm jet} \sim 2.1 \times 10^5$ yrs, and for $\theta = 30^{\circ}$ one obtains $t_{\rm jet} \sim 0.7 \times 10^5$ yrs." + Thus. we take the age of the large-scale jet in 3C 273 to be roughly fj~LO? yrs.," Thus, we take the age of the large-scale jet in 3C 273 to be roughly $t_{\rm jet} \sim 10^5$ yrs." + As the head/counter-head brightness asvmmetry gives only a lower limit on Z4. value 107 vrs should be considered as an upper limit for the time since formation of the considered structure.," As the head/counter-head brightness asymmetry gives only a lower limit on $\beta_{\rm head}$, value $10^5$ yrs should be considered as an upper limit for the time since formation of the considered structure." + The ratio of the projected separation of the jet head from the active center to the projected separation of the counter-head is For R=10 and a=0.8 one gets Q=11.3., The ratio of the projected separation of the jet head from the active center to the projected separation of the counter-head is For $R = 10^4$ and $\alpha = 0.8$ one gets $Q = 11.3$. +" That is. the projected distance of the counter-head from the quasar core is expected to be deprop=dpwi/Q@1.9""~5 kpc."," That is, the projected distance of the counter-head from the quasar core is expected to be $d_{\rm c-proj} = d_{\rm proj} / Q = 1.9'' \sim 5$ kpc." + Now. the optical (and X-ray) jet is visible starting from ~12” from the core.," Now, the optical (and X-ray) jet is visible starting from $\sim 12''$ from the core." +" It is nol clear. if this gap between (he active center and the first appearance of the optical structure is due to Doppler-hiding of the jet emission at distances <12"". or if it is due to intermittent/modulated jet activity leading to the formation of the ""partial. jet."," It is not clear, if this gap between the active center and the first appearance of the optical structure is due to Doppler-hiding of the jet emission at distances $< 12''$, or if it is due to intermittent/modulated jet activity leading to the formation of the `partial' jet." + Note. that ihe continuous radio emission in this region can be connected with the ‘false jet structure: obtained in the numerical simulation of the restarting jets bv Clarke&Burns(1991).. i.e. with the cocoon material collapsing on the abandoned jet channel.," Note, that the continuous radio emission in this region can be connected with the `false jet structure' obtained in the numerical simulation of the restarting jets by \citet{cla91}, i.e. with the cocoon material collapsing on the abandoned jet channel." + One mary also note. (hat ihe modulation in the jel kinetic power can involve solely modulation of the particle flux density. and not the jet bulk velocity.," One may also note, that the modulation in the jet kinetic power can involve solely modulation of the particle flux density, and not the jet bulk velocity." + Hf one agrees that the eap in the optical (and. N-rav) emission of the 3C: 273 jet is indeed due to modulated activity of the central engine. i.e. that the projected length of the considered large-scale jet is fig7LO”. the expected length of the counterjet 15 ↴∏∏⋟∖⇁↕↽≻≀↕↴↕⋅≀↕↴∐∐↲∩↲↕⋅⋅≀↕↪∖⊽≀↧↴↓⋟∏∐≺∢∐∪∐∪↓⋟⊔∐↲∙↿≼↲↥∖↽↕≼↲∖∖⇁↕∐≸↽↔↴≀↧↴∐≸↽↔↴↥≼↲∣⇥∶∐↾≓−≡⋅↽⊰∩≓⋅↕⋟∖⊽⋟∖⇁∐∪∖∖⊽∐∪∐⇂∎↓≸↽↔↴∏↕⋅≼↲ ⋮⋅↽⊰↓⋟∪↕⋅↕⇁∙⊜≺⋅↿∶⇀↱≻≀↧↴∐≺⇂↓∩⋅⊟," If one agrees that the gap in the optical (and X-ray) emission of the 3C 273 jet is indeed due to modulated activity of the central engine, i.e. that the projected length of the considered large-scale jet is $l_{\rm jet} \sim 10''$, the expected length of the counterjet is This parameter, as a function of the jet viewing angle $\theta = 10^{\circ} - 30^{\circ}$, is shown on figure 3 for $\Gamma_{\rm jet} = 5$ and 10." +≻↕⋅≺∢∪∐↕↕↽≻≀↧↴↕⋅↕⋟∖⊽∪∐⋅⊔∐↲∏↕↽≻↕↽≻≼↲↕⋅∐∐↓∐↓≯∪↕⋅↙∣⋅⊲↓⋝↓⋅⊓∙⇪↕⋟∖⊽≀↧↴↥⋟∖⊽∪↕↽≻," For comparison, the upper limit for $d_{\rm c-proj}$ is also presented." +↕⋅≼↲⋟∖⊽≼↲↕↥∩↲≺⇂⋅↴∏∐↲↕⋅≼↲↓⋟∪↕⋅≼↲⋅ ⊔∐↲∐∪↕↽≻↕↽≻↥≼↲↕⋅≀↧↴∐≺⇂∐∐∐↲−∏⋅≀↧↴∖↽≼↲↥≼↲∐≱≼↲≺∢↥⊳∖⇁≺∢≀↧↴∐≼↲≀↧⊔∖⇁∐∡∖↽≼↲⇀↸↕↽≻↥≀↧↴↕∐↥≀↧↴≺∢↳↽∪↓⋟⊔∐↲≺∢∪∏∐∥↲↕⋅−∙↿," Therefore, the Doppler and time-travel effects can easily explain lack of the counter-jet at the opposite side of the 3C 273 quasar." +≼↲↥≀↧↴↥⊔∐↲∪↕↽≻↕↽≻∪⊳∖⇁∐≼↲ ⋟∖⊽↕≼⇂≼↲∪↓≯⊔∐↲⊑↽⊰≼↕⊲⊐⊤⊑↽⊰≺↥∏≀↧↪∖⇁≀↧↴↕⋅⋅∖∖⊽≼↲↕↽≻↕⋅∪↕↽≻∪⊳∖⊽≼↲⋅⊔⋯↴↥≀↧⊥∖⇁∪⊔∐↲≀↧↴↕↽≻↕↽≻≀↧↴↕⋅≼↲∐↥↥⋯∢↳↽∪↓⋟⊔∐↲∐↕≸≟∐⊳∖⊽⋯⋅↓⋟≀↧↴≺∢≼↲ ∣↽≻↕⋅↕↖≺↽↔↴∐∏∐↲⋟∖⋱∖⊽↕≻≀↧↴↕⋅↥∪↓⋟⊔∐↲≺∢∪∏↕∐≼↲↕⋅−," We propose, that also the apparent lack of the high surface brightness part of the counter-lobe (analogous to the radio cocoon enveloping $12'' - 23''$ jet) can be explain in a similar way." +↥∪∣↽≻≼↲⋖⋡≀↧↴∐≀↧↴↥∪≸↽↔↴∪∏⋟∖⊽↥∪⊔∐↲↕⋅⋯∐∪≺∢∪≺∢∪∪∐≼↲∐∖↽≼↲↥∪↕↽≻↕∐≸↽↔↴⊔∣∣−∃⊑↽⊰∣∣∙↿≼↲↥↕⋝ ≺∢≀↧↴∐∣↽≻≼↲≼↲⇀↸↕↽≻↥≀↧↴↕∐↕∐≀↧⊔∖⊽↕∐↓∐≀↧↴↕⋅∖∖⊽≀↧∶∖⇁⋅↳∖↡∪∩↲⋅⊔⋯↴↥↓⋟∪↕⋅≀↧↴↕⋅≼↲↥≀↧↴∐∖↽↕⊳∖⇁∐≺∢∖↽≼↲↥∪≺∢∐∡∖↽∪↓⋟⊔∐↲∙↿≼↲↥↥∐↲⋯⇂⋅⊔∐↲ ∙↿≼↲↥∐," Note, that for a relativistic velocity of the jet head, the jet matter turned-back at the hot-spot region may be still relativistic in the observer frame." +⋯↴⊔≼↲↕⋅⊓∐⋅∐≼↲≼⇂−∣↽≻≀↧↴≺∢↳↽≀↧↴↥⊔∐↲∐∪⊢⋝∖⊽↕↽≻∪↥↕⋅≼↲≸↽↔↴↕∪∐∐↓≀↧∶∖↽∣↽≻≼↲⋝∖⊽∐∐↕⋅≼↲↥≀↧↴∐∖⇁↕⋝∖⊽∐≺∢↕∐⊔∐↲∪∣↽≻⊳∖⇁≼↲↕⋅∖↽≼↲↕⋅↓≯↕⋅≀↧↴∐∐↲⋅ This issue cannot be discussed in more details in the present. paper. but. we believe that," This issue cannot be discussed in more details in the present paper, but we believe that" +being conuuon iu radio pulsar systems and planctary systems(dxuutsonuetal.2007:Tebrard2010:Agolctal. 2010).. although in the latter it is larecly a nuisance parameter aud docs not coustrain the svsteus.,"being common in radio pulsar systems and planetary systems\citep{kcn+07,hdd+10,ack+10}, although in the latter it is largely a nuisance parameter and does not constrain the systems." + I discuss its applicability to eclipsing double WD systeuis. the required. observational precision and the resulting accuracy.," I discuss its applicability to eclipsing double WD systems, the required observational precision and the resulting accuracy." + Tn a svsteni with a circular orbit. oue often speaks of the primary and secondary eclipses as occurring exactly 1/2 period apart. but this is not the case.," In a system with a circular orbit, one often speaks of the primary and secondary eclipses as occurring exactly $1/2$ period apart, but this is not the case." + If the 1ienibers of the binary are of unequal mass the finite speed of light will cause an apparent shift iu the phase of the secoudary eclipse frou 2/2. where P is the period of the binary (Loeb2005:Fabrvckyv2010).," If the members of the binary are of unequal mass the finite speed of light will cause an apparent shift in the phase of the secondary eclipse from $P/2$, where $P$ is the period of the binary \citep{loeb05,fabrycky10}." + This is similar to the shifts in eclipse timing caused by a perturbing third body on a binary system (Schueider&Dovle1995:etal.Qianetal. 2009).. although here one only requires two xxdies aud the frequeney of the shift is known.," This is similar to the shifts in eclipse timing caused by a perturbing third body on a binary system \citep{sd95,ddj+98,ddk+00,sterken05,lkk+09,qdl+09}, although here one only requires two bodies and the frequency of the shift is known." + Iu the case of a planet with mass i9 outwards from the crust is in Tact much smaller than that generated by the hydrogen/helium burniug.," In \ref{s:results}, I show that the luminosity flowing outwards from the crust is in fact much smaller than that generated by the hydrogen/helium burning." +" The secoucd bouncary M!=dition. then. is T|,2~=Ti(mn). whe‘e TL take 1. froin (1999)."," The second boundary condition, then, is $T|_{r=R} = T_\circ(\dot{m})$, where I take $T_\circ$ from \citet{schatz99}." +. Here ii is the accretion rate per uuit area: the ficlucial rate used by Selaazetal.(1999) is the Edcdingtou rate appropriate for a Newtonian star of M=1.LAZ. and &=!LOkim accreting a solar composition plasma.," Here $\dot{m}$ is the accretion rate per unit area; the fiducial rate used by \citet{schatz99} + is the Eddington rate appropriate for a Newtonian star of $\Mg=1.4\Msun$ and $R=10\km$ accreting a solar composition plasma." + Numerically. this rate is nip=8.8x10ecm>7s batd is an excellent approximation to the lowest local accretion rate at which the lycl'ogen/helium ourniug Is stable (see.e.g..Bildsten1993)...," Numerically, this rate is $\dot{m_E}=8.8\ee{4}\gram\cm^{-2}\second^{-1}$ and is an excellent approximation to the lowest local accretion rate at which the hydrogen/helium burning is stable \citep[see, +e.g.,][]{bildsten98:_nuclear}." + At ii=mig. the temperature at the base ¢X tlie hydroger/helium burning shell is T;=5κ105 IN.," At $\dot{m}=\dot{m}_E$, the temperature at the base of the hydrogen/helium burning shell is $T_\circ=5\ee{8}\K$ ." + Although the Newtonian surface gravity tsed by Schatzetal.(1999). is less than the values used here. 75 is relatively insensitive to g (T;xg!/*:Bildste1 1998)). so I do uot adjust it for each model.," Although the Newtonian surface gravity used by \citet{schatz99} is less than the values used here, $T_\circ$ is relatively insensitive to $g$ $T_\circ\propto g^{1/7}$;\citealt{bildsten98:_nuclear}) ), so I do not adjust it for each model." +" This is not critical. as the thermal proile iu the crus Is insensitive to T.,(see& ?7))"," This is not critical, as the thermal profile in the crust is insensitive to $T_\circ$ (see \ref{s:results}) )." + The accretion rate enters equations (9)) and (10)) through εν. which is scalec to he accretion luminosity £4.," The accretion rate enters equations \ref{eq:entropy}) ) and \ref{eq:flux}) ) through $\eN$, which is scaled to the accretion luminosity $L_A$." + Because 7. is ouly a function of η. E use the same m for each moclel: 11e luminosity [rom this accretion is then different for each EOS aud mass.," Because $T_\circ$ is only a function of $\dot{m}$, I use the same $\dot{m}$ for each model; the luminosity from this accretion is then different for each EOS and mass." + The global accretion rate. as measured. by an observer infinitely far away. is CXyasli&Joss1982) Al=lrCin(14-2). and tle luminosity is For the fiducial local accretion rate ij. model thas Ly=L4—1.95x10Συ. thas L=sx10Seresty ΙΕ1Σ.. 2.12x10eres|: andMILS-I8..2.51x107eres+.," The global accretion rate, as measured by an observer infinitely far away, is \citep{ayasli82} $\dot{M}=4\pi R^2 \dot{m}/(1+z)$, and the luminosity is For the fiducial local accretion rate $\dot{m}_E$, model has $L_A=\LAo=1.95\ee{38}\erg\second^{-1}$; has $\LAo=2.28\ee{38}\erg\second^{-1}$; , $2.12\ee{38}\erg\second^{-1}$; and,$2.51\ee{38}\erg\second^{-1}$." + To solve the thermal structure. equations (9)) and (10)) are finite-cdifIereuced onto the mesh defined yy the integration of equations (2))-(5)).," To solve the thermal structure, equations \ref{eq:entropy}) ) and \ref{eq:flux}) ) are finite-differenced onto the mesh defined by the integration of equations \ref{e:radius}) \ref{e:pressure}) )." +" An initial guess is constructed by fixing the temperature hroughout the star to 7; aud integrating equation (9)) from L),29= 0.", An initial guess is constructed by fixing the temperature throughout the star to $T_\circ$ and integrating equation \ref{eq:entropy}) ) from $L|_{r=0}=0$ . + This trial guess is then iteratively refined. by a relaxation technique (Pressetal.1992).. The resolution of the mesh was ested by computing models with step fractions (see eq. [7]]), This trial guess is then iteratively refined by a relaxation technique \citep{pre92}.. The resolution of the mesh was tested by computing models with step fractions (see eq. \ref{eq:stepsize}] ]) +f=0.05 and f= 0.02.,$f=0.05$ and $f=0.02$ . +"For the determination, CSPEC data (?) with a time resolution of 1.024 s (4.096 s pre-trigger) were used.","For the determination, CSPEC data \citep{meegan09} with a time resolution of 1.024 s (4.096 s pre-trigger) were used." +" For the short GRBs, i.e. those with Too<2 s, time-tagged event ?) data were used with a fine time resolution of 64 ms and the same channel boundaries as CSPEC data."," For the short GRBs, i.e. those with $T_{90} \le 2$ s, time-tagged event \citep[TTE,][]{meegan09} data were used with a fine time resolution of 64 ms and the same channel boundaries as CSPEC data." + Detectors with source angles greater than 60° and those occulted by the spacecraft or solar panels were discarded., Detectors with source angles greater than $^\circ$ and those occulted by the spacecraft or solar panels were discarded. +" A maximum of three Nal detectors were used for each E, determination.", A maximum of three NaI detectors were used for each $E_p$ determination. +" In four cases (GRB 090929A, GRB 090904B, GRB 090618, and GRB 081007) only one Nal detector could be used due to the reasons mentioned above."," In four cases (GRB 090929A, GRB 090904B, GRB 090618, and GRB 081007) only one NaI detector could be used due to the reasons mentioned above." +" Where possible, both BGO detectors were included in the analysis if they were not occulted by the satellite during the prompt emission."," Where possible, both BGO detectors were included in the analysis if they were not occulted by the satellite during the prompt emission." +" Even if there was no apparent signal in the BGOs, they can help to determine an upper limit of the GRB signal in the spectra."," Even if there was no apparent signal in the BGOs, they can help to determine an upper limit of the GRB signal in the spectra." + The spectral analysis was performed with the software package (version 3.3rc8) and the GBM Response Matrices v1.8., The spectral analysis was performed with the software package (version 3.3rc8) and the GBM Response Matrices v1.8. +" To account for the changing orientation of the source with respect to the detectors caused by the slew of the spacecraft, the detector response matrices (DRM) were generated for every 2 degrees on the sky."," To account for the changing orientation of the source with respect to the detectors caused by the slew of the spacecraft, the detector response matrices (DRM) were generated for every 2 degrees on the sky." + For each burst we fitted for every energy channel a low-order polynomial to a user defined background interval before and after the prompt emission and interpolated this fit across the source interval., For each burst we fitted for every energy channel a low-order polynomial to a user defined background interval before and after the prompt emission and interpolated this fit across the source interval. +" Three model fits were applied to all time bins with a signal-to-noise (S/N) of at least 3.5 above the background model: a single power-law (PL), a power law function with an exponential high energy cutoff (COMP) and the Band function (?).."," Three model fits were applied to all time bins with a signal-to-noise (S/N) of at least 3.5 above the background model: a single power-law (PL), a power law function with an exponential high energy cutoff (COMP) and the Band function \citep{band93}." +" For three GRBs (GRB 090424, GRB 090618, and GRB 0909264) an effective area correction was applied to the BGO with respect to the Nal detectors to account for systematics which dominate the statistical errors due to the brightness of these events."," For three GRBs (GRB 090424, GRB 090618, and GRB 090926A) an effective area correction was applied to the BGO with respect to the NaI detectors to account for systematics which dominate the statistical errors due to the brightness of these events." + The best model fit is the function which provides the best Castor C-stat value (?).., The best model fit is the function which provides the best Castor C-stat value \citep{cash79}. + An improvement by AC-stat= 10 for every degree of freedom is required., An improvement by $\Delta$ $=10$ for every degree of freedom is required. + The profile of the Cash statistics was used to estimate the lo asymmetric error., The profile of the Cash statistics was used to estimate the $\sigma$ asymmetric error. +" The values obtained with this analysis method may be superseded by the GBM spectral catalogue released by the GBM team (Goldstein et al.,"," The values obtained with this analysis method may be superseded by the GBM spectral catalogue released by the GBM team (Goldstein et al.," + in preparation)., in preparation). + A first important issue which needs to be addressed is whether the bursts observed by GBM are drawn from the same distribution as the bursts which were observed byBATSE., A first important issue which needs to be addressed is whether the bursts observed by GBM are drawn from the same distribution as the bursts which were observed by. +". Because of the broader sensitivity of GBM to higher energies, there could be a significant deviation towards higher values."," Because of the broader sensitivity of GBM to higher energies, there could be a significant deviation towards higher values." +" To answer this question, we use the from which we extract the values which were obtained from the time averaged spectra (fluence spectral fits)."," To answer this question, we use the from which we extract the values which were obtained from the time averaged spectra (fluence spectral fits)." +" Ignoring the power-law (PL), Gaussian Log and Smoothly Broken Power Law (SBPL) fits, we elected to the COMP model or Band function for the purpose of this test."," Ignoring the power-law (PL), Gaussian Log and Smoothly Broken Power Law (SBPL) fits, we elected to the COMP model or Band function for the purpose of this test." +" We require ΔΕΡ/Ερx0.4 and the low-energy power-law index, α has an absolute error c,€0.4."," We require $\Delta E_{\rm{p}} /{E_{\rm{p}}} \le 0.4$ and the low-energy power-law index, $\alpha$ has an absolute error $\sigma_{\alpha} \le 0.4$." + GRBs which did not fulfill these criteria were rejected from the sample., GRBs which did not fulfill these criteria were rejected from the sample. + The Band function was always preferred over the COMP model in cases in which the high-energy power-law index £8 was constrained (og< 0.4)., The Band function was always preferred over the COMP model in cases in which the high-energy power-law index $\beta$ was constrained $\sigma_{\beta} < 0.4$ ). + Both long and short GRBs were included in this analysis., Both long and short GRBs were included in this analysis. + The so obtained distribution shown in Fig. 2.., The so obtained distribution shown in Fig. \ref{fig:epbatse}. + The same selection cut was applied to the 2-year GBM spectral catalogue., The same selection cut was applied to the 2-year GBM spectral catalogue. + The red histogram in Fig., The red histogram in Fig. + 2 shows this distribution., \ref{fig:epbatse} shows this distribution. + Both distributions peak at « 170 keV and show the same standard deviation., Both distributions peak at $\approx$ 170 keV and show the same standard deviation. + A KS test reveals that the difference between the two samples is not statistically meaningful (P— 18%))., A KS test reveals that the difference between the two samples is not statistically meaningful $P=18$ ). +" This means that the two histograms are drawn from the same distribution, in agreement with ?.."," This means that the two histograms are drawn from the same distribution, in agreement with \citet{nava10}." +" We note that, ? showed that the distribution of some GBM-GRBs extends to higher energies compared to (?).."," We note that, \citet{bissaldi11} showed that the distribution of some GBM-GRBs extends to higher energies compared to \citep{kaneko06}." +" However, this is of no surprise as ? demonstrated that bursts with higher fluence, i.e. higherEjso,, have, on average, higher (see also Sect.4.1))."," However, this is of no surprise as \citet{amati02} demonstrated that bursts with higher fluence, i.e. higher, have, on average, higher (see also \ref{subsec:amati}) )." +" Since ? only use bright GRBs, it is to be expected that their distribution is shifted to higher energies."," Since \citet{bissaldi11} only use bright GRBs, it is to be expected that their distribution is shifted to higher energies." +" We conclude that GBM, although being sensitive up to 40 MeV, does not find a previously undiscovered population of GRBs, consistent with ?.."," We conclude that GBM, although being sensitive up to 40 MeV, does not find a previously undiscovered population of GRBs, consistent with \citet{harris98}. ." +"center of the line is 7=nyouRe,zz105.",center of the line is $\tau= n_H \sigma_0 R_{\rm vir}\approx 10^7$. + For a thermal speed of ~10 km slat requires a shift iu frequency bv an amount 6A/Az3«107? to diffuse out of the optically thick core of a Voiet-profile (i.e. to a frequency where 7= 1)., For a thermal speed of $\sim 10$ km $^{-1}$ it requires a shift in frequency by an amount $\delta\lambda/\lambda\approx 3\times 10^{-3}$ to diffuse out of the optically thick core of a Voigt-profile (i.e. to a frequency where $\tau=1$ ). + This will significantly broaden the line. to ~1.000lius3: it world also further flatten the surfacebrightuess profile.," This will significantly broaden the line, to $\sim +1,000~{\rm km~s^{-1}}$; it would also further flatten the surface brightness profile." +" Depending on the iufall velocity aud neutral deusitv structure. the hne may exhibit a characteristic ""doublehwuup profile."," Depending on the infall velocity and neutral density structure, the line may exhibit a characteristic “double–hump” profile." + It would be very interesting to extract these quautities directly from à three.dimensional simulation iu the future. since the angular resolution aid spectral capabilities ofANGST should be sufficient to map the surface brightuess distribution. aud to determine the line profile. at least for the brightest halos.," It would be very interesting to extract these quantities directly from a three–dimensional simulation in the future, since the angular resolution and spectral capabilities of should be sufficient to map the surface brightness distribution, and to determine the line profile, at least for the brightest halos." + Here we simply note that the characteristic linewidths of —1000luus+. as well as the extended. and relatively shallow surtace briehtuess profiles. would be robust mdicators of the initial stages of the collapse.," Here we simply note that the characteristic line–widths of $\sim 1000~{\rm +km~s^{-1}}$, as well as the extended, and relatively shallow surface brightness profiles, would be robust indicators of the initial stages of the collapse." + We have considered the Lae flux from barvouic gas condensing and cooling inside Lighredshift galactic DA halos., We have considered the $\alpha$ flux from baryonic gas condensing and cooling inside high–redshift galactic DM halos. + Since the hymn in theuniverse is reionize bevond a redshift “-+6. the cooling radiation would not suffer stroue in the neutral ΤΝΤ below this redshift (cf.," Since the hydrogen in the universe is reionized beyond a redshift $z\approx 6$, the cooling radiation would not suffer strong scattering in the neutral IGM below this redshift (cf." + Rybicki Loeb 1999). but the halos woule still appear extended ou the sky with au augular diameters of =107.," Rybicki Loeb 1999), but the halos would still appear extended on the sky with an angular diameters of $\approx 10$." +. We have ignored the radiation of the initia hermal euergv of the gas., We have ignored the radiation of the initial thermal energy of the gas. + Most of this energy is radiatec iu the continua as Droiisstralilung. but is too faint to be observable withXO orN," Most of this energy is radiated in the continuum as Bremsstrahlung, but is too faint to be observable with or." +ALAL However. for sufficiently netalpoor halos. z10:4 of the initial thermal cucrey could be released by He! Lye cooling.," However, for sufficiently metal–poor halos, $\approx 10\%$ of the initial thermal energy could be released by $^+$ $\alpha$ cooling." + This cuiission ikelv occurs ou the haloassembly timescale. aud would accompany our hydrogen Lya signal at a wavelength 1 nues shorter. and with a z10 times lower line fiux.," This emission likely occurs on the halo–assembly time–scale, and would accompany our hydrogen $\alpha$ signal at a wavelength 4 times shorter, and with a $\approx10$ times lower line flux." + It is interesting to compare the overall biudiug euergv radiated in Lyo photous by the pristine halos aud the stellar Ίσα kuown to be produced in “normal” salaxies., It is interesting to compare the overall binding energy radiated in $\alpha$ photons by the pristine halos and the stellar $\alpha$ known to be produced in “normal” galaxies. +" The total specific cnerey radiated iu Lya is E(cool)z 20. where ο is the circular velocity,"," The total specific energy radiated in $\alpha$ is $E({\rm cool})\approx 2v_c^2$ , where $v_c$ is the circular velocity." + According to Keunicut (1998). 1 solar mass of gas evcled through stars releases 3.1os109 cre in Lye.," According to Kennicut (1998), 1 solar mass of gas cycled through stars releases $3.1\times 10^{49}$ erg in $\alpha$ ." +" Ass1ming that 10% of the eas is converted into stars; we fiud a specific energy of L(stars)=1.;«10SF, "," Assuming that $10\%$ of the gas is converted into stars, we find a specific energy of $E({\rm stars})=1.7\times 10^{-6}c^2$ ." +As a result. for a «‘200 αιἐν halo we fud É(cool)/E(stirs)=0.5.," As a result, for a $v_c=200$ km/s halo we find $E({\rm cool})/E({\rm +stars})= 0.5$." + This relatively laree ratio demonstrates that the total flux in the cooling radiatiou can be comparable to that im stellar Lya cunission lines., This relatively large ratio demonstrates that the total flux in the cooling radiation can be comparable to that in stellar $\alpha$ emission lines. +" Our predictions for the ἩNCS, aneular sizes. characteristic linewidth. srface brightness profiles. aud the umber of sources are in €5fayQOC aerecuuent wilh the two Lya “blobs” discovered at: hic3.09 ia 7S sq."," Our predictions for the fluxes, angular sizes, characteristic line–width, surface brightness profiles, and the number of sources are in good agreement with the two $\alpha$ “blobs” discovered at $z=3.09$ in a 78 sq." + ain field by Steidel et al. (, amin field by Steidel et al. ( +19909). xv1 eads us to believe. that examples of cooling Ίσα hal5 nav already iive been found.,"1999), which leads us to believe that examples of cooling $\alpha$ halos may already have been found." +" Our simple spherical model. however. xediets a ""doublehup? line profile. wuch is not seeu x Steidel et al."," Our simple spherical model, however, predicts a “double–hump” line profile, which is not seen by Steidel et al." + Further work is require to assess whether the 3D structure of the collapsiug halo can wash out the predicted double peak., Further work is required to assess whether the 3D structure of the collapsing halo can wash out the predicted double peak. + Our results show that a few «ozen cooling halos could be detecteclin the future out to zz:6Sinasinele UsU field. observed for 2.5 ksec withST.," Our results show that a few dozen cooling halos could be detected in the future out to $z\approx 6-8$ in a single $4^\prime\times4^\prime$ field, observed for 2.5 ksec with." +" In order to exteud tle redshift range over which this sudy is feasible. a large area survev withNGST wouk be desirable. with a relatively broad filter (to capture rarer. ... halos. over a larger redshift range). as well as waveleugth coverage extending down to c0.Lyra {ο capture halos at redshifts as low as olom 3),"," In order to extend the redshift range over which this study is feasible, a large area survey with would be desirable, with a relatively broad filter (to capture rarer, $z$ halos, over a larger redshift range), as well as wavelength coverage extending down to $\approx0.4\mu$ m (to capture halos at redshifts as low as $z\approx 3$ )." + Using a LAarrowband filter that minimizes the backeround woud allow the detection of additional. fainter sources. and a detailed study of the brighter halos.," Using a narrow–band filter that minimizes the background would allow the detection of additional, fainter sources, and a detailed study of the brighter halos." + The cooling halos would be a novel aud direct probe of ealaxy formation iu fie hiehredshift universe. aud of their evolutionary listory Toni ;zm6S to lower redshifts.," The cooling halos would be a novel and direct probe of galaxy formation in the high–redshift universe, and of their evolutionary history from $z\approx 6-8$ to lower redshifts." + ZII thauks the hosvitality of the ITP a the University of Califoruia at Santa Barbara. where some of this work. was carried out.," ZH thanks the hospitality of the ITP at the University of California at Santa Barbara, where some of this work was carried out." + The authors eratctully acknowledge discussions with T. Abel. L. Bildsten. C. Steidel. AL Steimmetz. N. watz. C. Ixocliuxds. and BR. Bernstein.," The authors gratefully acknowledge discussions with T. Abel, L. Bildsten, C. Steidel, M. Steinmetz, N. Katz, C. Kochanek, and R. Bernstein." + This research was supported by NASA through ΠΠ]de Fellowship erauts TF-O1101L.01-97A (to MIS) aud IIE- (to ZI). audthrough. Chaidra Fellowshipevant PE9-10008 (to EQ). aud bv the NSF under Cranut No.," This research was supported by NASA through Hubble Fellowship grants HF-01101.01-97A (to MS) and HF-01119.01-99A (to ZH), andthrough Chandra Fellowshipgrant PF9-10008 (to EQ), and by the NSF under Grant No." + PIIY91-07191 at the ITP., PHY94-07194 at the ITP. +are turbulent.,are turbulent. + Papaloizou Nelson (2003 hereafter DN2003). examined. and characterised tle turbuleuce obtained in a variety of ΑΠΟ disk models., Papaloizou Nelson (2003 – hereafter PN2003) examined and characterised the turbulence obtained in a variety of MHD disk models. + Nelson Papaloizou (2003 hereafter NP2003) exanuned the iueraction between a elobal cylindrical disk model aud ao dnnassve (5 .hpiter imasses) protoplanet., Nelson Papaloizou (2003 – hereafter NP2003) examined the interaction between a global cylindrical disk model and a massive (5 Jupiter masses) protoplanet. + A simular study was undertaken by Winters. Balbus. Dawley (2003).," A similar study was undertaken by Winters, Balbus, Hawley (2003)." + Papaloizou. Nelson. Sucllerove (2001 hereafter PNS2001) perforued elod exhindrical disk simulations aud local sheariis box simulations of turbulent disks interacting with protoplauets of different mass.," Papaloizou, Nelson, Snellgrove (2004 – hereafter PNS2004) performed global cylindrical disk simulations and local shearing box simulations of turbulent disks interacting with protoplanets of different mass." + The main focus of that paper was to characterise the changes im How morphology and disk structure as a fiuctiou of anet mass. auk to exanine the transition frou linear ο non linear interaction leading to eap formation.," The main focus of that paper was to characterise the changes in flow morphology and disk structure as a function of planet mass, and to examine the transition from linear to non linear interaction leading to gap formation." + Nelson Papaloizou (2OL hereafter NP2001) exauined the uieration of low and high mass protoplanets in turbucut disks bv exinuninse the time evolution of the ΤουςMes exerted on the planets bv the disks., Nelson Papaloizou (2004 – hereafter NP2004) examined the migration of low and high mass protoplanets in turbulent disks by examining the time evolution of the torques exerted on the planets by the disks. + Trev noticed that ow nass planets experienced stronglv varying forques due to interaction with the turbulent density fluctuations. and sugeestec that such plajets would undergo stochastic uieratiou rather than monotonic duwourd nuüeration rormally associated with tvpe I nuüeration iu laminar disks.," They noticed that low mass planets experienced strongly varying torques due to interaction with the turbulent density fluctuations, and suggested that such planets would undergo stochastic migration rather than monotonic inward migration normally associated with type I migration in laminar disks." + The plaucts. lowever. were maintained on fixec circular orbits and sO heir nügratiou could not be examunued directly.," The planets, however, were maintained on fixed circular orbits and so their migration could not be examined directly." + Iu this paper we xeseut the results of simulations of low mass protopalnets oniedae in turbulent. naenoetisec disks. iud alow tie plane orbits to evolve due to iuteraction with t1C (lis.," In this paper we present the results of simulations of low mass protoplanets embedded in turbulent, magnetised disks, and allow the planet orbits to evolve due to interaction with the disk." + Iu order to sample t10 roadise of outcomes. we cosider asuall ensemble of planets iu each simulation.," In order to sample the range of outcomes, we consider a small ensemble of planets in each simulation." + We flud that 1 all simulations performed. the Orces experieucec by the protoplauet are highlv variable. and as a result the protopanoet orbits evolve similarly to a random walk.," We find that in all simulations performed, the forces experienced by the protoplanet are highly variable, and as a result the protoplanet orbits evolve similarly to a random walk." + A sinie analvsis suggests that he heavier auets we consider ought to undergo inward migration xedonmimnautly due to the underlviung type I torques. but he simulations on the whole are not iu agreement with lis prediction.," A simple analysis suggests that the heavier planets we consider ought to undergo inward migration predominantly due to the underlying type I torques, but the simulations on the whole are not in agreement with this prediction." + Fourier analysis of the torques experieuced w the plauets indicates that they experieuce stochastic orces with a broad range of associated time scales of variation. ranging from the planet orbital period to the simulation run time itself.," Fourier analysis of the torques experienced by the planets indicates that they experience stochastic forces with a broad range of associated time scales of variation, ranging from the planet orbital period to the simulation run time itself." + These long time scale variations clearly coutri»ite to he long terii stochastic behaviour of the planets observed in the simulations., These long time scale variations clearly contribute to the long term stochastic behaviour of the planets observed in the simulations. + There is some evidence that the uuderlviug type I migration is nioified in turbulent disks. but this is not coucluzive.," There is some evidence that the underlying type I migration is modified in turbulent disks, but this is not conclusive." + The results also iudicate that AMID turbulence is able to drive siguLB.ficant erowth of eccenricitics for low Lass objects., The results also indicate that MHD turbulence is able to drive significant growth of eccentricities for low mass objects. + Iu particular. plauctesimals aud planets with Masses slnudar to the Earth cau obtain ecceutricitics ο~ 0.1.," In particular, planetesimals and planets with masses similar to the Earth can obtain eccentricities $e \sim 0.1$ ." + This clearly has potentially im)ortanf consequences for planctary accumulation models., This clearly has potentially important consequences for planetary accumulation models. + Heavier planets attain lower eccentricities appareutlv because their interaction with the disk at coorbital Lindhlacd resonances causes eccentricity damping (e.g. Artvinowiez 1993: Papaloizou Larwood 2000)., Heavier planets attain lower eccentricities apparently because their interaction with the disk at coorbital Lindblad resonances causes eccentricity damping (e.g. Artymowicz 1993; Papaloizou Larwood 2000). + The plan of the paper is as follows., The plan of the paper is as follows. + Iu section 2 we describe the governing equations.," In section \ref{eqns} + we describe the governing equations." + Du sections 3. and Lo we cleserihe the umimerical method and the system of uuts 1sed., In sections \ref{num_method} and \ref{units} we describe the numerical method and the system of units used. + The initial aud boundary conditions used int jio suunulations are described iu section 5.. aud the sinulatioj results are presented im section 6...," The initial and boundary conditions used in the simulations are described in section \ref{Init-bound}, and the simulation results are presented in section \ref{results}." + We discuss +1ο sinulatiou results mi sections 7.. ὃν and 9.. focusing oe1 particular ou the issues of the balance between type T uid stochastic migration. aud the ecceutricity evolution of planets axd planetesimals.," We discuss the simulation results in sections \ref{stochastic_torques}, \ref{eccentricity}, and \ref{discussion}, focusing in particular on the issues of the balance between type I and stochastic migration, and the eccentricity evolution of planets and planetesimals." + We sunuuarise the paper and raw conclusions iu section 10.., We summarise the paper and draw conclusions in section \ref{summary}. +" The equations of ideal ΑΠΟ written iu a frame rotating with uniform angular velocity 0,2. with 2 being the unit vector along the rotation axis asstmed to be in the vertical direction. are the continuity equation the equation of motion and the induction equation where v. P. p. and B denote the fluid velocity. pressure. density and magnetic field respectively."," The equations of ideal MHD written in a frame rotating with uniform angular velocity $\Omega_f {\bf {\hat z}} $, with $ {\bf {\hat z}} $ being the unit vector along the rotation axis assumed to be in the vertical direction, are the continuity equation the equation of motion and the induction equation where ${\bf v}$, $P$ , $\rho$, and ${\bf B}$ denote the fluid velocity, pressure, density and magnetic field respectively." +" The potential &Due|Pe, contains coutributious due to eravitv. Oo. aud the centrifugal poteutial 0,(1/2)051/2302Zr.D The gravitational potential has contributions from a central mass Af. aud IN planets with masses νε. Thus in cvliudical coordinates (7:0. 2). with the planets located at (ryjOp and the star located at the origin of the coordinate system.O) the gravitational potential is ὧςd,|σον1δι where T and Tere. as in the papers PN2003.. NP2003. PNS2001 and NP2001. we have neglected. the dependence of the eravitational potentials ou + along with the vertical stratification of the disk. for reasons of computational speed."," The potential $\Phi = \Phi_{rot} +\Phi_G$ contains contributions due to gravity, $\Phi_G$, and the centrifugal potential $\Phi_{rot} = +-(1/2)\Omega_f^2|{\bf {\hat z}}\times +{\bf r}|^2.$ The gravitational potential has contributions from a central mass $M_*$ and $N$ planets with masses $m_{pi}.$ Thus in cylindrical coordinates $(r, \phi, z)$ , with the planets located at $(r_{pi}, \phi_{pi}, 0)$ and the star located at the origin of the coordinate system, the gravitational potential is $\Phi_G = \Phi_c + \sum_{i=1}^N\Phi_{pi} ,$ where _c = and = Here, as in the papers PN2003, NP2003, PNS2004 and NP2004, we have neglected the dependence of the gravitational potentials on $z$ along with the vertical stratification of the disk, for reasons of computational speed." + Thus the simulations are of exlindrical disks (c.g. Ariitage 1998. 2001: Hawley 2000. 2001: Steiuacker Papaloizou 2002).," Thus the simulations are of cylindrical disks (e.g. Armitage 1998, 2001; Hawley 2000, 2001; Steinacker Papaloizou 2002)." + To model the effects of the reduction of the planetpotential with vertical height. we have incor»orated a softening leneth 5 in the potential.," To model the effects of the reduction of the planetpotential with vertical height, we have incorporated a softening length $b$ in the potential." + We use a locallyisothermal equation of state iu the form, We use a locallyisothermal equation of state in the form + , +Principal component analvsis (PCA:Pearson1901:Karhunen1947:Loeve1955). has been applied to SDSS data with the aim of classilication. noise-reduction and compression (e.g..Connollyetal.1995:Yip2004) for different. (vpes of objects.,"Principal component analysis \citep[PCA;][]{pearson01,karhunen47,loeve55} has been applied to SDSS data with the aim of classification, noise-reduction and compression \citep[e.g.,][]{connolly95,yip04} + for different types of objects." + The principal components (eigenvectors of the correlation/covariance matrix of (he database) represent a complete basis set [or a given database of spectra., The principal components (eigenvectors of the correlation/covariance matrix of the database) represent a complete basis set for a given database of spectra. + One of the advantages ofthe PCA decomposition is that the importance of an eigenvector (measured as the associated absolute value of the eigenvalue) decavs tvpically like a , One of the advantages of the PCA decomposition is that the importance of an eigenvector (measured as the associated absolute value of the eigenvalue) decays typically like a power-law. +Therefore. if one considers (hat only AZ principal components contribute significantly {ο the reconstruction of a spectrum. it can be seen (hat the vector a in Eq. (2))," Therefore, if one considers that only $M$ principal components contribute significantly to the reconstruction of a spectrum, it can be seen that the vector $\mathbf{a}$ in Eq. \ref{eq:basis_decomposition}) )" + is non-zero only in the first V. elements. and approximately zero in the rest.," is non-zero only in the first $M$ elements, and approximately zero in the rest." + Additionally. (he matrix W' is built from the principal components ordered [vom the absolute value of their associated eigenvalues as columns.," Additionally, the matrix $\mathbf{W}^\dag$ is built from the principal components ordered from the absolute value of their associated eigenvalues as columns." + Recently. MeGurketal.(2010). have applied PCA ιο SDSS stellar spectra.," Recently, \cite{mcgurk10} have applied PCA to SDSS stellar spectra." + They have analyzed a subset of the full spectral database of SDSS and caleulated the principal components separately for stars in intervals of 0.02 mag in the gy—r color., They have analyzed a subset of the full spectral database of SDSS and calculated the principal components separately for stars in intervals of 0.02 mag in the $g-r$ color. + The range of colors considered spans —0.2«q—r<0.9. corresponding to MIX spectral types À3 to 10.," The range of colors considered spans $-0.2 < g-r < 0.9$, corresponding to MK spectral types A3 to K3." + According to Iveziéetal.(2005).. this segregation in g—r color is roughly equivalent. to a segregalion in effective temperature due to the large correlation between (his parameter and the g—r color.," According to \cite{ivezic05}, this segregation in $g-r$ color is roughly equivalent to a segregation in effective temperature due to the large correlation between this parameter and the $g-r$ color." + It is also of interest to point out that the effect of reddening is limited bv selecting stars with an estimated. extinction below 0.3 mag in the r band., It is also of interest to point out that the effect of reddening is limited by selecting stars with an estimated extinction below 0.3 mag in the $r$ band. + Thanks to the binnine. the number of principal components needed in each interval (o reach noise level is highlv reduced.," Thanks to the binning, the number of principal components needed in each interval to reach noise level is highly reduced." + Thev demonstrate that the mean spectrum plus (three principal components (hereafter referred. (o as the first four principal components) are more (han enough to statistically reconstruct the stellar spectra at the noise level., They demonstrate that the mean spectrum plus three principal components (hereafter referred to as the first four principal components) are more than enough to statistically reconstruct the stellar spectra at the noise level. + As à caveat. note that the quality of the principal component decomposition of is only measured through the median difference.," As a caveat, note that the quality of the principal component decomposition of \cite{mcgurk10} is only measured through the median difference." + It is (hen expected that ~50% of the stus in each bin have a decomposition that reproduce the spectra with a difference arger than the noise level (see relsec:reconstiruction))., It is then expected that $\sim$ of the stars in each bin have a decomposition that reproduce the spectra with a difference larger than the noise level (see \\ref{sec:reconstruction}) ). + Wa different binning is proposed in the future leading to new (hopefully improved) principal components. our reconstruction scheme remains unchanged ancl can be computed using exactly (he same observations.," If a different binning is proposed in the future leading to new (hopefully improved) principal components, our reconstruction scheme remains unchanged and can be computed using exactly the same observations." + Thankfully. the segregation of (2005) is done using an observed quantity aud the bin can be known just using photonmetric data.," Thankfully, the segregation of \cite{ivezic05} + is done using an observed quantity and the bin can be known just using photometric data." + We take this highlv elficient PCA decomposition lor reconstructing SDSS stellar spectra Tom photometric measurements., We take this highly efficient PCA decomposition for reconstructing SDSS stellar spectra from photometric measurements. +respectively. aud CAT qs a constaut given by where a is the fine-structure coustaut. Ais the electrou's Compton waveleugth. e is the speed of light. aud 7 is Planck's coustaut.,"respectively, and $C_{ei}^{NR}$ is a constant given by where $\alpha$ is the fine-structure constant, $\lambda$ is the electron's Compton wavelength, $c$ is the speed of light, and $h$ is Planck's constant." + Tere. and in the following expressious. the units of e axe cre s1 1 | cur? Similarly. we have 30 avg For the relativistic clectrou-iou bremesstrablime enissivitv. we use au expression from Quige (1968).," Here, and in the following expressions, the units of $\epsilon$ are erg $^{-1}$ $^{-1}$ $^{-1}$ $^{-3}$ Similarly, we have where and For the relativistic electron-ion bremsstrahlung emissivity, we use an expression from Quigg (1968)." + Defining 4—hv/kpgT. then we have where £7 is the exponcutial integral. ο is the 2ud order modified Bessel function. 5 is Euler's coustaut and CFT is a constant eiven by with ry the classical electron radius.," Defining $\beta_1\equiv h\nu/k_B T$, then we have where $Ei$ is the exponential integral, $k_2$ is the 2nd order modified Bessel function, $\gamma$ is Euler's constant and $C^{ER}$ is a constant given by with $r_0$ the classical electron radius." + For the relativistic clectrou-clectrou bremsstraliluug emissivity. we use an expression from Alexanian (1968): Iu the transrelativistic region (CX~ 1). we use a weighted average of the NR aud ER expressious.," For the relativistic electron-electron bremsstrahlung emissivity, we use an expression from Alexanian (1968): In the transrelativistic region $X\sim1$ ), we use a weighted average of the NR and ER expressions." + Note that the above equations are slightly differeut from those in the references due to a umuber of typographical errors in the originals., Note that the above equations are slightly different from those in the references due to a number of typographical errors in the originals. + Taking the effects of refraction iuto account. the final calculated Iwininositv is," Taking the effects of refraction into account, the final calculated luminosity is" +presumably is au N-ray binary: it may show a weak extesion to the SW (Figure 1)).,presumably is an X-ray binary; it may show a weak extension to the SW (Figure \ref{fig1}) ). + aud Bateretal.(2001) report periojc variability iu source J. with the flux decreasiug to zero every c27 κs.," \citet{sam01a} and \citet{bau01} report periodic variability in source J, with the flux decreasing to zero every $\simeq 27$ ks." + Asstuning source J is withiithe Circinus galaxy. its hard spectrum aud high luminosity would steeest a inassive ALςOAL.) |dack-hole in au X-ray. binary as the likely origin for the X-ray. emission.," Assuming source J is within the Circinus galaxy, its hard spectrum and high luminosity would suggest a massive $\simgreat +80 \, M_{\odot}$ ) black-hole in an X-ray binary as the likely origin for the X-ray emission." + The fact that the colum1 densiy to source J is larger than the Galactic columu (Table 8)) supports an association with οσιs., The fact that the column density to source J is larger than the Galactic column (Table \ref{tbl-5}) ) supports an association with Circinus. + Alternatively. if source J is within our owl galaxy. it mig be associated with a magneic Catacysmic Variable system.," Alternatively, if source J is within our own galaxy, it might be associated with a magnetic Catacysmic Variable system." + The iain results of our X-ray. observations of the Ci‘cluus galaxy are as follows., The main results of our X-ray observations of the Circinus galaxy are as follows. + i) The nucleus coπας a bright. compact X-ray source plus emission exteuded by 260 pe i the general direction of the ionization cone.," i) The nucleus contains a bright, compact X-ray source plus emission extended by $\simeq 60$ pc in the general direction of the ionization cone." + Our observatious couliru that the observed nuclea spectrum arises ttrough reflection of a hard. X-ray source by neutra matter with a high colum density., Our observations confirm that the observed nuclear spectrum arises through reflection of a hard X-ray source by neutral matter with a high column density. + Our emission-line {luxes are generally consistent. wih those measured by wiΙ luticii ugher spectral resolution grating observevious., Our emission-line fluxes are generally consistent with those measured by \citet{sam01b} with much higher spectral resolution grating observations. +" TIe Fe Inq emission Is exteucec by up to 206) 26,", The Fe $\alpha$ emission is extended by up to 200 pc. + li There is also arge scale (up to 600 pc [roi ithe uuceus). extended emission bot along the plane€a of tle galaxy disk (i.e. to the NE :ud SW) ard perpendicular to il (i.e. to tje NAW," ii) There is also large scale (up to 600 pc from the nucleus), extended emission both along the plane of the galaxy disk (i.e. to the NE and SW) and perpendicular to it (i.e. to the NW)." + Tle specirui1 of the extended einisslou aloug the galaxy disk may be describe| as emission TOL1 [n]eas Hà COlisional eqülibrium with AT~0.6 keV aud tay JE üssO0Ciated with the starburst ring., The spectrum of the extended emission along the galaxy disk may be described as emission from gas in collisional equilibrium with $kT \sim 0.6$ keV and may be associated with the starburst ring. + Tiere is uo significait hard compote in excess of that expected by telescope-1ΗΤΟΙ scattering of the briel nuclear «xurce., There is no significant hard component in excess of that expected by telescope-mirror scattering of the bright nuclear source. + The absorbi coltunu density to gas in the galaxy disk exceeds tiat from Ol rown galaxy. i(catiug siguificaut djusic absorption by the disk of Circiuis.," The absorbing column density to gas in the galaxy disk exceeds that from our own galaxy, indicating significant intrinsic absorption by the disk of Circinus." + The la'ge-scale eas extending peryenclicular to he cli is Closely correlated with the high exetat]on optical-line enittiug gas., The large-scale gas extending perpendicular to the disk is closely correlated with the high excitation optical-line emitting gas. + The spectrum sulers no ijusic absorption since the gas is ou tje near side of the Circinus galaxy disk., The spectrum suffers no intrinsic absorption since the gas is on the near side of the Circinus galaxy disk. + The soft compone 1iiv be a thermal gas with ALT0.6 keV or may be cooler aud phoO-1OLized by the Seylert Cletus., The soft component may be a thermal gas with $kT \sim 0.6$ keV or may be cooler and photo-ionized by the Seyfert nucleus. + Harel eiuission is detected whicl ap28415 lo exceec ilat expected loni scattering of nuclear 1 yw the telescope mirrors., Hard emission is detected which appears to exceed that expected from scattering of nuclear light by the telescope mirrors. + We suggest that this har coniponelnt rests {rol scattering of ut --ieht iuto our liue of sight by elecrous ln an loulzec wind., We suggest that this hard component results from scattering of nuclear light into our line of sight by electrons in an ionized wind. + iii) Teu comp:wt X-ray sources are deteced in the inner ~ Lkος of the gaaxy., iii) Ten compact X-ray sources are detected in the inner $\sim 1$ kpc of the galaxy. + Their spectra nuay be described as power-laws with a sigui‘aut amount of inrinsic absorption. consistent wil ileir location in the inuer disk of Circinus. wlich is known to be üc+ Lin molecular gas.," Their spectra may be described as power-laws with a significant amount of intrinsic absorption, consistent with their location in the inner disk of Circinus, which is known to be rich in molecular gas." +" The source luminosities range from [xLO"")— to 1.0x10 el;es l,", The source luminosities range from $4 \times 10^{37}$ to $1.0 \times 10^{40}$ erg $^{-1}$. + The most |niious source (J) exhibits a har spectrum and is apparently au X-ray binary ii C‘clus with a acs-hole mass exceeding SOAL..," The most luminous source (J) exhibits a hard spectrum and is apparently an X-ray binary in Circinus with a black-hole mass exceeding $80 \, M_{\odot}$." + We thank Sylvain Veilleus and. Alessaudro Marconi for )OVicing their optical images of Circinus in computer readable format., We thank Sylvain Veilleux and Alessandro Marconi for providing their optical images of Circinus in computer readable format. + This research mace use of funding through NASA erant ΝΑ51021., This research made use of funding through NASA grant NAG-81027. +we consider a large range of (420) V...,we consider a large range of (4–20) $M_{\odot}$. +" This range includes most values of M, within the low metallicity (0.12. ) distribution of Belezvnskietal.(2010b).", This range includes most values of $M_{c}$ within the low metallicity $0.1 Z_{\odot}$ ) distribution of \citet{metal}. +". We note however. that for the more realistic scenario (hat accounts for early common envelope mergers as the stars pass through the Ilertzsprung eap. the range is more constrained. with M, around (49) M..."," We note however, that for the more realistic scenario that accounts for early common envelope mergers as the stars pass through the Hertzsprung gap, the range is more constrained, with $M_{c}$ around (4–9) $M_{\odot}$." + Figure 5 shows the ro M. space Lor three different detection scenarios: 1) cross correlation olll-L the best performing pair of advancecl detectors; 2) ALLY (through CP) the optimal combination of 4 advanced detectors: 3) cross correlation of two ET type detectors using two possible sensitivities (ET-D aud ET-D)., Figure 5 shows the $r_{0}$ $M_{c}$ space for three different detection scenarios: 1) cross correlation of H-L – the best performing pair of advanced detectors; 2) AHLV (through CP) – the optimal combination of 4 advanced detectors; 3) cross correlation of two ET type detectors using two possible sensitivities (ET-B and ET-D). + Zones encompassed by the (vo rates. i and i. are shown by the shaded areas.," Zones encompassed by the two rates, $r_{1}$ and $r_{2}$, are shown by the shaded areas." + The figure further confirms that advanced detectors are not likely to detect the BBII background at the rate ry., The figure further confirms that advanced detectors are not likely to detect the BBH background at the rate $r_{1}$. + Detection would require the high rate estimate. ro and LOAL..," Detection would require the high rate estimate, $r_{2}$ and $M_{c} \gtrsim 10 +M_{\odot}$ ." + Such a range lor ro M. has been predicted by Buliketal.(2011). through studies of the two BU-WR svstems. NGC300 N-1 and [CLO X-1.," Such a range for $r_{0}$ $M_{c}$ has been predicted by \citet{Bulik08} through studies of the two BH-WR systems, NGC300 X-1 and IC10 X-1." + A null detection would therefore confirm a lack of understanding in the binary evolution of such svstems based on the single source models emploved in this study., A null detection would therefore confirm a lack of understanding in the binary evolution of such systems based on the single source models employed in this study. + In regards to detection strategies lor SGWD signals. Figure 5 shows some improvenient in detectabilitv through the use of CP.," In regards to detection strategies for SGWB signals, Figure 5 shows some improvement in detectability through the use of CP." + As already noted in Table 2.. AIILV. can improve the detectability by 40% compared with only two Advanced LIGO detectors (1I-L).," As already noted in Table \ref{table_rates}, AHLV can improve the detectability by $40\%$ compared with only two Advanced LIGO detectors (H-L)." + For ET. for the entire range of M. the signal would be comfortably detected at the lower rate ry.," For ET, for the entire range of $M_{c}$ the signal would be comfortably detected at the lower rate $r_{1}$." + A detectable continuous background requires a rate of order LO?MpeMyr lor above.," A detectable continuous background requires a rate of order $10^{-3} \hspace{1mm} +\rm{Mpc}^{-3}\rm{Myr}^{-1}$ or above." + In comparison with ET-B. we find that a larger parameter space can be probed by ET-D due to an improved sensitivity at lower frequencies (<20 Iz).," In comparison with ET-B, we find that a larger parameter space can be probed by ET-D due to an improved sensitivity at lower frequencies $< 20$ Hz)." + In this paper we have estimated (he potential contribution of a population of coalescing DDIIs to à SGWD signal., In this paper we have estimated the potential contribution of a population of coalescing BBHs to a SGWB signal. + We are motivated by recent observations of BII-WR. star svstems (Crowtheretal.2010) and by new estimates in the metallicity abunclances of star forming ealaxies (Panteretal.2008) that have suggested Che rate of DDIIs in field populations mav be greater than previously expected., We are motivated by recent observations of BH-WR star systems \citep{Crowther} and by new estimates in the metallicity abundances of star forming galaxies \citep{2008MNRAS.391.1117P} that have suggested the rate of BBHs in field populations may be greater than previously expected. + We base the single source emissions on energy spectra caleulated from recent parameterized waveforms of Ajithοἱal.(2008.2009).," We base the single source emissions on energy spectra calculated from recent parameterized waveforms of \citet{IMR,spin_IMR}." +. Then. assumine (hat the DDILI rate traces the SER. with some delay time. we derive cosmic source rate evolution models and extrapolate our single-source model out to high redshifts.," Then, assuming that the BBH rate traces the SFR with some delay time, we derive cosmic source rate evolution models and extrapolate our single-source model out to high redshifts." + Rather (han a population svuthesis approach. we assume average properties (e.g.. Masses and spins) for the BBI population to determine the characteristics of the 5GWD signal ancl principal," Rather than a population synthesis approach, we assume average properties (e.g., masses and spins) for the BBH population to determine the characteristics of the SGWB signal and principal" +MO stars at 10 pe. or 900 K around GO stars at 10 pc. for angular separations larger than1.,"M0 stars at 10 pc, or 900 K around G0 stars at 10 pc, for angular separations larger than." +"0""... For smaller angular separations. results should be extremely valuable for slightly warmer companions."," For smaller angular separations, results should be extremely valuable for slightly warmer companions." + Finally. we have estimated the influence of two key data analysis parameters at LRS.," Finally, we have estimated the influence of two key data analysis parameters at LRS." + It is necessary to mask the planet signal during the analysis to avoid overestimating the scattered light level. which would lead to a mis-estimation of the planetary continuum.," It is necessary to mask the planet signal during the analysis to avoid overestimating the scattered light level, which would lead to a mis-estimation of the planetary continuum." + The method also relies on accurate wavelength calibration to be able to use the known wavelength dependence of the speckles to eliminate them., The method also relies on accurate wavelength calibration to be able to use the known wavelength dependence of the speckles to eliminate them. + A systematic error as small as 10 nm can have major consequences on the characterization of the observed objects., A systematic error as small as 10 nm can have major consequences on the characterization of the observed objects. +include this channel are incomplete.,include this channel are incomplete. + Gourgouliatos&Jeffery)(2006) studied the merger of two He WDs assuming complete conservation of momentum and found that the rotational velocity of the merger product could be >105kms~!., \citet{Gourgouliatos:2006} studied the merger of two He WDs assuming complete conservation of momentum and found that the rotational velocity of the merger product could be $\ga 10^{3} {\rm~km~s^{-1}}$. +" While there is undoubtedly some angular momentum lost during the merger, it is difficult to explain why nearly all single sdBs observed−− have projected rotational velocities of «10kms! "," While there is undoubtedly some angular momentum lost during the merger, it is difficult to explain why nearly all single sdBs observed have projected rotational velocities of $< 10 {\rm~km~s^{-1}}$ \citep{Geier:2009a}." +An advantage of the new H-merger channel described above is that the merger product will lose between ~0.1—0.3Mo of material while it is on the giant branch., An advantage of the new H-merger channel described above is that the merger product will lose between $\sim 0.1-0.3~M_{\sun}$ of material while it is on the giant branch. +" Angular momentum carried away by this material can spin down the star, resulting in a slowly rotating sdB. Contributions from the He WD 4- M dwarf formation channel for sdBs presented here might also play a role in determining the binary fraction of extreme horizontal branch (EHB) stars in globular clusters, and in the UV-upturn in elliptical galaxies."," Angular momentum carried away by this material can spin down the star, resulting in a slowly rotating sdB. Contributions from the He WD + M dwarf formation channel for sdBs presented here might also play a role in determining the binary fraction of extreme horizontal branch (EHB) stars in globular clusters, and in the UV-upturn in elliptical galaxies." +" The short-period binary fraction among EHB stars in globular clusters is much lower than that of field sdBs, and this has been attributed to the fact that the dominant formation channel for EHBs in old stellar populations is He WD mergers that result in a singleton sdB (Monial.| DOT.Bidin"," The short-period binary fraction among EHB stars in globular clusters is much lower than that of field sdBs, and this has been attributed to the fact that the dominant formation channel for EHBs in old stellar populations is He WD mergers that result in a singleton sdB \citep{Moni-Bidin:2008,Han:2008,Moni-Bidin:2011}." +" Theet formation channel presented here also produces singletons, and in some cases, especially if the merger product is mixed as considered above, the process can take >12 Gyr to produce a sdB. These mixed stars would exhibit the super-solar Sweigarthelium abundance invokedalessandro in some etEHBal] models (e.g. Bor), although star-by-star& Mengel[1979;rather than as a population."," The formation channel presented here also produces singletons, and in some cases, especially if the merger product is mixed as considered above, the process can take $\ga 12$ Gyr to produce a sdB. These mixed stars would exhibit the super-solar helium abundance invoked in some EHB models \citep[e.g.,][]{Sweigart:1979,Dalessandro:2011}, although star-by-star rather than as a population." +" Again, more work is needed to determine whether this channel contributes to the EHB population significantly at late times."," Again, more work is needed to determine whether this channel contributes to the EHB population significantly at late times." +" Finally, we note that sdBs produced by this merger channel could also contribute to the UV-upturn observed in elliptical galaxies."," Finally, we note that sdBs produced by this merger channel could also contribute to the UV-upturn observed in elliptical galaxies." +" The evolved stellar populations thought to inhabit elliptical galaxies would not produce the UV-excess seen in their spectral energy distrubutions, and proposed that emission from the sdBs formed (2007)through binary evolution might be the source of this radiation."," The evolved stellar populations thought to inhabit elliptical galaxies would not produce the UV-excess seen in their spectral energy distrubutions, and \citet{Han:2007} + proposed that emission from the sdBs formed through binary evolution might be the source of this radiation." +" The formation channel presented here offers an additional population of sdBs that supplies UV photons, perhaps on a different timescale."," The formation channel presented here offers an additional population of sdBs that supplies UV photons, perhaps on a different timescale." + Determining the contribution of singleton sdBs formed by He WD + M dwarf mergers to either the globular cluster or elliptical galaxy populations is further complicated by metallicity effects., Determining the contribution of singleton sdBs formed by He WD + M dwarf mergers to either the globular cluster or elliptical galaxy populations is further complicated by metallicity effects. +" We have shown that merging a He WD with an M dwarf can produce a low mass star of advanced evolutionary age or a helium rich star, either of which can evolve to become a sdB within a Hubble time."," We have shown that merging a He WD with an M dwarf can produce a low mass star of advanced evolutionary age or a helium rich star, either of which can evolve to become a sdB within a Hubble time." +" This model can explain the narrow mass range in singleton sdBs and the existence of long period sdB+MS binaries, if these systems were initially triples."," This model can explain the narrow mass range in singleton sdBs and the existence of long period sdB+MS binaries, if these systems were initially triples." + The sdBs produced by this formation channel might also contribute to the low binary fraction among EHB stars in globular clusters and the UV-excess in elliptical galaxies., The sdBs produced by this formation channel might also contribute to the low binary fraction among EHB stars in globular clusters and the UV-excess in elliptical galaxies. + Many aspects, Many aspects +au eusemble with static statistics or. assuming ergodicity. to the statistics of a chaotic system. observed over a sulliciently long. period oftimet.,"an ensemble with static statistics or, assuming ergodicity, to the statistics of a chaotic system observed over a sufficiently long period of." +. The work we discuss here amounts to an inverse approach of picking a zero mode and finding theHainiltonian?., The work we discuss here amounts to an inverse approach of picking a zero mode and finding the. +. We will work with the Fokker-Plauck equation. picking a probability density p and finding a corresponding dynamical system. (ο).," We will work with the Fokker-Planck equation, picking a probability density $\rho$ and finding a corresponding dynamical system, $\vec v(\vec x)$." + For the most part we will cousider the deterministic case. although the application oL the inverse method to a class of stochastic dynamical systems is discussecl in section T.," For the most part we will consider the deterministic case, although the application of the inverse method to a class of stochastic dynamical systems is discussed in section 7." +" Cousider a determiuistic dynamical system in an NV dimensional pliase space. ]t is convenient to use the laueuage of differential forms aud define the velocity one-Lorm eΞμμ, in terms of which the static. zero diffusion limit of the Fokker-Plauck equation cau be written as One cantherefore always (locally) write *(pe)=dA where A is an NV—2form?*.. or equivalently Given any distribution p. we can find dynamical systems (characterized by 0) such that p is an invariant distribution by making a choice of A."," Consider a deterministic dynamical system in an $N$ dimensional phase space, It is convenient to use the language of differential forms and define the velocity one-form $v=v_ndx^n$, in terms of which the static, zero diffusion limit of the Fokker-Planck equation can be written as One cantherefore always (locally) write $ {}^*(\rho v) = d{\cal A} $ where $\cal A$ is an $N-2$, or equivalently Given any distribution $\rho$ , we can find dynamical systems (characterized by $v$ ) such that $\rho$ is an invariant distribution by making a choice of ${\cal A}$." + Since the Hodge dual of A is a two-form. it is umore conveulent at large N to define the dynamics in terms of the probability distribution and the two-lorm “A.," Since the Hodge dual of ${\cal A}$ is a two-form, it is more convenient at large $N$ to define the dynamics in terms of the probability distribution and the two-form ${}^*{\cal A}$." + A generic choice of p aud A will give a velocity e which is not a polynomial function of the coordinates., A generic choice of $\rho$ and ${\cal A}$ will give a velocity $v$ which is not a polynomial function of the coordinates. + Du this article we will only cousider polynomial e on the phase space IE., In this article we will only consider polynomial $v$ on the phase space $\mathbb{R}^N$. + Of course non-polvionmial e may also arise in various physical settings aud for phase spaces with non-trivial topologies. such as classical spin systers.," Of course non-polynomial $v$ may also arise in various physical settings and for phase spaces with non-trivial topologies, such as classical spin systems." + In order to insure] that e is. polynomial.. let us define⋅ another /NT—2 otform Q0004=A/p-.9 ," In order to insure that $v$ is polynomial, let us define another $N-2$ form $\Omega \equiv {\cal A}/\rho^2$ ." +Then iu regions where pz0., Then in regions where $\rho\ne 0$. + The simplest way to iusure that ¢ is polynomial is totake polynomial p aud O9., The simplest way to insure that $v$ is polynomial is totake polynomial $\rho$ and $\Omega$ . + However a polynomial pis not normalizable. unless we restrict its range of support.," However a polynomial $\rho$is not normalizable, unless we restrict its range of support." + Let us therefore consider the followiug example for V—3., Let us therefore consider the following example for $N=3$. +In recent vears. computational N-body simulations have provided. important insights into the non-linear formation of structure by the clark matter.,"In recent years, computational $N$ -body simulations have provided important insights into the non-linear formation of structure by the dark matter." +" ? (NEW) observed a ""universal! density profile for dark matter haloes. suggesting that the profiles depend only on the mass of the halo. with relatively little scatter between them."," \citet{1997ApJ...490..493N} (NFW) observed a `universal' density profile for dark matter haloes, suggesting that the profiles depend only on the mass of the halo, with relatively little scatter between them." + They also noticed that the halo concentration parameter. describing the degree of profile steepness (defined. more. precisely. below) decreases with increasing halo mass. though the exact relation depencds on the cosmology at. hand.," They also noticed that the halo concentration parameter, describing the degree of profile steepness (defined more precisely below) decreases with increasing halo mass, though the exact relation depends on the cosmology at hand." + Several formulae. have been suggested for this relation (277). which rely on fitting some mechanism to haloes culled from AIN-body simulations.," Several formulae have been suggested for this relation \citep{1997ApJ...490..493N,2001MNRAS.321..559B,2001ApJ...554..114E} which rely on fitting some mechanism to haloes culled from $N$ -body simulations." + These studies found that the concentration. dependence on the power spectrum is caused primarily bw the slope of the linear power spectrum., These studies found that the concentration dependence on the power spectrum is caused primarily by the slope of the linear power spectrum. + Both this and the mass dependence of concentration can be explained by the epoch of the halo formation. since less massive haloes form at higher redshif when the universe was denser and this leads to a more concentrated. profile.," Both this and the mass dependence of concentration can be explained by the epoch of the halo formation, since less massive haloes form at higher redshift when the universe was denser and this leads to a more concentrated profile." + Another relation which appears to be universal is tha of the mass function (?).., Another relation which appears to be universal is that of the mass function \citep{2001MNRAS.321..372J}. + The distribution of halo masses in N-bocly simulations appears to be universal in the sense hat when mass is related to the Uuctuation amplitude of he linear power spectrum. the mass function has a universa orm.," The distribution of halo masses in $N$ -body simulations appears to be universal in the sense that when mass is related to the fluctuation amplitude of the linear power spectrum, the mass function has a universal form." + This relation has also been explored in detail in recen work (?7777).. defining precisely what is meant by the mass and confirming the universality of the mass function for a arge set of cosmological models.," This relation has also been explored in detail in recent work \citep{1999MNRAS.308..119S,2001MNRAS.321..372J,2001A&A...367...27W,2002astro.ph..7185W}, defining precisely what is meant by the mass and confirming the universality of the mass function for a large set of cosmological models." + While the above approaches have focused on individual ialoes in the simulations by counting them and. exploring heir structure. for many cosmological applications all hat we need is the dark matter power spectrum.," While the above approaches have focused on individual haloes in the simulations by counting them and exploring their structure, for many cosmological applications all that we need is the dark matter power spectrum." + This can be computed. from N-bocly simulations as well. but computational limitations prevent one from exploring a wee range of cosmological models or from achieving a high resolution on small scales.," This can be computed from $N$ -body simulations as well, but computational limitations prevent one from exploring a large range of cosmological models or from achieving a high resolution on small scales." + For this reason many fitting formulae have been developed. with increasing accuracy over the vears (??7??).. although these are still significantly limited on small scales by the dynamical range of simulations.," For this reason many fitting formulae have been developed with increasing accuracy over the years \citep{1991ApJ...374L...1H,1995MNRAS.276L..25J,1996MNRAS.280L..19P,2002astro.ph..7664S}, although these are still significantly limited on small scales by the dynamical range of simulations." + The close connection between the two descriptions has been highlighted. recently with the revival of the halo model. (??77)..," The close connection between the two descriptions has been highlighted recently with the revival of the halo model \citep{2000MNRAS.318..203S,2000MNRAS.318.1144P,2000ApJ...543..503M,2001ApJ...546...20S}." + For à [few cosmological models. it. was shown that with an appropriate choice of concentration mass dependence ancl mass function one can use the halo model to accurately predict the non-linear. dark matter power spectrum.," For a few cosmological models, it was shown that with an appropriate choice of concentration mass dependence and mass function one can use the halo model to accurately predict the non-linear dark matter power spectrum." + One of the questions we explore in this «ver is whether this agreement can be extended: to a wider range of models and whether the trends seen in the analysis of individual haloes are confirmed. also with the power spectrum. analysis., One of the questions we explore in this paper is whether this agreement can be extended to a wider range of models and whether the trends seen in the analysis of individual haloes are confirmed also with the power spectrum analysis. + Phere are several reasons why his is of interest: since the selection of individual haloes is somewhat subjective it is possible that those left out mav be systematically dillerent., There are several reasons why this is of interest: since the selection of individual haloes is somewhat subjective it is possible that those left out may be systematically different. + For example. they could be ess relaxed. more recently formed and so less concentrated.," For example, they could be less relaxed, more recently formed and so less concentrated." + An opposite elfect is that because the power spectrum. is a pair-weighted statistic. if there is à scatter in the mass-concentration relation then pair weighting increases the mean concentration relative to the simple particle weighting.," An opposite effect is that because the power spectrum is a pair-weighted statistic, if there is a scatter in the mass-concentration relation then pair weighting increases the mean concentration relative to the simple particle weighting." + On the other hand. if the analysis of individual haloes is in agreement with the power spectrum analysis over the range where both are reliable. then the same analysis can xe extended to smaller scales which are not. resolved. by cosmological N-body simulations that compute the power spectrum.," On the other hand, if the analysis of individual haloes is in agreement with the power spectrum analysis over the range where both are reliable, then the same analysis can be extended to smaller scales which are not resolved by cosmological $N$ -body simulations that compute the power spectrum." + “Phe reason for this is that the resolution scale or the halo structure can be extended: significantly by resimulating the representative regions of the haloes with a higher resolution simulation zoomed on that halo., The reason for this is that the resolution scale for the halo structure can be extended significantly by resimulating the representative regions of the haloes with a higher resolution simulation zoomed on that halo. + On he other hand. à power spectrum calculation. requires a arge simulation volume. so that the largest scales are in the inear regime. which then implies that the mass and. force," On the other hand, a power spectrum calculation requires a large simulation volume, so that the largest scales are in the linear regime, which then implies that the mass and force" +that the simplified model fails to reproduce the profile in question.,that the simplified model fails to reproduce the profile in question. +" The smallest 42,5, value obtained for this moce is only 2.4 which rejects the one-component microturbulen solution.", The smallest $\chi^2_{min}$ value obtained for this model is only 2.4 which rejects the one-component microturbulent solution. + Fhis example clearly demonstrates once more tha the analysis of absorption spectra may be very. sensitive to the model assumptions concerning the velocity Πο] structure., This example clearly demonstrates once more that the analysis of absorption spectra may be very sensitive to the model assumptions concerning the velocity field structure. +" The essential dillerence between the results of TT and ours lies in the estimation of the hvedrodvnamica velocities in the 2,=2.504 absorbing region.", The essential difference between the results of T and ours lies in the estimation of the hydrodynamical velocities in the $z_a = 2.504$ absorbing region. +" The microturbulent model. vielded 65,=bo14 km and boonc3 km | which is about 10 times smaller than y/2e, estimated by the RALC procedure.", The two-component microturbulent model yielded $b^{\rm D}_{blue} = b^{\rm D}_{red} = 14$ km $^{-1}$ and $b_{turb} \simeq 3$ km $^{-1}$ which is about 10 times smaller than $\sqrt{2}\sigma_t$ estimated by the RMC procedure. + For the additional parameter £/f of the mesoturbulent model. we found a value of =5. indicating that the space averaging along the line of sight) corresponds to an incomplete statistical sample anc. hence. significant deviations of the observed intensities from their expectation values Mav Occur.," For the additional parameter $L/l$ of the mesoturbulent model, we found a value of $\simeq 5$, indicating that the space averaging along the line of sight corresponds to an incomplete statistical sample and, hence, significant deviations of the observed intensities from their expectation values may occur." +" As for the other parameters (Nia. D/L. and 1»5;,). the ΗΛΙΟ method: vields in this particular case values which are similar to those of BATT. The total hydrogen column densities and the D/L ratios obtained are shown in Fig."," As for the other parameters $N_{\rm HI}$, D/H, and $T_{kin}$ ), the RMC method yields in this particular case values which are similar to those of T. The total hydrogen column densities and the D/H ratios obtained are shown in Fig." + 6 by the filled. diamond for the best RALC solution (panel in Fie., 6 by the filled diamond for the best RMC solution (panel in Fig. + 5)r and by the filled circle for the TT model (the error bars shown correspond to lo in accord with the BACLT data from Table 1D)., 5) and by the filled circle for the T model (the error bars shown correspond to $1\sigma$ in accord with the T data from Table 1). + The filled triangle and. square mark the (Na. D/LD) pairs found separately for the blue and red components.," The filled triangle and square mark the $N_{\rm HI}$, D/H) pairs found separately for the blue and red components." + Lhe D abundance for the red component. was assumed by D&TT as CD/ID = (DAD. = (DM) and. thus. there was no real measurements of the DLL value for the red. component in their model.," The D abundance for the red component was assumed by T as $_{red}$ = $_{blue}$ = $_{total}$ and, thus, there was no real measurements of the D/H value for the red component in their model." + This is marked. by arrows instead. of error. bars at the filled square in Fig., This is marked by arrows instead of error bars at the filled square in Fig. + 6., 6. + The projection of the 5-dimensional error surface onto the ‘log Nut log D/L plane was calculated. by the IUMC procedure using the Αν) method., The projection of the 5-dimensional error surface onto the `log $N_{\rm HI}$ – log D/H' plane was calculated by the RMC procedure using the $\Delta (\chi^2)$ method. +" Drawn are 68 and 95 confidence regions computed under the condition that the parameters. Zig. afey, and. Lf! are.fired. but. the velocity field configuration isfree."," Drawn are 68 and 95 confidence regions computed under the condition that the parameters $T_{kin}$, $\sigma_t / v_{th}$, and $L/l$ are, but the velocity field configuration is." + As seen. the BATT value for the total Nyy is located closely to the RALIC confidence regions. but the D/II ratio is systematically lower in the microturbulent model.," As seen, the T value for the total $N_{\rm HI}$ is located closely to the RMC confidence regions, but the D/H ratio is systematically lower in the microturbulent model." + Fie., Fig. +" 7 shows 68 and 95 conlidence regions. for the two parameters Zy;, and D/II computed. under. the assumption that Nyy. afen. and. L/f are fixed. but. the v(r)-configuration is free."," 7 shows 68 and 95 confidence regions for the two parameters $T_{kin}$ and D/H computed under the assumption that $N_{\rm HI}$ , $\sigma_t/v_{th}$, and $L/l$ are fixed, but the $u(x)$ -configuration is free." + The Kinetic temperature is found in the range from 15000 Ix to —22000 Ix. whereas D/II lies between ~3.3107 and ~45«107.," The kinetic temperature is found in the range from $\sim 15000$ K to $\sim 22000$ K, whereas D/H lies between $\sim 3.3\times10^{-5}$ and $\sim 4.5\times10^{-5}$." + In this figure. the filled svmbols label the RAIC ancl BATT best. fitting parameters in the same sense as in Fig.," In this figure, the filled symbols label the RMC and T best fitting parameters in the same sense as in Fig." + 6., 6. +" Note the marginal position of the IUMC solution (the filled diamond) which shows that there are points in the ΟΠΗ Zi, plane with VO2 values less than ανν=0.485 adopted for the best IRMC solution at the first stage of calculations.", Note the marginal position of the RMC solution (the filled diamond) which shows that there are points in the `D/H – $T_{kin}$ ' plane with $\chi^2$ values less than $\chi^2_{min} = 0.485$ adopted for the best RMC solution at the first stage of calculations. + Fig., Fig. +" 7 shows that also in the ΕΕ Ti;,' plane the D/L uncertainty region is shifted toward higherD/L values as compared with the ANTT data.", 7 shows that also in the `D/H – $T_{kin}$ ' plane the D/H uncertainty region is shifted toward higherD/H values as compared with the T data. +There are more null points in the high resolution case (dark curves) (han in (he low resolution (6135 664).,There are more null points in the high resolution case (dark curves) than in the low resolution (6135 664). + The majority of (he excess null points lie in a laver about one Mm thick., The majority of the excess null points lie in a layer about one Mm thick. + Over heights above one Ain the predicted null columns (dashed curves on relfig:ndbb) from the high resolution ancl low resolution cases are quite similar., Over heights above one Mm the predicted null columns (dashed curves on \\ref{fig:nd}b b) from the high resolution and low resolution cases are quite similar. +" The greatest disagreement between (he actual null column. ;N,(Cz). and the spectral estimate occurs within this same one Mm bottom laver."," The greatest disagreement between the actual null column, $N_n(z)$, and the spectral estimate occurs within this same one Mm bottom layer." + Above this height the two estimates are within a factor of two of reality [or both resolutions., Above this height the two estimates are within a factor of two of reality for both resolutions. + Since the bottom laver of the high resolution field has the largest kurtosis it is perhaps unsurprising that the greatest disagreement with the spectral estimate occurs (here., Since the bottom layer of the high resolution field has the largest kurtosis it is perhaps unsurprising that the greatest disagreement with the spectral estimate occurs there. + Perhaps more surprising is that kurtosis as large as 40 (the maximum ol the low resolution data) leads to disagreement by not more than a [actor of two., Perhaps more surprising is that kurtosis as large as 40 (the maximum of the low resolution data) leads to disagreement by not more than a factor of two. + The extent to which. for levels above one Mm. (he spectral estimates of high resolution and low resolution agree can be understood Irom a comparison of their power spectra 5(/:). as shown in relfig:spec..," The extent to which, for levels above one Mm, the spectral estimates of high resolution and low resolution agree can be understood from a comparison of their power spectra $S(k)$, as shown in \\ref{fig:spec}." +" A fast Fourier transform (FFT) of the L,x magnetogram returns an array of complex coefficients. δν. for the expansion Biny = 1986)."," A fast Fourier transform (FFT) of the $L_x\times L_y$ magnetogram returns an array of complex coefficients, $\hat{B}_{m,n}$, for the expansion B_z(x,y) = ." +. The two-dimensional power spectrum at wave number k=mAhX+nMS is⋉⋉ ⊳↔⊲∐↸∣⊔, The two-dimensional power spectrum at wave number $\kvec=m\Delta k_x\xhat+n\Delta k_y\yhat$ is) = . +. The two-dimensional power spectrum at wave number k=mAhX+nMS is⋉⋉ ⊳↔⊲∐↸∣⊔↕, The two-dimensional power spectrum at wave number $\kvec=m\Delta k_x\xhat+n\Delta k_y\yhat$ is) = . +SSC flux remain for Cars.,SSC flux remain for Gyrs. + Expansion of the fossil radio cocoon would nearly completely diminish these already weak fluxes., Expansion of the fossil radio cocoon would nearly completely diminish these already weak fluxes. + But compression can strongly increase the SSC flux even at very late stages., But compression can strongly increase the SSC flux even at very late stages. + This is shown iu Fie. 11..," This is shown in Fig. \ref{fig:grg}," + where a compression. described by b= ancl fy=500 Abvr (see Eq. À3)).," where a compression, described by $b = -1$ and $t_0 = 500$ Myr (see Eq. \ref{eq:expansion}) )," + was assumed., was assumed. + Within he displaved 3 Car evolution a compression of a factor €=7 is reached., Within the displayed 3 Gyr evolution a compression of a factor $\tilde{C} = 7$ is reached. + Although the compression here is artificially introduced. it should illustrate the consequences of the erowth of structures like eroups and filaments of galaxies in which nianv fossils of giant radio galaxies are expected to be embedded.," Although the compression here is artificially introduced, it should illustrate the consequences of the growth of structures like groups and filaments of galaxies in which many fossils of giant radio galaxies are expected to be embedded." + The expected augular area of a giant radio ealaxy ehost is. of. the order of 24300 2:2arcmün., The expected angular area of a giant radio galaxy ghost is of the order of 300 $^2$. + However. oulv the GAIRT. EVLA. and ATA telescopes (out of the sample listed in Tab. 1))," However, only the GMRT, EVLA, and ATA telescopes (out of the sample listed in Tab. \ref{tab:sensitivity}) )" + at GIIz frequencies have reasonable chances to detect such a source., at GHz frequencies have reasonable chances to detect such a source. + Aud this oulv if it is either cuviroumenutally compressed or if extremly long integration times are used (10°Lo’ Li)., And this only if it is either environmentally compressed or if extremly long integration times are used $10^2-10^3$ h). +" The Alilky Wav or the Andromeda galaxy harbor very uassive central black holes with masses of 2.6«109AL, (Cenzeletal.1997) aud ~3.107A, (INormendy&Bender.1999). respectively."," The Milky Way or the Andromeda galaxy harbor very massive central black holes with masses of $2.6\cdot 10^{6}\,M_\odot$ \cite{1997MNRAS.291..219G} and $\sim 3\cdot 10^{7}\,M_\odot$ \cite{1999ApJ...522..772K} respectively." + If the growth of these black roles was due to feeding of gas from an accretion disk. it can be expected that this process was accompanied wea relativistic jet outflow.," If the growth of these black holes was due to feeding of gas from an accretion disk, it can be expected that this process was accompanied by a relativistic jet outflow." + If 10 of the rest-iuass of he accreted gas was converted iuto jet-power. cuough radio plasiua should have been produced in order to fll au inter-ealactic volume of the order of 0.1 Mpc?μι).D3 (Mecina-Tauco&πια.2001) with outflows from our galaxy. ai ten times as much with outflows frou Audromeda.," If 10 of the rest-mass of the accreted gas was converted into jet-power, enough radio plasma should have been produced in order to fill an inter-galactic volume of the order of 0.1 $^3\,(B/\mu{\rm G})^{-2}$ \cite{2001APh....16...47M} with outflows from our galaxy, and ten times as much with outflows from Andromeda." + The term B denotes here the equipartition maenetic field strenethl as a measure of the internal energy density., The term $B$ denotes here the equipartition magnetic field strength as a measure of the internal energy density. + A iocerately sized nearby radio ghost of this origin iuav lave a radius of 200 kpc. a magnetic field strength of LG. a single power law electron population with spectral iudex s=2.5. and an normalization of C=5.10tom?.," A moderately sized nearby radio ghost of this origin may have a radius of 200 kpc, a magnetic field strength of $1\,\mu$ G, a single power law electron population with spectral index $s = 2.5$, and an normalization of $C = 5\cdot 10^{-7}\,{\rm cm^{-3}}$." + As in the other cases of radio plaslid. WO ussülio p=10 aud p»—32105.," As in the other cases of radio plasma, we assume $p_{1} =10$ and $p_{2} = 3\cdot +10^4$." + Similar to giaut radio galaxies. oue ects a very low SSC surface brightuess. as displaved in Fig. 12..," Similar to giant radio galaxies, one gets a very low SSC surface brightness, as displayed in Fig. \ref{fig:mw}." + Svuchrotron aud IC cooling is not able to remove the flux within 10 Cyr., Synchrotron and IC cooling is not able to remove the flux within 10 Gyr. + The brightness could increase drastically due to courpression. if the euvironniental pressure grew considerably iu the recent past due to accretion of matter onto the local eroup.," The brightness could increase drastically due to compression, if the environmental pressure grew considerably in the recent past due to accretion of matter onto the local group." + If such a compressed fossil radio cocoon were nearby it would produce a relatively big total SSC flux due to its very huge angular size (~100 dee?~108 arcuin?).," If such a compressed fossil radio cocoon were nearby it would produce a relatively big total SSC flux due to its very large angular size $\sim 100$ $^2 \sim +10^6$ $^2$ )." + Mavhe ATA aud GAIRT would have a chance to detect this. if these telescopes would still be sensitive to such laree scales.," Maybe ATA and GMRT would have a chance to detect this, if these telescopes would still be sensitive to such large scales." + A detection by PLANCK should fail oulv by roughly one order of magnitude., A detection by PLANCK should fail only by roughly one order of magnitude. + This leaves some hope that a sensitive ground (or balloon) based single dish telescope is able to detect the large scale CAIB decrement, This leaves some hope that a sensitive ground (or balloon) based single dish telescope is able to detect the large scale CMB decrement +relatively well reproduced.,relatively well reproduced. +" The generation of Ca II K in the hot, upper portion of the atmosphere is distinct from previous results, and is necessary to produce more Ca II K than Paschen series emission, which is observed during our strongest flare."," The generation of Ca II K in the hot, upper portion of the atmosphere is distinct from previous results, and is necessary to produce more Ca II K than Paschen series emission, which is observed during our strongest flare." + This result confirms that infrared emission is a useful constraint on the atmospheric heating during M dwarf atmospheres., This result confirms that infrared emission is a useful constraint on the atmospheric heating during M dwarf atmospheres. +" The strength of emission from He I A10830À is not predicted from our one-dimensional model, but including a detailed treatment of backwarming from the corona (e.g.,Allredetal.2006) may be warranted, based on solar results."," The strength of emission from He I $\lambda$ is not predicted from our one-dimensional model, but including a detailed treatment of backwarming from the corona \citep[e.g.,][]{Allred2006} may be warranted, based on solar results." +" Modeling He I A10830À is also complicated by its different emission strengths compared to PB and Py in the two flares on EV Lac, but these differences show that He I A10830A has potential to constrain different backwarming scenarios during a variety of flares."," Modeling He I $\lambda$ is also complicated by its different emission strengths compared to $\beta$ and $\gamma$ in the two flares on EV Lac, but these differences show that He I $\lambda$ has potential to constrain different backwarming scenarios during a variety of flares." +" The time-evolution of the largest flare is not reproduced by our one-dimensional models, but a combination of multiple models with different filling factors (e.g.Walkowicz2008;Kowalskietal.2010) or detailed radiative hydrodynamic modeling with non-thermal beam heating (e.g.Allredetal.2006) may provide a better match to the flare emission."," The time-evolution of the largest flare is not reproduced by our one-dimensional models, but a combination of multiple models with different filling factors \citep[e.g.][]{Walkowicz2008b,Kowalski2010} or detailed radiative hydrodynamic modeling with non-thermal beam heating \citep[e.g.][]{Allred2006} may provide a better match to the flare emission." + We thank J. R. A. Davenport and H. Uitenbroek for helpful discussions and H. Uitenbroek for the use of his RH code., We thank J. R. A. Davenport and H. Uitenbroek for helpful discussions and H. Uitenbroek for the use of his RH code. +" We also thank J. Holtzman for his assistance with the NSMU 1-m telescope and D. Monin for his help with the DAO 1.8-m. S. L. H., A. F. K., and E. J. H. acknowledge support from NSF grant AST 08-07205."," We also thank J. Holtzman for his assistance with the NSMU 1-m telescope and D. Monin for his help with the DAO 1.8-m. S. L. H., A. F. K., and E. J. H. acknowledge support from NSF grant AST 08-07205." + J. P. W. acknowledges support from NSF Astronomy Astrophysics postdoctoral Fellowship AST 08-02230., J. P. W. acknowledges support from NSF Astronomy Astrophysics postdoctoral Fellowship AST 08-02230. + B. M. T. acknowledges support from the Mary Gates Research Scholarship., B. M. T. acknowledges support from the Mary Gates Research Scholarship. +" This publication is based on observations obtained with the Apache Point Observatory 3.5-meter telescope, which is owned and operated by the Astrophysical Research Consortium."," This publication is based on observations obtained with the Apache Point Observatory 3.5-meter telescope, which is owned and operated by the Astrophysical Research Consortium." +" This publication also makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of"," This publication also makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of" +mask.,mask. + It is seen that with increasing value of Imax the accuracy improves although the error is surprisingly large for small reconstruction multipoles Imax., It is seen that with increasing value of $l_{\hbox{\scriptsize max}}$ the accuracy improves although the error is surprisingly large for small reconstruction multipoles $l_{\hbox{\scriptsize max}}$. +" With additional smoothing the total reconstruction error of the ILC map has the tendency to fall, but without additional smoothing the error is nearly constant at about 0.25."," With additional smoothing the total reconstruction error of the ILC map has the tendency to fall, but without additional smoothing the error is nearly constant at about 0.25." +" To reveal the locations of the most significant errors in the case of the KQ75 (7yr) mask, the local reconstruction error of the ILC map (without additional smoothing) is pictured in figure 8 for Imax=10."," To reveal the locations of the most significant errors in the case of the KQ75 (7yr) mask, the local reconstruction error of the ILC map (without additional smoothing) is pictured in figure \ref{Fig:q_ilc_KQ75_lmax_10} + for $l_{\hbox{\scriptsize max}}=10$." + The errors within the mask are shown in figure 8aa. The dark areas display errors with |g|>1 which are much more widespread than for the KQ85 (7yr) mask., The errors within the mask are shown in figure \ref{Fig:q_ilc_KQ75_lmax_10}a a. The dark areas display errors with $|q|\ge 1$ which are much more widespread than for the KQ85 (7yr) mask. + The errors outside the mask are shown in figure 8bb. To locate large errors we have pictured values of |g|>0.2 as dark blue or dark red., The errors outside the mask are shown in figure \ref{Fig:q_ilc_KQ75_lmax_10}b b. To locate large errors we have pictured values of $|q|\ge 0.2$ as dark blue or dark red. + The errors outside the mask are only slightly larger than in the case of the KQ85 (7yr) mask., The errors outside the mask are only slightly larger than in the case of the KQ85 (7yr) mask. +" Compared to the KQ85 (7yr) mask, the accuracy problems of the algorithm applied to the larger KQ75 (Tyr) mask are much stronger, and we conclude that this mask is too large in order to allow a reconstruction for Imax>7, and even the results for Imax«7 should be considered critical."," Compared to the KQ85 (7yr) mask, the accuracy problems of the algorithm applied to the larger KQ75 (7yr) mask are much stronger, and we conclude that this mask is too large in order to allow a reconstruction for $l_{\hbox{\scriptsize max}} \ge 7$, and even the results for $l_{\hbox{\scriptsize max}} < 7$ should be considered critical." + For this reason we concentrate us in the following on reconstructions using the smaller KQ85 (7yr) mask., For this reason we concentrate us in the following on reconstructions using the smaller KQ85 (7yr) mask. + Now we compare the total reconstruction error of the ILC map with those of 1000 CMB realizations of the ACDM concordance model., Now we compare the total reconstruction error of the ILC map with those of 1000 CMB realizations of the $\Lambda$ CDM concordance model. + In figure 9 this comparison is shown with the additional smoothing of 600 arcmin and in figure 10 without smoothing.," In figure \ref{Fig:Q_ilc_und_1000lcdm_KQ85_FWHM_600arcmin} + this comparison is shown with the additional smoothing of 600 arcmin and in figure \ref{Fig:Q_ilc_und_1000lcdm_KQ85_FWHM_0arcmin} + without smoothing." + A resolution of Λίιας=16 and a mask threshold πι=0.5 is used., A resolution of $N_{\hbox{\scriptsize side}} = 16$ and a mask threshold $x_{\hbox{\scriptsize th}}=0.5$ is used. +" As can be seen in the upper panel of figure 9 the total reconstruction error of the ILC map within the mask is located for Imax<8 outside the dark grey band containing of 1000 models, but between the maximum and minimum errors of these models which domain is depicted as the light grey band."," As can be seen in the upper panel of figure \ref{Fig:Q_ilc_und_1000lcdm_KQ85_FWHM_600arcmin} + the total reconstruction error of the ILC map within the mask is located for $l_{\hbox{\scriptsize max}}\le 8$ outside the dark grey band containing of 1000 models, but between the maximum and minimum errors of these models which domain is depicted as the light grey band." + For Imax>8 the total reconstruction error of the ILC map is rather typical., For $l_{\hbox{\scriptsize max}} > 8$ the total reconstruction error of the ILC map is rather typical. + It should be noted that the computation of the ILC reconstruction error assumes that the ILC map contains the, It should be noted that the computation of the ILC reconstruction error assumes that the ILC map contains the + ↓⊲↸∪↓⋅↿↓↕⋖⋅≼∼⋖≱↓↥↓↓≻⇂⇂⇂⋜↧↿↕⋖≱↓↥∢≱⇂∎∆⋂↸↙⇥⋮⊽⋯∣∆∙⇘⋡∖∖⊽⋖⋅∐↓⋅≱∖↿≼⇍∪⊔↓↓≻⋯∢⊾ ∆∪⋅↙⇥⋅∪⇂∎∢⋅⋯⇍↓⊔⋅∖⇁⋖⋅⊔↿⇂⋅∪↓⋅⋏∙≟⊲↓∖⇁∢⋅⊔∖⇁⋜↧↓⋯⊾⊳∖∪⇂⋅↿↓⊔⋅↓⋖⋅⊔⊳∖↓≻⋜⊔⋅⋜⋯↓⋖⊾↿∢⋅↓⋅⊳∖ ∪∫⊳∐⊓∣⊳⋜⋯∠⇂∐⋯⊐⋜↧⊔∠⇂↿↓↥∢⊾↓≻⋜⊔⋅⋜⋯↓∢⋅∩⋅↓⋅⊳∖∢≱⇂⋅↿↓↥⋖⋅↓⋅∢⋅↓⋜↧↿↕∖⇁⋖⋅ ⋖⋟∣⋡≱∖⋖⋅↓⋅∖⇁⋖⊾↓⋅−↓⋖⋅⊔≱∖−⋡∖∢⋟⊔↓⋅⊓⋅↓≻∪≱∖⋠⊔⊀↓∪⊔⊳∖↿∖∕∖⋅⋜↧⊔∠⇂∪⊐∣⋡∙∖⇁⊔⊳∖⊀↓⊔⋏∙≟⇂↓↕∢⋅ equations in 22.,"For the computation of $\langle\Delta\delta\theta_{\rm c,max}\rangle$, we first compute $\Delta\delta\theta_{\rm c}$ of each event for given values of the lens parameters $M$ , $D_{ol}$, and $D_{os}$ ) and the parameters of the relative observer-lens-source positions $\lambda_\odot$ and $\phi$ ) by using the equations in 2." + We then obtain the maximum value which is expected rom the assumed duration of observation., We then obtain the maximum value which is expected from the assumed duration of observation. + Since astrometric observations will be carried. out. lor events detected [rom yhotometric monitoring. we assume observation duration o be feXlul0/p.," Since astrometric observations will be carried out for events detected from photometric monitoring, we assume observation duration to be $-1 t_{\rm E} \leq +t_{\rm obs} \leq 10 t_{\rm E}$." + Since the lens proper motion vector ge has no preferred. orientation. the average value of the maximum centroid shifts is obtained. by assuming hat 6 is randomly. distributed in the range 0x©<2s.," Since the lens proper motion vector $\muvec$ has no preferred orientation, the average value of the maximum centroid shifts is obtained by assuming that $\phi$ is randomly distributed in the range $0 \leq \phi \leq 2\pi$." +" In addition. since. we are interested in all lensing events not in the events detectable by a specific lensing survey. 10 inipact. parameters of events have random clistribution in the range O""yin "," In addition, since we are interested in all lensing events not in the events detectable by a specific lensing survey, the impact parameters of events have random distribution in the range $0 \leq u_{\rm min} \leq 1.0$ ." +The ecliptic latitude of a star towards the Baacle’s window is 3~—655., The ecliptic latitude of a star towards the Baade's window is $\beta\sim -6^\circ\hskip-2pt .5$. + For the physical and cdsnamical distributions of thelens and source. we assume the same clistributions used for the computation ob (98οsuas):," For the physical and dynamical distributions of thelens and source, we assume the same distributions used for the computation of $f(\delta\theta_{\rm c,max})$." +" Figure 3 shows the obtained distributions fCGN90,us) o various tvpes of Galactic lensing events."," Figure 3 shows the obtained distributions $f(\langle \Delta\delta +\theta_{\rm c,max}\rangle)$ for various types of Galactic lensing events." + In Figure 4. we so AsO.present the distributions of the probability of detecting for given values of detection threshold. ὅθιμ. as a unction of (logarithmic) lens mass.," In Figure 4, we also present the distributions of the probability of detecting $\Deltavec\deltavec\thetavec_{\rm c}$ for given values of detection threshold, $\delta\theta_{\rm th}$, as a function of (logarithmic) lens mass." + From the figures. one inds the following facts.," From the figures, one finds the following facts." +" First. if observations are performed with the ground interferometers. it will be cillicult to detect A80, for nearly all bulee selt-Iensing events. since he detection. probability is less than even for events caused by lenses with AZ=1.0M..."," First, if observations are performed with the ground interferometers, it will be difficult to detect $\Deltavec +\deltavec \thetavec_{\rm c}$ for nearly all bulge self-lensing events since the detection probability is less than even for events caused by lenses with $M=1.0\ M_\odot$." + In addition. detection will be limited for only small [fractions of disk-bulge. and jdo-LMC events.," In addition, detection will be limited for only small fractions of disk-bulge and halo-LMC events." + For example. for these types of events caused by AZ=0.3M. the probabilities are 36% and 211 respectively.," For example, for these types of events caused by $M=0.3\ M_\odot$, the probabilities are $36\%$ and $21\%$, respectively." + Second. if events are observed by using the SIM. on the other hand. it is expected to detect the deviations [or majority of disk-bulge and. halo-LMC events ancl even [or some fraction of bulge scl-lensing events.," Second, if events are observed by using the SIM, on the other hand, it is expected to detect the deviations for majority of disk-bulge and halo-LMC events and even for some fraction of bulge self-lensing events." + For example. the detection probabilities for events with Al=0.3M. are and Lor disk-bulge and halo-LMC events and for bulge self-Iensing events.," For example, the detection probabilities for events with $M=0.3\ M_\odot$ are and for disk-bulge and halo-LMC events and for bulge self-lensing events." + In Table 1. we summarize the ceteetion probabilities which are. expected. from. the observations by using the SIM and ground interferometers.," In Table 1, we summarize the detection probabilities which are expected from the observations by using the SIM and ground interferometers." + We compute the distributions of themaximum astrometric source star image centroid shifts. 96.4. and the average maximun) deviations in the centroikd shift trajectories.," We compute the distributions of themaximum astrometric source star image centroid shifts, $\delta\theta_{\rm c,max}$, and the average maximum deviations in the centroid shift trajectories," +Comet 9P/Tempel 1. was observed in (he nights of July 2 - 9. 2005 UT at the UII 2.2m telescope using (he SNIFS spectrograph that is permanently mounted at the bent C'assegrain focus.,"Comet 9P/Tempel 1 was observed in the nights of July 2 - 9, 2005 UT at the UH 2.2m telescope using the SNIFS spectrograph that is permanently mounted at the bent Cassegrain focus." + The instrument is described in more detail by Aldering et al. (, The instrument is described in more detail by Aldering et al. ( +2002) and Lantz et al. (,2002) and Lantz et al. ( +2004).,2004). + The SNIFS instrument is designed to obtain photometrically calibrated spectra of supernovae against the background of their host galaxy., The SNIFS instrument is designed to obtain photometrically calibrated spectra of supernovae against the background of their host galaxy. + It is therefore well suited to obtain spectrophotometry of the gas and dust released [rom the comet nucleus by the impact of the Deep Lupact probe against (he background of the more extended coma., It is therefore well suited to obtain spectrophotometry of the gas and dust released from the comet nucleus by the impact of the Deep Impact probe against the background of the more extended coma. + Among the instruments used in the Earth-based Deep Impact observing campaign (Meech et al., Among the instruments used in the Earth-based Deep Impact observing campaign (Meech et al. + 2005). SNIFS is unique in its capability to obtain photometrically calibrated spectral and spatial data over a very. wide optical wavelength range.," 2005), SNIFS is unique in its capability to obtain photometrically calibrated spectral and spatial data over a very wide optical wavelength range." + SNIFS basically consists of a blue and a red spectrograph arm., SNIFS basically consists of a blue and a red spectrograph arm. +" After the two wavelength ranges are separated bv a dichroic beamsplitter. (he light in each arm is focused on a separate 15x15 lenslet array with 0.4” lenslets. forming a contiguous 6"" x6"" field of view."," After the two wavelength ranges are separated by a dichroic beamsplitter, the light in each arm is focused on a separate $\times$ 15 lenslet array with $\arcsec$ lenslets, forming a contiguous $\arcsec$$\times$ $\arcsec$ field of view." + Each lenslet produces an image of the telescope pupil. which then becomes effectively the entrance point into a grism spectrograph.," Each lenslet produces an image of the telescope pupil, which then becomes effectively the entrance point into a grism spectrograph." + Each of the 15x15 pupil images is dispersed and produces a spectrum on (he CCD detector., Each of the $\times$ 15 pupil images is dispersed and produces a spectrum on the CCD detector. + The lenslet array is rotated at such an angle around (he optical axis and against the orientation of the lenslet array Chat the 225 individual spectra do not overlap., The lenslet array is rotated at such an angle around the optical axis and against the orientation of the lenslet array that the 225 individual spectra do not overlap. + The dispersion is 0.22 nm/pixel in the blue channel. the resolution is about 2 pixels. giving a resolving power of Αλ z21000 at 440 nm.," The dispersion is 0.22 nm/pixel in the blue channel, the resolution is about 2 pixels, giving a resolving power of $\lambda/\Delta\lambda\approx$ 1000 at 440 nm." + The red channel has a dispersion of 0.29 nm/pixel and a resolving power of A/AA 221300 at 760 nm (Lantz et al.," The red channel has a dispersion of 0.29 nm/pixel and a resolving power of $\lambda/\Delta\lambda\approx$ 1300 at 760 nm (Lantz et al.," + 2004)., 2004). +" Spatially, one pixel of the exiracted spectrum corresponds (o one x 0.4"" lenslet element."," Spatially, one pixel of the extracted spectrum corresponds to one $\arcsec\times$ $\arcsec$ lenslet element." + The spectral resolution is not dependent on the image quality in, The spectral resolution is not dependent on the image quality in +The right half of the oop appears to match well this requirement.,The right half of the loop appears to match well this requirement. +" The loop is z1019 cu long aud lies ou the solar disk CX,=|2307. 3.4= 11707) (see also Fie. 2))."," The loop is $\approx 10^{10}$ cm long and lies on the solar disk $X_{sol}= +230""$, $Y_{sol}=+470""$ ) (see also Fig. \ref{fig:fov}) )." + We prefer a loop located ou the disk. because. ou the limb. more coronal structures are niet along the line of sight (as sugeested by a simple inspection of TRACE images) aud their contribution is more difficult to subtract.," We prefer a loop located on the disk, because, on the limb, more coronal structures are met along the line of sight (as suggested by a simple inspection of TRACE images) and their contribution is more difficult to subtract." + The iiultiowaveleusth observation allows for a cross-check of the results and for absolute calibration., The multi-wavelength observation allows for a cross-check of the results and for absolute calibration. + Data in multiple TRACE EUV filter passbauds allow for maging and filter ratio diaguosties. SoIIO/CDS data or spectroscopy. and Yolkol/SNT for imaging in N-rav iofter passbauds.," Data in multiple TRACE EUV filter passbands allow for imaging and filter ratio diagnostics, SoHO/CDS data for spectroscopy, and Yohkoh/SXT for imaging in X-ray hotter passbands." +" The good visibility both in the 171 andinthe 195 filter band cusures a good S/N ratio or filter ratio (and therefore temperature) diaeiLostics,", The good visibility both in the 171 and in the 195 filter band ensures a good S/N ratio for filter ratio (and therefore temperature) diagnostics. + It is also visible in tιο 281 filter band., It is also visible in the 284 filter band. + YolikoL/SXT data are of good quaitv. although mostly in a sineο filter ρα: a loop light arye can be derived from thoiu.," Yohkoh/SXT data are of good quality, although mostly in a single filter band; a loop light curve can be derived from them." + The SoIlIO/CDS observation inchides data in several s»ectral Ines. with a good nominal coverage in the 6.5 temperature scusitivity range.," The SoHO/CDS observation includes data in several spectral lines, with a good nominal coverage in the $4.5 < log(T) < 6.5$ temperature sensitivity range." + It is nuportaut for our analysis hat the daa give us information about the loop evolution., It is important for our analysis that the data give us information about the loop evolution. + A long-lived and steady loop can be better studied. because close to physical equilibriun coucitions.," A long-lived and steady loop can be better studied, because close to physical equilibrium conditions." + Although the selected loop eventually fades away. its observed intensity evolves slowly. aud is nearlv steady in a sequence of several TRACE images.," Although the selected loop eventually fades away, its observed intensity evolves slowly, and is nearly steady in a sequence of several TRACE images." + We can then reasonably asstune that the average properties of the loop plasma evolve slowly as well., We can then reasonably assume that the average properties of the loop plasma evolve slowly as well. +" The campaign dataset includes four relevant TRACE data cubes,", The campaign dataset includes four relevant TRACE data cubes. +" An overall umber of 32 1021«102| images for cach filter are available. with exposure times between 1 aud 39 s, between 2 and 16 s. aud between 6 aud 131 s. for the 171A.. the 195 and the 281 filter. respectively."," An overall number of 32 $1024 \times 1024$ images for each filter are available, with exposure times between 1 and 39 s, between 2 and 46 s, and between 6 and 131 s, for the 171, the 195 and the 284 filter, respectively." + In the 171 filter. the longest exposure time is the most frequent one (22 frames).," In the 171 filter, the longest exposure time is the most frequent one (22 frames)." + In the 195 filter. the exposure time is 28 s for 17 frames. 16 s for 6 frames.," In the 195 filter, the exposure time is 28 s for 17 frames, 46 s for 6 frames." + In the 281 filter. l? frames are taken with the longest exposure time.," In the 284 filter, 17 frames are taken with the longest exposure time." + The data have been processed usine the standard IDE proceduretrece_prep., The data have been processed using the standard IDL procedure. + A smaller region (512«512 pixels) of the whole field. of view the one cuclosing the loop has been extracted for analysis., A smaller region $512 \times 512$ pixels) of the whole field of view – the one enclosing the loop – has been extracted for analysis. + For each filter land. the images have been coaligued with cross-correlation between the 5124512 iaages.," For each filter band, the images have been coaligned with cross-correlation between the $512 \times 512$ images." + We have removed the clearly corrupted frame 11 from all three datasets., We have removed the clearly corrupted frame 11 from all three datasets. + In the 281 filter frames 10 and 21 are clearly damaged by cosmic ravs ancl removed., In the 284 filter frames 10 and 24 are clearly damaged by cosmic rays and removed. + Iu order to apply standard diagnostic mcthods to derive physical quantities. such as the temperature. or even to apply iore detailed loop models. we have to extract the chussion frou the loop aud exclude auy other contribution along the line of seht.," In order to apply standard diagnostic methods to derive physical quantities, such as the temperature, or even to apply more detailed loop models, we have to extract the emission from the loop and exclude any other contribution along the line of sight." + Backerounc subtraction nav not be trivial in a region so rich iu bright structures (e.g. Reale2002. Sclunelz et al.," Background subtraction may not be trivial in a region so rich in bright structures (e.g. Reale2002, Schmelz et al." + 2003)., 2003). + IIowever. we have taken advantage of a articularly fortunate situation: the loop disappears at re end of the uage sequence.," However, we have taken advantage of a particularly fortunate situation: the loop disappears at the end of the image sequence." + The ast nuages (around 10 UT) can then be used to derive a 1tlable backerouud. iu the assumption that the structures surrounding aud crossing the selected loop along the line of sieht do not change much during the observation sequence.," The last images (around 10 UT) can then be used to derive a reliable background, in the assumption that the structures surrounding and crossing the selected loop along the line of sight do not change much during the observation sequence." + The procedure has then been to simply subtract the last inaee from all the preceding images., The procedure has then been to simply subtract the last image from all the preceding images. + This has been done for cach filter image sequence., This has been done for each filter image sequence. +" This approach to subtract backeround has several advantages: if is in principle very accurate. if the loop under analysis is the structure which mostly varies iu the observation: if is direct. with no use of interpolation: it is applied pixel by pixel. allowiug us to derive ""backerounud-subtracted inuage and therefore to have a visual feedback. and to analyze all loop pixels imustead of sampling at selected positions."," This approach to subtract background has several advantages: it is in principle very accurate, if the loop under analysis is the structure which mostly varies in the observation; it is direct, with no use of interpolation; it is applied pixel by pixel, allowing us to derive ``background-subtracted image"" and therefore to have a visual feedback, and to analyze all loop pixels, instead of sampling at selected positions." + As drawbacks. this method caunot take nue-variatious of the vackeround enmuüsson iuto account and we cannot exclude that crossing structures vary during the obscrvaion.," As drawbacks, this method cannot take time-variations of the background emission into account and we cannot exclude that crossing structures vary during the observation." + We have estimated the average iue fluctuations during the observation by computing Xxel-bv-pixel the standard deviation of the count rate., We have estimated the average time fluctuations during the observation by computing pixel-by-pixel the standard deviation of the count rate. + We obtain an average standard deviation of both in he 171 audin the 195 filter band (not iucluded in error bars). hat we retain a reasonably acceptable value hat validates our analysis.," We obtain an average standard deviation of both in the 171 and in the 195 filter band (not included in error bars), that we retain a reasonably acceptable value that validates our analysis." + Although there is evidence of systematic effect due to co-evolving nearby structures. the overall validity of this approach is proven by the results obtained (Sec. 3)).," Although there is evidence of systematic effect due to co-evolving nearby structures, the overall validity of this approach is proven by the results obtained (Sec. \ref{sec:res}) )." +2008; Muench et al 2007; Rebull et al 2010).,2008; Muench et al 2007; Rebull et al 2010). +" These provide samples that are, in some cases, somewhat older than Taurus and which generally contain a higher proportion of stars of later spectral type (M stars)."," These provide samples that are, in some cases, somewhat older than Taurus and which generally contain a higher proportion of stars of later spectral type (M stars)." + Both these factors have been invoked when explaining cases where the distribution of different categories of infrared SEDs is rather different from that in Taurus., Both these factors have been invoked when explaining cases where the distribution of different categories of infrared SEDs is rather different from that in Taurus. +" A case where differences from Taurus have been the subject of much debate is the cluster IC 348, which was initially age-dated at roughly 2.5 Myr (Haisch et al 2001), but has since been revised to 4-5 Myr by Mayne et al (2007) and Mayne Naylor (2008)."," A case where differences from Taurus have been the subject of much debate is the cluster IC 348, which was initially age-dated at roughly 2.5 Myr (Haisch et al 2001), but has since been revised to 4-5 Myr by Mayne et al (2007) and Mayne Naylor (2008)." + Spitzer photometry has been acquired for this cluster by Lada et al (2006) and Muench et αἱ (2007) with revised photometry and extra 24um data being added by Currie Kenyon (2009)., Spitzer photometry has been acquired for this cluster by Lada et al (2006) and Muench et al (2007) with revised photometry and extra $24 \mu$ m data being added by Currie Kenyon (2009). +" Here Lada et al (2006) drew attention to a population of what they called ‘anaemic’ discs, being objects that exhibited discs that were weak compared with those typical of Taurus."," Here Lada et al (2006) drew attention to a population of what they called `anaemic' discs, being objects that exhibited discs that were weak compared with those typical of Taurus." +" This category includes sources which have alternatively been dubbed as ‘homologously depleted’ discs by Currie Kenyon (2009) and as three separate categories by Muzerolle et al (2010) (i.e. ‘weak excess’, ‘warm excess’ and ‘classical transition’ discs)."," This category includes sources which have alternatively been dubbed as `homologously depleted' discs by Currie Kenyon (2009) and as three separate categories by Muzerolle et al (2010) (i.e. `weak excess', `warm excess' and `classical transition' discs)." + Each of these designations is designed to suggest discs that are in a state of partial clearing., Each of these designations is designed to suggest discs that are in a state of partial clearing. +" The number of such sources is large in IC 348 (e.g. including sources where only an upper limit is available at [24] wm Lada et al (2006) classified 44 M3 to M5 stars in IC 348 as having anaemic discs, compared with 41 with optically thick discs; if only sources with a detection at [24] zm are included then the number of anaemic and optically thick discs are 18 and 31, respectively)."," The number of such sources is large in IC 348 (e.g. including sources where only an upper limit is available at [24] $\mu$ m Lada et al (2006) classified 44 M3 to M5 stars in IC 348 as having anaemic discs, compared with 41 with optically thick discs; if only sources with a detection at [24] $\mu$ m are included then the number of anaemic and optically thick discs are 18 and 31, respectively)." + 'The large number of discs that are apparently in a state of partial clearing has prompted us (Section 2) to investigate the expected trajectories in the infrared two colour plane for M star discs that clear according to a variety of scenarios., The large number of discs that are apparently in a state of partial clearing has prompted us (Section 2) to investigate the expected trajectories in the infrared two colour plane for M star discs that clear according to a variety of scenarios. + Our aim is therefore to deduce the likely physical state of discs from their infrared colours and to provide a framework that can be applied to the M stars in a range of clusters., Our aim is therefore to deduce the likely physical state of discs from their infrared colours and to provide a framework that can be applied to the M stars in a range of clusters. + We will avoid empirical classifications (e.g. those that relate infrared excesses to the distribution found in Taurus) and instead focus on the likely physical properties of the discs concerned., We will avoid empirical classifications (e.g. those that relate infrared excesses to the distribution found in Taurus) and instead focus on the likely physical properties of the discs concerned. + We will however discuss how our classification relates to the various empirical categories of cleared discs mentioned above., We will however discuss how our classification relates to the various empirical categories of cleared discs mentioned above. + In Section 3 we analyse the case of IC 348 by assessing how the distribution of sources in the infrared two colour plane can be mapped onto a distribution of discs in different evolutionary states., In Section 3 we analyse the case of IC 348 by assessing how the distribution of sources in the infrared two colour plane can be mapped onto a distribution of discs in different evolutionary states. +" We will show that - although some of the anaemic discs in this cluster are merely flat, optically thick discs with no evidence for clearing (Luhman et al 2010) - there are nevertheless more partially cleared discs among M stars in the intermediate age IC 348 cluster than in the case of M stars in the younger Taurus."," We will show that - although some of the anaemic discs in this cluster are merely flat, optically thick discs with no evidence for clearing (Luhman et al 2010) - there are nevertheless more partially cleared discs among M stars in the intermediate age IC 348 cluster than in the case of M stars in the younger Taurus." + Section 4 summarises our conclusions., Section 4 summarises our conclusions. + We consider a range of disc clearing scenarios and plot their trajectories in the K - [8] versus K - [24] plane., We consider a range of disc clearing scenarios and plot their trajectories in the K - [8] versus K - [24] plane. + K band emission is largely contributed by the star whereas that at 8um and 24m originates in a broad radial range in the disc (roughly 0.2-0.3 AU and 1-2 AU respectively for M-stars)., K band emission is largely contributed by the star whereas that at $8 \mu$ m and $24 \mu$ m originates in a broad radial range in the disc (roughly 0.2-0.3 AU and 1-2 AU respectively for M-stars). + Our choice of these bands is motivated by the availability of data acquired by IRAC and MIPS respectively and also by the fact that they are well separated in wavelength., Our choice of these bands is motivated by the availability of data acquired by IRAC and MIPS respectively and also by the fact that they are well separated in wavelength. +" As pointed out by Ercolano, Clarke Robitaille (2009), the shorter wavelength infrared bands are less useful for the study of disc clearing in M stars since they can be dominated by the star even in the case of an optically thick (uncleared) disc."," As pointed out by Ercolano, Clarke Robitaille (2009), the shorter wavelength infrared bands are less useful for the study of disc clearing in M stars since they can be dominated by the star even in the case of an optically thick (uncleared) disc." +" We first consider the limiting case of razor thin, flat, optically thick reprocessing discs, viewed at a range of inclination angles."," We first consider the limiting case of razor thin, flat, optically thick reprocessing discs, viewed at a range of inclination angles." + We then consider two scenarios for disc clearing: a) progressive uniform reduction of the disc surface density at all radii and b) the carving out of the optically thick disc by an inner cavity of progressively larger radius., We then consider two scenarios for disc clearing: a) progressive uniform reduction of the disc surface density at all radii and b) the carving out of the optically thick disc by an inner cavity of progressively larger radius. +" In each case we compute the SED using the radiative transfer code of Whitney et al (2003a,b)."," In each case we compute the SED using the radiative transfer code of Whitney et al (2003a,b)." + Figure 1 shows the result of this exercise in the case, Figure 1 shows the result of this exercise in the case +solar spectrum. but also this line is not clearly. present in the BUALER atlas of 7..,"solar spectrum, but also this line is not clearly present in the SUMER atlas of \citet{2001A&A...375..591C}." +" Oscillator strengths. for the ποαι transitions were taken from ? except for the 451.13 nm line for which ""Table 5. lists various values from the literature.", Oscillator strengths for the indium transitions were taken from \citet{1995KurCD..23.....K} except for the 451.13 nm line for which Table \ref{tab:loggf} lists various values from the literature. + We adopted the value of ?.., We adopted the value of \citet{2006crchandbook}. + The indium hyperfine structure must be taken into account because the nuclear spin of In is /—9/2., The indium hyperfine structure must be taken into account because the nuclear spin of In is $I = 9/2$. + Values of the magnetic dipole (24) and electric quadrupole (2) constants of the hvperline interaction [or the lower and upper levels of the nunultiplet 1 were taken from ? ancl ?.., Values of the magnetic dipole $A$ ) and electric quadrupole $B$ ) constants of the hyperfine interaction for the lower and upper levels of the multiplet 1 were taken from \citet{1981jackson} and \citet{1978JPhB...11.2821Z}. + The level splitting was evaluated from: where €=FF|1)F(A0).I0D. FE-—J|1.J|1Iold. ων and. J is the electronic angular momentum (oe.g..?2)..," The level splitting was evaluated from: where $C = F(F+1) - J(J+1) - I(I+1)$, $F = J+I, J+I-1, +\dots, |J-I|$ , and $J$ is the electronic angular momentum \citep[e.g.,][]{1992sobelman}." + For the upper level with J=1/2 only the first member in the Hamiltonian of the hvperfine interaction is present and is split into two sublevels (£= 4. 5). while the upper level is split into four sublevels (f°= 3. 1. 5. 6).," For the upper level with $J = 1/2$ only the first member in the Hamiltonian of the hyperfine interaction is present and is split into two sublevels $F =$ 4, 5), while the upper level is split into four sublevels $F =$ 3, 4, 5, 6)." + Llence. the selection rule (As?=1.0. 1) implies that 6 hyperfine components are expected in the 451.13 nm transition.," Hence, the selection rule $\Delta F = -1, 0, 1$ ) implies that 6 hyperfine components are expected in the 451.13 nm transition." + Relative intensities of these components were calculated from Wigner 6j coellicients assuming analogy with LS coupling (cf.2).., Relative intensities of these components were calculated from Wigner $6j$ coefficients assuming analogy with LS coupling \citep[cf.][]{1992sobelman}. + Table ο specifies the resulting hyperfine structure components., Table \ref{tab:compos} specifies the resulting hyperfine structure components. + Indium has two stable isotopes. but since the ratio of their abundances is ! Inτο μα = 95.7+ 4.3. the second isotope can be neglected.," Indium has two stable isotopes, but since the ratio of their abundances is $^{115}$ In: $^{113}$ In = 95.7: 4.3, the second isotope can be neglected." + ‘The radiative transfer code of ? was used for detailed synthesis of the 451.13 nm line profile., The radiative transfer code of \cite{1992ASPC...26..499C} was used for detailed synthesis of the 451.13 nm line profile. + As commonly done in solar abundance analysis (sco7). we assume local thermodynamical equilibrium (LTE) and the HIOLMUL. model of 2? for the. solar photosphere. including its microturbulence stratification.," As commonly done in solar abundance analysis \citep[see][]{2002JAD.....8....8R}, we assume local thermodynamical equilibrium (LTE) and the HOLMUL model of \citet{1974SoPh...39...19H} for the solar photosphere, including its microturbulence stratification." + For the oscillator strength of 451.13 nm we take the value of ?.., For the oscillator strength of 451.13 nm we take the value of \citet{2006crchandbook}. +" We computed line profis both for the meteoritic abundance value ο=0.50 and for the solar value zip,=1.60 listed by. 2.."," We computed line profiles both for the meteoritic abundance value $\Am += 0.80$ and for the solar value $\AInS = 1.60$ listed by \citet{2005ASPC..336...25A}." + Phe resulting profiles are compared with the observed. quict-sun profile in Fig. 4.., The resulting profiles are compared with the observed quiet-sun profile in Fig. \ref{fig:synthetic_profile}. + The vertical bars specify the hyperfine structure components., The vertical bars specify the hyperfine structure components. + Lt is obvious that neither computation fits the observed feature at all., It is obvious that neither computation fits the observed feature at all. + Figure 5. illustrates the steps that are required to force a better match., Figure \ref{fig:fit} illustrates the steps that are required to force a better match. + The svnthesized line was convoluted. with a broad. Gaussian profile with FWIIM=1.585 pm (1pm=10 nm). much wider than the instrumental broadening of the FES spectrometer at Witt Peak. and. it was shifted recward over AA=2.35 pm.," The synthesized line was convoluted with a broad Gaussian profile with $\mbox{FWHM} = 1.58$ pm $(1~\mbox{pm} = +10^{-3}$ nm), much wider than the instrumental broadening of the FTS spectrometer at Kitt Peak, and it was shifted redward over $\Delta +\lambda = 2.35$ pm." + With these ad-hoc measures a reasonable fit is obtained for indium abundance ly=1.50 (Fie. 5)), With these ad-hoc measures a reasonable fit is obtained for indium abundance $\AInS = 1.50$ (Fig. \ref{fig:fit}) ) + but the assumptions mace to obtain it are not justified., but the assumptions made to obtain it are not justified. + We conclude that the solar line at this wavelength in the quict-sun spectrum is probably not due to indium., We conclude that the solar line at this wavelength in the quiet-sun spectrum is probably not due to indium. + We use the appearance of the 451.13 nm line in the sunspot spectrum to provide an independent estimate., We use the appearance of the 451.13 nm line in the sunspot spectrum to provide an independent estimate. + In order to include Zeeman splitting we estimate the magnetic field to be 3000 C7 from. the 464.52 nm line observed at the same dav as the 451.13 nm in the Witt Peak Sunspot atlas., In order to include Zeeman splitting we estimate the magnetic field to be 3000 G from the 464.52 nm line observed at the same day as the 451.13 nm in the Kitt Peak Sunspot atlas. + Lines with hyperfine structure split in complex manner in the presence of magnetic fields (2).., Lines with hyperfine structure split in complex manner in the presence of magnetic fields \citep{1975A&A....45..269L}. + We employed. the code by ?.. , We employed the code by \citet{1978A&AS...33..157L}. . +The result is shown in Fig. 6.., The result is shown in Fig. \ref{fig:hfs_components_in_H}. + We assume that the orientation of the magnetic field in the observed sunspot is purely vertical and maintains only the σ components., We assume that the orientation of the magnetic field in the observed sunspot is purely vertical and maintains only the $\sigma$ components. + For the model atmosphere we use the semi-empirical umbral model M of ?.., For the model atmosphere we use the semi-empirical umbral model M of \citet{1986ApJ...306..284M}. +" Figure 7 compares the synthesized profile assuming the meteoritic abundance value ;dj,=0.80 to the observed profile assuming 60. per cent. stravlight."," Figure \ref{fig:sunspot_profile} + compares the synthesized profile assuming the meteoritic abundance value $\Am = 0.80$ to the observed profile assuming 60 per cent straylight." + The dotted curve is the computed. profile after convolution with instrumental broadening corresponding to the LTS resolution of onemillion., The dotted curve is the computed profile after convolution with instrumental broadening corresponding to the FTS resolution of onemillion. +No ad-hoc wavelength shift is,No ad-hoc wavelength shift is +The authors speculated (hat a thin. elobal ice film could result [rom freezing of water vapor emanating from beneath the surface.,"The authors speculated that a thin, global ice film could result from freezing of water vapor emanating from beneath the surface." + llowever. the thin. global ice lil hypothesis has (wo problems.," However, the thin, global ice film hypothesis has two problems." + First. (he racial temperature eradients on the sun-facing hemispheres of Themis aud Cybele are in the wrong direction for surface frost to form.," First, the radial temperature gradients on the sun-facing hemispheres of Themis and Cybele are in the wrong direction for surface frost to form." + The davside surfaces are warmer than the subsurface regions so that anv [ree water molecules would migrate towards. ancl freeze al. deeper lavers. nol αἱ the hot surface.," The dayside surfaces are warmer than the subsurface regions so that any free water molecules would migrate towards, and freeze at, deeper layers, not at the hot surface." + Second. even if a 45 nm ice laver could form (by freeze out on the night side. for example). its lifetime to sublimation would be very short. requiring an unreasonably large water mass flux [rom each asteroid in order to maintain steady state.," Second, even if a 45 nm ice layer could form (by freeze out on the night side, for example), its lifetime to sublimation would be very short, requiring an unreasonably large water mass flux from each asteroid in order to maintain steady state." + To see this. we first note that a 45 nm ice coating is too thin to have a substantial effect on the albedo. as shown by both models and measurements of non-absorbing coatings on grains (e.g. Lasue et al.," To see this, we first note that a 45 nm ice coating is too thin to have a substantial effect on the albedo, as shown by both models and measurements of non-absorbing coatings on grains (e.g. Lasue et al." + 2007)., 2007). + As a result. the temperature of the ice film would be set bv the temperature of {he erain material with which it sits in close physical contact.," As a result, the temperature of the ice film would be set by the temperature of the grain material with which it sits in close physical contact." +" For low Thenmis-like albeclos. Figure (3)) shows that the subsolar sublimation rate is of order din/di = 10? kg m7? 1 falling to dim/dl = "" kg m? ! at a subsolar angle of 607."," For low Themis-like albedos, Figure \ref{dmbdt}) ) shows that the subsolar sublimation rate is of order $dm/dt$ = $^{-5}$ kg $^{-2}$ $^{-1}$ , falling to $dm/dt$ = $^{-6}$ kg $^{-2}$ $^{-1}$ at a subsolar angle of $\degr$." + At these rates. an ice film 45 nm in thickness would sublimate away on timescales of only 5 s to 50 s over most of the sunlit surface of the asteroid.," At these rates, an ice film 45 nm in thickness would sublimate away on timescales of only 5 s to 50 s over most of the sunlit surface of the asteroid." + Rivkin et al. (, Rivkin et al. ( +2010) and Campins et al. (,2010) and Campins et al. ( +"2010) assert that the ice is widespread or global. meaning that the total mass loss rate due to sublimation from an r, = 100 km radius Themis or Cybele-like asteroid should be 4zxr2dm/dl! = 10? to 10 ke l. in steady state.","2010) assert that the ice is widespread or global, meaning that the total mass loss rate due to sublimation from an $r_n$ = 100 km radius Themis or Cybele-like asteroid should be $4 \pi r_n^2 dm/dt$ = $^5$ to $^6$ kg $^{-1}$, in steady state." + These rates are two to three orders of magnitude larger than our spectroscopic limits to the gas production (<390 kg + and «370 kg ! for Themis and Cybele. respectively) ancl so are observationallv ruled out.," These rates are two to three orders of magnitude larger than our spectroscopic limits to the gas production $<$ 390 kg $^{-1}$ and $<$ 370 kg $^{-1}$ for Themis and Cybele, respectively) and so are observationally ruled out." + Therefore. we conclude that the thin. global ice film hypothesis is inconsistent with the data.," Therefore, we conclude that the thin, global ice film hypothesis is inconsistent with the data." + Another explanation is needed., Another explanation is needed. + Themis and Cybele are (oo small to have retzüined. primordial heat. and (oo small to be significantly heated by the decay of long-lived radioactive elements trapped within (heir constituent rocks.," Themis and Cybele are too small to have retained primordial heat, and too small to be significantly heated by the decay of long-lived radioactive elements trapped within their constituent rocks." + Unlike some planetary satellites (for example. Enceladus) they. also lack anv source of flexural heating driven bx external periodic gravitational forces.," Unlike some planetary satellites (for example, Enceladus) they also lack any source of flexural heating driven by external periodic gravitational forces." + Therelore. we reject the possibility that surface ice could represent water vapor frozen on the surface alter being driven out [rom a warm interior bv internallv-driven fumarolie activity.," Therefore, we reject the possibility that surface ice could represent water vapor frozen on the surface after being driven out from a warm interior by internally-driven fumarolic activity." + Recent observations of another large asteroid suggest a different possibility., Recent observations of another large asteroid suggest a different possibility. + The 113 kin diameter (596) Scheila displaved (ransient activity after being struck by a body several tens of meters in diameter (Jewitt et al., The 113 km diameter (596) Scheila displayed transient activity after being struck by a body several tens of meters in diameter (Jewitt et al. + 2011. Ishiguro et al.," 2011, Ishiguro et al." + 2011 while Bodewits οἱ al., 2011 while Bodewits et al. + 2011 deduced a somewhat largerimpactor)., 2011 deduced a somewhat largerimpactor). + Dust ejected [rom Scheila was observed to disperse uuder the, Dust ejected from Scheila was observed to disperse under the +Iu the ludit of iunfuütelv large lydrodvunamic Revnuolds nuuber. A. the stability. coudition for Couette flow is eiven by Oyty ΟυRS (Lindau&Lifshitz1959).,"In the limit of infinitely large hydrodynamic Reynolds number, $R_{e}$, the stability condition for Couette flow is given by $\Omega_1R_1^2$ $<$ $\Omega_2R_2^2$ \citep{lan59}." +". Therefore. iu order to maximize the shear dow within the apparatus. the NAID experiment has been designed such4 that Ro/Ry=2and O4/05 = L. guarautecing that O4""H = ΟυR3."," Therefore, in order to maximize the shear flow within the apparatus, the NMD experiment has been designed such that ${R_2}/{R_1} = 2$and $\Omega_1/\Omega_2$ = 4, guaranteeing that $\Omega_1R_1^2$ = $\Omega_2R_2^2$." + Iu addition to stability coustraiuts. stress liuitatiousσα in the experiment require that an upper limit of Ου=33IIz be placed 6on the frequency of rotation of the outer evliuder.," In addition to stability constraints, stress limitations in the experiment require that an upper limit of ${\Omega_2} = 33\,\mbox{Hz}$ be placed on the frequency of rotation of the outer cylinder." + Of course lower rotation rate can be used oe1 both. NMD experiment and Princeton Plana Physics Laboratory (PPPL) experiment. but it is assumed for this analysis that the highest rates are of ereatest scientific interest.," Of course lower rotation rate can be used in both NMD experiment and Princeton Plasma Physics Laboratory (PPPL) experiment, but it is assumed for this analysis that the highest rates are of greatest scientific interest." + The asstuuption of stable Couette flow implies a laminar flow with no turbulence., The assumption of stable Couette flow implies a laminar flow with no turbulence. + Ou the other haud the initial acceleration of the fluid to the final state of Couette flow from an alternate initial state duplics a transient chhanced torque. because. just as in the accretion disk. the lanunar friction is too small.," On the other hand the initial acceleration of the fluid to the final state of Couette flow from an alternate initial state implies a transient enhanced torque, because, just as in the accretion disk, the laminar friction is too small." + However. iu the experimental apparatus. the trausieut. Couette flow profile is Wehuholtz uustable so that turbulence is a natural aud expected result of the spiun-up of the flow.," However, in the experimental apparatus, the transient, Couette flow profile is Helmholtz unstable so that turbulence is a natural and expected result of the ""spin-up"" of the flow." + Ou the other haud the Ekumiui flow creates a relative orque between O4 and O» that we expect to be balanced o» a weak turbulence as observed by (Tavlor1936) and analogous to the spiu-up turbulence., On the other hand the Ekman flow creates a relative torque between $\Omega_1$ and $\Omega_2$ that we expect to be balanced by a weak turbulence as observed by \citep{tay36} and analogous to the spin-up turbulence. + This turbulence nay also influence the stability conditions but primarily he ability to distinguish turbulence caused by the ALTRI youn the hydrodynamic turbulence caused by the Ekmau aver., This turbulence may also influence the stability conditions but primarily the ability to distinguish turbulence caused by the MRI from the hydrodynamic turbulence caused by the Ekman layer. + We therefore analyze the MBI stability concitions as a function of livdrodyvuamic turbulence preexisting in the liquid aud therefore of the Praudtl uuuber., We therefore analyze the MRI stability conditions as a function of hydrodynamic turbulence preexisting in the liquid and therefore of the Prandtl number. +" At aree enough levels of turbulence. the effective. electrical resistivity can also be increased and therefore decrease the uaenetie Reynolds umber. &,,. aud therefore itlucuce he coucitious of excitation of the MBI."," At large enough levels of turbulence, the effective electrical resistivity can also be increased and therefore decrease the magnetic Reynolds number, $R_m$, and therefore influence the conditions of excitation of the MRI." + Iu comparison to the New Alexico Dynamo Experiment. a simular experiment at the Princeton Plasma Physics Laboratoryhas been proposed to look for the MBRI iu a rotating liquid metal aunulus (Jietal.2001).," In comparison to the New Mexico Dynamo Experiment, a similar experiment at the Princeton Plasma Physics Laboratoryhas been proposed to look for the MRI in a rotating liquid metal annulus \citep{ji01}." +.. The PPPL experiment utilizes liquid eallimm. an easy to handle metal with properties simular to liquid ποπα (see Table 1).," The PPPL experiment utilizes liquid gallium, an easy to handle metal with properties similar to liquid sodium (see Table 1)." +" Note. however. the higher density aud higher resistivity of liquid eallimim. which limit the maxima rotation speed aud the masximuun achievable &,,."," Note, however, the higher density and higher resistivity of liquid gallium, which limit the maximum rotation speed and the maximum achievable $R_m$." + The dimensions of tle PPPL experiueut are slieltly different. enabling them to acquire larger shear flow rates. Jietal.(2001).," The dimensions of the PPPL experiment are slightly different, enabling them to acquire larger shear flow rates, \citet{ji01}." +. For Ry=5 cm aud Πο=15 cmthen ΔυοRy = 3 witha typical Oy/Q> = 9., For ${R_1} = 5$ cm and ${R_2} = 15$ cm then ${{R_2}/{R_1}}$ = 3 with a typical $\Omega_1/\Omega_2$ = 9. + The couditions for instability for both experiments are discussed iu Sec., The conditions for instability for both experiments are discussed in Sec. + 1., 4. +" The angular velocity of Couctte flow confined. between coaxial evlinders with radi Ry«rRe and cxliucdirical aneular velocities O4.Qs is given by where we define à aud b as The incompressible andI5 dissipative"" ATID equatious describing the dynamics of liquid metals are given as follows. where B ds the magnetic fiold. V is the velocity 4 is the magnetic diffusivity, p is pressure and 7 is the kinematic viscosity."," The angular velocity of Couette flow confined between coaxial cylinders with radii $R_1 < r 5 in the solar wind (c.g,Naravauctal.1989:Armstronget1900)"," Anisotropy in the scattering medium is generally expected, and has been diagnosed by elongated scatter-broadened images, with axial ratios of up to 3 found through strongly scattering regions of the Galaxy \cite[e.g.][]{lo93,fra94,wil94,tro98}, , and axial ratios $>$ 5 in the solar wind \cite[e.g.][]{nar89,arm90}." +", Compressible MITD turbulent models have been developed in which the magnetic field gives rise to an clongation of the clectron-density fluctuations. with potentially very large axial ratios (Litlwick&Coldreich2001)."," Compressible MHD turbulent models have been developed in which the magnetic field gives rise to an elongation of the electron-density fluctuations, with potentially very large axial ratios \citep{lit01}." +. The effect of this anisotropic medium ou the scintillation observables is ereatest when the screen is thin. the magnetic field perpendicular to the line of sight aud with little chanec of mmaguetic field direction in the scatterer.," The effect of this anisotropic medium on the scintillation observables is greatest when the screen is thin, the magnetic field perpendicular to the line of sight and with little change of magnetic field direction in the scatterer." + Iu order to produce the > 6:1 axial ratio which would be required for.. we see from Chandran&Backer(2002) hat the magnetic field iu the plane of the scattering screen nuiust rotate through less than a radians through the screen.," In order to produce the $>$ 6:1 axial ratio which would be required for, we see from \citet{cha01} that the magnetic field in the plane of the scattering screen must rotate through less than $\pi/4$ radians through the screen." + This nuplies that if anisotropy in the plana density structure causes the observed anisotropic scintles. the maguetic field must be well ordered through tle scattering screen (i.c. along Lue of sight).," This implies that if anisotropy in the plasma density structure causes the observed anisotropic scintles, the magnetic field must be well ordered through the scattering screen (i.e. along line of sight)." +" The appareut οι]. axial ratio required is somewhat unusual for high ealactic atitudes.but nav be related to theunusual nature, aud thinness of the screen."," The apparent $>$ 6:1 axial ratio required is somewhat unusual for high galactic latitudes,but may be related to theunusual nature, and thinness of the screen." + The discovery of distant quasars has allowed detailed absorption studies of the state of the high. redshift interealactic medium (LGAL) at a time when the universe was less than a billion vears old (???)..," The discovery of distant quasars has allowed detailed absorption studies of the state of the high redshift intergalactic medium (IGM) at a time when the universe was less than a billion years old \citep[][]{fan2006,willott2007,willott2009}." + Bevond z6 several of these quasars show a complete Ciunn-Peterson trough in heir spectra blueward of the Lye line (2).., Beyond $z\sim6$ several of these quasars show a complete Gunn-Peterson trough in their spectra blueward of the $\alpha$ line \citep[][]{white2003}. + However. the spectra of these distant. quasars also show enhanced. Lya ransmission in the region surrounding the quasar. implving he presence of either an LILL region (2).. or of à proximity zone.," However, the spectra of these distant quasars also show enhanced $\alpha$ transmission in the region surrounding the quasar, implying the presence of either an HII region \citep[][]{cen2000}, or of a proximity zone." + “Phe interpretation of these transmission regions has »en a matter of some debate., The interpretation of these transmission regions has been a matter of some debate. + Dillerent arguments in favour of a rapidly evolving LGAL at 26 are based. on the oxoperties of the putative LLL regions inferred around. the uighest redshift quasars (????)..," Different arguments in favour of a rapidly evolving IGM at $z>6$ are based on the properties of the putative HII regions inferred around the highest redshift quasars \citep[][]{wyithe2004,wyithe2005,mesinger2004,kramer2009}." +" On the other πα, ?.. ? and ? have demonstrated that the features in. high redshift. quasar spectra bluewarc of the Lye line. could also be produced. by a classical proximity zone."," On the other hand, \citet[][]{bolton2007}, \citet[][]{maselli2007} and \citet[][]{lidz2007} have demonstrated that the features in high redshift quasar spectra blueward of the $\alpha$ line could also be produced by a classical proximity zone." + In this case. the spectra provide no evidence for a rapidly evolving IGM.," In this case, the spectra provide no evidence for a rapidly evolving IGM." + Importanth. these. and other analyses rely on an assumed. value for the EUV spectral index to convert from. the observed. Luminosity (recivard of rest-frame Lya) to an ionizing Hux. which is the quantity of importance for stuclies of reionization.," Importantly, these, and other analyses rely on an assumed value for the EUV spectral index to convert from the observed luminosity (redward of rest-frame $\alpha$ ) to an ionizing flux, which is the quantity of importance for studies of reionization." + As a further example. a value for the EUV spectral index must be assumed to estimate the quasar contribution to the reionization of hvdrogen (c.g.7).," As a further example, a value for the EUV spectral index must be assumed to estimate the quasar contribution to the reionization of hydrogen \citep[e.g.][]{srbinovsky2007}." +. The spectral energy. distributions of luminous quasars are thought to show little evolution out to high. redshift (?).., The spectral energy distributions of luminous quasars are thought to show little evolution out to high redshift \citep[][]{fanrev2006}. + For example. broad. emission line ratios at z5 have similar values to those observed at. low recdshitt. (2?)..," For example, broad emission line ratios at $z\sim5$ have similar values to those observed at low redshift \citep[][]{haman1993,dietrich2003}." + Moreover. optical and infrared spectroscopy. of some 26 quasars has indicated a lack of evolution in the optical-UV spectral properties redward of bye (22)..," Moreover, optical and infrared spectroscopy of some $z\sim6$ quasars has indicated a lack of evolution in the optical-UV spectral properties redward of $\alpha$ \citep[][]{pentericci2003,vandenberk2001}." + At higher energies. the optical/llt -to-N-rav Dux ratios (e.g.77). ancl X-ray continuum shapes (2?) show at most mild. evolution from low redshift.," At higher energies, the optical/IR -to-X-ray flux ratios \citep[e.g. ][]{brandt2002,strateva2005} and X-ray continuum shapes \citep[][]{vignali2003} show at most mild evolution from low redshift." + However ? have recently reported hot-dust- quasars at 26 which have no counterparts in the more local Universe., However \citet{jiang2010} have recently reported hot-dust-free quasars at $z\sim6$ which have no counterparts in the more local Universe. + Fhese quasars are thought to be at an, These quasars are thought to be at an +]lere. On=n?—nj is the departure of neutron fraction from its thermodynamic equilibrium value 7 in the j-th (—hadron. fy condensed) phase.,"Here, $\delta {n_n^j} = n_n^j - {\bar n}_n^j$ is the departure of neutron fraction from its thermodynamic equilibrium value ${\bar n}_n^j$ in the j-th (=hadron, $K^-$ condensed) phase." + The reaction rate per unit volume lor the non-leptonic process in question was already calculated by others 2006)..," The reaction rate per unit volume for the non-leptonic process in question was already calculated by others \citep{Lin02,Nar}." + The relaxation time (7) lor the process in the hadronic phase is given bv (Lindblom&Owen2002) along with where py is (he Fermi momentum for A lyperons and is the angle averaged malrix element squared in the hadronic phase given by (Lindblom&Owen 2006)..," The relaxation time $\tau$ ) for the process in the hadronic phase is given by \citep{Lin02} + along with where $p_{\Lambda}$ is the Fermi momentum for $\Lambda$ hyperons and $<{|M_{\Lambda}|}^2>$ is the angle averaged matrix element squared in the hadronic phase given by \citep{Lin02,Nar}. ." +" In pure hadronie phase. the second term in Eq.(16) vanishes because on=(),"," In pure hadronic phase, the second term in Eq.(16) vanishes because $\delta n_p^h = 0$." + llowever. the calculation of the hadronic part of the mixed phase is a little bit involved and described below.," However, the calculation of the hadronic part of the mixed phase is a little bit involved and described below." + The relaxation time in the antikaon condensed phe has the same form as in Eq.(15)., The relaxation time in the antikaon condensed phase has the same form as in Eq.(15). + In this case. the angle averaged matrix element. TALP> and py are lo be caleulated in ihe condensed phase.," In this case, the angle averaged matrix element , $<{|M_{\Lambda}|}^2>$ and $p_{\Lambda}$ are to be calculated in the condensed phase." + Also. we calcula AURE ical potential ⋅⋅imbalance due to the non-leptonic hvperon process n+p=p+A and it is given by. - ↜⋅ =⋅ ⋅ ⋅ ⋅ ο.∖∖≼↲≼↲⇀↸↕↽≻↕⋅≼↲⋟∖⋱∖⊽≺↘∕∣∐⊔≼↲↕⋅∐↓⋟∖⊽∪↓≺↘∣∣∣∣∣⋝≀↧↴∐≺⇂∪∣↽≻↥≀↧↴↕∐⋂⋅↙↙∣↙∣∖∏⋟∖⊽↕∐↖⊂↽↔↴⊔∐↲↓∪∐∪∖∖⇁↕∐↖≺↽↔↴≺∢∪∐⋟∖⊽∏⋅≀↧↴∐∐⋟∖⊽⋅ ony) andthe chemical equilibrium in the strangeness changing process η—p+iv," Also, we calculate $\frac{\delta \mu}{\delta {n_n^K}}$ from the chemical potential imbalance due to the non-leptonic hyperon process $n + p \rightleftharpoons p + \Lambda~$ and it is given by, We express $\delta {\mu}$ in terms of $\delta{n_n^K}$ and obtain $\frac {\delta \mu}{\delta{n_n^K}}$ using thefollowing constraints, andthe chemical equilibrium in the strangeness changing process $n \rightleftharpoons p + K^-$ ," +spectroscopically observed galaxies were not chosen at raudom.,spectroscopically observed galaxies were not chosen at random. + Figure 3. illustrates another source of uoise., Figure \ref{fig:spikealign} illustrates another source of noise. + $ippose we have foud a siugle galaxy at recdshi 25., Suppose we have found a single galaxy at redshift $z_2$. + How many other galaxies shotld we expect to Liid in the recdshilt interval to—Azuw+As for an asstumed value of ry?, How many other galaxies should we expect to find in the redshift interval $z_2-\Delta z$ $\sigma$ (see Section \ref{sec:b_and_d}) ) and the expected number of background sources (same significance) from the logN-logS curves of \cite{giacconi01}. +.. Variations in the number of background sources with position on the skv (Cowieetal.2002) will change (he number of expected background sources by at most a factor of 3., Variations in the number of background sources with position on the sky \citep{cowie02} will change the number of expected background sources by at most a factor of 3. + The total number of counts for each detected source were calculated in 3 bands: the soft band (0.3-1 keV). medium band (1-2keV) and hard band (2-3keV).," The total number of counts for each detected source were calculated in 3 bands: the soft band (0.3-1 keV), medium band (1-2keV) and hard band (2-8keV)." + Counts were extracted from source regions determined by +o source ellipses fromweaedetect., Counts were extracted from source regions determined by $\sigma$ source ellipses from. + This over-estimates the source size. but the contribution from background is negligible.," This over-estimates the source size, but the contribution from background is negligible." + The background region lor each source was taken {ο be an ellipse with major ancl minor axes equal to 4 limes (he source axes alid excluding the source region and any other overlapping source regions., The background region for each source was taken to be an ellipse with major and minor axes equal to 4 times the source axes and excluding the source region and any other overlapping source regions. + Dackground ellipse radii were not allowed to exceed 5 ∪↕↽≻↕⇀↸≼↲↥⋝∖⊽⋜⋝≀↧↴∣↽≻∪∏↥∃↱≻∣∣⊔↥∪≀↧↴∖⇁∪↕≺⇂≺∢∪∐↥≀↧↴∐↓↕∐≀↧↴∐∪∐∐⋅∪↕∐ variations in the diffuse emission., Background ellipse radii were not allowed to exceed 50 pixels (about ) to avoid contamination from variations in the diffuse emission. + Source count rates were corrected using monochromatic exposure maps created for each band using a monochromatic response al the mean photon energv in each band: 0.65 keV (soft band). 1.5 keV (medium band) and 5 keV (hare bad).," Source count rates were corrected using monochromatic exposure maps created for each band using a monochromatic response at the mean photon energy in each band: 0.65 keV (soft band), 1.5 keV (medium band) and 5 keV (hard band)." + These maps take into account. vignetting and spatial variation of the CCD QE., These maps take into account vignetting and spatial variation of the CCD QE. + X-ray. colors were (hen calculated [or each source as: {11=(GM—ο) (soft). and H2=(H—M)/T (hard). where 5. M and // are the counts in the soft. medium and hard bands respectively. and Tis the total counts in all three bands combined.," X-ray colors were then calculated for each source as: $H1=(M-S)/T$ (soft), and $H2=(H-M)/T$ (hard), where $S$, $M$ and $H$ are the counts in the soft, medium and hard bands respectively, and $T$ is the total counts in all three bands combined." + We estimated fluxes [rom each source assuming a 5 keV thermal bremsstrahlung moclel wilh photoelectric absorption., We estimated fluxes from each source assuming a 5 keV thermal bremsstrahlung model with photoelectric absorption. + The ay was fixed al the Galactic value., The $n_H$ was fixed at the Galactic value. + No correctionLor, No correctionfor +radii because then connection to the cluster size becomes Increasinely tenuous and depeucdent ou the cluster profile.,radii because then connection to the cluster size becomes increasingly tenuous and dependent on the cluster profile. + Because of the ambieuity of which model profile to use. one inav wonder whether defining roy using one profile or the other leads to lavee differences in the calculated value of roy.," Because of the ambiguity of which model profile to use, one may wonder whether defining $r_{90}$ using one profile or the other leads to large differences in the calculated value of $r_{90}$." + We show in Figure 7 a comparison of the values of roy obtained uxiug the best fit Kine or EFF model., We show in Figure \ref{fig:r90 comparison} a comparison of the values of $r_{90}$ obtained using the best fit King or EFF model. + We find that although there is some systematic difference between the two that can be as large as the raukiugs of clusters according to size (aud hence any correlation one might cxamine using rog) Is maintained to large degree regardless of the model oue adopts.," We find that although there is some systematic difference between the two that can be as large as, the rankings of clusters according to size (and hence any correlation one might examine using $r_{90}$ ) is maintained to large degree regardless of the model one adopts." + The best fit parameters for cach candidate. along with the lo uncertainties. are prescuted in Table 2..," The best fit parameters for each candidate, along with the $\sigma$ uncertainties, are presented in Table \ref{tab:Structural Parameters}." + The listed inagnitude is calculated by integrating the fitted Ising profile., The listed magnitude is calculated by integrating the fitted King profile. + The complete set of profiles. images. aud structural parameters is presented in the online version of these Figures and Tables.," The complete set of profiles, images, and structural parameters is presented in the online version of these Figures and Tables." + Our measurcients of structural parameters constitute the largest such survey of SAIC cluster profiles. so the availability of comparison data is hited.," Our measurements of structural parameters constitute the largest such survey of SMC cluster profiles, so the availability of comparison data is limited." + There exist oulv four published studies of SAIC cluster profiles. three of which are by a single group of authors aud should be considered a single survey. Kontizasetal.(1982).. I&outizas& (1983).," There exist only four published studies of SMC cluster profiles, three of which are by a single group of authors and should be considered a single survey. \cite{kon82}, \cite{kon83}," +". and I&ontizasetal.(19500), hereafter collectively referred to as Ixontizas ot al."," and \cite{kon86}, hereafter collectively referred to as Kontizas et al.," + use photographic plates from the Ux. Scehlunidt and Anelo-Australian telescopes in Australia to measure 67 cluster profiles. while \lackey&Cülinore.(2003b) prescut 10 profiles measured from images obtained with theTelescope.," use photographic plates from the U.K. Schmidt and Anglo-Australian telescopes in Australia to measure 67 cluster profiles, while \cite{mac03b} present 10 profiles measured from images obtained with the." + All 10 clusters observed by Mackey appear in Ixoutizas et al..," All 10 clusters observed by \cite{mac03b} appear in Kontizas et al.," + but most were observed using different filter passbauds., but most were observed using different filter passbands. + Although we do not know whether the structural parameters are strouely dependent ou color. a couservative conrparison should be linited to parameters determined from images taken with similar filters.," Although we do not know whether the structural parameters are strongly dependent on color, a conservative comparison should be limited to parameters determined from images taken with similar filters." + An cxamination of Noutizas et al, An examination of Kontizas et al. +os observations in a variety of filters aud eimnulsious do suggest that a clusters profile may depend on the wavelength iu which it is observed. although this issue is uot specifically investigated.,"'s observations in a variety of filters and emulsions do suggest that a cluster's profile may depend on the wavelength in which it is observed, although this issue is not specifically investigated." + We restrict our Comparison to the simaller set of 28 clusters observed im a filter aud emulsion combination closely corresponding to our V- observations., We restrict our comparison to the smaller set of 28 clusters observed in a filter and emulsion combination closely corresponding to our $V$ -band observations. + Our cluster sample includes 25 from, Our cluster sample includes 25 from +filaments.,filaments. +" The relationship between the mass of the detected cores (when the SED is reliable and the distance is known, see previous paragraph) and the local beam-averaged H» filament column density is reported in Fig. 4.."," The relationship between the mass of the detected cores (when the SED is reliable and the distance is known, see previous paragraph) and the local beam-averaged $_2$ filament column density is reported in Fig. \ref{mcore-mback}." +" The points for the /=59° ffield mostly lie in the range of column densities (10?!cm?< 102cm?) that corresponds to Imag 10^7$ to nearly $10^8$ years or a density of $\approx 10^4$ for $t\approx$ a few $\times 10^6$ years. + The existence of the Oort ‘loud beyond the limit of the Kuiper belt implies that any interaction would have had. to happen before the bulk of 10 Oort cloud was ejected from the solar nebular disc. thus within a few 10 vears.," The existence of the Oort cloud beyond the limit of the Kuiper belt implies that any interaction would have had to happen before the bulk of the Oort cloud was ejected from the solar nebular disc, thus within a few $10^7$ years." +" This is possible if the sun was born in à cluster with a density of y=10"" that dissolved. or evolved to a lower density. within zc vears."," This is possible if the sun was born in a cluster with a density of $n \simgreat 10^{3}$ that dissolved, or evolved to a lower density, within $\approx 10^8$ years." + One of the implications of stellar encounters. cisrupting planetary systems in stellar clusters is that there should then be à population of frec-DLoating planets., One of the implications of stellar encounters disrupting planetary systems in stellar clusters is that there should then be a population of free-floating planets. + Such a population due to stellar encounters is unlikely to be significant. in most open clusters as these clusters are not sullicientIy long-lived., Such a population due to stellar encounters is unlikely to be significant in most open clusters as these clusters are not sufficiently long-lived. + Even fewer frec-Lloating planets are expected in the voung clusters due to the disruption of planetary systems., Even fewer free-floating planets are expected in the young clusters due to the disruption of planetary systems. + Alternatively. the more frequent disruption. of planetary systems in globular clusters should. result in a population of free-Hoating planets.," Alternatively, the more frequent disruption of planetary systems in globular clusters should result in a population of free-floating planets." +" For example. in clusters with ages zm[OLou vears ancl densitiesτει zn?10""7... any. planetary systems with separations <1 should have been disrupted and these planets liberated into the cluster."," For example, in clusters with ages $\approx +10^{10}$ years and densities $\simgreat 10^3$, any planetary systems with separations $\simgreat 1$ should have been disrupted and these planets liberated into the cluster." + Lf such systems resemble our own. then à number of planets would. be iberated. per event.," If such systems resemble our own, then a number of planets would be liberated per event." + The likelihood for finding free-Doating rlancts depends on their velocities., The likelihood for finding free-floating planets depends on their velocities. + In open clusters any free-loating planets are likely to have velocities after disruption well in excess of the escape speed (Smith Bonnell 2000)., In open clusters any free-floating planets are likely to have velocities after disruption well in excess of the escape speed (Smith Bonnell 2000). + In contrast. post-disruption velocities in Clobulars are more ikely to be comparable or less than the higher escape speeds here (Smith Bonnell 2000).," In contrast, post-disruption velocities in Globulars are more likely to be comparable or less than the higher escape speeds there (Smith Bonnell 2000)." + In either case. due to their ow-nmass. subsequent two-body encounters. will. increase heir velocity. dispersion and jus limit their lifetime in the cluster.," In either case, due to their low-mass, subsequent two-body encounters will increase their velocity dispersion and thus limit their lifetime in the cluster." + We have shown that voung planetary systems similar to the Solar svstem have a good chance of surviving their early vears if they have the good fortune to form in an open cluster environment., We have shown that young planetary systems similar to the Solar system have a good chance of surviving their early years if they have the good fortune to form in an open cluster environment. + Planetary svstenis formed in globular clusters. on the other hand. face two major obstacles to their reaching adulthood.," Planetary systems formed in globular clusters, on the other hand, face two major obstacles to their reaching adulthood." + Firstly. the natal disk from which planets could form must survive for at least a few million. vears.," Firstly, the natal disk from which planets could form must survive for at least a few million years." +" Lf the earliest. stages of a globular cluster include a high-density phase (ΦονLO"" 7)) then the cireumstellar disc can be truncated. inside the region where gas-giant planets are believed. to form.", If the earliest stages of a globular cluster include a high-density phase $\simgreat {\rm few } 10^5$ ) then the circumstellar disc can be truncated inside the region where gas-giant planets are believed to form. + Such a high density. phase is consistent with expectations based on the cllicteney of star formation in nearby embedded (voung) stellar elusters and on subsequent cluster dynamics., Such a high density phase is consistent with expectations based on the efficiency of star formation in nearby embedded (young) stellar clusters and on subsequent cluster dynamics. + This could explain the recent find of a Lack of close planets in 47 Tuc (Brown 2000. Gilliland 2000).," This could explain the recent find of a lack of close planets in 47 Tuc (Brown 2000, Gilliland 2000)." + Secondly. the planetary svstems must endure a constant bombardment from neighbouring star systems.," Secondly, the planetary systems must endure a constant bombardment from neighbouring star systems." + These interactions will destroy most planetary. systems. bevond about 0.3 over the lifetime of the cluster., These interactions will destroy most planetary systems beyond about 0.3 over the lifetime of the cluster. + We conclude that giant planet. formation may be made more dillieult in a globular cluster and that any that do form are unlikely to survive unless their orbits are $0.3AU..., We conclude that giant planet formation may be made more difficult in a globular cluster and that any that do form are unlikely to survive unless their orbits are $\simless 0.3$. + The planets thrown out by interactions would. be expected to forni a population of free substellar bodies in the cluster., The planets thrown out by interactions would be expected to form a population of free substellar bodies in the cluster. + The velocity obtained by them from the initial disruption ancl subsequent encounters are likely to be higher than the escape velocity of the cluster and thus free-Hoating planets should not [orm a significant population in stellar clusters., The velocity obtained by them from the initial disruption and subsequent encounters are likely to be higher than the escape velocity of the cluster and thus free-floating planets should not form a significant population in stellar clusters. + We thank Simon Coodwin. Pavel WKroupa and Douglas Legeic for insightFul discussions on the cluster evolution.," We thank Simon Goodwin, Pavel Kroupa and Douglas Heggie for insightful discussions on the cluster evolution." + We also thank the referee. John Chambers. for his suggestions.," We also thank the referee, John Chambers, for his suggestions." + for LAB acknowledges support from a PPARC Xdvanced Fellowship., for IAB acknowledges support from a PPARC Advanced Fellowship. + MID gratefully acknowledges the support of the ltoval Society through a URL., MBD gratefully acknowledges the support of the Royal Society through a URF. +analvsis.,analysis. + The steps in our candidate cluster identification procedure are: In Figure 10 the two most significant weak lensing peaks (labeled 0 and 1) are coincident wilh two well populated clusters., The steps in our candidate cluster identification procedure are: In Figure \ref{fig:sigmamap.scaled.ps} the two most significant weak lensing peaks (labeled 0 and 1) are coincident with two well populated clusters. + These (wo clusters appear as prominent “fingers” at reclshilt 0.540 ancl 0.413. respectively. in Figure 6..," These two clusters appear as prominent “fingers” at redshift 0.540 and 0.413, respectively, in Figure \ref{fig:cone.diagram.subaru.ps}." +" There are obviously many well populated 565;, probes without any associated significant weak lensing peak.", There are obviously many well populated $\sigma_{SH}$ probes without any associated significant weak lensing peak. + Many of the well-populated redshilt survey probes correspond to groups with small velocity dispersion., Many of the well-populated redshift survey probes correspond to groups with small velocity dispersion. +" From Figure 9 we would not expect these svstems wilh rest frame line-of-ight velocity dispersion σε,<500 kins ! to produce a significant signal in the A map.", From Figure \ref{fig:sensitivity.ps} we would not expect these systems with rest frame line-of-sight velocity dispersion $\sigma_{rf} \lesssim 500$ km $^{-1}$ to produce a significant signal in the $\kappa$ map. + There are also weak lensing peaks with no corresponding peak in (he redshift survey., There are also weak lensing peaks with no corresponding peak in the redshift survey. + It is interesting to note that none of the 5n5 unreliable peaks in Table Bi3.) (starred entries) coincide with well-populated probes in the redshift survey: removal of these unreliable peaks from consideration evidentlv increases the efficiency. of the lensing map., It is interesting to note that none of the 5 unreliable peaks in Table \ref{tbl:VDisp} (starred entries) coincide with well-populated probes in the redshift survey; removal of these unreliable peaks from consideration evidently increases the efficiency of the lensing map. + To further assess the meaning of the weak lensing peaks we examine (he recdshift distributions along the line-ol-sight toward each of the significant weak lensing peaks., To further assess the meaning of the weak lensing peaks we examine the redshift distributions along the line-of-sight toward each of the significant weak lensing peaks. + We ask, We ask +stars may not always be parts of the same dynamical system (c.g. Young Lo 1997).,stars may not always be parts of the same dynamical system (e.g. Young Lo 1997). + Atomic gas plavs a fundamental role in the formation and evolution of exponential-disks (c.g. Dalcanton. Sperecl Summers 1997: Doissier. 'pantzos 2000: Ferguson Clarke 2001).," Atomic gas plays a fundamental role in the formation and evolution of exponential-disks (e.g. Dalcanton, Spergel Summers 1997; Boissier Prantzos 2000; Ferguson Clarke 2001)." + As reviewed. hy he latter authors. the origin of stellar exponential-disks inds a natural explanation in. viscosity-clriven racial lows. under the assumption that the star formation and. viscous iniescales are comparable.," As reviewed by the latter authors, the origin of stellar exponential-disks finds a natural explanation in viscosity-driven radial flows, under the assumption that the star formation and viscous timescales are comparable." + Assuming this simultaneity.- the exponential-cisk scale-length is found either to increase with time. if the cosmologically-motivated gaseous. infall is concurrent with the previous two processes. or tO stay constant if the bull of the disk is) assembled before star formation and viscosity act in a significant manner (Ferguson Clarke 2001).," Assuming this simultaneity, the exponential-disk scale-length is found either to increase with time, if the cosmologically-motivated gaseous infall is concurrent with the previous two processes, or to stay constant if the bulk of the disk is assembled before star formation and viscosity act in a significant manner (Ferguson Clarke 2001)." + In the former case. successive stellar populations trace the settling of the newly infalling eas at cilferent cisk ages.," In the former case, successive stellar populations trace the settling of the newly infalling gas at different disk ages." + As a straightForward consequence. a radial color eradient is produced and the exponential-clisk scale-Iengths are expected to be larger in the optical bands than in the near-LI1t ones.," As a straightforward consequence, a radial color gradient is produced and the exponential-disk scale-lengths are expected to be larger in the optical pass-bands than in the near-IR ones." + Llowever. not only cdisk-galaxies but also disk-less galaxies may show a wavelength-dependence of. their characteristic scale-leneth (e.g. the cllective radius. ie. the racius which contains of the total luminosity). simply as a result of the well-known elfects of age and metallicity on broad-band colors of stellar populations (e.g. Bruzual Charlot 1993: Worthey 1994).," However, not only disk-galaxies but also disk-less galaxies may show a wavelength-dependence of their characteristic scale-length (e.g. the effective radius, i.e. the radius which contains of the total luminosity), simply as a result of the well-known effects of age and metallicity on broad-band colors of stellar populations (e.g. Bruzual Charlot 1993; Worthey 1994)." + In fact. color gradients along the radial coordinate of a galaxy may be due either to a gradient in age (with lixed metallicity) or to a gracient in metallicity (with fixed age) of its stellar populations (e.g. Peletier.. Valentijn Jameson 1990: Tamura et al.," In fact, color gradients along the radial coordinate of a galaxy may be due either to a gradient in age (with fixed metallicity) or to a gradient in metallicity (with fixed age) of its stellar populations (e.g. Peletier, Valentijn Jameson 1990; Tamura et al." + 2000: Saglia ct al., 2000; Saglia et al. + 2000: cle Jong 1996). whatever the causes of these gradients. are.," 2000; de Jong 1996), whatever the causes of these gradients are." + Furthermore. dust attenuation toward the galaxy center is able to reproduce cdillerences in the observed radial surface brightness distribution at two wavelengths. (eIn in the optical and near-Ht). due to the dilference in optical depth al these two wavelengths for a given dust. column censity. even under the hypothesis that a simple stellar population is present. and. without introducing a significant change in the observed total color (Witt. Phronson Capuano 1992).," Furthermore, dust attenuation toward the galaxy center is able to reproduce differences in the observed radial surface brightness distribution at two wavelengths (e.g. in the optical and near-IR), due to the difference in optical depth at these two wavelengths for a given dust column density, even under the hypothesis that a simple stellar population is present, and without introducing a significant change in the observed total color (Witt, Thronson Capuano 1992)." + In order to investigate the presence of color gradients and their origin (if any) in earlv-tvpe chwarfs. here we study the relationships (if any) between dillerent photometric parameters (effective radius re. bulge-to-total luminosity ratio DT. total opticalnear-LR color index HL and HH color profile) of IS Virgo cluster. dl and. dS0. galaxies. imaged by Cavazzi ct al. (," In order to investigate the presence of color gradients and their origin (if any) in early-type dwarfs, here we study the relationships (if any) between different photometric parameters (effective radius $r_e$, bulge-to-total luminosity ratio $B/T$, total optical–near-IR color index $-$ H and $-$ H color profile) of 18 Virgo cluster dE and dS0 galaxies, imaged by Gavazzi et al. (" +2001) in the B-bancel (0.44. jm) and L-band.,2001) in the B-band $\rm 0.44~\mu m$ ) and H-band. + This sample comprises objects one to a [ew magnitudes brighter than dwarf. elliptical. and. spheroidal galaxies seen in the Local Group (e.g. Mateo 1998). which form a cillerent population of early-type dwarls (e.g. Conselice. Gallagher Wyse 2001 and references therein) as witnessed also by their dilferent photometric parameters.," This sample comprises objects one to a few magnitudes brighter than dwarf elliptical and spheroidal galaxies seen in the Local Group (e.g. Mateo 1998), which form a different population of early-type dwarfs (e.g. Conselice, Gallagher Wyse 2001 and references therein), as witnessed also by their different photometric parameters." + D- (0.44pim). V- (0.55jum) and L-band (1.65sam) surface photometry of LT dwarf elliptical and lenticular galaxies plus l low-mass Ej pec/S0 galaxy was obtained by CGavazzi et al. (," B- $\rm 0.44~\mu m$ ), V- $\rm 0.55~\mu m$ ) and H-band $\rm 1.65~\mu m$ ) surface photometry of 17 dwarf elliptical and lenticular galaxies plus 1 low-mass E pec/S0 galaxy was obtained by Gavazzi et al. (" +2001 iereafter. referred to as GOL).,2001 – hereafter referred to as G01). +" These objects. with photographic magnitude m,<6.0. were selected from the Virgo Cluster Catalogue (VCC) of Binggeli. Sandage ‘Temmann (1985)."," These objects, with photographic magnitude $\rm m_p \le 16.0$, were selected from the Virgo Cluster Catalogue (VCC) of Binggeli, Sandage Tammann (1985)." + With the exception of 11078. they are all certain members of the cluster. where membership was assigned by Bineeeli. Sancdage “Tammann ancl Bineeeli. Popescu Vammann (1993).," With the exception of 1078, they are all certain members of the cluster, where membership was assigned by Binggeli, Sandage Tammann and Binggeli, Popescu Tammann (1993)." + Lerealter we refer to these 15 dwarl/low-mass carly-type galaxies as the VCC early-type dwarf sample., Hereafter we refer to these 18 dwarf/low-mass early-type galaxies as the VCC early-type dwarf sample. + riο., Fig. + ] gives a pictorial view of the projected spatia distribution of these galaxies on to the sky-region occupiec by the Virgo cluster., 1 gives a pictorial view of the projected spatial distribution of these galaxies on to the sky-region occupied by the Virgo cluster. + It shows that the chvarls under study lav either within a projected radial distance of 2 degrees from ALSs7 (associated. with cluster A). with the exception. of 6608 (laving in the corona between the previous region and a circle of 4 degrees radius centred on the maximum projected ealaxy density of cluster A). or within a projectec racial distance of 1.5 degrees from the centre of cluster D (sce Dinggeli. Tanimann Sandage LOST for the definitions of clusters A and B).," It shows that the dwarfs under study lay either within a projected radial distance of 2 degrees from 87 (associated with cluster A), with the exception of 608 (laying in the corona between the previous region and a circle of 4 degrees radius centred on the maximum projected galaxy density of cluster A), or within a projected radial distance of 1.5 degrees from the centre of cluster B (see Binggeli, Tammann Sandage 1987 for the definitions of clusters A and B)." + The 3D structure of the Virgo cluster is complex (e.g. cde Vaucouleurs 1961)., The 3D structure of the Virgo cluster is complex (e.g. de Vaucouleurs 1961). + Accorcling to Cavazzi et al. (, According to Gavazzi et al. ( +1999). the distance modulus fro of cluster A is 30.54+0.06. while. for cluster B. dominated by ΑΓ). pij=31.8440.10.,"1999), the distance modulus $\rm \mu_0$ of cluster A is $\rm 30.84 \pm 0.06$, while, for cluster B, dominated by 49, $\rm \mu_0 = 31.84 \pm 0.10$." + As a consequence. the galaxies associated with cluster Bare farther from us than those associated with cluster A. For the purposes of the present analysis. we assume that all the IS VCC galaxies under study lay at a distance of 17.0 Alpe to us. in agreement with COL.," As a consequence, the galaxies associated with cluster B are farther from us than those associated with cluster A. For the purposes of the present analysis, we assume that all the 18 VCC galaxies under study lay at a distance of 17.0 Mpc to us, in agreement with G01." + The VCC early-type dwarl sample contains 19 αν ealaxies. 1 dE.N/dSO.N galaxv and | di/clSO.N galaxy. where N stands for “nucleated”.," The VCC early-type dwarf sample contains 13 dE,N galaxies, 1 dE,N/dS0,N galaxy and 1 dE/dS0,N galaxy, where N stands for “nucleated”." + Such a. high. fraction of nucleated cvart. ellipticals reflects the facet that δν ealaxics are more luminous than non-nucleated να ellipticals and. therefore. their. fraction increases in à maenituce-limitecl sample such as the GOL one.," Such a high fraction of nucleated dwarf ellipticals reflects the fact that dE,N galaxies are more luminous than non-nucleated dwarf ellipticals and, therefore, their fraction increases in a magnitude-limited sample such as the G01 one." + Lt is also straigthforward to understand that dl.Ns are the easiest to detect at both optical ancl near-Il. pass-bands among di£s.," It is also straigthforward to understand that dE,Ns are the easiest to detect at both optical and near-IR pass-bands among dEs." + Though there are different: possibilities of producing nucleation. Conselice. Gallagher Wyse (2001) conclude that dis and db.s within 6 degrees [rom the centre of Virgo cluster A ancl with heliocentric radial velocity vκ2400kms have similar origins. since the velocity characteristics of these two populations are not significantly dilferent.," Though there are different possibilities of producing nucleation, Conselice, Gallagher Wyse (2001) conclude that dEs and dE,Ns within 6 degrees from the centre of Virgo cluster A and with heliocentric radial velocity $\rm v < 2400~km~s^{-1}$ have similar origins, since the velocity characteristics of these two populations are not significantly different." + In. particular. these authors list heliocentric racial velocities for 15 out of the 18 galaxies of the VCC carly-type dwarl sample.," In particular, these authors list heliocentric radial velocities for 15 out of the 18 galaxies of the VCC early-type dwarf sample." + Relying on their result. we assume that all the 18 galaxies under study have the same origin.," Relying on their result, we assume that all the 18 galaxies under study have the same origin." + In Tab., In Tab. + 1l. we list the VCC catalogue properties and the heliocentric radial velocities (Conselice. Gallagher Wyse 2001) of the individual galaxies relevant to this studv.," 1, we list the VCC catalogue properties and the heliocentric radial velocities (Conselice, Gallagher Wyse 2001) of the individual galaxies relevant to this study," +The distribution given bv equations 13. and LL were derived in the coutext of ple’)Xο3.,"The distribution given by equations \ref{eqGofx} and \ref{eqDiffeoft} + were derived in the context of $p(e') \propto e'^{-3}$." + As long as pte) follows a power law with c. we can write a selfsimülur distribution function fle.t).," As long as $p(e')$ follows a power law with $e'$, we can write a self-similar distribution function $f(e,t)$ ." + We write a generic function. pe’)=ByeOh. to account for the different slopes caused. lw differcut nass distributions (for 3>52.4 9>: for 5«2. y= 2).," We write a generic function, $p(e')=P_0 e'^{-(1+\eta)}$, to account for the different slopes caused by different mass distributions (for $3 > \gamma > 2$, $\eta = +\gamma$; for $\gamma < 2$, $\eta=2$ )." + The derivation of the distribution function proceeds analogously as in section 3.1.., The derivation of the distribution function proceeds analogously as in section \ref{secBEecc}. +" Equatiou 10 becomes two equations: a dinensiouless inteero-differcutial equation that specifies the shape. and au ordinary differential equation to specify the evolutiou of the eccentricity scale ο), "," Equation \ref{eqFofe} becomes two equations: a dimensionless integro-differential equation that specifies the shape, and an ordinary differential equation to specify the evolution of the eccentricity scale $e_c(t)$ ." +"The eeueral version of equation l1 is: In the limit of no cccoutricity dissipation (7;>o) equation 23. shows that ο)xft""1,"," The general version of equation \ref{eqDiffeoft} is: In the limit of no eccentricity dissipation $\tau_d \rightarrow +\infty$ ), equation \ref{eqDiffeoftgeneral} shows that $e_c(t) \propto +t^{1/(\eta-1)}$." + For all of the pie) discussed in section L.. the erowth of ¢.(4) is always faster than t3.," For all of the $p(e')$ discussed in section \ref{secMassSpec}, the growth of $e_c(t)$ is always faster than $t^{1/2}$." + The shape of the distribution function is determined through a Fourier transform of the general version of equation 12.., The shape of the distribution function is determined through a Fourier transform of the general version of equation \ref{eqFofg}. + For slopes of 1«4g 3. οι)=|cos(k+x)exp(κLuPK (77).," For slopes of $1<\eta<3$ , $g(x)=\int \cos (\vec k \cdot \vec x) \exp(-|\vec +k|^{\eta-1})d^2 \vec k $ \citep{S99,CSS07}." +" While there is only a closed foxii solution for jj= 2. giveu by equation 13.. all of these fictions are fat at low wr and fall off like.e I!13,"," While there is only a closed form solution for $\eta=2$ , given by equation \ref{eqGofx}, all of these functions are flat at low $x$ and fall off like $x^{-(\eta+1)}$." +" Tu fact. it is easy to show from equation LO that the high ο tail is given by when ft<τι, "," In fact, it is easy to show from equation \ref{eqFofe} that the high $e$ tail is given by when $t \ll \tau_d$." +For equilibrium distributions where é.(£)=0. fis replaced with zy. the timescale for the dissipation.," For equilibrium distributions where $\dot +e_c(t)=0$, $t$ is replaced with $\tau_d$, the timescale for the dissipation." + When p(c)xe| or steeper. the aceunulation of the smallest perturbations over time is more effective at raising the eccentricity of the binary than sinele huge perturbations.," When $p(e') \propto e'^{-4}$ or steeper, the accumulation of the smallest perturbations over time is more effective at raising the eccentricity of the binary than single large perturbations." + Tn this case. the evolution of the ecceutricity follows standard Brownian motion. where the distribution function ix οὐ...," In this case, the evolution of the eccentricity follows standard Brownian motion, where the distribution function is a Gaussian, and $e_c(t) +\propto t^{1/2}$." + Iu this section we compute e(f) aud {1} for several Iuiper belt binaries., In this section we compute $e_c(t)$ and $i_c(t)$ for several Kuiper belt binaries. + The “binary” of section 2. now refers to a hound pair of Iuiper belt objects. aud the “perturbers” are all of the other members of the Ikuiper belt.," The “binary” of section \ref{secSingleEnc} now refers to a bound pair of Kuiper belt objects, and the “perturbers” are all of the other members of the Kuiper belt." + For the highest mass NKBOs. the size προςτα is well determined to be a power law with an iudex slightly ercater than 4=Ll.," For the highest mass KBOs, the size spectrum is well determined to be a power law with an index slightly greater than $q=4$." + The lowest mass bodies; of about 30 km in radius. are less frequent than predicted by a single power law. however the parameters of a more general model are still uuder investigation (?2777?77?)..," The lowest mass bodies, of about 30 km in radius, are less frequent than predicted by a single power law, however the parameters of a more general model are still under investigation \citep{TB01,LJ02,PS05,FKH08,FH08}." + For this section we use the best fit of a single power law model to the high mass part of the spectrum provided bv ?.. who find ¢=125 aud a nuuber deusitv of 1 body per square degree brighter than maeuitude 23.1.," For this section we use the best fit of a single power law model to the high mass part of the spectrum provided by \citet{FKH08}, who find $q=4.25$ and a number density of 1 body per square degree brighter than magnitude 23.4." +" We assume an average distance of LO AU to the IKuiper belt aud a depth of 20 AU to fiud a volumetric ummber density yy293«10HemὉ,"," We assume an average distance of 40 AU to the Kuiper belt and a depth of 20 AU to find a volumetric number density $n_0=3 \times 10^{-41} ~{\rm + cm^{-3}}$." + To couvert the magnitudes of the objects to plivsieal sizes. we assuuie a constant ecometric albedo of 0.01. a constant physical deusity of L ecm7. aud take the R-band apparent magnitude of the Sun to be -27.6.," To convert the magnitudes of the objects to physical sizes, we assume a constant geometric albedo of 0.04, a constant physical density of 1 g ${\rm cm^{-3}}$, and take the R-band apparent magnitude of the Sun to be -27.6." +" We find that the magnitude 23.1 corresponds to a mass my=1.55«1073ο, equivalent to a radius of 75 kan."," We find that the magnitude 23.4 corresponds to a mass $m_0=1.75\times 10^{21}~{\rm g}$, equivalent to a radius of 75 km." + Most of the objects fouud between 30-50 AU are inclined by about 5-15 degrees relative to the plane of the solar system. aud have heliocentric ecceutricities of O.1-0.2.," Most of the objects found between 30-50 AU are inclined by about 5-15 degrees relative to the plane of the solar system, and have heliocentric eccentricities of 0.1-0.2." + Oi analysis so far has treated the perturbing bodies as unbound objects moving relative to the binary with a constant velocity., Our analysis so far has treated the perturbing bodies as unbound objects moving relative to the binary with a constant velocity. + When the perturbers are part of a disk orbiting the ceutral star. the orbital clements of the disk sot the paraiucters of the perturbation frequencies we calculate in section 3..," When the perturbers are part of a disk orbiting the central star, the orbital elements of the disk set the parameters of the perturbation frequencies we calculate in section \ref{secBE}." + The relative velocity between IDBOs. when they interact. is set by the size of their eccentricities aud inclinations. vy~€yaQy. where the subscript “IP denotes a holioceutrie orbital quantity.," The relative velocity between KBOs, when they interact, is set by the size of their eccentricities and inclinations, $v_p \sim e_{H} a +\Omega_H$, where the subscript “H” denotes a heliocentric orbital quantity." +" We asse a coustaut perturbing velocity with e,=1Ius. which correspouds to the typical helioceutrie cceceutricities and inclinatious of 100."," We assume a constant perturbing velocity with $v_p = 1~{\rm + km/s}$, which corresponds to the typical heliocentric eccentricities and inclinations of KBOs." + We asstune that these encounters occur isotropically in the frame of a binary. however tliis is not accurate.," We assume that these encounters occur isotropically in the frame of a binary, however this is not accurate." + A more detailed calculation of the angular distribution of relative velocities will only affect the cocfiicicuts ofthe perturbations., A more detailed calculation of the angular distribution of relative velocities will only affect the coefficients of the perturbations. + The disk does not specify a special direction for the perturbation vector Ae. so the perturbing frequency and the distribution Muction retain their axisvunuetry.," The disk does not specify a special direction for the perturbation vector $\Delta \vec e$, so the perturbing frequency and the distribution function retain their axisymmetry." +" The influence of the central star ou the binary aud the perturbers adds another constraint to our assumption of impulsive encounters: the timescale for an interaction must be shorter than the orbital ood. around the star: hfe,«1/055, or equivaleutly. b«ej;j0."," The influence of the central star on the binary and the perturbers adds another constraint to our assumption of impulsive encounters: the timescale for an interaction must be shorter than the orbital period around the star: $b/v_p \ll 1/\Omega_H$, or equivalently, $b \ll e_H +a$." + This guarautees that tho relative velocity is coustaut during the interaction., This guarantees that the relative velocity is constant during the interaction. + Tf the orbit of the binary is much different than the typical KBO orbit. there are several modifications to perturbation requencics experienced by the binary.," If the orbit of the binary is much different than the typical KBO orbit, there are several modifications to perturbation frequencies experienced by the binary." + One modification is due to the finite height of the disk of perturbers., One modification is due to the finite height of the disk of perturbers. + This heielt is set by their inclinations around the central star: for the I&uiper belt we refer to the average inclination as 0jgp., This height is set by their inclinations around the central star; for the Kuiper belt we refer to the average inclination as $\langle i \rangle_{KB}$. +" A binary with heliocentric inclination joo,7Ging uever travels above or below the perturbing disk height aud herefore experiences the maximal frequency of perturbations.", A binary with heliocentric inclination $i_{\rm CoM} \ll \langle i \rangle_{KB}$ never travels above or below the perturbing disk height and therefore experiences the maximal frequency of perturbations. + If ολη9“pase. the binary spends most of its orbit outside of the perturbing swarm.," If $i_{\rm CoM} \gg \langle +i \rangle_{KB}$, the binary spends most of its orbit outside of the perturbing swarm." + The frequency of perturbations to such a binary is reduced by the fraction of the time he binary leaves the disk. proportional to C2yp//coi.," The frequency of perturbations to such a binary is reduced by the fraction of the time the binary leaves the disk, proportional to $\langle i \rangle_{KB}/i_{\rm CoM}$." + The eccentricity of the binary in the disk reduces the effective density of perturbers in a similarmanucr if the epievecle of thebinary carries it outside of the region populatedby erturbers., The eccentricity of the binary in the disk reduces the effective density of perturbers in a similarmanner if the epicycle of thebinary carries it outside of the region populatedby perturbers. + If the heliocentric ecceutricitv or inclination of the binary is much ereater than the typical values for the Ixuiper olt. the relative velocity between the binary and a perturber is primarily dueto the non-circular helioceuntric motion," If the heliocentric eccentricity or inclination of the binary is much greater than the typical values for the Kuiper belt, the relative velocity between the binary and a perturber is primarily dueto the non-circular heliocentric motion" +noiseless spectra were computed with the Objectator’.,noiseless spectra were computed with the Object. + The G passband described in ? from the unfiltered light in the Astrometric Field (AF) measurements has not undergone any conceptual change., The $G$ passband described in \cite{2006MNRAS.367..290J} from the unfiltered light in the Astrometric Field (AF) measurements has not undergone any conceptual change. +" Since 2006, nearly all CCD devices have been built and some mirrors have already been coated, thus the measurements of the transmission curves provide updated values for the G passband."," Since 2006, nearly all CCD devices have been built and some mirrors have already been coated, thus the measurements of the transmission curves provide updated values for the $G$ passband." +" Sixty-two charge-coupled devices (CCDs) are used in AF, while BP and RP spectra are recorded in strips of 7 CCDs each."," Sixty-two charge-coupled devices (CCDs) are used in AF, while BP and RP spectra are recorded in strips of 7 CCDs each." + Twelve CCDs are used in the RVS instrument., Twelve CCDs are used in the RVS instrument. + Every CCD will have its own QE curve and there will be pixel-to- sensitivity variations., Every CCD will have its own QE curve and there will be pixel-to-pixel sensitivity variations. +" In addition, the reflectivity of the mirrors and prisms will change through their surfaces."," In addition, the reflectivity of the mirrors and prisms will change through their surfaces." +" will observe each object several times in each of the two fields of view at different positions in the focal plane (in different CCD), and each observation will have its own characteristics (dispersion, PSF, geometry, overall transmission, etc)."," will observe each object several times in each of the two fields of view at different positions in the focal plane (in different CCD), and each observation will have its own characteristics (dispersion, PSF, geometry, overall transmission, etc)." + The comparison of several observations of a large set of reference sources will allow an internal calibration that will smooth out the differences and will refer all the observations onto a mean instrument., The comparison of several observations of a large set of reference sources will allow an internal calibration that will smooth out the differences and will refer all the observations onto a mean instrument. + This internal calibration will yield epoch and combined spectra and integrated photometry for all sources with the mean instrument configuration., This internal calibration will yield epoch and combined spectra and integrated photometry for all sources with the mean instrument configuration. + The transmission of the optics and the QEs used in this paper have to be understood as corresponding to this averaged instrument., The transmission of the optics and the QEs used in this paper have to be understood as corresponding to this averaged instrument. + The passbands are derived by the convolution of the response curves of the optics and the QE curves of the CCDs and are shown in Fig. 3.., The passbands are derived by the convolution of the response curves of the optics and the QE curves of the CCDs and are shown in Fig. \ref{fig:Gaia_trans}. +" The mirrors are coated with Ag and are the same for all instruments, while the coatings of the prisms act as low-pass and high-pass bands for BP/RP."," The mirrors are coated with Ag and are the same for all instruments, while the coatings of the prisms act as low-pass and high-pass bands for BP/RP." +" Three different QE curves are in place: one ’yellow’ CCD for the astrometric field, an enhanced ""blue' sensitive CCD for the BP spectrometer and a ’red’ sensitive CCD for the RP and RVS spectrometers."," Three different QE curves are in place: one 'yellow' CCD for the astrometric field, an enhanced 'blue' sensitive CCD for the BP spectrometer and a 'red' sensitive CCD for the RP and RVS spectrometers." + We have used the most up-to-date information from partners to compute the passbands., We have used the most up-to-date information from partners to compute the passbands. +" Some of the data, however, are still (sometimes ad-hoc) model predictions and not yet real measurements of flight hardware."," Some of the data, however, are still (sometimes ad-hoc) model predictions and not yet real measurements of flight hardware." + The zero magnitudes have been fixed through the precise energy-flux measurement of Vega., The zero magnitudes have been fixed through the precise energy-flux measurement of Vega. +" ? gives a monochromatic measured flux of 3.46-1077! W m""? nm! at 555.6 nm, equivalent to 3.56-107! W m? nm! at 550 nm, being V=0.03 the apparent visual magnitude ofVega?."," \cite{1995A&A...296..771M} gives a monochromatic measured flux of $3.46\cdot 10^{-11}$ W $^{-2}$ $^{-1}$ at 555.6 nm, equivalent to $3.56 \cdot 10^{-11}$ W $^{-2}$ $^{-1}$ at 550 nm, being $V=0.03$ the apparent visual magnitude of." +". Thus, for a star with mssonm=0.0 we will measure a flux of 3.66-107! W m? nm'!."," Thus, for a star with $m_{\rm 550nm}= 0.0$ we will measure a flux of $3.66\cdot 10^{-11}$ W $^{-2}$ $^{-1}$." +" Vega's spectral energy distribution has been modelled according to ?,, who parameterizes it using Kurucz ATLASO models with Τε=9550 K, logg=3.95 dex, [Fe/H]=—0.5 dex and ἕ,=2 km s."," Vega's spectral energy distribution has been modelled according to \cite{Bessel98}, who parameterizes it using Kurucz ATLAS9 models with $T_{\rm eff}=9550$ K, $g=3.95$ dex, $[Fe/H]=-0.5$ dex and $\xi_{t}= +2$ km $^{-1}$." +" The integrated synthetic flux for a Vega-like star has been computed for the G,Ggp,Grp, and Ggys passbands."," The integrated synthetic flux for a Vega-like star has been computed for the $G$, and $G_{\rm RVS}$ passbands." + A magnitude equal to 0.03 has been assumed for each synthetic flux., A magnitude equal to 0.03 has been assumed for each synthetic flux. +" In that way, G= = = = V = 0.03 mag for a Vega-like star."," In that way, $G =$ $=$ $=$ = V = 0.03 mag for a Vega-like star." +" The derivation of the magnitudes in G,Gpp, and iis given as follows: where Gy stands for G,Gpp, and Ggvs."," The derivation of the magnitudes in $G$, and is given as follows: where $G_{X}$ stands for $G$, and $G_{\rm RVS}$." + F(A) is the flux of the source and F'**(4) is the flux of Vega (AOV spectral type) used as the zero point., $F(\lambda)$ is the flux of the source and $F^{vega}(\lambda)$ is the flux of Vega (A0V spectral type) used as the zero point. + Both thesefluxes are inenergy per wavelength and above the Earth's atmosphere., Both thesefluxes are inenergy per wavelength and above the Earth's atmosphere. + Gyis the apparent magnitude of Vega in the Gy passband., $ G^{Vega}_{X}$is the apparent magnitude of Vega in the $G_{X}$ passband. +" A, is the extinction.", $A_{\lambda}$ is the extinction. +" T(A) denotes the telescope transmission, Px(A) is the prism transmission (Px(A)=1 is assumed for the G passband) and finally, Qx(A)isthe detector response (CCD quantum efficiency)."," $T(\lambda)$ denotes the telescope transmission, $P_{X}(\lambda)$ is the prism transmission $P_{X}(\lambda)=1$ is assumed for the $G$ passband) and finally, $Q_{X}(\lambda)$isthe detector response (CCD quantum efficiency)." +" Therefore, the G, (πρ, and Grys passbands are defined by Sx(4)= T(A)Px(A)AQx(A)."," Therefore, the $G$ , , and $G_{\rm RVS}$ passbands are defined by $S_{X}(\lambda)=T(\lambda) P_{X}(\lambda) \lambda Q_{X}(\lambda)$ ." +"sum of (wo general Sérvsic profiles: the best fit for this model is an inner component with half-light radius 2, = aand Sénsic index η = 0.82 (approximately exponential) and a very sharp. nearly box-car outer component with AR, = and » = 0.12.","sum of two general Sérrsic profiles; the best fit for this model is an inner component with half-light radius $R_s$ = and Sérrsic index $n$ = 0.82 (approximately exponential) and a very sharp, nearly box-car outer component with $R_s$ = and $n$ = 0.12." +" The residuals have a spiral arm appearance in g'""- band: these features are not detected in residual fits in the R-band image. suggestive of blue color and likely some star formation."," The residuals have a spiral arm appearance in $g'$ -band; these features are not detected in residual fits in the R-band image, suggestive of blue color and likely some star formation." + The degree of concentration (low » of both fits) is surprising given (he red color and small amount of star formation in this galaxy., The degree of concentration (low $n$ of both fits) is surprising given the red color and small amount of star formation in this galaxy. + However. we note that (1) this may be {ο some degree an overestimate of (he concentration. which has been shown to be seeing-«dependent. and (2) while commonly. associated in older literature only with slow-decaving profiles such as de Vaucouleurs (η = 4). large surveys have shown that old. του. galaxies exhibit a wide range of profile indices [rom < 1 up to 5 2003).. ancl concentrated profiles are not necessarily surprising.," However, we note that (1) this may be to some degree an overestimate of the concentration, which has been shown \citep{bhb+03} to be seeing-dependent, and (2) while commonly associated in older literature only with slow-decaying profiles such as de Vaucouleurs $n$ = 4), large surveys have shown that old, red galaxies exhibit a wide range of profile indices from $<$ 1 up to 5 \citep{bhb+03}, and concentrated profiles are not necessarily surprising." + On 2006 May 31UTC. we obtained spectra of C using a sslit al an angle of 15.7 East of North to also include the nearby faint galaxy GI in the slit.," On 2006 May 31, we obtained spectra of $G^*$ using a slit at an angle of 15.7 East of North to also include the nearby faint galaxy `G1' in the slit." + several spectrophotometric standard stars were observed throughout the night at different airmasses., Several spectrophotometric standard stars were observed throughout the night at different airmasses. + Spectra of G* were obtained at à median airmass of 1.37., Spectra of $G^*$ were obtained at a median airmass of 1.37. + At this angle and with (his airmass. the differential slit losses are expected to be considerable. so we correct our resultant spectra using the broadband photometry as described above.," At this angle and with this airmass, the differential slit losses are expected to be considerable, so we correct our resultant spectra using the broadband photometry as described above." + The spectrum of G* (Figure 2)) exhibits prominent absorption features due to the IL I-4-IN doubletand the hydrogen Balmer series. as well as a weak emission line due to HI] al 2=0.287.," The spectrum of $G^*$ (Figure \ref{fig:keckobs}) ) exhibits prominent absorption features due to the II H+K doubletand the hydrogen Balmer series, as well as a weak emission line due to II] at $z=0.287$." + These spectral signatures suggest (hat galaxy G7 is a post-starburst svstem with a small amount of on-going star formation., These spectral signatures suggest that galaxy $G^*$ is a post-starburst system with a small amount of on-going star formation. + To determine the on-going star formation rate. we measure an equivalent width of WsH=41207A [ον the [OTI] line.," To determine the on-going star formation rate, we measure an equivalent width of $W_{\rm obs}= 4.1\pm 0.7$ for the II] line." + Given a significant differential slit loss. we scale the spectral continuum io match the observed broad-band flux in the g band. οί)=20.12€0.03 (corrected lor Galactic extinction). and estimate a total line flux of ΟΠ)=(2.3404)x10.I ere tem 7," Given a significant differential slit loss, we scale the spectral continuum to match the observed broad-band flux in the $g'$ band, $AB(g')=20.12 \pm 0.03$ (corrected for Galactic extinction), and estimate a total line flux of $f({\rm [O\,II]})=(2.3 \pm 0.4)\times +10^{-16}$ erg $^{-1}$ $^{-2}$." + At 2=0.287. the observed. line flux corresponds to a total huninosity of LOU)=(6.1£0.9)x10 ere I.," At $z=0.287$, the observed line flux corresponds to a total luminosity of $L({\rm [O\,II]})=(6.1\pm +0.9)\times 10^{40}$ erg $^{-1}$ ." + This indicates an on-going star formation rate of ~0.8 M. Jl following the empirical relation of IXennicut.(1998)... or 0.4 M. |. following Ixewlevοἱal.(2004) with noextinction correction for the observed L([O IH).," This indicates an on-going star formation rate of $\sim 0.8$ $_\odot$ $^{-1}$ , following the empirical relation of \citet{ken98}, or 0.4 $_\odot$ $^{-1}$, following \citet{kgj04} with noextinction correction for the observed $L({\rm [O\,II]})$ ." +(if coufirmed im three-dimensional simulations) would have to be cetermined by detailed umuuerical sinmlatious.,(if confirmed in three-dimensional simulations) would have to be determined by detailed numerical simulations. + We defer this study to fuure work., We defer this study to future work. +" We have shown that :vevery low level of turbuleut perturbations. 50—15λαός to the ICM cutirely consistent with the expectations for cosmological iutall. ealaxy motions. niergers, ¢x AGN activity can eutirelv alter the imaeuetic fick distribution resulting from he TIBI instability."," We have shown that a very low level of turbulent perturbations, $\sim 50-150 \, {\rm km/s}$ to the ICM — entirely consistent with the expectations for cosmological infall, galaxy motions, mergers, or AGN activity — can entirely alter the magnetic field distribution resulting from the HBI instability." + Tastead of prefercutially tangential naenetic fields. the fineUo field configuration can be casily raucdomizec.," Instead of preferentially tangential magnetic fields, the final field configuration can be easily randomized." + As exected. from simple theoretical considerations. this happens when the typical Froude 1ber (equation 11)) ΕΙΡ>OL).," As expected from simple theoretical considerations, this happens when the typical Froude number (equation \ref{eq:Fr_MHD}) ) $Fr^{\rm MHD} \gsim \mathcal{O}(1)$." + Note that weak. ow frequency perturbing: qnotions lead to trapped g- noces and result in prefercutially tangential gas motions. due to strong restoring buovancy forces iu the vertical direction: thus. maeuetic fields could in principle become aueenutial even in the absence of thermal concction and he DBI.," Note that weak, low frequency perturbing motions lead to trapped $g$ -modes and result in preferentially tangential gas motions, due to strong restoring buoyancy forces in the vertical direction; thus, magnetic fields could in principle become tangential even in the absence of thermal conduction and the HBI." + Wowever. this tangential velocity bias is also Met or FrygypZzO(1)," However, this tangential velocity bias is also lifted for $Fr_{\rm MHD} \gsim \mathcal{O}(1)$." + This has several imuuediate COILSCCQUOLICOCS: Qur stirring methods eusure by coustruction that the eusiineg turbulence is volune-filliue., This has several immediate consequences: Our stirring methods ensure by construction that the ensuing turbulence is volume-filling. + However. this is bv πο nieans euarauteed in nature.," However, this is by no means guaranteed in nature." + For stance. galactic wales will be relatively narrow. with a cross-section of order the galaxy size: similarly. rising ACN bubbles will not induce velocity fluctuations over a large solid angle.," For instance, galactic wakes will be relatively narrow, with a cross-section of order the galaxy size; similarly, rising AGN bubbles will not induce velocity fluctuations over a large solid angle." + A straightforward way to eusure volume-filline turbulence. as Is required to stem the OBI. is to excite trapped. g- modes which are repeatedly reflected and focused wihin a yosOlLnmicco reglo rwhere uw«aptD ast jscussed iui refsectiou:turbulence..," A straightforward way to ensure volume-filling turbulence, as is required to stem the HBI, is to excite trapped $g$ -modes which are repeatedly reflected and focused within a resonance region where $\omega < \omega_{\rm BV}^{\rm MHD}$, as discussed in \\ref{section:turbulence}." +" At the same time. uw>,MUD i required to overwhelian buovancy forces. an apparently contradicetorv requirement."," At the same time, $\omega > \omega_{\rm BV}^{\rm MHD}$ is required to overwhelm buoyancy forces, an apparently contradictory requirement." +" Of course. the assuniption of a suele frequency is too simplistic: stining notions cout:ün πας harmonics and will be scale depeuceut. eelcralv increasing iu frequeney as turbulence cascades QWrd smaller scaOs,"," Of course, the assumption of a single frequency is too simplistic: stirring motions contain many harmonics and will be scale dependent, generally increasing in frequency as turbulence cascades toward smaller scales." + Thus. laree scale ganodes coulL fall below the frequency. eusiudus rap]xus and amplification. but the resulting small scale urbulence could potentially still have turnover requencies exceediug Avulp.," Thus, large scale $g$ -modes could fall below the frequency, ensuring trapping and amplification, but the resulting small scale turbulence could potentially still have turnover frequencies exceeding $\omega_{\rm BV}^{\rm MHD}$." + We will examine this in atur‘o work., We will examine this in future work. + Although we have ocused on the IIBI in this paper. he same Froude number considerations apply with equa] force to the MTI unstable outer regions of the cluster. where temperature falls with radius and the AITI causes field lines to become prefercutially radial.," Although we have focused on the HBI in this paper, the same Froude number considerations apply with equal force to the MTI unstable outer regions of the cluster, where temperature falls with radius and the MTI causes field lines to become preferentially radial." + Tere d£ ΒΙΟsOL). turbulent motions can also overwhehnu buovant forces and randomize the field.," Here, if $Fr^{\rm MHD} > \mathcal{O}(1)$, turbulent motions can also overwhelm buoyant forces and randomize the field." + Receuth. there has been tantalizing evidence from the rvolarized Cluission surrounding the magnetic drapes of exdaxies sweeping up magnetic fields in the Vireo clustor. that outside a ceutral region. the maeuetic field wieght be prefereutially oriented racially (7).. as one wieght expect from the MTT.," Recently, there has been tantalizing evidence from the polarized emission surrounding the magnetic drapes of galaxies sweeping up magnetic fields in the Virgo cluster, that outside a central region, the magnetic field might be preferentially oriented radially \citep{pfrommer09}, as one might expect from the MTI." + If this result contiuues o hold up. this worId unuplv the Froude nuuuber is yclow the critical value at these radii (thus providing au iucdirect constraint on turbulent velocities). or additional physical processes. not modeled here. are at play.," If this result continues to hold up, this would imply the Froude number is below the critical value at these radii (thus providing an indirect constraint on turbulent velocities), or additional physical processes, not modeled here, are at play." + The software used in this work was iu part developed, The software used in this work was in part developed +"It is also interesting to note that the high T limits on the LAT bursts are reminiscent of a structured jet model, such as the two-component jet model where there is a narrow bright faster core surrounded by a slow wider jet, with the narrow jet on-axis to the observer (???)..","It is also interesting to note that the high $\Gamma$ limits on the LAT bursts are reminiscent of a structured jet model, such as the two-component jet model where there is a narrow bright faster core surrounded by a slow wider jet, with the narrow jet on-axis to the observer \citep{berger03b,huang04,racusin08}." + ? explore this model using the broadband data on the LAT GRB 090902B and find an acceptable fit., \cite{liu10} explore this model using the broadband data on the LAT GRB 090902B and find an acceptable fit. + Additional study of the other LAT GRBs in the context of this model would be needed to draw any stronger conclusions about the sample as a whole., Additional study of the other LAT GRBs in the context of this model would be needed to draw any stronger conclusions about the sample as a whole. +" As mentioned in Section ??,, the X-ray and UV/optical luminosity distributions of the LAT bursts are narrower than the GBM and BAT samples."," As mentioned in Section \ref{sec:lum}, the X-ray and UV/optical luminosity distributions of the LAT bursts are narrower than the GBM and BAT samples." +" There are several possible causes or related namely, the fact that a larger simplyfraction of the LAT dependencies,bursts are in the synchrotron spectral regime v>νε (83%) compared to the BAT and GBM bursts (50—60%), and that the LAT bursts have a narrow distribution (in log space) of Eso."," There are several possible causes or simply related dependencies, namely, the fact that a larger fraction of the LAT bursts are in the synchrotron spectral regime $\nu>\nu_c$ $83\%$ ) compared to the BAT and GBM bursts $50-60\%$ ), and that the LAT bursts have a narrow distribution (in log space) of $E_{\gamma,iso}$." + The high radiative efficiencies of the LAT bursts may be either another cause of the narrow luminosity distribution or a consequence., The high radiative efficiencies of the LAT bursts may be either another cause of the narrow luminosity distribution or a consequence. +" The region of luminosity parameter space fainter than the LAT bursts could be limited by the lower detection limits of the LAT instrument, and the ability to accurately localize only the brightest of the LAT burst forSwift follow-up."," The region of luminosity parameter space fainter than the LAT bursts could be limited by the lower detection limits of the LAT instrument, and the ability to accurately localize only the brightest of the LAT burst for follow-up." +" Nearly half of the LAT detections had position errors >0.5 degrees radius, which was simply not practical to initiate follow-up observations beginning many hours or days after the triggers."," Nearly half of the LAT detections had position errors $>0.5$ degrees radius, which was simply not practical to initiate follow-up observations beginning many hours or days after the triggers." +" In the future, ifSwift happens to trigger on one of these fainter long burstssimultaneously with a marginal LAT detection and a fainter afterglow, then we will know whether the luminosity clustering is only limited on the bright end."," In the future, if happens to simultaneously trigger on one of these fainter long bursts with a marginal LAT detection and a fainter afterglow, then we will know whether the luminosity clustering is only limited on the bright end." +" In addition to the simple redshift distribution comparison, we explore the luminosity functions of the different populations of GRBs."," In addition to the simple redshift distribution comparison, we explore the luminosity functions of the different populations of GRBs." +" We use the methods of both ? and ?,, which apply different statistical methods to constrain the luminosity function shapes for the three samples."," We use the methods of both \cite{virgili09} and \cite{wanderman10}, which apply different statistical methods to constrain the luminosity function shapes for the three samples." +" Simply due to instrumental selection the BAT, GBM, and LAT samples probe differenteffects, regions of the luminosity function."," Simply due to instrumental selection effects, the BAT, GBM, and LAT samples probe different regions of the luminosity function." +" GRBs bright enough to trigger GBM, will be brighter on average than BAT only bursts, because GBM is less sensitive than BAT."," GRBs bright enough to trigger GBM, will be brighter on average than BAT only bursts, because GBM is less sensitive than BAT." +" The LAT GRBs have the highest fluence of the GBM bursts, and given the similar redshift distributions (Section 3.2)), ?? ? "," The LAT GRBs have the highest fluence of the GBM bursts, and given the similar redshift distributions (Section \ref{sec:redshift}) \cite{virgili09,virgili11} \cite{wanderman10} " +D. Ricci. P. Gionnui oeidicates that the particle backeround doces not vary in time by more than 30% of the total backerouud.,"D. Ricci, P. Giommi indicates that the particle background does not vary in time by more than 30 of the total background." + The remaining background is the cosmic N-rav. background., The remaining background is the cosmic X-ray background. + Since the LECS oulv operates during satellite night time. iu coutrbution to the background from scattered solar N-ravs is negligible (Parmaretal.19995).," Since the LECS only operates during satellite night time, any contribution to the background from scattered solar X-rays is negligible \citep{parmar99b}." + However. DD scaled the remaining non-particle vackeround for 22199 aud 11795 bv a factor of Ll and 3.9. respectively. and justified the nagnitude of the scaling factor bv time-variable scattered solar N-ravs.," However, BB scaled the remaining non-particle background for 2199 and 1795 by a factor of 4.4 and 3.9, respectively, and justified the magnitude of the scaling factor by time-variable scattered solar X-rays." + This is grossly iuconsisteut with the negligible level of solar X-ray photous ueutioned above., This is grossly inconsistent with the negligible level of solar X-ray photons mentioned above. + Moreover. BB did no at all explain quantitatively how they arrived at this scaling factor.," Moreover, BB did not at all explain quantitatively how they arrived at this scaling factor." + Scaling is complicated. ECATINC he cluster fills the cutive field of view. aud thus he observed radial ταν intensity distribution is a combination of cluster X-rays and cosmic vackeround N-ravs.," Scaling is complicated, because the cluster fills the entire field of view, and thus the observed radial X-ray intensity distribution is a combination of cluster X-rays and cosmic background X-rays." + The cluster profile is uukuown a priori (containime potentially both thermal aud excess X-ray photons)., The cluster profile is unknown a priori (containing potentially both thermal and excess X-ray photons). + We must therefore assume hat their undertaking was entirely ad hoc., We must therefore assume that their undertaking was entirely ad hoc. + BB questioned the reliability of the low-energy calibration of the LECS., BB questioned the reliability of the low-energy calibration of the LECS. + The low-cnerey response used by us is based on ray trace simulations., The low-energy response used by us is based on ray trace simulations. + This is what is available to the general observer., This is what is available to the general observer. + DD quote Parmaretal.(1997) reearding a discrepancy by a factor of 1.5 at low energies (0.18 and 0.28 keV) vetween rav trace suaulations andl eround ieasurements., BB quote \citet{parmar97} regarding a discrepancy by a factor of 1.5 at low energies (0.18 and 0.28 keV) between ray trace simulations and ground measurements. + Wowever. Parinar ct al," However, Parmar et al." + suggested that the discrepancy may be caused by the scattered X-ray photons during the eround calibration mcasurements. and tha there is vet no convincing explanation. aud tha in-flight measurements are needed to resolve this.," suggested that the discrepancy may be caused by the scattered X-ray photons during the ground calibration measurements, and that there is yet no convincing explanation, and that in-flight measurements are needed to resolve this." + Since neither did BB offer an miproved in-Hieh calibration or rav-trace model. they esseutiallvy use he same calibration data as we did and therefore if our analysis would coutain flaws as a result of his effect. so the same will be true of theirs.," Since neither did BB offer an improved in-flight calibration or ray-trace model, they essentially use the same calibration data as we did and therefore if our analysis would contain flaws as a result of this effect, so the same will be true of theirs." + BB attempt to avoid potential calibration wroblems (without solving them) by switching to a radial profile analysis., BB attempt to avoid potential calibration problems (without solving them) by switching to a radial profile analysis. + First they noted that at low energies. the PFWIIM of the iustrumient is arge. in particular in the 0.10.3 keV baud.," First they noted that at low energies, the FWHM of the instrument is large, in particular in the 0.1–0.3 keV band." + Such a non-uniforni resolution is undesirable if radial oofiles iu different euergv bands are compared., Such a non-uniform resolution is undesirable if radial profiles in different energy bands are compared. + Therefore. they convolved the radial profile iu the Hel euergv and (0.52.2 keV) with a Caussian of FEWIIM.," Therefore, they convolved the radial profile in the high energy band (0.5–2.2 keV) with a Gaussian of FWHM." + Using a spectral model for the cluster. hey then compared this scaled. convolved 0.52.2 keV) profile with the observed. uuconvolved L10.3 keV. band.," Using a spectral model for the cluster, they then compared this scaled, convolved 0.5--2.2 keV profile with the observed, unconvolved 0.1–0.3 keV band." +" The comparison shows uo soft excess, even a small soft X-ray deficit in the ceuter. aud this leads BB to the conclusion that our analysis is wroug."," The comparison shows no soft excess, even a small soft X-ray deficit in the center, and this leads BB to the conclusion that our analysis is wrong." + There are several reasons why this simplified approach by BB is unacceptable., There are several reasons why this simplified approach by BB is unacceptable. + Specifically: l., Specifically: 1. + Couvolving he 0.52.2 keV nuage with a Gaussian does not render it compatible with the resolution of the 0.10.3 keV nuage., Convolving the 0.5–2.2 keV image with a Gaussian does not render it compatible with the resolution of the 0.1–0.3 keV image. + This is mainly due to the strong. non-Gaussian tails of the iustruieutal PSF. as we show in the next section.," This is mainly due to the strong, non-Gaussian tails of the instrumental PSF, as we show in the next section." + 2., 2. + Degradation of the nuages by smoothiug cdestrovs esseutial information., Degradation of the images by smoothing destroys essential information. + 3., 3. + The radial profile in the 0.10.3 keV band is also significautlv afecte by the low energve response of higher euergv photons (32 FWIIME at 0.28 keV)., The radial profile in the 0.1–0.3 keV band is also significantly affected by the low energy response of higher energy photons (32 FWHM at 0.28 keV). + Thus. the radial profile in this band is sensitive to spectral variations as a fiction of radius.," Thus, the radial profile in this band is sensitive to spectral variations as a function of radius." + l1., 4. + The effective vignetting corrections to be mace are dependent on both energy aud position. and these have heen appareutlv ucelected by BB.," The effective vignetting corrections to be made are dependent on both energy and position, and these have been apparently neglected by BB." + 5., 5. + The 0.52.2 keV band contains he Fe-L coniplex which can be quite stroug im moderately cool clusters such as 22199., The 0.5–2.2 keV band contains the Fe-L complex which can be quite strong in moderately cool clusters such as 2199. + In particular. the strength of this complex. depends on th. the amount of ceutral cool gas as well as uietallicity.," In particular, the strength of this complex depends on both the amount of central cool gas as well as metallicity." + Since both componcuts vary strongly with position. this biases the 0.52.2 keV flux.," Since both components vary strongly with position, this biases the 0.5–2.2 keV flux." + Iu particular. item 1 is very important for the analysis of the soft N-ray excess. as we show below.," In particular, item 1 is very important for the analysis of the soft X-ray excess, as we show below." + Iu order to understand what really happeus in the analysis of DD. we present here some siauulated radial profiles.," In order to understand what really happens in the analysis of BB, we present here some simulated radial profiles." + First. we generated a cluster cluission profile. for which we have closen," First, we generated a cluster emission profile, for which we have chosen" +polarisation may then remain very low or could. actually rise again. but this time with a position angle orthogonal to the initial direction.,"polarisation may then remain very low or could actually rise again, but this time with a position angle orthogonal to the initial direction." + Thus. the overall behaviour could be complex with an initial anti-correlation between Iux ancl polarisation followed by a period where they are correlated after a position angle swing of 90," Thus, the overall behaviour could be complex with an initial anti-correlation between flux and polarisation followed by a period where they are correlated after a position angle swing of $90\degr$." + One of the best studied objects in our sample is 3€2mJ and Stevens (1997). combine some of our results with centimetre monitoring and VLBI to make a detailed comparison with the predictions of the shock model of Alarscher Gear (1985)., One of the best studied objects in our sample is 3C273 and Stevens (1997) combine some of our results with centimetre monitoring and VLBI to make a detailed comparison with the predictions of the shock model of Marscher Gear (1985). + The most significant observation about 3€273 is that in late 1995 the [lux ancl polarisation both increased as the source [lared. however the initially parallel magnetic field parallel.," The most significant observation about 3C273 is that in late 1995 the flux and polarisation both increased as the source flared, however the initially parallel magnetic field parallel." + Examination of the spectral index shows this cannot be due to an optical depth ellect., Examination of the spectral index shows this cannot be due to an optical depth effect. + This behaviour is not therefore consistent with the plane shock mocdel predictions unless the source fortuitously undergoes a very large bend between the scales observed. by centimetre VLBI and that of the millimetre/submillimetre emission., This behaviour is not therefore consistent with the plane shock model predictions unless the source fortuitously undergoes a very large bend between the scales observed by centimetre VLBI and that of the millimetre/submillimetre emission. + Lind Blanelforc (1985) suggested that oblique and conical shocks could easilv Form in relativistic jets and showed that these geometries could have a dramatic clleet on predicted number counts., Lind Blandford (1985) suggested that oblique and conical shocks could easily form in relativistic jets and showed that these geometries could have a dramatic effect on predicted number counts. + These authors made little attempt to predict the direct. elect of such. shock structures on observations of individual objects., These authors made little attempt to predict the direct effect of such shock structures on observations of individual objects. + Cawthorne Cobb (1990) however. in a prescient but. largelv-ignored. paper. calculated the predicted: cllects of oblique and conical shock geometries on VLBI imagingoὃν and total polarised lux measurements of compact jet sources.," Cawthorne Cobb (1990) however, in a prescient but largely-ignored paper, calculated the predicted effects of oblique and conical shock geometries on VLBI imaging and total polarised flux measurements of compact jet sources." + Thev show that although in gencral such structures will produce significant. polarisation with position angle parellel to the jet. (i.e. an enhancement of the perpendicular component of the magnetic field) they can also give rise to the opposite orientation for certain cone opening ancl viewing angles., They show that although in general such structures will produce significant polarisation with position angle parellel to the jet (i.e. an enhancement of the perpendicular component of the magnetic field) they can also give rise to the opposite orientation for certain cone opening and viewing angles. + A clear prediction of the model is that when this happens the polarisation will below (« 10%)., A clear prediction of the model is that when this happens the polarisation will below $< 10\%$ ). + We believe that this twpe of shock geometry is entirely consistent with the behaviour we observe in many. sources: generally low polarisation. often parallel inferred magnetic ielel and. furthermore. rapid apparent changes between orthogonal magnetic field. configurations which can be correlated. or anti-correlated. with increasing Lux and/or xolarisation level.," We believe that this type of shock geometry is entirely consistent with the behaviour we observe in many sources: generally low polarisation, often parallel inferred magnetic field and, furthermore, rapid apparent changes between orthogonal magnetic field configurations which can be correlated or anti-correlated with increasing flux and/or polarisation level." + Examination of Figures 2 and 32 of Cawthorne Cobb shows that small changes in either cone opening angle. or angle of the jet axis to our line-of-sight. can »oduce a large swing in apparent magnetic field orientation.," Examination of Figures 2 and 3 of Cawthorne Cobb shows that small changes in either cone opening angle, or angle of the jet axis to our line-of-sight, can produce a large swing in apparent magnetic field orientation." + For example. in the case of BL Lacertae 2 and £F are anti- while the position angle. changes only slightly about the jet’s direction.," For example, in the case of BL Lacertae $P$ and $F$ are anti-correlated while the position angle changes only slightly about the jet's direction." + OJ287 (another BL Lac object) exhibits the greatest. variability in Εαν ancl polarisation in the whole sample., OJ287 (another BL Lac object) exhibits the greatest variability in flux and polarisation in the whole sample. + When the polarisation is high its position angle remains fairly unchanged at ~45 to the jet. despite large changes in lux.," When the polarisation is high its position angle remains fairly unchanged at $\sim 45\degr$ to the jet, despite large changes in flux." + However. on three other occasions it Ilips from being parallel to perpendicular to the jet.," However, on three other occasions it flips from being parallel to perpendicular to the jet." + Phere are still sources in which it may be necessary to invoke bending of the jet., There are still sources in which it may be necessary to invoke bending of the jet. + “Phe best example is 3€345. whose jet is known to be very curved even in the highest-Lrequcncy VLBI maps.," The best example is 3C345, whose jet is known to be very curved even in the highest-frequency VLBI maps." + Our data covers the ocurrence of an outburst and its subsequent gradual decline to the pre-Hare level., Our data covers the ocurrence of an outburst and its subsequent gradual decline to the pre-flare level. + The degree of polarisation ancl position angle. however. show a ot more variability (see Figure 3).," The degree of polarisation and position angle, however, show a lot more variability (see Figure 3)." + This. together with the act that the polarisation and the total intensity appear to be arecly anti-correlated (see Figure 5). is consistent with a jet xung viewed at an initially small angle. which curves away rom the line of sight as the shock evolves.," This, together with the fact that the polarisation and the total intensity appear to be largely anti-correlated (see Figure 5), is consistent with a jet being viewed at an initially small angle, which curves away from the line of sight as the shock evolves." + “This scenario is supported: by the prediction of Gopal-Ixrishna Wiita (1992) that the percentage polarisation and total intensity are anti-correlated as the viewing angle increases within the range determined by the critical value @=sinτι]. where E is the Lorentz factor.," This scenario is supported by the prediction of Gopal-Krishna Wiita (1992) that the percentage polarisation and total intensity are anti-correlated as the viewing angle increases within the range determined by the critical value $\theta_{c} = sin^{-1}(1/\Gamma)$, where $\Gamma$ is the Lorentz factor." + In fact. the jet of 3€345 has been estimated to lie within 2° from our line of sight by Wardle (1994) and as close as ~1 by Leppànnen (1995) (using the same analysis on à more recent. VLBI map).," In fact, the jet of 3C345 has been estimated to lie within $2\degr$ from our line of sight by Wardle (1994) and as close as $\sim1\degr$ by Leppännen (1995) (using the same analysis on a more recent VLBI map)." + The relatively low levels of polarisation measured by us on this source (<4% on average) are also consistent with a small viewing angle., The relatively low levels of polarisation measured by us on this source $< 4\%$ on average) are also consistent with a small viewing angle. + ]t is just. possible that a conspiracy of bending on small scales might also reproduce the elfects attributed to conical shocks in the previous section for OJ2NT. for example.," It is just possible that a conspiracy of bending on small scales might also reproduce the effects attributed to conical shocks in the previous section for OJ287, for example." + This might then explain the earlier tentative result that Z2 and £ tend to be correlated in most quasars and anti-correlated in the BL Lacs as being due to the two groups tending to be viewed either side of the critical viewing angle 6., This might then explain the earlier tentative result that $P$ and $F$ tend to be correlated in most quasars and anti-correlated in the BL Lacs as being due to the two groups tending to be viewed either side of the critical viewing angle $\theta_{c}$. + However. it is hard to explain the large degree of Lux variability with small or no change in position angle. also commonly. seen. in terms of bending.," However, it is hard to explain the large degree of flux variability with small or no change in position angle, also commonly seen, in terms of bending." + We suspect it is far more likely that whilst one or two sources do exhibit significant bending. in most. cases the jet merely “wiggles” a little about the axis. producing a mocdulation of the viewing angle of conical shock structures. whose opening angle also presumably evolves as it. travels down an expanding jet.," We suspect it is far more likely that whilst one or two sources do exhibit significant bending, in most cases the jet merely `wiggles' a little about the axis, producing a modulation of the viewing angle of conical shock structures, whose opening angle also presumably evolves as it travels down an expanding jet." + More. theoretical work on the expected: evolution of conical shock structures is probably required to make further more detailed comparisons of our results with the ideas of Cawthorne Cobb., More theoretical work on the expected evolution of conical shock structures is probably required to make further more detailed comparisons of our results with the ideas of Cawthorne Cobb. + Stevens (1997) have reached a very similar conclusion for the specific example of 3€273., Stevens (1997) have reached a very similar conclusion for the specific example of 3C273. +"As it is clear in Figure 1O the different estimates of the space density of Compton Thick AGN. derived using different seletion criteria (and methods). are in. remarkably good agreement with the suggested XLF of Compton Thick AGN (y,=1.55. y;=2.61. Log L,=44. Log Apa = with a possible hint of a XLF flattening below few times 10% (where. we point out. the XLF of absorbed AGN in the HBSS is not well defined since we have no objects in the sample).","As it is clear in Figure \ref{XLF_3} the different estimates of the space density of Compton Thick AGN, derived using different seletion criteria (and methods), are in remarkably good agreement with the suggested XLF of Compton Thick AGN $\gamma_1=1.55$, $\gamma_2=2.61$, Log $L_{\star} = 44$, Log $_{Thick}$ = -6.32) with a possible hint of a XLF flattening below few times $10^{42}$ (where, we point out, the XLF of absorbed AGN in the HBSS is not well defined since we have no objects in the sample)." + The good agreement seem to suggest that. at the sampled X-ray luminosities. the space density of optically Compton Thick AGN (e.g. objects like Arp 299. see DellaCecaetal. 2002)) is. at most. similar to that of optically selected Compton Thick AGN since the former population should be clearly missing in the optically selected sample of active galaxies defined in Simpson(2005) but should be present in the infrared or X-ray selected samples.," The good agreement seem to suggest that, at the sampled X-ray luminosities, the space density of optically Compton Thick AGN (e.g. objects like Arp 299, see \citealt{dellaceca2002}) ) is, at most, similar to that of optically selected Compton Thick AGN since the former population should be clearly missing in the optically selected sample of active galaxies defined in \cite{simpson2005} but should be present in the infrared or X-ray selected samples." + This fact is also supported by the consideration that the total number of Compton Thick AGN cannot be increased arbitrarely but we have to take into account the limits imposed by the local black mass density derived by Marconietal.(2004) from dynamical studies of local galaxy bulges ρω=4.01$155x10° Mo Mpc? for Hp=65).," This fact is also supported by the consideration that the total number of Compton Thick AGN cannot be increased arbitrarely but we have to take into account the limits imposed by the local black mass density derived by \cite{marconi2004} from dynamical studies of local galaxy bulges $\rho_{BH} = +4.0^{1.6}_{1.2} h^2_{65} \times 10^{5}$ $_{\sun}$ $^{-3}$ for $_0$ =65)." +" Using the formalism described in LaFrancaal.(2005) (see their equations 15. 16 and 17). assuming a radiative efficiency ~0.1. a bolometric conversion factor equal to 25 (Pozzietal. 2007)) and integrating the XLFs of AGN (unabsorbed. absorbed and Compton Thick) from z=4.5 to z=0 and from Ly ~3κ10 to ~107.. the limit of psy.=5.6h2,κ10° Me Mpe™ is violated if the XLF of Compton Thick AGN is more the ~ 4 times that of absorbed AGN. e.g. the upper envelope reported in Figure 10: we stress tha this is probably an upper envelope since we have not considered in the computation of the local black mass density the objects with luminosity below ~3x10%.."," Using the formalism described in \cite{lafranca2005} (see their equations 15, 16 and 17), assuming a radiative efficiency $\sim 0.1$, a bolometric conversion factor equal to 25 \citealt{pozzi2007}) ) and integrating the XLFs of AGN (unabsorbed, absorbed and Compton Thick) from z=4.5 to z=0 and from $L_X$ $\sim 3\times 10^{42}$ to $\sim 10^{49}$, the limit of $\rho_{BH} = +5.6 h^2_{65} \times 10^{5}$ $_{\sun}$ $^{-3}$ is violated if the XLF of Compton Thick AGN is more the $\sim$ 4 times that of absorbed AGN, e.g. the upper envelope reported in Figure 10; we stress tha this is probably an upper envelope since we have not considered in the computation of the local black mass density the objects with luminosity below $\sim 3\times 10^{42}$." +" Finally the comparison of ΤΕ, and F reported in Figure can be used to evaluated the ratio. Q. between Compton Thick and Compton Thin (Ny«107 em) AGN."," Finally the comparison of $_{optical}$ and F reported in Figure \ref{ratio6} can be used to evaluated the ratio, Q, between Compton Thick and Compton Thin $N_H < 10^{24}$ $^{-2}$ ) AGN." +" Assuming. as above. that the number of Compton Thick AGN is proportional to the number of AGN with Nj, in the range [4x107:«.1074 em: |. thus We derive that the density ratio between Compton Thick AGN and Compton Thin AGN decreases from Q=1.08+0.44 at -I0? to Q=0.57€022 at ~10"". to Q-2033z0.15 at -10? s."," Assuming, as above, that the number of Compton Thick AGN is proportional to the number of AGN with $N_H$ in the range $4\times 10^{21}; \sim 10^{24}$ $^{-2}$ ], thus We derive that the density ratio between Compton Thick AGN and Compton Thin AGN decreases from $Q=1.08\pm 0.44$ at $\sim 10^{43}$ to $Q=0.57\pm 0.22$ at $\sim 10^{44}$ to $Q=0.23\pm 0.15$ at $\sim 10^{45}$ ." + We have discussed here the cosmological properties of the 62 AGN belonging to the XMM-Hard Bright Serendipitous Survey. a complete and representative sample of bright (fy>7x1077 erg em? s!) serendipitous XMM-Newton sources selected in the 4.5—7.5 keV energy band on a sky area of ~25 deg-.," We have discussed here the cosmological properties of the 62 AGN belonging to the XMM-Hard Bright Serendipitous Survey, a complete and representative sample of bright $f_X \gtrsim 7\times 10^{-14}$ erg $^{-2}$ $^{-1}$ ) serendipitous XMM-Newton sources selected in the $4.5-7.5$ keV energy band on a sky area of $\sim 25$ $^{-2}$." + Since the HBSS sample is almost completely spectroscopically identified (ID rate ~ 97%)) 1t allows us to have an unprecedented and unbiased view of the extragalactic 4.5—7.5 keV sky in the bright flux regime., Since the HBSS sample is almost completely spectroscopically identified (ID rate $\sim$ ) it allows us to have an unprecedented and unbiased view of the extragalactic $4.5-7.5$ keV sky in the bright flux regime. + Using an Ny; dividing value of 4x107! em™ (see Section 2.1). the HBSS AGN sample is composed of 40unabsorbed (or marginally absorbed) AGN and 22 absorbed AGN.," Using an $N_H$ dividing value of $4\times 10^{21}$ $^{-2}$ (see Section 2.1), the HBSS AGN sample is composed of 40unabsorbed (or marginally absorbed) AGN and 22 absorbed AGN." + The main results reported and discussed in this paper are:, The main results reported and discussed in this paper are: +16pt PACS uuubers: 98.80.Es. 06.20.Jr. 98.62.Ra. 28.[1.-1. 03.30.p.,"16pt PACS numbers: 98.80.Es, 06.20.Jr, 98.62.Ra, 28.41.-i, 03.30.+p." + Tlje ]sste of a possible variation of fudamental physical coustaus has been put ou the agenda ol οςtemporary physics., The issue of a possible variation of fundamental physical constants has been put on the agenda of contemporary physics. + Recently. Webb groupm reported [1] a varyingabsorptio fiue-struct COLstall a hrough analyzing the multiple heavy elemeut transitions in the 1 speci:ur ol quasi-stelar objects (QSOs) on the Southern Hemisphere. whicl agrees with aud offers vigorTIS slyport to their previous research results [1.2.3.1.5.6.T]. οι the orther Hemisplere: Compared with laboratory data on atomic multiplet) structures. t1e observatio of the absorj(tiou lines of QSOs reveal that the fine-structureL constant a has ai obvio Clallge jute past several billion years.," Recently, Webb group reported \cite{webb06} a varying fine-structure constant $\alpha$ through analyzing the multiple heavy element transitions in the absorption spectra of quasi-stellar objects (QSOs) on the Southern Hemisphere, which agrees with and offers vigorous support to their previous research results \cite{webb06,Murphy03b,Murphy03a,murphy01b,murphy01a,webb01,webb99} + on the Northern Hemisphere: Compared with laboratory data on atomic multiplet structures, the observations of the absorption lines of QSOs reveal that the fine-structure constant $\alpha$ has an obvious change in the past several billion years." + This coufirmation stimulates1 the further stily ont Varlatlou of ine-strueture coustant both from thel theoretical 1interpretation [8.9] to establisl le niolivaticor and to supply more exact moclel aiaysis. aud the experimental measwenielts 10] to viele more precise data and more experimeal uethods.," This confirmation stimulates the further study on the variation of fine-structure constant both from the theoretical interpretation \cite{theo1,theo2} to establish the motivation and to supply more exact model analysis, and the experimental measurements \cite{experiment} to yield more precise data and more experimental methods." + Tle possibility of variability [9]of fundaimeutal «κ.)statts was pul [orward by Dirac iu 193M. allerwards. a lot of theoretical illus10 ald experimenta constraints [1:)] OL le Veποιο oL fundaineutal constants are preset," The possibility of variability of fundamental constants was put forward by Dirac \cite{dirac,peng} in 1937, afterwards, a lot of theoretical illustration and experimental constraints \cite{review} on the variation of fundamental constants are presented." + As we know. he constancy of the Adanenta coustants plays a siguificaut role in astronomy aud cosmology wlere the recdshilt Jeastres the look-back time.," As we know, the constancy of the fundamental constants plays a significant role in astronomy and cosmology where the redshift measures the look-back time." + If ignoriug the possibili iat the constants are varviug we wil avec1 cleviaed view of our universe., If ignoring the possibility that the constants are varying we will have a deviated view of our universe. + However. if such variations are esablished. corrections W.ould be a»plied to the 'elated ISSUES.," However, if such variations are established, corrections should be applied to the related issues." + ]t is μιS ecessaly to livesigale hat possibiliN. Tcspecially as tle 1leasurements become mo 'ep'ecise and/or when le lueasureimments are iade on the larger scale.," It is thus necessary to investigate that possibility, especially as the measurements become more precise and/or when the measurements are made on the larger scale." +" Besides. a [n]gene‘al featire of extra-dimensioual theories. such as Ixauza-Ixlein and striig heories. is lia ile “true” Fundamental coistatts of nature are cefiued in the [ull hieer imensional theory. so that the effective |-ίlimensional ""[undainenuta coustauts"" depecl. amoung other ilines.« on the structure and siyes of the extra-dimensions."," Besides, a general feature of extra-dimensional theories, such as Kaluza-Klein and string theories, is that the “true"" fundamental constants of nature are defined in the full higher dimensional theory, so that the effective 4-dimensional “fundamental constants” depend, among other things, on the structure and sizes of the extra-dimensions." +" The time L-cdimeusioiaud/jOr space evolution of hese sizes would have a sienilicautm result that tlie effective al ""[uudameutal cousants will also depei ou spacetime.", The time and/or space evolution of these sizes would have a significant result that the effective 4-dimensional “fundamental constants” will also depend on the spacetime. + What's more. the achievement of," What's more, the achievement of" +for that igh.,for that night. + This calculation assumes that the flat-Biekdiug error is domiuaed by shot noise. the actual error uay be larger if there are other systematic errors in the flat-fiekl.," This calculation assumes that the flat-fielding error is dominated by shot noise, the actual error may be larger if there are other systematic errors in the flat-field." + The effect of this error is reduced when the pointing is stable between images., The effect of this error is reduced when the pointing is stable between images. + We note tha because the PSF is so well-samped on the Megacau CCDs we do not expect iutra-plxe variaious in the quantum efficiency to make a significant coutribution to the error., We note that because the PSF is so well-sampled on the Megacam CCDs we do not expect intra-pixel variations in the quantum efficiency to make a significant contribution to the error. + Atimospleric scintillation also adds au effective constant. error tegae to he photometry., Atmospheric scintillation also adds an effective constant error term to the photometry. + This error can be estimated from Young(1967) as where we use cj; lor the coustant error te1u due to scintillation. d is the telescope cliameter in cua. X is the airmass. / is 1ie observatory altitude iu m. aud fepp Is the exposure time ins. TIe leading coellicieut is rather apxoxinate (we mutioly by 2.5ogyfe) to convert to magnitudes). as scintillatjon ¢an clauge by a &ictor o£ 2 in a few niuutes (e.tent) Young1993)).," This error can be estimated from \citet{young67} as where we use $c_{scint}$ for the constant error term due to scintillation, $d$ is the telescope diameter in cm, $X$ is the airmass, $h$ is the observatory altitude in m, and $t_{exp}$ is the exposure time in s. The leading coefficient is rather approximate (we multiply by $2.5\log_{10}({\rm e})$ to convert to magnitudes), as scintillation can change by a factor of 2 in a few minutes (e.g. \citealt{young93}) )." + For the second. night. ¢ur observatiοis were 60 SeCOids long. with the πμ raleine from 1.12 to 1.37.," For the second night, our observations were 60 seconds long, with the airmass ranging from 1.12 to 1.37." + The MMT iS locaed αἱ an :ittcle of 2606 11. alid has a diamee: of 650 cin.," The MMT is located at an altitude of 2606 m, and has a diameter of 650 cm." +" Therefore we expect a coustaul error term of ess al ivbout 0.15 unmag due to atinosj»heric sciitillation. and thus the total coustant error term slld ye [ess that 0.25 Πες,"," Therefore we expect a constant error term of less than about 0.15 mmag due to atmospheric scintillation, and thus the total constant error term should be less than 0.25 mmag." + Because eobtaius the PSF ouly ouce on the reference. the error in the PSF will οἱ contribt to tle errors in clilfereitial photometry.," Because one obtains the PSF only once on the reference, the error in the PSF will not contribute to the errors in differential photometry." + Instead. errors iu the kernel that is used to couvolve the PS ellectively acd a cousant erro “term to the photometry.," Instead, errors in the kernel that is used to convolve the PSF effectively add a constant error term to the photometry." + It is difficult to estimate a WLOLL exac wha that error shotd be. and. we suspect that tlie consta error terii that we have measur is due to this effect.," It is difficult to estimate a priori exactly what that error should be, and we suspect that the constant error term that we have measured is due to this effect." + Το test tis hypothesis we have also pe‘formed simple unit-weight aper shotometry on the 5btracted üunages. the 'esults lor a single chip on tle third night are show in Fig L..," To test this hypothesis we have also performed simple unit-weight aperture photometry on the subtracted images, the results for a single chip on the third night are shown in Fig \ref{apcompare}." + To correcty scale 1e fluxes we divided by the i1eeral of the PSF over the aper wdius., To correctly scale the fluxes we divided by the integral of the PSF over the aperture radius. + We varied the apertre radius to opinize the precisi rat the brlet eud wile provi correct alnjliπο fo ‘the siLilated variable stars mentiolec i1 tlie previous section., We varied the aperture radius to optimize the precision at the bright end while providing correct amplitudes for the simulated variable stars mentioned in the previous section. + Τιe aper 9iotoimetry Lielit curves were tien pu hrougl the cleaniug 'ocedures described i tlὁ previOUS section to ICvide a fair coiiparison wi hthe opimal PSy igαἱ curves., The aperture photometry light curves were then put through the cleaning procedures described in the previous section to provide a fair comparison with the optimal PSF light curves. + As expected. tuit-weieht aperture pOlnetiry perorLs WOrse lau PSF fitting [ου falULt stars as it ds subject icto a greater degree of s* background. |owever for he brighest stars aJeture photometry outperoris PSF [iling. and :ypears to slow no eviderce of a constant er‘Or term.," As expected, unit-weight aperture photometry performs worse than PSF fitting for faint stars as it is subject to a greater degree of sky background, however for the brightest stars aperture photometry outperforms PSF fitting, and appears to show no evidence of a constant error term." + This effect is well-kiown When uot usiug iuage subtractjon. aid condir115 OU slspicions that the coustant error term :wises from Uicertaiuties in the kernel propagate through PSF fitting.," This effect is well-known when not using image subtraction, and confirms our suspicions that the constant error term arises from uncertainties in the kernel propagated through PSF fitting." + Using aperture photometry on the subtracted images we acljeve a preclsio Las goo as 2360 iu:ig per exposure., Using aperture photometry on the subtracted images we achieve a precision as good as 360 $\mu$ mag per exposure. + As a check on our photometry we compare our light curves [or a few known variables with, As a check on our photometry we compare our light curves for a few known variables with +"Scalar-field-mediated long-range fifth forces have attracted much attention among cosmologists in recent years, and in most versions they come from a direct coupling between the matter species (usually dark matter only) and a cosmological scalar field.","Scalar-field-mediated long-range fifth forces have attracted much attention among cosmologists in recent years, and in most versions they come from a direct coupling between the matter species (usually dark matter only) and a cosmological scalar field." +" If they really exist, they might dramatically change the picture of cosmic structure formation, and alleviate or even solve some problems in the concordance ACDM model."," If they really exist, they might dramatically change the picture of cosmic structure formation, and alleviate or even solve some problems in the concordance $\Lambda$ CDM model." +" On the other hand, the range and magnitude of the fifth force are often model dependent: in one extreme, represented by our N models, the effective potential Ve+s(q) is fairly flat so that the mass mg is light and almost the same everywhere; the fifth force then has a fixed ratio to gravity, which is equivalent to a rescaling of the gravitational constant."," On the other hand, the range and magnitude of the fifth force are often model dependent: in one extreme, represented by our N models, the effective potential $V_{eff}(\varphi)$ is fairly flat so that the mass $m_\varphi$ is light and almost the same everywhere; the fifth force then has a fixed ratio to gravity, which is equivalent to a rescaling of the gravitational constant." +" In the opposite extreme, like our C models, Ves and thus the scalar field mass m, depends sensitively to the matter density in the way that m, could be very heavy in high density regions, where the fifth force is severely suppressed and thus negligible, but is quite light in low density regions, where the fifth force has a fixed ratio to gravity as in the N models."," In the opposite extreme, like our C models, $V_{eff}$ and thus the scalar field mass $m_\varphi$ depends sensitively to the matter density in the way that $m_{\varphi}$ could be very heavy in high density regions, where the fifth force is severely suppressed and thus negligible, but is quite light in low density regions, where the fifth force has a fixed ratio to gravity as in the N models." +" Furthermore, as emphasized by Li&Barrow(2010b),, the fifth force is often not the only impact the coupled scalar field could have on cosmology, nor even is it usually the most important one."," Furthermore, as emphasized by \citet{lb2010b}, the fifth force is often not the only impact the coupled scalar field could have on cosmology, nor even is it usually the most important one." +" In the N models, for example, the modification of the cosmic background expansion rate by the scalar coupling could be more influential in the course of structure formation (Li&Barrow 2010b)."," In the N models, for example, the modification of the cosmic background expansion rate by the scalar coupling could be more influential in the course of structure formation \citep{lb2010b}." +. 'The complexities indicate that the model-independent studies of the coupled scalar field might fail to account for the various effects due to the scalar field coupling (see 2 for a description) appropriately., The complexities indicate that the model-independent studies of the coupled scalar field might fail to account for the various effects due to the scalar field coupling (see \ref{sect:eqns} for a description) appropriately. +" So in this paper, we have studied the formations and properties of voids in the L, N and C models in parallel and compare their predictions."," So in this paper, we have studied the formations and properties of voids in the L, N and C models in parallel and compare their predictions." +" Voids are the largest objects in the Universe which are produced during the course of structure formation, and fill the vast majority of the space."," Voids are the largest objects in the Universe which are produced during the course of structure formation, and fill the vast majority of the space." + The importance of their properties in understanding the underlying cosmological scenario and global cosmological parameters has been emphasised by many authors., The importance of their properties in understanding the underlying cosmological scenario and global cosmological parameters has been emphasised by many authors. +" Recently, it has been claimed that a long-range fifth force could evacuate the space more efficiently and thus produce more voids than ACDM (Keselman,Nusser&Peebles2010;HellwingJuszkiewicz 2009)."," Recently, it has been claimed that a long-range fifth force could evacuate the space more efficiently and thus produce more voids than $\Lambda$ CDM \citep{knp2010, hj2009}." +". Those studies concentrate on the ReBEL model, where only a Yukawa-type fifth force is considered; because of the reason mentioned above, here we take into account all the main effects due to a scalar field coupling (which is arguably the most natural cause of fifth force), consider two qualitatively different types of modelsa and make more"," Those studies concentrate on the ReBEL model, where only a Yukawa-type fifth force is considered; because of the reason mentioned above, here we take into account all the main effects due to a scalar field coupling (which is arguably the most natural cause of a fifth force), consider two qualitatively different types of models and make more" + (e.g.Smithetal.2005:Comerford,"\citep[e.g.][]{Franx97, Ellis01, Kneib04b, Smail07, + Swinbank07, Bradley08}. \citep[e.g.][]{Smith05a,Comerford06,Sand08}." + zz;0.3 2009)..," $z{\ls}0.3$ \citep[e.g.][]{Kneib96,Broadhurst05acs,Smith05a,Limousin07a1689,Richard09}." + spectroscopically confirmed strong lensing clusters are known at z20.5 (Gladdersetal.2002:Inada2005:Borysetal. 2008).," spectroscopically confirmed strong lensing clusters are known at $z{>}0.5$ \citep{Gladders02,Inada03,Borys04,Sharon05,Swinbank07,Ofek08}." +. The Massive Cluster Survey (MACS:Ebel-ingetal.2001). offers an unprecedented opportunity to expand the available sample of strong lensing clusters at 0.3xz0.7., The Massive Cluster Survey \citep[MACS;][]{Ebeling01} offers an unprecedented opportunity to expand the available sample of strong lensing clusters at $0.3\le z\ls0.7$. + We present new results from this search: JJ1149.542223 (hereafter JJ1149; 11:49:34.3 422:23:42.5 |J2000]) at ς=0.544. one of a complete subsample of 12 MACS clusters at z>0.5 (Ebelingetal. 2007)..," We present new results from this search: $+$ 2223 (hereafter J1149; 11:49:34.3 $+$ 22:23:42.5 [J2000]) at $z=0.544$, one of a complete subsample of 12 MACS clusters at $z>0.5$ \citep{Ebeling07}. ." + Ins refsec:obs we deseribe the data: modeling and results are presented in refsec:results.. and summarized in refsec:summary..," In \\ref{sec:obs} we describe the data; modeling and results are presented in \\ref{sec:results}, and summarized in \\ref{sec:summary}." + We assume Ho=70kms!Mpe!. Qur=0.3 and O420.7; at z20.544. 1” corresponds to 6.35kpe.," We assume $\Ho=70\kms\Mpc^{-1}$, $\oM=0.3$ and $\oL=0.7$; at $z=0.544$ $1''$ corresponds to $6.35\kpc$." + All uncertainties and upper/lower limits are stated and/or plotted at 95% confidence., All uncertainties and upper/lower limits are stated and/or plotted at $95\%$ confidence. + JJ1149 was observed on 2004. April 22 with the Advanced Camera for Surveys (ACS) on-board the for 4.5ksec and 4.6kseethrough the F555W and F814W filters respectively (GO: 9722. PL: Ebeling).," J1149 was observed on 2004, April 22 with the Advanced Camera for Surveys (ACS) on-board the for $4.5\ksec$ and $4.6\ksec$through the F555W and F814W filters respectively (GO: 9722, PI: Ebeling)." +" These data were reduced using standard routines onto a 0.03""/pixel grid.", These data were reduced using standard routines onto a $0.03''/\!\pix$ grid. + The reduced data reveal, The reduced data reveal +Present velocities in the moclel solutiosare abulated in Table ΤΙe firs column repeats the model label in Table 1.,Present velocities in the model solutions are tabulated in Table The first column repeats the model label in Table 1. + The next three coltus are the Cartesian compoeuts of the galactoceuric velocity of the LNC (in the coordinae system it eqs [3.I] ancl [3.1])., The next three columns are the Cartesian components of the galactocentric velocity of the LMC (in the coordinate system in eqs \ref{eq:LMCvelocity}] ] and \ref{eq:SMCvelocity}] ]). + The valles ofn X57». in the Ífth column are the stuns of the three dilerences of 1Leastred aud inodel LIC velocity components.1 with the measureimeut. uncertaiuties in ecLatlon (3.1)D+) ) treated as staudarc «eviatious.," The values of $\chi_3^2$ in the fifth column are the sums of the three differences of measured and model LMC velocity components, with the measurement uncertainties in equation \ref{eq:LMCvelocity}) ) treated as standard deviations." + The next three coluns are the Cartesian com)o0nets of l actocentric velocity of M31. the uext three trauslate that to the galactocentric trallsverse alle al velocities of M31. atd the last columna is the heliocentric radial velocity of M31.," The next three columns are the Cartesian components of the galactocentric velocity of M31, the next three translate that to the galactocentric transverse and radial velocities of M31, and the last column is the heliocentric radial velocity of M31." + All models in Tables 1 and 2 are reasonable fits to the measured LMLC velocity., All models in Tables 1 and 2 are reasonable fits to the measured LMC velocity. + All except he last fit the measurecl redshift of M31. within reasonable allowance for the crude nature of the our-bods model.," All except the last fit the measured redshift of M31, within reasonable allowance for the crude nature of the four-body model." + The ciscrepancy in the redshift of M31 in the last 1iodel is beyoxd reasonable allowance., The discrepancy in the redshift of M31 in the last model is beyond reasonable allowance. + This case illust‘ates tlie existence of at least one solution to the four-body problem that its the measurecl velocity of the LMC aud gives M31 a traisve‘se velocity comparabe to Its racial ealactocentric velocity., This case illustrates the existence of at least one solution to the four-body problem that fits the measured velocity of the LMC and gives M31 a transverse velocity comparable to its radial galactocentric velocity. + ΤΙe large trausverse velocity of N31 COid be reconciled witl its measured dial velocity by iucreasiig the masses of N31 aud the MW. )ut alteripts in that direction spoil he fit to the velocity ofthe LMC.," The large transverse velocity of M31 could be reconciled with its measured radial velocity by increasing the masses of M31 and the MW, but attempts in that direction spoil the fit to the velocity of the LMC." +logarithmic presentation (magnitudes) chosen in Fig.,logarithmic presentation (magnitudes) chosen in Fig. + Ta ancl Th for the spectrophotometry. as well as in (he linear plot in Fig.," 7a and 7b for the spectrophotometry, as well as in the linear plot in Fig." + 2 and 3. we see a steepening of (he spectral energy distribution at the shortest wavelengths.," 2 and 3, we see a steepening of the spectral energy distribution at the shortest wavelengths." + In many comets. this region is dominated by. gas enission (CN.C.and CS).," In many comets, this region is dominated by gas emission $_3$ ,and $_2$ )." + By avoiding the emission features. as was done in our aperture photonmetry. or in comets wilh intrinsically low outgassing. evidence for a steeper slope of the reflectivity spectrum al short wavelengths is evident. lor example in Jewitt Meech (1986).," By avoiding the emission features, as was done in our aperture photometry, or in comets with intrinsically low outgassing, evidence for a steeper slope of the reflectivity spectrum at short wavelengths is evident, for example in Jewitt Meech (1986)." + Outside of the emission and absorption features. (he reflectivity of the ejecta cloud alter (he Deep Impact event in (he SNIFS observations can be roughly described bv. (wo linear fits.," Outside of the emission and absorption features, the reflectivity of the ejecta cloud after the Deep Impact event in the SNIFS observations can be roughly described by two linear fits." + From 350 nm to 22580 nm. the normalized reflectivitv. gradient as defined bv Jewitt Meech (1986) is 2222.64. per 100 nm.," From 350 nm to $\approx$ 580 nm, the normalized reflectivity gradient as defined by Jewitt Meech (1986) is $\approx$ per 100 nm." + From 580 nm to 940 nm. it is 227.576 per 100 nm.," From 580 nm to 940 nm, it is $\approx$ per 100 nm." + The two lines corresponding to these fits are included in Fig., The two lines corresponding to these fits are included in Fig. + 2., 2. + It is noteworthy that the break between these two slopes does not coincide with the wavelength. break between the blue ancl red channel of the SNIFS instrument at 520 nm. and is therefore considered real.," It is noteworthy that the break between these two slopes does not coincide with the wavelength break between the blue and red channel of the SNIFS instrument at 520 nm, and is therefore considered real." +" Similarly, (he VNIRIS spectrum is steeper al the short wavelength end. even (though the break is less pronounced (than in the SNIFS spectrum."," Similarly, the VNIRIS spectrum is steeper at the short wavelength end, even though the break is less pronounced than in the SNIFS spectrum." + We suggest that the small differences between these (wo spectra reflect residual calibration problems., We suggest that the small differences between these two spectra reflect residual calibration problems. + The tend towards a flatter reflectivity spectrum continues into the infrared. (he spectrum measured by VNIRIS is almost flat between 1500 nm and 2200 1m.," The tend towards a flatter reflectivity spectrum continues into the infrared, the spectrum measured by VNIRIS is almost flat between 1500 nm and 2200 nm." + All the spectrophotometric data obtained while the photometry aperture was dominated by impact ejected material show that this material πας a bluer reflectivity spectrum than the material usually released bv the comet., All the spectrophotometric data obtained while the photometry aperture was dominated by impact ejected material show that this material had a bluer reflectivity spectrum than the material usually released by the comet. + The dotted line in Fig., The dotted line in Fig. +" Τα, and Th fitted to all photometric data points is the average flux distribuGon in the data set taken about one half hour alter impact. when the ejecta cloud was still nearly unresolved. and al"," 7a and 7b fitted to all photometric data points is the average flux distribution in the data set taken about one half hour after impact, when the ejecta cloud was still nearly unresolved and at" +[Na/Fe]2 0.23 and with Na/Fe|2 0.28) falling outside the boundaries of Figs.,= 0.23 and with = 0.28) falling outside the boundaries of Figs. + 4. and 5.., \ref{fig:na.mg-fe} and \ref{fig:dX-dNa.limfe}. + These stars could be halo field counterparts of the Na-enhanced globular cluster stars. formed in the vicinity of an intermediate mass AGB star before its nucleosynthesis products were mixed into the interstellar medium.," These stars could be halo field counterparts of the Na-enhanced globular cluster stars, formed in the vicinity of an intermediate mass AGB star before its nucleosynthesis products were mixed into the interstellar medium." + The remaining c-capture elements. Si. Ca. and Ti are made by oxygen and silicon burning in massive stars. but also have a significant contribution from Ha. According to Tsujimoto et al. (1995..," The remaining $\alpha$ -capture elements, Si, Ca, and Ti are made by oxygen and silicon burning in massive stars, but also have a significant contribution from Ia. According to Tsujimoto et al. \cite{tsujimoto95}," + Table 3). the relative contributions of Ila to the solar abundances are negligible for Mg. for Si. for Ca. and for Fe.," Table 3), the relative contributions of Ia to the solar abundances are negligible for Mg, for Si, for Ca, and for Fe." + This explains why the amplitudes of the variations in aand aare smaller than in the case of (Table 5))., This explains why the amplitudes of the variations in and are smaller than in the case of (Table \ref{table:ratios}) ). + It is. however. puzzling that the variation in iis so small compared to the variation in ((only about one-third).," It is, however, puzzling that the variation in is so small compared to the variation in (only about one-third)." + Titanium was not included in the calculations of Tsujimoto et al., Titanium was not included in the calculations of Tsujimoto et al. + HII models underproduce Ti by a factor z2. e.g. Kobayashi et al. 2006)).," II models underproduce Ti by a factor $\simgt \! 2$, e.g. Kobayashi et al. \cite{kobayashi06}) )," + but according to Table 5 and Fig. 5..," but according to Table \ref{table:ratios} and Fig. \ref{fig:dX-dNa.limfe}," + the amplitude of the vvariations is larger than that of|., the amplitude of the variations is larger than that of. + Chromium is produced by both Type I and Ia SNe., Chromium is produced by both Type II and Ia SNe. + As seen from Fig., As seen from Fig. + 6 in NS10. |Cr/Fe] is close to zero and there is no significant difference in [Cr/Fe] between high- and low-c stars.," 6 in NS10, [Cr/Fe] is close to zero and there is no significant difference in [Cr/Fe] between high- and $\alpha$ stars." + Thus. chromium follows iron closely.," Thus, chromium follows iron closely." + This agrees with the calculations of Kobayashi et al. 2006..," This agrees with the calculations of Kobayashi et al. \cite{kobayashi06}," + who include nucleosynthesis contributions from both normal LIL with explosion energy ~10?! eerg. and more energetic core collapse SNe. so-called hypernovae (HNe) with. 10 times higher explosion energy.," who include nucleosynthesis contributions from both normal II with explosion energy $\sim \! 10^{51}$ erg, and more energetic core collapse SNe, so-called hypernovae (HNe) with 10 times higher explosion energy." + For masses above M... the fraction of of HNe Is assumed to be 0.5.," For masses above $M_{\odot}$, the fraction of of HNe is assumed to be 0.5." + In addition. contribution from Ha is taken into account with yields from Nomoto et al. (1997)).," In addition, contribution from Ia is taken into account with yields from Nomoto et al. \cite{nomoto97}) )." + The calculated is close to zero for metallicities ranging from [Fe/H]=—3 to solar., The calculated is close to zero for metallicities ranging from $\feh \simeq -3$ to solar. + Like in the case of [Cr/Fe]. there is no significant difference in bbetween high- and Iow- stars. but increases from about —0.4 ddex at [Fe/H]=-1.6 to -0.2ddex at [Fe/H]=—0.4.," Like in the case of , there is no significant difference in between high- and $\alpha$ stars, but increases from about $-0.4$ dex at $\feh = -1.6$ to $-0.2$ dex at $\feh = -0.4$." + This trend continues for disk stars so that [Mn/Fe|«0 at solar metallicity (e.g. Feltzing et al. 2007))., This trend continues for disk stars so that $\mnfe \simeq 0$ at solar metallicity (e.g. Feltzing et al. \cite{feltzing07}) ). + Gratton (1989)) suggested that the rise in iis caused by an overproduction of Mn relative to Fe in Ia as also predicted from the yields of Nomoto et al. (1997))., Gratton \cite{gratton89}) ) suggested that the rise in is caused by an overproduction of Mn relative to Fe in Ia as also predicted from the yields of Nomoto et al. \cite{nomoto97}) ). + Accordingly. one would expect the low-c halo stars to lie above the ttrend defined by the high-c stars. but this is not the case as seen from Fig. 2..," Accordingly, one would expect the $\alpha$ halo stars to lie above the trend defined by the $\alpha$ stars, but this is not the case as seen from Fig. \ref{fig:mn.cu.zn-fe}." + The explanation may be that the Mn yields of Ila are metallicity dependent as suggested from models by Badenes et al. (2008))., The explanation may be that the Mn yields of Ia are metallicity dependent as suggested from models by Badenes et al. \cite{badenes08}) ). + They find that the increase in neutron excess with metallicity leads to a faster increase of Mn/Cr inType la SNe than in core collapse SNe., They find that the increase in neutron excess with metallicity leads to a faster increase of Mn/Cr inType Ia SNe than in core collapse SNe. + Recalling that the IIa which enrich the low-c population are relatively metal-poor. this may cancel the expected overabundance of ffor the low-a population.," Recalling that the Ia which enrich the $\alpha$ population are relatively metal-poor, this may cancel the expected overabundance of for the $\alpha$ population." + In extreme systems such as the Sagittarius dwarf spheroidal (dSph) galaxy. the metallicity dependent Mn yield of Ia may even lead to a decrease of rrelative to the trend for disk stars as first suggested by MeWilliam et al. (2003))," In extreme systems such as the Sagittarius dwarf spheroidal (dSph) galaxy, the metallicity dependent Mn yield of Ia may even lead to a decrease of relative to the trend for disk stars as first suggested by McWilliam et al. \cite{mcwilliam03}) )" + and later shown in detail by Cescutti et al. (2008)), and later shown in detail by Cescutti et al. \cite{cescutti08}) ) + on the basis of chemical evolution models., on the basis of chemical evolution models. + Kobayashi Nomoto (2009)) have argued that if the tron abundance of the progenitors of Type Ia SNe is lower than —1. then the wind of the white dwarf in a binary system is too weak for an explosion to occur.," Kobayashi Nomoto \cite{kobayashi09}) ) have argued that if the iron abundance of the progenitors of Type Ia SNe is lower than $\feh \sim -1$ , then the wind of the white dwarf in a binary system is too weak for an explosion to occur." + The absence of IIa below [Fe/H]~-1 could explain that the trend of iis the same for high- and low-« stars. but then one has to assume different initial mass functions (ΜΕΣ) for the two populations in order to explain the differences in[α/Γε|.," The absence of Ia below $\feh \sim -1$ could explain that the trend of is the same for high- and $\alpha$ stars, but then one has to assume different initial mass functions (IMFs) for the two populations in order to explain the differences in." + According to Kobayashi et al. (20060).," According to Kobayashi et al. \cite{kobayashi06}) )," + an IMF biased towards low-mass III would lead to lower values of[o/Fe]. but because the difference in bbetween the high- and low-c populations increases with[Fe/H]. one has to assume a very complicated behavior of the IMF. t.e. a metallicity dependent IMF for the low-a stars and a constant IMF for the high-er stars.," an IMF biased towards low-mass II would lead to lower values of, but because the difference in between the high- and $\alpha$ populations increases with, one has to assume a very complicated behavior of the IMF, i.e. a metallicity dependent IMF for the $\alpha$ stars and a constant IMF for the $\alpha$ stars." + The rise in wwith ffor the high-« population cannot be explained as caused by Πα. because the constancy of eexcludes any significant contribution from Ia. Instead. the rise could be due to a metallicity-dependent yield of Mn in III. but the calculated yield ratio Mn/Fe show only a relatively weak increase with metallicity starting at [Fe/H]~—1.2 (Kobayashi et al. 2006..," The rise in with for the $\alpha$ population cannot be explained as caused by Ia, because the constancy of excludes any significant contribution from Ia. Instead, the rise could be due to a metallicity-dependent yield of Mn in II, but the calculated yield ratio Mn/Fe show only a relatively weak increase with metallicity starting at $\feh \sim -1.2$ (Kobayashi et al. \cite{kobayashi06}," + Fig., Fig. + 5)., 5). + Perhaps our assumption of LTE isleading to a spurious increase in wwith [Fe/H]., Perhaps our assumption of LTE isleading to a spurious increase in with . + According to Bergemann Gehren (2008)). the strengths of llines are affected by departures from LTE: the non-LTE corrections on the derived Mn abundances are positive and increase with," According to Bergemann Gehren \cite{bergemann08}) ), the strengths of lines are affected by departures from LTE; the non-LTE corrections on the derived Mn abundances are positive and increase with" +as approxinate since large eradieuts of the atinosplhieric xuwneters nav exist alone the LOS.,as approximate since large gradients of the atmospheric parameters may exist along the LOS. + The structure of he doseuflows is remarkably. but not surprisingly. similar o that seen iu the far red wing maguetoegrams.," The structure of the downflows is remarkably, but not surprisingly, similar to that seen in the far red wing magnetograms." + While stroug dowuflows of —5 lan | are observed in AR 10923. one finds velocities of around 6 kimi - and 10 aus tin ARs 10953 aud 11029 respectively.," While strong downflows of $\sim$ 5 km $^{-1}$ are observed in AR 10923, one finds velocities of around 6 km $^{-1}$ and 10 km $^{-1}$ in ARs 10953 and 11029 respectively." + The strong downflowing zones are surrounded by upflows which cau o identified with the Evershed flow., The strong downflowing zones are surrounded by upflows which can be identified with the Evershed flow. + The majority of the Stokes V. profile cimereie from he downfows exlibit a satellite or even an additional red lobe., The majority of the Stokes V profile emerging from the downflows exhibit a satellite or even an additional red lobe. + The Stokes 7 profiles also have highly inclined red wines. as illustrated in the top row of Figure 3 for he pixels marked with diamonds in Figure 2..," The Stokes $I$ profiles also have highly inclined red wings, as illustrated in the top row of Figure \ref{combo} for the pixels marked with diamonds in Figure \ref{velo}." + In AR 11029. some of the downuflows exhibit strouely redshiftec V profiles with laree area asviunetrnÉes (bottoni row of Figure 3)).," In AR 11029, some of the downflows exhibit strongly redshifted V profiles with large area asymmetries (bottom row of Figure \ref{combo}) )." + Upflows of about 2 kin + correspondiug o the EF are seen adjacent to the strong dowuflowius oitelies in all 3 ARs., Upflows of about 2 km $^{-1}$ corresponding to the EF are seen adjacent to the strong downflowing patches in all 3 ARs. + Figue L1. shows a cut passing through the strong downflowing patch located at the unbra-penunibra voundary of AR 10953., Figure \ref{con_super} shows a cut passing through the strong downflowing patch located at the umbra-penumbra boundary of AR 10953. + The variation of the Stokes xofiles along this cut is displaved in Figure 5. (black ines)., The variation of the Stokes profiles along this cut is displayed in Figure \ref{umbra_stokes} (black lines). + At the mubral edee aud to the right. one observes a distinct reduction iu the σοιπαπι intensity.," At the umbral edge and to the right, one observes a distinct reduction in the continuum intensity." + To the eft of the mubra-peuunbra boundary. the Stokes V xofile has two distinct red lobes while the IZ profile exhibits hiehlv inclined red wines.," To the left of the umbra-penumbra boundary, the Stokes V profile has two distinct red lobes while the $I$ profile exhibits highly inclined red wings." + With five lobes. he Stokes Q profile is verv asviuiietriic. 07332. bovoud he edge of the mubra.," With five lobes, the Stokes Q profile is very asymmetric, 32 beyond the edge of the umbra." + The anomalous profiles ling o the left of the wubra-pemmubra boundary were inverted using a 2 component atimuosphnere and setting all parameters. except the temperature. to be coustaut with height in order to estimate the plivsical parameters more precisely.," The anomalous profiles lying to the left of the umbra-penumbra boundary were inverted using a 2 component atmosphere and setting all parameters, except the temperature, to be constant with height in order to estimate the physical parameters more precisely." + The highly inclined red wines of the Stokes £ profiles as well as the double-recd-lobed WV profiles are well reproduced by the simple two-componcut atinosphere (ines with black filled circles in Figure 5))., The highly inclined red wings of the Stokes $I$ profiles as well as the double-red-lobed V profiles are well reproduced by the simple two-component atmosphere (lines with black filled circles in Figure \ref{umbra_stokes}) ). + The transition frou supersonic to nearly zero velocities along the cut cau be seen in Figure 6.. which shows that verv huge velocities nearlv twice the sound speed occur adjaceut/close to the imubra-peuunubra boundary and measure z τὸ kins | at a distance of σι.," The transition from supersonic to nearly zero velocities along the cut can be seen in Figure \ref{velo_super}, which shows that very large velocities nearly twice the sound speed occur adjacent/close to the umbra-penumbra boundary and measure $\approx$ 7.2 km $^{-1}$ at a distance of $-0\farcs64$." + At the uubral edee the faster couipoueut has a fill fraction of z which inereases with distance and bevond 0761 fills more than of the pixel., At the umbral edge the faster component has a fill fraction of $\approx$ which increases with distance and beyond $-0\farcs64$ fills more than of the pixel. + While the fast and slow compoucuts appear to differ by ~ 300 Ci the uncertainties in the retrieved paraueters sugeest that the uaeuitudes are nearly the same., While the fast and slow components appear to differ by $\approx$ 300 G the uncertainties in the retrieved parameters suggest that the magnitudes are nearly the same. + Both componoeuts have fell strengths iu excess of 2.2 kG. The average zenith rele in the unibra i$ z 1037 aud changes from at the mubra peummbra boundary to 137557 a ∙ ≯��↥⋅↑∐↸∖↴∖↴↕∪↖↖⇁↸⊳∪∐∏⋯∐↸∖∐↑∙↕∐↸⊳, Both components have field strengths in excess of 2.2 kG. The average zenith angle in the umbra is $\approx$ $^\circ$ and changes from $\pm$ $^\circ$ at the umbra penumbra boundary to $\pm$ $^\circ$ at $-0\farcs96$ for the slow component. +∪∐∏≻⋜∐⋅↕↴∖↴∪∟↑↕∐∖∑↸∖∐↕↕⋜⋯∶↴∙⊾↕↸∖ 6 ⋟↑∐↸∖↕⋟⋜↧↴∖↴↑↸⊳∪∐∏⋯∐↸∖∐↑↖↽⋜∐⋅↕↸∖↴∖↴↕≯↥⋅∪⋯↕⋅↱⊐∩∶∶∐↴∪⊔∶∶↓↴↕≯∪↥⋅ he same spatial locations.," In comparison, the zenith angle of the fast component varies from $\pm$ $^\circ$ to $\pm$ $^\circ$ for the same spatial locations." + The typical area of one dowuflowing patch varies Youn L.6 arcsec? for AR 10953 to as huge as 6 arcsec? as observed in AR 11029., The typical area of one downflowing patch varies from 1.6 $^2$ for AR 10953 to as large as 6 $^2$ as observed in AR 11029. + The two components could reside side-by-side in the same resolution clement or could be stacked one on top of the other iu the vertical direction., The two components could reside side-by-side in the same resolution element or could be stacked one on top of the other in the vertical direction. + Regardless of the exact configuration. supersonic velocities exist iu the presence of very strong magnetic fields.," Regardless of the exact configuration, supersonic velocities exist in the presence of very strong magnetic fields." + In addition. the polarity of the strong downflowing compoucut is the same as that of the sunspot. which rules out the possibility of them being Evershed flows returuing to the solar surface.," In addition, the polarity of the strong downflowing component is the same as that of the sunspot, which rules out the possibility of them being Evershed flows returning to the solar surface." + The strong fields would also inhibit convection. hence the downuflows appear to be unrelated to the Evershed phenomenon aud are likely to be caused by an alternative mechanism.," The strong fields would also inhibit convection, hence the downflows appear to be unrelated to the Evershed phenomenon and are likely to be caused by an alternative mechanism." +"law, the dust-to-gas ratio is required to be much lower than the Galactic standard in order to support the Compton-thick interpretation for the unsuccessful AGN detections.","law, the dust-to-gas ratio is required to be much lower than the Galactic standard in order to support the Compton-thick interpretation for the unsuccessful AGN detections." +" Of course, this is not due to a large-scale dust deficiency, since ULIRGs are, by definition, dust-rich systems."," Of course, this is not due to a large-scale dust deficiency, since ULIRGs are, by definition, dust-rich systems." +" Anyway, absorption features such as that of CO at 4.65 jm observed in IRAS 00397—1312 hint at large amounts of gas concentrated nearby a compact active core."," Anyway, absorption features such as that of CO at 4.65 $\mu$ m observed in IRAS $-$ 1312 hint at large amounts of gas concentrated nearby a compact active core." + A possible imbalance between the dust and gas components involving only the nuclear regions (i.e. within a region comparable in size with the dust sublimation radius) may be related to massive gaseous inflows/outflows during the most active phases of AGN accretion., A possible imbalance between the dust and gas components involving only the nuclear regions (i.e. within a region comparable in size with the dust sublimation radius) may be related to massive gaseous inflows/outflows during the most active phases of AGN accretion. +" 2) Whenever the AGN is not detected but the amplitude of a possible reflection component can be constrained, its upper limit is >500 times lower than the expected intrinsic keV AGN flux."," 2) Whenever the AGN is not detected but the amplitude of a possible reflection component can be constrained, its upper limit is $>500$ times lower than the expected intrinsic 2--10 keV AGN flux." + This is an order of magnitude lower than the usual reflection efficiency, This is an order of magnitude lower than the usual reflection efficiency +X-ray spectral evolution in the HID correlates with the X-ray variability properties (Belloni et al.,X-ray spectral evolution in the HID correlates with the X-ray variability properties (Belloni et al. + 2005) and with properties of the radio emission from a jet (Fender et al., 2005) and with properties of the radio emission from a jet (Fender et al. + 2004)., 2004). +" In the HID an increase in intensity is associated with an increase in the mass accretion rate, while a decrease in hardness corresponds to softening of the X-ray photon index."," In the HID an increase in intensity is associated with an increase in the mass accretion rate, while a decrease in hardness corresponds to softening of the X-ray photon index." +" A number of scenarios were presented to explain the spectral evolution of GBHs, i.e. the spectral softening (hardening) with increasing (decreasing) mass accretion rate (e.g. reviews in Remillard McClintock 2006; Done et al."," A number of scenarios were presented to explain the spectral evolution of GBHs, i.e. the spectral softening (hardening) with increasing (decreasing) mass accretion rate (e.g. reviews in Remillard McClintock 2006; Done et al." + 2007)., 2007). + One of the scenarios is that of the truncated accretion disc (e.g. Esin et al., One of the scenarios is that of the truncated accretion disc (e.g. Esin et al. + 1997)., 1997). + In this model at low mass accretion rates the standard accretion disc in the hard state is truncated far away from a black hole and a hot inner flow is formed close to the black hole., In this model at low mass accretion rates the standard accretion disc in the hard state is truncated far away from a black hole and a hot inner flow is formed close to the black hole. +" In such geometry, few disc photons can be intercepted by the hot flow and the resulting spectra have hard photon index, characteristic of the hard state."," In such geometry, few disc photons can be intercepted by the hot flow and the resulting spectra have hard photon index, characteristic of the hard state." +" As the mass accretion rate increases, the inner radius of the disc moves closer to the black hole resulting in an increased cooling of the electrons."," As the mass accretion rate increases, the inner radius of the disc moves closer to the black hole resulting in an increased cooling of the electrons." +" Consequently, the spectrum softens and the source evolves to a soft state."," Consequently, the spectrum softens and the source evolves to a soft state." + The soft state spectra seem to be well understood in terms of the multicolour disc black body emission from an untruncated (extending to the innermost stable circular orbit) disc accompanied by a weak Comptonised hard tail., The soft state spectra seem to be well understood in terms of the multicolour disc black body emission from an untruncated (extending to the innermost stable circular orbit) disc accompanied by a weak Comptonised hard tail. + Alternative hard state models not involving a truncated disc were proposed (see Done et al., Alternative hard state models not involving a truncated disc were proposed (see Done et al. + 2007 for strengths and weaknesses of each model)., 2007 for strengths and weaknesses of each model). + These include e.g. a patchy outflowing corona above a disc extending to the last stable orbit (Beloborodov 1999a; Malzac et al., These include e.g. a patchy outflowing corona above a disc extending to the last stable orbit (Beloborodov 1999a; Malzac et al. +" 2001) and the jet origin of the hard X-rays (Markoff, Falcke Fender 2001)."," 2001) and the jet origin of the hard X-rays (Markoff, Falcke Fender 2001)." +" However, several recent studies have shown that in the hard state at very low mass accretion rates, below a few per cent of the Eddington rate, the spectra of GBHs begin to soften again while the luminosity decreases (e.g. Ebisawa et al."," However, several recent studies have shown that in the hard state at very low mass accretion rates, below a few per cent of the Eddington rate, the spectra of GBHs begin to soften again while the luminosity decreases (e.g. Ebisawa et al." +" 1994; Revnivtsev, Trudolyubov Borozdin 2000; Corbel et al."," 1994; Revnivtsev, Trudolyubov Borozdin 2000; Corbel et al." + 2004; Jonker et al., 2004; Jonker et al. + 2004; Kalemci et al., 2004; Kalemci et al. + 2005; Wu Gu 2008; Dunn et al., 2005; Wu Gu 2008; Dunn et al. + 2010)., 2010). +" Interestingly, a similar spectral evolution with luminosity has been reported also in the case of AGN."," Interestingly, a similar spectral evolution with luminosity has been reported also in the case of AGN." +" Above a certain luminosity, the photon index softens with increasing luminosity (e.g. Porquet et al."," Above a certain luminosity, the photon index softens with increasing luminosity (e.g. Porquet et al." + 2004; Shemmer et al., 2004; Shemmer et al. + 2006; Saez et al., 2006; Saez et al. +" 2008; Sobolewska Papadakis 2009), but at low accretion rates the opposite trend is observed: the photon index hardens while the luminosity increases (Constantin et al."," 2008; Sobolewska Papadakis 2009), but at low accretion rates the opposite trend is observed: the photon index hardens while the luminosity increases (Constantin et al." +" 2009; Gu Cao 2009), just like in GBHs."," 2009; Gu Cao 2009), just like in GBHs." +" As mentioned, it is generally believed that the hard power-law like X-rays are produced from Compton up-scatter of soft disc photons by energetic electrons in a hot corona located close to the black hole."," As mentioned, it is generally believed that the hard power-law like X-rays are produced from Compton up-scatter of soft disc photons by energetic electrons in a hot corona located close to the black hole." + The high energy cut-offs observed in the hard state spectra suggest that the population of electrons is thermal (e.g. Gierliásski et al., The high energy cut-offs observed in the hard state spectra suggest that the population of electrons is thermal (e.g. Gierlińsski et al. +" 1999; Rodriguez, Corbel Tomsick 2003; Miyakawa et al."," 1999; Rodriguez, Corbel Tomsick 2003; Miyakawa et al." +" 2008; Joinet, Kalemci Senziani 2008; Motta, Belloni Homan 2009)."," 2008; Joinet, Kalemci Senziani 2008; Motta, Belloni Homan 2009)." +" Within this framework, the main parameter that determines the spectral shape of the intrinsic hard ray continuum in accreting sources is the ratio of heating-to-cooling compactnesses,/£,,, where compactness is defined as a dimensionless luminosity, where L is the luminosity of a spherical region of radius R, and or is the Thomson cross section."," Within this framework, the main parameter that determines the spectral shape of the intrinsic hard X-ray continuum in accreting sources is the ratio of heating-to-cooling compactnesses, where compactness is defined as a dimensionless luminosity, where $L$ is the luminosity of a spherical region of radius $R$, and $\sigma_T$ is the Thomson cross section." +" In this paper we study how the compactness ratio,ln/€s,, evolves with GBH luminosity in the hard state."," In this paper we study how the compactness ratio, evolves with GBH luminosity in the hard state." +" We consider the rise and decay parts of the outbursts of two confirmed black hole binaries, when their luminosity is less than ~ 0.1-0.3 of their Eddington limit."," We consider the rise and decay parts of the outbursts of two confirmed black hole binaries, when their luminosity is less than $\sim 0.1$ –0.3 of their Eddington limit." +" We fitted their spectra with a disc black-body component (to account for their disc emission in soft X-rays) and theEQPAIR model of Coppi (1999) to determine¢,/€;.", We fitted their spectra with a disc black-body component (to account for their disc emission in soft X-rays) and the model of Coppi (1999) to determine. +". Since this parameter is mainly determined by the disc/corona geometry, our aim is to infer and constrain the evolution of the source geometry in the hard state, and investigate which of the current theoretical models are consistent with our results."," Since this parameter is mainly determined by the disc/corona geometry, our aim is to infer and constrain the evolution of the source geometry in the hard state, and investigate which of the current theoretical models are consistent with our results." +" In this work, we re-analyse all the archival RXTE observations of aand339-4,, available up to 2007."," In this work, we re-analyse all the archival RXTE observations of and, available up to 2007." + Both sources are well studied systems containing a dynamically confirmed black hole primary (see references in Tab., Both sources are well studied systems containing a dynamically confirmed black hole primary (see references in Tab. + 1)., 1). + The sselected data cover in great detail the period of its 2005 outburst., The selected data cover in great detail the period of its 2005 outburst. +" In addition, the mass and distance to aare relatively well constrained (Tab."," In addition, the mass and distance to are relatively well constrained (Tab." +" 1; but see Foellmi 2009, and Sec."," 1; but see Foellmi 2009, and Sec." +" 4.3), which allows for accurate conversion of the observed fluxes into the Eddington luminosity ratios."," 4.3), which allows for accurate conversion of the observed fluxes into the Eddington luminosity ratios." + The sselected data extend over a time-scale of several years., The selected data extend over a time-scale of several years. +" They cover reasonably well its 2002/2003 and 2004/2005 outbursts (02 and 03, respectively) and include observations taken in the period of 1996-1999 (01)."," They cover reasonably well its 2002/2003 and 2004/2005 outbursts (o2 and o3, respectively) and include observations taken in the period of 1996–1999 (o1)." +" Even though the mass and distance constraints of aare not as tight as those ofJ1655-40,, we choose this system for our study due to a large number of hard state observations displayed in its multiple outbursts."," Even though the mass and distance constraints of are not as tight as those of, we choose this system for our study due to a large number of hard state observations displayed in its multiple outbursts." + Both, Both +to those observed at 9 and jan cau be attributed to silicate absorption. which Is nof iucInded in this model.,"to those observed at 9 and $\mu$ m can be attributed to silicate absorption, which is not included in this model." + However. it is expected to be present based on the CÓ absorption measured at[.," However, it is expected to be present based on the CO absorption measured at." +754mà&. The conclusion that the SED uceds two blackbody conrponeuts does not chanee much even if we use spiral galaxy. templates., The conclusion that the SED needs two blackbody components does not change much even if we use spiral galaxy templates. + The infrared uninositv Lgs is derived to be 9.1:«1029Ls. which is consistent with 1.0«ΤοL: using the uecthod of(1995).," The infrared luminosity $L_{\mathrm{IR}}$ is derived to be $9.1\times 10^{10}\ \mathrm{L}_{\sun}$, which is consistent with $1.0 \times 10^{11}\ \mathrm{L}_{\sun}$ using the method of." +.. We note that the contribution at wavoleugtlis onecr than to the total luuinosity is expected to be sinall for IRAS 01250|2832., We note that the contribution at wavelengths longer than to the total luminosity is expected to be small for IRAS 01250+2832. + While here are no sigus of / and [OTH] eiuissiou lines in Figure 2((00). Ta and [NT Ines are ¢‘learly detected.," While there are no signs of $\beta$ and [OIII] emission lines in Figure \ref{fig:opt_spec}( (b), $\alpha$ and [NII] lines are clearly detected." + The eniission line is strouger than Io. sugecstingOO hat IRAS 01250|2832 is a low-ionization nuclear cuission-line region (LINER) ealaxy.," The emission line is stronger than $\alpha$, suggesting that IRAS 01250+2832 is a low-ionization nuclear emission-line region (LINER) galaxy." + Ilowever. he other indicators of LINERs. and cunission lues. are rot seen because of the weakness of the lines. relative to the stellar coutinuuuu.," However, the other indicators of LINERs, and emission lines, are not seen because of the weakness of the lines, relative to the stellar continuum." + The 3o upper fiuit to the IJ tux is estimated to be «1016cress1ο7.," The $\sigma$ upper limit to the $\beta$ flux is estimated to be $\times 10^{-16}\ +\mathrm{ergs}\ \mathrm{s}^{-1}\ \mathrm{cm}^{-2}$." + This upper init is not useful to estimate the reddening from the Bahuer ratio., This upper limit is not useful to estimate the reddening from the Balmer ratio. + Without applying anv reddine correction. we caleulate an Πα hue luninosity of «10L;. which is comparable to that of low-luninositv ACNS (LLACNs) fouud in the optical spectroscopic survey of nearby galaxies1997)...," Without applying any reddening correction, we calculate an $\alpha$ line luminosity of $\times 10^5\ \mathrm{L}_{\sun}$, which is comparable to that of low-luminosity AGNs (LLAGNs) found in the optical spectroscopic survey of nearby galaxies." + A comparison with LLAGNs is discussed in Section 5.., A comparison with LLAGNs is discussed in Section \ref{sec:dis}. + As shown in Section 3.. both galaxies show ucar-infrared continua from hot dust with Tuus—=)nοGOOTS. although they differ in other wavs.," As shown in Section \ref{sec:multi}, both galaxies show near-infrared continuum from hot dust with $T_{\mathrm{dust}}=500-600\mathrm{K}$, although they differ in other ways." + The origin of the energy source heating tus dust. however. reclaims unclear.," The origin of the energy source heating this dust, however, remains unclear." +" Fits 1idicate that the Iunünositv of this hot dust compoucut is 2.os1079 Lane 6.6«101L.. for LEDA 81271 and IRAS 01250|2832. Yspectively,"," Fits indicate that the luminosity of this hot dust component is $2.7 \times 10^{10}\ \mathrm{L}_{\odot}$ and $6.6 \times 10^{10}\ \mathrm{L}_{\odot}$ for LEDA 84274 and IRAS 01250+2832, respectively." + If we assmme one single opically thick spherical cutting region. the size of the οιτας regions wouk be 0.7 pe and 1.6 pe in diameter for LEDA 81271 and IRAS 01250|2832. respectively.," If we assume one single optically thick spherical emitting region, the size of the emitting regions would be 0.7 pc and 1.6 pc in diameter for LEDA 84274 and IRAS 01250+2832, respectively." + One possibility is that we are observing an OB star cluster that has a luge luninosity of Ly>LOL. ina compact volune of a cubic parsec. aud that heats up the siuroundiug dust to > 500K. Towever. the relaxation time of the dynamically bound system cau be estimated to be LO®10° years.," One possibility is that we are observing an OB star cluster that has a huge luminosity of $L_{\mathrm{IR}} > 10^{10} \mathrm{L}_{\odot}$ in a compact volume of a cubic parsec, and that heats up the surrounding dust to $>$ 500K. However, the relaxation time of the dynamically bound system can be estimated to be $10^6 - 10^7$ years." + Thus. this situation is unlikely to be observed.," Thus, this situation is unlikely to be observed." + A inore likely possibility is that the object is a compact central supermassive black hole surrounded by a hot accretion disk., A more likely possibility is that the object is a compact central supermassive black hole surrounded by a hot accretion disk. + However. no optical specta shows amy evidence of the hard photous produced. by an ACN.," However, no optical spectrum shows any evidence of the hard photons produced by an AGN." + The various ciiissiou-line ratios of LEDA S127 Lin the optical baud show that it is au IHILregion-like galaxy. as concluded., The various emission-line ratios of LEDA 84274 in the optical band show that it is an HII-region-like galaxy as concluded. + TRAS 01250|2832 shows no emission lines except for Ta aud [NT]., IRAS 01250+2832 shows no emission lines except for $\alpha$ and [NII]. + The and nou-detection of PAIT e1iissiou may support the presence of an obscured, The weak- and non-detection of PAH emission may support the presence of an obscured +where AZ; can be either. of the progenitors Af; or Ale.,where $M_i$ can be either of the progenitors $M_1$ or $M_2$. + We recall that the conditional mass function and the mereer rate in the EPS mocel is not symmetric with respect to the two progenitor masses., We recall that the conditional mass function and the merger rate in the EPS model is not symmetric with respect to the two progenitor masses. + This remains an unsolved problem., This remains an unsolved problem. + Below we simply show the results for both choices., Below we simply show the results for both choices. +" According to the notation of Falkkhouri&Ala(2007)... we call the merger rate ""option A when A; is assigned to the smaller progenitor A». and “option D when Ad;=Mj."," According to the notation of \cite{FM07}, we call the merger rate “option A” when $M_i$ is assigned to the smaller progenitor $M_2$, and “option B” when $M_i=M_1$." + In Lig. 1..," In Fig. \ref{NM_compare}," + we illustrate the accuracy of eq. (15)), we illustrate the accuracy of eq. \ref{NM}) ) +. by comparing ib with the exact solution from ZIIO6 ancl the analytic approximation based on eq. (, by comparing it with the exact solution from ZH06 and the analytic approximation based on eq. ( +7) of STO02.,7) of ST02. + The figure shows the conditional mass functions at four different look-back times (As=0.1.0.03.0.01. 0.003) for a descendant halo of mass LOYAL. at redshift zero.," The figure shows the conditional mass functions at four different look-back times $\Delta +z=0.1, 0.03, 0.01, 0.003$ ) for a descendant halo of mass $10^{13}M_{\odot}$ at redshift zero." + The approximation of S'TO2 is seen to overprediet the number of lower mass progenitors by up to a factor of 2 to 10 for Azες0.03. whereas eq. (15))," The approximation of ST02 is seen to overpredict the number of lower mass progenitors by up to a factor of 2 to 10 for $\Delta z \lsim 0.03$, whereas eq. \ref{NM}) )" + of this paper is accurate when Az is as small as 0.003., of this paper is accurate when $\Delta z$ is as small as 0.003. + For the halo merger rate. we compare the predictions of our ellipsoidal model with the Millennium. simulation merger rate determined by Fakhouri&Ala(2007) using the “stitching” method.," For the halo merger rate, we compare the predictions of our ellipsoidal model with the Millennium simulation merger rate determined by \cite{FM07} using the “stitching” method." +" Γον find that the halo merger rate in the simulation converges well when the look-back time A: approaches zero and can be deseribed by a simple universal fitting formula: where 34=12«107AJ.. £=0.098. cl=0.0289. αι=0.083. a2=2.01. a4=0409. and a,=0.371."," They find that the halo merger rate in the simulation converges well when the look-back time $\Delta z$ approaches zero and can be described by a simple universal fitting formula: where $\tilde{M}=1.2\times 10^{12}M_{\odot}$, $\tilde{\xi}=0.098$, $A=0.0289$, $\alpha_1=0.083$ , $\alpha_2=-2.01$ , $\alpha_3=0.409$, and $\alpha_4=0.371$." + Their Fig., Their Fig. + 15 illustrates the large discrepancy. between eq. (18)), 15 illustrates the large discrepancy between eq. \ref{B_Mi}) ) + and the prediction of the standard spherical EPS model., and the prediction of the standard spherical EPS model. + Kies., Figs. + 2. (for option A) ancl 3. (option D) show the ratio between the halo merger rate Bin of our ellipsoidal collapse model. (eq. (16))), \ref{mr1} (for option A) and \ref{mr2} (option B) show the ratio between the halo merger rate $B/n$ of our ellipsoidal collapse model (eq. \ref{B0}) )) + and. that of the Millennium simulation (eq.(18))) for three descendant halo masses ancl four redshifts., and that of the Millennium simulation \ref{B_Mi}) )) for three descendant halo masses and four redshifts. + Phe spherical collapse model (eq. (17))), The spherical collapse model (eq. \ref{B0_spherical}) )) + is also shown for comparison., is also shown for comparison. + The minimum halo mass is chosen to be 2«107737. as set by the halo mass resolution in the Millennium simulation., The minimum halo mass is chosen to be $2\times 10^{10}M_{\odot}$ as set by the halo mass resolution in the Millennium simulation. + Comparison of the two figures shows that the two choices of AZ; give similar results [or major mergers but vield very different predictions for £«1. where option A (Fig. 2))," Comparison of the two figures shows that the two choices of $M_i$ give similar results for major mergers but yield very different predictions for $\xi\ll 1$, where option A (Fig. \ref{mr1}) )" + agrees better with the Millennium than option D (Fig. 33)), agrees better with the Millennium than option B (Fig. \ref{mr2}) ). + We note that the two options predict. different. power-law dependencies on € at £x1: [or SCM)xAL. option A gives Byrncx£?. hut option D gives Binx€t. which is independent. of the density variance on the scale of thesmaller. progenitor mass.," We note that the two options predict different power-law dependencies on $\xi$ at $\xi\ll 1$: for $S(M)\propto +M^{-\gamma}$, option A gives $B/n\propto\xi^{\gamma/2-2}$, but option B gives $B/n\propto\xi^{-1.5}$, which is independent of the density variance on the scale of thesmaller progenitor mass." + Lt is also interesting to note that option A is implicitly used in some Monte Carlo methocs: for example. Coleetal.(2000) select the mass of the first. progenitor from the lower half of the conditional mass function (i.e. M; 1075em7?.. volume gas densities of à> 10° em"".. and temperatures T< 20 K22).. Several studies suggest that IRDCs have the potential of harboring the earliest stages of massive star formation and indeed evidence for this is found toward distinct regions within them(???)."," Millimeter and (sub)millimeter molecular studies reveal that some clumps within IRDCs have column densities of $>$ $^{23}$, volume gas densities of $n >$ $^{5}$ , and temperatures $T <$ 20 K. Several studies suggest that IRDCs have the potential of harboring the earliest stages of massive star formation and indeed evidence for this is found toward distinct regions within them." +", mapped the (J. AK) = (1.1) and (2.2) inversion transitions of ammonia (NH3i) in the IRDC GII.II-0.12. with. the Etfelsberg 100m telescope and found gas temperatures of the order of 15 K for several clumps within this cloud."," mapped the $J,K$ ) $=$ (1,1) and (2,2) inversion transitions of ammonia $_3$ ) in the IRDC G11.11-0.12 with the Effelsberg 100m telescope and found gas temperatures of the order of 15 K for several clumps within this cloud." + The panel of Fig., The panel of Fig. + 1. shows an overview of the region., \ref{Fcont} shows an overview of the region. + Furthermore. reported the detection of 6.7 GHz class Η methanol (CH:OH) and 22.2 GHz water (ΠΟ) masers in the IRDC Core GII.II-0.12P1 (hereafter GII.HIPI)X.," Furthermore, reported the detection of 6.7 GHz class II methanol $_3$ OH) and 22.2 GHz water $_2$ O) masers in the IRDC Core G11.11-0.12P1 (hereafter G11.11P1)." + Both CHiOH and H2O masers are known as tracers of massive star formation., Both $_3$ OH and $_2$ O masers are known as tracers of massive star formation. + They found that these masers were associated with à SCUBA dust continuum peak and ascribed the kinematics of the methanol masing spots to a maser amplification from a Keplerian disk., They found that these masers were associated with a SCUBA dust continuum peak and ascribed the kinematics of the methanol masing spots to a maser amplification from a Keplerian disk. + Recently. observed this filamentary IRDC with the PACS (at 70. 100. and 160 jim) and the SPIRE (250. 350. and 500 ym) instruments on board of theObservatory. with resolutions in the range of ~6’—40”.," Recently, observed this filamentary IRDC with the PACS (at 70, 100, and 160 $\mu$ m) and the SPIRE (250, 350, and 500 $\mu$ m) instruments on board of the, with resolutions in the range of $\sim$." +. For GII.TIPI. they obtain from a modified blackbody fit to the PACS data. a dust temperature of 24 K. a luminosity of 1346 L.... and a mass of 240M.," For G11.11P1, they obtain from a modified blackbody fit to the PACS data, a dust temperature of 24 K, a luminosity of 1346 , and a mass of 240." +.. and have used a two-component model to fit single-dish observations of NHs and CH;OH spectra. respectively. and derived temperatures of - 15-18 K for the extended component (with size of ~20” corresponding to 0.35 pe) and ~47-60 K for the inner component (with a size of ~3” corresponding to 0.05 pe).," and have used a two-component model to fit single-dish observations of $_3$ and $_3$ OH spectra, respectively, and derived temperatures of $\sim$ 15–18 K for the extended component (with size of $\sim$ corresponding to 0.35 pc) and $\sim$ 47–60 K for the inner component (with a size of $\sim$ corresponding to 0.05 pc)." + Methanol. which is a slightly asymmetric top molecule. has been used to derive physical parameters such as density and temperature in IRDCs(?).. high-mass protostellar objects?).. massive young stars as well as in low- protostellar systems (?).," Methanol, which is a slightly asymmetric top molecule, has been used to derive physical parameters such as density and temperature in IRDCs, high-mass protostellar objects, massive young stars as well as in low-mass protostellar systems ." +". In particular. carried out a study toward 13 massive star-forming regions and found three types of CH30H abundance (Xcu.oq=Neuou/Ng.) profiles: Xcu.og.~1077 for the coldest sources. from 1077 to 1077 for warmer sources, and 1077 for hot cores."," In particular, carried out a study toward 13 massive star-forming regions and found three types of $_3$ OH abundance $X_{\rm CH_3OH} \equiv N_{\rm CH_3OH}/N_{\rm{H_2}}$ ) profiles: $X_{\rm CH_3OH} \sim 10^{-9}$ for the coldest sources, from $10^{-9}$ to $10^{-7}$ for warmer sources, and $10^{-7}$ for hot cores." + CH3OH has also been associated with outflows where the methanol abundance enhancements have been found to be a factor as large as 0000222)., $_3$ OH has also been associated with outflows where the methanol abundance enhancements have been found to be a factor as large as 000. + In this paper. we present aresecond resolution millimeter continuum and line observations toward GI.IIPI with the aim to determining its physical and chemical structure.," In this paper, we present arcsecond resolution millimeter continuum and line observations toward G11.11P1 with the aim to determining its physical and chemical structure." + In Sect., In Sect. + 2. we describe our observations carried out with the IRAM Plateau de Bure Interferometer.," 2, we describe our observations carried out with the IRAM Plateau de Bure Interferometer." + In Sect., In Sect. + 3. we present continuum and line results together with the analysis.," 3, we present continuum and line results together with the analysis." + The discussion is presented in Sect., The discussion is presented in Sect. + 4 and the summary is given in Sect., 4 and the summary is given in Sect. + 5., 5. + ΕΠΠΡΙ was observed with the IRAM six element array Plateau de Bure Interferometer in D and C configurations in 2005 and 2006. respectively.," G11.11P1 was observed with the IRAM six element array Plateau de Bure Interferometer in D and C configurations in 2005 and 2006, respectively." + During the 2006 observations. one antenna was equipped with the prototype New Generation Receiver.," During the 2006 observations, one antenna was equipped with the prototype New Generation Receiver." + Because of a difference in the frequency scheme of this receiver. visibilities obtained in the image sideband in this antenna were discarded.," Because of a difference in the frequency scheme of this receiver, visibilities obtained in the image sideband in this antenna were discarded." + The receivers were tuned single side-band at 3 mm and double side-band at | mm., The receivers were tuned single side-band at 3 mm and double side-band at 1 mm. + The 3 mm receivers were centered at 96.64 GHz and the | mm receivers at241.81 GHz (see Table 1))., The 3 mm receivers were centered at 96.64 GHz and the 1 mm receivers at241.81 GHz (see Table \ref{Tobs}) ). +" At 3 mm.the C'S 2 > I line and the CH;OH 2,— 1; 3,=0 "," At 3 mm,the $^{34}$ S 2 $\rightarrow$ 1 line and the $_{3}$ OH $_{k} \rightarrow$ $_{k}$ $v_{t} = 0$ " +Echelle Spectrograph (UVES) on the VLT 8.21 Isueven telescope at Paranal. in 1999.,"Echelle Spectrograph (UVES) on the VLT 8.2m Kueyen telescope at Paranal, in 1999." + The instrunoeut is described in D'Odorico et al. (, The instrument is described in D'Odorico et al. ( +2000).,2000). +" Two exposures of 1500 8 cach. covering the spectral range from 3650 to 1900 aand from 6700 to 10000 WWere obtained with a resolution of z6.9 ku s! and z5.7 haa C respectively,"," Two exposures of 4500 s each, covering the spectral range from 3650 to 4900 and from 6700 to 10000 were obtained with a resolution of $\approx 6.9$ km $^{-1}$ and $\approx 5.7$ km $^{-1}$ respectively." + The individual spectra were reduced using the UVES data reduction pipcline implemented in the ESO package., The individual spectra were reduced using the UVES data reduction pipeline implemented in the ESO package. + The final spectrum reaches a S/N varving from 20 to 20., The final spectrum reaches a S/N varying from 20 to 35. + QSO 0317.3819 shows a camped Lyo system a EDS3.025 which has been studied in detail by Centurion et al. (, QSO 0347–3819 shows a damped $\a$ system at $z_{\rm abs} = 3.025$ which has been studied in detail by Centurion et al. ( +1998). Ledoux et al. (,"1998), Ledoux et al. (" +1998) and from TTRES-Keck observations bv Prochaska Wolfe (1999).,1998) and from HIRES-Keck observations by Prochaska Wolfe (1999). + The UVES observations however provide the first high-quality data im the UV (A6700 À))., The UVES observations however provide the first high-quality data in the UV $\l < 4900$ ) and in the near-IR $\l > 6700$ ). +" ""They allow the abundance measurements of new features such as O. P. Àr and Zu. in addition to the N. S. Si and Fe abundances measured in the previous studies."," They allow the abundance measurements of new features such as O, P, Ar and Zn, in addition to the N, S, Si and Fe abundances measured in the previous studies." +" Full abuudancee analysis of the DLA svstem at ian,=3.025 will be presented iu a future paper.", Full abundance analysis of the DLA system at $z_{\rm abs} = 3.025$ will be presented in a future paper. + Hore we focus ou the deuterium detection aud the D/II ratio measurement., Here we focus on the deuterium detection and the D/H ratio measurement. + The absorption profiles of the DLA system at tan.=3.025 are characterized by two dominating componcuts (2 and 3) separated by about 20 km with the red (ie slightlv stronger than the due as it can be seen chom the nou-saturated metal lines in Fie. 1.., The absorption profiles of the DLA system at $z_{\rm abs} = 3.025$ are characterized by two dominating components (2 and 3) separated by about 20 km $^{-1}$ with the red one slightly stronger than the blue as it can be seen from the non-saturated metal lines in Fig. \ref{low-ion}. + The strong aud saturated metal lines reveal hat additional material in sinaller amount is present recdwards the two mai catures (components [. 5. 6 2x T)," The strong and saturated metal lines reveal that additional material in smaller amount is present redwards the two main features (components 4, 5, 6 and 7)." + The region on the due side of the main absorption components is sharpaud relatively free from iaterial with ouly one weal coluponent (conponent 1) at about S0 kn 1, The region on the blue side of the main absorption components is sharpand relatively free from material with only one weak component (component 1) at about $-30$ km $^{-1}$. + Τι otal seven components are needed to fit the metal lines absorption profiles. with two maim compoucuts containing about of the total column deusity por trausition.," In total seven components are needed to fit the metal lines absorption profiles, with two main components containing about of the total column density per transition." +" The DLA system af tans=3.025 js a vorv good candidate for the ceuterimm analysis since it shows a relatively siuuple velocitv structure dominated by two strong components, a low metallicity of =1.25. indicatiug tha he measured D/II will be representative"," The DLA system at $z_{\rm abs} = 3.025$ is a very good candidate for the deuterium analysis since it shows a relatively simple velocity structure dominated by two strong components, a low metallicity of $\approx -1.25$ , indicating that the measured D/H will be representative" +The y Dor stars are variable late A and F-type stars.,The $\gamma$ Dor stars are variable late A and F-type stars. + Their variability was identified as caused by pulsation by ?.. and classified them as a new class of pulsators and defined the features of this group.," Their variability was identified as caused by pulsation by \cite{balona1994}, , and \cite{kaye1999} classified them as a new class of pulsators and defined the features of this group." + These stars are pulsating with high-order g-modes in a range of periods betweenapproximately 0.3 and 3 days., These stars are pulsating with high-order $g$ -modes in a range of periods betweenapproximately $0.3$ and $3$ days. + The observational y Dor IS covers a part of the Hertzsprung-Russel Diagram (HRD) between 7200—7700K on the zero-age main sequence (ZAMS) and 6900—7500K above it (2)). between the solar-like stars domain and the 0 Scuti (0 Set) IS.," The observational $\gamma$ Dor IS covers a part of the Hertzsprung-Russel Diagram (HRD) between $7200-7700~K$ on the zero-age main sequence (ZAMS) and $6900-7500~K$ above it \citealt{handler1999}) ), between the solar-like stars domain and the $\delta$ Scuti $\delta$ Sct) IS." + We note that they are located between stars with à deep convective envelope (CE) and stars with a radiative envelope. in the region of the HR diagram where the depth of the CE changes rapidly with the effective temperature of the star.," We note that they are located between stars with a deep convective envelope (CE) and stars with a radiative envelope, in the region of the HR diagram where the depth of the CE changes rapidly with the effective temperature of the star." +" Nowadays 66 stars have been confirmed as bonafide y Doradus (?)). and thanks to the space missions CoRoT (?)) and Kepler (?)). the number of y Dor candidates is rapidly increasing (see e.g. 2.. 2.. 2., 2))."," Nowadays 66 stars have been confirmed as $bona~fide$ $\gamma$ Doradus \citealt{henry2007}) ), and thanks to the space missions CoRoT \citealt{baglin2006}) ) and Kepler \citealt{gilliland2010}) ), the number of $\gamma$ Dor candidates is rapidly increasing (see $e.g.$ \citealt{uytterhoeven2008}, \citealt{mathias2009}, \citealt{hareter2010}, \citealt{balona2011}) )." + The observational limits of the y Doradus IS have been established last by ? (HSO2 hereafter). and in the rest of the paper these limits will be adopted to define the observational y Dor IS.," The observational limits of the $\gamma$ Doradus IS have been established last by \cite{handler2002} (HS02 hereafter), and in the rest of the paper these limits will be adopted to define the observational $\gamma$ Dor IS." + ? use the frozen convection approximation to propose the modulation of the radiative flux at the base of the CE as the excitation mechanism., \cite{guzik2000} use the frozen convection approximation to propose the modulation of the radiative flux at the base of the CE as the excitation mechanism. + This mechanism has been confirmed by ? using a time-dependent convection (TDC) treatment (2.. 2)).," This mechanism has been confirmed by \cite{dupret2005} using a time-dependent convection (TDC) treatment \citealt{gabriel1996}, , \citealt{grigahcene2005}) )." +" Because the depth of the CE plays à major role in the driving mechanism of y Dor pulsations. the theoretical predictions of stability are very sensitive to the parameter « defining the mean free path of a convective element (A=axH,. where H, is the pressure scale height) in the classical mixing-length treatment of convection (MLT. ?))."," Because the depth of the CE plays a major role in the driving mechanism of $\gamma$ Dor pulsations, the theoretical predictions of stability are very sensitive to the parameter $\alpha$ defining the mean free path of a convective element $\Lambda=\alpha \times H_p$, where $H_p$ is the pressure scale height) in the classical mixing-length treatment of convection (MLT, \citealt{bohmvitense1958}) )." + Using TDC treatment. ? obtained good agreement between theoretical and observational y Dor IS for models computed with a=2.00.," Using TDC treatment, \cite{dupret2004} obtained good agreement between theoretical and observational $\gamma$ Dor IS for models computed with $\alpha = 2.00$." + These theoretical works on y Dor stars systematically studied MS models., These theoretical works on $\gamma$ Dor stars systematically studied MS models. + However. as shown in Fig. l..," However, as shown in Fig. \ref{HRdiag}," + MS and evolutionary tracks cross the observed y Dor IS., MS and evolutionary tracks cross the observed $\gamma$ Dor IS. + Although the time spent by a star of 1.8 M. to cross the IS during its PMS evolution is ten times less than the time spent during the MS phase in the same region of HR diagram. recent photometric observations of young clusters (NGC 884. ?)) have revealed the presence of y Dor candidates that. given the age of the cluster. should be in the PMS phase.," Although the time spent by a star of 1.8 $M_\odot$ to cross the IS during its PMS evolution is ten times less than the time spent during the MS phase in the same region of HR diagram, recent photometric observations of young clusters (NGC 884, \citealt{saesen2010}) ) have revealed the presence of $\gamma$ Dor candidates that, given the age of the cluster, should be in the PMS phase." + A strong effort has also been made to find PMS pulsators in NGC2264 (?)). another young open cluster.," A strong effort has also been made to find PMS pulsators in NGC2264 \citealt{zwintz2009}) ), another young open cluster." +" Moreover. the PMS/MS status of HR 8799, ay Dor variable hosting four planets (or brown dwarfs) (?.. 2)). is still a matter of debate (2.. 2))."," Moreover, the PMS/MS status of HR 8799, a $\gamma$ Dor variable hosting four planets (or brown dwarfs) \citealt{marois2008}, \citealt{marois2010}) ), is still a matter of debate \citealt{moya2010a}, , \citealt{moromartin2010}) )." + It is then timely to theoretically study the seismic propertiesof PMS y Dor in order to derive possible differences between their spectra and those of y Dor in the MS phase., It is then timely to theoretically study the seismic propertiesof PMS $\gamma$ Dor in order to derive possible differences between their spectra and those of $\gamma$ Dor in the MS phase. + This is the aim of this paper. which ts structured as follows.," This is the aim of this paper, which is structured as follows." + InSect., InSect. +"photoevaporationrate!,, at which point the remaining disc material is rapidly cleared.","photoevaporation, at which point the remaining disc material is rapidly cleared." + Viscous evolution alone with v«R predicts that accretion rates evolve as: where ἐν is the viscous timescale at [ι., Viscous evolution alone with $\nu\propto R$ predicts that accretion rates evolve as: where $t_{\nu}$ is the viscous timescale at $R_1$. + This evolution should therefore be observed in discs before XPE sets in., This evolution should therefore be observed in discs before XPE sets in. +" We can equate the fraction of disc-bearing pre-main sequence stars at a given time (fa), with the fraction of stars in the X-ray luminosity function that have luminosities less than a cut-off X-ray luminosity L.(fa)."," We can equate the fraction of disc-bearing pre-main sequence stars at a given time $f_d$ ), with the fraction of stars in the X-ray luminosity function that have luminosities less than a cut-off X-ray luminosity $L_c(f_d)$." +" In order for objects with X-ray luminosities equal to L« to be about to lose their discs, the viscous accretion rate must be equal to My,(Lc) at this point."," In order for objects with X-ray luminosities equal to $L_c$ to be about to lose their discs, the viscous accretion rate must be equal to $\dot{M}_w(L_c)$ at this point." +" We have performed this simple exercise using the disc fractions for nearby clusters compiled by Mamajek (2009), the Taurus X-ray luminosity function and the XPE theory developed above."," We have performed this simple exercise using the disc fractions for nearby clusters compiled by Mamajek (2009), the Taurus X-ray luminosity function and the XPE theory developed above." +" The result is shown in Figure 5,, where each point represents the current accretion rate off in a cluster implied by XPE."," The result is shown in Figure \ref{fig:null}, where each point represents the current accretion rate cut-off in a cluster implied by XPE." + We scale our results on disc fractions assuming an initial close binary fraction of by considering that the 0.3Myr old cluster NGC 2024 (Haisch et al., We scale our results on disc fractions assuming an initial close binary fraction of by considering that the 0.3Myr old cluster NGC 2024 (Haisch et al. +" 2001a), which shows a disc fraction of86%,, is too young for any disc to have been destroyed by photoevaporation or planet formation, but only through binary interactions."," 2001a), which shows a disc fraction of, is too young for any disc to have been destroyed by photoevaporation or planet formation, but only through binary interactions." +" The solid line in the plot represents a suitable fit of Equation 6 to the data, from this fit we can extract an initial accretion rate of Λ1.«(0)=5x10°°Mo yr-!and a viscous time of ty=7x 10°yr."," The solid line in the plot represents a suitable fit of Equation \ref{eqn:mdot} to the data, from this fit we can extract an initial accretion rate of $\dot{M}_*(0)=5\times10^{-8}$ and a viscous time of $t_\nu=7\times10^{5}$ yr." +" From these two values we can calculate an initial disc mass of Ma(0)=0.07Mo,, which is similar to the canonical value of the stellar mass) at which viscous angular momentum transport takes over from self-gravity."," From these two values we can calculate an initial disc mass of $M_d(0)=0.07$, which is similar to the canonical value of the stellar mass) at which viscous angular momentum transport takes over from self-gravity." +" Along with giving us appropriate initial conditions for our disc population model, the above also provides a stringent test of the hypothesis that X-rays are key to disc evolution and dispersal."," Along with giving us appropriate initial conditions for our disc population model, the above also provides a stringent test of the hypothesis that X-rays are key to disc evolution and dispersal." +" If the X-rays were not the dominant dispersal mechanism, there is no a priori reason to expect a ‘null’ model constructed only using knowledge of the X-ray luminosity function and observed disc fractions to reproduce a plausible evolution of the accretion rates seen in CTTs, both in terms of the time exponent (in Equation 6)) and its initial value."," If the X-rays were not the dominant dispersal mechanism, there is no a priori reason to expect a `null' model constructed only using knowledge of the X-ray luminosity function and observed disc fractions to reproduce a plausible evolution of the accretion rates seen in CTTs, both in terms of the time exponent (in Equation \ref{eqn:mdot}) ) and its initial value." +" In fact, increasing or decreasing the spread about the median of the Taurus X-ray luminosity function by a factor of ~5 or greater makes a fit of Equation 6 to the ‘null’ model impossible."," In fact, increasing or decreasing the spread about the median of the Taurus X-ray luminosity function by a factor of $\sim$ 5 or greater makes a fit of Equation \ref{eqn:mdot} to the `null' model impossible." +" Although this agreement could be fortuitous, it is reassuring that the X-ray luminosity function, disc lifetimes and accretion histories are consistent with our XPE hypothesis."," Although this agreement could be fortuitous, it is reassuring that the X-ray luminosity function, disc lifetimes and accretion histories are consistent with our XPE hypothesis." +" Furthermore, in order to uniquely specify the viscous evolution we must pick suitable values of a and R; which in turn specifies νο."," Furthermore, in order to uniquely specify the viscous evolution we must pick suitable values of $\alpha$ and $R_1$ which in turn specifies $\nu_0$." +" While any combination of R; and a that give the required viscous time will reproduce the same ‘null’ viscous model (i.e. non-photoevaporating), a disc evolution model that includes photoevaporation mildly breaks this degeneracy."," While any combination of $R_1$ and $\alpha$ that give the required viscous time will reproduce the same `null' viscous model (i.e. non-photoevaporating), a disc evolution model that includes photoevaporation mildly breaks this degeneracy." +" By performing a fit (by eye) of a viscously evolving photoevaporating disc population to the disc fractions used to derive the ‘null’ model we obtain values of a=2.5x107? and Γι= 18AU although due to the large scatter in the disc fractions and only mild breaking of the a, R, degeneracy, we estimate errors on these values of a factor of 2-3."," By performing a fit (by eye) of a viscously evolving photoevaporating disc population to the disc fractions used to derive the `null' model we obtain values of $\alpha=2.5\times 10^{-3}$ and $R_1=18$ AU although due to the large scatter in the disc fractions and only mild breaking of the $\alpha$, $R_1$ degeneracy, we estimate errors on these values of a factor of 2-3." +" In Figure 6 we show the obtained fit to the disc fractions compiled by Mamajek (2009) for our viscously evolving photoevaporating disc model with a single set of initial conditions: Ma(0)=0.07Mo,, a=2.5x10? and Ri= 18AU."," In Figure \ref{fig:df} we show the obtained fit to the disc fractions compiled by Mamajek (2009) for our viscously evolving photoevaporating disc model with a single set of initial conditions: $M_d(0)=0.07$, $\alpha=2.5\times10^{-3}$ and $R_1=18$ AU." +" Finally, Figure 7 shows the predicted evolution of accretion rate with time for individual disc models (each line shows the evolution of accretion rate with time for one disc model, for a given value of the X-ray photoevaporation rate)."," Finally, Figure \ref{fig:mdott} shows the predicted evolution of accretion rate with time for individual disc models (each line shows the evolution of accretion rate with time for one disc model, for a given value of the X-ray photoevaporation rate)." + This clearly shows that a spread in accretion rates, This clearly shows that a spread in accretion rates +the grid-based density field (centre column). showing a wealth of sub-grid structures. suggests that the tracer particles have the ability to provide a truly staggering improvement in resolution in the density field.,"the grid-based density field (centre column), showing a wealth of sub-grid structures, suggests that the tracer particles have the ability to provide a truly staggering improvement in resolution in the density field." + The improved resolution is all the more remarkable considering that the tracer particles are merely advected with the grid-based velocity tield at essentially no extra computational expense., The improved resolution is all the more remarkable considering that the tracer particles are merely advected with the grid-based velocity field at essentially no extra computational expense. + Column density plots such as those shown in Fig., Column density plots such as those shown in Fig. + 3. in general tend to highlight dense features. since all structures along the line of sight contribute to the projected field (which also tends to be the case in observations).," \ref{fig:coldens512} in general tend to highlight dense features, since all structures along the line of sight contribute to the projected field (which also tends to be the case in observations)." + The features in column density plots are therefore reflected by statistics such as the PDF (Figs. 6-—8)), The features in column density plots are therefore reflected by statistics such as the PDF (Figs. \ref{fig:pdflin}- \ref{fig:pdftails}) ) + and quantities such as the maximum density (Fig. 2)., and quantities such as the maximum density (Fig. \ref{fig:rhomax}) ). + However volumetric quantities such as the volume tilling factor of the material and the velocity field. reflected in statistics such as power spectra and structure functions. are better illustrated by cross-section slices.," However volumetric quantities such as the volume filling factor of the material and the velocity field, reflected in statistics such as power spectra and structure functions, are better illustrated by cross-section slices." + For this reason we show cross section slices of density at the midplane of the computational domain ἐς= 0.5). showing a resolution study of the initial shock development at | dynamical time (Fig. +))," For this reason we show cross section slices of density at the midplane of the computational domain $z=0.5$ ), showing a resolution study of the initial shock development at 1 dynamical time (Fig. \ref{fig:slicerho_t1}) )" +" and a comparison of the evolved snapshots at the end of the simulations (///.,= LO). showing only the highest resolution (Fig. 53)."," and a comparison of the evolved snapshots at the end of the simulations $t/t_{d}=10$ ), showing only the highest resolution (Fig. \ref{fig:slicerho_t10}) )." + The plots show the density tield using (left columns in Figs., The plots show the density field using (left columns in Figs. + 4. and 5). (centre column in both Figs.)," \ref{fig:slicerho_t1} and \ref{fig:slicerho_t10}) ), (centre column in both Figs.)" + and for the tracer particle density field computed from he calculations (right columns)., and for the tracer particle density field computed from the calculations (right columns). + Figs., Figs. + 4. and S show clearly that the grid results are better resolved in low density regions., \ref{fig:slicerho_t1} and \ref{fig:slicerho_t10} show clearly that the grid results are better resolved in low density regions. + The resolution in the SPH calculations is concentrated towards high density regions which till relatively little of the volume., The resolution in the SPH calculations is concentrated towards high density regions which fill relatively little of the volume. + Comparing individual shock structures in Fig., Comparing individual shock structures in Fig. + 4. shows that in general the shocks have better definition in TLASH.. with the shock widths in the highest resolution calculation similar to those obtained at 256* inFLASH.," \ref{fig:slicerho_t1} shows that in general the shocks have better definition in , with the shock widths in the highest resolution calculation similar to those obtained at $256^{3}$ in." + This is as might be expected given the relative crudeness of the shock capturing scheme (artificial. viscosity) in the SPH code compared to the PPM shock capturing scheme (2). employed inPLASH., This is as might be expected given the relative crudeness of the shock capturing scheme (artificial viscosity) in the SPH code compared to the PPM shock capturing scheme \citep{ColellaWoodward1984} employed in. +. In the more evolved snapshots (Fig. 59).," In the more evolved snapshots (Fig. \ref{fig:slicerho_t10}) )," + the grid results show many well-defined shock features in low density regions that are much less well resolved in the SPH calculations., the grid results show many well-defined shock features in low density regions that are much less well resolved in the SPH calculations. +" Some numerical artefacts are visible in the lowest resolution SPH calculations in the earliest snapshot (/=1/,. top left panel of Fig. 45» "," Some numerical artefacts are visible in the lowest resolution SPH calculations in the earliest snapshot $t=1 t_{d}$, top left panel of Fig. \ref{fig:slicerho_t1}) )" +"due to the ""breaking"" of the initial regular lattice on which the particles were placed as it is distorted by the flow.", due to the “breaking” of the initial regular lattice on which the particles were placed as it is distorted by the flow. + Interestingly similar artefacts are visible — and more accentuated — in the low resolution tracer particle plots (top right panel)., Interestingly similar artefacts are visible — and more accentuated — in the low resolution tracer particle plots (top right panel). + These effects are not obviously visible either in the SPH or the tracer particles at higher resolution (middle and bottom rows of Fig. 43) , These effects are not obviously visible either in the SPH or the tracer particles at higher resolution (middle and bottom rows of Fig. \ref{fig:slicerho_t1}) ) +or at later times (Fig. 5)), or at later times (Fig. \ref{fig:slicerho_t10}) ) +" once the particles have adopted a more ""natural"" arrangement.", once the particles have adopted a more `natural' arrangement. + There are no obvious artefacts at low resolution in the grid based calculation., There are no obvious artefacts at low resolution in the grid based calculation. + Density slices calculated from the tracer particles in the calculation are shown in the rightmost panels of Figs., Density slices calculated from the tracer particles in the calculation are shown in the rightmost panels of Figs. + 4 and 5.. using the SPH density summation (6)) iterated self-consistently with the smoothing length according to €7)).," \ref{fig:slicerho_t1} and \ref{fig:slicerho_t10}, using the SPH density summation \ref{eq:rhosum}) ) iterated self-consistently with the smoothing length according to \ref{eq:hrho}) )." + Comparison with the grid-based density field at | dynamical time. the tracer particles appear to substantially increase the resolution in high density regions.," Comparison with the grid-based density field at 1 dynamical time, the tracer particles appear to substantially increase the resolution in high density regions." + Whilst most of the features have close correspondence to those visible in the grid slices (centre column of Fig. 43).," Whilst most of the features have close correspondence to those visible in the grid slices (centre column of Fig. \ref{fig:slicerho_t1}) )," +" it is notable that a dense shock structure appears in the lower part of the LAE,=1 snapshots at all resolutions that is completely absent from both the SPH and grid density fields.", it is notable that a dense shock structure appears in the lower part of the $t/t_{d}=1$ snapshots at all resolutions that is completely absent from both the SPH and grid density fields. + The absence of this feature even at 512* in the centre column of Fig. 4..," The absence of this feature even at $512^{3}$ in the centre column of Fig. \ref{fig:slicerho_t1}," + yet clearly present at 128° in the tracer particles. suggests that it may be an artefact of tracer particles clustering below the grid seale.," yet clearly present at $128^{3}$ in the tracer particles, suggests that it may be an artefact of tracer particles clustering below the grid scale." + At later times (right panel of Fig. 5)), At later times (right panel of Fig. \ref{fig:slicerho_t10}) ) + this is even more evident by the fact that the tracer particles are strongly concentrated in high density regions and largely evacuated from low density regions (.e.. large parts of the panels are saturated at the density floor of the plot due to the absence of a contribution from tracer particles even with iterated smoothing lengths).," this is even more evident by the fact that the tracer particles are strongly concentrated in high density regions and largely evacuated from low density regions (i.e., large parts of the panels are saturated at the density floor of the plot due to the absence of a contribution from tracer particles even with iterated smoothing lengths)." + The difference between the density slices and column density plots shows that in general. (not the same as equal computational expense). SPH codes are better at resolving dense structures (highlighted by projections through the volume). whilst grid codes are better at resolving volumetric structures (highlighted by slices though the volume).," The difference between the density slices and column density plots shows that in general, (not the same as equal computational expense), SPH codes are better at resolving dense structures (highlighted by projections through the volume), whilst grid codes are better at resolving volumetric structures (highlighted by slices though the volume)." + Many studies have demonstrated that the density probability distribution function (PDF) in supersonic turbulence is well represented by a log-normal distribution (e.g.27222222). Le. where the mean of the logarithm of density Inp is related to the standard deviation σ of Inp by The appearance of a log-normal form in isothermal flows can be understood analytically as a consequence of the multiplicative central limit theorem assuming that individual density perturbations are independent and random (???). ," Many studies have demonstrated that the density probability distribution function (PDF) in supersonic turbulence is well represented by a log-normal distribution \citep[e.g.][]{pnj97,pvs98,klessen00,kritsuketal07,FederrathKlessenSchmidt2008,ls08,FederrathDuvalKlessenSchmidtMacLow2009}, i.e., where the mean of the logarithm of density $\ln \rho$ is related to the standard deviation $\sigma$ of $\ln \rho$ by The appearance of a log-normal form in isothermal flows can be understood analytically as a consequence of the multiplicative central limit theorem assuming that individual density perturbations are independent and random \citep{vs94,pvs98,np99}. ." +In physical terms this means that density fluctuations at a given location are constructed by successive passages of shocks with a jump amplitude independent of the local density ¢22?)..," In physical terms this means that density fluctuations at a given location are constructed by successive passages of shocks with a jump amplitude independent of the local density \citep{bpetal07,kritsuketal07,FederrathDuvalKlessenSchmidtMacLow2009}." + Furthermore the width of the PDF for Inp is found to be related to the rms Mach number according to where the factor b.z1/2 has been suggested by early numerical experiments (e.g.2)., Furthermore the width of the PDF for $\ln\rho$ is found to be related to the rms Mach number according to where the factor $b \approx 1/2$ has been suggested by early numerical experiments \citep[e.g.][]{pnj97}. + More recently ? find a much lower value of 6zz0.26 whilst ?. find 6=0.37., More recently \citet{kritsuketal07} find a much lower value of $b\approx 0.26$ whilst \citet{beetzetal08} find $b=0.37$. + 1 has also recently measured b.=0.5c0.05 in the Taurus Molecular Cloud. based on a method for inferring the 3D variance from 2D observations developed by ?..," \citet{brunt10} has also recently measured $b=0.5\pm 0.05$ in the Taurus Molecular Cloud, based on a method for inferring the 3D variance from 2D observations developed by \citet{bfp10a}." + ? and ? reconcile these results by showing that the width of the PDF depends not only on the RMS Mach number but also on the relative degree of compressible and solenoidal modes in the forcing. with b.=0.33 appropriate for purely solenoidal forcing and b=! for purely compressive forcing.," \citet{FederrathKlessenSchmidt2008} and \citet{FederrathDuvalKlessenSchmidtMacLow2009} reconcile these results by showing that the width of the PDF depends not only on the RMS Mach number but also on the relative degree of compressible and solenoidal modes in the forcing, with $b=0.33$ appropriate for purely solenoidal forcing and b=1 for purely compressive forcing." + ? — performing calculations ata range of Mach numbers — suggestthat the relationship (15)) should be adjusted. finding av=O72In(10.5.47)|0.20 from a three-parameter tit for hydrodynamic turbulence.," \citet{ls08} — performing calculations ata range of Mach numbers --- suggestthat the relationship \ref{eq:bfac}) ) should be adjusted, finding $\sigma^{2} = -0.72 \ln \left(1 + 0.5 \mathcal{M}^{2} \right) + 0.20$ from a three-parameter fit for hydrodynamic turbulence." + For the purposes of the comparison at hand we simply fit the PDFs using a single parameter b based on Eqs. (13)H€15))., For the purposes of the comparison at hand we simply fit the PDFs using a single parameter $b$ based on Eqs. \ref{eq:lognormal}) \ref{eq:bfac}) ). + Time-averaged PDFs of s—In(p/po) for the three SPH, Time-averaged PDFs of $s\equiv\ln(\rho/\rho_{0})$ for the three SPH +severe than that of the Earth due to the Moon's smaller mass.,severe than that of the Earth due to the Moon's smaller mass. + Comparing F, Comparing Fig. +"‘ie, 13. to Fig.", \ref{fig:moonlat} to Fig. + &bb shows this is inceec the case., \ref{fig:fevcomp1}b b shows this is indeed the case. + At high cuts. the variaion iu the latitude distribution teuds to the predicted cosie (see Fie.," At high cuts, the variation in the latitude distribution tends to the predicted cosine (see Fig." + 2 in Le Feuvre and Wieczorek. 2006).," 2 in Le Feuvre and Wieczorek, 2006)." + However. when examining the real case of all luiar ónipacis we see only a ~105€ (0.012+0.001 depression at the poles when taking the ratio of the cerived crater deusity within of the poles to the crater density in a baud centered ou tle equaor.," However, when examining the real case of all lunar impacts we see only a $\sim 10$ $0.912 \pm 0.004$ ) depression at the poles when taking the ratio of the derived crater density within of the poles to the crater density in a band centered on the equator." + In contrast. (their Fig.3) fiuc a polar/equatorial ratio of roughy609c.," In contrast, \citet{fev06} (their Fig.3) find a polar/equatorial ratio of roughly." +. The source oL this large cliscrepaucy is unclear since the Moon in our simulations had. zero orbital inclination aud spin obliquity. the same conditions used by LeFeuvreaudWieczorek (2006).. aud the latter also used the Bottkeef«£L.(2002) model as au impactor source.," The source of this large discrepancy is unclear since the Moon in our simulations had zero orbital inclination and spin obliquity, the same conditions used by \citet{fev06}, , and the latter also used the \citet{bottke02} model as an impactor source." + Despite the variation we observe being small. researehers should be aware of this spatial variation iu the crater distribution when determining ages of surfaces (see Sec. 6)).," Despite the variation we observe being small, researchers should be aware of this spatial variation in the crater distribution when determining ages of surfaces (see Sec.\ref{sec-con}) )." +from ?..,from \cite{2008MNRAS.384.1178B}. + Comparing the magnitudes and colors that we measure in (his paper with those in for clusters A. D. C and D. we find differences of V5 0.3mag and (V.—£)yx 0.Imag.," Comparing the magnitudes and colors that we measure in this paper with those in \cite{2009ApJ...698L..77H} for clusters A, B, C and D, we find differences of $V_0$$\leq$ 0.3mag and $(V-I)_0\leq$ 0.1mag." + For cluster 5. 2. measures a V magnitude of 18.5 (at ~2rj. which roughly corresponds to our annulus size).," For cluster S, \cite{2008AJ....135.1482S} measures a $V$ magnitude of 18.5 (at $\sim2r_h$, which roughly corresponds to our annulus size)." + As we measure }jy~18.5. the difference between our measurements is the exlinction value of 0.14.," As we measure $V_0$$\sim$ 18.5, the difference between our measurements is the extinction value of 0.14." +" Our crude estimate for the cluster magnitude limit is currently 95, 220 (M,z—4.8).", Our crude estimate for the cluster magnitude limit is currently $g'_{lim}$ $\approx 20$ $M_{g} \approx -4.8$ ). + We will quantify (his more accurately in an upcoming paper by inserüng lake clusters and testing recovery rates using our search methods., We will quantify this more accurately in an upcoming paper by inserting fake clusters and testing recovery rates using our search methods. + Although our eurrent search limit is comfortably aint. there are small numbers of süll less Iuminous clusters known (o exist in the Milky Way. for example (the laintlest. sparse Palomar-tvpe objects: see Figure 10)).," Although our current search limit is comfortably faint, there are small numbers of still less luminous clusters known to exist in the Milky Way, for example (the faintest, sparse Palomar-type objects; see Figure \ref{mv_rh}) )." + We can therefore place no quantitative limits on the numbers of such objects vet to be found in M33., We can therefore place no quantitative limits on the numbers of such objects yet to be found in M33. + Note that cluster D (2). is a magnitude fainter than our estimated limit. but was found with £57 mmaeing.," Note that cluster D \citep{2009ApJ...698L..77H} is a magnitude fainter than our estimated limit, but was found with $HST$ imaging." + We would not expect (o recover such a cluster independently with the MegaCam data., We would not expect to recover such a cluster independently with the MegaCam data. + Finally. we measured the structural parameters of all six outer clusters. including the concentration parameter. and core. hall-lisht and tidal radii;," Finally, we measured the structural parameters of all six outer clusters, including the concentration parameter, and core, half-light and tidal radii." + We use the GRIDFIT code described by ?.. which fits various Ixineg-tvpe cluster models convolved will the measured PSF to each object.," We use the GRIDFIT code described by \cite{2008MNRAS.384..563M}, which fits various King-type cluster models convolved with the measured PSF to each object." + Here we attempt to fit 2.. 2 and ? models to each object.," Here we attempt to fit \cite{1962AJ.....67..471K}, \cite{1966AJ.....71...64K} and \cite{1975AJ.....80..175W} + models to each object." + We also use (he KFIT2D code of ? with the ? model as an independent measure., We also use the KFIT2D code of \cite{2002AJ....124.2615L} with the \cite{1966AJ.....71...64K} model as an independent measure. + The results of all fits are shown in Table 4.. ancl examples of the fits are shown in Figures 8..," The results of all fits are shown in Table \ref{clusterradii}, and examples of the fits are shown in Figures \ref{radprofs}." + We also include an independent measurement of the hall-light radii using the curve of erowth of the clusters (r;4)., We also include an independent measurement of the half-light radii using the curve of growth of the clusters $_{ap}$ ). + For A and D. not all of the three models converged to successful fits. but the other four clusters gave high consistency among themselves for their radii.," For A and D, not all of the three models converged to successful fits, but the other four clusters gave high consistency among themselves for their radii." + Fitting models to cluster A was not successful because of its diffuse nature. while cluster D was extremely," Fitting models to cluster A was not successful because of its diffuse nature, while cluster D was extremely" +"?,, we adopt a standard index a=2.2.","\citet{drury}, we adopt a standard index $\alpha=2.2$." +" Thenormalization constant Qo can be obtained from the total power injected in relativistic protons and electrons, L,4=Lp+Le."," Thenormalization constant $Q_{0}$ can be obtained from the total power injected in relativistic protons and electrons, $L_{\rm{rel}}=L_{p}+L_{e}$." +" This power is assumed to be a fraction of the luminosity of the corona, Lia=qraLc, with qq=107? (?).."," This power is assumed to be a fraction of the luminosity of the corona, $L_{\rm{rel}}=q_{\rm rel} L_{\rm{c}}$, with $q_{\rm rel}=10^{-2}$ \citep{blandford02}." +" The way in which energy is divided between hadrons and leptons is unknown, but different scenarios can be taken into account by setting L,=ale."," The way in which energy is divided between hadrons and leptons is unknown, but different scenarios can be taken into account by setting $L_{p}=aL_{e}$." +" We consider models with a=100 (proton-dominated scenario, as for Galactic cosmic rays) and a=1 (equipartition between both species)."," We consider models with $a=100$ (proton-dominated scenario, as for Galactic cosmic rays) and $a=1$ (equipartition between both species)." +" To obtain the pion distribution, we use the pion injection due to pp collisions (?) and py interactions (?).."," To obtain the pion distribution, we use the pion injection due to $pp$ collisions \citep{fletcher} and $p \gamma$ interactions \citep{atoyan}." + The injection of muons is calculated using the expressions from ?.., The injection of muons is calculated using the expressions from \citet{lipari}. +" The target fields are those of the corona in the case of matter, and the corona-plus-disk for photons."," The target fields are those of the corona in the case of matter, and the corona-plus-disk for photons." +" Once the dominant energy loss process is identified, the transport equations can be decoupled without a significant loss of accuracy (say less than ~ 10%)."," Once the dominant energy loss process is identified, the transport equations can be decoupled without a significant loss of accuracy (say less than $\sim 10 \%$ )." + This approximation simplifies considerably the calculations., This approximation simplifies considerably the calculations. + A full treatment is being developed by the authors and preliminary results have been used for comparison and accuracy estimates., A full treatment is being developed by the authors and preliminary results have been used for comparison and accuracy estimates. +" Expressions to calculate the synchrotron spectrum can be found, for example, in ?.."," Expressions to calculate the synchrotron spectrum can be found, for example, in \citet{blumenthal}. ." + The power radiated by a single particle of energy E and pitch angle a is given by, The power radiated by a single particle of energy $E$ and pitch angle $\alpha$ is given by +This model is able to fit a wide range of observational constraints such as the Main Belt size distribution. the number of large asteroid families produced by the disruption of D> 100 km parent bodies over the past 3 to 4 Gyr. the existence of a D = 460 km crater on the intact basaltic crust of Vesta. and the relatively constant crater production rate of the Earth and Moon over the last 3 Gyr.,"This model is able to fit a wide range of observational constraints such as the Main Belt size distribution, the number of large asteroid families produced by the disruption of $D >$ 100 km parent bodies over the past 3 to 4 Gyr, the existence of a $D$ = 460 km crater on the intact basaltic crust of Vesta, and the relatively constant crater production rate of the Earth and Moon over the last 3 Gyr." + Later. Bottke et al. (2005b))," Later, Bottke et al. \cite{Bottke2005b}) )" + performed a study aimed at linking the collisional history of the asteroid Main Belt to its dynamical excitation and depletion., performed a study aimed at linking the collisional history of the asteroid Main Belt to its dynamical excitation and depletion. + This work combines the collistonal evolution code created by Bottke et al. (2005a)), This work combines the collisional evolution code created by Bottke et al. \cite{Bottke2005a}) ) + with dynamical results from Petit et al. (2001).," with dynamical results from Petit et al. \cite{Petit2001}) )," + as well as the removal of bodies from the Main. Belt due to the action of resonances and the Yarkovsky effect. which enter the near-Earth asteroid (NEA) population.," as well as the removal of bodies from the Main Belt due to the action of resonances and the Yarkovsky effect, which enter the near-Earth asteroid (NEA) population." + This collisional and dynamical evolution code also satisfies the above constraints and successfully reproduces the observed NEA size distribution., This collisional and dynamical evolution code also satisfies the above constraints and successfully reproduces the observed NEA size distribution. + It is worth noting that Bottke et al. (2005b)), It is worth noting that Bottke et al. \cite{Bottke2005b}) ) + validate the pseudo-time approximation proposed by Bottke et al. (2005a))., validate the pseudo-time approximation proposed by Bottke et al. \cite{Bottke2005a}) ). + Here. we construct a collisional model based on the one described in Bottke et al. (2005a))," Here, we construct a collisional model based on the one described in Bottke et al. \cite{Bottke2005a}) )" + with some dynamical considerations taken from Bottke et al. (2005b))., with some dynamical considerations taken from Bottke et al. \cite{Bottke2005b}) ). + From this. we track the simultaneous evolution of both the NEA and Main Belt populations by simulating the effects of an intense collisional evolution in the early massive Main Belt from the pseudo-time approximation proposed by those authors.," From this, we track the simultaneous evolution of both the NEA and Main Belt populations by simulating the effects of an intense collisional evolution in the early massive Main Belt from the pseudo-time approximation proposed by those authors." + The initial population used here follows the idea proposed by Bottke et al. (2005a. 2005b)).," The initial population used here follows the idea proposed by Bottke et al. \cite{Bottke2005a, Bottke2005b}) )." + In fact. our starting size distribution for D> 200 km uses the number of observed Main Belt asteroids. with a few objects added in. to account for the Eos and Themis parent bodies.," In fact, our starting size distribution for $D>$ 200 km uses the number of observed Main Belt asteroids, with a few objects added in, to account for the Eos and Themis parent bodies." + For ~ 120 300 km using the IRAS/color-albedo-derived diameters cited in Farinella Davis (1992)).," Moreover, they include the observed asteroids for $D >$ 300 km using the IRAS/color-albedo-derived diameters cited in Farinella Davis \cite{Farinella1992}) )." + For collisions. between Main Belt asteroids. the value adoptec in the collisional algorithm for the intrinsic collision probability is (Pj)= 2.86% I0 75 km 7 yr 7! and the mean impact velocity is (V)= 5.3 km s! (Bottke et al. 1994)).," For collisions between Main Belt asteroids, the value adopted in the collisional algorithm for the intrinsic collision probability is $\langle P_{\text{i}} \rangle =$ $ \times$ 10 $^{-18}$ km $^{-2}$ yr $^{-1}$ and the mean impact velocity is $\langle V \rangle = $ 5.3 km $^{-1}$ (Bottke et al. \cite{Bottke1994}) )." + To compute impacts on Ceres and Vesta. we use the particular values of (Pi) derived by O’Brien et al. (2011))," To compute impacts on Ceres and Vesta, we use the particular values of $\langle P_{\text{i}} \rangle$ derived by O'Brien et al. \cite{OBrien2011}) )" + for each of these bodies., for each of these bodies. + The values adopted for (P) are 3.70 x 1075 km yr7! for Ceres and 2.97 x 107! km 7 yr 7! for Vesta.," The values adopted for $\langle P_{\text{i}} +\rangle$ are 3.70 $\times$ $^{-18}$ $^{-2}$ $^{-1}$ for Ceres and 2.97 $\times$ $^{-18}$ km $^{-2}$ yr $^{-1}$ for Vesta." + As for the disruption law. we use the impact energy required for dispersal Oy derived by Benz Asphaug (1999)) for basalt at 3 ws 75.," As for the disruption law, we use the impact energy required for dispersal $Q_{D}$ derived by Benz Asphaug \cite{Benz1999}) ) for basalt at 3 s $^{-1}$." + While the mean impact velocity (V) for collisions between Main Belt asteroids is 5.3 kms7!. we adopt the Op law for 3 km s! since Bottke et al. (2005a))," While the mean impact velocity $\langle V \rangle$ for collisions between Main Belt asteroids is 5.3 km $^{-1}$ , we adopt the $Q_{D}$ law for 3 km $^{-1}$ since Bottke et al. \cite{Bottke2005a}) )" + show that it produces very good fits to the observational constraints., show that it produces very good fits to the observational constraints. + The differential fragment size distribution (FSD) produced by each catastrophic disruption event is represented by where D is the diameter. dN is the number of fragments in the size range (D.D+ dD). B is a constant. and p is the power-law index.," The differential fragment size distribution (FSD) produced by each catastrophic disruption event is represented by where $D$ is the diameter, $\text{d}N$ is the number of fragments in the size range $D$ $D+\text{d}D$ ), $B$ is a constant, and $p$ is the power-law index." + The FSDs used here are based on those observed in asteroid families like Themis or Flora (Bottke et al. 2005a))., The FSDs used here are based on those observed in asteroid families like Themis or Flora (Bottke et al. \cite{Bottke2005a}) ). + According to Tanga et al. (1999)).," According to Tanga et al. \cite{Tanga1999}) )," + the Themis family was produced by the super-catastrophic breakup of a D= 369 km body. while the Flora family was created by the barely-catastrophic breakup of a D= 164 km body.," the Themis family was produced by the super-catastrophic breakup of a $D =$ 369 km body, while the Flora family was created by the barely-catastrophic breakup of a $D =$ 164 km body." + Bottke et al. (2005a)), Bottke et al. \cite{Bottke2005a}) ) + show that FSDs resulting from super-catastrophic disruption events are represented well by a single p value. although this is not true for FSDs produced by barely-catastrophic breakups.," show that FSDs resulting from super-catastrophic disruption events are represented well by a single $p$ value, although this is not true for FSDs produced by barely-catastrophic breakups." + From this. Bottke et al. (2005a))," From this, Bottke et al. \cite{Bottke2005a}) )" + developed two different FSDs to describe the possible outcomes of a catastrophic collision., developed two different FSDs to describe the possible outcomes of a catastrophic collision. + On the one hand. for D> 150 km disruption events. the diameter of the largest remnant is assumed to be 50 the diameter of the parent body.," On the one hand, for $D >$ 150 km disruption events, the diameter of the largest remnant is assumed to be 50 the diameter of the parent body." + Moreover. the power-law index p of the differential FSD between the largest remnant and 1/60 the diameter of the parent body is -3.5. while the p value is -1.5 for smaller fragments.," Moreover, the power-law index $p$ of the differential FSD between the largest remnant and 1/60 the diameter of the parent body is -3.5, while the $p$ value is -1.5 for smaller fragments." + On the other hand. for disruption events amongD< 150 kn= bodies. the largest remnant is 80 the diameter of the pare=> body.," On the other hand, for disruption events among$D <$ 150 km bodies, the largest remnant is 80 the diameter of the parent body." + Moreover. the power-law index p of the differential FSD between the largest remnant and 1/3 the diameter of the pare=," Moreover, the power-law index $p$ of the differential FSD between the largest remnant and 1/3 the diameter of the parent" +mass content required within 100 ,mass content required within $''$ +Accretion processes are understood to be the non-sef-gravitating flow of a compressible astrophysical fluid. driven by the externa gravitational field of a massive astrophysical object. like an ordinary star or a compact object or. what is perhaps of greatest interes in the context of accretion studies. a black hole.,"Accretion processes are understood to be the non-self-gravitating flow of a compressible astrophysical fluid, driven by the external gravitational field of a massive astrophysical object, like an ordinary star or a compact object or, what is perhaps of greatest interest in the context of accretion studies, a black hole." + The matter falling into the potential well of an accretor is commonly modeled in terms of a fluid continuum. and standard. fluid dynamical equations. eustomized in the Newtonian framework of space and time. sufitice well to provide a satisfactory description of the entire accretion process (Frankeal.2002).," The matter falling into the potential well of an accretor is commonly modelled in terms of a fluid continuum, and standard fluid dynamical equations, customized in the Newtonian framework of space and time, suffice well to provide a satisfactory description of the entire accretion process \citep{fkr02}." +. While this be so. in recent times fractal modelling of astrojohysieal accretion is generating some interest (Roy2007:Roy&Ray3007).," While this be so, in recent times fractal modelling of astrophysical accretion is generating some interest \citep{roy07,rnr07}." +. One astrophysical material that ought readily o lend itself to a fractal approach — us opposed to a continuum approach — is the inerstellar medium (ISM)., One astrophysical material that ought readily to lend itself to a fractal approach — as opposed to a continuum approach — is the interstellar medium (ISM). + It is recognised that the ISM is not entirely to |be seen as a fluid continuum. and for many purposes the ISM is beieved to possess a self-similar hierarchical structure over several orders οmagnitude in scale (Larson1981:Falgaroneetal.1992:Heitjüusen1998).," It is recognised that the ISM is not entirely to be seen as a fluid continuum, and for many purposes the ISM is believed to possess a self-similar hierarchical structure over several orders of magnitude in scale \citep{lars,falg92,heith}." +.. Direct H absorption observaions and interstellar scintillation measurements suggest that the structure extends down to a scale of 10au (Crovisieretal.1985:Langer1995:Faison1998) and »ossibly even to sub-au scales (Hilletal.2005).," Direct H absorption observations and interstellar scintillation measurements suggest that the structure extends down to a scale of $10\, \mathrm{au}$ \citep{crov,lang,fais} and possibly even to $\mathrm{au}$ scales \citep{hill}." +. Numerous theories have attemped to explain the origin. evolution and mass distribuion of these clouds and it has been established. from boh observations (Elmegreen&Falgarone1996) and numerical simulations al.1998:Semelin&Combes 2000).. that the interstellar mediuim has a elumpy hierarchical self-similar structure wi ha Tactal dimension in three-dimensional space.," Numerous theories have attempted to explain the origin, evolution and mass distribution of these clouds and it has been established, from both observations \citep{elme} and numerical simulations \citep{burk,kless,seme}, that the interstellar medium has a clumpy hierarchical self-similar structure with a fractal dimension in three-dimensional space." + The main reason for this is still not wroperly understood. but it can be the consequence o an underlying fractal geometry that may arise due to turbulent processes in the mediurn.," The main reason for this is still not properly understood, but it can be the consequence of an underlying fractal geometry that may arise due to turbulent processes in the medium." + A comprehensive mathematical description of an accreting system — either a fluid continuum or a fractal structure — will necessarily 1ave to fall within the broad domain of nonlinear dynamics., A comprehensive mathematical description of an accreting system — either a fluid continuum or a fractal structure — will necessarily have to fall within the broad domain of nonlinear dynamics. + This is the principal basis of the analytical met10ds adopted for this study, This is the principal basis of the analytical methods adopted for this study. + Tn he context of spherically symmetric accretion. a previous work furnished a self-consistent description of tye hydrodynamies in a fractal medium (Roy2007).," In the context of spherically symmetric accretion, a previous work furnished a self-consistent description of the hydrodynamics in a fractal medium \citep{roy07}." +.. A similar description has been provided in this work for the case of a conserved rotational flow. which. from a general Huid dynamical perspective. has become quite thoroughly understood (Chandrasekhar1981).," A similar description has been provided in this work for the case of a conserved rotational flow, which, from a general fluid dynamical perspective, has become quite thoroughly understood \citep{sc81}." +". In the contex ) ""uccretion studies particularly. on many occasions such flows are devised to be an inviscid sub-Keplerian compressible flow. and as such. this model has become in accretion-related literature by now 2007)."," In the context of accretion studies particularly, on many occasions such flows are devised to be an inviscid sub-Keplerian compressible flow, and as such, this model has become well-established in accretion-related literature by now \citep{az81,fuk87, +c89,nf89,skc90,ky94,yk95,par96,msc96,skc96,lyyy97,das02,dpm03,ray03, +bdw04,das04,abd06,dbd06,crd06,gkrd07}." +. As a first step. the physical processes in a fractal medium have been analysed by fractional integration and differentiation therein)..," As a first step, the physical processes in a fractal medium have been analysed by fractional integration and differentiation \citep[][and references +therein]{zas}." + To do so. the fractal medium has had to be replaced by a continuous medium and the integrals on the network," To do so, the fractal medium has had to be replaced by a continuous medium and the integrals on the network" +»enetrate the interstellar dust far more casily than optical wavelengths.,penetrate the interstellar dust far more easily than optical wavelengths. + Furthermore. carly Ix. giants. which have by zw the highest space density for the giants. have a very restricted range of absolute magnitudes.," Furthermore, early K giants, which have by far the highest space density for the giants, have a very restricted range of absolute magnitudes." + This means that hey naturally form a dense clump on an infrarecl LR diagram., This means that they naturally form a dense clump on an infrared HR diagram. + At the distance of interest these giants will have a I magnitude of 12 to 14 making them simple to detect ina ew seconds on even a small telescope., At the distance of interest these giants will have a $K$ magnitude of 12 to 14 making them simple to detect in a few seconds on even a small telescope. + In this paper we assume that the distance to the GC is S προ and that all positions quoted. are on. the Galactic plane unless otherwise statec," In this paper we assume that the distance to the GC is 8 kpc, and that all positions quoted are on the Galactic plane unless otherwise stated." + We will also assume absolute magnitudes for IX2-31IE of Αιξ 1.65 Mg 1.5 and AM 0.89 as in Table 2 of Wainscoat et al. (, We will also assume absolute magnitudes for K2-3III of $M_K$ $-$ 1.65 $M_H$ $-$ 1.5 and $M_J$ $-$ 0.89 as in Table 2 of Wainscoat et al. ( +1992) and interstellar extinctions as given in Reike Lebolsky (1985) ο ly ΕΕ ο...,"1992) and interstellar extinctions as given in Reike Lebofsky (1985) $A_K$ $A_V$, $A_H$ $A_V$ and $A_J$ $A_V$." +" During 1999 June observations of a series of 20.12 arcmin fieles were observed alone the Galactic plane between f=0° and f=37"". using CALN. the facility Ht camera on"," During 1999 June observations of a series of $20\times12$ arcmin fields were observed along the Galactic plane between $l$ $^\circ$ and $l$ $^\circ$, using CAIN, the facility IR camera on" +The binary lreeuency we report here For brown dwarls in the Pleiades is consistent with that observed for similar objects. similar separation and mass ratio ranges (han in the field. as shown in Figure 7..,"The binary frequency we report here for brown dwarfs in the Pleiades is consistent with that observed for similar objects, similar separation and mass ratio ranges than in the field, as shown in Figure \ref{bin_freq_vs_spt_Pleiades+field}." + It is comparable to that of slightly more massive field late-Al/early-L cwarfs. and close to the lrequency observed for field T-dwaarls. which have masses comparable to the brown clwarls of our Pleiades sample.," It is comparable to that of slightly more massive field late-M/early-L dwarfs, and close to the frequency observed for field T-dwarfs, which have masses comparable to the brown dwarfs of our Pleiades sample." + Deep spectroscopic surveys on unbiased samples should provide answers to these questions and determine how many small mass ratio/small separation binaries we missed., Deep spectroscopic surveys on unbiased samples should provide answers to these questions and determine how many small mass ratio/small separation binaries we missed. + In his statistical analvsis of the photometric binary properties in the Pleiades. shows that the distribution of mass ratios lor late (wpe stars should be similar to that in the field.," In his statistical analysis of the photometric binary properties in the Pleiades, shows that the distribution of mass ratios for late type stars should be similar to that in the field." + The distribution is expected to be bimodal. with a major peak al q—0.4 and a minor one al o1.," The distribution is expected to be bimodal, with a major peak at $q$ =0.4 and a minor one at $\sim$ 1." + In a more recent observational study of unbiased samples of spectroscopic binaries of F to Ix dwarls in the field and in the Pleiades cluster. refine the results of in the range of periods shorter (than 10 vrs.," In a more recent observational study of unbiased samples of spectroscopic binaries of F to K dwarfs in the field and in the Pleiades cluster, refine the results of in the range of periods shorter than 10 yrs." + They report a dass ratio distribution with a primary peak al q—l. decreasing towards smaller mass ratios. with a broad secondary peak around q—0.4.," They report a mass ratio distribution with a primary peak at $q$ =1, decreasing towards smaller mass ratios, with a broad secondary peak around $q$ =0.4." + They observe no dillerence between the distributions of mass ratio of E.G and Ix stars. and find (hat (hese are identical in the field and in the Pleiacles.," They observe no difference between the distributions of mass ratio of F–G and K stars, and find that these are identical in the field and in the Pleiades." + If confirmed. the lack of multiple svstems with small mass ratios would then imply a major difference between the distributions of mass ratios (and therefore the formation and evolution processes) of late (vpe stars ancl brown dwarls.," If confirmed, the lack of multiple systems with small mass ratios would then imply a major difference between the distributions of mass ratios (and therefore the formation and evolution processes) of late type stars and brown dwarfs." + The current studies are inconclusive regarding that question since the observed lack might well be due (ο a combination of the following reasons:, The current studies are inconclusive regarding that question since the observed lack might well be due to a combination of the following reasons: +our results.,our results. +" In the tests of (2005),, this projected nfh-nearest-neighbor environment estimator proved to be the most robust indicator of local galaxy density for the DEEP2 survey."," In the tests of , this projected $n^{\rm th}$ -nearest-neighbor environment estimator proved to be the most robust indicator of local galaxy density for the DEEP2 survey." +" To correct for the redshift dependence of the DEEP2 sampling rate, each surface density value is divided by the median X3 of galaxies at that redshift within a window of Az=0.04; correcting the measured surface densities in this manner converts the “3 values into measures of overdensity relative to the median density by the notation 1+63 here) and effectively accounts(given for the redshift variations in the selection rate2005)."," To correct for the redshift dependence of the DEEP2 sampling rate, each surface density value is divided by the median $\Sigma_3$ of galaxies at that redshift within a window of $\Delta z = 0.04$; correcting the measured surface densities in this manner converts the $\Sigma_3$ values into measures of overdensity relative to the median density (given by the notation $1 + \delta_3$ here) and effectively accounts for the redshift variations in the selection rate." +". Finally, to minimize the effects of edges and holes in the survey geometry, we exclude all galaxies within 1 h-! comoving Mpc of a survey boundary, reducing our sample to 17,767 galaxies in the redshift range 0.75 \! 10^{10.8}\ {\rm M}_{*}/h^{-2}\ {\rm + M}_{\sun}$ independent of color, but preferentially misses red galaxies at lower masses Figure \ref{cmd_fig}) )." +" Figure 1 shows the distribution of galaxies in magnitude space for the entire DEEP2 sample at 0.75«« 1.25, with lines of constant stellar mass overlaid."," Figure \ref{cmd_fig} shows the distribution of galaxies in color-magnitude space for the entire DEEP2 sample at $0.75 < z < +1.25$ , with lines of constant stellar mass overlaid." +" As shown in many previous studies2008),, selecting by stellar mass as opposed to optical luminosity selects a different portion of the galaxy population due to the dependence of stellar mass-to-light ratio on rest-frame color."," As shown in many previous studies, selecting by stellar mass as opposed to optical luminosity selects a different portion of the galaxy population due to the dependence of stellar mass-to-light ratio on rest-frame color." + A B-band luminosity-selected sample is biased towards lower stellar masses for blue galaxies and higher stellar masses for red galaxies., A $B$ -band luminosity-selected sample is biased towards lower stellar masses for blue galaxies and higher stellar masses for red galaxies. +" Now, both locally and at z1, the local environment of galaxies on the red sequence has been shown to depend on luminosity such that more luminous systems favor higher-density regions on average2006)."," Now, both locally and at $z \sim 1$ , the local environment of galaxies on the red sequence has been shown to depend on luminosity such that more luminous systems favor higher-density regions on average." +". Thus, relative to à random population of blue galaxies, red galaxies of equivalent stellar mass will be (less luminous and) in lower-density environments than red galaxies selected to have the same luminosity."," Thus, relative to a random population of blue galaxies, red galaxies of equivalent stellar mass will be (less luminous and) in lower-density environments than red galaxies selected to have the same luminosity." +" That is, taking into account the known correlation between local environment and galaxy luminosity, for a galaxy sample selected to have fixed stellar mass (versus fixed one expects to find a weaker color-densityluminosity) relation."," That is, taking into account the known correlation between local environment and galaxy luminosity, for a galaxy sample selected to have fixed stellar mass (versus fixed luminosity) one expects to find a weaker color-density relation." +" However, it remains unclear whether or not the correlation between galaxy environment and rest-frame color found at fixed luminosity at z~1 is entirely a projection of the correlation(Cooper between2006) environment and luminosity in concert with the dependence of stellar mass-to-light ratio on color such that at fixed stellar mass there is no color-density relation."," However, it remains unclear whether or not the correlation between galaxy environment and rest-frame color found at fixed luminosity at $z \sim 1$ is entirely a projection of the correlation between environment and luminosity in concert with the dependence of stellar mass-to-light ratio on color such that at fixed stellar mass there is no color-density relation." +" As discussed in l, several recent analyses have arrived at this conclusion."," As discussed in \ref{sec_intro}, several recent analyses have arrived at this conclusion." +" As highlighted in 81, the goal of this work is to study the relationship between galaxy color and local environment at fixed stellar mass."," As highlighted in \ref{sec_intro}, the goal of this work is to study the relationship between galaxy color and local environment at fixed stellar mass." + Recent analyses using a variety of data sets have approached this task using galaxy samples in stellar-mass-selected bins across a range of environments., Recent analyses using a variety of data sets have approached this task using galaxy samples in stellar-mass-selected bins across a range of environments. +" Here, we first investigate whether this methodology is appropriate."," Here, we first investigate whether this methodology is appropriate." +" Finding it is not — that is, finding that the stellar mass function is different in different environments — we then apply improved techniques which account for the correlation between stellar mass and environment in an examination of the color-density relation at z~1."," Finding it is not — that is, finding that the stellar mass function is different in different environments — we then apply improved techniques which account for the correlation between stellar mass and environment in an examination of the color-density relation at $z \sim 1$." +" In contrast to recent results in the literature, we find that there is a significant color-density relation at fixed stellar mass."," In contrast to recent results in the literature, we find that there is a significant color-density relation at fixed stellar mass." + 'The most likely reason for this discrepancy is that both larger measurement errors and systematics in other data sets smear out the underlying environment dependence., The most likely reason for this discrepancy is that both larger measurement errors and systematics in other data sets smear out the underlying environment dependence. +" Finally, we emphasize that absence of evidence is not evidence of that is, not finding a correlation between color and environment at fixed stellar mass does not directly indicate an intrinsic lack of correlation."," Finally, we emphasize that absence of evidence is not evidence of that is, not finding a correlation between color and environment at fixed stellar mass does not directly indicate an intrinsic lack of correlation." +" By making such an assumption, the conclusions of several recent analyses have been rendered difficult to interpret."," By making such an assumption, the conclusions of several recent analyses have been rendered difficult to interpret." +" In order to study the relationship between galaxy properties and environment at fixed stellar mass, the galaxy sample under study is often restricted to a narrow range in stellar mass such that correlations between"," In order to study the relationship between galaxy properties and environment at fixed stellar mass, the galaxy sample under study is often restricted to a narrow range in stellar mass such that correlations between" +M85 and M99 means that the pre-explosionSpitzer limits on M85-OT and 110fqs are not deep enough by a factor of few to constrain their progenitors to similar depths (see Figure 12)).,M85 and M99 means that the pre-explosion limits on M85-OT and 10fqs are not deep enough by a factor of few to constrain their progenitors to similar depths (see Figure \ref{fig:prog_mir}) ). + M85-OT is located in the lenticular galaxy M85 (also in the Virgo cluster)., M85-OT is located in the lenticular galaxy M85 (also in the Virgo cluster). +" Fortunately, this galaxy was observed"," Fortunately, this galaxy was observed" +"by active regions that cover a substantial fraction of the stellar photosphere (e.g.,????)..","by active regions that cover a substantial fraction of the stellar photosphere \citep[e.g.,][]{Wolter2009, Czesla2009, Huber2009, Huber2010}." +" This high level of activity, mainly diagnosed by photospheric spots, is expected to be also detectable in chromospheric lines excited by enhanced chromospheric heating."," This high level of activity, mainly diagnosed by photospheric spots, is expected to be also detectable in chromospheric lines excited by enhanced chromospheric heating." +" Indeed, sshows strong chromospheric emission-line cores in its lines as well as in the Ca IRT lines."," Indeed, shows strong chromospheric emission-line cores in its lines as well as in the Ca IRT lines." +" We quantified the strength of the emission by determining the Mt. Wilson S-index and a logRi, value of 4.458+0.051.", We quantified the strength of the emission by determining the Mt. Wilson S-index and a $\log{R'_{\mathrm{HK}}}$ value of $4.458\pm0.051$. + Our results agree well with those reported by ? and place aamong the most active known planet host-stars., Our results agree well with those reported by \citet{Knutson2010} and place among the most active known planet host-stars. +" Furthermore, we studied the CaIRT and derived a value of 0.298+0.006 for the Κιτ index, which again demonstrates that iis a highly active star."," Furthermore, we studied the CaIRT and derived a value of $0.298\pm0.006$ for the $R_\mathrm{IRT}$ index, which again demonstrates that is a highly active star." + The presence of starspots and strong chromospheric heating suggests that coronal heating is substantial as well., The presence of starspots and strong chromospheric heating suggests that coronal heating is substantial as well. +" Indeed, our 15 ks oobservation yields a clear detection of coronal X-ray emission characterizedby a thermal spectrum with a temperature of 1 keV. Combining CoRoT-2A'ss X-ray luminosity of 1.9x10? wwith its spectral type of G7, we derived an activity level of—4.2,, showing that iis a very active star also by X-ray standards."," Indeed, our 15 ks observation yields a clear detection of coronal X-ray emission characterizedby a thermal spectrum with a temperature of $1$ keV. Combining s X-ray luminosity of $1.9\times 10^{29}$ with its spectral type of G7, we derived an activity level of, showing that is a very active star also by X-ray standards." +" Although optical studies (??) suggested a large inhomogeneity in the distribution of active regions, which is very likely also true for the distribution of X-ray emission across the stellar disk, an X-ray transit could neither be detected in the X-ray count rate nor in the hardness ratio."," Although optical studies \citep{Lanza2009, Huber2010} suggested a large inhomogeneity in the distribution of active regions, which is very likely also true for the distribution of X-ray emission across the stellar disk, an X-ray transit could neither be detected in the X-ray count rate nor in the hardness ratio." + This indicates that either no prominent source of X-ray emission was occulted during this particular transit or that the emission is distributed too homogeneously to cause an X-ray transit detectable with Chandra., This indicates that either no prominent source of X-ray emission was occulted during this particular transit or that the emission is distributed too homogeneously to cause an X-ray transit detectable with . +". In any case, we emphasize that our ssnapshot covers no more than 4 the optically observed “beating pattern"" (e.g.,?) with a period of ~50 d, so that it remains insufficient to obtain a representative picture of CoRoT-2A’ss corona."," In any case, we emphasize that our snapshot covers no more than $4$ the optically observed “beating pattern” \citep[e.g.,][]{Alonso2008} with a period of $\approx 50$ d, so that it remains insufficient to obtain a representative picture of s corona." + One of the key quantities needed to understand the evolution not only of the ssystem but of all planetary systems is their age., One of the key quantities needed to understand the evolution not only of the system but of all planetary systems is their age. +" Based on our analysis, we appliedseveral techniques to estimate the age ofCoRoT-2A."," Based on our analysis, we appliedseveral techniques to estimate the age of." +". From the EW of the lithium line at 6708 iin the spectrum ofCoRoT-2A,, we inferred an age comparable with that of the Pleiades, ie., ~100 Ma."," From the EW of the lithium line at $6708$ in the spectrum of, we inferred an age comparable with that of the Pleiades, i.e., $\approx 100$ Ma." +" Furthermore, we derived a Li abundance of Aj;=+2.6 dex, which suggests an age between 100 and 250 Ma."," Furthermore, we derived a Li abundance of $A_\mathrm{Li}=+2.6$ dex, which suggests an age between 100 and 250 Ma." +" Applying the relation provided by ?,Eq.1,, we used the strength of the eemission-line cores measured by the logAj, index to estimate a “chromospheric age"" of 670*290 Ma for CoRoT-2A.."," Applying the relation provided by \citet[][Eq.~1]{Donahue1998}, we used the strength of the emission-line cores measured by the $\log{R'_{\mathrm{HK}}}$ index to estimate a “chromospheric age” of $670^{+200}_{-280}$ Ma for ." + The coronal activity provides another age estimate., The coronal activity provides another age estimate. +" Using the relation between X-ray luminosity and age for late-F to early-M dwarfs presented in ?,, we calculated an age of 230*200 Ma."," Using the relation between X-ray luminosity and age for late-F to early-M dwarfs presented in \citet{SanzF2010}, we calculated an age of $230_{-40}^{+200}$ Ma." + An additional estimate can be obtained from gyrochronology., An additional estimate can be obtained from gyrochronology. +" Using the relation presented by ?,, we determined an age of 76+7 Ma forC"," Using the relation presented by \citet{Barnes2007}, we determined an age of $76\pm7$ Ma for." +"oRoT-2A.. However, ? note that gyrochronology tends to underestimate the stellar age if (B-V) >0.6, which is true forCoRoT-2A,, owing to the sparseness of the open cluster sample used for calibration in case of blue stars."," However, \citeauthor{Barnes2007} note that gyrochronology tends to underestimate the stellar age if $($ $)>0.6$, which is true for, owing to the sparseness of the open cluster sample used for calibration in case of blue stars." +" ? modeled the evolution of the star, CoRoT-2A,, and its planet simultaneously and found two classes of solutions reproducing the observed properties of the ssystem: first, a solution in which iis a very young star with an age of 30 to 40 Ma and second, a solution with a more evolved main-sequence host-star with an age of 130 to 500 Ma."," \citet{GuillotHavel2011} modeled the evolution of the star, , and its planet simultaneously and found two classes of solutions reproducing the observed properties of the system: first, a solution in which is a very young star with an age of $30$ to $40$ Ma and second, a solution with a more evolved main-sequence host-star with an age of $130$ to $500$ Ma." +" None of the above age indicators, not even the gyrochronological age estimate, favors the solution with a very young host-star, rendering this class of evolutionary scenarios found by ? unlikely."," None of the above age indicators, not even the gyrochronological age estimate, favors the solution with a very young host-star, rendering this class of evolutionary scenarios found by \citet{GuillotHavel2011} unlikely." +" In summary, we conclude that combining our outcomes with published results both observational and theoretical favors an age between 100 and 300 Ma forCoRoT-2A."," In summary, we conclude that combining our outcomes with published results both observational and theoretical favors an age between 100 and 300 Ma for." +". This suggests that iis a young main-sequence star that has already left the zero-age main sequence, which for a G7 star of solar mass is situated at an age of 30 Ma (?).."," This suggests that is a young main-sequence star that has already left the zero-age main sequence, which for a G7 star of solar mass is situated at an age of 30 Ma \citep{Siess2000}." + Photometric colors are often used for a rough spectral classification., Photometric colors are often used for a rough spectral classification. + The magnitudes provided by SIMBAD yield a B-V color index of 0.854 mag forCoRoT-2A., The magnitudes provided by SIMBAD yield a B-V color index of $0.854$ mag for. +". Comparing this value with the color index expected for a G7 star of age 200 Ma with slightly increased metallicity (Z=0.01) (?)., we calculated a color excess ofmag."," Comparing this value with the color index expected for a G7 star of age $200$ Ma with slightly increased metallicity $0.01$ ) \citep{Siess2000}, we calculated a color excess of." +". Thus, aappears redder than expected; we attribute this to interstellar extinction."," Thus, appears redder than expected; we attribute this to interstellar extinction." +" Combining the B-V color excess with the relation given by 9 we obtain a column density of 9x107° cm, which is consistent with the upper limit of 2x10?! cm? derived from our X-ray observations."," Combining the B-V color excess with the relation given by \citet{Bohlin1978} + we obtain a column density of $9\times 10^{20}$ $^{-2}$ , which is consistent with the upper limit of $2\times 10^{21}$ $^{-2}$ derived from our X-ray observations." +" Converting the EWs of the interstellar Na D absorption lines into a column density of via the line-ratio method (?),, we obtained another consistent estimate of ~10?!cm? for the hydrogen column density (?).."," Converting the EWs of the interstellar Na D absorption lines into a column density of via the line-ratio method \citep{Stromgren1948}, we obtained another consistent estimate of $\approx 10^{21}~\textrm{cm}^{-2}$ for the hydrogen column density \citep{Ferlet1985}." +" Assuming a density of one particle per cm? for the interstellar medium, the hydrogen column density inferred from the color excess directly translates into a distance estimate of 290 pc, which is consistent with our previous estimate of 270 pc."," Assuming a density of one particle per $^{3}$ for the interstellar medium, the hydrogen column density inferred from the color excess directly translates into a distance estimate of $290$ pc, which is consistent with our previous estimate of $270$ pc." +" According to our spectroscopic analysis, ccan be classified as a G7-type dwarf and, according to the evolutionary model, should have an absolute visual brightness of 5.1 mag."," According to our spectroscopic analysis, can be classified as a G7-type dwarf and, according to the evolutionary model, should have an absolute visual brightness of $5.1$ mag." +" Assuming a value of R=3.1 (?) for the ratio of total visual extinction, Ay, and E(B-V), we derive for CoRoT-2A."," Assuming a value of $R=3.1$ \citep{Schultz1975} for the ratio of total visual extinction, $_V$ , and , we derive for ." +". Combining this with the apparent visual brightness of 12.57mag, we derived an extinction-corrected spectroscopic parallax of 250 pc."," Combining this with the apparent visual brightness of $12.57$mag, we derived an extinction-corrected spectroscopic parallax of $250$ pc." + In Sect., In Sect. + 2.7 we estimated the distance to the ssystem from the Wilson-Bappu width of the eemission linecores and obtained 140*°-40 to 1908)0 pe depending onthe details of the calibration., \ref{sec:ActivityIndicators} we estimated the distance to the system from the Wilson-Bappu width of the emission linecores and obtained $140_{-40}^{+50}$ to $190_{-50}^{+60}$ pc depending onthe details of the calibration. + We further, We further +»hotosphliere is shown in FigureoO ??bb. The spectrum is in oOgood agreemente with the calibration of the peak-up image with an average flux across the 13-26 jmi passband of the peak-up array of 83 mJv. compared wilh the 8848 mJv measured in (he peak-up images.,"photosphere is shown in Figure \ref{HD69830LoRes}b b. The spectrum is in good agreement with the calibration of the peak-up image with an average flux across the 18-26 $\mu$ m passband of the peak-up array of 83 mJy, compared with the $\pm$ 8 mJy measured in the peak-up images." + The average7 to 35 yam spectrum shows qualitatively the same features as in with nunerous features [rom small grains evident throughout the spectrum., The average7 to 35 $\mu$ m spectrum shows qualitatively the same features as in with numerous features from small grains evident throughout the spectrum. + Luprovements from the additional observing time include higher signal (o noise ratios al longer wavelengths and better control of svstematics around 3 and 14 pam. We use this improved spectrum for mineralogical analvsis in 6?? below., Improvements from the additional observing time include higher signal to noise ratios at longer wavelengths and better control of systematics around 8 and 14 $\mu$ m. We use this improved spectrum for mineralogical analysis in $\S$ \ref{model} below. +" We put a limit on any temporal variations across (he 1. vear observing sequence [ον the best LoRes data by noting that the uncertainty in (he average excess. GF4,4/Fauci. averaged over the ranges with significant excess. 9.5-11.5 aand 16-32jan.. is and per spectral element. respectively."," We put a limit on any temporal variations across the 1 year observing sequence for the best LoRes data by noting that the uncertainty in the average excess, $\sigma F_{dust}/ F_{dust}$, averaged over the ranges with significant excess, 9.5-11.5 and 16-32, is and per spectral element, respectively." + These variations are only slightly larger than the variation seen in (he spectra of ILD68146 which showed no fractional excess al the level of 2—3%3t on three separate occasions across the whole 7 to 35 bband., These variations are only slightly larger than the variation seen in the spectra of HD68146 which showed no fractional excess at the level of $2-3$ on three separate occasions across the whole 7 to 35 band. + Figure ??bb shows that the differences in the fractional excess Irom each spectrum relative to the average is ~1% in regions of good SNR and away [rom a few bad pixels., Figure \ref{HD69830LoRes}b b shows that the differences in the fractional excess from each spectrum relative to the average is $\sim$ in regions of good SNR and away from a few bad pixels. + The average LoRes spectrum is available in electronic form (Table 4))., The average LoRes spectrum is available in electronic form (Table \ref{IRSLRSdata}) ). + To facilitate (he search for narrow spectral features in the HiRes spectrum. we sublractecl a spline curve fitted to a running median-smoothed (25 point) version of the spectrum.," To facilitate the search for narrow spectral features in the HiRes spectrum, we subtracted a spline curve fitted to a running median-smoothed (25 point) version of the photosphere-subtracted spectrum." + We applied a 5 point smoothing (Llammine) filter with weights (0.04. 0.24.0.45. 0.24.0.04). corresponding roughly to the Hikes instrumental response. for further rejection of bad pixels and residual linge.," We applied a 5 point smoothing (Hamming) filter with weights (0.04, 0.24,0.45, 0.24,0.04), corresponding roughly to the HiRes instrumental response, for further rejection of bad pixels and residual fringing." + Close-ups of the filtered. star-subtracted spectrum are shown in Fieure 5..," Close-ups of the filtered, star-subtracted spectrum are shown in Figure \ref{FlattenHiresPanels}." + The local maxima in this spectrum do not stand out above (he noise to a significant degree. nor do they line up with anv prominent known spectral features.," The local maxima in this spectrum do not stand out above the noise to a significant degree, nor do they line up with any prominent known spectral features." + In most cases local maxima al ~36 can be traced back to artifacts in (he raw data or to complex structure in the small-erain emission., In most cases local maxima at $\sim3\sigma$ can be traced back to artifacts in the raw data or to complex structure in the small-grain emission. + Upper limits on the fluxes at interesting line locations are given in Table 5.., Upper limits on the fluxes at interesting line locations are given in Table \ref{HiResLines}. . + Simulated spectral lines at the level of our upper limits are shown (Figure 5))., Simulated spectral lines at the level of our upper limits are shown (Figure \ref{FlattenHiresPanels}) ). +indicate the profile error-bars derived assuming Poisson statistics.,indicate the profile error-bars derived assuming Poisson statistics. + In the same Fig., In the same Fig. +" 2 we fit the profile with a King (1962) model, adopting king parameters (core and tidal radius, and center mass density) from Harris (1996) compilation."," 2 we fit the profile with a King (1962) model, adopting king parameters (core and tidal radius, and center mass density) from Harris (1996) compilation." +" The fit is good within the uncertainties, and therefore we conclude that Arp 2 follows a like density profile."," The fit is good within the uncertainties, and therefore we conclude that Arp 2 follows a King-like density profile." +" It decreases all the way to the edge of the field we covered, slightly beyond the nominal half-mass radius."," It decreases all the way to the edge of the field we covered, slightly beyond the nominal half-mass radius." + The resulting color magnitude diagrams (CMDs) are shown in the two panels of Fig., The resulting color magnitude diagrams (CMDs) are shown in the two panels of Fig. + 3., 3. +" In the left panel, the V versus B-V diagram is shown, while in the right panel we present the V versus V-I. The CMD on the left panel is absolutely identical to the one presented by Buonanno et al.(1994), apart from the slightly different area coverage and the magnitude limit, which in our case is about one magnitude fainter."," In the left panel, the V versus B-V diagram is shown, while in the right panel we present the V versus V-I. The CMD on the left panel is absolutely identical to the one presented by Buonanno et al.(1994), apart from the slightly different area coverage and the magnitude limit, which in our case is about one magnitude fainter." + All the typical features of a globular cluster CMD are present., All the typical features of a globular cluster CMD are present. +" The MS, RGB, HB -located entirely blue-ward the RR Lyrae instability strip-, and the Asimptotic Giant Branch (AGB)."," The MS, RGB, HB -located entirely blue-ward the RR Lyrae instability strip-, and the Asimptotic Giant Branch (AGB)." +" An additional feature which has been overlooked in the past is the plume of blue stars right above the turn off point (TO), which is quite common in globular clusters, and it is composed of candidate blue straggler stars."," An additional feature which has been overlooked in the past is the plume of blue stars right above the turn off point (TO), which is quite common in globular clusters, and it is composed of candidate blue straggler stars." + This plume is the target of our investigation., This plume is the target of our investigation. +" We look for BSS candidates following the commonly used criteria (Ahumada Lapasset 1995, 2007; Sandage 1953), which is illustrated in Fig."," We look for BSS candidates following the commonly used criteria (Ahumada Lapasset 1995, 2007; Sandage 1953), which is illustrated in Fig." + 4., 4. +" Together with BSS (blue box), we also indicated the location of HB (red box), RGB (red dots), and a sample of MS stars (yellow box), which we are going to compare."," Together with BSS (blue box), we also indicated the location of HB (red box), RGB (red dots), and a sample of MS stars (yellow box), which we are going to compare." +" We counted 41 BSS candidates, and 28 HB stars."," We counted 41 BSS candidates, and 28 HB stars." +" They are listed in Table 1 and 2, respectively, where we indicate stars' identification (our numbering, ID), equatorial coordinates for the 2000.0 equinox, magnitude V and color B-V. These can also be useful for future spectro-scopic Besides, again following Fig 4, we counted 213 RGB and 517 MS stars, which we do not list here for space reasons."," They are listed in Table 1 and 2, respectively, where we indicate stars' identification (our numbering, ID), equatorial coordinates for the 2000.0 equinox, magnitude V and color B-V. These can also be useful for future spectro-scopic Besides, again following Fig 4, we counted 213 RGB and 517 MS stars, which we do not list here for space reasons." +" As for MS stars, we stress that they have been extracted in a region of the MS which is not affected by We stress that the numbers we reported have been computed using the classical definition of BSS locus and assuming that contamination from field stars is negligible, which seems to be the case, since the field of view is very small (0.0044 squared degrees)."," As for MS stars, we stress that they have been extracted in a region of the MS which is not affected by We stress that the numbers we reported have been computed using the classical definition of BSS locus and assuming that contamination from field stars is negligible, which seems to be the case, since the field of view is very small (0.0044 squared degrees)." +" However, we do not have at our disposal a control field to verify this directly."," However, we do not have at our disposal a control field to verify this directly." +" Therefore, we investigated the amount of contamination by computing synthetic CMDs of stars in the direction of Arp 2 assuming a Galactic model which includes bulge, halo, thin and thick disks (Girardi et a. 2005)."," Therefore, we investigated the amount of contamination by computing synthetic CMDs of stars in the direction of Arp 2 assuming a Galactic model which includes bulge, halo, thin and thick disks (Girardi et a. 2005)." + We generated several CMDs by varying the random seed and added photometric errors as from Arp 2 photometry., We generated several CMDs by varying the random seed and added photometric errors as from Arp 2 photometry. + The results are shown in Fig., The results are shown in Fig. +" 5, where the left panel shows the Galaxy CMD in the direction of Arp 2, and the right panel the CMD of Arp 2 as in Fig."," 5, where the left panel shows the Galaxy CMD in the direction of Arp 2, and the right panel the CMD of Arp 2 as in Fig." + 4., 4. + In both panel we indicate the boxes used for selecting HB (red) and BSS (blue) stars., In both panel we indicate the boxes used for selecting HB (red) and BSS (blue) stars. +" A quick glance at this figure is sufficient to conclude that most of the contamination affects the lower MS, and in general contaminating stars are redder than the typical BSS colors."," A quick glance at this figure is sufficient to conclude that most of the contamination affects the lower MS, and in general contaminating stars are redder than the typical BSS colors." +" Some contamination is present in the RGB area but, provided the high number of RGB stars in Arp 2, we do not expect their statistics to be significantly affected."," Some contamination is present in the RGB area but, provided the high number of RGB stars in Arp 2, we do not expect their statistics to be significantly affected." +" To properly assess the probable membership of BSS, it is necessary to measure their radial velocity or their proper motion (Mathieu Geller 2009; Liu et al."," To properly assess the probable membership of BSS, it is necessary to measure their radial velocity or their proper motion (Mathieu Geller 2009; Liu et al." + 2008)., 2008). +" Since we are relying only on photometry, we will keep considering our BSS as candidates, based on their location in the CMD."," Since we are relying only on photometry, we will keep considering our BSS as candidates, based on their location in the CMD." +" To get more insight on their properties and origin, we started by considering their surface distribution, and compared it with the surface distribution of HB stars."," To get more insight on their properties and origin, we started by considering their surface distribution, and compared it with the surface distribution of HB stars." +" This is illustrated in Fig 6, which shows radial density profile of the two populations."," This is illustrated in Fig 6, which shows radial density profile of the two populations." + Here we plot the number of stars per squared arcmin as computed in concentric bins 10 arcsecs wide., Here we plot the number of stars per squared arcmin as computed in concentric bins 10 arcsecs wide. +" Except for the difference in the inner side of the cluster, the two profiles are identical."," Except for the difference in the inner side of the cluster, the two profiles are identical." +" We stress that the difference in the very central bin, although real, is exagerated by the small number"," We stress that the difference in the very central bin, although real, is exagerated by the small number" +The radio-pulsar system PSR JO737-3039 is the only. binary pulsar kuown to cousist of two racli pulsars: PSR JO737-3039 A (Bureayetal.2003) and PSR J0737-3039 B (Lyneetal.2001)..,"The radio-pulsar system PSR J0737-3039 is the only binary pulsar known to consist of two radio pulsars: PSR J0737-3039 A \citep{Burgay2003} + and PSR J0737-3039 B \citep{Lyne2004}. ." + Table eives the parameters of this system., Table \ref{tab:system-parameters} gives the parameters of this system. + This unicue configuration las permitted measurements of spi orientation for both dulsars (Fercinanetal.2008:Lyutikov&Thom2501.2005:Bretoret2008): pulsar A's spin is tiled from the orbital anguar moment vector by ll degrees a confidence (Ferμιαetal. 2008): pulsar B's by 130.0L5 deg‘ees αἱ O0.754 ο)uliclence.," This unique configuration has permitted measurements of spin orientation for both pulsars \citep{Ferdman2008,Lyutikov2005,Breton2008}: pulsar A's spin is tilted from the orbital angular momentum vector by 14 degrees at confidence \citep{Ferdman2008}; ; pulsar B's by $130.0^{+1.4}_{-1.2}$ degrees at $99.7$ confidence." + Here we argue that this arge dillerence between le two pulsar sydin tilts requires tliat the origin of most of B's spin is connected to its supernova (SN) explosion: he spin of B's progeiitor. expected to be aligned with he pre-SN orbit due to idal interactious. cannot be invoked o explain the present-day 1uisaligted spin of pulsar B. PSR JOT37-3039 B is currently believed t¢» have formed [ron an eectron-capture supernova trieeered in a mnassive O-Ne-Me white dwarl (vandenHeuvel2000:vaudenHetvel2007:Bretouetal.2008:Wong 2010).," Here we argue that this large difference between the two pulsar spin tilts requires that the origin of most of B's spin is connected to its supernova (SN) explosion; the spin of B's progenitor, expected to be aligned with the pre-SN orbit due to tidal interactions, cannot be invoked to explain the present-day misaligned spin of pulsar B. PSR J0737-3039 B is currently believed to have formed from an electron-capture supernova triggered in a massive O-Ne-Mg white dwarf \citep{vanDenHeuvel2004,Willems2004,Piran2005,Stairs2006,Wang2006,Willems2006,vanDenHeuvel2007,Breton2008,Wong2010}." +. Our results demoustrate that. wlaever the detais of its formation 1jechanisi1. the supernova that formed PSR J0737-3039 B prodiced the majority of its current spit.," Our results demonstrate that, whatever the details of its formation mechanism, the supernova that formed PSR J0737-3039 B produced the majority of its current spin." + U the source of the present-day spin of pulsar B is a single. iinpulsive kick. then this kick imist. be off-cener so that it tumbles the pulsar to its current orientatio1.," If the source of the present-day spin of pulsar B is a single, impulsive kick, then this kick must be off-center so that it tumbles the pulsar to its current orientation." + Using const‘alnts on the SN kick maguitude derived [rom the orbital aucl kinematic Ρααλλοters of the systeu (Wongetal.2010) we iud that this kick must. have been displaced from the center of mass of the exploditig star by at east 1 kin ancl probably 5-10 kin., Using constraints on the SN kick magnitude derived from the orbital and kinematic parameters of the system \citep{Wong2010} we find that this kick must have been displaced from the center of mass of the exploding star by at least 1 km and probably 5–10 km. + Such offset cistauces are a signifi‘al| fraction of tle expected radii of neutrou stars., Such offset distances are a significant fraction of the expected radii of neutron stars. + Oll-center kicks were first suggested in Spruit&pünuey(1998) on purely theoretical grouuds., Off-center kicks were first suggested in \citet{Spruit1998} on purely theoretical grounds. + PSR JO737-3039 likely evolved from two stars originally massive enough to uudergo supernova (SN) explosionsaud [orm two neutrou stars (Tauris&vandenHeuvel2006) at theend of their, PSR J0737-3039 likely evolved from two stars originally massive enough to undergo supernova (SN) explosionsand form two neutron stars \citep{Tauris2006} at theend of their +Young cireunistellar disks around pre-Main Sequence (PMS)nim stars:D are thouelit to host] the birth of planetsU,Young circumstellar disks around pre-Main Sequence (PMS) stars are thought to host the birth of planets. +t According to the core ὃνaccretion scenario. the formation of planets involves a variety of plivsical mechanisuis frou the coagulation of μπα sized particles up to the gas-accretion pliase leading to tle build up of gas giants.," According to the core accretion scenario, the formation of planets involves a variety of physical mechanisms from the coagulation of $\mu$ m sized particles up to the gas-accretion phase leading to the build up of gas giants." + One oft the most criticalHS steps which: is: leftJ to be explained: is] how this 0erowth of solids]. proceeds] fon ΠΠο: ⋡∙ ∙ ↴∖↴↕∑↸∖≼↧≼↧∏↴∖↴↑∶↴∙↥⋅⋜∐∐↴∖↴↑∪↨↘↽↕⊔≓↴∖↴↕∑↸∖≼⊔⋅⋯⊳↨↘↽↴∖↴∙," One of the most critical steps which is left to be explained is how this growth of solids proceeds from mm/cm-sized dust grains to km-sized rocks, called planetesimals." +⋯↕↸∖≼⊔≻⋜⋯↸∖↑↸∖↴∖↴∐⊔⋜↧↕↴∖↴∙ ∙ This is crucial because it is frou the exavitational-driveu collision of these plauctesimals that both the rocky planets aud the LEauth-likerocky coresof giant planets are Itinmatelv supposed to be formed., This is crucial because it is from the gravitational-driven collision of these planetesimals that both the rocky Earth-like planets and the rocky cores of giant planets are ultimately supposed to be formed. + Different 1iechiauisuis been proposed in the. literature to. explain the. mS of planctesimals., Different mechanisms have been proposed in the literature to explain the formation of planetesimals. + In general. these mechliauisuis 53 the local acctunulation of particles with sizes of prayer ?100mu at densities which are high enough to make M clumps unstable to exavitational collapse (Chiang UYYoudin2010).," In general, these mechanisms induce the local accumulation of particles with sizes of $\sim 1-100$ mm at densities which are high enough to make these clumps unstable to gravitational collapse \citep[][]{Chiang:2010}." +". It is therefore very important to well "" the carly phases of coagulation of siuall dust EL m: orderHN to set the right iuitialHEUS conditionsHE forJ theCOSCIICÓ . governing the formation of planetesinials.", It is therefore very important to well characterize the early phases of coagulation of small dust grains in order to set the right initial conditions for the mechanisms governing the formation of planetesimals. + cast sophisticated sticemodels: of: dust evolution⋅ in observed Πιο απο:several effects like dust coagulation. Arrayof motions.∙ have been: builtass Duas f about (Draueretal.2008:Birusticl20104).," Recently, sophisticated models of dust evolution in disks including several effects like dust coagulation, fragmentation and radial motions, have been built \citep{Brauer:2008,Birnstiel:2010a}." +".. Coutiuuuuau observations in the müillimeter coustrall fundamental parameters of(sith- the dust population iu the disk.; e.g.] theN total. dustη mass.jus the! vacliWEὰ dust surface deus. iud UA ΛΗΛradial-depeudeut oh ist af ses 9 avont ~M0.0 nnn bpansSUIS&¢a ""n"" ο.."," Continuum observations in the (sub-)millimeter constrain fundamental parameters of the dust population in the disk, e.g. the total dust mass, the radial-dependent dust surface density, and the size distribution of dust grains at sizes of about $\sim 0.1-10$ mm \citep[see][]{Williams:2011}." +" cose dn M outSCC QO PTCS e me OCLCISOFT ¢στ CVOy16Q teHCL SLCCn PoM outo ""the first4 stages4 of aplauctesimalie» formation,. (BirusticB,10h) ↸∖", These observational constraints can be used to test the models of dust evolution and shed light onto the first stages of planetesimal formation \citep{Birnstiel:2010b}. +"⋪∙⊇∩↸∏⋝∙∙ le »‘ MEadtial Acsad oltEte VOrs EVLALure ‘APas muro- Tí ULLB los L 2n"" |soeCYCTow.12 ΜΟΝΟ a uu...can Iuercase LUId continmun sensitivityο at lous wavelengths,", The recent initial upgrades of the Very Large Array into the Expanded Very Large Array \citep[EVLA;][]{Perley:2011} allowed a significant increase in continuum sensitivity at long wavelengths. + We prescut uv LA[DVobservations E∖ ; T : ORR Th haveformation »mid x . η nnuatte., We present new EVLA observations at about 7 mm of the 253-1536 binary system in the Orion Nebula Cluster. +" theuC induce ilaed »arBAUM e the me CM nn L valOPUSC M 1»AD obDUONC ο ηerethese a MN Uo »li MN& A i t""—1ISTony phieavacated ‘tl 1characterize -,n|", The projected angular separation of the two PMS stars is about 1.1 $arcsec$ which corresponds to a projected physical separation of 460 AU at the ONC distance of $\sim$ 420 pc \citep{Kraus:2009}. +" NMi BUae4 Ἡm revea dde . nOF» 1 ALEC CLISIS SCC AlsaDSOLYDIIO Varo) s(,e miechanisuniserains COMP AMON,:ana 1546536a."," Optical images with the Hubble Space Telescope (HST) has revealed the presence of a large disk seen in absorbtion around the east companion, 253-1536a." +" a¢WillsluusM(2009)\ the binary 2907at 0.58 nua MMwith the Sub-Millinieter ""ERecently. (SMA): and. estimated∖↴⋅⋠∖ foray theο 253-1536aΠΟ diskpms,ταῖς a disks∙ AL.1. 0.07.whic alesh thismaak sdisk listhe niosmost fracinentationlnassive everand observedradial ‘in the ONC.", \citet{Mann:2009} observed the binary at 0.88 mm with the Sub-Millimeter Array (SMA) and estimated for the 253-1536a disk a mass of about 0.07 $M_{\odot}$ which makes this disk the most massive ever observed in the ONC. + They also thisdetected athe Electronic address: Incciseso.ore the other PAIS star. 253-1536b. aud," They also detected a fainter disk around the other PMS star, 253-1536b, and" +92.035 GITz as a hydrogen recombinations line is suspect.,92.035 GHz as a hydrogen recombinations line is suspect. + The ouly other plausible identification for this feature is a blend of CTIZ;CN lines from the Jo = 5-1 transition. however if correct. CIT4CN would be surprisingly stroug in these two galaxies.," The only other plausible identification for this feature is a blend of $_3$ CN lines from the J = 5-4 transition, however if correct, $_3$ CN would be surprisingly strong in these two galaxies." + The only spectral line detected in all 10 galaxies isIICO!., The only spectral line detected in all 10 galaxies is. +. was detected in mine galaxies. TON. IENC and CS were detected in seven galaxies and wwas detected in six galaxies.," was detected in nine galaxies, HCN, HNC and CS were detected in seven galaxies and was detected in six galaxies." + Because our saunple of ealaxies vary in distance from 2.9 to LOL AIpc. the absolute detection threshold is uot the same for these ealaxies. however. in all subsequent analysis we utilize lue ratios.," Because our sample of galaxies vary in distance from 2.9 to 101 Mpc, the absolute detection threshold is not the same for these galaxies, however, in all subsequent analysis we utilize line ratios." + The richest spectrmu is that for NGC 253. where 16 of the 2323 spectral features listed in Table 2 were detected.," The richest spectrum is that for NGC 253, where 16 of the 33 spectral features listed in Table 2 were detected." + We note that there have been many spectroscopic Observations of these same galaxies. aud a ΠΠΟΙ of the spectral lines in Table 2. not detected iu our survey. were detected iu more seusitive nieasurenments focused on single spectral lines.," We note that there have been many spectroscopic observations of these same galaxies, and a number of the spectral lines in Table 2, not detected in our survey, were detected in more sensitive measurements focused on single spectral lines." +" In oulv six galaxies. Arp 220. NGC LOGS, NGC 253, M82. IC 312. and Maffei 2. five or more spectral features are detected."," In only six galaxies, Arp 220, NGC 1068, NGC 253, M82, IC 342, and Maffei 2, five or more spectral features are detected." + In NGC 6210 the only line detectable is.. and in two other galaxies. NGC 3690 and NGC 1258. 'we detect bbut not IICN.," In NGC 6240 the only line detectable is, and in two other galaxies, NGC 3690 and NGC 4258, we detect but not HCN." + Iu the following section. the teiiplate fits are used to examine several line iutensitv ratios and investigate variations in these ratios from galaxy. to ealaxy., In the following section the template fits are used to examine several line intensity ratios and investigate variations in these ratios from galaxy to galaxy. + We first examine the CO isotopic ratios., We first examine the CO isotopic ratios. + In the six galaxies where both aand were detected. the average ratio wwas 1.5.," In the six galaxies where both and were detected, the average ratio was 4.5." + The spread in this ratio was relatively simall. rangiue from 3.3 imn NCC 3079 to 7.8 in Maffei 2.," The spread in this ratio was relatively small, ranging from 3.3 in NGC 3079 to 7.8 in Maffei 2." + These measured ratios are similar to those found for massive GAICs in the disk of the Milkv Wavy (Penziasetal.1972) and for Ser B2 (Cuuuiusetal.1986)., These measured ratios are similar to those found for massive GMCs in the disk of the Milky Way \citep{pen72} and for Sgr B2 \citep{cum86}. + A survev of huninous star-forming reeious in the Milkv Way (Locuecn2009) found irafios between 3 aud 16. with the average regiou having a ratio of about 6. again verv simular to the values ueasured in our gaaxy saluple.," A survey of luminous star-forming regions in the Milky Way \citep{loe09} found ratios between 3 and 16, with the average region having a ratio of about 6, again very similar to the values measured in our galaxy sample." + This ratio cau be affected x optical depth: 1rowever. this lowest transition of CO is dutrinsically wea sso it is expected that these isotopic Ines are optically thin.," This ratio can be affected by optical depth; however, this lowest transition of CO is intrinsically weak, so it is expected that these isotopic lines are optically thin." + Thus. this ratio likely reflects the abundance ratio of the isotopes of atomic carbon aud oxveen.," Thus, this ratio likely reflects the abundance ratio of the isotopes of atomic carbon and oxygen." + In the Miky Way- both the 12€ P ΤΟ) ratio: aud he 160/150 ratio have a strong dependence on galactic radius (Wilson 1999).. both increasing with iucreasing ealactic radius.," In the Milky Way both the $^{12}$ $^{13}$ C ratio and the $^{16}$ $^{18}$ O ratio have a strong dependence on galactic radius \citep{wil99}, , both increasing with increasing galactic radius." + Wisou&Rood(1991) sugeest that both C and DO are secondary unclear products. while °C and 1O are primary nuclear products.," \citet{wil94} suggest that both $^{13}$ C and $^{18}$ O are secondary nuclear products, while $^{12}$ C and $^{16}$ O are primary nuclear products." +" Ratios of primary ο secondary products. such as ο 0, are expected ο be a good indicator of the chemical evolution of the Galaxy."," Ratios of primary to secondary products, such as $^{12}$ $^{13}$ C, are expected to be a good indicator of the chemical evolution of the Galaxy." +" However ratios of secondary products. such as 0Ο, should not vary ereathy as is observed."," However ratios of secondary products, such as , should not vary greatly as is observed." +" We did not detect the J=1-0 transitions of IIMCN, UWeCO!. or INC or the JH2-1 transition of CP'S in anv of the galaxies in our sample. however. these limits provide information ou the optical depth of the main lines."," We did not detect the J=1-0 transitions of $^{13}$ CN, $^{13}$ $^+$, or $^{13}$ C or the J=2-1 transition of $^{34}$ S in any of the galaxies in our sample, however, these limits provide information on the optical depth of the main lines." + The most sensitive limits on the isotopic line streneths were set im NGC 253 aud M82., The most sensitive limits on the isotopic line strengths were set in NGC 253 and M82. + In NGC. 255 the 3-0 lower limits ou the isotopic iuteusitv ratios were ICN/II?CN > 19. CO! /ID?2CO! > 16. and CS/C?!S > &.," In NGC 253 the $\sigma$ lower limits on the isotopic intensity ratios were $^{13}$ CN $>$ 19, $^+$ $^{13}$ $^+$ $>$ 16, and $^{34}$ S $>$ 8." + In Mas? the 3-0 lower limits were HCN/IPPCN 12. HCO! ALB CO! = 19. aud CS/C?!S > 5.," In M82 the $\sigma$ lower limits were $^{13}$ CN $>$ 12, $^+$ $^{13}$ $^+$ $>$ 19, and $^{34}$ S $>$ 5." + Tf we asstine isotopic abundances measured or NGC 253 μπασος by Omout(2007).. we conclude that the main isotopic lines of IICN. IINC and CS have optical depths aot}Mo," If we assume isotopic abundances measured or NGC 253 summarized by \citet{omo07}, we conclude that the main isotopic lines of HCN, $^+$, HNC and CS have optical depths $<$ 3." +e Both CO aud IICN emission are often used as tracers of the molecular eas in galaxies (Omout2007)., Both CO and HCN emission are often used as tracers of the molecular gas in galaxies \citep{omo07}. +. Since the rausitious of CO aud IICN have quite disparate critical deusities. they may be expected to trace different deusity uolecular gas. aud thus their ratio is a measure of the douse gas fraction (Paglionectal.1998).," Since the transitions of CO and HCN have quite disparate critical densities, they may be expected to trace different density molecular gas, and thus their ratio is a measure of the dense gas fraction \citep{pag98}." +. 12 CO is outside he frequency range ofthe RSR for these very low redshift galaxies: however. we believe that uma be a iimchli better probe of the gas.," $^{12}$ CO is outside the frequency range of the RSR for these very low redshift galaxies; however, we believe that may be a much better probe of the gas." + The ccluission likely arises from lieher column deusitvὉ uolecular gas than CO. and much of the eenission may be produced in the same gas responsible or the IICN emission.," The emission likely arises from higher column density molecular gas than CO, and much of the emission may be produced in the same gas responsible for the HCN emission." + Thus. the irafio may be a good diagnostic of the density of he molecular gas most directly connected to the star παπαο. activity iu the nuclear starburst regions of hese galaxies.," Thus, the ratio may be a good diagnostic of the density of the molecular gas most directly connected to the star formation activity in the nuclear starburst regions of these galaxies." + We find that the ratio varies sieuificantly from galaxy to galaxy. with the areest ratio of 2.2 found in Arp 220 and the smallest ratio found iu NGC 1258. where the 3-0 upper Init was ouly 0.30.," We find that the ratio varies significantly from galaxy to galaxy, with the largest ratio of 2.2 found in Arp 220 and the smallest ratio found in NGC 4258, where the $\sigma$ upper limit was only 0.30." + We discuss later how this ratio can provide au inportaut constraint on the mean gas deusity., We discuss later how this ratio can provide an important constraint on the mean gas density. + Early models of the chemistry of N-rav imradiated eas sugeested that ICO! would be uuder-abundaut iu gas near a hard ταν source (Lepp&Daearno1996:Mal-onevetal. 1996)..," Early models of the chemistry of X-ray irradiated gas suggested that $^+$ would be under-abundant in gas near a hard X-ray source \citep{lep96, mal96}. ." + These results led o the suggestion that the ICO! /IICN. ratio may distineuish between PDR aud NDR dominated eas aud tlis between central regions of galaxies donünated bw citrer starbursts or AGNs., These results led to the suggestion that the $^+$ /HCN ratio may distinguish between PDR and XDR dominated gas and thus between central regions of galaxies dominated by either starbursts or AGNs. + Subsequent observations (Nohnoetal.2001:etal.2008). seemed to coufiia this prediction.," Subsequent observations \citep{koh01, gra06, ima07, baa08} seemed to confirm this prediction." + These observations also showed au auti-correlatiou between the observed HCN/CO ratio and the ICO! /TICN ratio., These observations also showed an anti-correlation between the observed HCN/CO ratio and the $^+$ /HCN ratio. + However. the more recent theoretical work of Meijeriuk&Spaaus(2005) and Aleijerinketal.(2007) places this interpretation in question.," However, the more recent theoretical work of \citet{mei05} and \citet{mei07} places this interpretation in question." + Meijerinketal.(2007) showed that in the high deusitv eas. the IICO! /TICN ratio is lavecr in NDR regious than in PDR regions. just the opposite of that sugeested bv Lepp&Dalgarno(1996).," \citet{mei07} showed that in the high density gas, the $^+$ /HCN ratio is larger in XDR regions than in PDR regions, just the opposite of that suggested by \citet{lep96}." +. They also noted astroug density dependence for this ratio iu bothPDR and XDR eas., They also noted astrong density dependence for this ratio in bothPDR and XDR gas. + In Figme 2 we plot the ΟΙ /TICN ratio versus the irafio., In Figure 2 we plot the $^+$ /HCN ratio versus the ratio. + We find a similar trend to that found im previousobservational papers. that is. the ICO! /TICN ratio is inversely correlated with the iratfio.," We find a similar trend to that found in previousobservational papers, that is, the $^+$ /HCN ratio is inversely correlated with the ratio." + The agreement of our result with past papers, The agreement of our result with past papers +fits to projected spectra extracted from the plume were preferred © single-temperature fits. with temperatures of 0.7 and 1.5 keV. Outside this region the temperature increases quickly to the east o around 3.7 keV. To the west. there is a plateau of cooler gas at around 2.5 keV. before the temperature rises at a radius of around 190 aresec.,"fits to projected spectra extracted from the plume were preferred to single-temperature fits, with temperatures of 0.7 and 1.5 keV. Outside this region the temperature increases quickly to the east to around 3.7 keV. To the west, there is a plateau of cooler gas at around 2.5 keV, before the temperature rises at a radius of around 190 arcsec." + Deeper observations (2). confirmed his picture. highlighting the clear east-west asymmetry of the emperature distribution.," Deeper observations \citep{Fabian05} + confirmed this picture, highlighting the clear east-west asymmetry of the temperature distribution." + EPIC data confirmed the ~0.7keV component inthe core (2).. also finding the temperature of the ICM to drop to around 3.4 keV beyond 120 kpe radius.," EPIC data confirmed the $\sim 0.7\keV$ component inthe core \citep{SandersEnrich06}, also finding the temperature of the ICM to drop to around 3.4 keV beyond 120 kpc radius." + The observations also clearly showed that the metallicity of the ICM is inversely correlated with its temperature (2??)..," The observations also clearly showed that the metallicity of the ICM is inversely correlated with its temperature \citep{SandersCent02,Fabian05,SandersEnrich06}." + An interesting feature of this cluster is that the metallicity of the gas towards the centre is significantly supersolar., An interesting feature of this cluster is that the metallicity of the gas towards the centre is significantly supersolar. + The Fe metallicity peaks between 1.5 and .(22)..," The Fe metallicity peaks between 1.5 and \citep{Fabian05,SandersEnrich06}." + Si and S peak around2Z.. and Ni peaks around.," Si and S peak around, and Ni peaks around." +. In addition the metallicity of the gas appears to decline in the very. central regions (?).., In addition the metallicity of the gas appears to decline in the very central regions \citep{SandersCent02}. + The multiple detections of cool X-ray emitting gas in the core of Centaurus provides an excellent opportunity to test the picture that there is only a range in 2—3 in X-ray gas temperature in clusters of galaxies., The multiple detections of cool X-ray emitting gas in the core of Centaurus provides an excellent opportunity to test the picture that there is only a range in 2–3 in X-ray gas temperature in clusters of galaxies. + We therefore undertook a deep ROS observation of Centaurus. which. when combined with the existing observation. gives a total exposure of around 160 ks.," We therefore undertook a deep RGS observation of Centaurus, which, when combined with the existing observation, gives a total exposure of around 160 ks." + In this paper we assume Ho—70kms!Μρο|. which gives an angular scale of 213 pe per aresec for Centaurus.," In this paper we assume $H_0 = 70 \kmpspMpc$, which gives an angular scale of 213 pc per arcsec for Centaurus." + We assume the Solar metallicities of ?.., We assume the Solar metallicities of \cite{AndersGrevesse89}. + Error bars are quoted as 16 and limits as 20., Error bars are quoted as $\sigma$ and limits as $\sigma$ . + We processed the two source datasets listed in Table | using Science Analysis System (SAS)) version 7.1.0. with the pipeline.," We processed the two source datasets listed in Table \ref{tab:observations} using Science Analysis System ) version 7.1.0, with the pipeline." + We processed the Ist and 2nd order spectra. including 99 per cent of the point spread function (PSF) and 97 per cent of the pulse-height distribution. in order to get as many source photons as possible without increasing background too much.," We processed the 1st and 2nd order spectra, including 99 per cent of the point spread function (PSF) and 97 per cent of the pulse-height distribution, in order to get as many source photons as possible without increasing background too much." + We examined the observation light-curves for CCD number 9 at absolute values of the cross dispersion greater than 1.5x10+ (using values of FLAG of 8 and 16)., We examined the observation light-curves for CCD number 9 at absolute values of the cross dispersion greater than $1.5\times10^{-4}$ (using values of FLAG of 8 and 16). +" The lightcurves were relatively consistent at values of around 0.1s.|, except for some short flaring in the longer observation."," The lightcurves were relatively consistent at values of around $0.1 \ps$, except for some short flaring in the longer observation." + We filtered this observation. excluding time periods with count rates greater than 0.28|.," We filtered this observation, excluding time periods with count rates greater than $0.2 \ps$." + Centaurus fills the entire field of view ofthe RGS instruments., Centaurus fills the entire field of view of the RGS instruments. + We therefore required blank-sky background spectra to subtract instrumental and external backgrounds., We therefore required blank-sky background spectra to subtract instrumental and external backgrounds. + As we used a 97 per cent pulse-height distribution eut we could not use that standard tool., As we used a 97 per cent pulse-height distribution cut we could not use that standard tool. + Instead we selected five deep RGS observations of point-like sources from relatively low Galactic latitude to generate background spectra (Table 1))., Instead we selected five deep RGS observations of point-like sources from relatively low Galactic latitude to generate background spectra (Table \ref{tab:observations}) ). + We processed. these observations with the same parameters as Centaurus. cleaning flares in the same way. and excluding the inner 90 per cent PSF (where the sources lie) to generate the background spectra.," We processed these observations with the same parameters as Centaurus, cleaning flares in the same way, and excluding the inner 90 per cent PSF (where the sources lie) to generate the background spectra." + We combined with the separate background observations to make RGS | and RGS 2 spectra for the two spectral orders., We combined with the separate background observations to make RGS 1 and RGS 2 spectra for the two spectral orders. + We used to add the spectra and responses from the two foreground Centaurus observations. after reprocessing including the correct attitude values.," We used to add the spectra and responses from the two foreground Centaurus observations, after reprocessing including the correct attitude values." + The background spectra contained some invalid spectral channels which did not correspond with the foreground spectra. so we marked these channels as invalid in the foreground spectra.," The background spectra contained some invalid spectral channels which did not correspond with the foreground spectra, so we marked these channels as invalid in the foreground spectra." + We grouped the foreground spectra to have a minimum of 25 counts per spectral bin., We grouped the foreground spectra to have a minimum of 25 counts per spectral bin. + We checked the background spectra were the same by applying them to the foreground. individually., We checked the background spectra were the same by applying them to the foreground individually. + The backgrounds were indistinguishable in the 6.5 to 27 range., The backgrounds were indistinguishable in the 6.5 to 27 range. + We show in Fig., We show in Fig. + |. the full fluxed spectrum using the 99 per cent PSF with 97 per cent of the pulse-height distribution., \ref{fig:spectrum} the full fluxed spectrum using the 99 per cent PSF with 97 per cent of the pulse-height distribution. + A 99 per cent PSF corresponds to roughly the inner 160 aresee width in the cross-dispersion direction., A 99 per cent PSF corresponds to roughly the inner 160 arcsec width in the cross-dispersion direction. + This was created by combining the first and second order spectra for both observations together with the taskRGSPLUXER.. subtracting the combined background spectr," This was created by combining the first and second order spectra for both observations together with the task, subtracting the combined background spectra." + We do not show the spectrum at wavelengths longer than as the background becomes increasingly important., We do not show the spectrum at wavelengths longer than as the background becomes increasingly important. + We note that the output from is for display purposes only., We note that the output from is for display purposes only. + We do no use it to obtain quantitative information., We do not use it to obtain quantitative information. + In the plot we also show the spectrum extracted from the inner 90 per cent of the PSF (which corresponds to around 60 aresee width in the cross-dispersion direction)., In the plot we also show the spectrum extracted from the inner 90 per cent of the PSF (which corresponds to around 60 arcsec width in the cross-dispersion direction). + In addition we plot the difference between the two spectra. which is equivalen to the spectrum extracted between 60 and 160 arcsec in the cross-dispersion direction.," In addition we plot the difference between the two spectra, which is equivalent to the spectrum extracted between 60 and 160 arcsec in the cross-dispersion direction." + In the lower panel we show smoothed mode (2) spectra for plasmas with Solar metallicity at temperatures of 0.5. 0.7 and | keV for comparison.," In the lower panel we show smoothed model \citep{SmithApec01} + spectra for plasmas with Solar metallicity at temperatures of 0.5, 0.7 and 1 keV for comparison." + These models are plotted with arbitrary normalisation to have roughly the same range in values., These models are plotted with arbitrary normalisation to have roughly the same range in values. + ote that the spectrum also contains lines from gas hotter than | keV. The spectrum shows a variety of emission lines. from N. O. e. Mg. Si and Fe in several ionisation states.," Note that the spectrum also contains lines from gas hotter than 1 keV. The spectrum shows a variety of emission lines, from N, O, Ne, Mg, Si and Fe in several ionisation states." + Most interesting are hose lines indicating cool X-ray emitting gas. particularly strong in the 90 per cent PSF spectrum.," Most interesting are those lines indicating cool X-ray emitting gas, particularly strong in the 90 per cent PSF spectrum." + Fe L lines from Fe down o Fe are observed., Fe L lines from Fe down to Fe are observed. + The strong N line. in particular. is interesting.," The strong N line, in particular, is interesting." + We show a zoom-up of the spectrum between |2 to rom the 90 per cent PSF in Fig. 2.., We show a zoom-up of the spectrum between 12 to from the 90 per cent PSF in Fig. \ref{fig:spectrumzoom}. + The plot shows we clearly observe several distinct Fe lines., The plot shows we clearly observe several distinct Fe lines. + These lines are relatively narrow. indicating that they come from a relatively small region (See Section 3.13).," These lines are relatively narrow, indicating that they come from a relatively small region (See Section \ref{sect:xdisp}) )." + Absent from the spectra is any evidence for redshift). which is a strong indicator of gas less than 0.2 keV. Different lines are sensitive to gas at different temperatures.," Absent from the spectra is any evidence for O emission (which would appear at 21.8 and at this redshift), which is a strong indicator of gas less than 0.2 keV. Different lines are sensitive to gas at different temperatures." + The strength of lines from a particular ion are governed by how much of an element is in the form of that ion. the abundance of the element and the density of the gas.," The strength of lines from a particular ion are governed by how much of an element is in the form of that ion, the abundance of the element and the density of the gas." + We plot in Fig., We plot in Fig. + 3 the fraction of an element which is in the form of a particular ion as a function of temperature. for those ions from which we observe lines (plus O which we do not observe).," \ref{fig:ioneq} the fraction of an element which is in the form of a particular ion as a function of temperature, for those ions from which we observe lines (plus O which we do not observe)." + These results are from the calculations of ionisation equilibrium of ? (which are used by the model)., These results are from the calculations of ionisation equilibrium of \cite{Mazzotta98} (which are used by the model). + We show in Fig., We show in Fig. + 4. the image formed by plotting the dispersion angle of detected photons against the cross-dispersion angle., \ref{fig:xdispimage} the image formed by plotting the dispersion angle of detected photons against the cross-dispersion angle. + Photons outside of the first order spectrum were removed by making an energy-cut using the pulse-invariant CCD energy values., Photons outside of the first order spectrum were removed by making an energy-cut using the pulse-invariant CCD energy values. + It shows the combined RGS1 and ΚΟ cross-dispersion image for the two observations. exposure-corrected for bad pixels.," It shows the combined RGS1 and RGS2 cross-dispersion image for the two observations, exposure-corrected for bad pixels." + The horizontal axis shows increasing wavelength. while the off-axis angle in the cross-dispersion direction is shown vertically.," The horizontal axis shows increasing wavelength, while the off-axis angle in the cross-dispersion direction is shown vertically." + It canbe seen that some lines. e.g. Fe XVII. are much more centrally concentrated than others. e.g. O VIII.," It canbe seen that some lines, e.g. Fe , are much more centrally concentrated than others, e.g. O ." +2010)).,. +". Also, the survival of an old thin disk with a mean age of ~ 5-8 Gyr (Norrisetal.|2006) means that most of the action in the central regions occurred before z ~ 0.5-1, and that there have been no major mergers more recently."," Also, the survival of an old thin disk with a mean age of $\sim$ 5–8 Gyr \citep{2006MNRAS.367..815N} means that most of the action in the central regions occurred before $z$ $\sim$ 0.5–1, and that there have been no major mergers more recently." + At larger radii there are generic expectations from major mergers for rotation profile behavior., At larger radii there are generic expectations from major mergers for rotation profile behavior. +" These remnants are generally expected to have rapid outer rotation resulting from both residual disk spin and the conversion of orbital into internal angular al]momentum m in stark contrast to the declining rotation observedet in (CretionBOOI).,NGC 3115."," These remnants are generally expected to have rapid outer rotation resulting from both residual disk spin and the conversion of orbital into internal angular momentum \citep[e.g.,][]{2000MNRAS.316..315B,2001ApJ...554..291C}, in stark contrast to the declining rotation observed in NGC 3115." +" To make this difference more explicit, we searched through the literature for extended rotation profiles from simulations of major merger remnants, choosing a representative example that comes close to reproducing the central rotation of NGC 3115's bulge and MRGC system."," To make this difference more explicit, we searched through the literature for extended rotation profiles from simulations of major merger remnants, choosing a representative example that comes close to reproducing the central rotation of NGC 3115's bulge and MRGC system." + The chosen remnant is the result of a 1:10 spiral-spiral merger from (2005). which we overplot in Fig.," The chosen remnant is the result of a 1:10 spiral-spiral merger from \citet{2005A&A...437...69B}, which we overplot in Fig." +" 2g, showing the discrepancy in the outer regions between the high rotation predicted and the low rotation observed."," 2g, showing the discrepancy in the outer regions between the high rotation predicted and the low rotation observed." +" Gas-rich 1:1 merger remnants with small pericenters can also produce declining outer rotation, but the outer “dry” part of the remnant is generally expected to show kinematical misalignment with the inner regions (Hoffmanetαἱ.2010,andin preparation). "," Gas-rich 1:1 merger remnants with small pericenters can also produce declining outer rotation, but the outer “dry” part of the remnant is generally expected to show kinematical misalignment with the inner regions \citep[][and in preparation]{2010ApJ...723..818H}. ." +"Possible examples of this scenario include NGC 5128 (Pengetal. and NGC 4125 (Puet but other cases like 2004)NGC 3115 with decreasing but al.|2010),,well-aligned rotation suggest there must be another explanation (cf."," Possible examples of this scenario include NGC 5128 \citep{2004ApJ...602..685P} and NGC 4125 \citep{2010A&A...516A...4P}, but other cases like NGC 3115 with decreasing but well-aligned rotation suggest there must be another explanation (cf." + NGC 821 and NGC et[Proctoral.|2009]; 2009;; and early 3377:arguments along these lines by Her[1995))., NGC 821 and NGC 3377: \citealp{2009MNRAS.398...91P}; \citealp{2009MNRAS.394.1249C}; and early arguments along these lines by \citealt{1995A&A...293...20S}) ). +" Without exhaustive simulations of major mergers, we cannot rule out the possibility that finely tuned parameters (viewing angle, impact parameter, etc.)"," Without exhaustive simulations of major mergers, we cannot rule out the possibility that finely tuned parameters (viewing angle, impact parameter, etc.)" + would reproduce the observed kinematics of such systems., would reproduce the observed kinematics of such systems. +" Nonetheless, it seems more natural to consider a two-phase assembly scenario (Section ??)) in which ETGs form inside-out."," Nonetheless, it seems more natural to consider a two-phase assembly scenario (Section \ref{intro}) ) in which ETGs form inside-out." +" In this case, inner bulges form at high redshift while subsequent outer bulge and halo growth is driven primarily by dry minor-merger accretion events."," In this case, inner bulges form at high redshift while subsequent outer bulge and halo growth is driven primarily by dry minor-merger accretion events." + The satellites fall in from many different directions and provide little net rotational support ∢⊽2007} 2010)..," The satellites fall in from many different directions and provide little net rotational support \citep{2002ApJ...581..799V,2006MNRAS.365..747A,2007A&A...476.1179B,2010A&A...515A..11Q}." +" The radial decline in rotation of the MRGC system could then represent a transition from an inner bulge formed in violent, dissipative processes at high redshift, to an outer spheroid (around one third of the bulge mass in the case of NGC 3115) built largely from accreted material over a more protracted period."," The radial decline in rotation of the MRGC system could then represent a transition from an inner bulge formed in violent, dissipative processes at high redshift, to an outer spheroid (around one third of the bulge mass in the case of NGC 3115) built largely from accreted material over a more protracted period." +" The MPGCs also show a marked rotational decrease, albeit at a larger radius."," The MPGCs also show a marked rotational decrease, albeit at a larger radius." +" Here the theoretical picture is less clear, but we postulate an inner metal-poor stellar halo formed in-situ at high z followed by the accretion of outer material that also creates the outer bulge (cf. ≻⋅ "," Here the theoretical picture is less clear, but we postulate an inner metal-poor stellar halo formed in-situ at high $z$ followed by the accretion of outer material that also creates the outer bulge (cf. \citealt{2009ApJ...702.1058Z}) )." +"Declining metallicity profiles are expected in this two-phase assembly scenario since the lower-mass accreted systems should be more metal-poor ctthanal] the central galaxy (Naabetal]2009,B009).."," Declining metallicity profiles are expected in this two-phase assembly scenario since the lower-mass accreted systems should be more metal-poor than the central galaxy \citep{2009ApJ...699L.178N,2009ApJ...697.1290B}." +" The prediction (see §??)) is of a downward [Bezansontransition from an inner metallicity profile, whose shape reflects the detailed in-situ star formation history, to an outer profile flattened by radial mixing and primarily composed of accreted material."," The prediction (see \ref{intro}) ) is of a downward transition from an inner metallicity profile, whose shape reflects the detailed in-situ star formation history, to an outer profile flattened by radial mixing and primarily composed of accreted material." +" We assume this holds for both the stellar and GC metallicity profiles, though systematic offsets may arise fromthe difference between the ensemble"," We assume this holds for both the stellar and GC metallicity profiles, though systematic offsets may arise fromthe difference between the ensemble" +where the cooling function is Our notation is standard: à; G2.) is the number density of ions (electrons) and 7/ is the temperature (in energy units throughout the paper).,where the cooling function is Our notation is standard: $n_{\rm i}$ $n_{\rm e}$ ) is the number density of ions (electrons) and $T$ is the temperature (in energy units throughout the paper). + We also define. for future use. the total number density n— fone.," We also define, for future use, the total number density $n = n_{\rm i} + n_{\rm e}$ ." +" The numerical constants εν=0.086. Ca=0.58 and C,=0.63 are selected to correspond to an average metallicity Z=0.3 Z.. for which the mean mass per particle is ji=0.597my. the mean mass per electron is ji=pefe)1.150, and ny=0.9270, (Sutherland&Dopita 1993).."," The numerical constants $C_1 = 0.086$, $C_2=0.58$ and $C_3=0.63$ are selected to correspond to an average metallicity $Z=0.3~{\rm Z}_\odot$ , for which the mean mass per particle is $\mu=0.597 m_{\rm p}$, the mean mass per electron is $\mu_{\rm e} = \mu (n/n_{\rm e}) = 1.150 m_{\rm p}$ and $n_{\rm i}=0.927 n_{\rm e}$ \citep{sd93}. ." + The cooling function is dominated by Bremsstrahlung above and by metal lines below 7~1keV., The cooling function is dominated by Bremsstrahlung above $T\sim 1~{\rm keV}$ and by metal lines below $T\sim 1~{\rm keV}$. +" Since the temperature equilibration time between ions and electrons fj4~LOkwr near the centres and ~|Myr near the temperature maximum of cool-core clusters. which is smaller than all other timescales that will be relevant to us (see Section ?2)). we assume 4;=7,1."," Since the temperature equilibration time between ions and electrons $t_{\rm i-e,eq}\sim 10~{\rm kyr}$ near the centres and $\sim 1~{\rm Myr}$ near the temperature maximum of cool-core clusters, which is smaller than all other timescales that will be relevant to us (see Section \ref{sec:conduction}) ), we assume $T_{\rm i}=T_{\rm e}=T$." +" Even in unrelaxed clusters like Coma. where the temperature is relatively high (27)=8.2keV: Arnaudet 2001)) and the electron density is relatively low (9,23.10.ὁ —4.10em ?:see Section ?2)). fweg 2-170Myr."," Even in unrelaxed clusters like Coma, where the temperature is relatively high $T\simeq 8.2~{\rm keV}$; \citealt{arnaud01}) ) and the electron density is relatively low $n_{\rm e}\simeq 3\times 10^{-3}$ – $4\times 10^{-5}~{\rm cm}^{-3}$; see Section \ref{sec:coma}) ), $t_{\rm i-e,eq}\simeq 2$ – $170~{\rm Myr}$." + Normalised to conditions representative of the centres of clusters. the (per unit volume) is in the Bremsstrahlung regime (2°1 keV).," Normalised to conditions representative of the centres of cool-core clusters, the (per unit volume) is in the Bremsstrahlung regime $T\gtrsim 1~{\rm keV}$ )." + There is a rapidly growing body of observational evidence for the presence of appreciable magnetic fields in the ICM (forareview.seeCarilli&Taylor 2002).," There is a rapidly growing body of observational evidence for the presence of appreciable magnetic fields in the ICM \citep[for a review, see][]{ct02}." +. Randomly tangled magnetic fields with strength £~1 — I0μα and characteristic scale ~1 — 10kpc are consistently found. with fields in the cool cores of cooling-flow clusters somewhat stronger than elsewhere.," Randomly tangled magnetic fields with strength $B\sim 1$ – $10~\mu{\rm G}$ and characteristic scale $\sim 1$ – $10~{\rm kpc}$ are consistently found, with fields in the cool cores of cooling-flow clusters somewhat stronger than elsewhere." + The presence of a magnetic field alters the form of the thermal pressure when Qj/pil1. where $3;=οὐἑηιὸ is the ion cyclotron frequency and £j;=AlznAucAnili is the ion-ion collision frequency: Ay is the ion-ion Coulomb logarithm (Braginskit 1965)..," The presence of a magnetic field alters the form of the thermal pressure when $\Omega_{\rm i}/\nu_{\rm ii}\gg 1$, where $\Omega_{\rm i}=eB/m_{\rm i}c$ is the ion cyclotron frequency and $\nu_{\rm ii}= 4\sqrt{\pi}n_{\rm i}\lambda_{\rm ii} e^4/3m^{1/2}_{\rm i}T^{3/2}$ is the ion-ion collision frequency; $\lambda_{\rm ii}$ is the ion-ion Coulomb logarithm \citep{braginskii65}. ." +" This is certainly the case in the cool cores of galaxy clusters. where typical values of the electron density no. temperature 7' and magnetic-field strength 2 imply As aresult. thermal pressure becomes anisotropic with respect to the local magnetic field direction b: where p, (iiis the thermal pressure perpendicular (parallel) to the local magnetic field. p=(2/3)p,|(1/3)pj is the total thermal pressure. | is the unit dyadic and we have defined the collisional viscous stress tensor In the Braginskii (i.e. collisional) limit. appropriate for the large-scale motions in the ICM since their dynamical timescales are =>pul$fh‘the ion contribution to the viscous stress dominates thatof the electrons by a factor proportional to (ms£m.)7."," This is certainly the case in the cool cores of galaxy clusters, where typical values of the electron density $n_{\rm e}$, temperature $T$ and magnetic-field strength $B$ imply As a result, thermal pressure becomes anisotropic with respect to the local magnetic field direction $\bb{b}$: where $p_\perp$ $p_{||}$ ) is the thermal pressure perpendicular (parallel) to the local magnetic field, $p=(2/3)p_\perp + (1/3)p_{||}$ is the total thermal pressure, $\bb{\mathsf{I}}$ is the unit dyadic and we have defined the collisional viscous stress tensor In the Braginskii (i.e. collisional) limit, appropriate for the large-scale motions in the ICM since their dynamical timescales are $\gg \nu^{-1}_{\rm ii}\gg \Omega^{-1}_{\rm i}$, the ion contribution to the viscous stress dominates thatof the electrons by a factor proportional to $(m_{\rm i}/m_{\rm e})^{1/2}$." + Thus. in what follows. we neglect the electron contribution to the viscous stress.," Thus, in what follows, we neglect the electron contribution to the viscous stress." + The viscous stress tensor appears both in the momentum equation. as a form of momentum transport. and in the energy equation. as a form of heating.," The viscous stress tensor appears both in the momentum equation, as a form of momentum transport, and in the energy equation, as a form of heating." +" In these two equations. g is the gravitational acceleration. q, is the electron collisional heat flux and οαἱ=Off|22V is the convective derivative."," In these two equations, $\bb{g}$ is the gravitational acceleration, $\bb{q}_{\rm e}$ is the electron collisional heat flux and ${\rm d}/{\rm d}t\equiv\partial/\partial t + \bb{u}\bcdot\del$ is the convective derivative." + We assume an ideal gas equation of state. p=n7 (both for each species and for the two combined because 7;—7.=7).," We assume an ideal gas equation of state, $p=nT$ (both for each species and for the two combined because $T_{\rm i}=T_{\rm e}=T$ )." + The electron contribution to the collisional heat flux dominates that of the ions by a factor of (nmitie (Braginskii1963)., The electron contribution to the collisional heat flux dominates that of the ions by a factor of $(m_{\rm i}/m_{\rm e})^{1/2}$ \citep{braginskii65}. +. Differences between the perpendicular and parallel pressures in a magnetised plasma are due to the conservation of the first adiabatic invariant for each particle. jj.=me3(2Bconst (on time scales PN lj ," Differences between the perpendicular and parallel pressures in a magnetised plasma are due to the conservation of the first adiabatic invariant for each particle, $\mu = mv^2_\perp/2B = {\rm const}$ (on time scales $\gg \Omega_{\rm i}^{-1}$ )." +Therefore. any change in the field strength must be accompanied by a corresponding change in the perpendicular pressure. pj/Dconst.," Therefore, any change in the field strength must be accompanied by a corresponding change in the perpendicular pressure, $p_\perp/B\sim{\rm const}$." + In a turbulent plasma such as the ICM. time-dependent fluctuations in the magnetic-tield strength. are inevitable.," In a turbulent plasma such as the ICM, time-dependent fluctuations in the magnetic-field strength are inevitable." + Accordingly. a patchwork of regions of positive or negative pressure anisotropy will emerge. corresponding to locally increasing or decreasing magnetic-field strength.," Accordingly, a patchwork of regions of positive or negative pressure anisotropy will emerge, corresponding to locally increasing or decreasing magnetic-field strength." + If the pressure anisotropy |pi—pul=LPfda. firehose and mirror instabilities are triggered at spatial and temporal microscales (Schekochihinetal.2005.andreferencestherein)..," If the pressure anisotropy $|p_\perp - p_{||}| \gtrsim B^2/4\pi$, firehose and mirror instabilities are triggered at spatial and temporal microscales \citep[and references therein]{sckhs05}." +/ Equations (7)) and (89) break down at these scales. and the perpendicular and parallel pressures must be determined by a kinetic calculation Schekochihinetal.2010:Rosin 2010).," Equations \ref{eqn:momentum}) ) and \ref{eqn:energy}) ) break down at these scales, and the perpendicular and parallel pressures must be determined by a kinetic calculation \citep[e.g.][]{scrr10,rsrc10}." +. It is usually the case that thepressure anisotropy —and thusthe viscous stress — is regulated by the nonlinear evolution of these microscale instabilities. which tend to pin the pressure anisotropy at marginalstability values (seeRosinetal.2010.and therein): where €=I for the firehose instability or 1/2 for the mirror The (tion) plasma beta parameter is the ratio of the Gon) thermal and magnetic pressures. normalised here to conditions representative of the deep interiors," It is usually the case that thepressure anisotropy –and thusthe viscous stress – is regulated by the nonlinear evolution of these microscale instabilities, which tend to pin the pressure anisotropy at marginalstability values \citep[see][and references therein]{rsrc10}: : where $\xi = -1$ for the firehose instability or $1/2$ for the mirror The (ion) plasma beta parameter is the ratio of the (ion) thermal and magnetic pressures, normalised here to conditions representative of the deep interiors" +" t amplitudes:2 b,(a, y,z,t) 2 — sin(Amer)£ éy, (15) TA sin 2 cx+1) éy. (16) u,(z,y,z,t)= (27—1) generic forcing the solution(11))-(12)) nonlinear(L1))-(12)) havevanisha vanishingexactly. LorentzT'his subset forceof ","This is a two-scale approach, and the average and fluctuating parts can be represented as the large-scale and small-scale fields or, introducing a suitable cut-off wavenumber $K$ (for instance the grid resolution if this is applied to numerical simulations), as the and “lesser” and “greater” functions The relevant quantities to be modeled in eqs. \ref{eq:aeq1}) \ref{eq:aeq3}) )" +"andthe terms solutions(11))-(12)) approximationarevalidan exact forsolutiont< atalltimes, notAsancanbe o onlyΚΑ) iTj.e the sheared forcing O (1))-(2))ANAproved[andbyalso (1))-(3))) develops evenforsmall cations) values of the resistivity,but inthis"," are the “turbulent” stress tensors Phenomenological modeling and numerical simulations \citep{yo90,yo91} have shown that these stress tensor can be approximated with where the coefficients $\nu_t$ and $\eta_t$ are called turbulent viscosity and resistivity, and for a plasma in coronal conditions have much higher values than $\nu$ and $\eta$." +" section weare interested in the diffusive effects onnegligiblethe linear artificiallydynamics, i.e."," Inserting \ref{eq:tdiff1}) \ref{eq:tdiff2}) ) in the equations for the mean fields \ref{eq:aeq1}) \ref{eq:aeq2}) ), we obtain a set of equations for the mean fields that has except that $\nu \rightarrow \nu_t$ and $\eta \rightarrow \eta_t$." + suppressedwhen nonlinearwill discussterms suchare or (we acase in our (5 Conclusions). We now consider the, Then for a system embedded in a strong axial field \citep{mon82} equations \ref{eq:eq1}) \ref{eq:eq3}) ) that we use to model the system are also a one-point closure model if the dissipative coefficients are considered as ones. + (4))-(5))]effect of standarddiffusion solutions (19): these arethesolutions linearized equations obtained from (4))-(D]) retaining alsothediffusive terms.," \cite{hp92} use the results of an eddy damped quasi-normal Markovian approximation \citep{pfl76} + to express the coefficients $\nu_t$ and $\eta_t$ as a function of the energy flux $\epsilon$ flowing along the inertial range." +" In the linear regime, (i5))),as the magnetic field growsin time (tap),(13), the diffusive [V?b,« b,/€?]becomesincreasingly bigger"," Additionally they that the 1D boundary forcing velocity leads the large-scalesto evolve in a laminar (fields are 1D and directed along $y$, the same direction of the forcing) steady state $\partial_t =0$ )." +" until diffusion balancesthe magneticfield growth, andthesystem reachesasaturated equilibrium state. diffusion,the magnetic field will evolve as", Equations \ref{eq:eq1}) \ref{eq:eq3}) ) and their boundary forcing [of which our forcing \ref{eq:f0}) \ref{eq:f1}) ) is representative] are used to compute the flux of energy $S$ entering the system due to the dragging of the field-lines footpoints. +" z,t) = [ul(a,y) muw? b,(x,y, (a, v)] I). hexp( (17) x= The diffusive timescale associatedwith the Reynolds numberReis rg (2 where£,is the len", $S$ is a function of the system parameters and the effective diffusivity coefficients $\nu_t$ and $\eta_t$ that are the only unknown variables in both energy fluxes $S$ and $\epsilon$. +"gth- scale of the forcing pattern, Re/(21)?thatforthe pattern (1))- (2))is given by 4, = ¢/4 where£ is the orthogonal computational box length. fieldRMHD b, isaresmallval", The solution of the problem is achieved requiring that the flux $S$ entering the system at the large scales is equal to the flux $\epsilon$ flowing from the large to the small scales. +"idcompared as far astothe orthogonaldominantaxial magnetic field Bo=Boé,.", As a matter of fact their that we have computed in the previous section \ref{par3}) ). + Inparticular incompressibility holds as far asthe pertu, This was obtained neglecting the nonlinear terms in eqs. \ref{eq:eq1}) \ref{eq:eq2}) ) +rbed magnetic pressure can, and retainingthe diffusive terms. + be neglected compared to that of strong field b?« cà.Therefore the solutions found," They obtain it in a similar way, by that the induced fields will retain the 1D symmetry of the forcing." + thein thissection arevalid as faras the saturated values of the magnetic field satisfy the previous condition. In allthe presented 4. EFFECTIVE DIFFUSIVITY: ONE-POINT CLOSURE MODELS," Thus the nonlinear terms vanish, as can be proved by direct substitutions of the generic fields $\mathbf{b_{_\perp}} = f(x)\, \mathbf{\hat{e}_y}$, $\mathbf{u_{_\perp}} = g(x)\, \mathbf{\hat{e}_y}$, with $f$ and $g$ generic functions." +" thecomplexity ofthe Parker problem, simplified modelsGiven have been derived. have developed an effective diffusivity that is in", Our simulations investigate the large-scale dynamics and as we show in \ref{sec:ns} the large-scale flow is not laminar and it is steady only in a statistical sense. + effecta one-pointclosuremodel. Inordermodel, Turbulence cannot be confined only to the small scales. +" todiscuss the impact ofourwork the relevantone-point ontheirclosure results,theory we(Biskamp)B2003)..", We discuss the implications for the findings and scaling laws of \cite{hp92} in section \ref{sec:con} devoted to our conclusions. +brieflysummarize In orderto investigate basicproperties of the Parker," In this section we present a series of numerical simulations, summarized in Table \ref{tbl}." +" model and compare them withobservational such theglobal heating rate and required energyconstraints, flux, the detailedas dynamics of turbulent fluctuations (that are essentialtodeterminehow the individual field-lines are heate", We will first describe the results of simulations A–E that model with different resolutions and associated different Reynolds numbers a coronal layer driven by the sheared velocity pattern \ref{eq:f0}) ) at the top plate $z=L$ and a vanishing velocity \ref{eq:f1}) ) atthe bottom plate $z=0$. +"dandhence magnetic fieldsinto averageand fluctuating parts: B-(B-b, u-(u-«ü (21) I", In all simulations the computational box has an aspect ratio of $10$ with $\ell = 1$ and $L=10$. +"ncompressible MHD equationsgive formean fieldsthe following equations: à,(u) + (u)- V(u)= -V(P) +(B)- V(B) -V (παbb) --v V?(u), (22) +Vx (a xb) 4-5V?(B),(23) V"," We present here the results of run A, a simulation performed with a numerical grid of $512 \times 512 \times 200$ points, normal (n=1) diffusion with a Reynolds number $Re=800$ ." +"-(B) =V-b=0,(24) V.(u)- V.4—- where symbols havethe usual meaning,andinparticular vandηarethe microsco"," The Alfvénn velocity is $v_A = 200\, km\, s^{-1}$ corresponding to a ratio $c_A = v_A/u_{ph} = 200$ ." +picviscosityand resistivity ofthe plasma. If itis possibleto modelthe terms that, The total duration is $600$ axial Alfvénn crossing times $\tau_A = L/v_A$ . + contain the small-scale fluctuationstheneqs. (22])-(24)) allowto advancethe meanfields., We add to the system a perturbation (naturally present in the coronal environment) for the magnetic and velocity +The total ἐν luminosity of each cluster. integrated to either Has Hoo or Asoo. 18 given in Table 3..,"The total $K$ luminosity of each cluster, integrated to either $R_{\rm + rms}$ , $R_{200}$ or $R_{500}$, is given in Table \ref{tab-groups2}." + We also show the total number of galaxies with redshifts and NIR data within each radius., We also show the total number of galaxies with redshifts and NIR data within each radius. +" We have shown above that { can easily be measured with a precision about five times better than that of 34,4. a point that has been noted by others (e.g.?).."," We have shown above that $L_K$ can easily be measured with a precision about five times better than that of $M_{\rm dyn}$, a point that has been noted by others \citep[e.g.][]{Popesso-III}." + This makes it a very useful indicator of system mass. although of course it is tracking a fundamentally different quantity than AZ.," This makes it a very useful indicator of system mass, although of course it is tracking a fundamentally different quantity than $M_{\rm dyn}$." + In the top panel of Figure 6 we show the correlation between these two quantities., In the top panel of Figure \ref{fig-MdLk} we show the correlation between these two quantities. + The clusters were selected to span a factor of only three in AM. but they show a factor ~LO spread in Ly.," The clusters were selected to span a factor of only three in $M_{\rm dyn}$, but they show a factor $\sim 10$ spread in $L_K$." +" Note that the apparent lack ofcorrelation is likely a consequence of limited dynamic range in M44. together with significant scatter between 34,4, and Lj."," Note that the apparent lack of correlation is likely a consequence of limited dynamic range in $M_{\rm dyn}$, together with significant scatter between $M_{\rm dyn}$ and $L_K$." + Most of the clusters are consistent with Adj/7Lj=100. shown as the solid line.," Most of the clusters are consistent with $M_{\rm dyn}/L_K=100$, shown as the solid line." + The green and red points indicate X-ray underluminous systems. which will be discussed below.," The green and red points indicate X-ray underluminous systems, which will be discussed below." + Note these most of these have Adiτις ratios in good agreement with the rest of the sample.," Note these most of these have $M_{\rm + dyn}/L_K$ ratios in good agreement with the rest of the sample." + To compare with data from ?. we compute /?»o5 and Aloo in precisely the same way they do. using equations 2. and 3..," To compare with data from \citet{RBGMR} we compute $R_{200}$ and $M_{200}$ in precisely the same way they do, using equations \ref{eqn-r200} and \ref{eqn-m200}." + We measure £y also within /7»00. and show the correlation with Alouc in the bottom panel of Figure 6..," We measure $L_K$ also within $R_{200}$, and show the correlation with $M_{200}$ in the bottom panel of Figure \ref{fig-MdLk}." + The data of ? are shown as the small crosses., The data of \citet{RBGMR} are shown as the small crosses. + The solid line represents a mass-to-light ratio of MonofLa(erκου).=LOO. while the dotted line shows the relation found by 2.. Ligx AL. ," The solid line represents a mass-to-light ratio of $M_{\rm 200}/L_K(r1 halos is 1/VN in the measurement of the mean of the distribution and 1/V2N in the standard deviation."," Specifically, since $\log_{10}\c2$ is Gaussian distributed, the fractional sampling error with $N \gg 1$ halos is $1/\sqrt{N}$ in the measurement of the mean of the distribution and $1/\sqrt{2 N}$ in the standard deviation." + Figure 4 shows the result of increasing the standard deviation by its 1-o sampling error; increasing the mean by its l-o error would have a smaller effect.," Figure \ref{fig:NetoDist} + shows the result of increasing the standard deviation by its $\sigma$ sampling error; increasing the mean by its $\sigma$ error would have a smaller effect." +" While larger simulations will reduce the sampling noise, the Figure shows that this uncertainty is already smaller than the effect of the measurement errors in the cluster masses."," While larger simulations will reduce the sampling noise, the Figure shows that this uncertainty is already smaller than the effect of the measurement errors in the cluster masses." +" Including the rather conservative observational uncertainties that we have assumed in M»oo and 0g, and averaging over Gaussian error distributions in these two observables, we obtain probabilities of 8.596, 3.996, 7.996, and 1396, for agreement between the ACDM simulations and A1689, Cl0024, A1703, and RXJ1347, respectively."," Including the rather conservative observational uncertainties that we have assumed in $\M2$ and $\tE$ , and averaging over Gaussian error distributions in these two observables, we obtain probabilities of $8.5\%$, $3.9\%$, $7.9\%$, and $13\%$, for agreement between the $\Lambda$ CDM simulations and A1689, Cl0024, A1703, and RXJ1347, respectively." +" If we considered just one of the clusters, the large Einstein radius problem would only constitute around a 2-c discrepancy."," If we considered just one of the clusters, the large Einstein radius problem would only constitute around a $\sigma$ discrepancy." +" However, we have four independent objects selected from the population of cluster lenses, and all four are discrepant (in the same direction)."," However, we have four independent objects selected from the population of cluster lenses, and all four are discrepant (in the same direction)." +" The total probability of the theoretical prediction yielding four clusters with such large values of θε is 3x107?, which corresponds to a 4-σ discrepancy."," The total probability of the theoretical prediction yielding four clusters with such large values of $\tE$ is $3 \times +10^{-5}$, which corresponds to a $\sigma$ discrepancy." +" We emphasize that we have included in this calculation the lensing and projection biases, as well as the measurement errors in the cluster masses and Einstein radii."," We emphasize that we have included in this calculation the lensing and projection biases, as well as the measurement errors in the cluster masses and Einstein radii." +" We have presented perhaps the clearest, most robust current conflict between observations and the standard ACDM model."," We have presented perhaps the clearest, most robust current conflict between observations and the standard $\Lambda$ CDM model." +" This model is highly successful in fitting large scale structure measurements, which in turn strongly constrain the free parameters of the model and thus produce precise predictions for comparison with data on smaller scales."," This model is highly successful in fitting large scale structure measurements, which in turn strongly constrain the free parameters of the model and thus produce precise predictions for comparison with data on smaller scales." +" Structure on these scales is non-linear and potentially affected by gas physics, but clusters provide perhaps the best opportunity for a robust comparison between the models and the theory."," Structure on these scales is non-linear and potentially affected by gas physics, but clusters provide perhaps the best opportunity for a robust comparison between the models and the theory." +" Clusters are so large and massive that their evolution is dominated by gravity, especially since their high virial temperature prevents most of the intracluster gas from cooling."," Clusters are so large and massive that their evolution is dominated by gravity, especially since their high virial temperature prevents most of the intracluster gas from cooling." +" The evolution of clusters including gravitational collapse and virialization can now be accurately numerically simulated, with sufficient resolution for studying cluster structure and for simulating lensing in projection, and in sufficient volumes to produce large samples in a cosmological context."," The evolution of clusters including gravitational collapse and virialization can now be accurately numerically simulated, with sufficient resolution for studying cluster structure and for simulating lensing in projection, and in sufficient volumes to produce large samples in a cosmological context." +" At the same time, observations of clusters combining weak and strong lensing now produce accurate virial mass determinations."," At the same time, observations of clusters combining weak and strong lensing now produce accurate virial mass determinations." +" Given the virial mass, the cleanest measure of the halo structure is the effective Einstein radius, which is easily obtained observationally from a model constrained by large numbers of arcs and directly measures the central mass density."," Given the virial mass, the cleanest measure of the halo structure is the effective Einstein radius, which is easily obtained observationally from a model constrained by large numbers of arcs and directly measures the central mass density." +" We derived the theoretical predictions for cluster lensing in ACDM using the distribution of 3-D halo profiles measured by Netoetal.(2007) in the Millennium simulation, after correcting it for lensing and projection biases based on Hennawietal. (2007)."," We derived the theoretical predictions for cluster lensing in $\Lambda$ CDM using the distribution of 3-D halo profiles measured by \citet{Neto} in the Millennium simulation, after correcting it for lensing and projection biases based on \citet{Hennawi}. ." +. These analyses of numerical samples expressed halo structure in terms of the NFW concentration parameter., These analyses of numerical samples expressed halo structure in terms of the NFW concentration parameter. +" We found two key results (Figure 1)) based on the halo analysis by Hennawietal. (2007):: first, that the distribution of 3-D concentrations of the lens population is the same as that of the general halo population except for a shift upwards by a factor of 1.17; and second, that the concentrations measured in projection are related to the 3-D concentrations, such that the ratio follows a lognormal distribution which corresponds to a factor of 1.14 shift plus a factor of 1.33 spread."," We found two key results (Figure \ref{fig:Hennawi}) ) based on the halo analysis by \citet{Hennawi}: first, that the distribution of 3-D concentrations of the lens population is the same as that of the general halo population except for a shift upwards by a factor of 1.17; and second, that the concentrations measured in projection are related to the 3-D concentrations, such that the ratio follows a lognormal distribution which corresponds to a factor of 1.14 shift plus a factor of 1.33 spread." +" The concentration parameter is higher for relaxed halos than for unrelaxed, and it declines slowly with halo mass, resulting ina predicted Einstein radius that increases roughly linearly with mass for relaxed halos(Figure 2))."," The concentration parameter is higher for relaxed halos than for unrelaxed, and it declines slowly with halo mass, resulting ina predicted Einstein radius that increases roughly linearly with mass for relaxed halos(Figure \ref{fig:NetoMean}) )." +" We compared the theoretical predictions with the observed Og for four clusters, A1689, Cl0024, A1703,and"," We compared the theoretical predictions with the observed $\tE$ for four clusters, A1689, Cl0024, A1703,and" +increases as the scale of dissipation decreases and that i decreases as the length of the computational domain in the azimuthal direction is increased.,increases as the scale of dissipation decreases and that it decreases as the length of the computational domain in the azimuthal direction is increased. + Lt is not clear to wha extend zero-mean [ux calculations for long times are elfectec by the error that we found ancl we would suggest that al calculations in a shearing box check that mean quantities are maintained to expected. values., It is not clear to what extend zero-mean flux calculations for long times are effected by the error that we found and we would suggest that all calculations in a shearing box check that mean quantities are maintained to expected values. + This paper does pose some questions of which the mos obvious is whether or not à change in the balance of mean components of the magnetic field. along with the strength of the magnetic field. always gives rise to a change in the accretion rates.," This paper does pose some questions of which the most obvious is whether or not a change in the balance of mean components of the magnetic field, along with the strength of the magnetic field, always gives rise to a change in the accretion rates." + This issue is being investigated at. present., This issue is being investigated at present. + We would like to thank Steve Balbus. John Lawley. Pierre Lesallre and. Jim Stone for suggestions and. comments on during this work.," We would like to thank Steve Balbus, John Hawley, Pierre Lesaffre and Jim Stone for suggestions and comments on during this work." + We wish to thank the Eeole Normale Superieure for the supercomputer known as JxD on which these calculations were carried out., We wish to thank the Ecole Normale Superieure for the supercomputer known as JxB on which these calculations were carried out. + We also wish to thank the referee for helpful suggestions., We also wish to thank the referee for helpful suggestions. +associated with hydrogen lines.,associated with hydrogen lines. + These candidates are selected the same way the deuterim candidates are selected. in all respects but one: the control sample candidates are drawn from the red side of hydrogen absorbers. rather than he blue side where the real deuteriuni feature appears.," These candidates are selected the same way the deuterium candidates are selected, in all respects but one: the control sample candidates are drawn from the red side of hydrogen absorbers, rather than the blue side where the real deuterium feature appears." + To make a larecr siuuple. the velocity bin to accept a pretend candidate is also larger than that or a deuterimu candidate (ic. |60.100 kiui/sec rather than |82+1σ] skin/sec).," To make a larger sample, the velocity bin to accept a pretend candidate is also larger than that for a deuterium candidate (i.e., $[-60, -100]$ km/sec rather than $[-82\pm 1\sigma]$ km/sec)." + The pretend candidates are all interlopers. drawn frou. a population with the same statistical properties as the deuteriun iuterlopers. iuclhudiug heir joiut correlations in velocity. column density aud width.," The pretend candidates are all interlopers, drawn from a population with the same statistical properties as the deuterium interlopers, including their joint correlations in velocity, column density and width." + The properties of wo sauples can then be compared statistically. using the Doppler parameters and colin densities from the line fits.," The properties of two samples can then be compared statistically, using the Doppler parameters and column densities from the line fits." + For a fair comparison we have also assenibled a uniformi sauiple of deutermuua absorbers from the same spectra as the pretend ασιαπα absorbers. based," For a fair comparison we have also assembled a uniform sample of deuterium absorbers from the same spectra as the pretend deuterium absorbers, based" +The BSG studies of the less massive galaxies NGC 300 (Kudritzkietal.2008) and M33 (Uetal.2009). resulted in gradients of 0.08 and 0.07 dex Κροτ. respectively. steeper than M81 but still very shallow.,"The BSG studies of the less massive galaxies NGC 300 \citep{kud08} and M33 \citep{u09} resulted in gradients of 0.08 and 0.07 dex $^{-1}$, respectively, steeper than M81 but still very shallow." + For the metallicity correction of Cepheid distance moduli this has severe consequences. as will be discussed in section 7.," For the metallicity correction of Cepheid distance moduli this has severe consequences, as will be discussed in section 7." + As first demonstrated by Kudritzkietal.(2003). there is a very simple and compelling way to use BSGs for distance determinations., As first demonstrated by \citet{kud03} there is a very simple and compelling way to use BSGs for distance determinations. + Massive stars with masses in the range from 12 to 40 M. evolve through the BSG stage at roughly constant luminosity., Massive stars with masses in the range from 12 to 40 $_\odot$ evolve through the BSG stage at roughly constant luminosity. + In addition. since the evolutionary timescale is very short when crossing through the BSG domain. the amount of mass lost in this stage is small.," In addition, since the evolutionary timescale is very short when crossing through the BSG domain, the amount of mass lost in this stage is small." + As a consequence. the evolution proceeds at constant mass and constant lumimosity.," As a consequence, the evolution proceeds at constant mass and constant luminosity." + This has a very simple. but very nportant consequence for the relationship between gravity and effective temperature along the evolution towards the RSG stage. namely that the flux-weighted gravity log gr. defined as log er = log g - 4og (Το 10). stays constant.," This has a very simple, but very important consequence for the relationship between gravity and effective temperature along the evolution towards the RSG stage, namely that the flux-weighted gravity log $_{F}$, defined as log $_{F}$ = log g - 4log $_{\rm eff}$ $^{4}$ ), stays constant." + As shown in detail by Kudritzki et al. (, As shown in detail by Kudritzki et al. ( +2008) this immediately leads to the flux-weighted gravity-luminosity relationship (FGLR): In practice this means that. after careful calibration the lummosity of BSGs can be inferred by a purely spectroscopicli method from measurements of the effective temperature and effective gravity alone.,"2008) this immediately leads to the flux-weighted gravity–luminosity relationship (FGLR): In practice this means that, after careful calibration the luminosity of BSGs can be inferred by a purely spectroscopic method from measurements of the effective temperature and effective gravity alone." + Using the new spectral diagnostic techniques described above. Kudritzkietal.(2008) determied blue supergiant temperatures and gravities for a large sample of BSGs in NGC 300.," Using the new spectral diagnostic techniques described above, \citet{kud08} determined blue supergiant temperatures and gravities for a large sample of BSGs in NGC 300." + They then used the comparisor of the calculated spectral energy distributions with multi-color HST photometry to precisely determine interstellar reddening and extinction. in order to obtain de-reddened visual and bolometric magnitudes.," They then used the comparison of the calculated spectral energy distributions with multi-color HST photometry to precisely determine interstellar reddening and extinction, in order to obtain de-reddened visual and bolometric magnitudes." + This revealed a beautiful and tight FGLR reftig 13))., This revealed a beautiful and tight FGLR \\ref{fig13}) ). + Including the results from quantitative spectroscopy of eight more galaxies then led to a first calibration reffigl+ =)., Including the results from quantitative spectroscopy of eight more galaxies then led to a first calibration \\ref{fig14} ). + With a relatively small residual scatter. of z 0.3 mag the observed FGLR ts an excellent tool to determine accurate spectroscopic distance to galaxies., With a relatively small residual scatter of $\approx$ 0.3 mag the observed FGLR is an excellent tool to determine accurate spectroscopic distance to galaxies. + It requires multicolor photometry and low resolution (5A)) spectroscopy to determine effective temperature and gravity and. thus. flux-weighed gravity directly from the spectrum.," It requires multicolor photometry and low resolution ) spectroscopy to determine effective temperature and gravity and, thus, flux-weighed gravity directly from the spectrum." + With effective temperature. gravity and metallicity determined one also knows the bolometric correction. which 15 small for A supergiants. which means that errors in the stellar parameters do not largely affect the determination of bolometric magnitudes.," With effective temperature, gravity and metallicity determined one also knows the bolometric correction, which is small for A supergiants, which means that errors in the stellar parameters do not largely affect the determination of bolometric magnitudes." + Moreover. one knows the intrinsic stellar SED and. therefore. can determine interstellar reddening and extinction. from the multicolor photometry. which then allows for the accurate determination of the reddening-free apparent bolometric magnitude.," Moreover, one knows the intrinsic stellar SED and, therefore, can determine interstellar reddening and extinction from the multicolor photometry, which then allows for the accurate determination of the reddening-free apparent bolometric magnitude." + The application. of the FGLR then yields absolute magnitudes and. thus. the distance modulus.," The application of the FGLR then yields absolute magnitudes and, thus, the distance modulus." + The first distance determination of this type has been carried out by Urbanejaetal.(2008) who studied blue supergiants in WLM. one of the faintest dwarf irregular galaxies in the Local Group.," The first distance determination of this type has been carried out by \citet{urbaneja08} who studied blue supergiants in WLM, one of the faintest dwarf irregular galaxies in the Local Group." + The quantitative spectral analysis of VLT FORS spectra yields an extremely low metallicity of the young stellar population in this galaxy with an average of -0.9 dex below the solar value., The quantitative spectral analysis of VLT FORS spectra yields an extremely low metallicity of the young stellar population in this galaxy with an average of -0.9 dex below the solar value. + The interstellar extinction Is again extremely patchy ranging from 0.03 to 0.30 mag in E(B-V) (note that the foreground value given by Schlegeletal.1998 18 0.037 mag)., The interstellar extinction is again extremely patchy ranging from 0.03 to 0.30 mag in E(B-V) (note that the foreground value given by \citealt{schlegel98} is 0.037 mag). + The individually de-reddened FGLR - in apparent bolometric magnitude - is shown in reffig]5. yielding a distance modulus of 24.99 £0.10 mag in very good agreement with the TRGB distance al.2007) and the K-band Cepheid distance (Gierenetal. 2008)., The individually de-reddened FGLR - in apparent bolometric magnitude - is shown in \\ref{fig15} yielding a distance modulus of 24.99 $\pm{0.10}$ mag in very good agreement with the TRGB distance \citep{rizzi07} and the K-band Cepheid distance \citep{gieren08}. +. Uetal.(2009) have used KECK DEIMOS and ESI spectra to determine a distance to the Triangulum galaxy M33., \citet{u09} have used KECK DEIMOS and ESI spectra to determine a distance to the Triangulum galaxy M33. + The case of M33 is particularly interesting. since many independent distance determinations have been carried out for this galaxy during the last decade using a variety of techniques. including Cepheids. RR Lyrae. TRGB. red clump stars. planetary nebulae. horizontal branch stars and long-period variables.," The case of M33 is particularly interesting, since many independent distance determinations have been carried out for this galaxy during the last decade using a variety of techniques, including Cepheids, RR Lyrae, TRGB, red clump stars, planetary nebulae, horizontal branch stars and long-period variables." + The surprising result of all of these studies has been that the distance moduli obtained with these different methods differ by as much as 0.6 mag. which ts more than in linear distance.," The surprising result of all of these studies has been that the distance moduli obtained with these different methods differ by as much as 0.6 mag, which is more than in linear distance." + The FGLR-method yields a long distance modulus for M33 of 24.93 +0.1] mag. in basic agreement with a TRGB distance of 24.84 0.10 mag obtained by the same authors from HST ACS imagine.," The FGLR-method yields a long distance modulus for M33 of 24.93 $\pm{0.11}$ mag, in basic agreement with a TRGB distance of 24.84 $\pm{0.10}$ mag obtained by the same authors from HST ACS imaging." + The long distance modulus agrees also very well with the eclipsing binary distance obtained by Bonanosetal.(2006)., The long distance modulus agrees also very well with the eclipsing binary distance obtained by \citet{bonanos06}. +. U et al., U et al. + relate the difference between their result and the published Cepheid distances to the difference in accounting for interstellar reddening (see reftig 1))., relate the difference between their result and the published Cepheid distances to the difference in accounting for interstellar reddening (see \\ref{fig1}) ). + Kudritzkietal.(2011). analyzed Keck LRIS spectra of BSGs in M81 and applied the FGLR method to obtain a distance modulus of 27.7 +0.1 mag in good agreement with recent TRGB work reffig16))., \citet{kud11} analyzed Keck LRIS spectra of BSGs in M81 and applied the FGLR method to obtain a distance modulus of 27.7 $\pm{0.1}$ mag in good agreement with recent TRGB work \\ref{fig16}) ). + The coNparisor with Cepheid distances ts discussed in the next section., The comparison with Cepheid distances is discussed in the next section. +Bruch&Schimpke(1992) reviewed the discovery history of this star aud published a spectru1 that shows i somewhat brighter aud bluer than our mean specrum.,\citet{bruchschimpke92} reviewed the discovery history of this star and published a spectrum that shows it somewhat brighter and bluer than our mean spectrum. + They described their spectrum as resemblir© that of a dwarf nova ou the decline (rom outhirst. while ours appears to represe a more nearly quiescent state.," They described their spectrum as resembling that of a dwarf nova on the decline from outburst, while ours appears to represent a more nearly quiescent state." + The continuum shows weak. broad. features that resemble the absorption xukls of a secondary star. but we were unable o match these couvincinely to or spectral-type standards. so they may not arise from a secoixary.," The continuum shows weak, broad features that resemble the absorption bands of a secondary star, but we were unable to match these convincingly to our spectral-type standards, so they may not arise from a secondary." + Our data come οι two short runs separaed by two years: the F1 hi period is present in both data sets. and is definitive in te combined data. but the cycle count between runs is not deternine.," Our data come from two short runs separated by two years; the 4.1 h period is present in both data sets, and is definitive in the combined data, but the cycle count between runs is not determined." + Our spectrin1 resembles the one obtained by Szkody&Howell(1992).. except that the flux level in our spectdur is somewhat lower aud the emission equivalent width appears to be greater.," Our spectrum resembles the one obtained by \citet{szkodyhowell92}, except that the flux level in our spectrum is somewhat lower and the emission equivalent width appears to be greater." + Like them. we detect an M-type companion: they estimated the spectral ype to be in the rauge MO to M5. aud from lal estimated the distaice to be 110 pc. for their laest possible spectral type.," Like them, we detect an M-type companion; they estimated the spectral type to be in the range M0 to M5, and from that estimated the distance to be $> 110$ pc, for their latest possible spectral type." + They did uot have a Poy with which to«'Oustraiu the size ol the Roche lobe., They did not have a $P_{\rm orb}$ with which to constrain the size of the Roche lobe. + Our 3.85 li period is based on Πα radia velocities from a sinee observing rtu in 2005 Septeuber., Our 3.85 h period is based on $\alpha$ radial velocities from a single observing run in 2005 September. + We obtainec shotometry in 2005 5eptember that showed the st:iP Lear V15.0 ou two separate nights: the svuthesized V. magniuce from our nean spectrin is also neal 15.0., We obtained photometry in 2005 September that showed the star near $V = 18.0$ on two separate nights; the synthesized $V$ magnitude from our mean spectrum is also near 18.0. + Using the secondary star spectrum (Table 7)) we firul VZ Aqr to ye considerably ereale0 “thar the miuimunui cistauce fouud by Szkody&Howell(1992., Using the secondary star spectrum (Table \ref{tab:inferences}) ) we find VZ Aqr to be considerably greater than the minimum distance found by \citet{szkodyhowell92}. + Warner(1987) louud au empirical ‘elaticoiship between the absolute visual magiudes of dwarf novae al max]uinum leght aud their «η] periods., \citet{warner87} found an empirical relationship between the absolute visual magnitudes of dwarf novae at maximum light and their orbital periods. + This predicts M:=3.8 at VZ Aqrs period., This predicts $M_V = +3.8$ at VZ Aqr's period. + VZ Aqr reaches V.=11.3. whic WOd iniply a distance near 320 pe.," VZ Aqr reaches $V = 11.3$, which would imply a distance near 320 pc." + Given this. otr estimate of OtJOC:20.—220) pe is probably soLewhat ο‘eater than the true distance.," Given this, our estimate of $600 (+350, -220)$ pc is probably somewhat greater than the true distance." + As noted above. the normalization of the spectrum used for the distaie calculation is corroborated by the plotometry derived. from direct. imagine.," As noted above, the normalization of the spectrum used for the distance calculation is corroborated by the photometry derived from direct imaging." + The lagest uncertaintv in the distance calculation is the spectral classification of the secoudary star., The largest uncertainty in the distance calculation is the spectral classification of the secondary star. + A closer distance would suggest a spectral typesonewhat cooler than our estimate., A closer distance would suggest a spectral typesomewhat cooler than our estimate. + The X-ray source RXJ2133.72-5107. was discovered by the ROSAT Calactic Plaue Survey as all X-ray source. aud subsequently ideutilied as à DQ Her-type CV by Motchetal.(1998).," The X-ray source RXJ2133.7+5107 was discovered by the $ROSAT$ Galactic Plane Survey as an X-ray source, and subsequently identified as a DQ Her-type CV by \citet{motch98}." +". Bonuet-Bidaudetal.(2006) presented photometry which revealed a 570 s modulation. related to the white-dwarl spin period. aud spectroscopy showing a radial-velocity period of 7.193(16) h. or 0.2098(7) d. which is evideutly 2,4,"" "," \citet{bonnetrx2133} presented photometry which revealed a 570 s modulation, related to the white-dwarf spin period, and spectroscopy showing a radial-velocity period of 7.193(16) h, or 0.2998(7) d, which is evidently $P_{\rm orb}$ ." +Our Ha radial velocities show iodulation at 0.297132(3) d:, Our $\alpha$ radial velocities show modulation at 0.297432(3) d; +by metallicity variations.,by metallicity variations. + Thus. 1t is interesting to carry out this sensitivity study taking advantage of the well-populated white dwarf color-magnitude diagram. to test whether just modeling the white dwarf population can exclude the presence of subpopulations generated by progenitors with a metallicity different from the one measured spectroscopically.," Thus, it is interesting to carry out this sensitivity study taking advantage of the well-populated white dwarf color-magnitude diagram, to test whether just modeling the white dwarf population can exclude the presence of subpopulations generated by progenitors with a metallicity different from the one measured spectroscopically." + To perform this study. we first considered varying fractions fz of an extreme subpopulation with zero metallicity.," To perform this study, we first considered varying fractions $f_Z$ of an extreme subpopulation with zero metallicity." + The pre-white dwarf lifetimes were taken from Marigo et al. (, The pre-white dwarf lifetimes were taken from Marigo et al. ( +2001). whilst the carbon-oxygen stratification in the white dwarf models was kept unchanged. given the small effect of the progenitor initial chemical composition on the final carbon-oxygen profiles and cooling times at fixed white dwarf mass — see. for instance. Salaris et al. (,"2001), whilst the carbon-oxygen stratification in the white dwarf models was kept unchanged, given the small effect of the progenitor initial chemical composition on the final carbon-oxygen profiles and cooling times at fixed white dwarf mass – see, for instance, Salaris et al. (" +2010) and Renedo et al. (,2010) and Renedo et al. ( +2010).,2010). + We also neglected the delay introduced by Ne sedimentation. to account for the negiglible abundance of this element in Z=0 models.," We also neglected the delay introduced by $^{22}$ Ne sedimentation, to account for the negiglible abundance of this element in $Z=0$ models." + The reason for this is the following., The reason for this is the following. + Ne is produced during the helium burning phase by the chain of reactions Ναy) SFB) Olu. y)7Ne.," $^{22}$ Ne is produced during the helium burning phase by the chain of reactions $^{14}$ $(\alpha, \gamma)^{18}$ $(\beta^+)^{18}$ $(\alpha, +\gamma)^{22}$ Ne." + The net effect is to transform essentially all '4N into Ne., The net effect is to transform essentially all $^{14}$ N into $^{22}$ Ne. +" In the extreme case ofZ=0 stars some ""N is produced when the CNO cycle is activated by the C produced by 3« reactions ignited by the high temperatures during the main sequence phase of metal free stars.", In the extreme case of $Z=0$ stars some $^{14}$ N is produced when the CNO cycle is activated by the $^{12}$ C produced by $\alpha$ reactions ignited by the high temperatures during the main sequence phase of metal free stars. + However. its abundance mass fraction is €107? (Weiss et al.," However, its abundance mass fraction is $\la 10^{-9}$ (Weiss et al." + 2000)., 2000). + The results of our simulations are shown in Fig. 3.., The results of our simulations are shown in Fig. \ref{Z0}. + We begi by discussing the color-magnitude diagram shown in upper left panel., We begin by discussing the color-magnitude diagram shown in upper left panel. + Obviously. white dwarfs resulting from metal-poor progenitors detach from the bulk of the population. and several of these synthetic white dwarfs can be found below the well-defied cut-off of the observed cooling sequence. as expected. because the lack of Ne causes a faster cooling.," Obviously, white dwarfs resulting from metal-poor progenitors detach from the bulk of the population, and several of these synthetic white dwarfs can be found below the well-defined cut-off of the observed cooling sequence, as expected, because the lack of $^{22}$ Ne causes a faster cooling." + The upper right panel of this figure shows the corresponding luminosity function., The upper right panel of this figure shows the corresponding luminosity function. + The overall agreement with the observed luminosity function is poor. especially in the region between the two peaks.," The overall agreement with the observed luminosity function is poor, especially in the region between the two peaks." + An increase of the binary fraction to reproduce the bright peak better would not improve the modeling of the regio between the peaks., An increase of the binary fraction to reproduce the bright peak better would not improve the modeling of the region between the peaks. + The natural question to address is then which is the maximum fraction of metal-poor white dwarf progenitors that can be accommodated within the observational white-dwarf luminosity function?, The natural question to address is then which is the maximum fraction of metal-poor white dwarf progenitors that can be accommodated within the observational white-dwarf luminosity function? + To this purpose we have computed synthetic white dwarf samples with decreasing fractions of metal-poor progenitors. and we ran a y test.," To this purpose we have computed synthetic white dwarf samples with decreasing fractions of metal-poor progenitors, and we ran a $\chi^2$ test." +" We found that the maximum allowed fraction of metal-poor progenitors is f,=0.12.", We found that the maximum allowed fraction of metal-poor progenitors is $f_Z=0.12$. + Obviously. the assumption that this subpopulation has zero metallicity is probably to extreme.," Obviously, the assumption that this subpopulation has zero metallicity is probably to extreme." + Consequently. we repeated the same calculation for a subpopulation of solar metallicity — see the bottom panels of Fig. 3..," Consequently, we repeated the same calculation for a subpopulation of solar metallicity – see the bottom panels of Fig. \ref{Z0}." + In this case the maximum fraction of solar-metallicity progenitors is fz=0.08., In this case the maximum fraction of solar-metallicity progenitors is $f_Z=0.08$. + We now focus on the possibility of determining the fraction of non-DA white dwarfs) im NGC 079]., We now focus on the possibility of determining the fraction of non-DA white dwarfs in NGC 6791. + The spectral evolution of white dwarf atmospheres is still a controversial question. and although the ratio of white dwarfs with pure hydrogen atmosphere versus white dwarfs with hydrogen-deficient atmospheres is known for the local field. very few determinations exist for open and globular clusters.," The spectral evolution of white dwarf atmospheres is still a controversial question, and although the ratio of white dwarfs with pure hydrogen atmosphere versus white dwarfs with hydrogen-deficient atmospheres is known for the local field, very few determinations exist for open and globular clusters." + Moreover. although for the field white dwarf population the canonical percentage is around80.. observations show that this ratio depends on the effective temperature — see. for instance. Tremblay Bergeron (2008) and references therein.," Moreover, although for the field white dwarf population the canonical percentage is around, observations show that this ratio depends on the effective temperature – see, for instance, Tremblay Bergeron (2008) and references therein." + However. the only reliable determinations for open clusters are those of Kalirat et al. (," However, the only reliable determinations for open clusters are those of Kalirai et al. (" +"2005) for the rich. young cluster NGC 2099, and Rubin et al. (","2005) for the rich, young cluster NGC 2099, and Rubin et al. (" +2008) for NGC 1039.,2008) for NGC 1039. + Kalirai et al. (, Kalirai et al. ( +"2005) found a clear deficit of non-DA white dwarfs in NGC 2099, whereas Rubin et al. (","2005) found a clear deficit of non-DA white dwarfs in NGC 2099, whereas Rubin et al. (" +2008) found that the fraction of non-DA white dwarfs in the open cluster NGC 1039 is ~10%. at most.,"2008) found that the fraction of non-DA white dwarfs in the open cluster NGC 1039 is $\sim +10\%$, at most." + Clearly. investigating the DA to non-DA ratio in another open cluster is therefore of greatest interest.," Clearly, investigating the DA to non-DA ratio in another open cluster is therefore of greatest interest." + We addressed this question by simulating the cluster population of white dwarfs with an increasing fraction of DA stars., We addressed this question by simulating the cluster population of white dwarfs with an increasing fraction of non-DA stars. + The non-DA fractions adopted here are 0.0. 0.1. 0.2 and 0.4. respectively.," The non-DA fractions adopted here are $f_{\rm non-DA}=0.0$ , 0.1, 0.2 and 0.4, respectively." + For the sake of conciseness. we only show the results for fij;p4=0.1 — left panel — and 0.2 — right panel.," For the sake of conciseness, we only show the results for $f_{\rm non-DA}=0.1$ – left panel – and 0.2 – right panel." + As shown in Fig., As shown in Fig. + 4. the white-dwarf luminosity function is sensitive to the ratio of non-DA to DA white dwarts., \ref{noDA} the white-dwarf luminosity function is sensitive to the ratio of non-DA to DA white dwarfs. + We find that when the fraction of non-DA white dwarfs ts increased. the agreement with the observational white-dwarf luminosity function. rapidly degrades.," We find that when the fraction of non-DA white dwarfs is increased, the agreement with the observational white-dwarf luminosity function rapidly degrades." + To be precise. when the fraction of non-DA white dwarfs is foon-pa=0.1. the agreement is quite poor. and when the fraction of non-DA white dwarfs is that of field white dwarfs. foon-pa=0.2. the quality of the fit to the observational white-dwarf luminosity function is unacceptable.," To be precise, when the fraction of non-DA white dwarfs is $f_{\rm non-DA}=0.1$, the agreement is quite poor, and when the fraction of non-DA white dwarfs is that of field white dwarfs, $f_{\rm +non-DA}=0.2$, the quality of the fit to the observational white-dwarf luminosity function is unacceptable." + This is because for the age of NGC 6791 non-DA and DA white dwarfs pile-up at similar luminosities., This is because for the age of NGC 6791 non-DA and DA white dwarfs pile-up at similar luminosities. + As a consequence. adding single non-DA white dwarfs lowers the height of the bright peak compared to the faint one.," As a consequence, adding single non-DA white dwarfs lowers the height of the bright peak compared to the faint one." + To quantify which the maximum fraction of non-DA white dwarfs that can be accommodated within the observational errors is. we conducted a y test. and we found that for fractions of non-DA white dwarfs larger than ~0.1 the probability rapidly drops below ~0.7. whereas for ωρα=0.0 the probability is ~0.9.," To quantify which the maximum fraction of non-DA white dwarfs that can be accommodated within the observational errors is, we conducted a $\chi^2$ test, and we found that for fractions of non-DA white dwarfs larger than $\sim 0.1$ the probability rapidly drops below $\sim 0.7$, whereas for $f_{\rm non-DA}=0.0$ the probability is $\sim 0.9$." + Consequently. the fraction of non-DA white dwarfs in NGC 6791 can roughly be at most half the value found for field white dwarfs.," Consequently, the fraction of non-DA white dwarfs in NGC 6791 can roughly be at most half the value found for field white dwarfs." + This result qualitatively agrees with the findings of Kalirat et al. (, This result qualitatively agrees with the findings of Kalirai et al. ( +2005). who find that for NGC 2099 this deficit of non-DA white dwarfs is even higher.,"2005), who find that for NGC 2099 this deficit of non-DA white dwarfs is even higher." + As a matter of fact. Kalirai et al. (," As a matter of fact, Kalirai et al. (" +2005) found that for this cluster all white dwarfs in their sample were of the DA type.,2005) found that for this cluster all white dwarfs in their sample were of the DA type. + Our results also point in the same direction. although a fraction of ~5% 1s still compatible with the observed white-dwarf luminosity function of NGC 6791. in agreement with the findings of Kalirai et al. (," Our results also point in the same direction, although a fraction of $\sim 5\%$ is still compatible with the observed white-dwarf luminosity function of NGC 6791, in agreement with the findings of Kalirai et al. (" +2007).,2007). + Finally. we considered also. the possibility that the fraction of non-DA white dwarfs changes with the effective temperature. which OCCUIS with field white dwarfs.," Finally, we considered also the possibility that the fraction of non-DA white dwarfs changes with the effective temperature, which occurs with field white dwarfs." + In particular. we assumed that for effective temperatures higher than 60000 K. the fraction of non-DA white dwarfs is fÁuu-b4=0.2 and for temperatures ranging from 50000 K to 60000 K. ωρα= 0.0. as suggested by observations," In particular, we assumed that for effective temperatures higher than 000 K, the fraction of non-DA white dwarfs is $f_{\rm non-DA}=0.2$ and for temperatures ranging from 000 K to 000 K, $f_{\rm non-DA}=0.0$ , as suggested by observations" +the local overdensity 0 is smaller than a threshold. 6<35. and above. 027054. we identify galaxies with a probability,"the local overdensity $\delta$ is smaller than a threshold, $\delta < \delta_{th}$, and above, $\delta > +\delta_{th}$, we identify galaxies with a probability." + A (threshold was also used. in ?) where the bias factor was determined from the amount of matter in volds., A threshold was also used in \citet{Ei99} where the bias factor was determined from the amount of matter in voids. + Furthermore. hvdrodvnamic simulations of 2). and 7) have confirmed that galaxy formation is inellicient in low density regions where the density is determined. on galactic scale.," Furthermore, hydrodynamic simulations of \citet{WHK97} and \citet{CO99} have confirmed that galaxy formation is inefficient in low density regions where the density is determined on galactic scale." + The probability. clistribution for 9On is only a slight modification which hinders a strong increase of the galaxy clustering at high local densities.," The probability distribution for $\delta > +\delta_{th}$ is only a slight modification which hinders a strong increase of the galaxy clustering at high local densities." + Physically. it models the merging of small galaxies in high density regions.," Physically, it models the merging of small galaxies in high density regions." + This mocüfication becomes mainly ellective for models which are hiehly evolved at galaxy scales. such as SCDÀM and AC DAL.," This modification becomes mainly effective for models which are highly evolved at galaxy scales, such as SCDM and $\Lambda$ CDM." + For a discussion of such a local bias prescription. compare also 2)..," For a discussion of such a local bias prescription, compare also \citet{MPH98}." + A two-parameter model for galaxy. identification is similar to the method used by 2). to produce. mock samples of the 2dE- and Sloan Digital Sky surveys., A two-parameter model for galaxy identification is similar to the method used by \citet{CHWF98} to produce mock samples of the 2dF- and Sloan Digital Sky surveys. + Lt was also emploved for LORS mock samples in ?).., It was also employed for LCRS mock samples in \citet{DMRT99}. . + According to the motivation. we expect that the threshold. overdensity δρ determines the size distribution of voids in the mock samples.," According to the motivation, we expect that the threshold overdensity $\delta_{th}$ determines the size distribution of voids in the mock samples." +" We vary its value between 9,5,=O0.9...2. but with a prevalence of values near zero."," We vary its value between $\delta_{th} = -0.9 +\dots 2$, but with a prevalence of values near zero." + We also checked. the 2-point correlation function of mock samples in comparison with the redshift space correlation function of the LORS ealaxies given by 2). and with a reconstruction of the real space correlation function of similarly bright APAL galaxies given by 72)..., We also checked the 2-point correlation function of mock samples in comparison with the redshift space correlation function of the LCRS galaxies given by \citet{Tu97} and with a reconstruction of the real space correlation function of similarly bright APM galaxies given by \citet{Ba96}. + For reproducing the correlation function. the suppression of galaxy numbers in high density regions as modeled. by Iq. (," For reproducing the correlation function, the suppression of galaxy numbers in high density regions as modeled by Eq. (" +3) is important. (see also 2))).,3) is important (see also \citet{JMB98}) ). + The parameters of the 11 mock samples we use are given in Table 2., The parameters of the 11 mock samples we use are given in Table \ref{fit}. + In Fig., In Fig. + 6. we compare the correlation functions of one mock sample for cach CDM model with the data of APAL galaxies in real space according to ?)..," 6, we compare the correlation functions of one mock sample for each CDM model with the data of APM galaxies in real space according to \citet{Ba96}." + (The correlation function of the SCDAL mock samples 2 and 3λ reproduce the correlation function in the highlyA clustered region rr«rgà5.5h1 “Ape., The correlation function of the SCDM mock samples 2 and 3 reproduce the correlation function in the highly clustered region $r < r_0 \approx 5.5 \mhmpc$ . + Here. ro denotes the correlation. length. and. at smaller scales. the correlation function is well described by a power law £=(rfru)B6," Here, $r_0$ denotes the correlation length, and, at smaller scales, the correlation function is well described by a power law $\xi = (r/r_0)^{-1.6}$." +" ""Phe SCDAL models. however. cannot reproduce the correlation function at. larger. raclii."," The SCDM models, however, cannot reproduce the correlation function at larger radii." + ltods well known that the SCDM model has. insullicient power on large scales to reproduce the observed. clustering of galaxies., It is well known that the SCDM model has insufficient power on large scales to reproduce the observed clustering of galaxies. + There is no possibility to cure this. dilliculty with our simple bias prescription., There is no possibility to cure this difficulty with our simple bias prescription. + The correlation function of mock sample Lis not shown. but it looks similar to that of mock sample 2.," The correlation function of mock sample 1 is not shown, but it looks similar to that of mock sample 2." + The correlation function. of mock sample 7 for the ACDAL ancl of the mock sample S for the OCDAL mode reproduce the correlation function. between h*XIpe 10 \mhmpc$." + Obviously. the ugh threshold in this model leads to a strong suppression of he mock galaxy density in medium censity regions. and herefore to a suppression of the correlation function. on hese scales.," Obviously, the high threshold in this model leads to a strong suppression of the mock galaxy density in medium density regions, and therefore to a suppression of the correlation function on these scales." + As Fig., As Fig. + 6 demonstrates. the mock sample 11 of the BCDAL model leads to a good fit of the correlation unction over the total range shown.," 6 demonstrates, the mock sample 11 of the BCDM model leads to a good fit of the correlation function over the total range shown." + The LORS correlation unction in redshift space of ο) is similarly fitted (see a similar comparison with CDM mocels in that paper), The LCRS correlation function in redshift space of \citet{Tu97} is similarly fitted (see a similar comparison with CDM models in that paper). + Voids in the mock samples are found with the same algorithm as in the LORS data., Voids in the mock samples are found with the same algorithm as in the LCRS data. + Here we search for. voids both in square areas of the simulation box and in volumes representing a similar wedge-like ecometry as in the LORS data., Here we search for voids both in square areas of the simulation box and in volumes representing a similar wedge-like geometry as in the LCRS data. + For the mock prescription 6 in the OCDAL model. we also selected. 10 realizations with a wedge geometry.," For the mock prescription 6 in the OCDM model, we also selected 10 realizations with a wedge geometry." + To this aim. we place a fictitious observer in one corner of the simulation box andproduce a wedege-likesection of SO«1.5 degree extension. as in the LORS slices. and. select. the galaxies in the distance range between 200 and 350. Mpe..," To this aim, we place a fictitious observer in one corner of the simulation box andproduce a wedge-likesection of $80 \times 1.5$ degree extension, as in the LCRS slices, and select the galaxies in the distance range between 200 and 350 ." +Fig. 4..,Fig. \ref{fig:qsoheat}. +" The temperatures are shown at redshifts 10, 8, 7 and 6 with ionized fractions 0.01, 0.54, 0.96, 0.999 respectively."," The temperatures are shown at redshifts 10, 8, 7 and 6 with ionized fractions 0.01, 0.54, 0.96, 0.999 respectively." +" In the inner parts of the “Τι bubble"" the amplitude of Ti is about zz109? K. The secondary electrons created by high energy X-ray radiation thermalizes to these high temperature values.", In the inner parts of the $\mathrm{T_k}$ bubble” the amplitude of $\mathrm{T_k}$ is about $\approx 10^{6.5}$ K. The secondary electrons created by high energy X-ray radiation thermalizes to these high temperature values. + Also contributing to extremely high temperatures in the very inner parts of the bubble is Compton heating (Thomasetal.2009)., Also contributing to extremely high temperatures in the very inner parts of the bubble is Compton heating \citep{thomas09}. +. The mean free path of X-rays are extremely large resulting in a spatial extent of heating that reaches many Mpcs., The mean free path of X-rays are extremely large resulting in a spatial extent of heating that reaches many Mpcs. +" Thus, we see that already at redshift 10 (top-left) the average temperature of the IGM is of the order of 10? K and overlap of the temperature bubbles occur much before that of the ionization bubble."," Thus, we see that already at redshift 10 (top-left) the average temperature of the IGM is of the order of $10^3$ K and overlap of the temperature bubbles occur much before that of the ionization bubble." +" This example might be unrealistic, because the soft X-ray background constraint (Dijkstra,Haiman,Loeb2004) is not strictly observed, but again this serves just as an illustrative example."," This example might be unrealistic, because the soft X-ray background constraint \citep{dijkstra04a} is not strictly observed, but again this serves just as an illustrative example." + Figure., Figure. + 5 shows the evolution of T as a function of redshift., \ref{fig:qsospin} shows the evolution of $\mathrm{T_s}$ as a function of redshift. +" Owing to a high secondary J, produced due to X-ray photons, Ts is coupled to T' for the large part."," Owing to a high secondary $\mathrm{J_o}$ produced due to X-ray photons, $\mathrm{T_s}$ is coupled to $\mathrm{T_k}$ for the large part." +" The snapshots of T, show a peculiar ring-like behaviour (Refer.", The snapshots of $\mathrm{T_s}$ show a peculiar ring-like behaviour (Refer. + Fig. 5)), Fig. \ref{fig:qsospin}) ). +" This is because towards the central part of the bubble around the source, the IGM is highly ionized and JoοςΧητ, obtains an extremely low value."," This is because towards the central part of the bubble around the source, the IGM is highly ionized and $\mathrm{J_o} \propto \mathrm{x_{HI}}$, obtains an extremely low value." +" On the other hand J. progressively gets lower away from the source, regions (>S5Mpc)."," On the other hand $\mathrm{J_o}$ progressively gets lower away from the source, regions $>$ 5Mpc)." + Therefore only a relatively narrow zone (few hundred kpcs) in between the ionizing front and regions further out has J. high enough to decouple T. from Toms., Therefore only a relatively narrow zone (few hundred kpcs) in between the ionizing front and regions further out has $\mathrm{J_o}$ high enough to decouple $\mathrm{T_s}$ from $\mathrm{T_{CMB}}$. + Figure., Figure. +" 6 shows ὁΤι for redshifts 10, 9, 8 and 7 in panels top-left to bottom-right, respectively."," \ref{fig:qsobright} shows $\delta \mathrm{T_b}$ for redshifts 10, 9, 8 and 7 in panels top-left to bottom-right, respectively." +" The ὃΤι, plotted in this figure are high enough to be detectable by upcoming telescope's like LOFAR and MWA, whose sensitivities should reach 6T;,>5mK (Labropoulosetal.2009)."," The $\delta \mathrm{T_b}$ plotted in this figure are high enough to be detectable by upcoming telescope's like LOFAR and MWA, whose sensitivities should reach $\delta \mathrm{T_b} > 5 \mathrm{mK}$ \citep{panos09}." +". We see in the top-left panel of this figure that even though the number of sources in the field is small, they are efficient in both increasing Τι. dramatically and providing sufficient J, to ""light-up"" the Universe in the 21-cm differential brightness temperature."," We see in the top-left panel of this figure that even though the number of sources in the field is small, they are efficient in both increasing $\mathrm{T_k}$ dramatically and providing sufficient $\mathrm{J_o}$ to “light-up” the Universe in the 21-cm differential brightness temperature." + The ó'T inside the spheres are zero because they are highly ionized (xur> 0.99)., The $\delta \mathrm{T_b}$ inside the spheres are zero because they are highly ionized $\mathrm{x_{HII}}>0.99$ ). + In theobservable Universe we know that stars and quasars do co-exist., In theobservable Universe we know that stars and quasars do co-exist. +" Although, there are indications of the quasar number-density peaking around redshift two (Nusser&Silk1993) and declining thereof, there are also measurements by Fanetal.(2006) of mass (> 105M) quasars at z>6."," Although, there are indications of the quasar number-density peaking around redshift two \citep{nusser93} and declining thereof, there are also measurements by \citet{fan06} of high-mass $>10^8 +\mathrm{M}_\odot$ ) quasars at $z > 6$." + This allows us to envisage a scenario of reionization in which stars and quasars (or miniqsos) contributed to the ionization and heating of the IGM in a combined fashion., This allows us to envisage a scenario of reionization in which stars and quasars (or miniqsos) contributed to the ionization and heating of the IGM in a combined fashion. +" As a final example-application of BEARS,, we present our"," As a final example-application of , we present our" +The observations were mace at the Teide Observato1v (OT) ou the island of Tenerife (Spain) ou the 1.5 1i CarQS Sáuuchez Telescope (CST).,The observations were made at the Teide Observatory (OT) on the island of Tenerife (Spain) on the 1.5 m Carlos Sánnchez Telescope (CST). + The images were taken with he common user NIB camera. CAIN. equipped with a NICAMOS3 2567 detector array and standard broad baxd NIR filters JiNN. coole to LN» temperature.," The images were taken with the common user NIR camera, CAIN, equipped with a NICMOS3 $256^2$ detector array and standard broad band NIR filters $JHK_{\rm s}K$, cooled to $_2$ temperature." + CAIN rolds two cdiffereut optical set-ups. both fully erxogenic. which provide two plate scales: the narrow camera. givi18o Ll oaresec per pixel aud the wide one. with 1l arcsec oer pixel. used for this worzs," CAIN holds two different optical set-ups, both fully cryogenic, which provide two plate scales: the narrow camera, giving 0.4 arcsec per pixel, and the wide one, with 1 arcsec per pixel, used for this work." +" All the galaxies lave becu observed in at leas two filters. J aud A, (or Iv). duri18o several campaigns roni 1998 onwards."," All the galaxies have been observed in at least two filters, $J$ and $K_{\rm s}$ (or $K$ ), during several campaigns from 1998 onwards." + Typical seci18o value was. on average.o a litte dn excess of 1 aresec.," Typical seeing value was, on average, a little in excess of 1 arcsec." + As mentioned in he preceding section. this first sample was selected. taking into account several preseriptious: The observed sample till now coutaims more than he ten galaxies. NGC33LL NCGC3686. NGOC39238. NGC39!la2Mi NGC125LL NGC03. NOCIBLL NOCHLs. NGCG62381 and NGC7IT9. which constitute the body of this paper able 13).," As mentioned in the preceding section, this first sample was selected taking into account several prescriptions: The observed sample till now contains more than the ten galaxies, NGC3344, NGC3686, NGC3938, NGC3953, NGC4254, NGC4303, NGC4314, NGC5248, NGC6384 and NGC7479, which constitute the body of this paper (table \ref{Tab:rc3}) )." + The remainig ones will be presented iu subsequent papers., The remaining ones will be presented in subsequent papers. + The observing strategv has Όσοι iu all cases he classical ON.OFF inethlioc. iu which alternative exJOSTULCS : the ealaxy and the adjacent sky are taken uutil completing the otal exposure time.," The observing strategy has been in all cases the classical ON–OFF method, in which alternative exposures of the galaxy and the adjacent sky are taken until completing the total exposure time." + The inteeration time of a single frame was determined by the linear part of the well depth of the NICAIOS detector aud t10 8sv flux. which is by far tιο donunant contribution to the measured signal.," The integration time of a single frame was determined by the linear part of the well depth of the NICMOS detector and the sky flux, which is by far the dominant contribution to the measured signal." +" Typical iutegratiou times per frame range from 6 to 12 sin A, and from 20 to 30 s in J.", Typical integration times per frame range from 6 to 12 s in $K_{\rm s}$ and from 20 to 30 s in $J$. + Severa franes are taken per poiuti1ο position until the exaud total equals the timescale of the variation of the sky backeround. which was sct at two uuuutes with a sutiicicut safety narelu.," Several frames are taken per pointing position until the grand total equals the timescale of the variation of the sky background, which was set at two minutes with a sufficient safety margin." + This is then the time between nodding positions (talie 2))., This is then the time between nodding positions (table \ref{Tab:caracteristicas}) ). + The final images showing the surface photometry of cach galaxy are displaved in Figs. 1. 2. 3.," The final images showing the surface photometry of each galaxy are displayed in Figs. $\ref{Fig:sf3344-3686}$, $\ref{Fig:sf3938-3953}$, $\ref{Fig:sf4254-4303}$," + 1 aud 5., $\ref{Fig:sf4314-5248}$ and $\ref{Fig:sf6384-7479}$. + The data have been reduced using several combinatious of IBAF tasks., The data have been reduced using several combinations of IRAF tasks. + The read-out mode has in all cases been the standard Fowler mode. in which N non-destructive reads are taken after the detector reset aud then iuteerated for the required time and the detector read Α times again.," The read-out mode has in all cases been the standard Fowler mode, in which N non-destructive reads are taken after the detector reset and then integrated for the required time and the detector read $N$ times again." + Dv so doing the determination of the pedestal level oft1C signal is eiven bv the average of the first Α reads. and he inage signal is defined by the difference between t1C average of the last NV reads aud that of the first oues.," By so doing the determination of the pedestal level of the signal is given by the average of the first $N$ reads, and the image signal is defined by the difference between the average of the last $N$ reads and that of the first ones." + T1C S/N ratio of the image is improved by this method., The S/N ratio of the image is improved by this method. + We have followed the standard process for treatiis the data to correct for bias and dark current. axd flattield calibration.," We have followed the standard process for treating the data to correct for bias and dark current, and flatfield calibration." + Then we subtracted the skv fireL, Then we subtracted the sky from + Then we subtracted the skv fireLL, Then we subtracted the sky from +the Sun's polarity reversal the build-up of the polar fields was slow (Dikpatietal2004). resulting in unusually weak polar fields at the end of evele 23 compared to those in evcles 2] and 22.,"the Sun's polarity reversal the build-up of the polar fields was slow \citep{ddgaw2004}, resulting in unusually weak polar fields at the end of cycle 23 compared to those in cycles 21 and 22." + In order to understand the cause of such a weak polar field al the end of evcle 23 and its consequences for the solar-terrestrial environment. many scientists have extensively emploved simulations [rom f(Iux-transport dvnamo models (Dikpati&CharbonneanDikpati.deToma&Gilman2008:Dikpatietal2010) and surface transport models Lean&Sheeley2005:Schrijver.DeRosaTitle2002:SehrijverLin 2008).," In order to understand the cause of such a weak polar field at the end of cycle 23 and its consequences for the solar-terrestrial environment, many scientists have extensively employed simulations from flux-transport dynamo models \citep{dc99,ddg2008,dgdu2010} and surface transport models \citep{wls2005,sdt2002,sl2008}." +. In both these classes of models the polar fields originate [rom the decay of tilted. bipolar active regions. namely tlie so-called Babcock-Leighton mechanism (Baheock1959: 1964).," In both these classes of models the polar fields originate from the decay of tilted, bipolar active regions, namely the so-called Babcock-Leighton mechanism \citep{babcock1959, leighton1964}." +. The ingredients (advection and diffusion) that directly. influence the latitucinal transport of the radial fields in the two classes of models are the same., The ingredients (advection and diffusion) that directly influence the latitudinal transport of the radial fields in the two classes of models are the same. + Iowever. one of ihe differences in the evolutionarv patterns of the polar fields is that. in flux-transport dvnamo models. poloidal fields produced at the surface by the Dabcock-Leighton effect are axisvimmnmetrie (ie. in the r—0 plane) and thev evolve due to advection and diffusion. by the action of both the Iatitudinal and radial components of the meridional flow as well as by the action of a depth-cepencent turbulent diffusivity.," However, one of the differences in the evolutionary patterns of the polar fields is that, in flux-transport dynamo models, poloidal fields produced at the surface by the Babcock-Leighton effect are axisymmetric (i.e. in the $r-\theta$ plane) and they evolve due to advection and diffusion by the action of both the latitudinal and radial components of the meridional flow as well as by the action of a depth-dependent turbulent diffusivity." + By contrast. surface. transport models include a more realistic longitude dependence of the Dabcock-Leighton effect in the eeneralion of polar fields. and the radial component of the fields generated evolve at the surface by the action of latitudinal component of the meridional flow ancl a constant surface ciffusivity.," By contrast, surface transport models include a more realistic longitude dependence of the Babcock-Leighton effect in the generation of polar fields, and the radial component of the fields generated evolve at the surface by the action of latitudinal component of the meridional flow and a constant surface diffusivity." + The purpose of (his paper is to demonstrate that [flux-transport diamo models. aud surface transport models. despite some differences in the ingredients. produce remarkably similar response in the polar fields” patterns to the changes in the meridional flow-speed when the same latitudinal profile lor the poleward surface [low is used.," The purpose of this paper is to demonstrate that flux-transport dynamo models and surface transport models, despite some differences in the ingredients, produce remarkably similar response in the polar fields' patterns to the changes in the meridional flow-speed when the same latitudinal profile for the poleward surface flow is used." + Given that understanding of the polar fields’ behaviour is a kev (ο understanding the recveling of magnetic flux for the operation of a dvnanmo. and hence (he properties of future solar cvcles. we also examine in (his paper whether there are any inconsistencies or contradictions between these (wo classes of models when applied to the Sun.," Given that understanding of the polar fields' behaviour is a key to understanding the recycling of magnetic flux for the operation of a dynamo, and hence the properties of future solar cycles, we also examine in this paper whether there are any inconsistencies or contradictions between these two classes of models when applied to the Sun." + The polar field puzzle of evele 23 has become a Far more important issue now that the start of evele 24 has been slugeish., The polar field puzzle of cycle 23 has become a far more important issue now that the start of cycle 24 has been sluggish. + We illustrate in simple mumnerical terms just how sensitive (he amplitude of the polar field on the Sun and in models is to changes in the strength of the source of its field. namely (he emergence and decay of active regions.," We illustrate in simple numerical terms just how sensitive the amplitude of the polar field on the Sun and in models is to changes in the strength of the source of its field, namely the emergence and decay of active regions." + We know that the amplitude of evele 23 was weaker (han that of evele 22., We know that the amplitude of cycle 23 was weaker than that of cycle 22. + Wat the end of a given evele the polar field) has one unit. in the next evele it takes two units of polar fields coming Irom the surface poloidal source {ο reverse (he remnant polar field and have (he new polar fields reach minus one unit.," If at the end of a given cycle the polar field has one unit, in the next cycle it takes two units of polar fields coming from the surface poloidal source to reverse the remnant polar field and have the new polar fields reach minus one unit." + But if the surface poloidal source is smaller in the new evcle than the previous one. as evcle," But if the surface poloidal source is smaller in the new cycle than the previous one, as cycle" +uunercal computations of the explosion phase.,numerical computations of the explosion phase. + Some iuprovenieuts in this respect have been already added to the preseut version of the code (see sect., Some improvements in this respect have been already added to the present version of the code (see sect. + 2.3. for details)., \ref{sec:code:IniCond} for details). + At the same time. we are working Gu collaboration with A. Chicfi and M. Limonei}) at interfacing it with the output of a lvdvocwnamical code that follows the οον explosion and the explosive uucleosvuthliesis. starting from pre-SN models obtained through a stellar evolutionary code.," At the same time, we are working (in collaboration with A. Chieffi and M. Limongi) at interfacing it with the output of a hydrodynamical code that follows the CC-SN explosion and the explosive nucleosynthesis, starting from pre-SN models obtained through a stellar evolutionary code." + Since we cousider the effects of the central compact remnant on the evolution of the ejecta. we adopt a fully general relativistic treatiment.," Since we consider the effects of the central compact remnant on the evolution of the ejecta, we adopt a fully general relativistic treatment." + The equations governing the relativistic radiation lydrodyvnaimics of the expanding cjecta in spherically svaunietry. are reported iu Zinpierictal.(1996.1998). aud Dalbergetal.(2000).," The equations governing the relativistic radiation hydrodynamics of the expanding ejecta in spherically symmetry are reported in \citet{zampieri96,zampieri98} and \citet{balberg00}." + The main physical variables that describe the behavior of the ejecta are the gas mass density p. aud the gas internal cherev per uuit mass € and pressure p (miasured in the fane comoving with the ejecta).," The main physical variables that describe the behavior of the ejecta are the gas mass density $\rho$, and the gas internal energy per unit mass $\epsilon$ and pressure $p$ (measured in the frame comoving with the ejecta)." + Those describing the radiation Ποιά are the radiation cucrey density wy aud Bux «4 (both in units of erg 2)., Those describing the radiation field are the radiation energy density $w_0$ and flux $w_1$ (both in units of erg $^{-3}$ ). + We refer to Zampicri(1998) for the full set of equations aud related «quantities. while here we sunuuarize for couvenicuce the eas chorey equation and the first two moments of the radiative transfer equations. whose treatiment has beeu deeply modified in the preseut analysis.," We refer to \citet{zampieri98} for the full set of equations and related quantities, while here we summarize for convenience the gas energy equation and the first two moments of the radiative transfer equations, whose treatment has been deeply modified in the present analysis." + They read: where foaud gp are the Lagrangian time and inass contained within a comoving spherical shell of radius r (a conuua denotes partial derivates with respect to the corresponding variable}. ᾱ (00 inetrie coefficient) is a function of £ and ji (computed from Eq. [," They read: where $t$ and $\mu$ are the Lagrangian time and mass contained within a comoving spherical shell of radius $r$ (a comma denotes partial derivates with respect to the corresponding variable), $a$ (00 metric coefficient) is a function of $t$ and $\mu$ (computed from Eq. [" +6| in Zunpierietal. 1998)). b=l/(1xi?p). B=agT! (up blackbody radiation constant). Q is the heating rate of radioactive decays from the isotopes svuthesized im the SN explosion (see sect. 2.1)).,"6] in \citealt{zampieri98}) ), $b=1/(4\pi r^2 \rho)$, $B=a_R T^4$ $a_R$ blackbody radiation constant), $Q$ is the heating rate of radioactive decays from the isotopes synthesized in the SN explosion (see sect. \ref{sec:code:physics}) )," + and Ap aud hy are Planck mean and Rossclaud mean opacity. respectively.," and $k_P$ and $k_R$ are Planck mean and Rosseland mean opacity, respectively." + The dependence ou the gas temperature Lois contained in €. p. kp aud Ay. aud is specified through the equations of state (see sect. 2.1) Ap," The dependence on the gas temperature $T$ is contained in $\epsilon$, $p$, $k_P$ and $k_R$, and is specified through the equations of state (see sect. \ref{sec:code:physics}) )." + aud Ag are calculated interpolating the TOPSopacitios as a function of T and p (see again sect. 2.1))., $k_P$ and $k_R$ are calculated interpolating the TOPSopacities as a function of $T$ and $\rho$ (see again sect. \ref{sec:code:physics}) ). + Finally. the function f (Eddineton factor). relating the secoud-order moment of the radiation intensity to wy. is calculated using Eqs. [," Finally, the function $f$ (Eddington factor), relating the second-order moment of the radiation intensity to $w_0$, is calculated using Eqs. [" +12] and [13] iu Zanrpicrietal.(1998).,12] and [13] in \citet{zampieri98}. + Iu order to solve the complete svsteni of equations of relativistic radiation hvdrodyaimuies. the old. versiou of the code adopts a semi-mupliit Lagraugiui finite difference scheme where the time step is controlled by he Courant coudition and the requirement that the ractional variation of the variables iu oue time-step be smaller than1056.," In order to solve the complete system of equations of relativistic radiation hydrodynamics, the old version of the code adopts a semi-implicit Lagrangian finite difference scheme where the time step is controlled by the Courant condition and the requirement that the fractional variation of the variables in one time-step be smaller than." + The energy equation (Eq. |1]|), The energy equation (Eq. \ref{eq:energy}] ]) + aud he zero-th moment of the radiative transfer equation (Eq. [2]]), and the zero-th moment of the radiative transfer equation (Eq. \ref{eq:w0}] ]) + form a non-linear svsteui of equations in the gas eniperature Z7 and are then solved poiut-by-poiut on the conrputational erid using a Newton-Raplsou iterative nethod (seetheAppendixinZampierietal.1998.forcletails)., form a non-linear system of equations in the gas temperature $T$ and are then solved point-by-point on the computational grid using a Newton-Raphson iterative method \citep[see the Appendix in][for details]{zampieri98}. +. We have deeply modified the mmuerical treatineut xeviouxlv adopted by implementing a filly implicit Lagrangian finite differcuce scheme., We have deeply modified the numerical treatment previously adopted by implementing a fully implicit Lagrangian finite difference scheme. + This allows for a inajor iÀuprovenient in the nunuerical stability aud overall computational cfiicicncy of the code. especially during those phases when fast motious of steep eracicuts occur (e.8. the radiative recombination phase).," This allows for a major improvement in the numerical stability and overall computational efficiency of the code, especially during those phases when fast motions of steep gradients occur (e.g. the radiative recombination phase)." + The first nonieut equation for the radiative flux ay (Eq. 911), The first moment equation for the radiative flux $w_1$ (Eq. \ref{eq:w1}] ]) + is row solved together with Eqs. [1] , is now solved together with Eqs. \ref{eq:energy}] ] +aud |2]| iu a fully nuplicit scheme on the whole computational grid. that requires a modification. of the temporal ceuteriug of he variables.," and \ref{eq:w0}] ] in a fully implicit scheme on the whole computational grid, that requires a modification of the temporal centering of the variables." + This leads to a highlv uou-luear svsteii of equations that is solved through a Newtou-Raphsou iterative method and iatrix inversion packages that minimise the CPU time aud the required storage space., This leads to a highly non-linear system of equations that is solved through a Newton-Raphson iterative method and matrix inversion packages that minimise the CPU time and the required storage space. + Iu the Appendix we report more details on the finite difference form of the Eqs. |1]. |2]]," In the Appendix we report more details on the finite difference form of the Eqs. \ref{eq:energy}] ], \ref{eq:w0}] ]" + aud [3]. aud. the miuerical procedure adopted to solve then.," and \ref{eq:w1}] ], and the numerical procedure adopted to solve them." + Iu the preseut analysis we consider the evolution of the ejecta after the explosionphaset., In the present analysis we consider the evolution of the ejecta after the explosion. +. At this stage. the SN shock wave has already propagated through tle euvelope of the progenitor star redistributing the explosion energv through it. and the evolution starts when the euvelope is essentiallv frec-coastiug and in homologous expausion.," At this stage, the SN shock wave has already propagated through the envelope of the progenitor star redistributing the explosion energy through it, and the evolution starts when the envelope is essentially free-coasting and in homologous expansion." + We asstune that if is comprised of a musture of hydrogen. helium aud heavier elemieuts;," We assume that it is comprised of a mixture of hydrogen, helium and heavier elements." + As oxvecn is expected to be the most abuudaut heavy clement. we further assune that it represents the entire metal componoeut in the euvelope's final composition (seeBalbereetal. 2000).," As oxygen is expected to be the most abundant heavy element, we further assume that it represents the entire metal component in the envelope's final composition \citep[see][]{balberg00}." +". The amass fraction ofCONG is asmuued to be concentrated towards the ceuter aud to vary as a fiction of Lagraugian lass p as: where Nsexy is tle initial mass fraction of a the inner boundaryyg of the ejecta. νε Is a munuerical coustant whose value is essentially related to the exteu of iiixiug of throughout the envelope. and 475,4; 15"," The mass fraction of is assumed to be concentrated towards the center and to vary as a function of Lagrangian mass $\mu$ as: where $X_{\mathrm{^{56}{Ni,0}}}$ is the initial mass fraction of at the inner boundary of the ejecta, $K_{mix}$ is a numerical constant whose value is essentially related to the extent of mixing of throughout the envelope, and $\mu_{max}$ is" +a flat rotation curve of l= —B = 15 kms ! for the LGD. B= -12 km ! |:and for the GB. B= -19 km | |. a value similar to our estimation.,"a flat rotation curve of $A$ = $-B$ = 15 km $^{-1}$ $^{-1}$; for the LGD, $B$ = -12 km $^{-1}$ $^{-1}$;and for the GB, $B$ = -19 km $^{-1}$ $^{-1}$, a value similar to our estimation." + But regardless ol the numerical results. we can conclude too that the global kinematics of the GB cliffers eveally Irom the kinematics of the LGD. and that the presence of this stellar svsteni affects the estimation of (he parameters describing the kinematics of the solar neighborhood.," But regardless of the numerical results, we can conclude too that the global kinematics of the GB differs greatly from the kinematics of the LGD, and that the presence of this stellar system affects the estimation of the parameters describing the kinematics of the solar neighborhood." + On the other hand. the A term is generally inferior in absolute value to the estimation bv Frogel&Stothers(1977).," On the other hand, the $K$ term is generally inferior in absolute value to the estimation by \citet{Fro77}." +. We have checked (hat when solving (he equations without {his term. the results for the Oort constants do not change significativelv.," We have checked that when solving the equations without this term, the results for the Oort constants do not change significatively." + Thus we do not consider it wise to conclude auvthing about the possible expansion movements of (he svstem from these results., Thus we do not consider it wise to conclude anything about the possible expansion movements of the system from these results. + The detailed study of the local irregularities in the kinematics of the voung stars by Torraetal.(2000).. from a sample of O and B stars. reveals that for heliocentric distances lower than 600 pe and age groups under 90 Myr (1e... for a sample with a hieh proportion of GB members). (he value of the Oort constant D is much greater in absolute value than expected for the LGD: -13.6 2 2.0 due to the ring of gas near the centre. leading to absorption of about 8S6 per cent of the soft Dux.," Toward the Galactic centre, the hydrogen column density is about $N_H\sim 6\times 10^{22}$ $^{-2}$ due to the ring of gas near the centre, leading to absorption of about 86 per cent of the soft flux." + In the hard.X-ray. band. the absorption is negligible.," In the hard–X-ray band, the absorption is negligible." + For the persistent-source assumption. we assume that the accretion [low emits isotropically. so we simply need to integrate the Iuminosity function over the entire galaxy with the transformation: where D is the distance to a given point in the Galaxy.," For the persistent-source assumption, we assume that the accretion flow emits isotropically, so we simply need to integrate the luminosity function over the entire galaxy with the transformation: where $D$ is the distance to a given point in the Galaxy." + Figure 3 shows the predicted number of sources as a function of [Lux integrated over the entire Galaxy for the persistent-source assumption., Figure 3 shows the predicted number of sources as a function of flux integrated over the entire Galaxy for the persistent-source assumption. + Despite the much lower assumed efficiency. the number of. detectable black holes becomes comparable to the number of detectable neutron stars for. egg~LO1cvsGNsg/NNs):m ," Despite the much lower assumed efficiency, the number of detectable black holes becomes comparable to the number of detectable neutron stars for $\epsilon_{BH}\sim 10^{-4}\epsilon_{NS}(N_{BH}/N_{NS})^{0.8}$ ." +mIhe number of⋅ black holes above a certain. Dux at high. flux scales approximately: as Αι):'=104Lpl2 near !f=101576s erg 27s +., The number of black holes above a certain flux at high flux scales approximately as $N(>F) = 10^4F^{-1.2}$ near $F=10^{-15}\epsilon_{-5}$ erg $^{-2}$ $^{-1}$. + Given the Datness of this dependence. the best detection strategy is to cover as nich area of thesky as possible.," Given the flatness of this dependence, the best detection strategy is to cover as much area of thesky as possible," +boundary (r= 505) at t~260 in the 2.5D simulations and att«330 in the 3D simulations.,boundary $r=505$ ) at $t\approx260$ in the 2.5D simulations and at $t\approx330$ in the 3D simulations. +" The latter are subject to more numerical dissipation of kinetic energy, because the grid there is not symmetric in azimuthal direction."," The latter are subject to more numerical dissipation of kinetic energy, because the grid there is not symmetric in azimuthal direction." +" This reduces the injected Poynting flux, see Fig. 11.."," This reduces the injected Poynting flux, see Fig. \ref{fig:eflow}." +" Apart from that, 2.5D and 3D simulations give, for our purposes, comparable results."," Apart from that, 2.5D and 3D simulations give, for our purposes, comparable results." + Fig., Fig. + 3 shows how the magnetic field is wound up inside the jet in one of the simulations., \ref{fig:flines} shows how the magnetic field is wound up inside the jet in one of the simulations. + A typical density and temperaturedistribution is shown in Fig. 4.., A typical density and temperaturedistribution is shown in Fig. \ref{fig:rhot}. . +s and use a value D.=1 for the eritical field in all our calculations.,s and use a value $\Bc = 1$ for the critical field in all our calculations. + When we start our calculations with anv arbitrary magnetic field configuration. the code relaxes to a periodic solution for a proper set of parameters.," When we start our calculations with any arbitrary magnetic field configuration, the code relaxes to a periodic solution for a proper set of parameters." + What we discuss below are properties of such relaxed periodic solutions., What we discuss below are properties of such relaxed periodic solutions. + Durnev (1997) did not allow the toroidal flux to be depleted at the bottom of the convection zone due to magnetic buovancy., Durney (1997) did not allow the toroidal flux to be depleted at the bottom of the convection zone due to magnetic buoyancy. + To study the effect of flux depletion. we present some calculations in which we allow flix depletion in the following simple manner.," To study the effect of flux depletion, we present some calculations in which we allow flux depletion in the following simple manner." + At the limes of eruption after interval 7. we find out at which point the toroidal field has the maximum value μις (> D).," At the times of eruption after interval $\tau$, we find out at which point the toroidal field has the maximum value $\Bm$ $>\Bc$ )." + While putting the two flux rings at the top. we also decrease Das by an amount αμ al the maxinum point.," While putting the two flux rings at the top, we also decrease $\Bm$ by an amount $f_d \Bm$ at the maximum point." +" Then /; becomes a second parameter in the problem in addition to A"" in our problem.", Then $f_d$ becomes a second parameter in the problem in addition to $K'$ in our problem. +" After finding the co-latitude 9,, where the toroidal field is maximum. the next (vo poleward grid points are taken as £4. A. and the next (wo equatorward erid points are taken as 85. 041."," After finding the co-latitude $\ter$ where the toroidal field is maximum, the next two poleward grid points are taken as $\theta_1$, $\theta_2$ , and the next two equatorward grid points are taken as $\theta_3$, $\theta_4$." + The flux rings are assumed to go 3 erid points deep Ar is taken 3 grid points below the surface)., The flux rings are assumed to go 3 grid points deep $\Delta r$ is taken 3 grid points below the surface). +" Figure 2 shows how the dvnaimo period T; changes with the parameter A"" when fy is held constant.", Figure 2 shows how the dynamo period $T_d$ changes with the parameter $K'$ when $f_d$ is held constant. + The different curves correspond to dillerent values of fy., The different curves correspond to different values of $f_d$. + When we ego to the limit of CSD model by putting A'=0. we find the period to be 66 vrs.," When we go to the limit of CSD model by putting $K'=0$, we find the period to be 66 yrs." + When fy=0 {there is no flux depletion at the bottom). we find that the change in the period with A’ does not follow any particular trend.," When $f_d = 0$ there is no flux depletion at the bottom), we find that the change in the period with $K'$ does not follow any particular trend." + 7; at first increases slightly with increasing A' and then comes down to a value close to that of the CSD model., $T_d$ at first increases slightly with increasing $K'$ and then comes down to a value close to that of the CSD model. + This behaviour for fj;=0 may result [rom the facet. that in (his case we are actually creating flux (in the form of erupted double rings) without any depletion., This behaviour for $f_d =0$ may result from the fact that in this case we are actually creating flux (in the form of erupted double rings) without any depletion. + More meaningful behaviour follows lor the other valuesof fy (such as 0.25. 0.5. 0.75).," More meaningful behaviour follows for the other valuesof $f_d$ (such as 0.25, 0.5, 0.75)." +" The period decreases with increasing A"" and", The period decreases with increasing $K'$ and +A large population of ohsenrecl powerful quasars called tvpe-2 quasars has long been preclictecl by the widely accepted unified model for active galactic nuclei (AGNs: Antonucci,A large population of obscured powerful quasars called type-2 quasars has long been predicted by the widely accepted unified model for active galactic nuclei (AGNs; Antonucci +If we take an astroplivsical situation (such as an ACN or a protostar) with specific plivsical conditions. it is ikely that the arguments that support the adoption of the selfreeulation constraint. followed in this paper. fail outside a well-defined radial range. either at παπα or a larec radi.,"If we take an astrophysical situation (such as an AGN or a protostar) with specific physical conditions, it is likely that the arguments that support the adoption of the self-regulation constraint, followed in this paper, fail outside a well-defined radial range, either at small or at large radii." + For example. we may recall that oei the contest of the dynamics of spiral galaxies the relevant Q profile is argued to be flat iu the outer disk. ut is thought to increase nisvards inside a circle of radius ro often identified as the radial scale of influence of the bulge: even in the absence of a bulge. the central parts of the disk are thought to be generally hotter (e.e.. see Bertin Lin. 1996)).," For example, we may recall that in the context of the dynamics of spiral galaxies the relevant $Q$ profile is argued to be flat in the outer disk, but is thought to increase inwards inside a circle of radius $r_Q$ often identified as the radial scale of influence of the bulge; even in the absence of a bulge, the central parts of the disk are thought to be generally hotter (e.g., see Bertin Lin, \cite{bertinlin}) )." + Iu our context. we may then nuagiue an accretion disk where at siiall radii self-reeulation fails. Q becomes large. and. correspondingly. the disk selferavity ceases to be nuportaut.," In our context, we may then imagine an accretion disk where at small radii self-regulation fails, $Q$ becomes large, and, correspondingly, the disk self-gravity ceases to be important." + This discussion sugeests that it should be iuterestiug o explore the possibility where Eq. (8)), This discussion suggests that it should be interesting to explore the possibility where Eq. \ref{jeans}) ) + is replaced by a condition of the onu ο/aGo=Qi). with a (Q profile hat decreases monotonically with radius and reaches he sclfveeulation value Q oulv beyond a certain radial scale re.," is replaced by a condition of the form $c\kappa/\pi G \sigma = Q(r)$, with a $Q$ profile that decreases monotonically with radius and reaches the self-regulation value $\bar{Q}$ only beyond a certain radial scale $r_Q$." + What would be the impact of such a choice on he structure of the accretion disk?, What would be the impact of such a choice on the structure of the accretion disk? + What might be the physical arguineuts leading to the justification of such a xofile?, What might be the physical arguments leading to the justification of such a profile? +" In particular. what would set the scale rey for given values of the parameters a. M,. AT. and J?"," In particular, what would set the scale $r_Q$ for given values of the parameters $\alpha$, $M_{\star}$, $\dot{M}$, and $\dot{J}$?" + Note again that we are reversing the standard poiut of view. whereby one nav ask what is the Q profile for an accretion disk. based ou the structure caleulated. from a eiven choice of the enerev equations.," Note again that we are reversing the standard point of view, whereby one may ask what is the $Q$ profile for an accretion disk, based on the structure calculated from a given choice of the energy equations." + hnuposiug. as wo are eolug to do. a eiven profile Qtr) mu. at first sight. appear to be arbitrary.," Imposing, as we are going to do, a given profile $Q(r)$ may, at first sight, appear to be arbitrary." + Iu reality. the freedom in the choice of the profile allows us ο test quantitatively how the clwnamical characteristics Vt). Moise). e(r). and f(r) of the disk change when je selfreeulation coustraint is partially relaxed. in the oe11ΟΥ) clisk. πι a varicty of wavs.," In reality, the freedom in the choice of the profile allows us to test quantitatively how the dynamical characteristics $V(r)$, $M_{disk}(r)$, $\epsilon(r)$, and $h(r)$ of the disk change when the self-regulation constraint is partially relaxed, in the inner disk, in a variety of ways." + It is up to us to est the differeut possibilities (which may correspond to colpletely differcut sets of οποίονo balance equations iu 16 inner disk) that might be considered., It is up to us to test the different possibilities (which may correspond to completely different sets of energy balance equations in the inner disk) that might be considered. +" For our purposes. since we wish to study the deviations from the standard ""Ikepleriur case. we only need to take into account that 1e relevant physical processes match so that in the outer disk sclfreeulation is enforced."," For our purposes, since we wish to study the deviations from the standard “Keplerian” case, we only need to take into account that the relevant physical processes match so that in the outer disk self-regulation is enforced." + Note that in the transition region where matching between the inner aud the outer disk occurs. for reasons CXPLESSC¢ in Sect.," Note that in the transition region where matching between the inner and the outer disk occurs, for reasons expressed in Sect." + 3. it niv be practically imuipossible to define. Youn firs xinciples. a satisfactory set of euergv equations able » include all the desired radiation processes and the non-linear effects associated with Jeaus instability.," 3, it may be practically impossible to define, from first principles, a satisfactory set of energy equations able to include all the desired radiation processes and the non-linear effects associated with Jeans instability." + This procedure draws considerable μιxxt from a recent analysis of “standard” disks (Bardot ct al. 1998))," This procedure draws considerable support from a recent analysis of “standard"" disks (Bardou et al. \cite{bardou}) )" + aa.πος at detecting evidence for tle importance of disk selt-eravity in the outer disk., aimed at detecting evidence for the importance of disk self-gravity in the outer disk. + Based on au extension of the μαandard «-disks (characterized by Ivamers’ opacity and by neglect of radiation pressure). the effects of the disk selberavitv have becu here incorporated by meaus of anu inproved thickness prescription (somewhat in the spirit of our Appendix A} aud of a modified viscosity prescription. but he (Ixepleria1) O profile is left nualtered.," Based on an extension of the “standard"" $\alpha$ -disks (characterized by Kramers' opacity and by neglect of radiation pressure), the effects of the disk self-gravity have been here incorporated by means of an improved thickness prescription (somewhat in the spirit of our Appendix A) and of a modified viscosity prescription, but the (Keplerian) $\Omega$ profile is left unaltered." + Therefore. this study is ideally suited to describe the conditions of our inner disk. as we intend to partially relax the selfregulation requirement.," Therefore, this study is ideally suited to describe the conditions of our inner disk, as we intend to partially relax the self-regulation requirement." + A very important result of the analysis by Bardou et al. (1998)), A very important result of the analysis by Bardou et al. \cite{bardou}) ) +" is that their ""staucdaid description breaks down bevoud a radius re. well iuside which the local stability parameter behaves approxinately as QOcp77: as it might have been anticipated. the location where the standard model breaks down coincides with the location where Q becomes approximately equal to unity."," is that their “standard"" description breaks down beyond a radius $r_Q$ , well inside which the local stability parameter behaves approximately as $Q \sim r^{-9/8}$; as it might have been anticipated, the location where the standard model breaks down coincides with the location where $Q$ becomes approximately equal to unity." + In couchision. the analysis by Bardou et.," In conclusion, the analysis by Bardou et." + al (1998)) encourages us to consider the following choice of Q profile to be used instead of Eq. (8)). (, al \cite{bardou}) ) encourages us to consider the following choice of $Q$ profile to be used instead of Eq. \ref{jeans}) ). ( +"The formula is nieant to be used as a seni-enipircal tool: one should keep im τή, that the exact form of the Q profile will be determined by the detailed energwprocesses occummiug m the mner disk aud by the progressively important role of collective",The formula is meant to be used as a semi-empirical tool; one should keep in mind that the exact form of the $Q$ profile will be determined by the detailed energyprocesses occurring in the inner disk and by the progressively important role of collective +orientation.,orientation. + This is the Intrinsic-Intrinsic (II) correlation., This is the Intrinsic-Intrinsic (II) correlation. + Background galaxies will be lensed by foreground gravitational potentials which govern the orientation of foreground galaxies., Background galaxies will be lensed by foreground gravitational potentials which govern the orientation of foreground galaxies. + This causes an anti-correlation between the foreground/background galaxies known as the Gravitational-Intrinsic (GI) correlation., This causes an anti-correlation between the foreground/background galaxies known as the Gravitational-Intrinsic (GI) correlation. +" Broadly, there are two approaches to dealing with IAs."," Broadly, there are two approaches to dealing with IAs." +" The first, known as nulling"", places steps in the weak lensing pipeline which remove the IA signal."," The first, known as “nulling”, places steps in the weak lensing pipeline which remove the IA signal." + The effect of II correlations can be removed by downweighting physically close galaxy pairs (Heymansetal.|20042003;," The effect of II correlations can be removed by downweighting physically close galaxy pairs \citep{heymansbhmtw04,kings03,heymansh03,takadaw04}." + The GI term is more problematic as it affects all pairs of galaxies which are not physically close., The GI term is more problematic as it affects all pairs of galaxies which are not physically close. + In principle a particular linear combination of tomographic shear power spectra can be used to remove the GI signal if the redshifts of the galaxies are known ," In principle a particular linear combination of tomographic shear power spectra can be used to remove the GI signal if the redshifts of the galaxies are known \citep{joachimi_schneider_2008,joachimi_schneider_2009}." +The other approach tries to model the IA signal we[2009).. would expect for a particular survey., The other approach tries to model the IA signal we would expect for a particular survey. + These IA contributions can then be incorporated into the predictions for the measured shear signal and any free parameters in the ΤΑ model can be varied and marginalised over (Albrechtetal.||2006; 2009).," These IA contributions can then be incorporated into the predictions for the measured shear signal and any free parameters in the IA model can be varied and marginalised over \citep{detf,bridleandking,bernstein_2008,joachimi_bridle_2009}." + 'This is the approach we investigate., This is the approach we investigate. + To carry this out it is necessary to make physically motivated models for IAs., To carry this out it is necessary to make physically motivated models for IAs. + Ignoring IAs completely will bias estimates of cosmological parameters (Hirata&Seljak|2004;|Mandelbaumοὐal.|2006;;Bridle& King||2007].," Ignoring IAs completely will bias estimates of cosmological parameters \citep{hiratas04,mandelbaumhisb06,hirataea07,bridleandking}." +". In addition, other cosmological data sets, such as galaxy surveys, can be used to gain empirical knowledge about the IA effect, as well as its variation with luminosity, colour and any other variables."," In addition, other cosmological data sets, such as galaxy surveys, can be used to gain empirical knowledge about the IA effect, as well as its variation with luminosity, colour and any other variables." +" Some of the modelling approaches make simultaneous use of the galaxy shear - galaxy shear correlation function and the galaxy position - galaxy shear correlation function, as measured from the same imaging survey (Albrechtetαἱ.Joachimi&Bridle |2009)."," Some of the modelling approaches make simultaneous use of the galaxy shear - galaxy shear correlation function and the galaxy position - galaxy shear correlation function, as measured from the same imaging survey \citep{detf,bernstein_2008,joachimi_bridle_2009}." +". Where ""shear"" has contributions from both gravitational and intrinsic shear.", Where “shear” has contributions from both gravitational and intrinsic shear. +" This was first identified as an important additional statistic for learning about galaxy formation by and was recently suggested as a powerful tool for removing IAs by (2009), which was demonstrated in "," This was first identified as an important additional statistic for learning about galaxy formation by \cite{hu_jain_2004} and was recently suggested as a powerful tool for removing IAs by \cite{zhang09}, which was demonstrated in \cite{joachimi_bridle_2009}." +"Cosmic shear was first detected observationally a decade ago (Baconetal.||2000200052000) and the strength of the signal as a function of galaxy separation has since been measured by many teams, most recently by (2008) [Masseyetal.] (seealso2009)."," Cosmic shear was first detected observationally a decade ago \citep{baconre00,vanwaerbekeea00,wittmanea00,Kaiser:2000if} and the strength of the signal as a function of galaxy separation has since been measured by many teams, most recently by \cite{fuea08_mnras} and \cite{Massey:2007wb} \citep[see also][]{schrabbackea09}." +. A andcompilation of recent cosmic shear results including a homogeneous additional treatment of systematics was made public by , A compilation of recent cosmic shear results including a homogeneous additional treatment of systematics was made public by \cite{benjaminea07}. +'The use of photometric redshift information is now (2007)..starting to allow the signal to be evaluated as a function of galaxy redshift (Masseyetal.2007|Schrabbacket al.|2009].," The use of photometric redshift information is now starting to allow the signal to be evaluated as a function of galaxy redshift \citep{massey_growth2007_mnras,schrabbackea09}." +.. The cosmological constraints in these recent papers are calculated assuming there are no TAs., The cosmological constraints in these recent papers are calculated assuming there are no IAs. +" However, if IAs are non-negligible then ignoring them will lead to a bias on cosmological parameters."," However, if IAs are non-negligible then ignoring them will lead to a bias on cosmological parameters." + The bias in og was estimated to be between 1 and 20 per cent for a CFHTLS-like survey by and .., The bias in $\sigma_8$ was estimated to be between 1 and 20 per cent for a CFHTLS-like survey by \citet{mandelbaumea06} and \citet{hirataea07}. + Schneider&Bridle and (2009) obtained a similar result in an approximate Fisher matrix prediction., \citet{schneiderb09} and \citet{mandelbaumea09} obtained a similar result in an approximate Fisher matrix prediction. + (2007) showed that for future surveys the equation of state parameter w may be biased by order unity if IAs are significant and ignored., \citet{bridleandking} showed that for future surveys the equation of state parameter $w$ may be biased by order unity if IAs are significant and ignored. + used COMBO-17 measurements of the II signal from shear-shear correlations between galaxies close in redshift jointly with cosmic shear RCS and VIRMOS-DESCART shear-shear correlation data to constrain a simple intrinsic alignment model amplitude simultaneously with cosmological parameters., \citet{heymansbhmtw04} used COMBO-17 measurements of the II signal from shear-shear correlations between galaxies close in redshift jointly with cosmic shear RCS and VIRMOS-DESCART shear-shear correlation data to constrain a simple intrinsic alignment model amplitude simultaneously with cosmological parameters. + They marginalised over possible amplitudes of the II signal and found the fitted value of og was reduced by 0.03 relative to the value found when intrinsic alignments were ignored., They marginalised over possible amplitudes of the II signal and found the fitted value of $\sigma_8$ was reduced by 0.03 relative to the value found when intrinsic alignments were ignored. +" estimated the amplitude of the GI signal marginalised over a range of cs, Qm values allowed by the cosmic shear data."," \citet{fuea08_mnras} estimated the amplitude of the GI signal marginalised over a range of $\sigma_8$, $\Omega_m$ values allowed by the cosmic shear data." +" They found it to be consistent with zero, and this conclusion held when various different scale ranges were used for each of the fits for cosmology or for the IA amplitude parameter."," They found it to be consistent with zero, and this conclusion held when various different scale ranges were used for each of the fits for cosmology or for the IA amplitude parameter." + They concluded that they found no evidence for a non-zero GI signal., They concluded that they found no evidence for a non-zero GI signal. + took significant steps to reduce the contamination of their cosmic shear constraints by IAs by excluding the auto-correlations for the 5 narrowest redshift bins and excluding luminous red galaxies (LRGs) from their analysis., \citet{schrabbackea09} took significant steps to reduce the contamination of their cosmic shear constraints by IAs by excluding the auto-correlations for the 5 narrowest redshift bins and excluding luminous red galaxies (LRGs) from their analysis. +" They also showed results using only the autocorrelations, which were similar to those excluding the autocorrelations results, leading them to conclude that intrinsic alignments are not a significant contaminant."," They also showed results using only the autocorrelations, which were similar to those excluding the autocorrelations results, leading them to conclude that intrinsic alignments are not a significant contaminant." +" Many current and future surveys are planned with cosmic shear as a major design driver, in particular from the ground the Canada-France-Hawaii Telescope Legacy Survey the KIlo-Degree Survey (KIDS), the Panoramic (CFHTLSfI],Survey Telescope and Rapid Response System (Pan-STARRS]]surveys, the Dark Energy Survey the Large Synoptic Survey Telescope and(DESf]. space missions and the Joint Dark Energy(LSSTT]. Mission"," Many current and future surveys are planned with cosmic shear as a major design driver, in particular from the ground the Canada-France-Hawaii Telescope Legacy Survey, the KIlo-Degree Survey (KIDS), the Panoramic Survey Telescope and Rapid Response System surveys, the Dark Energy Survey, the Large Synoptic Survey Telescope, and space missions and the Joint Dark Energy Mission." + clid?|The majority of observational constraints(ΡΕΜΠ. on galaxy IAs have been carried out at low redshift (Brownet2000) butal. these have recently been extended towards the redshifts relevant to cosmic shear surveys ," The majority of observational constraints on galaxy IAs have been carried out at low redshift \citep{brownthd02,heymans04,mandelbaumhisb06} but these have recently been extended towards the redshifts relevant to cosmic shear surveys \citep{hirataea07,mandelbaumea09}." +These studies have used spectroscopic galaxy surveys to calculate the galaxy position - galaxy shear correlation function and/or the galaxy shear - galaxy shear correlation function., These studies have used spectroscopic galaxy surveys to calculate the galaxy position - galaxy shear correlation function and/or the galaxy shear - galaxy shear correlation function. + Constraints calculated from these correlation functions have been fitted with simple models for IAs using a fixed cosmological model., Constraints calculated from these correlation functions have been fitted with simple models for IAs using a fixed cosmological model. +" In this paper we calculate constraints on cosmological parameters from cosmic shear data, taking into account the likely contamination from IAs for a range of IA models."," In this paper we calculate constraints on cosmological parameters from cosmic shear data, taking into account the likely contamination from IAs for a range of IA models." + We simultaneously fit an [A model and cosmological parameters to IA correlation functions., We simultaneously fit an IA model and cosmological parameters to IA correlation functions. +" We then perform a joint analysis of cosmic shear and IA data, varying both cosmology and parameters within the IA model."," We then perform a joint analysis of cosmic shear and IA data, varying both cosmology and parameters within the IA model." +"range of observed galaxies, in Figure 10..","range of observed galaxies, in Figure \ref{ConcClump}." + It is apparent though that some of the simulations are excessively clumpy in comparison to their observed counterparts., It is apparent though that some of the simulations are excessively clumpy in comparison to their observed counterparts. +" As can be garnered from Table 1, all these simulated galaxies which are clumpy outliers only occur when viewed at an inclination of 90°."," As can be garnered from Table 1, all these simulated galaxies which are clumpy outliers only occur when viewed at an inclination of $\degrees$." +" This group of galaxies display approximately average concentration values, whilst being excessively clumpy, in comparison to both their observed and simulated galaxy counterparts."," This group of galaxies display approximately average concentration values, whilst being excessively clumpy, in comparison to both their observed and simulated galaxy counterparts." +" In regards to the excessively clumpy dwarfs, we note that the high frequency structure present in these simulated galaxies is consistent with the power spectrum analysis of the associated ISM by Pilkington et al. ("," In regards to the excessively clumpy dwarfs, we note that the high frequency structure present in these simulated galaxies is consistent with the power spectrum analysis of the associated ISM by Pilkington et al. (" +2011).,2011). +" In Figure 10,, the MUGS sample demonstrates an approximately equivalent trend to the observed galaxy sample, despite their excessive bulge sizes."," In Figure \ref{ConcClump}, the MUGS sample demonstrates an approximately equivalent trend to the observed galaxy sample, despite their excessive bulge sizes." +" This is unexpected, as the central bulge component is disregarded in the computation of the clumpiness, but is included for the concentration parameter."," This is unexpected, as the central bulge component is disregarded in the computation of the clumpiness, but is included for the concentration parameter." +" However, with respect to the Dwarf and UW samples, the MUGS sample contains galaxies that are generally more concentrated."," However, with respect to the Dwarf and UW samples, the MUGS sample contains galaxies that are generally more concentrated." +" It is likely that the greater mass, velocity dispersion, and higher star formation threshold of the MUGS sample all contribute to both the larger bulge sizes and concentration of these galaxies, with respect to the other simulated galaxy samples."," It is likely that the greater mass, velocity dispersion, and higher star formation threshold of the MUGS sample all contribute to both the larger bulge sizes and concentration of these galaxies, with respect to the other simulated galaxy samples." +" Furthermore, it is likely that these characteristics produced the earlier-type discs in the MUGS sample, which are expected to be less clumpy in nature."," Furthermore, it is likely that these characteristics produced the earlier-type discs in the MUGS sample, which are expected to be less clumpy in nature." +" In Figure 11,, it can be seen that there is a strong positive correlation between the clumpiness and asymmetry of observed galaxies."," In Figure \ref{ClumpAsym}, it can be seen that there is a strong positive correlation between the clumpiness and asymmetry of observed galaxies." +" This correlation arises from the later-type galaxies tending to be clumpy and asymmetric, due to their star forming regions and intrinsic structure, and earlier-type galaxies tending to be devoid of structure and star forming regions, which pertains to them being more smooth and symmetric."," This correlation arises from the later-type galaxies tending to be clumpy and asymmetric, due to their star forming regions and intrinsic structure, and earlier-type galaxies tending to be devoid of structure and star forming regions, which pertains to them being more smooth and symmetric." + The simulated galaxies appear to follow the same correlation., The simulated galaxies appear to follow the same correlation. +" However, the sample of highly symmetric observed galaxies are not reproduced within the simulations."," However, the sample of highly symmetric observed galaxies are not reproduced within the simulations." +" In Figure 11,, the Dwarf sample of galaxies form three groups; those which lie within the normal range, those which are excessively clumpy, and those that are excessively asymmetric."," In Figure \ref{ClumpAsym}, the Dwarf sample of galaxies form three groups; those which lie within the normal range, those which are excessively clumpy, and those that are excessively asymmetric." +" As previously discussed, those galaxies that are excessively clumpy all have 90° inclination angles."," As previously discussed, those galaxies that are excessively clumpy all have $\degrees$ inclination angles." +" Figure 11 shows that the high frequency spatial clumpiness of these galaxies is not directly related to asymmetry, as those galaxies that demonstrate excessive clumpiness possess a wide range of asymmetries with respect to other galaxies from the same sample."," Figure \ref{ClumpAsym} shows that the high frequency spatial clumpiness of these galaxies is not directly related to asymmetry, as those galaxies that demonstrate excessive clumpiness possess a wide range of asymmetries with respect to other galaxies from the same sample." + 'The group of simulations which are seemingly highly asymmetric outliers at the top of Figure 11 is in fact just one simulated galaxy (DG2) viewed at various inclinations., The group of simulations which are seemingly highly asymmetric outliers at the top of Figure \ref{ClumpAsym} is in fact just one simulated galaxy (DG2) viewed at various inclinations. + This particular galaxy has a large star forming complex at z=0 which is offset from the centre of the galaxy (see Governato et al., This particular galaxy has a large star forming complex at $z=0$ which is offset from the centre of the galaxy (see Governato et al. +" 2010), explaining both the clumpiness and asymmetry of this galaxy."," 2010), explaining both the clumpiness and asymmetry of this galaxy." +" In Figure 12,, there is an apparent negative correlation between asymmetry and concentration for both observed and simulated galaxies."," In Figure \ref{ConcAsym}, there is an apparent negative correlation between asymmetry and concentration for both observed and simulated galaxies." +" This can be attributed to the fact that later-type galaxies are both diffuse and asymmetric, and earlier-type galaxies are generally dense with less internal structure."," This can be attributed to the fact that later-type galaxies are both diffuse and asymmetric, and earlier-type galaxies are generally dense with less internal structure." + Within the Dwarf galaxy sample there is again a single galaxy viewed at various inclinations that demonstrates low concentration values coupled with extremely high asymmetry values., Within the Dwarf galaxy sample there is again a single galaxy viewed at various inclinations that demonstrates low concentration values coupled with extremely high asymmetry values. + The large star forming complex in this simulation has not resulted in a concentration being outside the region defined by observed galaxies., The large star forming complex in this simulation has not resulted in a concentration being outside the region defined by observed galaxies. +" We have applied measures of concentration (C), asymmetry (A) and clumpiness (S) to a sample of simulated galaxies which have a range of masses and morphologies, as well as to a sample of observed galaxies."," We have applied measures of concentration (C), asymmetry (A) and clumpiness (S) to a sample of simulated galaxies which have a range of masses and morphologies, as well as to a sample of observed galaxies." + We have explored the correlations between these parameters as well as between each of them with B-V colour., We have explored the correlations between these parameters as well as between each of them with B-V colour. +" In general, reasonable agreement was found between the simulated and observed populations in these relations, although some differences become apparent, as summarised below."," In general, reasonable agreement was found between the simulated and observed populations in these relations, although some differences become apparent, as summarised below." +" Overall, the trend generated by the observed galaxy"," Overall, the trend generated by the observed galaxy" +Tow do galaxies ect their gas?,How do galaxies get their gas? + This important question jas never been fully answered. either through observation or through uunerical simulation.," This important question has never been fully answered, either through observation or through numerical simulation." + oobservations of the nearby universe sugeest that ealaxyv uecreers and collisions are an important aspect of his process (Ilibbard van Corkom 1996). but tidal interactions do not guarantee that the gas settles to one or other galaxy.," observations of the nearby universe suggest that galaxy mergers and collisions are an important aspect of this process (Hibbard van Gorkom 1996), but tidal interactions do not guarantee that the gas settles to one or other galaxy." + The most spectacular interaction phenomenon is the Maecllanic SStream that trails from the LAIC-SAIC system (10:1 nass ratio) in orbit about the Cialaxy., The most spectacular interaction phenomenon is the Magellanic Stream that trails from the LMC-SMC system (10:1 mass ratio) in orbit about the Galaxy. + Since its cliscovery (Waunuier Wiixon 1972: Matthewson et al 1979). there je been repeated attempts to explain the Stream iu crius of tidal aud/or viscous forces (q.v.," Since its discovery (Wannier Wrixon 1972; Matthewson et al 1979), there have been repeated attempts to explain the Stream in terms of tidal and/or viscous forces (q.v." + Mastropietro et al., Mastropietro et al. + 2005: Counors. IKawata Cübson 2005).," 2005; Connors, Kawata Gibson 2005)." + Tucleed. he Stream has become a benchmark against which to judge the credibility of | gas codes in explaining eas processes in galaxies.," Indeed, the Stream has become a benchmark against which to judge the credibility of $+$ gas codes in explaining gas processes in galaxies." + A fully consistent model of the Stream continues to clude even the most sophisticated codes., A fully consistent model of the Stream continues to elude even the most sophisticated codes. +" Tere. we demonstrate that deletections along the Stream (Weiner Williams 1996: Putiman et al 2003) are providing new iusights ou the present state and evolution of the eoas,"," Here, we demonstrate that detections along the Stream (Weiner Williams 1996; Putman et al 2003) are providing new insights on the present state and evolution of the gas." + At a distance of Dz:55 kpc. the expected ssigual excited by the cosimic and Galactic UV backerounds are about 3 mR aud 25 mh respectively (Bland-Hawthoru Maloney 1999. 2002). significautly lower than the mean signal of LOO) 200 mR. and much lower than the few bright detections iu the range LOOτοῦ wR (Weiner. Vogel Williams 2002).," At a distance of $D\approx 55$ kpc, the expected signal excited by the cosmic and Galactic UV backgrounds are about 3 mR and 25 mR respectively (Bland-Hawthorn Maloney 1999, 2002), significantly lower than the mean signal of $-$ 200 mR, and much lower than the few bright detections in the range $400-750$ mR (Weiner, Vogel Williams 2002)." + This signal cannot have a stellar origin since repeated atteuipts to detect stars alone the Stream have failed (c.g. Ostheimer. Majewski Iunkel 1997).," This signal cannot have a stellar origin since repeated attempts to detect stars along the Stream have failed (e.g. Ostheimer, Majewski Kunkel 1997)." + Some ofthe Stream clouds exhibit counipressiou frouts and heac-tail morphologies (Brians et al 2005) aud this i sueeestive of coufiucment by a tenuous external medi., Some of the Stream clouds exhibit compression fronts and head-tail morphologies (Brünns et al 2005) and this is suggestive of confinement by a tenuous external medium. + But the cloud:halo deusitv ratio (gj=p-/pn) necessary for confinement can be orders of magnitudeαγ than that required to achieve shock-induced comission (ee. Quilis Moore 2001)., But the cloud:halo density ratio $\eta = \rho_c/\rho_h$ ) necessary for confinement can be orders of magnitude than that required to achieve shock-induced emission (e.g. Quilis Moore 2001). +" Tacdeed. the best estimates of the halo density at the distance of the Stream (py,~10 cin: Breeman 2007) are far too tenuous to induce stroug ecluission at a cloud face."," Indeed, the best estimates of the halo density at the distance of the Stream $\rho_h \sim 10^{-4}$ $^{-3}$; Bregman 2007) are far too tenuous to induce strong emission at a cloud face." + It is therefore surprising to discover that the brightest detections lie at the leading edges of cclouds 2002) and thus appear to indicate that shock processes are somehow involved., It is therefore surprising to discover that the brightest detections lie at the leading edges of clouds 2002) and thus appear to indicate that shock processes are somehow involved. + We now present a iiodel that gocs a long way towards explaining the nuuvsterv., We now present a model that goes a long way towards explaining the mystery. + The basic premise is that a teuuous external medi not only coufines clouds. but also disrupts them with the passage of tine.," The basic premise is that a tenuous external medium not only confines clouds, but also disrupts them with the passage of time." +" The erowth time for Ixelvin-Uehuholtz (KIT) instabilities is eiven by rgàAquf, where A ds the waveleugth of the erowiug mode. and ¢y, "," The growth time for Kelvin-Helmholtz (KH) instabilities is given by $\tau_{\rm KH} \approx \lambda \eta^{0.5}/v_h$ where $\lambda$ is the wavelength of the growing mode, and $v_h$ " +the equation of motion. +0 delyo= VP22. and the induction equation of ideal MIID. Vblimes((vblimesB)).,"the equation of motion, + = P, and the induction equation of ideal MHD, = )." + (14)7 For reasons that will become clear. an internal energy. equation is not needed at {his slage.," For reasons that will become clear, an internal energy equation is not needed at this stage." + The equilibrium state is a differentially rotating disk. aud we work in the usual cvlindrical coordinate system. HR.6.Z.," The equilibrium state is a differentially rotating disk, and we work in the usual cylindrical coordinate system, $R, \phi, Z$." + The angular velocity is O(CR). and we shall restrict ourselves to a local analvsis at the midplane.," The angular velocity is $\Omega(R)$, and we shall restrict ourselves to a local analysis at the midplane." + Thus. we may ignore buovant forces. which depend upon eradients in pressure and entropy.," Thus, we may ignore buoyant forces, which depend upon gradients in pressure and entropy." +" In the equilibrium state. it is assumed (hat σι,=0."," In the equilibrium state, it is assumed that $\sigma_{ij} =0$." + Indeed. the point of this calculation is to show that anv development of viscous transport along a field line is highly unstable.," Indeed, the point of this calculation is to show that any development of viscous transport along a field line is highly unstable." + The initial magnetic fiekl lines are wrapped around cvlinders. and are unaffected by the shear.," The initial magnetic field lines are wrapped around cylinders, and are unaffected by the shear." + We consider next small departures [rom the equilibrium flow., We consider next small departures from the equilibrium flow. + Linearly perturbed quantities are denoted by àv.0o;;. etc.," Linearly perturbed quantities are denoted by $\bb{\delta v}, \delta\sigma_{ij}$, etc." + We work in the local WIXB limit. with the space-time dependence of all perturbed quantities given by exp(5/4ker).," We work in the local WKB limit, with the space-time dependence of all perturbed quantities given by $\exp(\gamma t + i\bb{k}\bcdot\bb{r})$." + Thus. 5 is à growthli or decay rate if il is real. and an angular frequency if it is imaginary.," Thus, $\gamma$ is a growth or decay rate if it is real, and an angular frequency if it is imaginary." + The wavenumber & as well as the assumed constancy of + require some further explanation., The wavenumber $\bb{k}$ as well as the assumed constancy of $\gamma$ require some further explanation. +" The wavenumber has radial. azimuthal anc vertical components hg.m/R.hz respectively,"," The wavenumber has radial, azimuthal and vertical components $k_R, m/R, k_Z$ respectively." + Since we are working in a local shearing svstem. the radial wavenumber 4; will formally depend on time (Goldreich&Lynelen-Bell1965:BalbusHawlev1992): key) ο) —de. where (0) is the initial value of Ay.," Since we are working in a local shearing system, the radial wavenumber $k_R$ will formally depend on time \citep{glb65, bh92}: k_R(t) = k_R(0) -, where $k_R(0)$ is the initial value of $k_R$." + For our present purposes however. the time dependence of fy will prove irrelevant. as the radial wavenunber clisappears early in the analvsis.," For our present purposes however, the time dependence of $k_R$ will prove irrelevant, as the radial wavenumber disappears early in the analysis." + It is For (his reason (hat we may also assume a simple exponential time dependence: in general the problem is more complex., It is for this reason that we may also assume a simple exponential time dependence; in general the problem is more complex. +Receutly. ? investigated the dependence of the mass-o-lght ratios of large-scale structure on cosmological xuwanieters.,"Recently, \citet{tinker05} investigated the dependence of the mass-to-light ratios of large-scale structure on cosmological parameters." + Tn particular. they study simulations that reproduce the observed ealaxy aneular correlation Muction aud luminosity function.," In particular, they study simulations that reproduce the observed galaxy angular correlation function and luminosity function." +" They then inter the halo occupation distribution (ΠΟΡΟ) and conditional luminosity ""uuction (CLE) for several values of σα (σε is the rms ductuation iu spheres of radius sftMIpe). yielding a wediction for the dependence of mass-to-light ratio ou ilo mass."," They then infer the halo occupation distribution (HOD) and conditional luminosity function (CLF) for several values of $\sigma_8$ $\sigma_8$ is the rms fluctuation in spheres of radius $\Mpc$ ), yielding a prediction for the dependence of mass-to-light ratio on halo mass." +" Comparing their simulations to observed mass-o-lght ratios of cluster virial regious. ? concluded hat models with values of σς and/or @,, smaller than hose found bv 7? provide the best fits."," Comparing their simulations to observed mass-to-light ratios of cluster virial regions, \citet{tinker05} concluded that models with values of $\sigma_8$ and/or $\Omega_m$ smaller than those found by \citet{tegmark04} provide the best fits." +" Using a siuilar CLF approach with different paraimctrization. ? also conchnude that σς and/or 9,, are sinaller than suggested bv ?7.."," Using a similar CLF approach with different parametrization, \citet{2003MNRAS.345..923V} + also conclude that $\sigma_8$ and/or $\Omega_m$ are smaller than suggested by \citet{tegmark04}." + 7. show that the iufall roegious of laree- halos (those with Afoyy 234101!5 TAL.) in their sinulatious contain significantly more mass than the mass profiles inferred frou: CAIRNS (sce their Figure 9).," \citet{tinker05} show that the infall regions of large-mass halos (those with $M_{200}\geq$ $\times$ $^{14} +h^{-1}M_{\odot}$ ) in their simulations contain significantly more mass than the mass profiles inferred from CAIRNS (see their Figure 9)." + They sugeest that either the caustic masses are systematically uderestinated at huge radi or that the observations conflict with the predictions., They suggest that either the caustic masses are systematically underestimated at large radii or that the observations conflict with the predictions. + This discrepancy is especially interesting because it refers to mass ratios ancl is thus incdependeut of galaxy bias., This discrepancy is especially interesting because it refers to mass ratios and is thus independent of galaxy bias. + Figure 2? shows a simular plot for the CIRS clusters., Figure \ref{ctinker} shows a similar plot for the CIRS clusters. + The scatter is large. but t CIRS clusters are iu wich better agreement with the predictions of than are the CAIRNS clusters.," The scatter is large, but the CIRS clusters are in much better agreement with the predictions of \citet{tinker05} than are the CAIRNS clusters." + However. amoung clusters with Afyy 2395%) member of the cluster (SandersZhaoetal. 1993).," Accurate photometry of the star S986 [ID number from Sanders 1977; also known as F111 (Fagerholm 1906), and MMJ 5624 (Montgomery, Marschall, Janes 1993)] indicates that it falls at the turnoff in the cluster's color-magnitude diagram (CMD), and proper motion studies identify it as a high probability $\ge 95\%$ ) member of the cluster \citep{sanders,girard,zhao}." +". 5986 was previously identified as a sinele-linecl spectroscopic binary by Mathieu. Latham. Griffin (1990) with a period 0.0006 d. Another interesting aspect of this svstem is the fact that the primary is on a circular orbit. indicating that tidal interactions between the stars have damped oul any initial eccentricity,"," S986 was previously identified as a single-lined spectroscopic binary by Mathieu, Latham, Griffin (1990) with a period $P = 10.3386 \pm 0.0006$ d. Another interesting aspect of this system is the fact that the primary is on a circular orbit, indicating that tidal interactions between the stars have damped out any initial eccentricity." + Over (ime. cireularized main sequence binaries should be found at longer and longer periods as these interactions have sufficient. time to work in wider and wider binaries (Mathieu Mazel 1988).," Over time, circularized main sequence binaries should be found at longer and longer periods as these interactions have sufficient time to work in wider and wider binaries (Mathieu Mazeh 1988)." + 5986 is the longest period circularized binary known in the cluster. and has probably requirecl most of the clusters lifetime to become circularized.," S986 is the longest period circularized binary known in the cluster, and has probably required most of the cluster's lifetime to become circularized." + As Mathieu et al. (, As Mathieu et al. ( +1990) discuss. the secondary star in the binary must be al least about 2 magnitudes fainter than the primary at 5200 because i( is a single-lined svstem.,"1990) discuss, the secondary star in the binary must be at least about 2 magnitudes fainter than the primary at 5200 because it is a single-lined system." + This indicates (hat the primary must contribute most of the light coming from (he svstem. and therefore must be very close to the tiuwnolf mass.," This indicates that the primary must contribute most of the light coming from the system, and therefore must be very close to the turnoff mass." + A lower limit on the mass of the secondary. is placed by the mass function For the binary: approximately 0.51 M.in (he case of 5986 (assuming a primary mass of 1.25 ))., A lower limit on the mass of the secondary is placed by the mass function for the binary: approximately 0.51 in the case of S986 (assuming a primary mass of 1.25 ). + Mathieu et al., Mathieu et al. + stated that residuals of the orbital solution correlated with phase. and thal a weak secondary cross correlation peak could be seen.," stated that residuals of the orbital solution correlated with phase, and that a weak secondary cross correlation peak could be seen." + Later Melo. Pasquini. De Aledeiros (2001) clelinilively detected a secondary peak in the cross-correlation function for the svstem. and measured a rotational velocity vsin?/=53+0.6n.," Later Melo, Pasquini, De Medeiros (2001) definitively detected a secondary peak in the cross-correlation function for the system, and measured a rotational velocity $v \sin i = 5.3 \pm 0.6$." + Careful examination of their cross correlation function indicates that the secondary. peak is rather close to systematic radial velocity [ου AGT., Careful examination of their cross correlation function indicates that the secondary peak is rather close to systematic radial velocity for M67. + As a byproduct of our project to monitor the partiallv-eclipsing blue strageler $1082 (period 1.0677978 d). we made extensive observations of the fields near the core of M67.," As a byproduct of our project to monitor the partially-eclipsing blue straggler S1082 (period 1.0677978 d), we made extensive observations of the fields near the core of M67." + The period of $936 has unfortunate aliases with the period of Earth's rotation so that only one eood apparition of the primary eclipse occurs during nighttime hours for a given observing site per month., The period of S986 has unfortunate aliases with the period of Earth's rotation so that only one good apparition of the primary eclipse occurs during nighttime hours for a given observing site per month. + This may explain the reason that eclipses have not previously been detected, This may explain the reason that eclipses have not previously been detected +on a relaxation timescale) is only weakly dependent on (he cluster mass.,on a relaxation timescale) is only weakly dependent on the cluster mass. + If we look in detail al the local relaxation timescale this scales as (Davies. Piotto De Angeli 2004. as derived from Binney Tremaine 1987) where σ is the velocity dispersion of the cluster stars and pis the mass density.," If we look in detail at the local relaxation timescale this scales as (Davies, Piotto De Angeli 2004, as derived from Binney Tremaine 1987) where $\sigma$ is the velocity dispersion of the cluster stars and $\rho$ is the mass density." +" We can take and pxM. usinge the above assumptions. to show that /,LoM71/2/In(0.4.N.)."," We can take $\sigma \propto \sqrt{M/r_{\rm h}} \propto M_{\rm c}^{1/2}$ and $\rho \propto M_{\rm c}$, using the above assumptions, to show that $t_{\rm r} \propto M_{\rm c}^{1/2} / \ln \left( 0.4 N \right)$ ." + IIere Af. is the cluster core-mass. A/ is the total cluster mass and ry is the hall-mass radius.," Here $M_{\rm c}$ is the cluster core-mass, $M$ is the total cluster mass and $r_{\rm h}$ is the half-mass radius." + The timescale for a typical binary in the core of a globular cluster to have a close encounter with another star scales as (Davies. Piotto De Angeli 2004) where » is the number density and η~p if the average stellar mass is of the order of AM... as it is in an evolved cluster core.," The timescale for a typical binary in the core of a globular cluster to have a close encounter with another star scales as (Davies, Piotto De Angeli 2004) where $n$ is the number density and $n \sim \rho$ if the average stellar mass is of the order of $M_\odot$ , as it is in an evolved cluster core." + This gives us F7., This gives us $t_{\rm enc} \propto M_{\rm c}^{-1/2}$ . + To escape (he core a binary nist acquire a boost in energy of the order of GAL./2re (where G is the Gravitational constant).," To escape the core a binary must acquire a boost in energy of the order of $G \, M_{\rm c} / 2 \, r_{\rm c}$ (where $G$ is the Gravitational constant)." +" So. assuming that (he average enerev inmparted in an encounter does not vary strongly with mass. we have ljxMET,"," So, assuming that the average energy imparted in an encounter does not vary strongly with mass, we have $t_{\rm ej} \propto M_{\rm c}^{1/2}$." + This rather siniplilied analvsis returns Hénnons result and shows that as A/ (or A) increases there will be relatively less binary convection as both the ejection and relaxation timescales increase., This rather simplified analysis returns Hénnon's result and shows that as $M$ (or $N$ ) increases there will be relatively less binary convection as both the ejection and relaxation timescales increase. + However. the effect on the observed core binary fraction can be expected to be minimal.," However, the effect on the observed core binary fraction can be expected to be minimal." + We cannot definitivelv use our results to make predictions regarding globular clusters such as 47 Tucanae because the central densitv in these clusters is at least an order of magnitude higher than that reached by our models., We cannot definitively use our results to make predictions regarding globular clusters such as 47 Tucanae because the central density in these clusters is at least an order of magnitude higher than that reached by our models. + However. we note that our model with the highest core density showed the greatest increase in core binary fraction.," However, we note that our model with the highest core density showed the greatest increase in core binary fraction." + Furthermore. we have considered a range of cluster (vpes.," Furthermore, we have considered a range of cluster types." + We also note that proper-motion cleaned. colou-maegnitude diagrams recently presented lor 6397 (Richer et al.," We also note that proper-motion cleaned colour-magnitude diagrams recently presented for $\,6397$ (Richer et al." + 2006) and MA (Richer et al., 2006) and M4 (Richer et al. + 2004) show a distinct. lack of binaries in regions outside of the cluster centre (his cannot be reconciled with a large primordial binary population., 2004) show a distinct lack of binaries in regions outside of the cluster centre – this cannot be reconciled with a large primordial binary population. + We have presented a range of simulations tvpical of rich open clusters and mocderate-size elobular clusters., We have presented a range of simulations typical of rich open clusters and moderate-size globular clusters. + In each case we find that the fraction of binaries in the core of a cluster does not decreaseas the cluster evolves., In each case we find that the fraction of binaries in the core of a cluster does not decreaseas the cluster evolves. + In [act the overriding trend is for an increasein, In fact the overriding trend is for an increasein +and 0.2.,and 0.2. + The number rates per redshilt bin (left) and the cumulative rate (right) are given., The number rates per redshift bin (left) and the cumulative rate (right) are given. + The reader can readily notice the effect of bias behind the halo., The reader can readily notice the effect of bias behind the halo. + With the galactie size halo may. Lhe survey can detect supernovae up to redshift z~3 (Fie.," With the galactic size halo $m_{d1}$, the survey can detect supernovae up to redshift $z \sim 3$ (Fig." + 7)., 7). + This limit increases {ο zo5 (Fig., This limit increases to $z \sim 5$ (Fig. + 8) lor the cluster-size halo mj., 8) for the cluster-size halo $m_{d2}$. + The lowest panel in these (wo figures show the relative difference of the cases with e—0.1 and e=0.2 with respect to €=0.0., The lowest panel in these two figures show the relative difference of the cases with $\epsilon = 0.1$ and $\epsilon = 0.2$ with respect to $\epsilon = 0.0$. + The 2 eurves do not show significant difference for the redshift bins in [ront of the halo., The 2 curves do not show significant difference for the redshift bins in front of the halo. +" In the regime behind the halo. the difference becomes remarkable: it increases up to redshilt 2=1.4 for my, and z=1.7 for mis."," In the regime behind the halo, the difference becomes remarkable: it increases up to redshift $z=1.4$ for $m_{d1}$ and $z=1.7$ for $m_{d2}$." + The difference doesn’t vary remarkably bevond the maximum point., The difference doesn't vary remarkably beyond the maximum point. + To further see how ellipticity changes the expected rate of observed supernovae we put the result of our caleulations for different ellipticities [ον a given range of magnitude limits on the same plot., To further see how ellipticity changes the expected rate of observed supernovae we put the result of our calculations for different ellipticities for a given range of magnitude limits on the same plot. + Figure 9 shows the number rate of observed (wpe la supernovae (upper panel) for ellipticities e=0.1 and e=0.2 together with their relative difference wilh respect to the case wilh no ellipticity (lower panel)., Figure 9 shows the number rate of observed type Ia supernovae (upper panel) for ellipticities $\epsilon = 0.1$ and $\epsilon = 0.2$ together with their relative difference with respect to the case with no ellipticity (lower panel). + Both halo masses. mij aud mio are at redshift zy= 0.2.," Both halo masses, $m_{d1}$ and $m_{d2}$ are at redshift $z_{d}=0.2$ ." +" Figures 10 and 11 show the results of the same calculations with halos at recdshilts ;—0.5 and z=1.0. respectively,"," Figures 10 and 11 show the results of the same calculations with halos at redshifts $z=0.5$ and $z=1.0$, respectively." +" The number rates in each figure increase smoothly up to (he magnitude limit at which (tlie survey is deep enough to detect (he supernovae as [ar as the halo itself. e.g. Πρι=22.4 for a concordance cosmology of (O,,.6. μη) = (0.3. 0.7. 0.61)."," The number rates in each figure increase smoothly up to the magnitude limit at which the survey is deep enough to detect the supernovae as far as the halo itself, e.g, $m_{lim}=22.4$ for a concordance cosmology of $\Omega_{m}, \omega_{\Lambda}, h_{100}$ ) = (0.3, 0.7, 0.67)." + From that point on the rates increase very rapidly as the magnitude limit goes up., From that point on the rates increase very rapidly as the magnitude limit goes up. + That is caused by (he halo lensing and hence amplifvine the supernovae which would otherwise be too dim to be observed., That is caused by the halo lensing and hence amplifying the supernovae which would otherwise be too dim to be observed. + The relative differences depicted in these figures show (hat even al a magnitude limit of 25. effect of ellipticity cannot be ignored as it significantly changes the number/percentage of (he observed supernovae: lor instance. the relative difference for e—0.2 with dellecting halo mis at redshift 2=1.0 (Fig.," The relative differences depicted in these figures show that even at a magnitude limit of 25, effect of ellipticity cannot be ignored as it significantly changes the number/percentage of the observed supernovae; for instance, the relative difference for $\epsilon=0.2$ with deflecting halo $m_{d2}$ at redshift $z=1.0$ (Fig." +" 11) exceeds [or the magnitude limit of mj;4,=2T.", 11) exceeds for the magnitude limit of $m_{lim}=27$. + Aiming behind massive halos seem to be a good way to enhance the high-redshift supernovae surveys., Aiming behind massive halos seem to be a good way to enhance the high-redshift supernovae surveys. +" The cumulative gains of such surveys seem insignificant al low recshilts (2,« 0.2) but the resulis are remarkable at hieher redshifts.", The cumulative gains of such surveys seem insignificant at low redshifts $z_{s}<0.2$ ) but the results are remarkable at higher redshifts. + For deep observations where Mim225. the geometry of the intervening halo cannot be ignored.," For deep observations where $m_{lim}>25$, the geometry of the intervening halo cannot be ignored." + We have shown that introducing ellipticity in (he (gravitational potential of) the mass distribution of a deflecting iilo (here. for a galactic halo of mass 1.0xLOPAL5.!1 as well as a middle-size cluster of galaxies with a mass of 1.0x10!4.A 1) can affect the rate of observed supernovae by a ew percent.," We have shown that introducing ellipticity in the (gravitational potential of) the mass distribution of a deflecting halo (here, for a galactic halo of mass $1.0 \times 10^{12} M_{\odot} h^{-1}$ as well as a middle-size cluster of galaxies with a mass of $1.0 \times 10^{14} M_{\odot} h^{-1}$ ) can affect the rate of observed supernovae by a few percent." + It wasshown that the farther (he supernova survey probes. (he more significant," It wasshown that the farther the supernova survey probes, the more significant" +in ugrizy would save both projects time while achieving better performance in measuring the dark energy EOS.,in $ugrizy$ would save both projects time while achieving better performance in measuring the dark energy EOS. +" Here, we use SNAP and LSST as references to model an ideal 10,000 square degree survey (named ""ideal 10k"") in bands to comparable depth as SNAP."," Here, we use SNAP and LSST as references to model an ideal 10,000 square degree survey (named “ideal 10k”) in bands to comparable depth as SNAP." +" We assume that its galaxy redshift distribution follows with z,=0.5.", We assume that its galaxy redshift distribution follows with $z_* = 0.5$. +" The projected galaxy number density πρ is 70 arcmin?, and the distribution peaks at 2z,."," The projected galaxy number density $\bar{n}_g$ is 70 $^{-2}$, and the distribution peaks at $2z_*$ ." +" For LSST, we adopt 2.=0.3 and n,=40 arcmin~? (LSSTScienceCollaborations"," For LSST, we adopt $z_* = 0.3$ and $\bar{n}_g = 40$ $^{-2}$ \citep{lsst09}." + The model parameters of the survey data are summarized2009).. in1., The model parameters of the survey data are summarized in. +". The galaxy distribution n;(z) in the ith bin is sampled from n(z) by (Maetal.2006;Zhan2006) where the subscript p denotes space, 2B, and define the extent of bin i, and P(a,b;z) is the probabilityzp, of assigning a galaxy thatis at true redshift z to the bin between zy=a and b."," The galaxy distribution $n_i(z)$ in the $i$ th bin is sampled from $n(z)$ by \citep{ma06,zhan06d} + where the subscript p denotes space, $z_{{p},i}^{\rm B}$ and $z_{{p},i}^{\rm E}$ define the extent of bin $i$, and $\mathcal{P}(a,b;z)$ is the probability of assigning a galaxy that is at true redshift $z$ to the bin between $z_{p} = a$ and $b$." +" We approximate the error to be Gaussian with bias óz and rms σι...+z), and the probability becomes The normalization [(0,oo; implies that galaxies with a negative have been 2)excluded from n(z)."," We approximate the error to be Gaussian with bias $\delta z$ and rms $\sigma_z=\sigma_{z0} (1+z)$, and the probability becomes The normalization $I(0,\infty; z)$ implies that galaxies with a negative have been excluded from $n(z)$." + We use 40 bias dz and 40 rms c; parameters evenly spaced between z=O and 5 to model the error distribution in the space; the bias and rms at any redshift are Ζ-2ρlinearly interpolated from these 80 parameters., We use 40 bias $\delta z$ and 40 rms $\sigma_z$ parameters evenly spaced between $z = 0$ and 5 to model the error distribution in the$z$ $z_p$ space; the bias and rms at any redshift are linearly interpolated from these 80 parameters. + Note that the parameters are assigned independent of galaxy bins., Note that the parameters are assigned independent of galaxy bins. + We assume that 750=0.03 for the ideal survey and σερ=0.05 for LSST., We assume that $\sigma_{z0} = 0.03$ for the ideal survey and $\sigma_{z0} = 0.05$ for LSST. +" Uncertainties of the parameters (or, the error distribution in have a large impact on the dark energy constraints general)from WL and are referred to as systematics."," Uncertainties of the parameters (or, the error distribution in general) have a large impact on the dark energy constraints from WL and are referred to as systematics." +" Therefore, the prior on the error distribution is an important quantity to specify when reporting WL constraints on dark energy."," Therefore, the prior on the error distribution is an important quantity to specify when reporting WL constraints on dark energy." +" To reduce the dimension of the investigation, we set a simple function for all the priors on the bias parameters, op(óz)=0.20,, and peg the priors on rms parameters to those on the bias parameters: op(oz)=V2ep(6z)."," To reduce the dimension of the investigation, we set a simple function for all the priors on the bias parameters, $\sigma_\mathrm{P}(\delta z) = 0.2 \sigma_z$, and peg the priors on rms parameters to those on the bias parameters: $\sigma_\mathrm{P}(\sigma_z) = \sqrt{2} \sigma_\mathrm{P}(\delta z)$." +" For Gaussian errors, these priors correspond to a calibration sample of 25 spectra per redshift interval of the parameters."," For Gaussian errors, these priors correspond to a calibration sample of 25 spectra per redshift interval of the parameters." +" We set op(6z)=0.3σ., reflecting larger uncertainties with fewer filter bands."," We set $\sigma_\mathrm{P}(\delta z) = 0.3 \sigma_z$, reflecting larger uncertainties with fewer filter bands." +" However, such difference in the priors is not important if one performs a joint analysis of the BAO and WL techniques, which takes advantage of the self-calibration of error distribution by galaxy power spectra (Schneideretal.2006;ZhanZhangetal.2009,referencedherein) LSST will benefit from KDUST yJH data in a number of ways."," However, such difference in the priors is not important if one performs a joint analysis of the BAO and WL techniques, which takes advantage of the self-calibration of error distribution by galaxy power spectra \citep[referenced herein]{schneider06, zhan06d, zhang09} + LSST will benefit from KDUST $yJH$ data in a number of ways." +" In the 10,000 deg? overlap region, KDUST data will (1) improve photo-zss directly, (2) increase the galaxy sample with those that would not meet the LSST optical photometry selection criteria, or whose could not be reliably determined in the absence of the deep yJH data, or whose shape could not be measured well because of the larger seeing at the LSST site, and (3) provide calibration of various systematic errors such as those in shear measurements."," In the 10,000 $^2$ overlap region, KDUST data will (1) improve s directly, (2) increase the galaxy sample with those that would not meet the LSST optical photometry selection criteria, or whose could not be reliably determined in the absence of the deep $yJH$ data, or whose shape could not be measured well because of the larger seeing at the LSST site, and (3) provide calibration of various systematic errors such as those in shear measurements." +" Even in the non-overlap region, LSST could still improve zss and shear measurements because of the calibration within the overlap region."," Even in the non-overlap region, LSST could still improve s and shear measurements because of the calibration within the overlap region." + This is reflected in the last column of where we construct a joint survey combining LSST and KDUST., This is reflected in the last column of where we construct a joint survey combining LSST and KDUST. +" For the SN data, we assume that KDUST would obtain a SNAP-like sample of 2000 SNe reaching redshift 1.7 as well as a sample of 1000 local and nearby SNe."," For the SN data, we assume that KDUST would obtain a SNAP-like sample of 2000 SNe reaching redshift $1.7$ as well as a sample of 1000 local and nearby SNe." + Details of the assumptions for the SNAP experiments and the calculation of the Fisher matrices can be found in(Pogosianetal.2005) and in (Zhaoetal. 2009).., Details of the assumptions for the SNAP experiments and the calculation of the Fisher matrices can be found in\citep{Pogosian:2005ez} and in \citep{Zhao:2008bn}. . +" In this section, we estimate the constraints on the dark energy EOS from the joint survey of KDUST and LSST using BAO, WL, and SN techniques."," In this section, we estimate the constraints on the dark energy EOS from the joint survey of KDUST and LSST using BAO, WL, and SN techniques." +" The angular power spectra of the galaxy number density n(0) and (E-mode) shear γ(θ) can be written as (Hu&Jain2004;Zhan2006) (0) = dz H(z)DA WP correspond(2)WY ()s((s 2), PXYwhere lower case subscripts to the tomographic bins, upper case superscripts label theobservables, e.g., X=g for galaxies or * for shear, A(k;z) is the dimensionless power spectrum of the density field, and k= €/Da(z)."," The angular power spectra of the galaxy number density $n(\boldsymbol{\theta})$ and (E-mode) shear $\gamma(\boldsymbol{\theta})$ can be written as \citep{hu04b,zhan06d} + ) = d H(z) (z) W_i^X(z) W_j^Y(z) (k; z), where lower case subscripts correspond to the tomographic bins, upper case superscripts label theobservables, e.g., $X= \mbox{g}$ for galaxies or $\gamma$ for shear, $\Delta^2_\delta(k;z)$ is the dimensionless power spectrum of the density field, and $k = \ell/D_{\rm A}(z)$ ." +" The window functions are (2) =0(2) (2) = pes ποτε, b(z) is the linear galaxy clustering bias, DAGI)""and €), andHo are, respectively, the"," The window functions are (z) = (z) = d where $b(z)$ is the linear galaxy clustering bias, and $\Omega_{\rm m}$ and$H_0$ are, respectively, the" +to an accuracy of a fraction of a percent at all radii.,to an accuracy of a fraction of a percent at all radii. +" Our fiducial model for the distribution function hasR, =Ro /3 andR, = 3R;,, and oo such that eg(Ro)=0.2vg."," Our fiducial model for the distribution function has = /3 and = 3, and $\sigma_0$ such that $\sigmaR(\Ro) = 0.2 \vo$." +" As shown by2000), the model described above with the Sun atRo = 0.9Rorg—whereRorg is the radius at which a circular orbit is in the outer Lindblad resonance with the bar—at a current angle of 25? with the bar, with a bar strength a=0.01, and integrating for four bar periods, reproduces the Hercules feature in the local velocity distribution while agreeing with other photometric and kinematical observations of the bar2010)."," As shown by, the model described above with the Sun at = 0.9—where is the radius at which a circular orbit is in the outer Lindblad resonance with the bar—at a current angle of $^{\circ}$ with the bar, with a bar strength $\alpha = 0.01$, and integrating for four bar periods, reproduces the Hercules feature in the local velocity distribution while agreeing with other photometric and kinematical observations of the bar." +" In what follows, unless indicated otherwise, we fix all of the parameters of the model at these fiducial values."," In what follows, unless indicated otherwise, we fix all of the parameters of the model at these fiducial values." + All velocities are always considered to be with respect to their local standard of rest in the absence of a bar., All velocities are always considered to be with respect to their local standard of rest in the absence of a bar. + only simulated the velocity distribution at the position of the Sun for various combinations of the model parameters defined in the previous Section., only simulated the velocity distribution at the position of the Sun for various combinations of the model parameters defined in the previous Section. +" Nevertheless, his results on how the velocity distribution at the Sun changes with the angle between the Sun-Galactic center line and the bar could also be interpreted as showing the velocity distribution on the Solar circle for different Galactocentric azimuths, fixing the bar angle."," Nevertheless, his results on how the velocity distribution at the Sun changes with the angle between the Sun-Galactic center line and the bar could also be interpreted as showing the velocity distribution on the Solar circle for different Galactocentric azimuths, fixing the bar angle." +" In this way, these simulations can make predictions for what we might find when we study the velocity distribution in regions beyond those probed by theHipparcos mission1997)."," In this way, these simulations can make predictions for what we might find when we study the velocity distribution in regions beyond those probed by the mission." +" InFigure2, I present the predictions for the two-dimensional velocity distributions near the Solar circle for the full 360? range in Galactocentric azimuth for the fiducial model from §??."," In, I present the predictions for the two-dimensional velocity distributions near the Solar circle for the full $^{\circ}$ range in Galactocentric azimuth for the fiducial model from ." +" Only the range —90°<à90? is shown here, since the barred Galaxy is symmetric with respect to rotations through 180°; the predictions for the other side of the Galaxy can be obtained from those shown by shifting the azimuths by 180°."," Only the range $-90^{\circ} +\leq \phi \leq 90^{\circ}$ is shown here, since the barred Galaxy is symmetric with respect to rotations through $^{\circ}$; the predictions for the other side of the Galaxy can be obtained from those shown by shifting the azimuths by $^{\circ}$." +" The predicted velocity distributions on the Solar circle are not shown here, but they can be inferred fromFigure 2 in(2000)."," The predicted velocity distributions on the Solar circle are not shown here, but they can be inferred from 2 in." + It is clear from thisFigure that we can trace the Hercules stream going around the Galaxy and when looking further in toward the Galactic center or further out., It is clear from this that we can trace the Hercules stream going around the Galaxy and when looking further in toward the Galactic center or further out. +" Furthermore, the effect of the bar is not confined to a narrow range in radii, but rather the effects of the bar and especially its outer Lindblad resonance are felt through a large range of radii (0.6 0$ may certainly differ from line to line in the proof. +" We decompose the quantity [u6(f)—4?(0)| iuto two pieces: In order to estimate e(£). we iterate inequality (5.3)) and we finally obtain for 4*(0)=uy—c"".and f£C[0.T| with T=nAt: The above inequality gives: and. from inequality (5.5)) of Proposition 5.2.. we cau show in the same way asabove that we also have: Choosing particularly Af=Ce|loge|. we deduce that eAf=Ce|loge|«T. aud (from (5.11)). (5.12))) that: with e in (5.13)) depending ou the choice of €>0."," We decompose the quantity $|u^{\eps}(t)-u^{0}(t)|$ into two pieces: In order to estimate $e(t)$, we iterate inequality \ref{Reb3}) ) and we finally obtain for $u^{\eps}(0)=u_{0}=v^{0}$,and $t\in [0,T]$ with $T=n\D t$: The above inequality gives: and, from inequality \ref{Reb3bis}) ) of Proposition \ref{mitl_f}, we can show in the same way asabove that we also have: Choosing particularly $\D t = C \eps |\log \eps|$, we deduce that $\eps \ll \D t = C \eps |\log \eps| \ll T $, and (from \ref{Reb4}) ), \ref{Reb5}) )) that: with $c$ in \ref{Reb6}) ) depending on the choice of $C>0$." + finally inequality (1.7)) could now be easily deduced fous (5.103) aud (5.13)).," finally, inequality \ref{error}) ) could now be easily deduced from \ref{Reb7}) ) and \ref{Reb6}) )." + LI Iu this section. as an application of our previous results on ODEs. we give the proof of some error estimates for the homogenization of lincar transport equations.," $\hfill{\Box}$ In this section, as an application of our previous results on ODEs, we give the proof of some error estimates for the homogenization of linear transport equations." + Namely we prove Theorems 1.5. and 1.9..," Namely, we prove Theorems \ref{theo3} and \ref{theo4}." + We start with Theorem Las keeping the same notations of Subsection ??.., We start with Theorem \ref{theo3} keeping the same notations of Subsection \ref{sub1.2}. + The proof is divided into four steps., The proof is divided into four steps. + The first three steps are devoted to the definition of the limit solution VU. aud to provethat it is a viscosity solution.," The first three steps are devoted to the definition of the limit solution $V^{0}$, and to provethat it is a viscosity solution." +" The proof of the error estimate is done in the last Because the homogenized vector Ποια 7 is uot Lipschitz. we define our solution. V"" to (1.11)) in au indirect way using the cliaracteristies."," The proof of the error estimate is done in the last Because the homogenized vector field $\o{a}$ is not Lipschitz, we define our solution $V^{0}$ to \ref{transport_eqn0}) ) in an indirect way using the characteristics." + Precisely. for (f)€(0.6)& S2. = Gra»). we define V?tfe) as follows: where the curve XPtrifoe):rC€»Nrtoryco EB.," Precisely, for $(t,x)\in (0,\infty)\times +\R^{2}$ $x=(x_{1},x_{2})$ , we define $V^{0}(t,x)$ as follows: where the curve $X^{0}(\t;t,x):\t\in \R\rightarrow X^{0}(\t;t,x)\in +\R^{2}$ ," +The phenomenon of spot formation on the stellar surfaces is known for a long time.,The phenomenon of spot formation on the stellar surfaces is known for a long time. + Detailed. studies of stars exhibiting surface features showed that the formation of temperature or chemical spots is closely related to the presence of magnetic field in the stellar atmospheres (?).., Detailed studies of stars exhibiting surface features showed that the formation of temperature or chemical spots is closely related to the presence of magnetic field in the stellar atmospheres \citep{Donati:2009}. + Nevertheless. there are exceptional cases when spectropolarimetric studies of high sensitivity detect no magnetic field but spots are still present on the stellar surface.," Nevertheless, there are exceptional cases when spectropolarimetric studies of high sensitivity detect no magnetic field but spots are still present on the stellar surface." + This is observed in chemically peculiar (CP) stars of mercury-manganese (HgMn) type., This is observed in chemically peculiar (CP) stars of mercury-manganese (HgMn) type. + The first discovery of spots ina HgMn star was reported for a AAnd (2).. which also shows an evolution of spot structure (?)..," The first discovery of spots in a HgMn star was reported for $\alpha$ And \citep{Adelman:2002}, which also shows an evolution of spot structure \citep{Kochukhov:2007}." + Currently we know six other spotted HeMn stars: HR 1185 and HR8723 (?).. AR Aur (??).. HD 11753. HD 53244 and HD 221507 (?)..," Currently we know six other spotted HgMn stars: HR 1185 and HR8723 \citep{Kochukhov:2005}, AR Aur \citep{Hubrig:2006, Folsom:2010}, HD 11753, HD 53244 and HD 221507 \citep{Briquet:2010}." + All these stars exhibit spots of mostly heavy chemical elements., All these stars exhibit spots of mostly heavy chemical elements. + According to theoretical models adopted for CP stars. physical processes responsible for the spot formation are associated with magnetic field.," According to theoretical models adopted for CP stars, physical processes responsible for the spot formation are associated with magnetic field." + In order to enlarge the sample of spotted HgMn stars studied in detail. we have performed a comprehensive analysis of another HgMn star.," In order to enlarge the sample of spotted HgMn stars studied in detail, we have performed a comprehensive analysis of another HgMn star." + 66 Eri (HR 1657. HD 32964. HIP 23794) is à well-known binary system with nearly identical components.," 66 Eri (HR 1657, HD 32964, HIP 23794) is a well-known binary system with nearly identical components." + Using the radial velocities determined by ? and his own observations. ? found the orbital period of the system to be P=5.523 days. which was improved by the later studies (?2)..," Using the radial velocities determined by \citet{Frost:1924} and his own observations, \citet{Young:1976} found the orbital period of the system to be $P\approx5.523$ days, which was improved by the later studies \citep{Yuschenko:2001, Catanzaro:2004}." +" The orbital analysis yields a mass ratio My/M,! very close to unity (?2).."," The orbital analysis yields a mass ratio $M_\mathrm{B}/M_\mathrm{A}$ very close to unity \citep{Yuschenko:2001, Catanzaro:2004}." + Photometric studies of 66 Eri are controversial., Photometric studies of 66 Eri are controversial. + ? has estimated the times of possible eclipses based on the orbital elements of the system., \citet{Young:1976} has estimated the times of possible eclipses based on the orbital elements of the system. + His photometric observations at expected times of eclipses did not show variability., His photometric observations at expected times of eclipses did not show variability. + Young concluded that the orbital inclination angle is less than, Young concluded that the orbital inclination angle is less than. +80°.. Later. ? detected weak variability with a period different from the orbital one.," Later, \citet{Schneider:1987} detected weak variability with a period different from the orbital one." + This weak photometric variability was not confirmed by ?.. who in turn suggested variability with half of the orbital period.," This weak photometric variability was not confirmed by \citet{Yuschenko:1999}, who in turn suggested variability with half of the orbital period." + ? reported this star as an X-ray source., \citet{Berghofer:1994} reported this star as an X-ray source. + In the later study ? detected the third. low-mass companion. which is likely to be the actual source of the X-ray radiation coming from the system.," In the later study \citet{Hubrig:2001} detected the third, low-mass companion, which is likely to be the actual source of the X-ray radiation coming from the system." + This was directly confirmed with the X-ray imaging by ?.., This was directly confirmed with the X-ray imaging by \citet{Stelzer:2006}. + The early chemical analysis of 66 Eri by ? showed overabundances of Hg. Cr and Y in the primary component. while the secondary was reported to be normal.," The early chemical analysis of 66 Eri by \citet{Young:1976} showed overabundances of Hg, Cr and Y in the primary component, while the secondary was reported to be normal." + ? determined Hg abundance in a large number of HgMn stars. including 66 Ert.," \citet{Woolf:1999} determined Hg abundance in a large number of HgMn stars, including 66 Eri." + They confirmed the overabundance of mercury in the primary component., They confirmed the overabundance of mercury in the primary component. + A detailed abundance analysis of 66 Eri was presented by ?.. who studied chemical composition of both components of the binary system.," A detailed abundance analysis of 66 Eri was presented by \citet{Yuschenko:1999}, who studied chemical composition of both components of the binary system." + Combining spectroscopy and photometry. they determined .2]11002100K and -=109004100K for the component B and A. respectively.," Combining spectroscopy and photometry, they determined $=11100\pm100~K$ and $=10900\pm100~K$ for the component B and A, respectively." + The similarity of the physical parameters of the components also follows from their luminosity ratio Ly/L4=0.95+0.05., The similarity of the physical parameters of the components also follows from their luminosity ratio $L_\mathrm{B}/L_\mathrm{A}=0.95\pm 0.05$. + The rotational velocity of both stars is equal to 117 citepYuschenko: 1999.., The rotational velocity of both stars is equal to 17 \\citep{Yuschenko:1999}. + 66 Eri is very similar to another double-line binary with an HgMn component — AR Aur (?).., 66 Eri is very similar to another double-line binary with an HgMn component – AR Aur \citep{Hohlova:1995}. + Despite the fact that no magnetic field was found in AR Aur. it shows chemical inhomogeneities (?)..," Despite the fact that no magnetic field was found in AR Aur, it shows chemical inhomogeneities \citep{Folsom:2010}." + The similarity in the two HgMn SB2 stars inspired. us to analyse 66 Eri with new high-precision observational data., The similarity in the two HgMn SB2 stars inspired us to analyse 66 Eri with new high-precision observational data. + The paper is structured as follows., The paper is structured as follows. + In Sect. 2..," In Sect. \ref{obs}," + we describe observational material and describe the data reduction process., we describe observational material and describe the data reduction process. + Section 3. presents the least squares deconvolution analysts., Section \ref{lsd} presents the least squares deconvolution analysis. + In Sect., In Sect. + 4. we discuss the measurements of magnetic field in 66 Eri., \ref{mf} we discuss the measurements of magnetic field in 66 Eri. + Section 5. deseribes the spectral disentangling., Section \ref{sd} describes the spectral disentangling. + Determination of the system parameters is given in Sect. 6.., Determination of the system parameters is given in Sect. \ref{fp}. . + Sect., Sect. + 7 presents an analysis of the spectral variability., \ref{lpv} presents an analysis of the spectral variability. + Interpretation of the line. variability in. terms of surface, Interpretation of the line variability in terms of surface +In Fig.,In Fig. + 5. the filled square wilh abscissa 4 is lower than the corresponding thumb-rule value.," 5, the filled square with abscissa 4 is lower than the corresponding thumb-rule value." + This is abnormal and due to insufficient time length of the run: the curve Πορ) did not reach its asvanptote in (his case., This is abnormal and due to insufficient time length of the run: the curve $n_{Cgr}$ =f(t) did not reach its asymptote in this case. + Finally. if one is interested in the fraction of oxygen available for silicate grains. an upper limit for it is ποπο). which is plotted in Fig.," Finally, if one is interested in the fraction of oxygen available for silicate grains, an upper limit for it is $n_{O}(f)/n_{O}(0)$, which is plotted in Fig." + 6., 6. + Back in Fie., Back in Fig. + 4 and 5. dotted lines have been drawn to illustrate the application of the rule of {ham recalled in the Introduction.," 4 and 5, dotted lines have been drawn to illustrate the application of the rule of thumb recalled in the Introduction." + As expected. the latter approximation is seen to agree with our more elaborate calculations only in the two opposite limits of ne(0)/no(0).," As expected, the latter approximation is seen to agree with our more elaborate calculations only in the two opposite limits of $n_{C}(0)/n_{O}(0)$." + The difference is considerable in between. which is the most often encountered range in the sky (see lor instance Kwok et al. (1997))).," The difference is considerable in between, which is the most often encountered range in the sky (see for instance Kwok et al. \cite{kwo}) )." +Noue of these five stars appears particularly unusual.,None of these five stars appears particularly unusual. + They all prove to have periods iu the ange occupied by the SU UMa stars., They all prove to have periods in the range occupied by the SU UMa stars. + Superhuumps are evidently detected (but not well measured) in DM Lyr. and presumably they have not yet turued up iu the other four stars only because the objects have not been observed loug or intensively enough.," Superhumps are evidently detected (but not well measured) in DM Lyr, and presumably they have not yet turned up in the other four stars only because the objects have not been observed long or intensively enough." + IL one or more of the other four objects ooves after exteusive monitoring to be au SU UMa star. it will present an interesting anomaly.," If one or more of the other four objects proves after extensive monitoring to be an SU UMa star, it will present an interesting anomaly." + We thank the NSF for support through AST 9987331., We thank the NSF for support through AST 9987334. + Tim Miller obtained he direct unages of FT Cam., Tim Miller obtained the direct images of FT Cam. + This research mace use of the Simbad database. operated at CDS. Strasbourg. France.," This research made use of the Simbad database, operated at CDS, Strasbourg, France." + (Christianson1995).. IIubble(1925) Dubble(1929)..," \citep{Christianson1995}, \citet{Hubble1925} \citet{Hubble1929}, \citep{BS1965}." + (Magnieretal.1997:KaluznyL998:Mochejska2000). al.2004).," \citep{Magnier1997,Kaluzny1998,Mochejska2000} \citep{Ansari2004}." +. (Welchetal.1986:Macdore1990) (Masseyetal.2006). ," \citep{Welch1986,FM1990} \citep{Massey2006} " +The ain of (is paper is to present fully-kinetic PIC simulations of decaving electromagnetic fluctuations at electron scales.,The aim of this paper is to present fully-kinetic PIC simulations of decaying electromagnetic fluctuations at electron scales. + In doing so we address the following open problems., In doing so we address the following open problems. + It is still unknown whether a linear approximation lor the damping rate of the fluctuations. that would ellectively describe the waves as an ensemble of linear modes. is fully justifiable and at which scale that approximation becomes valid.," It is still unknown whether a linear approximation for the damping rate of the fluctuations, that would effectively describe the waves as an ensemble of linear modes, is fully justifiable and at which scale that approximation becomes valid." + Moreover. there is an open debate about the scale al which such fluctuations are expected to be completely dissipated. and what mechanism is responsible for the dissipation.," Moreover, there is an open debate about the scale at which such fluctuations are expected to be completely dissipated, and what mechanism is responsible for the dissipation." + As we will show. our results do not support a scenario where turbulent fluctuations can be described as an ensemble of the least damped linear waves. not even al verv small scales. although the observed steepening of the power spectra might be associated with the steepening of the dispersion curves of linear The feasibility of the simulations presented in this paper has been greatly enhanced by using a semi-implict method both for the field solver and the particle mover. and we will discuss some computational issues (hat have emerged in this study. and Chat should be taken into account for future The paper is organised as Iollows.," As we will show, our results do not support a scenario where turbulent fluctuations can be described as an ensemble of the least damped linear waves, not even at very small scales, although the observed steepening of the power spectra might be associated with the steepening of the dispersion curves of linear The feasibility of the simulations presented in this paper has been greatly enhanced by using a semi-implicit method both for the field solver and the particle mover, and we will discuss some computational issues that have emerged in this study, and that should be taken into account for future The paper is organised as follows." + Section 2 briefly describes the PIC code. the parameters used. (he issues related (o the initialization of the simulations. and compares this paper with previous works.," Section 2 briefly describes the PIC code, the parameters used, the issues related to the initialization of the simulations, and compares this paper with previous works." + The main results are described in Section 3., The main results are described in Section 3. + The emphasis will be on the observed nonlinear cascade. the ilentilication of linear modes. and particle heating.," The emphasis will be on the observed nonlinear cascade, the identification of linear modes, and particle heating." + The conclusions and discussion of future work are given in Section 4., The conclusions and discussion of future work are given in Section 4. + We perform simulations of an ion-electron plasma in a two-dimensional periodic box in Cartesian geometry (roy).," We perform simulations of an ion-electron plasma in a two-dimensional periodic box in Cartesian geometry $(x,y)$." + The code used is a full-kinetic. electromagnetic. parallel PIC code. calledPARSER2D.," The code used is a fully-kinetic, electromagnetic, parallel PIC code, called." +. The main feature of the code is the use of an implicit moment method for advancing the fields in time and a predictor-corrector routine to advance the particles., The main feature of the code is the use of an implicit moment method for advancing the fields in time and a predictor-corrector routine to advance the particles. + A thorough description of the algorithm and the code ean be found in (2009)., A thorough description of the algorithm and the code can be found in \citet{markidis09}. +. The implicituess of the scheme allows a relaxation of the stability conditions ἱνρισα] of an explicit code., The implicitness of the scheme allows a relaxation of the stability conditions typical of an explicit code. + In particular the cell size Avr is not required to be comparable with the Debve length. (he timestep A’ can be larger than the inverse plasma freeueney and. in general. the [actor cM/.Ne (where ¢ is the speed of light) can be larger than," In particular the cell size $\Delta x$ is not required to be comparable with the Debye length, the timestep $\Delta t$ can be larger than the inverse plasma frequency and, in general, the factor $c\Delta t/\Delta x$ (where $c$ is the speed of light) can be larger than" +‘Toemark ct al. (,Tegmark et al. ( +1993. hereafter ‘1j) presented a formulation of the expansion of isotropic galactic winds in an expanding universe.,"1993, hereafter TSE) presented a formulation of the expansion of isotropic galactic winds in an expanding universe." + In. this formulation. the injection of thermal energy. produces an outflow. of radius A. which consists of a dense shell of thickness A containing a cavity.," In this formulation, the injection of thermal energy produces an outflow of radius $R$, which consists of a dense shell of thickness $R\delta$ containing a cavity." +" A fraction 1fm of the mass of the gas is piled up in the shell. while a fraction f, of the gas is distributed inside thecavity."," A fraction $1-f_m$ of the mass of the gas is piled up in the shell, while a fraction $f_m$ of the gas is distributed inside thecavity." +" We normally assume ὁ<<1. fi,«1. that is. most of the gas is located inside a thin shell."," We normally assume $\delta\ll1$, $f_m\ll1$, that is, most of the gas is located inside a thin shell." + Fhis is called. theapprovimalion., This is called the. +" The evolution of the shell radius /? expanding out of a halo of mass AM. is described by the following svstem of equatIons: where a dot represents a time derivative. Q. O,. and Lf are the total density. parameter. barvon density. parameter. and Llubble parameter at. time /.. respectively, L is (the Luminosity. p is the pressure inside the cavity resulting from this luminosity. and po is the external pressure of the IGM."," The evolution of the shell radius $R$ expanding out of a halo of mass $M_{\rm gal}$, is described by the following system of equations: where a dot represents a time derivative, $\Omega$, $\Omega_b$, and $H$ are the total density parameter, baryon density parameter, and Hubble parameter at time $t$, respectively, $L$ is the luminosity, $p$ is the pressure inside the cavity resulting from this luminosity, and $p_{\rm ext}$ is the external pressure of the IGM." + The four terms in equation (34)) represent. from. left to right. the driving pressure of the outflow. the drag due to sweeping up the IGM and accelerating it from velocity 44 to velocity R. and the eravitational deceleration caused. by the expanding shell and by the halo itself.," The four terms in equation \ref{rdotdot}) ) represent, from left to right, the driving pressure of the outflow, the drag due to sweeping up the IGM and accelerating it from velocity $HR$ to velocity $\dot R$, and the gravitational deceleration caused by the expanding shell and by the halo itself." + Phe two terms in equation (35)) represent the increase in pressure caused. by injection of thermal energy. and the drop in pressure caused by the expansion of the wind. respectively.," The two terms in equation \ref{pdot}) ) represent the increase in pressure caused by injection of thermal energy, and the drop in pressure caused by the expansion of the wind, respectively." + The external pressure. po. depends upon the density and temperature of the ICM.," The external pressure, $p_{\rm ext}$, depends upon the density and temperature of the IGM." +" sin PMGOT. we will assume a photohcated LGAL mace of ionizecl hydrogen and. singly-ionized helium. (mean molecular mass Ξ 0.611). with a fixed temperature Zi,=Lot (Alacdauetal.2001). and an IGM density equal to the mean barvon density pi."," As in PMG07, we will assume a photoheated IGM made of ionized hydrogen and singly-ionized helium (mean molecular mass $\mu=0.611$ ), with a fixed temperature $T_{\rm IGM}=10^{4}{\rm K}$ \citep{mfr01} and an IGM density equal to the mean baryon density $\bar\rho_b$." + The external pressure at redshift z is then given by: The luminosity £ is the rate of energy. deposition. or dissipation within the wind and is given by: where Lazy; and Liz are the total luminosity responsible for generating the wind. as given by equations (13)) and (12)). respectively.," The external pressure at redshift $z$ is then given by: The luminosity $L$ is the rate of energy deposition or dissipation within the wind and is given by: where $L_{\rm SNe}$ and $L_{\rm SW}$ are the total luminosity responsible for generating the wind, as given by equations \ref{lumSN}) ) and \ref{lumSW}) ), respectively." + Leap represents the cooling due to Compton drag against CMD photons and is given by: where σι is the Thomson cross section. and 255 is the present CAIB temperature.," $L_{\rm comp}$ represents the cooling due to Compton drag against CMB photons and is given by: where $\sigma_t$ is the Thomson cross section, and $T_{\gamma0}$ is the present CMB temperature." + The expansion of the wind is initially clriven by. the luminosity., The expansion of the wind is initially driven by the luminosity. +" After the SNe turn ο, the outflow enters the “post-SN The pressure inside the wind. keeps civing the expansion. but this pressure drops since there is no energy input from SNe."," After the SNe turn off, the outflow enters the “post-SN The pressure inside the wind keeps driving the expansion, but this pressure drops since there is no energy input from SNe." + Eventually. the pressure will drop down to the level of the external LGAL pressure.," Eventually, the pressure will drop down to the level of the external IGM pressure." + At that point. theexpansion of the wind will simply follow the Llubble Ios.," At that point, theexpansion of the wind will simply follow the Hubble flow." + In the TSE model. the barvon density inside the cavity is pp=polOfnfA5). while the barvon density inside the shell is p;=polMfu)fd(1.8)']," In the TSE model, the baryon density inside the cavity is $\rho_i=\rho_b(t)f_m/(1-\delta)^3$, while the baryon density inside the shell is $\rho_s=\rho_b(t)(1-f_m)/[1-(1-\delta)^3]$." + This gives a mass Ad=dUpu)/53 inside the volume of radius 2. which is precisely the mass of the IGM. within that. ractius in the absence of a wind.," This gives a mass $M=4\pi R^3\rho_b(t)/3$ inside the volume of radius $R$, which is precisely the mass of the IGM within that radius in the absence of a wind." + Therefore. in the PSE model. the material inside the shell is swept LGAL material. while the material inside the cavity is GM material left behind.," Therefore, in the TSE model, the material inside the shell is swept IGM material, while the material inside the cavity is IGM material left behind." + Hence. the PSE model does not predict. the distribution of that mass inside the cavity.," Hence, the TSE model does not predict the distribution of that mass inside the cavity." + This means that any distribution we chose would not violate the assumptions on which the PSE model is based., This means that any distribution we chose would not violate the assumptions on which the TSE model is based. + The simplest. approximation for the cistribution of metals in the wind. consists of assuming that the metals carried by the galactic wind are spread. evenly inside the cavity (see Scannapiecoetal.200:> PALGO?T: Baraietal. 2011))., The simplest approximation for the distribution of metals in the wind consists of assuming that the metals carried by the galactic wind are spread evenly inside the cavity (see \citealt{sfm02}; PMG07; \citealt{bmg11}) ). + This poses a problem for the metals cjectecl near the end. of the post-SN phase. just. before the wind. joins the Llubble flow.," This poses a problem for the metals ejected near the end of the post-SN phase, just before the wind joins the Hubble flow." + These metals would have to be carried across the entire radius of the cavity. at velocities that exceed the wind. velocity.," These metals would have to be carried across the entire radius of the cavity, at velocities that exceed the wind velocity." + Processes such as turbulence and diffusion could homogenize the distribution of metals inside the cavity. but only over a finite time period.," Processes such as turbulence and diffusion could homogenize the distribution of metals inside the cavity, but only over a finite time period." + In this paper. we take the opposite approach. by assuming no mixing.," In this paper, we take the opposite approach, by assuming no mixing." + Lence. the gas that escapes the galaxy early. on will travel larger distances than the gas that escapes later.," Hence, the gas that escapes the galaxy early on will travel larger distances than the gas that escapes later." + Since the metallicity and composition of the ISM evolves with time. the galactic wind will acquire both a metallicity graclient and a composition gradient. with the inner parts containing a larger proportion of metals.," Since the metallicity and composition of the ISM evolves with time, the galactic wind will acquire both a metallicity gradient and a composition gradient, with the inner parts containing a larger proportion of metals." + To simulate such wind. we use a systeni of concentric spherical shells.," To simulate such wind, we use a system of concentric spherical shells." + At the end of every timestep. the code caleulates the amount of gas that will be added to the galactic wind: where /; is the time corresponding to the timestep.," At the end of every timestep, the code calculates the amount of gas that will be added to the galactic wind: where $t_i$ is the time corresponding to the timestep." + After the first time step. the wind reaches a radius A?—fsGM).," After the first time step, the wind reaches a radius $R_1\equiv R_{\rm GW}(\Delta t)$." + We deposit (he wind material produced. during that. time step into the sphere of radius fwGM). which constitutes our central shell.," We deposit the wind material produced during that time step into the sphere of radius $R_{\rm GW}(\Delta t)$, which constitutes our central shell." + After the second timestep. the wind now reaches racdus As—Ba(2A/).," After the second timestep, the wind now reaches radius $R_2\equiv R_{\rm GW}(2\Delta t)$." +" We first transfer the wind material located:between O ancl Z2, into a shell of inner radius A, and outer radius {οι and we then deposit the wind material produced. during the second. timestep into the central shell."," We first transfer the wind material locatedbetween 0 and $R_1$ into a shell of inner radius $R_1$ and outer radius $R_2$ , and we then deposit the wind material produced during the second timestep into the central shell." + Phis process is then repeated., This process is then repeated. +" At every timestep n. à new shell is created. between radii £2), and R, all the wind material is shifted outward by one shell."," At every timestep $n$ , a new shell is created between radii $R_n$ and $R_{n-1}$ , all the wind material is shifted outward by one shell," +hole (i.e. magnetosphere) reopens during the outburst decline. the P29 oscillation should reappear and decrease back (o its quiescent period.,"hole (i.e. magnetosphere) re–opens during the outburst decline, the P29 oscillation should re–appear and decrease back to its quiescent period." + In the LIMA model. the DNO period should decrease as more and more angular momentum is accreted. into the belt during the rise to outburst.," In the LIMA model, the DNO period should decrease as more and more angular momentum is accreted into the belt during the rise to outburst." + The P29 (QPO) signal would also experience a period change. for two reasons: il is being driven bv the faster DNO and the inner radius of (he disk where reprocessing is occurring is shrinking.," The P29 (QPO) signal would also experience a period change, for two reasons: it is being driven by the faster DNO and the inner radius of the disk where reprocessing is occurring is shrinking." + On (he decline from outburst. (he periods should increase.," On the decline from outburst, the periods should increase." + A strong periodIuminositv relationship through the outburst should exist. as is the case for DNOs of other svstems (see Woudt Warner 2002 and references therein).," A strong period–luminosity relationship through the outburst should exist, as is the case for DNOs of other systems (see Woudt Warner 2002 and references therein)." + In both magnetic accretor scenarios. the P29 signal should vary. during the outburst.," In both magnetic accretor scenarios, the P29 signal should vary during the outburst." + Yet as we have shown here. this is not the case in WZ See: the P29 signal remains constant in period on the decline from outburst. and will the same period it has in quiescence.," Yet as we have shown here, this is not the case in WZ Sge: the P29 signal remains constant in period on the decline from outburst, and with the same period it has in quiescence." + In act. just the presence of (he P29 signal in the absence of the P28 signal during the outburst decay presents a significant problem for the magnetic accretor models.," In fact, just the presence of the P29 signal in the absence of the P28 signal during the outburst decay presents a significant problem for the magnetic accretor models." + In the DQ Ier model. if (he magnetosphere is crushed onto the white dwarf thereby «quenching the P28 signal. the inner edge of the disk is now coinciclent with the white dwarl’s surface.," In the DQ Her model, if the magnetosphere is crushed onto the white dwarf thereby quenching the P28 signal, the inner edge of the disk is now coincident with the white dwarf's surface." + So not only is there 10 inner disk region to reprocess any modulation. there is no modulation to reprocess.," So not only is there no inner disk region to reprocess any modulation, there is no modulation to reprocess." + Ànd vel the P29 signal is quite strong. stronger in fact than in quiescence. al least in the 2001 September observations.," And yet the P29 signal is quite strong, stronger in fact than in quiescence, at least in the 2001 September observations." + As in the DQ Her model. the LIAIA moclel recquires the presence of the DNO al 28 s to drive the QPO al 29 s. The complete absence of the P28 signal in (he observations presented here is vexing.," As in the DQ Her model, the LIMA model requires the presence of the DNO at 28 s to drive the QPO at 29 s. The complete absence of the P28 signal in the observations presented here is vexing." + We clearly do not understaxd (he mechanism producing the P29 siena., We clearly do not understand the mechanism producing the P29 signal. + The continued presence of the P29 signal during the outburst decay. as the disk reforms and the mass accretion rate and white dwarI temperature dramatically change. suggests (hat a clock of exceptional (long.term) stability is involved.," The continued presence of the P29 signal during the outburst decay, as the disk reforms and the mass accretion rate and white dwarf temperature dramatically change, suggests that a clock of exceptional (long–term) stability is involved." + The most inmediate candidate is the rotation of the white dwarf. but how this could work is not at all apparent.," The most immediate candidate is the rotation of the white dwarf, but how this could work is not at all apparent." + We conclude that while the rotating magnetic accretor models remain viable. (hey. are sorely incomplete.," We conclude that while the rotating magnetic accretor models remain viable, they are sorely incomplete." + We present ultraviolet light curves of the dwarl nova WZ See as it declined Ivom its 2001 July superoutburst., We present ultraviolet light curves of the dwarf nova WZ Sge as it declined from its 2001 July superoutburst. + The observations were mace with the“ST STIS and were obtained on 2001 September. October. November and. December.," The observations were made with the STIS and were obtained on 2001 September, October, November and December." + The wellknown 28.96 s perioclicity was present al all [our epochs. but the 27.87 s periodicity was absent.," The well–known 28.96 s periodicity was present at all four epochs, but the 27.87 s periodicity was absent." + We also note the appearance of a QPO with period —18 s in the September light curve., We also note the appearance of a QPO with period $\sim$ 18 s in the September light curve. +distribution as the initial VLMB distribution in part fails to match the current VLMB population.,distribution as the initial VLMB distribution in part fails to match the current VLMB population. +" Whilst high-density clusters can be evolved to something resembling the ? distribution, low-density clusters hardly process their VLMB population at all resulting in far too many wide- and intermediate-separation VLMBs."," Whilst high-density clusters can be evolved to something resembling the \citet{Basri06} distribution, low-density clusters hardly process their VLMB population at all resulting in far too many wide- and intermediate-separation VLMBs." + Therefore we can conclude fairly robustly thatpopulation., Therefore we can conclude fairly robustly that. + This raises the obvious question of what are the binary fraction and separation distribution of the birth VLMB population?, This raises the obvious question of what are the binary fraction and separation distribution of the birth VLMB population? + To answer this we have to address two inter-related questions., To answer this we have to address two inter-related questions. +" Firstly, do all clusters produce the same birth populations?"," Firstly, do all clusters produce the same birth populations?" +" And secondly, what is the mixture of cluster densities that contribute to the field?"," And secondly, what is the mixture of cluster densities that contribute to the field?" +" It is the combination of cluster densities rather than masses that is important, as"," It is the combination of cluster densities rather than masses that is important, as" +"Sharpless 104(Sh2-104, Sharpless 1959)) is an optically visible Galactic rregion with a bubble morphology, excited by an O6V star (Cramptonetal,1978;Lahulla,1985).","Sharpless 104, \citealt{sharpless1959}) ) is an optically visible Galactic region with a bubble morphology, excited by an O6V star \citep{crampton1978, lahulla1985}." +". It is located ~ 4kpc from the Sun (Deharvengetal., 2003), with galactic coordinates 74.7620;+0.60 (J2000)."," It is located $\sim4\,$ kpc from the Sun \citep{deharveng2003}, , with galactic coordinates $74.7620; ++0.60$ (J2000)." +" Deharvengetal.(2003) proposed aas a strong candidate for massive triggered star formation through the collect-and-collapse process (Elmegreen&Lada, 1977).", \citet{deharveng2003} proposed as a strong candidate for massive triggered star formation through the collect-and-collapse process \citep{elmegreen1977}. +". The ionized region is also visible at radio wavelengths (Fich,1993),, and an ultracompact (UC) rregion, coincidant with the IRAS 20160+3636 source, lies at its eastern border (Condonetal. 1998))."," The ionized region is also visible at radio wavelengths \citep{fich1993}, and an ultracompact (UC) region, coincidant with the IRAS 20160+3636 source, lies at its eastern border \citealt{condon1998}) )." +" We present new submm images and spectra taken towards wwith the Space Observatory (Pilbrattetal.,2010).", We present new submm images and spectra taken towards with the Space Observatory \citep{pilbratt2010}. +". These observations allow us to map a wavelength range not easily accessed before, providing new insights into the dust and gas properties of Sh2-104."," These observations allow us to map a wavelength range not easily accessed before, providing new insights into the dust and gas properties of ." +". The observations were taken on 2009 December 17 simultaneously with PACS (Poglitschetal.,2010) and SPIRE (Griffinetal.,2010),, as part of the guaranteed-time projects “Evolution of Interstellar Dust"" of SPIRE (Abergeletal., 2010),, and HOBYS of PACS (Motteetal., 2010).."," The observations were taken on 2009 December 17 simultaneously with PACS \citep{poglitsch2010} and SPIRE \citep{griffin2010}, as part of the guaranteed-time key-projects “Evolution of Interstellar Dust” of SPIRE \citep{abergel2010}, , and HOBYS of PACS \citep{motte2010}. ." +" A 15’x region was imaged with PACS at 100 and 160 4m (at resolutions of 10"" and 14""), and with SPIRE at 250, 350 and 500m (at resolutions of 18"", 25"" and 36"")."," A $15'\times15'$ region was imaged with PACS at $100$ and $160\,\mu$ m (at resolutions of $10''$ and $14''$ ), and with SPIRE at $250$, $350$ and $500\,\mu$ m (at resolutions of $18''$, $25''$ and $36''$ )." +" Spectra were taken with the SPIRE-FTS long and short wavelength receivers (SLW and SSW, respectively) at seven different positions with sparse sampling, covering the 194—671 um range."," Spectra were taken with the SPIRE-FTS long and short wavelength receivers (SLW and SSW, respectively) at seven different positions with sparse sampling, covering the $194-671\,\mu$ m range." + The resolution at the receivers’ central pixels varies between 17—19” for SSW and 29—42” for SLW., The resolution at the receivers' central pixels varies between $17-19''$ for SSW and $29-42''$ for SLW. +" The data were reduced with the HIPE software version 2.0 with the latest standard calibration (Swinyardetal.,2010).", The data were reduced with the HIPE software version 2.0 with the latest standard calibration \citep{swinyard2010}. +". Figure 1. shows a color-composite image of wwith PACS 100 um (blue), SPIRE 250 um (green) and SPIRE 500 um (red)."," Figure \ref{fig-sh104-main} shows a color-composite image of with PACS $100\,\mu$ m (blue), SPIRE $250\,\mu$ m (green) and SPIRE $500\,\mu$ m (red)." +" Different regions of interest, addressedin thefollowing sections, are superimposed."," Different regions of interest, addressedin thefollowing sections, are superimposed." +" We can see that the interior of the bubble is brighter inthe PACS band, showingthe hotter temperatures of the material in this region."," We can see that the interior of the bubble is brighter inthe PACS band, showingthe hotter temperatures of the material in this region." + On the, On the +where p=p—2/2.,where $r=p-\pi/2$. +" As a resilt of the reduction of our analysis into two solutions it is necessary to consider (he sign of the expression: 9=—cos/cosóxzsinícosrsino aud for S>0 reverse sign of àp. respectively,"," As a result of the reduction of our analysis into two solutions it is necessary to consider the sign of the expression: $S=-\cos{i}\cos{\delta} \mp \sin{i}\cos{r}\sin{\delta}$ and for $S\ge 0$ reverse sign of $\delta_D$, respectively." + Separately we repeat all calculations using superealactic coordinate svstem (Hawley&Peebles1975)., Separately we repeat all calculations using supergalactic coordinate system \citep{h4}. +. In order to detect non-random elects in the distribution of the investigated angles: dp. y and p we carried out three different statistical tests.," In order to detect non-random efects in the distribution of the investigated angles: $\delta_D$, $\eta$ and $p$ we carried out three different statistical tests." + At first. we checked whether the distributions of the investigated angles (05. 7 and p) in each individual cluster were isolropic.," At first, we checked whether the distributions of the investigated angles $\delta_D$, $\eta$ and $p$ ) in each individual cluster were isotropic." + In analvzing of the distribution of the two angles dy). 7) il is possible to use galaxies ol any orientation - including face-on galaxies.," In analyzing of the distribution of the two angles $\delta_D$, $\eta$ it is possible to use galaxies of any orientation - including face-on galaxies." + Therefore for analysis of the distribution of the angles 95. and jj all galaxies’ members were considered.," Therefore for analysis of the distribution of the angles $\delta_D$, and $\eta$ all galaxies' members were considered." + It is very difficult to determine in a precise manner (he position angles for galaxies seen [ace-on aud nearly [ace-on., It is very difficult to determine in a precise manner the position angles for galaxies seen face-on and nearly face-on. + Moreover. these angles can vield reliable information with respect to galaxy. planes only. Lor ealaxies seen edge-on.," Moreover, these angles can yield reliable information with respect to galaxy planes only for galaxies seen edge-on." + Thus. in (he study of the position angles distribution. lace -on and nearly [ace-on galaxies were excluded [rom the analvsis.," Thus, in the study of the position angles distribution, face -on and nearly face-on galaxies were excluded from the analysis." + In this case galaxys members with axial ratio b/ax0.75 were taken into consideration only., In this case galaxy's members with axial ratio $b/a \le 0.75$ were taken into consideration only. + In all applied statistical tests the entire range of the investigated 0 angle (where for 6 , In all applied statistical tests the entire range of the investigated $\theta$ angle (where for $\theta$ +full-fledged cooling catastrophe.,full-fledged cooling catastrophe. +" At the same time, tsouna exceeds tayn, making the core region gravitationally unstable and causing the gas to collapse to the cluster center under gravity."," At the same time, $t_{\rm sound}$ exceeds $t_{\rm dyn}$, making the core region gravitationally unstable and causing the gas to collapse to the cluster center under gravity." +" Meanwhile, the gas can no longer maintain pressure equilibrium since too.rmax(Mmax) were removed(M. from ox)u..the sample, where Mmax=[e--10?""(o/200km s-1)?*1Ms."," Galaxies with $r_i > r_{\rm max}(M_{\rm max})$ were removed from the sample, where $M_{\rm max} = [\epsilon + 10^{\alpha_u}(\sigma/200\kms)^{\beta_u}]M_\odot$ ." +" Each galaxy was first assigned 90 separate values of uusing a step size of 10°! from 10!9M, to 10199M.", Each galaxy was first assigned 90 separate values of using a step size of $10^{0.1}$ from $10^{1.0}M_\odot$ to $10^{10.0}M_\odot$. +" In this case, the high mass cut was made by applying the a,=8.1,6,4.2 relation of G09 and the a,=8.2,0,=4.9 relation of FF05."," In this case, the high mass cut was made by applying the $\alpha_u=8.1, \beta_u=4.2$ relation of G09 and the $\alpha_u = 8.2, \beta_u = 4.9$ relation of FF05." + Figure 2 shows the distribution of observable galaxies in the pplane assuming every galaxy within 100 Mpc can host any and that δὲ=071., Figure \ref{fig:2} shows the distribution of galaxies in the plane assuming every galaxy within 100 Mpc can host any and that $\Re=0\farcs1$. +" The fit to this sample (red line) is a—84,083.5."," The fit to this sample (red line) is $\alpha = 8.4, \beta = 3.5$." +" However, galaxies host single (or binary) SMBHs, therefore it is shrewd to assign each galaxy a single (uniformly sampled) random value for iin the range 10!—10!?Mo."," However, galaxies host single (or binary) SMBHs, therefore it is shrewd to assign each galaxy a single (uniformly sampled) random value for in the range $10^1 - 10^{10}M_\odot$." + The distribution of galaxies in the pplane using a random sample of iis shown in Figure 3 using the red open circles., The distribution of galaxies in the plane using a random sample of is shown in Figure \ref{fig:3} using the red open circles. +" In this case, the low cut was made using δὲ=071, andthe high mass cut was made using a rrelation of a,=8.1,8,4.2,€0.4 (G09)."," In this case, the low cut was made using $\Re=0\farcs1$, andthe high mass cut was made using a relation of $\alpha_u=8.1, \beta_u=4.2, \epsilon=0.4$ (G09)." +" The rrelation fit to these galaxies (red line) is 04,=8.3,By4.1,e0.2 dex."," The relation fit to these galaxies (red line) is $\alpha_u=8.3, \beta_u=4.1, \epsilon=0.2$ dex." +" An rrelation of a,=8.3,B,4.6,¢0.4 dex is found using the high mass rrelation of FF05."," An relation of $\alpha_u=8.3, \beta_u=4.6, \epsilon=0.4$ dex is found using the high mass relation of FF05." +" Figure 3 also shows allobserved galaxies based on the combined catalogs of Graham (2008b), Hu(2008) and G09."," Figure \ref{fig:3} also shows all galaxies based on the combined catalogs of \cite{2008PASA...25..167G}, \cite{2008MNRAS.386.2242H} and G09." +" No distinction is made between “good” and “bad” eestimates, or differences in quoted o,.;; all estimates are plotted "," No distinction is made between “good” and “bad” estimates, or differences in quoted ; all estimates are plotted (143 total)." +The similarity(143total).between the ddistribution of random mass SMBHs and observed SMBHs masses is striking., The similaritybetween the distribution of random mass SMBHs and SMBHs masses is striking. +" However, as this"," However, as this" + istribution of specific elenents within the ejecta., distribution of specific elements within the ejecta. + This ‘line polarization” las bee1 observed to change markedly near maxi light., This “line polarization” has been observed to change markedly near maximum light. + The signature Si AG355A Hine has exhibited. liue. polarization in a number of SNe Ta: SNe 1999by (ITowell et 22001). 200101 AVang et 22003). 2002bf. 199t. 2003du. 200Ldt (Leonard et 22005). 200£dt (Wange 22006). and 2006X (Patat et 22009).," The signature Si $\lambda$ line has exhibited line polarization in a number of SNe Ia: SNe 1999by (Howell et 2001), 2001el (Wang et 2003), 2002bf, 1997dt, 2003du, 2004dt (Leonard et 2005), 2004dt (Wang et 2006), and 2006X (Patat et 2009)." + Absorption lires of other clemmecuts have also been detected. notably Fe lines (SN 1997dt: Leonard et 22005). andtre Ca IIR triplet (SN 2001: Wane et 22003: SN 2008: Patat et 22009).," Absorption lines of other elements have also been detected, notably Fe lines (SN 1997dt: Leonard et 2005), and the Ca IR triplet (SN 2001el: Wang et 2003; SN 2006X: Patat et 2009)." + For a review of polarimetric studies of SNe Ta. see Wang Wheeler (2008).," For a review of polarimetric studies of SNe Ia, see Wang Wheeler (2008)." +" SN 2011lfe occrred in ΑΠΟ. aud was discovered ou 2011x August 21 by the Palomar Trausicit Factory (PTF: Brown et 22011. Nugent et 220]la. 201110),"," SN 2011fe occurred in M101, and was discovered on 2011 August 24 by the Palomar Transient Factory (PTF: Brown et 2011, Nugent et 2011a, 2011b)." + The xoxiuitv of MOL. 76.2~6 \Ipe. aud the location of the SN zr from the host ealaxy core and spira arms. suggested hat the SN would become the brighest SN Ia since SN 1972E. It was predicted to have a visual peak. brighter han 10.0 mae.," The proximity of M101, $\sim$ 6.2 Mpc, and the location of the SN far from the host galaxy core and spiral arms, suggested that the SN would become the brightest SN Ia since SN 1972E. It was predicted to have a visual peak brighter than 10.0 mag." + Studies of the lieht crve suggest that he SN was discovered just 0.5 days after the explosion. and the explosion time ds constrainc“dl to verv high xecision CNugent et 220115).," Studies of the light curve suggest that the SN was discovered just 0.5 days after the explosion, and the explosion time is constrained to very high precision (Nugent et 2011b)." + Optica spectra revealed SN 2011fe to be a normal SN Ta. with «letectious of CL AGHSO and À7231 in absorption (Cenτο et 22011).," Optical spectra revealed SN 2011fe to be a normal SN Ia, with detections of C $\lambda$ 6580 and $\lambda$ 7234 in absorption (Cenko et 2011)." + Studies of pre-explosion images of the site of SN 2011fe place the strictest upper limits vet on the Iuninositi vof any SN Ia progenitor. arguing against a sinele-clegcuerate progeuitor containing a giant donor star (Li et 22011).," Studies of pre-explosion images of the site of SN 2011fe place the strictest upper limits yet on the luminosity of any SN Ia progenitor, arguing against a single-degenerate progenitor containing a giant donor star (Li et 2011)." + SN 2U0llfe was the ucarest Type Ia explosion iu several decades. providing an uuprecedeuted opportunity to obtain spectropolarinetry of a normal SN Ia with modest-aperture telescopes.," SN 2011fe was the nearest Type Ia explosion in several decades, providing an unprecedented opportunity to obtain spectropolarimetry of a normal SN Ia with modest-aperture telescopes." + We initiatc “la campaien to obtain απ1ορος spectropolarinetrv of SN 2011fe at Steward Observatory ($0). using the 1.5Lan Ikuiper aud," We initiated a campaign to obtain multi-epoch spectropolarimetry of SN 2011fe at Steward Observatory ), using the 1.54-m Kuiper and" +at late times ο TAlwr does not necessary require a spread in initial conditions as some authors have suggested. is necessary outside the NPIS framework (e.g. Armitage et al.,at late times $>1$ Myr does not necessary require a spread in initial conditions as some authors have suggested is necessary outside the XPE framework (e.g. Armitage et al. + 2003: Alexander Armitage. 2009).," 2003; Alexander Armitage, 2009)." + Observationallv here is however. a spread. in accretion rates seen at. carly imes κλίνες (e.g. Hartmann et al.," Observationally there is however, a spread in accretion rates seen at early times $<$ 1Myr (e.g. Hartmann et al." + 1998)., 1998). + This variability cannot be fit with a single set of initial conditions since whotoevaporation has had. no time to act on the disc., This variability cannot be fit with a single set of initial conditions since photoevaporation has had no time to act on the disc. + The zilure to match the spread in accretion rates at early. times « [Myr may not be surprising. since at carly times the angular momentum transport mechanism may be dominated ον self-gravity and accretion may be episodic (e.g. Lodato Rice. 2005).," The failure to match the spread in accretion rates at early times $<1$ Myr may not be surprising, since at early times the angular momentum transport mechanism may be dominated by self-gravity and accretion may be episodic (e.g. Lodato Rice, 2005)." +" In reality the zero time point in our models corresponds to the point at which the transition [rom a self-eravitating to a viscous disc occurs. as indicated: by the determination of AZ;(0)=O.LAZ,."," In reality the zero time point in our models corresponds to the point at which the transition from a self-gravitating to a viscous disc occurs, as indicated by the determination of $M_d(0)=0.1M_*$." + This may explain. why our initial accretion rate is significantly lower than some of the accretion. rates measured. for the voungest objects (Llartmann οἱ al.," This may explain, why our initial accretion rate is significantly lower than some of the accretion rates measured for the youngest objects (Hartmann et al." + 1998)., 1998). + Furthermore. better agreement for the early time data could. casily be obtained by assuming a range of initial surface density. profiles.," Furthermore, better agreement for the early time data could easily be obtained by assuming a range of initial surface density profiles." + Indeed our choice of a self-similar surface density distribution at. zero time has no physical basis other than convenience (in fact it would be extremely surprising for dises to be born with the surface density distribution of the zero time similarity solution of Equation 3 elven viscous angular momentum transport. is not a key process during the disc formation stage)., Indeed our choice of a self-similar surface density distribution at zero time has no physical basis other than convenience (in fact it would be extremely surprising for discs to be born with the surface density distribution of the zero time similarity solution of Equation \ref{eqn:big} given viscous angular momentum transport is not a key process during the disc formation stage). + We emphasise. that anv initial surface density cüstribution with the same initial viscous parameters ALO). ἐν and a will tend to the same evolution after a few viscous times as shown in Lvnden-Bell Pringle (1974).," We emphasise, that any initial surface density distribution with the same initial viscous parameters $M_d(0)$, $t_\nu$ and $\alpha$ will tend to the same evolution after a few viscous times as shown in Lynden-Bell Pringle (1974)." + For this reason. we do not attempt to explain disc evolution at early times here. since we are mainls interested in the question of cise dispersal. for which only the viscous evolution phase at z- LALvr is relevant.," For this reason, we do not attempt to explain disc evolution at early times here, since we are mainly interested in the question of disc dispersal, for which only the viscous evolution phase at $>1$ Myr is relevant." + We have used the methods and initial conditions derived in the previous section to construct à population svnthesis model for the evolution of discs dominated by viscosity. and APE., We have used the methods and initial conditions derived in the previous section to construct a population synthesis model for the evolution of discs dominated by viscosity and XPE. + We have calculated 500 disc models based on à randonr sampling of the Taurus X-ray luminosity function., We have calculated 500 disc models based on a random sampling of the Taurus X-ray luminosity function. + Our disc evolution models are computed. by solving Equation 3 numerically using the method set out in Owen et al. (, Our disc evolution models are computed by solving Equation \ref{eqn:big} numerically using the method set out in Owen et al. ( +2010). Following the evolution of the cise until the disc is cleared to LOOAU.,"2010), following the evolution of the disc until the disc is cleared to 100AU." + At radii larger than LOOAU the photoevaporation rates are extremely uncertain and we cannot be confident in results that continue the evolution bevond this radius., At radii larger than 100AU the photoevaporation rates are extremely uncertain and we cannot be confident in results that continue the evolution beyond this radius. + Llowever. for the sake of completeness we will discuss the possible qualitative evolution of these remnant discs in section 5.3.," However, for the sake of completeness we will discuss the possible qualitative evolution of these remnant discs in Section 5.3." + We now turn our attention to some specific predictions [rom these models and. where possible. compare them with observations.," We now turn our attention to some specific predictions from these models and, where possible, compare them with observations." + As discussed in Section 2. Drake et al. (," As discussed in Section 2, Drake et al. (" +2009) suggested that coronal X-rays suppress the accretion Low onto voung solar-vpe stars through the driving of a photoevaporating wind.,2009) suggested that coronal X-rays suppress the accretion flow onto young solar-type stars through the driving of a photoevaporating wind. + This photoevaporation starved accretion phase can explain he tentative negative correlation between mass acerction rate and. stellar N-rav. luminosity reported by Drake ct al (2000)., This photoevaporation starved accretion phase can explain the tentative negative correlation between mass accretion rate and stellar X-ray luminosity reported by Drake et al (2009). + Moreover the reduction in disc lifetime in strong X-ray sources can explain the observation that the X-ray uminosities of accreting T ‘Tauri stars are systematically ower than those of non-accretors., Moreover the reduction in disc lifetime in strong X-ray sources can explain the observation that the X-ray luminosities of accreting T Tauri stars are systematically lower than those of non-accretors. + Vhe XPE models of Owen et al (2010) clearly show hat there is indeed a phase in the disc evolution (before he opening of the gap) where the effects of this ‘starving’ are apparent in the racial dependence of the accretion rate., The XPE models of Owen et al (2010) clearly show that there is indeed a phase in the disc evolution (before the opening of the gap) where the effects of this `starving' are apparent in the radial dependence of the accretion rate. + In Figure S we compare the accretion rate ancl surface density profiles of the median disc model undergoing NPE. .5MIvr before the gap opens. against those of a dise which is only subject. to. viscous evolution.," In Figure \ref{fig:psa} we compare the accretion rate and surface density profiles of the median disc model undergoing XPE, 0.5Myr before the gap opens, against those of a disc which is only subject to viscous evolution." + Inside. TO AU. the accretion rate drops before it reaches the star. compared o the standard. case where the accretion rate tends to à constant throughout the entire disc., Inside $70$ AU the accretion rate drops before it reaches the star compared to the standard case where the accretion rate tends to a constant throughout the entire disc. + This can be compared o the EUV photoevaporation model: in this case the mass-oss profile is narrowly peaked. between 1 1OAU (for solar vpe stars) and the total mass-loss rate is considerably less (10I'M. 0). HE, This can be compared to the EUV photoevaporation model: in this case the mass-loss profile is narrowly peaked between $1-10$ AU (for solar type stars) and the total mass-loss rate is considerably less $\sim 10^{-10}$ ). +TThis results in. a shorter and much ess pronounced period of ‘starving Le. the disc is only alfected inside a few AU., This results in a shorter and much less pronounced period of `starving' i.e. the disc is only affected inside a few AU. + In contrast. the photoevaporation starved accretion lasts for. 220-3054. of the disc lifetime in he X-rav model. with significant. consequences for. elobal disc evolution: i.e. a fattening of the surface density. profile ancl a significant drop in the aceretion rate through the disc.," In contrast, the photoevaporation starved accretion lasts for $\sim$ of the disc lifetime in the X-ray model, with significant consequences for global disc evolution: i.e. a flattening of the surface density profile and a significant drop in the accretion rate through the disc." +" 1n Figure5 9 we show the evolution of the surface density for the median disc model (1.0. the dise with the median X- luminosity of 1.110"" cre + which corresponds to a photoevaporation rate of 7.1.10° 13) undergoing the stages of gap-opening and final clearing.", In Figure \ref{fig:median} we show the evolution of the surface density for the median disc model (i.e. the disc with the median X-ray luminosity of $1.1\times10^{30}$ erg $^{-1}$ which corresponds to a photoevaporation rate of $7.1\times10^{-9}$ ) undergoing the stages of gap-opening and final clearing. + This shows the drop in surface density through the disc between 1. TOA before the gap opens (as shown in Figure 8))., This shows the drop in surface density through the disc between $1-70$ AU before the gap opens (as shown in Figure \ref{fig:psa}) ). + Moreover the broad. photoevaporation profile also causes the steady erosion of the disc during the draining of the inner hole. so," Moreover the broad photoevaporation profile also causes the steady erosion of the disc during the draining of the inner hole, so" +90° rotation in position angle between these two limiting cases for the entire profile.,$90^\circ$ rotation in position angle between these two limiting cases for the entire profile. +" For intermediate field strengths, there is a position angle rotation across the profile that occurs at different velocity shifts."," For intermediate field strengths, there is a position angle rotation across the profile that occurs at different velocity shifts." +" In the axial field case, there is never a position angle rotation for an edge-on disk."," In the axial field case, there is never a position angle rotation for an edge-on disk." +" For the sshapes, differences in the polarizations are especially clear, with results for the toroidal field in Figure 7 to be compared against those for an axial field in Figure 5.."," For the shapes, differences in the polarizations are especially clear, with results for the toroidal field in Figure \ref{fig7} to be compared against those for an axial field in Figure \ref{fig5}." + What is the source of these differences between the axial field and the toroidal one?, What is the source of these differences between the axial field and the toroidal one? + The field orientation with respect to the viewer is clearly the key to the interpretation., The field orientation with respect to the viewer is clearly the key to the interpretation. +" For the axial case, the field at every point in the disk has some component of the magnetic vector directed toward the observer (if seen at i< 90°) or away from the observer (if seen at i> 90°)."," For the axial case, the field at every point in the disk has some component of the magnetic vector directed toward the observer (if seen at $i<90^\circ$ ) or away from the observer (if seen at $i>90^\circ$ )." +" Thus, an axial field leads to a net projected magnetic flux of one sign or the other, which is true for every isovelocity loop."," Thus, an axial field leads to a net projected magnetic flux of one sign or the other, which is true for every isovelocity loop." +" The toroidal field is manifestly different, since one side of the disk has components toward the observer and the other side has them away."," The toroidal field is manifestly different, since one side of the disk has components toward the observer and the other side has them away." +" For an axisymmetric toroidal field, the projected net magnetic flux is identically zero for the entire disk, but is oppositely signed in isovelocity loops for blueshifted velocities versus redshifted ones."," For an axisymmetric toroidal field, the projected net magnetic flux is identically zero for the entire disk, but is oppositely signed in isovelocity loops for blueshifted velocities versus redshifted ones." +" In terms of the semi-classical precession description, flipping the field by 180? amounts to a precession in the opposite direction."," In terms of the semi-classical precession description, flipping the field by $180^\circ$ amounts to a precession in the opposite direction." +" In the axial field case, the precession of the radiating oscillator is uniform — entirely clockwise (cw) or counterclockwise (ccw)."," In the axial field case, the precession of the radiating oscillator is uniform – entirely clockwise (cw) or counterclockwise (ccw)." +" Both cw and ccw precessions occur for a toroidal field configuration, with one precession occurring in half the line profile, and the opposite for the other half."," Both cw and ccw precessions occur for a toroidal field configuration, with one precession occurring in half the line profile, and the opposite for the other half." +" To illustrate this effect, Figure 8 shows line profile results for a toroidal field that now goes in the other direction as compared to Figure 6.."," To illustrate this effect, Figure \ref{fig8} shows line profile results for a toroidal field that now goes in the other direction as compared to Figure \ref{fig6}." +" The pprofiles are nearly the same, but the pprofiles are nearly mirror images of one another."," The profiles are nearly the same, but the profiles are nearly mirror images of one another." +" slight differences are a result of the stellar occultation, which doesnot flip when the field orientation is reversed."," slight differences are a result of the stellar occultation, which does flip when the field orientation is reversed." +" A large literature has developed over the last twenty years in relation to the magnetorotational instability (MRI; Balbus Hawley 1991, 1998)."," A large literature has developed over the last twenty years in relation to the magnetorotational instability (MRI; Balbus Hawley 1991, 1998)." +from the phase variation and/or the period change.,from the phase variation and/or the period change. + The analvsis of the amplitude: variation using the maximum brightness data does not give any definite. solution [ου the modulation. period. either.," The analysis of the amplitude variation using the maximum brightness data does not give any definite solution for the modulation period, either." + The maximum brightnessniiximunm) phase plots of the seasonal light curves also do not help to determine the modulation. period. (see Fig 9))., The maximum brightness--maximum phase plots of the seasonal light curves also do not help to determine the modulation period (see Fig \ref{v18egg}) ). + We conclude that the modulation properties and the pulsation period of VIS vary probably on a similar time-scale. making the determination of the modulation period [rom the available data impossible.," We conclude that the modulation properties and the pulsation period of V18 vary probably on a similar time-scale, making the determination of the modulation period from the available data impossible." + Light-curve modulation is probable according to the CCD V. data (Stormetal.1991.IX00)., Light-curve modulation is probable according to the CCD $V$ data \citep[K00]{s91}. +. Phe pulsation-period. variation is complex. but it can be fitted with a smooth cubic function for the period between 1952. and 1987 as shown in Vig. 10..," The pulsation-period variation is complex, but it can be fitted with a smooth cubic function for the period between 1952 and 1987 as shown in Fig. \ref{v19oc}." + If this part of the combined observations is transformed in time to eliminate the period variation as described in Paper LE the modified data show clear evidence of an amplitude modulation with a ἐνe39 d period.," If this part of the combined observations is transformed in time to eliminate the period variation as described in Paper I, the modified data show clear evidence of an amplitude modulation with a $P_{m}\approx39$ d period." + Fig., Fig. + 11. shows the amplitude spectrum. of the maximum brightness data between 1952 and. LOST. and the data phased with the Iargest-amplitude frequency. 0.0254 cel+ (39-4 0).," \ref{v19max} shows the amplitude spectrum of the maximum brightness data between 1952 and 1987, and the data phased with the largest-amplitude frequency, 0.0254 $^{-1}$ (39.4 d)." + The star is far from the centre with no close companion allecting the photometry., The star is far from the centre with no close companion affecting the photometry. + The minima of the 1196 and KOO CCD V light curves differ conspicuously in phase and magnitude as shown in Fig. 12.., The minima of the R96 and K00 CCD $V$ light curves differ conspicuously in phase and magnitude as shown in Fig. \ref{v24}. + Ht clearly indicates that the light curve of V24 is not stable., It clearly indicates that the light curve of V24 is not stable. + No maximum light was measured in ROG., No maximum light was measured in R96. + The star lies in a crowded region. the photographic data are seriously defective.," The star lies in a crowded region, the photographic data are seriously defective." + Lhe pulsation-periocd variation is, The pulsation-period variation is + ∣⋅∏∣∖↗⋅⋅⋔⊜∣⊃⋯↾∪∏↾⊖⋯∣⊃⊖∣⋪∐↾⋯⋪⊜⋅≏⋯≣↭∏⋪∪∣��⋝⇁∣⋪∐⊓⋂⊜∖⇁⋂∣∖⇁⊜⋋ approximately along the firehose-instability threshold as pip increases.,"$r> 71 R_{\sun}$, the proton temperature anisotropy ratio evolves approximately along the firehose-instability threshold as $\beta_{\parallel \rm p}$ increases." + This numerical solution is broadly consistent with a number of observations. as illustrated in Figures2... 3.. 4.. and 6.. supporting the idea that AW turbulence may be one of the primary mechanisms responsible for heating coronal holes and accelerating the solar wind (??)..," This numerical solution is broadly consistent with a number of observations, as illustrated in Figures\ref{fig:swn}, \ref{fig:swdv}, \ref{fig:swT}, and \ref{fig:swq}, supporting the idea that AW turbulence may be one of the primary mechanisms responsible for heating coronal holes and accelerating the solar wind \citep{parker65,coleman68}." + Perhaps the most notable achievement of our model is that it comes close to explaining observations of perpendicular proton temperatures. even though the heating in the model is provided by low-frequency AW turbulence rather than resonant cyclotron interactions.," Perhaps the most notable achievement of our model is that it comes close to explaining observations of perpendicular proton temperatures, even though the heating in the model is provided by low-frequency AW turbulence rather than resonant cyclotron interactions." + The main uncertainties in our results are associated with the stochastic heating rate in strong AW/KAW turbulence. the wavenumber anisotropy (Κι) in reflection-driven AW/KAW turbulence. the total turbulent heating rate at large r. and the effects of solar rotation on the temperature anisotropy ratio 715/7) ," The main uncertainties in our results are associated with the stochastic heating rate in strong AW/KAW turbulence, the wavenumber anisotropy $k_\parallel /k_\perp$ ) in reflection-driven AW/KAW turbulence, the total turbulent heating rate at large $r$, and the effects of solar rotation on the temperature anisotropy ratio $T_{\perp \rm p}/T_{\parallel \rm p}$." +One of our principal objectives in p-this work has been to to connect theoretical studies of microphysical processes with observations of macrophysical quantities in the solar wind., One of our principal objectives in this work has been to to connect theoretical studies of microphysical processes with observations of macrophysical quantities in the solar wind. + By comparing our model to observations. we have been able to obtain a new test of the viability of AW turbulence as a mechanism for heating the solar wind and coronal holes.," By comparing our model to observations, we have been able to obtain a new test of the viability of AW turbulence as a mechanism for heating the solar wind and coronal holes." + At this point. the results of this test are encouraging. but not fully conclusive. because of the uncertainties described above.," At this point, the results of this test are encouraging, but not fully conclusive, because of the uncertainties described above." + However. as our understanding of kinetic plasma physics and turbulence in the solar wind progresses. it will be possible to use models such as the one we have developed to obtain increasingly rigorous tests of competing theories and. ultimately. to gain greater insight into coronal heating and the origin of the solar wind.," However, as our understanding of kinetic plasma physics and turbulence in the solar wind progresses, it will be possible to use models such as the one we have developed to obtain increasingly rigorous tests of competing theories and, ultimately, to gain greater insight into coronal heating and the origin of the solar wind." + We thank Steve Cranmer. Joe Hollweg. Greg Howes. Phil Isenberg. Yuan-Kuen Ko. Jean Perez. and Jason Tenbarge for helpful discussions.," We thank Steve Cranmer, Joe Hollweg, Greg Howes, Phil Isenberg, Yuan-Kuen Ko, Jean Perez, and Jason Tenbarge for helpful discussions." + This work was supported in part by grant NNX11AJ37G from NASA's Heliophysies Theory Program. NSF grant AGS-0851005. NSF/DOE grant. AGS-1003451. DOE grant DE-FG02-07-ER46372. NSF/DOE grant 0812811. and NSF grant ATM-0752503.," This work was supported in part by grant NNX11AJ37G from NASA's Heliophysics Theory Program, NSF grant AGS-0851005, NSF/DOE grant AGS-1003451, DOE grant DE-FG02-07-ER46372, NSF/DOE grant PHY-0812811, and NSF grant ATM-0752503." + The derivation of the equations in our model begins with Kulsrud’s formulation of collisionless MHD for a proton-electron plasma (?).., The derivation of the equations in our model begins with Kulsrud's formulation of collisionless MHD for a proton-electron plasma \citep{kulsrud83}. + Kulsrud’s approach was to expand all quantities in the Vlasov and Maxwell equations in powers of 1/e. where e is the proton charge. and to consider the limite>co.," Kulsrud's approach was to expand all quantities in the Vlasov and Maxwell equations in powers of $1/e$, where $e$ is the proton charge, and to consider the limit$e\rightarrow \infty$." + This limit corresponds to the case in which the Debye length Ap and proton gyroradius are much smaller than the length scales over which the macroscopic quantities vary appreciably., This limit corresponds to the case in which the Debye length $\lambda_{\rm D}$ and proton gyroradius $\rho_{\rm p}$ are much smaller than the length scales over which the macroscopic quantities vary appreciably. + The fundamental variables in pyKulsrud’s theory are the mass density p.the fluid velocity U (which ts the same for electrons and protons to lowest order in 1/e). the magnetic field B. the proton and electron distribution functions fj and f.. and the parallel component of the electric field E. given by E)=b. E. where b= B/B.," The fundamental variables in Kulsrud's theory are the mass density $\rho$,the fluid velocity $\bm{U}$ (which is the same for electrons and protons to lowest order in $1/e$), the magnetic field $\bm{B}$ , the proton and electron distribution functions $f_{\rm + p}$ and $f_{\rm e}$, and the parallel component of the electric field $\bm{E}$ , given by $E_\parallel = \bm{\hat{b}} \cdot \bm{E}$ where $\bm{\hat{b}} = \bm{B}/B$ ." + To lowestorder in | /e. these variables satisfy the equations," To lowestorder in $1/e$ , these variables satisfy the equations" +that describe the merger cllicicney parameter ας) ancl the activily parameter (Ba)1.,that describe the merger efficiency parameter $x(z)$ and the activity parameter $(F\sigma)^{-1}$. + We present appropriate [ornis for these functions in equations (16) and (1S) respectively. but stress that these forms are not unique.," We present appropriate forms for these functions in equations (16) and (18) respectively, but stress that these forms are not unique." + As more data becomes available. other functional forms or (ree-form fitting functions may be more appropriate.," As more data becomes available, other functional forms or free-form fitting functions may be more appropriate." +" By mocdifving the activity. parameter (F0,1. introducing the total fraction of luminosity absorbed by dust 24. and including a template SED [for star-forming galaxies in the rest frame ultraviolet waveband. the L-band counts can also be reproduced."," By modifying the activity parameter $(F\sigma)_0^{-1}$, introducing the total fraction of luminosity absorbed by dust $A$, and including a template SED for star-forming galaxies in the rest frame ultraviolet waveband, the $B$ -band counts can also be reproduced." + ba Table22 we summarize these parameters ancl the most important pieces of data used to constrain them., In 2 we summarize these parameters and the most important pieces of data used to constrain them. + The values of the parameters required to fit the data in the 35-Ix. model are also listed., The values of the parameters required to fit the data in the 35-K model are also listed. +other wavelengths will be reprocessed and emitted in the mid-IR.,other wavelengths will be reprocessed and emitted in the mid-IR. + For these reasons. the X-rayX-ray. and mid-IRmid-IB reguregimes arer excellentlent wavelengthslengthsin in which to detect and study AGNA," For these reasons, the X-ray and mid-IR regimes are excellent wavelengths in which to detect and study AGN." +"GN, Recent deep survevs with the Chandra X-ray Observatory have resolved many X-ray sources in the ΠΕ and. provide information about the nature of (he X-ray radiation.", Recent deep surveys with the Chandra X-ray Observatory have resolved many X-ray sources in the HDF and provide information about the nature of the X-ray radiation. + The PAIS Chandra X-ray survey. (Alexander 2003) has detected 20 sources in the original IIDE and an additional 2 sources of lower significance which are listed in their supplementary catalog., The 2Ms Chandra X-ray survey (Alexander 2003) has detected 20 sources in the original HDF and an additional 2 sources of lower significance which are listed in their supplementary catalog. + Of these 22 detections. 18 are included. in our variabilitv. study.," Of these 22 detections, 18 are included in our variability study." + Two were not included because their optical fluxes. were too faint to be included in our survey. and an additional pair fell too close to the edge of the CC'D (o obtaim accurate nuclear photometry in both epochs., Two were not included because their optical fluxes were too faint to be included in our survey and an additional pair fell too close to the edge of the CCD to obtain accurate nuclear photometry in both epochs. +" Of these 18 sources. we find seven that match (within 1.2"") the positions ol our variable nuclei (see columns 10 and 11 of Table 1)."," Of these 18 sources, we find seven that match (within $\arcsec$ ) the positions of our variable nuclei (see columns 10 and 11 of Table 1)." + The filled svimbols in Figure 4 represent (he 18 X-ray. sources included in our survey and show the level of variability significance for each source., The filled symbols in Figure 4 represent the 18 X-ray sources included in our survey and show the level of variability significance for each source. + In addition. we have found several variables coincident with source positions from the ISOCAM 154a survey of the ΠΟΤΕ (Aussel 1999) and the 1.4GIIz radio survey (Richards 1999).," In addition, we have found several variables coincident with source positions from the ISOCAM $\micron$ survey of the HDF (Aussel 1999) and the 1.4GHz radio survey (Richards 1999)." + These are listed in columns 12 through 14 of Table 1., These are listed in columns 12 through 14 of Table 1. + Below. we discuss the variable ewlaxv nuclei (hat overlap with one or more of these multi-wavelength Slrvevs.," Below, we discuss the variable galaxy nuclei that overlap with one or more of these multi-wavelength surveys." + This z=0.960 earlv-tvpe spiral galaxy is one of only two broad-line AGN in ihe IIDF (see Section 6) and is a bright X-ray source detected with Chandra in the soft. hard and ultrahard bands (Hornscheiemer 2000: Branclt 2001 hereafter LI00. BOla) with a photon index of 0.67.," This z=0.960 early-type spiral galaxy is one of only two broad-line AGN in the HDF (see Section 6) and is a bright X-ray source detected with Chandra in the soft, hard and ultrahard bands (Hornscheiemer 2000; Brandt 2001a – hereafter H00, B01a) with a photon index of 0.67." + We detect it as an optical variable al 6.50 sienilicance., We detect it as an optical variable at $\sigma$ significance. + As previously mentioned. it is the only object that was also detected in our I-band survey of the HDF (SGP).," As previously mentioned, it is the only object that was also detected in our I-band survey of the HDF (SGP)." + Spectroscopic detection of broad Mgll (Phillips 1997). as well as 1.4GIHz radio (Richards 19993) and ISOCAAL (Aussel 1999) detections for this source all corroborate the AGN nature of this galaxy.," Spectroscopic detection of broad MgII (Phillips 1997), as well as 1.4GHz radio (Richards 1999a) and ISOCAM (Aussel 1999) detections for this source all corroborate the AGN nature of this galaxy." + Spectral fitting of the X-ray. data has revealed a large intrinsic column densitv which appears to be related to the AGN (BOla)., Spectral fitting of the X-ray data has revealed a large intrinsic column density which appears to be related to the AGN (B01a). + This elliplical galaxy αἱ z=0.474 is a 3.20 variable., This elliptical galaxy at z=0.474 is a $\sigma$ variable. + The original 166ks Chandra exposure did not detect (is source in the hard band. but BOla report hard. X-ray. counts from the deeper 479.7ks exposure.," The original 166ks Chandra exposure did not detect this source in the hard band, but B01a report hard X-ray counts from the deeper 479.7ks exposure." + The photon index determined [rom (he 2Ms exposure is 1.8., The photon index determined from the 2Ms exposure is 1.8. + This galaxy is also a radio source with a steep radio spectrum (a—1.0)., This galaxy is also a radio source with a steep radio spectrum $\alpha$ =1.0). + Its position is coincident with an ISO source from the Aussel (1999) supplementary table of lower sienificance detections., Its position is coincident with an ISO source from the Aussel (1999) supplementary table of lower significance detections. + LOO note that the N-rav luminosity for this source is consistent with that expected from hot gas in an elliptical but the nuclear variability detected here suggests this galaxy mav also host an AGN., H00 note that the X-ray luminosity for this source is consistent with that expected from hot gas in an elliptical but the nuclear variability detected here suggests this galaxy may also host an AGN. +the radiation field incident on a realistic test. globule are reported.,the radiation field incident on a realistic test globule are reported. + Firstly. the effects on molecular line profiles of changing this field from the CAIB to a more realistic ISRE is investigated.," Firstly, the effects on molecular line profiles of changing this field from the CMB to a more realistic ISRF is investigated." + Secondly. the ISHE is moclilied to simulate the radiation field in the vicinity. of embedded massive stars.," Secondly, the ISRF is modified to simulate the radiation field in the vicinity of embedded massive stars." + Finally the ISRE is modified. by increasing he CAIB temperature. to simulate the radiation. field. in which molecular clouds at high-redshift) will be found.," Finally the ISRF is modified by increasing the CMB temperature, to simulate the radiation field in which molecular clouds at high-redshift will be found." + Our study lacks the more self-consistent approach of he combined. hydrodynamical/chemical/racliative transfer models of Rawlings ancl Yates (2001). but serves to show the sensitivities and hence to highlight the clagnostic strengths (and weaknesses) of line profile analyses.," Our study lacks the more self-consistent approach of the combined hydrodynamical/chemical/radiative transfer models of Rawlings and Yates (2001), but serves to show the sensitivities and hence to highlight the diagnostic strengths (and weaknesses) of line profile analyses." + Phe discussion is limited to two well known molecular racers used to diagnose collapsing cores: +2) and MOCO κα. 5 2).," The discussion is limited to two well known molecular tracers used to diagnose collapsing cores: $^+$ $\to$ 2) and $^{13}$ CO $\to$ 1, $\to2$ )." + This allows cirect comparison with other work: previous studies (eg., This allows direct comparison with other work; previous studies (eg. + Rawlings ancl Yates. 2001) have shown that the transition is particularly likely to be strongly. selil-reversed. ancl asymmetric. whilst the elfects on the CO lines has implications for high-redshift molecular observations.," Rawlings and Yates, 2001) have shown that the $^+$ transition is particularly likely to be strongly self-reversed and asymmetric, whilst the effects on the CO lines has implications for high-redshift molecular observations." + The discussion is also limited to zero beam ollset positions so as to allow a simple comparison of the etfects discussed in this paper., The discussion is also limited to zero beam offset positions so as to allow a simple comparison of the effects discussed in this paper. + The radiative transfer code used in this work isSMMOL. an approximate A iterative code that solves multi-level LIE rachative transfer problems (see Rawlines&Yates2001 for full details).," The radiative transfer code used in this work is, an approximate $\Lambda-$ iterative code that solves multi-level non-LTE radiative transfer problems (see \citealt{rawlings&yates01} for full details)." + The results generated. by this code. can be viewed: with some confidence because a series of recent benchmarking exercises have compared. several such codes. including for exampleRATRAN. an accelerated. Monte-C'arlo code described by Hogerheijde&vanderTak(2000).," The results generated by this code can be viewed with some confidence because a series of recent benchmarking exercises have compared several such codes, including for example, an accelerated Monte-Carlo code described by \citet{hogerheijde&vandertak00}." +. Both andRATRAN. despite the very cillerent numerical methods. usec. are able to vield. the same results when applied to test cases very similar to the nioclel runs described here.," Both and, despite the very different numerical methods used, are able to yield the same results when applied to test cases very similar to the model runs described here." + The benchmarking has been described by vanZaclel-holletal. (2002)., The benchmarking has been described by \citet{vanzadelhoff.et.al02}. +. lor our numerical studies. atest globule was constructed. using the class 0 source. D335. which is one of the best. observed (ancl modelled) protostellar infall candidates Zhouetal.1993:Choi1995:Wilneretal. 2000)).," For our numerical studies, a test globule was constructed using the class 0 source B335, which is one of the best observed (and modelled) protostellar infall candidates \citealt{zhou.et.al93,choi.et.al95,wilner.et.al00}) )." + Phe physical parameters of the test globule (following Rawlings Yates 2001) are based. upon he models of B335 of Zhou et al. (, The physical parameters of the test globule (following Rawlings Yates 2001) are based upon the models of B335 of Zhou et al. ( +1993) and. Choi et al. (,1993) and Choi et al. ( +1995).,1995). + At. each. of fiftv points in a radial eric (similar to that of Choietal. 1995)) the racius. censity. ractional abundance. gas temperature. dust. temperature. radial velocity. and microturbulent velocity. are. specified.," At each of fifty points in a radial grid (similar to that of \citealt{choi.et.al95}) ) the radius, density, fractional abundance, gas temperature, dust temperature, radial velocity and microturbulent velocity are specified." + The density and velocity profiles 9(r)and. ο] are taken rom the Shu (1977) inside-out collapse mocdel. with the ohvsical parameters as specified in Table 1.," The density and velocity profiles $n(r)~\mbox{and}~v(r)$ ] are taken from the Shu (1977) inside-out collapse model, with the physical parameters as specified in Table 1." + D335 is being used. because there is a well developed model for it. but it is not claimed that B3352 itself is being subjected to any of he elfects explored in this paper.," B335 is being used because there is a well developed model for it, but it is not claimed that B335 itself is being subjected to any of the effects explored in this paper." + Alodifving the radiation field incident on the elobule will alfect the cust temperature., Modifying the radiation field incident on the globule will affect the dust temperature. + To account for this. the dust emperature in the elobule is calculated for cach radiation ield using the dust radiative transfer. code. described: in Efstathiou&Rowan-Robinson(1994).," To account for this, the dust temperature in the globule is calculated for each radiation field using the dust radiative transfer code described in \cite{efstathiou&rowan-robinson94}." +. For the case of a stancard ISRE at z=0. it was verified that the racial profile of the dust temperature is comparable to that deduced from dust continuum observations of B335 (Zhou et al..," For the case of a standard ISRF at z=0, it was verified that the radial profile of the dust temperature is comparable to that deduced from dust continuum observations of B335 (Zhou et al.," + 1990)., 1990). + As in Rawlines and. Yates (2001). we assume that the dust and eas are thermally well coupled.," As in Rawlings and Yates (2001), we assume that the dust and gas are thermally well coupled." + Although this assumption is probably not. valid in the low densivn c10em7) outer envelope. we again note that it holds in the denser line-forming core regions.," Although this assumption is probably not valid in the low density $n<10^5~{\rm cm}^{-3}$ ) outer envelope, we again note that it holds in the denser line-forming core regions." + In fact. the dust/gas temperature changes turn out to only have a second. order effect on the line profiles compared. with changing the radiation field.," In fact, the dust/gas temperature changes turn out to only have a second order effect on the line profiles compared with changing the radiation field." + The collapse model is not well-justified. ancl more reliable evaluations of the temperature profile are now available (Shirleyctal.2000) but this approach provides a useful and well-known benchmark against which to test the elfects discussed in this paper.," The collapse model is not well-justified, and more reliable evaluations of the temperature profile are now available \citep{shirley.et.al00} but this approach provides a useful and well-known benchmark against which to test the effects discussed in this paper." + Most of the transitions that we consider in this study are very optically thick. so that the line profiles. are relatively insensitive to the absolute values of the fractional abundances (1).," Most of the transitions that we consider in this study are very optically thick, so that the line profiles are relatively insensitive to the absolute values of the fractional abundances $X_{\rm +i}$ )." + This result is in marked cillerence to the findings of Ward-Thompson ancl Buckley (2000) who found strong qualitative and quantitative dillerences when Vz was varied between 10., This result is in marked difference to the findings of Ward-Thompson and Buckley (2000) who found strong qualitative and quantitative differences when $X_{\rm i}$ was varied between $10^{-9}-10^{-8}$. + We suspect that this is a result of the inability of theSrENHOLAL code to deal with extreme optical depths., We suspect that this is a result of the inability of the code to deal with extreme optical depths. + However. as emphasised in Rawlings and Yates (2000). racialvariations in the abundances can have profound. elfects on the line. profiles.," However, as emphasised in Rawlings and Yates (2000), radial in the abundances can have profound effects on the line profiles." + We do not. want. to confuse the interpretation of our results with chemical issues. so we simply adopt a two-phase chemical scheme. with separate abundances within and exterior to the infall radius (ring): Choi et al. (," We do not want to confuse the interpretation of our results with chemical issues, so we simply adopt a two-phase chemical scheme, with separate abundances within and exterior to the infall radius $r_{\rm inf}$ ); Choi et al. (" +1995) used a single constant abundance in thei work.,1995) used a single constant abundance in their work. + The abundances used in our model - which are spatial averages taken from Πο., The abundances used in our model - which are spatial averages taken from fig. + 1 of Rawlings and Yates (2000). are also given in Table 1.," 1 of Rawlings and Yates (2000), are also given in Table 1." + Most molecular line transport codes adopt the CMD as the incident radiation field vanZadelbholetal.(2002)., Most molecular line transport codes adopt the CMB as the incident radiation field \citet{vanzadelhoff.et.al02}. +.. While his is the dominant source of radiation at the wavelengths of he molecular transitions under consideration here. à proper reatment should include the full interstellar radiation field.," While this is the dominant source of radiation at the wavelengths of the molecular transitions under consideration here, a proper treatment should include the full interstellar radiation field." + vanDishoeck(1994) bas reviewed how such a radiation 101 is constructed.," \citet{vandishoeck94} + has reviewed how such a radiation field is constructed." + I contains three dominant components: starlight (mainly from D. stars). dust-enshrouded: massive stars. and the CMD.," It contains three dominant components: starlight (mainly from B stars), dust-enshrouded massive stars, and the CMB." + Lt ds these latter two components hat are modified in this work and discussed below., It is these latter two components that are modified in this work and discussed below. + Firstly hough. the effect. of replacing the CAIB with a realistic ISRE was investigated.," Firstly though, the effect of replacing the CMB with a realistic ISRF was investigated." + In this work. the radiation Lele constructed by Lewansetal.(2001) was emploved.," In this work, the radiation field constructed by \citet{evans.et.al01} was employed." + This is a combination of the radiation field introduced. by Black(1004) with that of Draine(1978)., This is a combination of the radiation field introduced by \citet{black94} with that of \citet{draine78}. +. The dust. radiative transfer code was used to firstly. calculate. the gas/dust temperature before the line profiles were generated by the molecular line transport codo., The dust radiative transfer code was used to firstly calculate the gas/dust temperature before the line profiles were generated by the molecular line transport code. + The inclusion of the Black-Draine ISRE had almost no discernible ellect on the line profile shapes for both species., The inclusion of the Black-Draine ISRF had almost no discernible effect on the line profile shapes for both species. + This is because the CMD component of the radiation field vastly dominates the line formation at these wavelengths., This is because the CMB component of the radiation field vastly dominates the line formation at these wavelengths. +halos: Figure 2. illustrates.,halos; Figure \ref{ptdt} illustrates. + This is in qualitative agreement with recent work CPhomas. Maraston Bencler 2002).," This is in qualitative agreement with recent work (Thomas, Maraston Bender 2002)." + Most of the results presented here were obtained while L was a postdoc at. Fermilab. supported by the DOL and. NASA erant. NAG 5-10842.," Most of the results presented here were obtained while I was a postdoc at Fermilab, supported by the DOE and NASA grant NAG 5-10842." + Ed like to thank Scott Docdelson. Josh Fricman. Albert Stebbins and Liz Duty for making Fermilab a rewarding place to work.," I'd like to thank Scott Dodelson, Josh Frieman, Albert Stebbins and Liz Duty for making Fermilab a rewarding place to work." + In the model discussed in the main text. halos grow bv binary mergers with one another.," In the model discussed in the main text, halos grow by binary mergers with one another." + The formation rate of a halo with AZ particles is given by evaluating which expresses the fact that formation in this mocel happens by binary mergers. with probability. of merger proportional to the mass of the merging pair. and the abundance of each type of clump.," The formation rate of a halo with $M$ particles is given by evaluating which expresses the fact that formation in this model happens by binary mergers, with probability of merger proportional to the mass of the merging pair, and the abundance of each type of clump." + The associated destruction rate is related to This system of equations for n(AM.5) is solved. by equation (1)): this was one of the results in Sheth Pitman (1991).," The associated destruction rate is related to This system of equations for $n(M,b)$ is solved by equation \ref{nm}) ); this was one of the results in Sheth Pitman (1997)." + The conditional formation rate of m-subclumps within an AM-parent. while given by a similar expression. is slightly dilferent.," The conditional formation rate of $m$ -subclumps within an $M$ -parent, while given by a similar expression, is slightly different." + Lt is, It is + ?2))., \citealt{gkw02}) \citep{dkg07}. + (2).. ?? (?)..," \citet{kas07,mer08} \citep{dkg08}." + ο (??)..?. 1048.," $\sim$ \citep{kgw+03,wkt+04}." +1—5937 (e.g.?).. (2???)..,"\citet{dkg09} $-$ \citep[e.g.][]{es10}. \citep{roz+05,cri+07,igz+07,gri+07}." + ο ~40% ~9 , \citet{gri+07} $\sim$ $\sim$ +requency £z. the emissivity 3. dust temperature Z;. and FLR uminositv μι (which governs the normalisation of the 'unction).,"frequency $\nu$, the emissivity $\beta$, dust temperature $T_{d}$, and FIR luminosity $L_{FIR}$ (which governs the normalisation of the function)." +" The first model allows ?10 vary (the 7""beta-[ree"" moclel) while the second model fixes emissivity to 3=2"," The first model allows $\beta$ to vary (the “beta-free” model) while the second model fixes emissivity to $\beta\,=\,2$." +" Both models have Zi, and Lpig as free. parameters.", Both models have $T_{d}$ and $L_{FIR}$ as free parameters. + The advantage of allowing emissivity to vary in the first. mocel allows a reassessment of the emissivity constraints. which iive been placed on ULIIBCs in rast studies (e.g.3L15etal. 2009)..," The advantage of allowing emissivity to vary in the first model allows a reassessment of the emissivity constraints which have been placed on ULIRGs in past studies \citep[e.g. $\beta\,=\,$1.5 or +2.0;][]{chapman05a,casey09b,casey09c,younger09a}." + In αστοί. our measurements ο 2 are mace independent of any epriori constraint on d; or Lire.," In addition, our measurements of $\beta$ are made independent of any $a\ priori$ constraint on $T_{d}$ or $L_{FIR}$." + We choose to make the second. mocel rigid as fits from the first model can be unphysical. as might be the case if the FLR Hux densities are particularly. faint or allected: hy source confusion.," We choose to make the second model rigid as fits from the first model can be unphysical, as might be the case if the FIR flux densities are particularly faint or affected by source confusion." + Only 1033212 and 033237 are 1poorly fit to à beta-[ree model (these are the two galaxies with tentative recshilt identifications). since they do not have data ancl have unconstraining upper limits in the FIR.," Only J033212 and J033237 are poorly fit to a beta-free model (these are the two galaxies with tentative redshift identifications), since they do not have data and have unconstraining upper limits in the FIR." + We use only the fixed 9 ~==22 model for these two., We use only the fixed $\beta$ 2 model for these two. + The remaining seven galaxies have reliable beta-free. SED fits. and [from them we measure 3. Lines. ane LgsLone (summarised in. Table 1)).," The remaining seven galaxies have reliable beta-free SED fits, and from them we measure $\beta$, $T_{dust}$, and $L_{FIR (8-1000\mu m)}$ (summarised in Table \ref{tab:observations}) )." + Both fixed beta and beta-free fits are shown in Figure 4.., Both fixed beta and beta-free fits are shown in Figure \ref{fig:firsed}. + We find a mean emissivity of F==11.734018 and a mean dust temperature of T 55246 hh. The FUR luminosities (S-1000//21)) must be. corrected o account for micd-infrarecl (8-25//m)) emission from PALL and power law sources (c.g.Menéndez-Delmoestreetal.2009) above the single FUR mocified blackbody., We find a mean emissivity of $\beta$ $\pm$ 0.13 and a mean dust temperature of $T_{d}$ $\pm$ K. The FIR luminosities ) must be corrected to account for mid-infrared ) emission from PAH and power law sources \citep[e.g.][]{menendezdelmestre09a} above the single FIR modified blackbody. + We tether the opeetal.(2008) SMG SED to flux densities (as seen in Figure 4)) to estimate the unmiinosity deficit of the single temperature blackhock., We tether the \citet{pope08a} SMG SED to flux densities (as seen in Figure \ref{fig:firsed}) ) to estimate the luminosity deficit of the single temperature blackbody. + Εις deficit varies substantially object to object due to the large spread in flux densities ancl blackbody properties in the WWein tail., This deficit varies substantially object to object due to the large spread in flux densities and blackbody properties in the Wein tail. + On average. we find that he contribution o£ the PAIL and AGN emission. account. for. 0.04-E0.03 cledlex of luminosity which we add to the EL luminosities as a correction factor.," On average, we find that the contribution of the PAH and AGN emission account for $\pm$ dex of luminosity which we add to the FIR luminosities as a correction factor." + Although the mid-Ilt. properties. of the sample can vary substantially. this deficit translates to no more than a ~10% increase in LR. luminosity for these 2107 H ssvstems.," Although the mid-IR properties of the sample can vary substantially, this deficit translates to no more than a $\sim$ increase in FIR luminosity for these $>$ $^{13}$ systems." + The corrected luminosities are given in Table 1.., The corrected luminosities are given in Table \ref{tab:observations}. + We also overplot the composite SMCG spectrum. from Popeetal.(2008)... normalised to the integrated flux density in Figure 4..," We also overplot the composite SMG spectrum, from \citet{pope08a}, normalised to the integrated flux density in Figure \ref{fig:firsed}." + While the SMG| composite is carefully. derived based. on mid-HI. to ELI. data of SMCs o date. it fails to fit the BLAST. FIR data on a case ov case basis.," While the SMG composite is carefully derived based on mid-IR to FIR data of SMGs to date, it fails to fit the BLAST FIR data on a case by case basis." + In. some cases. it underfoverestimates the EL luminosities by cH ddex.," In some cases, it under/overestimates the FIR luminosities by $\pm$ dex." + Vhis illustrates how a 24yeni--normalised SED fitting procedure. which is common in the iterature (c.g.Desaietal.2009). places poor constraints on he breadth of EL properties of ULIRG samples. especially in the absence of direct. PLR measurements.," This illustrates how a -normalised SED fitting procedure, which is common in the literature \citep[e.g.][]{desai09a} places poor constraints on the breadth of FIR properties of ULIRG samples, especially in the absence of direct FIR measurements." + Recent hieh-resolution EL observations (e.g.Youngeretal.2010). have demonstrated that ccounterparts are often misidentifications and clo not correspond to the FUR Iuminous source., Recent high-resolution FIR observations \citep[e.g.][]{younger10a} have demonstrated that counterparts are often misidentifications and do not correspond to the FIR luminous source. + Although multiple dust. temperature blackbodies: are found to fit well to local ULIBCs in the literature (forex-ample.seeClementsetal. 2010).. strong assumptions must be mace regarding the FIR luminosity of normalisation. to decompose the sparse FLR data down into multiple blackbody components.," Although multiple dust temperature blackbodies are found to fit well to local ULIRGs in the literature \citep[for example, + see][]{clements09a}, strong assumptions must be made regarding the FIR luminosity or normalisation, to decompose the sparse FIR data down into multiple blackbody components." + Given the uncertainty of the ELE luminosities or flux densities at any given wavelength. we decide to forgo multiple dust. temperature fitting Lor well constrained. single dust temperature blackbody fits.," Given the uncertainty of the FIR luminosities or flux densities at any given wavelength, we decide to forgo multiple dust temperature fitting for well constrained, single dust temperature blackbody fits." + LE multiple blackbodies provide a more physical SED fit. then our derived emissivities. from the single blackbocly fits. could be uncerestimatect.," If multiple blackbodies provide a more physical SED fit, then our derived emissivities, from the single blackbody fits, could be underestimated." +"lead to a sharp increase in [Ba/Fe] (or [Ba/Eu]) against [Fe/H], as observed in the Fnx dSph.","lead to a sharp increase in [Ba/Fe] (or [Ba/Eu]) against [Fe/H], as observed in the Fnx dSph." +" To validate the above processes, we model two cases Galaxy and the Fnx dSph) to demonstrate how the (thedifferent IMFs change the path of chemical evolution between the elements, Ba, Eu and Fe."," To validate the above processes, we model two cases (the Galaxy and the Fnx dSph) to demonstrate how the different IMFs change the path of chemical evolution between the elements, Ba, Eu and Fe." + The basis for the model is that the galaxy is formed through an infall of material from outside., The basis for the model is that the galaxy is formed through an infall of material from outside. +" With this framework, the SFR is assumed to be proportional to the gas fraction with a constant rate coefficient such as v—0.4 Gyr-! for the Galaxy disk (Tsujimotoetal."," With this framework, the SFR is assumed to be proportional to the gas fraction with a constant rate coefficient such as $\nu$ =0.4 $^{-1}$ for the Galaxy disk \citep{Tsujimoto_10}." +" Here, v is the fraction of the gas mass that is2010).. converted into stars per Gyr."," Here, $\nu$ is the fraction of the gas mass that is converted into stars per Gyr." +" For the infall rate, we apply a formula that is proportional to texp(—t/tin) with a timescale of infall of Tin, which is assigned to 7,—5 Gyr for the Galaxy disk (Yoshiietal. 1996)."," For the infall rate, we apply a formula that is proportional to $t \exp(-t/\tau_{\rm in})$ with a timescale of infall of $\tau_{\rm in}$, which is assigned to $\tau_{\rm in}$ =5 Gyr for the Galaxy disk \citep{Yoshii_96}. ." +". For the Galactic halo, the values of (v, Tin)=(0.3, 0.1) are assigned for the duration of star formation Agr=0.5 Gyr, thus reproducing the abundance distribution function (ADF) of halo stars (Ryan&Norris1991)."," For the Galactic halo, the values of $\nu$, $\tau_{\rm in}$ )=(0.3, 0.1) are assigned for the duration of star formation $\Delta_{\rm SF}$ =0.5 Gyr, thus reproducing the abundance distribution function (ADF) of halo stars \citep{Ryan_91}." +". The Galaxy IMF is assumed to be a power-law mass spectrum with a slope of -1.35, e.g., a Salpeter IMF, with a mass range (mi, m,)=(0.05Meo, 50 (Tsujimotoetal.1997)."," The Galaxy IMF is assumed to be a power-law mass spectrum with a slope of -1.35, e.g., a Salpeter IMF, with a mass range $m_l$, $m_u$ )=(0.05, 50 ) \citep{Tsujimoto_97}." +". The IMF is always normalizedΜο) to unity between m, and m,, and is combined with the nucleosynthesis yields stated in the following paragraph as well as with the Fe yield of 0.64 from SNe Ia (Iwamotoetal.1999)."," The IMF is always normalized to unity between $m_l$ and $m_u$, and is combined with the nucleosynthesis yields stated in the following paragraph as well as with the Fe yield of 0.64 from SNe Ia \citep{Iwamoto_99}." +". It is assumed that the lifetime tr, of SN Ia progenitors spans over some range according to a distribution function ", It is assumed that the lifetime $t_{\rm Ia}$ of SN Ia progenitors spans over some range according to a distribution function $g(t_{\rm Ia})$. +"Here we assume that the fraction fri, of the stars that g(t14).eventually produce SNe Ia for 3—8Mo in the solar neighborhood is 0.05 with a box-shaped g(ti) for 0.5