ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 This gives a dynamical time of 0.8 Cyr. which is an underestimate if he tails do not lie in the plane of the sky: thus the tidal ails are ονOS Cvr old.," This gives a dynamical time of 0.8 Gyr, which is an underestimate if the tails do not lie in the plane of the sky; thus the tidal tails are $>0.8$ Gyr old."3 This lower limit is consistent with he age derived [from the fraction of galaxy light contained within the tails., This lower limit is consistent with the age derived from the fraction of galaxy light contained within the tails.4 The presence of two symmetric tidal tails is generally aken to be a signature of a recent major merger involving wo. approximately equal mass spiral galaxies (see e.g. 2)).," The presence of two symmetric tidal tails is generally taken to be a signature of a recent major merger involving two, approximately equal mass spiral galaxies (see e.g. \pcite{toomre72}) )."5 It the tidal features in Fig., If the tidal features in Fig.6 5. are indeed. genuine tidal tails hen we could. conclude that NGC 1700 has experienced a major merger during its recent history., \ref{fig:resid} are indeed genuine tidal tails then we could conclude that NGC 1700 has experienced a major merger during its recent history.7 Alternatively. if the eatures are merely plumes of tically disturbed material. the situation is less clear.," Alternatively, if the features are merely plumes of tidally disturbed material, the situation is less clear."8 While a major merger could not be ruled. out. the situation of a disc galaxy merging into an existing elliptical would be possible.," While a major merger could not be ruled out, the situation of a disc galaxy merging into an existing elliptical would be possible."9 We present in Fig., We present in Fig.10D δ the D1 colour histogram5 [for NGC 1700 GCs from the Ixeck data., \ref{fig:BIhist} the $B-I$ colour histogram for NGC 1700 GCs from the Keck data.11 Phe histogram appears bimodal with a blue peak at ο£=1.54-£0.05 and a second peak O4440.07 magnitudes recder at Bo4—1.98+£0.05., The histogram appears bimodal with a blue peak at $B-I=1.54\pm0.05$ and a second peak $0.44\pm0.07$ magnitudes redder at $B-I=1.98\pm0.05$.12 This bimodality does not appear to be an artifact of the data onning ancl is still present if the histogram bin boundaries are changed., This bimodality does not appear to be an artifact of the data binning and is still present if the histogram bin boundaries are changed.13 For the subsequent. discussion. anc analysis we define the population as those GC's possessing )s-DdX1.75 and the population with colours l5«D«X0., For the subsequent discussion and analysis we define the population as those GCs possessing $0.8<B-I\leq1.75$ and the population with colours $1.75<B-I<3.0$.14 A statistical analysis using the algorithm (Ashman. Bird ορ 1994). detects xmocdality in the distribution with z99 per cent confidence.," A statistical analysis using the algorithm (Ashman, Bird Zepf 1994) detects bimodality in the distribution with $>99$ per cent confidence."15 The algorithm assigned a colour cut between the blue and red populations of D./=Ls. thus confirming our initial visual estimate.," The algorithm assigned a colour cut between the blue and red populations of $B-I=1.8$, thus confirming our initial visual estimate."16 Phe ο4 distribution of GC's in the Milky Way is also shown in Fig., The $B-I$ distribution of GCs in the Milky Way is also shown in Fig.17 S. (shaded area)., \ref{fig:BIhist} (shaded area).18 The peak of this distribution is at (2ZJ)o~1.5 which is similar to the peak of the blue population of NGC 1700., The peak of this distribution is at $(B-I)_0\sim1.5$ which is similar to the peak of the blue population of NGC 1700.19 Is the bimocality of the D.7 histogram evidence for two distinct. GC populations in NGC 17007, Is the bimodality of the $B-I$ histogram evidence for two distinct GC populations in NGC 1700?20 In order to address this question. one has to consider the expected number of contaminating sources within our final sample.," In order to address this question, one has to consider the expected number of contaminating sources within our final sample."21 As the number of predicted stars colour selection is small. we can immediately conclude that the contamination bv foreground stars in our final sample is negligible.," As the number of predicted stars colour selection is small, we can immediately conclude that the contamination by foreground stars in our final sample is negligible."22 Another source of contamination is background. galaxies., Another source of contamination is background galaxies.23 Our automatic and. visual checks have removed. obvious ealaxies but it is possible that small. unresolved background ealaxies remain.," Our automatic and visual checks have removed obvious galaxies but it is possible that small, unresolved background galaxies remain."24 For our mean D magnitude of 24.5. we expect to be detecting sources oul to à mean redshift: of ~OS (7).," For our mean $B$ magnitude of 24.5, we expect to be detecting sources out to a mean redshift of $z\sim0.8$ \cite{kookron92}."25 At this redshift’ all morphological tvpes of galaxies (with the exception of irregular types) have typical Bf colours in excess of 2.5., At this redshift all morphological types of galaxies (with the exception of irregular types) have typical $B-I$ colours in excess of 2.5.26 This is significantly receler than the peak of the red population and we can thus be fairly, This is significantly redder than the peak of the red population and we can thus be fairly27"C. 1, Odean? The discovery of a possible accelerated expansion of our present uuilverse from ype Ia supernovae (|1])). is perhaps the most remarkable cosmological finding of recent vears.","C. J. $^{2}$ } The discovery of a possible accelerated expansion of our present universe from type Ia supernovae \cite{super1}) ), is perhaps the most remarkable cosmological finding of recent years."28" Furthermore. the flatucss of the universe (O5,= 1) determined w Cosmic Microwave Backeromnd observations (5). togheter with the low natter density (Quarter,< 0.1) inferred from: Large Scale Structure. ([3]}) are sugeesting the presence of a cosmological coustant with high statistical sjeuificauce."," Furthermore, the flatness of the universe $\Omega_{tot}=1$ ) determined by Cosmic Microwave Background observations \cite{flat}) ), togheter with the low matter density $\Omega_{matter}<0.4$ ) inferred from Large Scale Structure \cite{lowmat}) ) are suggesting the presence of a cosmological constant with high statistical significance."29 Towever. the CAIB|LSS result relies ou the assumption of a articular class of models based on adiabatic prinordial fluctuations. cold dark matter and a cosmological constant as dark cucrey compoucut.," However, the CMB+LSS result relies on the assumption of a particular class of models, based on adiabatic primordial fluctuations, cold dark matter and a cosmological constant as dark energy component."30 Iu the ollowing we will refer to this class of model as A-Cold Dark Matter (A-CDAD., In the following we will refer to this class of model as $\Lambda$ -Cold Dark Matter $\Lambda$ -CDM).31 This weak poiut. shared by most of the current studies. should not be overlooked: it wight be possible that a different solution to the dark euerey scenario than a cosmological coustaut cau affect the CMD|LSS determination.," This weak point, shared by most of the current studies, should not be overlooked: it might be possible that a different solution to the dark energy scenario than a cosmological constant can affect the CMB+LSS determination."32 It is therefore Πιο to investigate if the actual CMD data is in complete agrecnent with the A-CDAL sccuario or if we are losing relevaut scientific informations by restricting the current analysis to a subset of models., It is therefore timely to investigate if the actual CMB data is in complete agreement with the $\Lambda$ -CDM scenario or if we are losing relevant scientific informations by restricting the current analysis to a subset of models.33 Tere first we check to what extent modifications to the standard A-CDÀ scenario areneeded by current CMD observations with a model-indepenuden analysis obtained fitting the actual data with a phenomenological fiction au characterizing the observed multiple peaks through a Monte Carlo Markov Chain CMCMXC) algorithm. which allows us to investigate a large uuuber of parameter simultancously (15 im our case).," Here first we check to what extent modifications to the standard $\Lambda$ -CDM scenario are by current CMB observations with a model-independent analysis obtained fitting the actual data with a phenomenological function and characterizing the observed multiple peaks through a Monte Carlo Markov Chain (MCMC) algorithm, which allows us to investigate a large number of parameter simultaneously $15$ in our case)."34 We found a very good agreemenu between the position. relative amplitude aud width of the peaks obtaiue through the model independent approach with the same features expected in a d[-purzuneters model template of A-CDM spectra.," We found a very good agreement between the position, relative amplitude and width of the peaks obtained through the model independent approach with the same features expected in a $4$ -parameters model template of $\Lambda$ -CDM spectra."35 Second. since the A-CDN is a good fit to the CMD data. we then move to other possible candidates for the dark energv component to see what kind of constraint we can obtain.," Second, since the $\Lambda$ -CDM is a good fit to the CMB data, we then move to other possible candidates for the dark energy component to see what kind of constraint we can obtain."36 The common characteristic of alternative scenarios to a cosmological constant.," The common characteristic of alternative scenarios to a cosmological constant,"37reduce the dimensionality of the feature space by combining redundant features. e.g. the equivalent widths of the Balmer lines to a sun of equivalent widths.,"reduce the dimensionality of the feature space by combining redundant features, e.g. the equivalent widths of the Balmer lines to a sum of equivalent widths."38 The remaimine set of features is then evaluated with the iuethods described in Sect. ??.., The remaining set of features is then evaluated with the methods described in Sect. \ref{Sect:Evalu}.39 For supervised classification. a is needed.," For supervised classification, a is needed."40 For our purposes. we define a learuiug sample to be a κο of n; objects for which the feature vectors ave known. and for which it is known to what class they belong.," For our purposes, we define a learning sample to be a set of $n_{l}$ objects for which the feature vectors are known, and for which it is known to what class they belong."41⊺∐↸∖↴∖↴↸∖≼⊳↕⋜↧↴∖∷∖↴↸∖↴∖↴↸⊳⋜⋯↴⋝↸∖≺∐∖↴∐↸∖≺↧∙↸∖∙∶↴↜⊾⋅⋅↴⋝∙↖⇁∶↴∙↕⋅⋯∏≻↕∐∩⋜↧∖↴↸∖↑∪↕ ∙ ∪↴⋝⋅↿≱↸∖↸⊳↑∖↴⋜↧↸⊳↸⊳∪↥⋅≼∐∐∩⊾↑∪↑↕∐∖∐⋅↴∖↴↑↸∖∐⋜∐⋅↻⋜∐⋅⋜↧⋯↸∖↑↸∖↥⋅↴∖↴↸∖∩⊺↥∟↕↕⋜∏⋝↸∖↕≋↸∖↸⊳↑∶↕≻↸∖↸⊳↕↴∖↴↕≺≻∐↕⊰∏↕↸∖↴∖↴ ↕∪∶↴∙⊾∙↙∕⊪⊟∖∐∩∪↥⋝↖⇁⋯⋜↧∐⋯∐↖↽⋜↕∖↴∖↴↕∩⊾∐↕∐∩⊾↸⊳↕⋜↕∖↴∖↴↸∖∖↴↑∪⋜↧∖↴↸∖↑ of spectra by comparison with reference objects.," These classes can be defined, e.g., by grouping a set of objects according to their stellar parameters (e.g. $T_{\mbox{\scriptsize eff}}$, $\log g$, [Fe/H]), or by manually assigning classes to a set of spectra by comparison with reference objects."42 With the help of a learning sample. information on the class- probability deusities plaO;) can be oOgained.," With the help of a learning sample, information on the class-conditional probability densities $p(\vec{x}|\Omega_j)$ can be gained."43 e ∟∕↙∣↨↕∕⋅↕↴∖↴↑∐↸∖⋯⋅≺⋔⋜⋔∐↕↑∙↖↽↑∪∪↴⋝↴∖↴↸∖↥⋅↖↸∖≼↧↕⋟↸∖⋜↕⊓∐⋅↸∖↖↽↸∖↸⊳↑∪↥⋅↕∐⋜↧↥⋅↸∖⋅↿≱↸∖↸⊳↑↕∪↕⊔↴∏↸∖∙ the range ax...z|dx iu the class O;., $p(\vec{x}|\Omega_j)d\!\vec{x}$ is the probability to observe a feature vector in the range $\vec{x}\dots \vec{x}+d\!\vec{x}$ in the class $\Omega_j$.44 We inspected the ouc-dimensional classconditional larisprobability distributions of the classes coveredby the saluples used iu this work. aud qualitatively found their shapes to agree well with Gaussians.," We inspected the one-dimensional class-conditional probability distributions of the classes covered by the learning samples used in this work, and qualitatively found their shapes to agree well with Gaussians."45 We hence model pla]Q;)by multivariate normal distributions. 1.6.. wherej denotes class umber. 44; tho mean feature vector of class O5. aud Xj the covariance matrix. of class Q;. ⊀≚↸⊳↸∖∐," We hence model $p(\vec{x}|\Omega_j)$ by multivariate normal distributions, i.e., where $j$ denotes class number, $\vec{\mu}_j$ the mean feature vector of class $\Omega_j$, and $\Sigma_j$ the covariance matrix of class $\Omega_j$."46⊓⋅⋜↧↕↕↴∖∷∖↴⋯∖↕∐⋜⋯↑∪⋯⋜↧↑↕↸⊳↸⊳↕⋜↕↴∖↴↴∖↴↕∐↸⊳⋜↕⊓∪∐↕↴∖↴↑↕∐∖ construction of a decision rule which is optimal for the given classification problem., A central issue in automatic classification is the construction of a decision rule which is optimal for the given classification problem.47 In the WES. we use three decision rules: the Baves rule. a niuinun cost rule. and," In the HES, we use three decision rules: the Bayes rule, a minimum cost rule, and a rejection rule."48" In the ""pure"" DS phase the star will be puffier for a higher (o0)/m, ratio, as can be seen from the left panel of Fig.4."," In the “pure” DS phase the star will be puffier for a higher $\sv/m_{\chi}$ ratio, as can be seen from the left panel of \ref{radius}."49. This is expected due to the much higher DM heating in that case: a larger radius is required to balance the DM energy production and the radiated luminosity. which scales as /2?.," This is expected due to the much higher DM heating in that case: a larger radius is required to balance the DM energy production and the radiated luminosity, which scales as $R^2$."50" For instance. in the boosted AH4 case the maximum radius is at about 2x 10'cem, whereas for the 100 GeV non-boosted WIMP, the DS will have a maximum radius of 10! cm."," For instance, in the boosted AH4 case the maximum radius is at about $2\times 10^{14}$ cm, whereas for the $100$ GeV non-boosted WIMP, the DS will have a maximum radius of $10^{14}$ cm."51 However. as mentioned before. the KH contraction will set in carlier in the boosted case.," However, as mentioned before, the KH contraction will set in earlier in the boosted case."52 This phase corresponds to the sharp decrease in radius in Fig.4., This phase corresponds to the sharp decrease in radius in \ref{radius}.53". The final radii, as the DS enters the ZAMS are similar in both cases, at around 6x10! em."," The final radii, as the DS enters the ZAMS are similar in both cases, at around $6\times 10^{11}$ cm."54"are no longer in the realm of cosmology. but are dealing with ""messy"" astrophysics.","are no longer in the realm of cosmology, but are dealing with “messy” astrophysics."55 Fortunately. there is an alternative way to study the dark matter distribution.," Fortunately, there is an alternative way to study the dark matter distribution."56 ? already note that the blow-out process can only be effective in dwarf galaxies., \citet{Navarro:1996p192} already note that the blow-out process can only be effective in dwarf galaxies.57 In more massive galaxies. such as spiral galaxies. the potential well is too deep to efficiently remove the gas.," In more massive galaxies, such as spiral galaxies, the potential well is too deep to efficiently remove the gas."58 Finding and investigating more massive dark-matter dominated galaxies may therefore be a more effective way to explore the core/cusp Issue., Finding and investigating more massive dark-matter dominated galaxies may therefore be a more effective way to explore the core/cusp issue.59 These galaxies. fortunately. do exist. and are called Low Surface Brightness (LSB) galaxies.," These galaxies, fortunately, do exist, and are called Low Surface Brightness (LSB) galaxies."60 The term LSB galaxies is used here to indicate late-type. gas-rich. dark-matter-dominated disk galaxies.," The term LSB galaxies is used here to indicate late-type, gas-rich, dark-matter-dominated disk galaxies."61 Their optical component is well-described by an exponential disk with an (extrapolated) inclination-corrected central surface brightness fainter than j/op~23 mag arcsec (???)..," Their optical component is well-described by an exponential disk with an (extrapolated) inclination-corrected central surface brightness fainter than $\mu_{0,B} \sim 23$ mag $^{-2}$ \citep{McGaugh:1994p947,McGaugh:1995p958,deBlok:1995p952}."62 Despite their low surface brightness. their integrated luminosity is a few magnitudes brighter than that of late-type dwarf galaxies (Mp—18 to ~—20 for LSB galaxies. as opposed to Mp=—16 for the dwarf galaxies).," Despite their low surface brightness, their integrated luminosity is a few magnitudes brighter than that of late-type dwarf galaxies $M_B \sim -18$ to $\sim -20$ for LSB galaxies, as opposed to $M_B \ga -16$ for the dwarf galaxies)."63 As noted. they are gas-rich (My/LgZV: 2??22)). and their interstellar medium has a low metallicity (22)...," As noted, they are gas-rich $M_{HI}/L_B \ga 1$; \citealt{Schombert:1992p1053,McGaugh:1997p1066,Schombert:2001p1060}) ), and their interstellar medium has a low metallicity \citep{McGaugh:1994p950,deBlok:1998p1076}."64 Their optical appearance is dominated by an exponential disk with a young. blue population. with little evidence for a dominant old population.," Their optical appearance is dominated by an exponential disk with a young, blue population, with little evidence for a dominant old population."65 Additionally. these galaxies do not have large dominant bulges. and seem to have had a star formation history with only sporadic star formation (???)..," Additionally, these galaxies do not have large dominant bulges, and seem to have had a star formation history with only sporadic star formation \citep{vanderHulst:1993p956,vandenHoek:2000p1081,Gerritsen:1999p1104}."66 Central light concentrations. if present at all. tend to be only fractionally brighter than that of the extrapolated exponential disk.," Central light concentrations, if present at all, tend to be only fractionally brighter than that of the extrapolated exponential disk."67 In terms of their spatial distribution. they are found on the outskirts of the large scale structure filaments (?2)..," In terms of their spatial distribution, they are found on the outskirts of the large scale structure filaments \citep{Bothun:1993p973,Mo:1994p949}."68" In short. most observational evidence indicates that these galaxies have had a quiescent evolution. with little evidence for major merging episodes. interactions. or other processes that might have stirred up the baryonic and dark matter (see also ??.,"," In short, most observational evidence indicates that these galaxies have had a quiescent evolution, with little evidence for major merging episodes, interactions, or other processes that might have stirred up the baryonic and dark matter (see also \citealt{Bothun:1997p937,Impey:1997p1001}."69 As for the term “LSB galaxies”. there is some confusion in the literature about what type of galaxies it applies to.," As for the term “LSB galaxies”, there is some confusion in the literature about what type of galaxies it applies to."70 The type of LSB galaxies most commonly studied. in particular with regards to the core/cusp controversy. are the late-type LSB galaxies whose properties are described above.," The type of LSB galaxies most commonly studied, in particular with regards to the core/cusp controversy, are the late-type LSB galaxies whose properties are described above."71 The other type of LSB galaxies often discussed in the literature are the massive. early-type. bulge-dominated LSB galaxies.," The other type of LSB galaxies often discussed in the literature are the massive, early-type, bulge-dominated LSB galaxies."72 These galaxies have properties entirely different from the late-type LSB galaxies (??)..," These galaxies have properties entirely different from the late-type LSB galaxies \citep{Sprayberry:1995p977,Pickering:1997p988}."73 The massive LSB galaxies are a lot more luminous and their optical appearance is dominated by a bright central bulge with a clearly detectable old population (?).., The massive LSB galaxies are a lot more luminous and their optical appearance is dominated by a bright central bulge with a clearly detectable old population \citep{Beijersbergen:1999p1156}.74 Many of them have low-level AGN activity (?).., Many of them have low-level AGN activity \citep{Schombert:1998p1225}.75 All indications are that the evolution of these galaxies has been entirely different from that of late-type LSB galaxies: if anything. they resemble SO galaxies with extended disks. rather than late-type galaxies.," All indications are that the evolution of these galaxies has been entirely different from that of late-type LSB galaxies: if anything, they resemble S0 galaxies with extended disks, rather than late-type galaxies."76 The presence of the dominant bulge also indicates that their central dynamies are likely to be dominated by the stars. rather than dark matter.," The presence of the dominant bulge also indicates that their central dynamics are likely to be dominated by the stars, rather than dark matter."77 In the following. the term “LSB galaxies” therefore refers to type LSB galaxies only.," In the following, the term “LSB galaxies” therefore refers to late-type LSB galaxies only."78 The first detailed studies of large samples of LSB galaxies soon led to the picture of them being unevolved. gas-rich disk galaxies. as described above.," The first detailed studies of large samples of LSB galaxies soon led to the picture of them being unevolved, gas-rich disk galaxies, as described above."79 The observation that they followed the same Tully-Fisher relation as normal galaxies (2) was intriguing. as this implied they had to be dark-matter dominated.," The observation that they followed the same Tully-Fisher relation as normal galaxies \citep{Zwaan:1995p951} was intriguing, as this implied they had to be dark-matter dominated."80 Follow-up radio synthesis observations in HI (?)) soon confirmed this., Follow-up radio synthesis observations in HI \citep{deBlok:1996p5} soon confirmed this.81" Though the resolution of these early observations was limited. the derived rotation curves clearly resembled those of late-type dwarf and ""normal"" disk galaxies: a slow rise. followed by à gradual flattening."," Though the resolution of these early observations was limited, the derived rotation curves clearly resembled those of late-type dwarf and “normal” disk galaxies: a slow rise, followed by a gradual flattening."82 When expressed in terms of scale lengths. the rotation curves of LSB and HSB galaxies of equal luminosity turned out to be very similar. indicating that LSB galaxies are in general low density objects (?)..," When expressed in terms of scale lengths, the rotation curves of LSB and HSB galaxies of equal luminosity turned out to be very similar, indicating that LSB galaxies are in general low density objects \citep{deBlok:1996p44}."83 Mass models derived using the rotation curves clearly showed that for reasonable assumptions for the stellar mass-to-light ratio. Y.. the dynamics of LSB galaxies had to be dominated by dark matter (?)..," Mass models derived using the rotation curves clearly showed that for reasonable assumptions for the stellar mass-to-light ratio, $\Upsilon_\star$, the dynamics of LSB galaxies had to be dominated by dark matter \citep{deBlok:1997p22}."84 Assuming that the stars had to dominate the dynamics in the inner parts (the so-called maximum disk solution) led to unrealistically high YT. values. and. even when taken at face value. still showed a need for a moderate amount of dark matter at small radii (see also 2)).," Assuming that the stars had to dominate the dynamics in the inner parts (the so-called maximum disk solution) led to unrealistically high $\Upsilon_{\star}$ values, and, even when taken at face value, still showed a need for a moderate amount of dark matter at small radii (see also \citealt{McGaugh:1998p34}) )."85 The distribution of the dark matter at first sight seemed similar to that in gas-rich dwarf galaxies (?).., The distribution of the dark matter at first sight seemed similar to that in gas-rich dwarf galaxies \citep{deBlok:1997p22}.86 Because of the limited resolution of the data. ?— did not attempt fits with the NFW model. but noted that the halos had to be extended. diffuse and low density.," Because of the limited resolution of the data, \citet{deBlok:1997p22} did not attempt fits with the NFW model, but noted that the halos had to be extended, diffuse and low density."87 A first attempt at comparing the HI. data with CDM predictions was made by ?.., A first attempt at comparing the HI data with CDM predictions was made by \citet{McGaugh:1998p34}.88 Rather than making fits to the rotation curve. they simply assumed that the typical velocity Vsoo of the halo had to equal the outer (maximum) rotation velocity of the galaxy.," Rather than making fits to the rotation curve, they simply assumed that the typical velocity $V_{200}$ of the halo had to equal the outer (maximum) rotation velocity of the galaxy."89 The strict cosmological relation between ο and ου then automatically yields a value of ο compatible with ACDM., The strict cosmological relation between $c$ and $V_{200}$ then automatically yields a value of $c$ compatible with $\Lambda$ CDM.90 Adopting these values. the resulting halo rotation curve turned out to be very different from the observed curve. in a similar way as the ? analysis: the NEW curve is too steep and rises too quickly in the inner parts.," Adopting these values, the resulting halo rotation curve turned out to be very different from the observed curve, in a similar way as the \citet{Moore:1994p86} analysis: the NFW curve is too steep and rises too quickly in the inner parts."91 The only way the halo curve could be made to resemble the observed curve. was by abandoning the cosmological (c.σου) relation.," The only way the halo curve could be made to resemble the observed curve, was by abandoning the cosmological $(c,V_{200})$ relation."92 Similar conclusions. were derived by ?.., Similar conclusions were derived by \citet{Cote:2000p77}.93 They presented high-resolution HI observations of dwarfs in the nearby Centaurus and Sculptor groups. and noted that the derived rotation curves did not agree with the NFW model.," They presented high-resolution HI observations of dwarfs in the nearby Centaurus and Sculptor groups, and noted that the derived rotation curves did not agree with the NFW model."94 A possible explanation that was soon put forward was that there were still unrecognized systematic effects in the data. that would give the false impression of a core-like behaviour.," A possible explanation that was soon put forward was that there were still unrecognized systematic effects in the data, that would give the false impression of a core-like behaviour."95 Initially. attention focussed on the resolution of the ?| HI observations.," Initially, attention focussed on the resolution of the \citet{deBlok:1996p5} HI observations."96 These had beam sizes of ~ 15’. resulting in the HI disks of the LSB galaxies investigated having a diameter of between 3 and 18 independent beams.," These had beam sizes of $\sim 15''$ , resulting in the HI disks of the LSB galaxies investigated having a diameter of between 3 and 18 independent beams."97" This limited resolution can potentially affect the shapes of the rotation curves through a process called ""beam smearing”. as also mentioned in ?.."," This limited resolution can potentially affect the shapes of the rotation curves through a process called “beam smearing”, as also mentioned in \citet{deBlok:1996p5}."98 In observations with limited resolution. the beam smearing process decreases the observed velocities (compared to the true velocities). and in extreme cases can turn any steeply rising rotation curve into a slowly rising solid-body one.," In observations with limited resolution, the beam smearing process decreases the observed velocities (compared to the true velocities), and in extreme cases can turn any steeply rising rotation curve into a slowly rising solid-body one."99 This would therefore give the impression of a core being present in the data. while the true distribution could still be cuspy.," This would therefore give the impression of a core being present in the data, while the true distribution could still be cuspy."100 In their paper. ? argued. through modelling of these beam smearing effects. as well as the direct detections of steeply rising rotation curves m the data. that while some beam smearing was indeed present. the effect was not strong enough to completely “hide” the dynamical signature of a cusp. and concluded that the data were consistent with the existence of dark matter cores.," In their paper, \citet{deBlok:1997p22} argued, through modelling of these beam smearing effects, as well as the direct detections of steeply rising rotation curves in the data, that while some beam smearing was indeed present, the effect was not strong enough to completely “hide” the dynamical signature of a cusp, and concluded that the data were consistent with the existence of dark matter cores."101 An alternative interpretation was given in?)who used the ? data. along with high-resolution literature rotation curves," An alternative interpretation was given in \citet{vandenBosch:2000p188} who used the \citet{deBlok:1997p22} data, along with high-resolution literature rotation curves"102et al.,et al.103 Then Chandra follow up observations of the region detected three sources (Tomsick et al., Then Chandra follow up observations of the region detected three sources (Tomsick et al.104" 2008): the same source detected by XRT, a new one located inside the new ISGRI error circle (J174435.4-274453, diamond point) reported in the 4th IBIS catalogue and a third one just at its border (J174427.3-274324 box Within the INTEGRAL/IBIS error circle detects only one source at a position compatible with that of the Chandra source J174435.4-274453 indicating that this could be a possible counterpart."," 2008): the same source detected by XRT, a new one located inside the new ISGRI error circle (J174435.4-274453, diamond point) reported in the 4th IBIS catalogue and a third one just at its border (J174427.3-274324 box Within the INTEGRAL/IBIS error circle detects only one source at a position compatible with that of the Chandra source J174435.4-274453 indicating that this could be a possible counterpart."105" The source spectrum is poorly sampled by XMM as this is only a 4.6 sigma detection but we were able to estimate the 0.2-12 keV observed flux of 8 x 10:14 erg cm? s! fully compatible with that of Chandra of 7 x10!* erg cm? s. However, we note that within the IBIS error box there is also an XMM-Slew source: XMMSL1 J174429.4-274609 (circle point in the figure) whose coordinates are reported in table 2."," The source spectrum is poorly sampled by XMM as this is only a 4.6 sigma detection but we were able to estimate the 0.2-12 keV observed flux of 8 $\times$ $^{-14}$ erg $^{-2}$ $^{-1}$ fully compatible with that of Chandra of $\sim$ 7 $\times$ $^{-14}$ erg $^{-2}$ $^{-1}$ However, we note that within the IBIS error box there is also an XMM-Slew source: XMMSL1 J174429.4-274609 (circle point in the figure) whose coordinates are reported in table 2."106 This source with a 0.2-12 keV flux of 1.64 x 1077? erg cm? s! is the brightest in the high energy error circle and it is also extremely variable as it was seen only once out of four observations of the region made at different epochs., This source with a 0.2-12 keV flux of 1.64 $\times$ $^{-12}$ erg $^{-2}$ $^{-1}$ is the brightest in the high energy error circle and it is also extremely variable as it was seen only once out of four observations of the region made at different epochs.107" This source is associated only to an infrared object (2MASS 17442946-2746114) within the XMM-Slew (5.1"") positional uncertainty with J, H and K magnitudes of 15.13, 12.88 and 12.85 The XMM upper limit on the source flux is 0.4 x 107% erg οπι s! in the same waveband implying a dynamic range of around IGR J17445-2747 is reported in the 4th IBIS catalogue as a transient bursting source since it was significantly detected at ~ 130 level (20-100 keV) only during its outburst activity lasting for a total of ~ 30 days and reaching a peak flux of ~ 30 mCrab or 4.6x 10:10 erg cm s! (20-100 keV)."," This source is associated only to an infrared object (2MASS 17442946-2746114) within the XMM-Slew $^{\prime\prime}$ ) positional uncertainty with J, H and K magnitudes of 15.13, 12.88 and 12.85 The XMM upper limit on the source flux is 0.4 $\times$ $^{-13}$ erg $^{-2}$ $^{-1}$ in the same waveband implying a dynamic range of around IGR J17445-2747 is reported in the 4th IBIS catalogue as a transient bursting source since it was significantly detected at $\sim$ $\sigma$ level (20–100 keV) only during its outburst activity lasting for a total of $\sim$ 30 days and reaching a peak flux of $\sim$ 30 mCrab or $\times$ $^{-10}$ erg $^{-2}$ $^{-1}$ (20–100 keV)."108" On the contrary the source was not ?detected in the total dataset for an on-source exposure time of — 7.3 Ms, providing an upper limit to the flux of 0.1 mCrab (20-40 keV) and resulting in a dynamical range of ~ 300."," On the contrary the source was not detected in the total dataset for an on-source exposure time of $\sim$ 7.3 Ms, providing an upper limit to the flux of 0.1 mCrab (20–40 keV) and resulting in a dynamical range of $\sim$ 300."109" Therefore, given the transient nature of both IGR J17445-2747 and XMMSL1 J174429.4-274609, we conclude that the two sources are very likely associated."," Therefore, given the transient nature of both IGR J17445-2747 and XMMSL1 J174429.4-274609, we conclude that the two sources are very likely associated."110 IGR J18538-0102 is a newly discovered INTEGRAL source listed in the fourth IBIS survey (Bird et al., IGR J18538-0102 is a newly discovered INTEGRAL source listed in the fourth IBIS survey (Bird et al.111 2010)., 2010).112 Recently Stephen et al (2010) provided an improved position for the source using the association with an XMM Slew catalogue source (2XMM J185348.4-010229)., Recently Stephen et al (2010) provided an improved position for the source using the association with an XMM Slew catalogue source (2XMM J185348.4-010229).113 These authors also noted that IGR J18538-0102 is spatially coincident with a hot spot in the supernova remnant candidate G32.1-0.9 detected in X-rays by ROSAT and ASCA (Folgheraiter et al., These authors also noted that IGR J18538-0102 is spatially coincident with a hot spot in the supernova remnant candidate G32.1-0.9 detected in X-rays by ROSAT and ASCA (Folgheraiter et al.114 1997): but it has a much harder spectrum and higher absorption than observed in the supernova remnant., 1997): but it has a much harder spectrum and higher absorption than observed in the supernova remnant.115 This suggests the possibility that IGR J18538-0102 could be a more distant Galactic source or a background AGN and its alignment with G32.1-0.9 is only coincidental., This suggests the possibility that IGR J18538-0102 could be a more distant Galactic source or a background AGN and its alignment with G32.1-0.9 is only coincidental.116 Halpern and Gotthelf (2010) then reported on the XMM observation used here and further discussed a possible infrared/optical counterpart of the source., Halpern and Gotthelf (2010) then reported on the XMM observation used here and further discussed a possible infrared/optical counterpart of the source.117" We re-analysed the XMM data in order to combine them with IBIS ones, performing for the first time a broad band spectral analysis and discussing further the nature of this object."," We re-analysed the XMM data in order to combine them with IBIS ones, performing for the first time a broad band spectral analysis and discussing further the nature of this object."118 The EPIC 0.2-12 keV image shown in figure 9 with the INTEGRAL error circle indicates that there is only one X-ray counterpart., The EPIC 0.2-12 keV image shown in figure 9 with the INTEGRAL error circle indicates that there is only one X-ray counterpart.119" Archival searches within the positional uncertainty finds the infrared object (2MASS 18534847-0102295) discussed by Halpern and Gotthelf which has J, H, and K magnitudes of 14.16, 14 and 12.50 respectively."," Archival searches within the positional uncertainty finds the infrared object (2MASS 18534847-0102295) discussed by Halpern and Gotthelf which has J, H, and K magnitudes of 14.16, 14 and 12.50 respectively."120" It coincides with the USNO-B1 0889-0406090 object (R= 15.2 magnitudes) and with the soft X-ray source 1RXH J185348.2-010228 detected by the Next, we concentrated on broad band spectral"," It coincides with the USNO-B1 0889-0406090 object (R= 15.2 magnitudes) and with the soft X-ray source 1RXH J185348.2-010228 detected by the Next, we concentrated on broad band spectral"121For the MID sample with 35 bandpowers and 5 parameters. V7=21.,"For the MID sample with 35 bandpowers and 5 parameters, $\chi^2 = 21$."122 We find 0.14. in good agreement with the values reported in ?..," We find $k_{BAO} = 0.14$ , in good agreement with the values reported in \citet{eisenstein/seo/white:2007}."123 In Fig., In Fig.124 5 we show that the Path) term accounts for the barvonic features in. {ο(Ας and the polynomial in Á& adequately lits the smooth correction lor the. MID sample.while halolit underestimates the smooth correction by ~4% at &=0.2.," \ref{fig:DMnonlinear3} we show that the $P_{\rm smear}(k)$ term accounts for the baryonic features in $P_{DM}(k)$, and the polynomial in $k$ adequately fits the smooth correction for the MID sample,while halofit underestimates the smooth correction by $\sim 4\%$ at $k=0.2$ ."125 The NEAR and FAR fits are similar., The NEAR and FAR fits are similar.126 In Table 3. we list [its for the NEAR. MID. and FAR power spectra out to a maximum A of 0.2 and 0.4 {Mpeή.," In Table \ref{table:nonlinearfits} we list fits for the NEAR, MID, and FAR power spectra out to a maximum $k$ of 0.2 and 0.4 $h \; {\rm Mpc}^{-1}$."127 When hoe54=0.2 hMpec‘only the first three terms in the polvnomial expansion are necessary [or a good Fig.," When $k_{max,fit} = 0.2$ $h \; {\rm Mpc}^{-1}$, only the first three terms in the polynomial expansion are necessary for a good Fig."128 6 shows diagonal elements of the normalized covariance matrix. Cy;/P(h;)?.," \ref{fig:diagcov} shows diagonal elements of the normalized covariance matrix, $C_{ii}/\bar{P}(k_i)^2$."129 We estimate (he errors from (he diagonal variances (Eqn. 15)):, We estimate the errors from the diagonal variances (Eqn. \ref{cijerrDM}) );130 these may nol capture the (rue errors since off-diagonal elements should be present in the &-point function as well., these may not capture the true errors since off-diagonal elements should be present in the 8-point function as well.131 Nevertheless. when we use these error estimates to compute 4? for the model in Eqn. 13..," Nevertheless, when we use these error estimates to compute $\chi^2$ for the model in Eqn. \ref{cijmodel},"132 we find 4?=1600 for 1296 degrees of freedom (0<hk 0.4): if we restrict the covariance matrix to the 196 elements with both & bands between 0.056 and 0.21. we find 4?=262.," we find $\chi^2 = 1600$ for 1296 degrees of freedom $0 \leq k \leq 0.4$ ); if we restrict the covariance matrix to the 196 elements with both $k$ bands between 0.056 and 0.21, we find $\chi^2 = 262$."133 In (his case there are no [vee parameters and we deem the model a reasonable fit., In this case there are no free parameters and we deem the model a reasonable fit.134 If we allow the amplitude of the beat coupling term to vary. we find a best fit value 0.96 for the [ull matrix (47= 1564) and 0.84 for the 0.056<fh0.21 subsample (47= 218).," If we allow the amplitude of the beat coupling term to vary, we find a best fit value 0.96 for the full matrix $\chi^2 = 1564$ ) and 0.84 for the $0.056 \leq k \leq 0.21$ subsample $\chi^2 = 218$ )."135 We note that for the DC mode realizations of our 42 simulations. thevariance is a factor of 0.83 lower (han the expected variance (in agreement wilh the expected random variation for a single mocle. B-sim1= 15%).," We note that for the DC mode realizations of our 42 simulations, thevariance is a factor of 0.83 lower than the expected variance (in agreement with the expected random variation for a single mode, $N_{sim}^{-1/2} = 15\%$ )."136 We conclude that Eqn., We conclude that Eqn.137 19 is an excellent lit to our dark matter covariance Another point of interest in Fig., \ref{cijmodel} is an excellent fit to our dark matter covariance Another point of interest in Fig.138 G is that the inverse of the diagonal elements of the inverse covariance matrix are nearly equal to the Gaussian expectation (dashed curve)., \ref{fig:diagcov} is that the inverse of the diagonal elements of the inverse covariance matrix are nearly equal to the Gaussian expectation (dashed curve).139 This means (hal while the beat-coupling does not introduce additional errors on the measurement ol the bandpowers. the measured values will be covariant.," This means that while the beat-coupling does not introduce additional errors on the measurement of the bandpowers, the measured values will be covariant."140 However. for a beat-coupling term in (he form of Eqn. 13..," However, for a beat-coupling term in the form of Eqn. \ref{cijmodel},"141 only information on the overall amplitude of P(/) is lost., only information on the overall amplitude of $P(k)$ is lost.142 However. large scale structure analvses traditionally mareinalize over (he;unplitude of (f). since ox and bias are," However, large scale structure analyses traditionally marginalize over theamplitude of $P(k)$ , since $\sigma_8$ and bias are"143Due to tle sensitive dependence of chaotic systems on initial conditions. their yehavior over sufficientv long times is unpredictable in practice. even though the uuderlyiug dyuamics is ceterministic.,"Due to the sensitive dependence of chaotic systems on initial conditions, their behavior over sufficiently long times is unpredictable in practice, even though the underlying dynamics is deterministic."144 Iustead of attempting to accurately describe a phase space trajecto'N over a loug duration. it makes more sense to try to calculate statistical properties of the system. such as equal time moments anc he frequency with which the system coordinates lie within different regions o. phase space.," Instead of attempting to accurately describe a phase space trajectory over a long duration, it makes more sense to try to calculate statistical properties of the system, such as equal time moments and the frequency with which the system coordinates lie within different regions of phase space."145 Typically. statistical )'operties are caleulated by direct numerical simulation.," Typically, statistical properties are calculated by direct numerical simulation."146 The evolution ol the αν1anuical SVsem is observed oLa computer. starting with a particular iuljal condition. al dtle staIntics are σέuputed (ror1 averages over data poliuts generated at reetular time iuΟΥΝεils.," The evolution of the dynamical system is observed on a computer, starting with a particular initial condition, and the statistics are computed from averages over data points generated at regular time intervals."147 It IS assuimed (that the result COLVverges ο tlie exac statistics fast compared to the the ea Wwich nuneric ο) are alljXified by t1ο chaotic iature of the system., It is assumed that the result converges to the exact statistics fast compared to the the rate at which numerical errors are amplified by the chaotic nature of the system.148 FreLLL all aestheti yoint of view. direct. nunjerical simuilation is not an appealing way to πριte staIntIcs. si'e this approacl1 is not foruulated nOev dn terms of the variables oue is “Ulal vd19ο»ed in. amely the statistical quaitities.," From an aesthetic point of view, direct numerical simulation is not an appealing way to compute statistics, since this approach is not formulated solely in terms of the variables one is actually interested in, namely the statistical quantities."149 The'e are equations which deal directly WIitt the statisticM. such as an equation due ic» Hopf [1.2] which governs the genueratlug functiOlla OL edual iue moments.," There are equations which deal directly with the statistics, such as an equation due to Hopf \cite{Hopf,Frisch} which governs the generating functional of equal time moments."150 A better XllOWL equ:lo nopeated to Hopfs equation by Fou‘ier transforjalion. is ——e Fokker-Plauck equajon describin& the time evolutio1 of a probability clistdutiou ove phase space.," A better known equation, related to Hopf's equation by Fourier transformation, is the Fokker-Planck equation describing the time evolution of a probability distribution over phase space."151 Iu sonje specia systelis. icl as the oue described i1 [3].. al ala‘Lic solutio for t lesatistics exists. evel Or na very 'ge nuniaber of degrees of freedom.," In some special systems, such as the one described in \cite{Brad}, an analytic solution for the statistics exists, even for a very large number of degrees of freedom."152 In this article. we will describe au inverse nethoc to CoLstruc chaotic dynanical syslenis. startiig with a iuvaqan »obabilits* distributico) amd a wo-foru having a relatively simple allaNie structure.," In this article, we will describe an inverse method to construct chaotic dynamical systems, starting with an invariant probability distribution and a two-form having a relatively simple analytic structure."153 This uethoc allows oue to generate. it priuciple. iufinite classes of dyiizunical systelis for which some salistical properties are knoWIL exeactly.," This method allows one to generate, in principle, infinite classes of dynamical systems for which some statistical properties are known exactly."154 While we give examples with three aud four cegrees ol reecoinm. we do not anticipae proiive obstructions in applying the inverse inethocl to syselas witl a very large number of «eerees of freedoi.," While we give examples with three and four degrees of freedom, we do not anticipate prohibitive obstructions in applying the inverse method to systems with a very large number of degrees of freedom."155 Our starting point is an analytica exp'ession for au lnvarlit probability distribuion pGr) which is. by construction. a sinooth 1jeastwe inau.W dilueu1al phase space.," Our starting point is an analytical expression for an invariant probability distribution $\rho(\vec x)$ which is, by construction, a smooth measure in an $N$ dimensional phase space."156 H well known that the geometry of a «‘haotic iuvariaut set may be fractal. €aving a fractional information cdimeusio1 less than AN.," It well known that the geometry of a chaotic invariant set may be fractal, having a fractional information dimension less than $N$."157 However. eve1wihb information diinensiou less than JN. an invariant distribution with suppor in JN dimerSlOHS navy still be relevall to the statistics of a chaotic trajectory as a p‘obabili istributio noon the ¢haotic invaγαι1 set upon projection to lower integer «]melnsion.," However, evenwith information dimension less than $N$, an invariant distribution with support in $N$ dimensions may still be relevant to the statistics of a chaotic trajectory as a probability distribution on the chaotic invariant set upon projection to lower integer dimension."158 We eiveοἱ several exalgles where pr) desc‘ibes the statistics of chaotic trajectories αIO »ojection to lower «ΠΗΙΘΗΣΙΟΗ., We give several examples where $\rho(\vec x)$ describes the statistics of chaotic trajectories upon projection to lower dimension.159 There are exaiples for which we hiave fouud 1jumerical eviderce that the initial distribution por). with N«imensioual su)IOI. gives accirate results even fcor connected uoments (cumulauts) which do nol aciilt projecion to lower integer dimeusio[un such as <THE>. dn uv3.," There are examples for which we have found numerical evidence that the initial distribution $\rho(\vec x)$, with N-dimensional support, gives accurate results even for connected moments (cumulants) which do not admit projection to lower integer dimension, such as $<xyz>_c$ in $N=3$."160 This may be ECALse je. information dimensioL which we have 10 vet. calcilated. Is very 1earM7 NV.," This may be because the information dimension, which we have not yet calculated, is very nearly $N$."161 HoweVer. we s»eculate lat the H«pf Luctional Vj)=<<expij-*)> may be 5lieently well )ehaved hat is Foirier transform. wης diis by coustrueion an invariant distribiion. be support in NV clitnensious aud is equal to /)(4).," However, we speculate that the Hopf functional $\Psi(\vec j)= <\exp(i\vec j\cdot162\vec x)>$ may be sufficiently well behaved that its Fourier transform, which is by construction an invariant distribution, has support in $N$ dimensions and is equal to $\rho(\vec x)$."163 IP so. pr) de1uines all polynomial moments eoEiply7e{ 2.1thougl 1rere should be «Iler expectation νιtes of fuuctions ou phase spac whic Lea1 uot be obtained rom pr). «lue ) the fractional iuf‘mation dimension.," If so, $\rho(\vec x)$ determines all polynomial moments $<x^ny^mz^l\cdots>$, although there should be other expectation values of functions on phase space which can not be obtained from $\rho(\vec x)$, due to the fractional information dimension."164 We also fii that. iniLALLY nnstauces. he ratio of frequen«‘ies with which «il'erent regions of phase space ar visited by a chaotic trajectory is determi( by the distribuion pGr). even when the detaileca eeometry of the chaotic 1ivarlant set is euite complicated or LDUISLLOWLL.," We also find that, in many instances, the ratio of frequencies with which different regions of phase space are visited by a chaotic trajectory is determined by the distribution $\rho(\vec x)$ , even when the detailed geometry of the chaotic invariant set is quite complicated or unknown."165M;27 M.,$M_i\gtrsim7\ \Msun$ .166.7 reach a difference of up to 0.4M. in the final masses derived from different metallicities. their study covering a broad metallicity range: Z in between 0.0001. and 0.1.," \citealt{2007arXiv0710.2397M} reach a difference of up to $0.4\ \Msun$ in the final masses derived from different metallicities, their study covering a broad metallicity range: Z in between $0.0001$ and $0.1$."167 They also notice a minimum of the IFAM lor Z=0.04., They also notice a minimum of the IFMR for $Z=0.04$.168 Various semi-empirical linear lits have been derived over the last decade., Various semi-empirical linear fits have been derived over the last decade.169 A few examples are: ? (based on open-cluster data lor the range 2.5—6.5M.: claàming (hat the IEMBR can be modelled by a mean relationship about which there exists some intrinsic scatter. and (hat they ‘cannot justilv the use of any but a linear relationship to model the cluster data): ? (a linear fit to some 27 WDs. menibers of clusters such as the ILvades. Praesepe. M35. NGC2516 and the Pleiades. over initial-mass range of 2.7—6AL. ): T (claiming that the IFAIR is both linear and without anv metallicity dependence): Although the relations obtained. as shown in Fig. 7..," A few examples are: \citet{2005MNRAS.361.1131F} (based on open-cluster data for the range $2.5-6.5\ \Msun$; claiming that the IFMR can be modelled by a mean relationship about which there exists some intrinsic scatter, and that they `cannot justify the use of any but a linear relationship to model the cluster data'): \citet{2006MNRAS.369..383D} (a linear fit to some $27$ WDs, members of clusters such as the Hyades, Praesepe, M35, NGC2516 and the Pleiades, over initial-mass range of $2.7-6\ \Msun$ ): \citet{2007ASPC..372...85W} (claiming that the IFMR is both linear and without any metallicity dependence): Although the relations obtained, as shown in Fig. \ref{fig:ifmr},"170 are quite far [rom linear. the closest linear fit that we can suggest. without using anv artificial anchoring. is which falls slightly above the upper (Pop.," are quite far from linear, the closest linear fit that we can suggest, without using any artificial anchoring, is which falls slightly above the upper (Pop."171II) curve around the lower initial masses ὃν and below the lower (Pop.,"II) curve around the lower initial masses $1.5-2.5\ \Msun$ ), and below the lower (Pop."172I) curve for higher intermediate masses. around 5M...,"I) curve for higher intermediate masses, around $5\ \Msun$."173 This fit is very similar {ο the linear fit of ? (shown in Fig. 7)).," This fit is very similar to the linear fit of \citet{2005MNRAS.361.1131F} (shown in Fig. \ref{fig:ifmr}) ),"174 although the latter is limited io the range 2.5 to 6.5M..., although the latter is limited to the range $2.5$ to $6.5\ \Msun$.175 Clearly. (he. relation obtained represents the set of parameters assumed. mostly those related to the mass-loss recipe.," Clearly, the relation obtained represents the set of parameters assumed, mostly those related to the mass-loss recipe."176 The value of jpg; used here was linearly increasecl from 0.4 at 0.8AL. to 3.0 αἱ 9M..., The value of $\eta_{\rm Reim}$ used here was linearly increased from 0.4 at $0.8\ \Msun$ to 3.0 at $9\ \Msun$.177" A preliminary comparison that we performed. keeping all parameters fixed and changing only mass-loss laws. indeed showed somedifferences in the final WD masses, with a spread of less than 1056."," A preliminary comparison that we performed, keeping all parameters fixed and changing only mass-loss laws, indeed showed somedifferences in the final WD masses, with a spread of less than $10\%$ ."178 More precisely. for our solar model parameters (see 84.3)). selling Are=0.6.Hus50.the derived final WD masses were all in the range 0.53—0.57AL. (or between 0.51—0.56 lor slightly higher mass-loss rates obtained by using Huge;=lOO.Bassus 10).," More precisely, for our solar model parameters (see \ref{canon}) ), setting $\eta_{Rei}=0.6,\ R_{thresh}=50$,the derived final WD masses were all in the range $0.53-0.57\ \Msun $ (or between $0.51-0.56$ for slightly higher mass-loss rates obtained by using $\eta_{Rei}=1.0,\ R_{thresh}=10$ )."179 Performing the same comparison lor 3M.(Z= 0.01). but usingHie;= 2.0. we found final WD masses tobe in the range 0.61—0.67 AZ.," Performing the same comparison for $3\ \Msun\ (Z=0.01)$ , but using$\eta_{Rei}=2.0$ we found final WD masses tobe in the range $0.61-0.67\ \Msun $ ."180contained in them Fieuve 2.,contained in their Figure 2.181 The need for supersolar netallicity is clear for M. dwifs (0.2καιλενUT). where the average metallicity of the planet-hosting stars is [Fe‘TH = 0.1.," The need for supersolar metallicity is clear for M dwarfs $0.2 < M_\ast/M_\sun < 0.7$ ), where the average metallicity of the planet-hosting stars is [Fe/H] = 0.4."182" Metal-rich stars prestunably ounce carried ποτάτοι disks. aud so the planet-metallicity correlation or AL chwarts supports «nr results; aud those of others (Sekix""1998: ¥Youdin&Shu2002: Leeetal.50101: see also Jolausenetal.20090: Bai&Stone201043) hat planectesimals formi much more readily iu inetal-rich enviroments."," Metal-rich stars presumably once carried metal-rich disks, and so the planet-metallicity correlation for M dwarfs supports our results, and those of others \citealt{sekiya98};; \citealt{youdinshu02}; \citealt{leeetal10}; ; see also \citealt{johansenetal09}; \citealt{baistone10}) ) that planetesimals form much more readily in metal-rich environments."183 In particular the data for AI chwarts indicate that a mere factor of 10°!=2.5Γ increase ni nkπαν above soar substantially decreases the probability of planet occmreuce., In particular the data for M dwarfs indicate that a mere factor of $10^{0.4} = 2.5$ increase in metallicity above solar substantially increases the probability of planet occurrence.184 This is consistent with our finding of a super-near trend between maxiuui dust-to-gas ratio aud buk inetallicity refssec:superlinear and Appendix C))., This is consistent with our finding of a super-linear trend between maximum dust-to-gas ratio and bulk metallicity \\ref{ssec:superlinear} and Appendix \ref{app:superlinear}) ).185 However. the planet-uetallicitv correlation weakens svstclnatically with iucreasing stellar mass (Johusonal. 2010).," However, the planet-metallicity correlation weakens systematically with increasing stellar mass \citep{johnsonetal10}."186. For À sars (docAL/M.« 2.0). 10 οςurelation is arenaijv not present.," For A stars $1.4 < M_\ast/M_\sun < 2.0$ ), the correlation is arguably not present."187 This calls iuto uestion the need for supersolar metallicities to form uaeexnaals., This calls into question the need for supersolar metallicities to form planetesimals.188 The observatious of Jolinsonetal.(2010) welt still be reconciles with eravitatioual instability if uore lnassive stars los more lnassive disks. although lish nass would have ο scale with stellar mass in a aster than linear way o lower the threshold Toonue Clsiv (equation 10)).," The observations of \citet{johnsonetal10} might still be reconciled with gravitational instability if more massive stars host more massive disks, although disk mass would have to scale with stellar mass in a faster than linear way to lower the threshold Toomre density (equation \ref{eqn:muToomre}) )."189 The possibility also remains that he observations are no actually a direct or sensitive robe of the theorv., The possibility also remains that the observations are not actually a direct or sensitive probe of the theory.190 Ti6 observations concern stellar notalicity. which might at best correlate with the global notalicity of the disk. 1iteerated over both disk height and disk radius.," The observations concern stellar metallicity, which might at best correlate with the global metallicity of the disk, integrated over both disk height and disk radius."191 By comparison. theory concerns the local Levalicity X fhe. iuteer‘ated over height but uot radius.," By comparison, theory concerns the local metallicity $\Sigmad/\Sigmag$ , integrated over height but not radius."192 This local inetallicitv (not to be confused with the local dust-o-gas ratio pi) cali evolve substautially frou its elobal value. as a consequence of radial particle drifts aud photoevaporation (c.e.. CY10).," This local metallicity (not to be confused with the local dust-to-gas ratio $\mu$ ) can evolve substantially from its global value, as a consequence of radial particle drifts and photoevaporation (e.g., CY10)."193 Rather than look to their parent stars for evidenc for local disk curichment. we can look to the plaucts theniselves.," Rather than look to their parent stars for evidence for local disk enrichment, we can look to the planets themselves."194 If planetesimals cau only form iu metalenriched cnvirouuents. we expect that the resultant planets will also be inetal-enxiched.," If planetesimals can only form in metal-enriched environments, we expect that the resultant planets will also be metal-enriched."195 Caullotetal.(2006) congmitted the bulk metallicities of the first iinue extrasolar planets discovered to be transiting. all of wluch are lie(Xo Jupiters.," \citet{guillotetal06}196 computed the bulk metallicities of the first nine extrasolar planets discovered to be transiting, all of which are hot Jupiters."197 The results are listed in Table .. ogether with the modeled bulk metallicities of Jupiter and Saturn.," The results are listed in Table \ref{tab:metal}, together with the modeled bulk metallicities of Jupiter and Saturn."198 All cleven are indeed metal-euriched. by actors ranging from 2[7 relative to the Sun. aud 220 το]:dive to their host stars.," All eleven are indeed metal-enriched, by factors ranging from 2–47 relative to the Sun, and 2--20 relative to their host stars."199" One caveat behind these results is that models of hot Jupiter iuteriors are sub.ject o the uncertainty over the extra soiree of imternal reat responsible for their unexpectedly large radi {see, e.g.+S. Batvein&Stevenson2010.. who also describe a mousing solution)."," One caveat behind these results is that models of hot Jupiter interiors are subject to the uncertainty over the extra source of internal heat responsible for their unexpectedly large radii (see, e.g., \citealt{batyginstevenson10}, who also describe a promising solution)."200 To inflate planetary radii. Cuillotetal.(2006) iucluded iu each hot Jupiter model al aclditicmal source of power equal to of the received stellar irradiation (Cuullot&Showman2002).," To inflate planetary radii, \citet{guillotetal06}201 included in each hot Jupiter model an additional source of power equal to of the received stellar irradiation \citep{guillotshowman02}."202. The |lk ietallicities inferred from the models depend ou the details of this extra energy source., The bulk metallicities inferred from the models depend on the details of this extra energy source.203 Modulo this caveat. CVCLY planet is euriched iu metals by at least a factor of —2 above solar. which is cousisteut with our fixlue that forming planctesimalsbv gravitational instability requires metal enrichimeuts of this order.," Modulo this caveat, every planet is enriched in metals by at least a factor of $\sim$ 2 above solar, which is consistent with our finding that forming planetesimalsby gravitational instability requires metal enrichments of this order."204 We thank Xuc-Niug Bai. John Joliusou. Eve OstriSOT. Juu Stone. aud Neal Turner for discussions. aud Tristan Caullot for the data in Table 1..," We thank Xue-Ning Bai, John Johnson, Eve Ostriker, Jim Stone, and Neal Turner for discussions, and Tristan Guillot for the data in Table \ref{tab:metal}."205 Nuc-Ning Bai. Anders Johansen. Jim Stone. and Andrew Yordiu provied valuable feedback on a draft version of his paper.," Xue-Ning Bai, Anders Johansen, Jim Stone, and Andrew Youdin provided valuable feedback on a draft version of this paper."206 We are erateful to Stuart Weideuschillius for al iusieliful referees report that put our work iuto beter contest., We are grateful to Stuart Weidenschilling for an insightful referee's report that put our work into better context.207" This research was supported bv the National Scie'6 Foundation. in part through TeraCwid resources provied by Purdue University uuder eraut number TC-AST090079,"," This research was supported by the National Science Foundation, in part through TeraGrid resources provided by Purdue University under grant number TG-AST090079."208 AT.L. acknowledges support frou an NSF σαιate Fellowship., A.T.L. acknowledges support from an NSF Graduate Fellowship.209 For wmuerical estimates in this paper. we adopt the stand disk mode derived in the review by (2010).," For numerical estimates in this paper, we adopt the standard disk model derived in the review by \citet{chiangyoudin10}."210. The disk has surface densities in gas (eg) aud dust (d)., The disk has surface densities in gas (g) and dust (d).211" The dimensionless parameters £ audζω=(N/X,)/0.015. typically of order unity. describe how much total mass the disk has relative to the nininimiuuass solar nebula. aud how metal-rich the disk is compared with a eas of solar abundances. respectively,"," The dimensionless parameters $F$ and$\Zr \equiv (\Sigma/\Sigmag)/0.015$, typically of order unity, describe how much total mass the disk has relative to the minimum-mass solar nebula, and how metal-rich the disk is compared with a gas of solar abundances, respectively."212" The minimnucniass solar nebula CF=1. Zí4= 1) uses a condensate lass fraction for solarabundances of X4/X,=(0.015 (Lodders. 2003)..."," The minimum-mass solar nebula $F=1$, $\Zr=1$ ) uses a condensate mass fraction for solarabundances of $\Sigmad/\Sigmag = 0.015$ \citep{lodders03}. ."213" Values of Ζω>1 correspond to supersolar metallicities X4/X,> 0.015.", Values of $\Zr > 1$ correspond to supersolar metallicities $\Sigmad/\Sigmag > 0.015$ .214 Iuteerated to r=100 AU.equation CÀ1)) vields a total disk mass of 0.037 AL...," Integrated to $r = 100\AU$ ,equation \ref{eq_sigmag})) yields a total disk mass of $0.03 F M_{\odot}$ ."215 At the disk midplane. the gas temperature. scale height. aud density are given by," At the disk midplane, the gas temperature, scale height, and density are given by"216are (at least) viscously coupled.,are (at least) viscously coupled.217 If all of the material that enters the disc at large radii is coplanar. (hen conservation of total angular momentum implies that the total integrated angular momentum about any axis perpendicular to that of the initial co must vanish at all times.," If all of the material that enters the disc at large radii is coplanar, then conservation of total angular momentum implies that the total integrated angular momentum about any axis perpendicular to that of the initial $\boldsymbol \omega$ must vanish at all times."218 This means that if some inner mean annulus of gas tilis in one direction. there will be a corresponding counter-tilt elsewhere.," This means that if some inner mean annulus of gas tilts in one direction, there will be a corresponding counter-tilt elsewhere."219 Turbulent viscosity allows (he radial distribution of (ills to be non-trivial and because jet power is likely dominated by inner annuli. the tilt of the inner-most annuli are particularly relevant for predicting jel wobble because they dominate the accretion power.," Turbulent viscosity allows the radial distribution of tilts to be non-trivial and because jet power is likely dominated by inner annuli, the tilt of the inner-most annuli are particularly relevant for predicting jet wobble because they dominate the accretion power."220 In what follows. we assume that the axis of anv annular section of a jet tracks (he orbital axis of the corresponding disc annulus to which that jet section is anchorecl.," In what follows, we assume that the axis of any annular section of a jet tracks the orbital axis of the corresponding disc annulus to which that jet section is anchored."221 Thus the jet wobble directly tracks the dise wobble., Thus the jet wobble directly tracks the disc wobble.222 llere we apply (he above formulae to thin accretion disces and jet wobble., Here we apply the above formulae to thin accretion discs and jet wobble.223" For a thin. non-sell-gravitating disc in hydrostatic equilibrium where c, is the sound speed. A is the central object mass. and // is (he density scale height."," For a thin, non-self-gravitating disc in hydrostatic equilibrium where $c_s$ is the sound speed, $M$ is the central object mass, and $H$ is the density scale height."224 The Shakura-Sunvaev (Shakura&Sunvaev(1973))) viscosity ν in hyedrostatic equilibriumE. then satislies. v=occcuf>liucoodles. where a is. the viscosity.- parameter.," The Shakura-Sunyaev \cite{ss73}) )viscosity $\nu$ in hydrostatic equilibrium then satisfies $\nu \equiv \alpha c_s H \sim v_{ed}^2/ t_{ed} \sim v_{ed}^2H/c_s$, where $\alpha$ is the viscosity parameter."225" Then (e.g. Blackman 1993) vy~ale, and SO The dise accretion rate can be modeled as Αρ)=μα...y (e.g. (1999))). where My is the accretion rate at the outer edge of the dise. rj, is the radius of the outer edge. and 0«s Iis a parameter."," Then (e.g. Blackman 1998) $v_{ed}\sim \alpha^{1/2}c_s$ and so The disc accretion rate can be modeled as $\dot{M}_a(r) = \dot{M_{o}}(r/r_o)^s$ (e.g. \cite{bb99}) ), where $\dot{M_{0}}$ is the accretion rate at the outer edge of the disc, $r_o$ is the radius of the outer edge, and $0< s< 1$ is a parameter."226 The total mass outflow rate from ry (o r is then M(r)=AL—(rfr;y]., The total mass outflow rate from $r_o$ to $r$ is then $\dot{M}(r) = \dot{M_o}[1-(r/r_o)^s]$.227 Taking the derivative. we obtain the outflow mass loss rate by a small annulus of width dr at radius r to be," Taking the derivative, we obtain the outflow mass loss rate by a small annulus of width $dr$ at radius $r$ to be"228LONE. IRS 16C. and IRS 168W (N97). it could therefore be a transition object just comme out of the LBV phase.,"16NE, IRS 16C, and IRS 16SW (N97), it could therefore be a transition object just coming out of the LBV phase."229 This would be consistent with the e aud M profiles of Garcia-Seeura. Mac Low Langer (1996).," This would be consistent with the $v$ and $\dot\mathrm{M}$ profiles of Garcia-Segura, Mac Low Langer (1996)."230 Ihuuphrevs Davidson (1991) point out that a WN9/Ofpe star appears vorv ιο like au LBV at ninm brightucss and thus the distinction between the two types is often bhurecd., Humphreys Davidson (1994) point out that a WN9/Ofpe star appears very much like an LBV at minimum brightness and thus the distinction between the two types is often blurred.231 However. the large TeἩ of IRS 13EL. compared to a ΠοΤΠ of ~1 for the IRS 16 sources (N97). makes an LBV/WNL determination problematic.," However, the large He/H of IRS 13E1, compared to a He/H of $\sim 1$ for the IRS 16 sources (N97), makes an LBV/WNL determination problematic."232 Observational aud theoretical countcrareuments iuclude the fact that the identity of WR 122. the calibrating WNL source used by NOT. has been called into doubt (Crowther Smith 1999) and recent work (c.g... Langer et al.," Observational and theoretical counterarguments include the fact that the identity of WR 122, the calibrating WNL source used by N97, has been called into doubt (Crowther Smith 1999) and recent work (e.g., Langer et al."233 1999) sugeestsOO nix 1n luassive stars is more efücient than previously thought. resulting ina larger Πο at the start of the WNL phase.," 1999) suggests mixing in massive stars is more efficient than previously thought, resulting in a larger He/H at the start of the WNL phase."234 Hence an LBV/WNL classification is certainly within reason (although see below)., Hence an LBV/WNL classification is certainly within reason (although see below).235 Secoud. we note that there are <27 massive Πο stars in the GC (Bhun. Ramirez. Selleren 1999).Given the observed frequency. ff. of WR binary svstcms (1254Sfος van der Hucht et al.," Second, we note that there are $\simgt 27$ massive HeI stars in the GC (Blum, Ramírrez, Sellgren 1999).Given the observed frequency, $f$ , of WR binary systems $12\% \simlt f \simlt 50\%$; van der Hucht et al."236 1981). it is likely hat some of the GC ΠΟ stars are binaries as well.," 1981), it is likely that some of the GC HeI stars are binaries as well."237 Iu act. IRS 16SW is thought to be an eclipsing binary with a period of ~10 days (Ott. Eckart Cenzel 1999).," In fact, IRS 16SW is thought to be an eclipsing binary with a period of $\sim 10$ days (Ott, Eckart Genzel 1999)."238 Thus it is possible that IRS 13E is also a binary svete. containing ‘or example a WNIO primary with a ZAMS mass of ~100AI; and a somewhat less massive companion that is either an O star or another WR star. or. possibly. a hassive compact object.," Thus it is possible that IRS 13E is also a binary system, containing for example a WN10 primary with a ZAMS mass of $\sim 100~\mathrm{M}_{\sun}$ and a somewhat less massive companion that is either an O star or another WR star, or, possibly, a massive compact object."239 Of the single aud binary scenarios. the latter is preferred.," Of the single and binary scenarios, the latter is preferred."240 As previously mentioned. the model of N97 underprediets the K-baud ΠΟΠ emission for IRS EL by a factor of 3: the colliding winds of a binary will produce more Ile! (Marcheuko et al.," As previously mentioned, the model of N97 underpredicts the K-band HeII emission for IRS 13E1 by a factor of $\sim 3$; the colliding winds of a binary will produce more $^+$ (Marchenko et al."241 1997). poteutially explaining this deficicney.," 1997), potentially explaining this deficiency."242 Also. the ionizing flax from a massive O star would explain why IRS 13E stauds out in Pa-o and [FOIT].," Also, the ionizing flux from a massive O star would explain why IRS 13E stands out in $\alpha$ and [FeIII]."243 An carly-type binary system will also have strone shocks as a result of colliding stellar winds., An early-type binary system will also have strong shocks as a result of colliding stellar winds.244 The N-ray hinunosity of a binary svsteim will be brighter than that fron a solitary star so that in order of increasing X-rav Duninuositv one qualitatively has (with everything else equal) WR. O. O/O. WR/O. WR/WR.," The X-ray luminosity of a binary system will be brighter than that from a solitary star so that in order of increasing X-ray luminosity one qualitatively has (with everything else equal) WR, O, O/O, WR/O, WR/WR."245 Towever. this is mmocdified by the binary separation: if the binaries are too close. absorption will suppress the observed N-ray cluission but if they are too far apart the shocks are largely adiabatic and do not produce significant additional N-ray huuinosity (Pittard Stevens 1997).," However, this is modified by the binary separation: if the binaries are too close, absorption will suppress the observed X-ray emission but if they are too far apart the shocks are largely adiabatic and do not produce significant additional X-ray luminosity (Pittard Stevens 1997)."246 The various WR sources of IRS 16 Gucludiug IRS L6SW) do not appear as yout sources in the observations., The various WR sources of IRS 16 (including IRS 16SW) do not appear as point sources in the observations.247 A solitary WB or even a WR with a DB or later companion may nof ο Visible with due to the large column density between here aud the GC., A solitary WR or even a WR with a B or later companion may not be visible with due to the large column density between here and the GC.248 Using-. aud a Ravinoud-SuuithM thermal plasina mmodel (which assumes optically thin N-rav line aud continu ciuiission: Ravinoud Suüth 1977) iu ionizafion equilibria one can simulate the spectu of a solitary O-star placed at the CC., Using and a Raymond-Smith thermal plasma model (which assumes optically thin X-ray line and continuum emission; Raymond Smith 1977) in ionization equilibrium one can simulate the spectrum of a solitary O-star placed at the GC.249 Assiuuiug an ISM-corrected. N-vay luminosity (0.5-10.0 keV) L4~0.25L: (from κΊων~10'. sec e.g. Waldron. et al.," Assuming an ISM-corrected X-ray luminosity (0.5-10.0 keV) $\mathrm{L_x} \sim 0.25~\mathrm{L}_{\sun}$ (from $L_{x}/L_{bol} 250\sim 10^{-7}$, see e.g. Waldron, et al."251 1998). a characteristic temperature kT~0.5 keV (represcutative of typica solitary O-stars. see Chichowski. et al.," 1998), a characteristic temperature $\mathrm{kT} \sim 0.5$ keV (representative of typical solitary O-stars, see Chlebowski, et al."252 1989). au intervening column deusity Nj~5«107? ? (typical for the GC. see eg. Zrlka et al.," 1989), an intervening column density $_\mathrm{H} 253\sim 5 \times 10^{22}$ $^{-2}$ (typical for the GC, see e.g., Zylka et al."254" 1995), and solu abuudauces hroughout. a 50 ksec observation. spimune the 0.5-10 το. band. would detect Z3 photons. and the O-star would not staud out above the background."," 1995), and solar abundances throughout, a 50 ksec observation, spanning the 0.5-10 keV band, would detect $\simlt 3$ photons, and the O-star would not stand out above the background."255 Thus the IRS 16 sources bleud iuto the diffuse background seen in the central ~5” of the mace in Daganotf et al. (, Thus the IRS 16 sources blend into the diffuse background seen in the central $\sim 5''$ of the image in Baganoff et al. (2561999).,1999).257 Note that this hints that either the ποσα IRS 16SW companion docs not have a siguificaut stellar wind aud thus is of tvpe D or later (and therefore Προς a lower svsten mass than estimated by Ott et al., Note that this hints that either the unseen IRS 16SW companion does not have a significant stellar wind and thus is of type B or later (and therefore implies a lower system mass than estimated by Ott et al.258 1999). or that the circumstellar absorption aud/or binary separation were unfavorable.," 1999), or that the circumstellar absorption and/or binary separation were unfavorable."259 Iu coutrast. Fig.," In contrast, Fig."260 2— shows a theoretical spectrinnfor a hvpothoetica (05L; GC Naav SOUECC simular to the WR/O binary 22 VeL which has a 18.5," \ref{fig:WRO} shows a theoretical spectrumfor a hypothetical $0.5~\mathrm{L}_{\sun}$ GC X-ray source similar to the WR/O binary $\gamma^2$ Vel, which has a 78.5"261component (Robin 1-2 Gyr).,component (Robin 1-2 Gyr).262 Then the best fit FWHM of the Ciaussiaus are (3.2Hy aud (11.5ry5 with fluxes of (2.1840.26)x10.!pholonscm2s Land (5.36£0.5)x101pholonscm2g respectively. the disk flux being (1.83£0.27)xLO?pholonsen7s1. providing a Bulge to Disk ratio of Ο.Τ.," Then the best fit FWHM of the Gaussians are $(3.2_{-1.0}^{+1.0})^\circ$ and $(11.8_{-1.5}^{+1.9})^\circ$ with fluxes of $(2.48 \pm 0.26) \times 10^{-4}~photons~cm^{-2}~s^{-1}$ and $(5.36 \pm 0.5) \times 10^{-4}~photons~cm^{-2}~s^{-1}$ respectively, the disk flux being $ (1.83 \pm 0.27) \times 10^{-3}~photons~cm^{-2}~s^{-1}$, providing a Bulge to Disk ratio of 0.44."263 Usiug the ratio calculated by Ixuóddlseder et al. (, Using the ratio calculated by Knöddlseder et al. (2642005. Table 3) to infer the 511 keV line huninosities aud the factor (6./55411) = 1.61 from Brown Leventhal (1987). we obtaiu annihilation rates of 1.1.xLOMs| in the bulge and 0.8xLOMSs| in the disk.,"2005, Table 3) to infer the 511 keV line luminosities and the factor $e^{+}/\gamma_{511})$ = 1.64 from Brown Leventhal (1987), we obtain annihilation rates of $1.1\times 10^{43} s^{-1}$ in the bulge and $0.8\times 10^{43} s^{-1}$ in the disk."265 We then attempted to describe the exteuded spatial distribution superimposed on the central bulge with various spatial geometries., We then attempted to describe the extended spatial distribution superimposed on the central bulge with various spatial geometries.266 Simple geometric shapes (i.e. two cdimeusional Craussiaus) as well as more pliysical maps (CO. NIB. Robin disk GRobin et ab.," Simple geometric shapes (i.e. two dimensional Gaussians) as well as more physical maps (CO, NIR, Robin disk (Robin et al.,"267 2003)) were Fig., 2003)) were Fig.268 13. stummarizes the result of the correlation map study. with the NA? ( which varies similarly as the reduced masximtun loe-likelihood ratio) plotted for each of the tracer maps.," \ref{fig:traceur511} summarizes the result of the correlation map study, with the $\Delta\chi^2$ ( which varies similarly as the reduced maximum log-likelihood ratio) plotted for each of the tracer maps."269 Best 'esults. are obtained for a Robin disk (in the 0.15-3 Cyr range correspoudiug to au old stellar »opulation) or NIR/DIRBE 107: aud 1.254: maps. which happen to be good tracers of the 7°Al ine emission (Ixnódcdlseder et al..," Best results are obtained for a Robin disk (in the 0.15-3 Gyr range corresponding to an old stellar population) or NIR/DIRBE $\mu$ and $\mu$ maps, which happen to be good tracers of the $^{26}Al$ line emission (Knöddlseder et al.,"270 1999)., 1999).271 Simple bi-climensional Giaussiauns of latitude FWHAL aud longitude FWHM ~250° give also good results., Simple bi-dimensional Gaussians of latitude FWHM $\sim5-7^\circ$ and longitude FWHM $\sim250^\circ$ give also good results.272 We note that the disk exhibits a arger longitude exteusion thau the previoulsy reported values: first by OSSE (Ixiuzer et al..," We note that the disk exhibits a larger longitude extension than the previoulsy reported values: first by OSSE (Kinzer et al.,"273 2001). nut the study is based on a longitudinally truncated data set distribution aud more recently by Weincdeuspointuer et al.," 2001), but the study is based on a longitudinally truncated data set distribution and more recently by Weindenspointner et al.,"274 2008., 2008.275 Even though it is difficult to describe the emission iu greater detail. his result represents a good indication for a bulge/disk structure.," Even though it is difficult to describe the emission in greater detail, this result represents a good indication for a bulge/disk structure."276 Extended disk structure flux (for he most plausible. disks). is. around B1.7-—x10.73photonscm>7?s|! and the Bulge/diskf. ratios. range rom 0.25 to 0.7., Extended disk structure flux (for the most plausible disks) is around $1.7 \times 10^{-3}~photons~cm^{-2}~s^{-1}$ and the Bulge/disk ratios range from 0.25 to 0.7.277 This analysis excludes single halo mocels (inodelled by axisyiumetrie Gaussiaus)., This analysis excludes single halo models (modelled by axisymmetric Gaussians).278 However. in he past. OSSE data have often been compared with bulge models iucludiug some nou-Craussiau Xxoadeniug (wines). featuring a bulge + halo central geometry.," However, in the past, OSSE data have often been compared with bulge models including some non-Gaussian broadening (wings), featuring a bulge + halo central geometry."279 We have tested this kiud of coufiguratiou NN consideriug a stellar halo (or spheroid) moclel proposed by Robin et al. (, We have tested this kind of configuration by considering a stellar halo (or spheroid) model proposed by Robin et al. (2802003).,2003).281 The central regiou »olile is built following the law: N represents a normalisation constant aud x.v.z. the cartesian coordinates iu the bulge reference frame.," The central region profile is built following the law: N represents a normalisation constant and x,y,z, the cartesian coordinates in the bulge reference frame."282" We obtain a good fit to the data with the axis ratio. e = 0.5. in = -2.6. «,—200 pe and Ry=s.5 kpe."," We obtain a good fit to the data with the axis ratio, $\epsilon$ = 0.8, m = -2.6, $a_{c}$ =200 pc and $R_{0}$ =8.5 kpc."283 The 2105 and 1.254 NIR/DIRBE and Robin 1-3 Gyr maps remain the best tracers, The $\mu$ and $\mu$ NIR/DIRBE and Robin 1-3 Gyr maps remain the best tracers284"star, and the Keplerian value is assumed otherwise (Wellstein2001).","star, and the Keplerian value is assumed otherwise \citep{Wellstein01}."285". The change of the orbital period due to mass transfer and stellar wind mass loss is considered according to Podsiadlowski,Joss&Hsu(1992).", The change of the orbital period due to mass transfer and stellar wind mass loss is considered according to \citet{Podsiadlowski92}.286. We follow Brookshaw&Tavani(1993) to determine the amount of the specific angular momentum carried away from the orbit by stellar winds., We follow \citet{Brookshaw93} to determine the amount of the specific angular momentum carried away from the orbit by stellar winds.287 Tidal synchronizationis considered following Wellstein(2001) (seealsoDetmersetal.2008)., Tidal synchronizationis considered following \citet{Wellstein01} \citep[see also][]{Detmers08}.288" We assume a synchronization time scale according to Tassoul(1987,2000) who considered tidally driven meridional circulations as the main mechanism for tidal dissipation: where q denotes the mass ratio and d the orbital separation."," We assume a synchronization time scale according to \citet{Tassoul87, Tassoul00} who considered tidally driven meridional circulations as the main mechanism for tidal dissipation: where $q$ denotes the mass ratio and $d$ the orbital separation."289 This prescription gives a much shorter time scale than that given by Zahn(1977)., This prescription gives a much shorter time scale than that given by \citet{Zahn77}.290". Given that the physics of tidal dissipation is much debated in the literature (Langer2009), we introduce a parameter to investigate how an extremely fast/slow synchronizationfsync may influence the results."," Given that the physics of tidal dissipation is much debated in the literature \citep{Langer09}, we introduce a parameter $f_\mathrm{sync}$ to investigate how an extremely fast/slow synchronization may influence the results."291" In most cases, however, we use fsync=1."," In most cases, however, we use $f_\mathrm{sync} = 1$."292" A few sequences are also computed with Τογπο of (1977) for comparison: where J is the moment of the star, and E» a constant measuring the coupling between the tidal potential and the gravity mode."," A few sequences are also computed with $\tau_\mathrm{sync}$ of \citet{Zahn77} for comparison: where $I$ is the moment of the star, and $E_2$ a constant measuring the coupling between the tidal potential and the gravity mode."293" Using the data of Table 1 in Zahn we constructed a fitting formula for Es as the following:(1977), where Reony is the radius of the convective core."," Using the data of Table 1 in \citet{Zahn77}, we constructed a fitting formula for $E_2$ as the following: where $R_\mathrm{conv}$ is the radius of the convective core."294 Note that both prescriptions by Tassoul and Zahn are not appropriate for a star with a convective envelopeδ., Note that both prescriptions by Tassoul and Zahn are not appropriate for a star with a convective envelope.295". However, the role of tidal synchronization is significant only on the main sequence, and not important in late evolutionary stages as discussed below."," However, the role of tidal synchronization is significant only on the main sequence, and not important in late evolutionary stages as discussed below."296" We computed 45 model sequences for initial masses of the primary star mostly from 12 to 25 Mo at two different metallicities (Z= 0.02 and for different mass ratios, initial orbital periods, and 0.004),WR mass loss rates, as summarized in Table. 1.."," We computed 45 model sequences for initial masses of the primary star mostly from 12 to 25 $\mathrm{M}_\odot$ at two different metallicities $Z=$ 0.02 and 0.004), for different mass ratios, initial orbital periods, and WR mass loss rates, as summarized in Table. \ref{tab1}."297 The initial rotational velocity at the equatorial surface of each star is set to be of the Keplerivan value., The initial rotational velocity at the equatorial surface of each star is set to be of the Keplerivan value.298" We could not calculate more massive systems because of a numerical difficulty encountered during the mass transfer phases, except for Seq."," We could not calculate more massive systems because of a numerical difficulty encountered during the mass transfer phases, except for Seq."299" 26 where a primary star of 60 is considered with a rather large WR mass loss rate Mo(i.e., fwr= 3)."," 26 where a primary star of 60 is considered with a rather large WR mass loss rate (i.e., $f_\mathrm{WR} = 3$ )."300 The adopted initial orbital periods corresponds either to Case A or to Case B mass transfer., The adopted initial orbital periods corresponds either to Case A or to Case B mass transfer.301" In the present study, we do not consider Case C systems, but briefly discuss the possible outcomes of Case C mass transfer in Sect. ??.."," In the present study, we do not consider Case C systems, but briefly discuss the possible outcomes of Case C mass transfer in Sect. \ref{sect:dischydrogen}."302 The evolution of the primary stars is followed up to neon burning in most cases., The evolution of the primary stars is followed up to neon burning in most cases.303" We also present non-rotating single helium star models to discuss SNe Ibe progenitors in binary systems with initial masses larger than 25Mo,, and also to compare them with binary star models (Sect. ??))."," We also present non-rotating single helium star models to discuss SNe Ibc progenitors in binary systems with initial masses larger than 25, and also to compare them with binary star models (Sect. \ref{sect:sn}) )."304" In this section, we focus our discussion on the evolution of primary stars and investigate whether binary evolution via Case A or Case B mass transfer could lead to diverse pre-collapse conditions of SNe Ibc in terms of the amount of core angular momentum."," In this section, we focus our discussion on the evolution of primary stars and investigate whether binary evolution via Case A or Case B mass transfer could lead to diverse pre-collapse conditions of SNe Ibc in terms of the amount of core angular momentum."305" Although the evolution of mass-accreting secondary stars is a matter of extreme interest as discussed in Braun&Langer(1995),, Petrovicetal.(2005a) and Cantielloetal.(2007),, it is beyond the scope of this paper."," Although the evolution of mass-accreting secondary stars is a matter of extreme interest as discussed in \citet{Braun95}, \citet{Petrovic05a} and \citet{Cantiello07}, it is beyond the scope of this paper."306" Here, we first present some results including the Spruit-Tayler dynamo with our fiducial assumption on synchronization time (i.e., fsync= 1), showing that the final amount of angular momentum in the core of the primary star is not much affected by different histories of mass loss (i.e., Case AB or Case B; Sect. ??))."," Here, we first present some results including the Spruit-Tayler dynamo with our fiducial assumption on synchronization time (i.e., $f_\mathrm{sync}=1$ ), showing that the final amount of angular momentum in the core of the primary star is not much affected by different histories of mass loss (i.e., Case AB or Case B; Sect. \ref{sect:fiducial}) )."307" Then, we discuss the influences of different assumptions on tidal synchronization and transport process of angular momentum (Sect. ??))."," Then, we discuss the influences of different assumptions on tidal synchronization and transport process of angular momentum (Sect. \ref{sect:nonfiducial}) )."308 The evolution of the primary star in a close binary system is characterized by the rapid loss of mass due to Roche-lobe overflow., The evolution of the primary star in a close binary system is characterized by the rapid loss of mass due to Roche-lobe overflow.309" As an example, the evolution of the primary star in Seq."," As an example, the evolution of the primary star in Seq."310 14 is described in Figs., 14 is described in Figs.311" 2 and ὃ,, where our fiducial value of fsync=1 is adopted, including"," \ref{fig:kippseq9} and \ref{fig:hrseq9}, , where our fiducial value of $f_\mathrm{sync}=1$ is adopted, including"312station region and the Mach cones orientation at the outer boundaries.,simulation region and the Mach cones orientation at the outer boundaries.313 In 81.3 we discuss both factors., In 4.3 we discuss both factors.314" Ilere. we present results of sinulations for à fixed elougated simulation region Rowe.=θε, Zina,=200r; for three different outer boundary conditions on D,,: (1) a standard “free” boundary condition. (2) avtorce-free™ boundary condition. aud (3) a ""force-balauce boundary concditiou."," Here, we present results of simulations for a fixed elongated simulation region $R_{max}=50 r_i$ , $Z_{max}=200 r_i$ for three different outer boundary conditions on $B_\phi$: (1) a standard “free” boundary condition, (2) a“force-free” boundary condition, and (3) a “force-balance” boundary condition."315" First. we performed simulatious for the simplest standard “free” boundary coudition on ο 0DB,/0n= 0, "," First, we performed simulations for the simplest standard “free” boundary condition on $B_\phi$, $\partial B_\phi/\partial n=0$ ."316We observed that this boundary condition may cive an artificial force on the boundary which iuflueuces the flow within the computational region., We observed that this boundary condition may give an artificial force on the boundary which influences the flow within the computational region.317" For example. if we suppose that on the top boundary 0ID,,/0:=0. then the radial component of the current-density equals to zero. deco(efο =0. which means that the poloidal cureut-deusitv has oulv a z-conipoueut j,jit."," For example, if we suppose that on the top boundary $\partial B_\phi/\partial z=0$, then the radial component of the current-density equals to zero, $j_r=318-(c/4\pi){\partial B_\phi}/{\partial z}$ $=0$, which means that the poloidal current-density has only a $z$ -component ${\bf j}_p=j_z\hat{\bf z}$."319 This meaus that the poloidal curreut-density is not parallel to the poloidal maguetic field , This means that the poloidal current-density ${\bf j}_p$ is not parallel to the poloidal magnetic field ${\bf B}_p$.320"Consequcutlyj,, there is a force (deusity) Jj«B,/ez0 B,.acting in the o direction. opposite to the rotation of the disk."," Consequently, there is a force (density) ${\bf j}_p\times{\bf B}_p/c\neq 0$ acting in the $\phi$ direction, opposite to the rotation of the disk."321" Figure 5 shows the SCOTTY,", Figure 5 shows the geometry.322 These ‘boundary forces act such wav that the flow never reaches a stationary state., These `boundary' forces act such way that the flow never reaches a stationary state.323 To check this fact. aud to be sure that this is not an effect of non-stationarity of our initial configuration. we did simulations for cases which went to a stationary state with other outer boundary conditions.," To check this fact, and to be sure that this is not an effect of non-stationarity of our initial configuration, we did simulations for cases which went to a stationary state with other outer boundary conditions."324" After establishing stationarity. we substituted the outer boundary couditious on B., toa “tree” boundary condition."," After establishing stationarity, we substituted the outer boundary conditions on $B_\phi$ to a “free” boundary condition."325" We observed that the stationary state was destroved for the reasous ientioned above,", We observed that the stationary state was destroyed for the reasons mentioned above.326 Figures Ga.b demonstrate one stage of this destruction. when the poloidal velocity decreased aud became less than fast magnetosonic speed iu all of the computational reeion.," Figures 6a,b demonstrate one stage of this destruction, when the poloidal velocity decreased and became less than fast magnetosonic speed in all of the computational region."327 Even the fluxes of mass and other physical paralucters through the bouncdarics are not constants in this simulation., Even the fluxes of mass and other physical parameters through the boundaries are not constants in this simulation.328 Also. matter with iuaguetie flux euters the region from the rieht-haud side. which is due to the flow being sub-fast maguetosouic.," Also, matter with magnetic flux enters the region from the right-hand side, which is due to the flow being sub-fast magnetosonic."329" To avoid this artificial force. we proposed a “force-free” outer boundary condition ou B,, (Romanova et al."," To avoid this artificial force, we proposed a “force-free” outer boundary condition on $B_\phi$ (Romanova et al."330 1997) which we discuss in the next subsection., 1997) which we discuss in the next subsection.331 Another possibility to consideris that the toroidal component of the magnetic force is zero ou the outer boundaries., Another possibility to consideris that the toroidal component of the magnetic force is zero on the outer boundaries.332" That is. j,|B,=0 on the outer boundaries."," That is, ${\bf j}_p\parallel{\bf B}_p = 0$ on the outer boundaries."333 We can write this condition as We performed simulations with this boundary condition in the elongated region aud observed that the flow reached a stationary state (sce Figures 6 cd).," We can write this condition as We performed simulations with this boundary condition in the elongated region and observed that the flow reached a stationary state (see Figures 6 c,d)."334 This flow las many characteristics of stationary flow., This flow has many characteristics of stationary flow.335 Fluxes of mass. energy. and momentum. mnteerated over different cross-sections. are coustants.," Fluxes of mass, energy, and momentum, integrated over different cross-sections, are constants."336 Iutegrals of motion along magnetic field lines are also constants., Integrals of motion along magnetic field lines are also constants.337 The flow iscollimated iuside the simulation region (see Fieures 6c. d).," The flow is inside the simulation region (see Figures 6c, d)."338 However. more detailed anualvsis (see 8112) shows that this collimation is artificial.," However, more detailed analysis (see 4.2) shows that this collimation is artificial."339" The “force-free” boundary condition for D,, is superior to the “free” boundary condition. because it leads to a stationary state. but it does not give the plysically correct flow."," The “force-free” boundary condition for $B_\phi$ is superior to the “free” boundary condition, because it leads to a stationary state, but it does not give the physically correct flow."340 Iu reality. the magnetic force should not be zero on the boundary.," In reality, the magnetic force should not be zero on the boundary."341 There is a maenetic force pushing matter outward through the outer boundaries., There is a magnetic force pushing matter outward through the outer boundaries.342 One cau see from Fieure 6d that the poloidal current-density (dashed lues) is uot parallel to the poloidal maguetic feld (solid lines)., One can see from Figure 6d that the poloidal current-density (dashed lines) is not parallel to the poloidal magnetic field (solid lines).343 However. ou the bouudaries (Fieure 6d) the two vectors are forced to be parallel aud thus the poloidal force equals zero.," However, on the boundaries (Figure 6d) the two vectors are forced to be parallel and thus the poloidal force equals zero."344 This boundary condition is better than the “free” boundary condition in the sense that there is no strong artificial force at the boundary., This boundary condition is better than the “free” boundary condition in the sense that there is no strong artificial force at the boundary.345 From the other side. when we put the force equal to zero. it is analogous to application of a force equal to the real force but with the opposite sign.," From the other side, when we put the force equal to zero, it is analogous to application of a force equal to the real force but with the opposite sign."346 This is one of the factors which may lead to artificial collimation., This is one of the factors which may lead to artificial collimation.347 Another possible factor (Mach cones orientation) depends on the shape of the simulation region aud ds discussed in 81.2., Another possible factor (Mach cones orientation) depends on the shape of the simulation region and is discussed in 4.2.348" As a next step for improving the outer boundary condition on D,. we take into account the fact that the magnetic field is not force-free aud j, is uot parallel to B,,."," As a next step for improving the outer boundary condition on $B_\phi$, we take into account the fact that the magnetic field is not force-free and ${\bf j}_p$ is not parallel to ${\bf B}_p$."349" We start from equation (16) for B., aud write it iu the forma where we asstune that the density at the boundary is much less than that at the Alfvéun surface. p« for mpDrn."," We start from equation (16) for $B_\phi$ and write it in the form where we assume that the density at the boundary is much less than that at the Alfvénn surface, $\rho \ll \rho_A$ for $r^2 \gg r_A^2$."350 Then. we obtain where we supposed that pr?=FOL aud took iuto account that Ὁ aud p4 are constauts along magnetic feld lines.," Then, we obtain where we supposed that $\rho r^2 = F(\Psi) r^\alpha$ and took into account that $\Omega$ and $\rho_A$ are constants along magnetic field lines."351 Finally. we obtain the outer boundary condition as where à is a parameter.," Finally, we obtain the outer boundary condition as where $\alpha$ is a parameter."352 In this case we got stationary flows which arecollimated iu the simulation region (sce Figures Go. £f).," In this case we got stationary flows which are in the simulation region (see Figures 6e, f)."353 Fluxes through the outer surfaces aud integrals along maguetic field lines are well conserved. as in the case of collinated flow. described in 811.2.," Fluxes through the outer surfaces and integrals along magnetic field lines are well conserved, as in the case of collimated flow, described in 4.1.2."354 The question arises. which boundary condition is correct. “force-free” or “force-balauce”ο," The question arises, which boundary condition is correct, “force-free” or “force-balance”?"355 The Uforee-balance’ coucdition is clearly the physical coudition because it does not generate an artificial force on the boundary., The ``force-balance'' condition is clearly the physical condition because it does not generate an artificial force on the boundary.356 However. it is more dif&cultto apply because there is no direct method for determining the parameter a.," However, it is more difficultto apply because there is no direct method for determining the parameter $\alpha$ ."357 It can only be obtained iteratively using additional simulations. which is very time consunmiug.," It can only be obtained iteratively using additional simulations, which is very time consuming."358 Our analysis, Our analysis359here for simplicity). whose scalings can be derived from simple dimensional considerations (as shown above).,"here for simplicity), whose scalings can be derived from simple dimensional considerations (as shown above)."360" For example. F,4x and FuexΕμμ} for PLSs D and F. respectively. using the notations of Granot&Sari(2002)..."," For example, $F_{\rm\nu,D} \approx F_{\nu,{\rm max}}(\nu/\nu_m)^{1/3}$ and $F_{\rm\nu,F}\approx F_{\nu,{\rm max}} (\nu/\nu_c)^{-1/2}$ for PLSs D and F, respectively, using the notations of \citet{GS02}. ."361" This implies that F2,/F.p.=eal—xl? tay=4/3 and by= -bD and ΕλΕν=UaoSU qas=3/4 and b,= —1/4)."," This implies that $F'_{\nu,D}/F_{\nu,D}362=\zeta^{4/3}\alpha^{-1}\to\kappa\lambda^{1/3}$ $a_D = 4/3$ and $b_D =363-1$ ) and $F'_{\nu,F}/F_{\nu,F}364=\zeta^{3/4}\alpha^{-1/4}\to\kappa^{2/3}\lambda^{1/12}$ $a_F = 3/4$ and $b_F = -1/4$ )."365" As illustrative examples of how the sealings for self-absorbed PLSs may be derived. one can readily obtain that FammUR/EDYQiγιο«R implying FlPap= quyΟΙ=O and by= 2). while foryl PLS A Yin is replaced by y-096O/F [obtained from requiring vosvaa)~ DteBfm,.cyy;]. implying F4«1?“Rep,|* and BIR=icaloanIpICU qu ο."," As illustrative examples of how the scalings for self-absorbed PLSs may be derived, one can readily obtain that $F_{\rm\nu,B} \approx \pi(R/\Gamma D)^2(2\nu^2/c^2)\Gamma\gamma_m m_e366c^2 \propto \nu^2R^2$ implying $F'_{\nu,B}/F_{\nu,B}367=\zeta^{0}\alpha^{2}\to\kappa^{2/3}\lambda^{-2/3}$ $a_B = 0$ and $b_B368= 2$ ), while for PLS A $\gamma_m$ is replaced by $\gamma_e(\nu)369\propto (\nu/\Gamma B)^{1/2}$ [obtained from requiring $\nu\sim \nu_{\rm370syn}(\gamma_e) \sim \Gamma(eB/m_e c)\gamma_e^2$ ], implying $F_{\rm\nu,A} \propto \nu^{5/2}R^2\rho_{\rm u}^{-1/4}$ and $F'_{\nu,A}/F_{\nu,A}371=\zeta^{-1/4}\alpha^{11/4}\to\kappa^{2/3}\lambda^{-11/12}$ $a_A =372-1/4$ and $b_A = 11/4$ )."373 Therefore. these scalings (or a; and bj) do not depend on the external density profile or on the details of the dynamics (and are the same in the relativistic and Newtonian self-similar regimes. when the dynamics are not self-similar. or for the reverse shock).," Therefore, these scalings (or $a_i$ and $b_i$ ) do not depend on the external density profile or on the details of the dynamics (and are the same in the relativistic and Newtonian self-similar regimes, when the dynamics are not self-similar, or for the reverse shock)."374 All of the ditterent scalings are summarized in table 2.., All of the different scalings are summarized in table \ref{tab:PLS}.375 The freedom in the choice of units in the dynamical equations that describe the evolution of ditferent types of physical systems and in their solutions. has been outlined and elucidated.," The freedom in the choice of units in the dynamical equations that describe the evolution of different types of physical systems and in their solutions, has been outlined and elucidated."376 The main results are summarized in Table I.., The main results are summarized in Table \ref{tab:sum}.377 While the emphasis was on numerical solutions of the dynamical equations through simulations. similar scalings hold equally well for analytic solutions of the same equations.," While the emphasis was on numerical solutions of the dynamical equations through simulations, similar scalings hold equally well for analytic solutions of the same equations."378 The number of free parameters N; that describe the family of physical systems that corresponds to a given solution of such a set of equations is given by max(O.3—Αμ) (Eq. 1).," The number of free parameters $N_{\rm f}$ that describe the family of physical systems that corresponds to a given solution of such a set of equations is given by $\max(0,3-N_{\rm udc})$ (Eq. \ref{eq:N_f}] ]),"379 where Nye is the number of independent (in terms of their units) universal dimensional constants (UDCs. such as c. ο. fe m. etc).," where $N_{\rm udc}$ is the number of independent (in terms of their units) universal dimensional constants (UDCs, such as $c$, $G$, $\hbar$, $m_e$, etc.)."380 This corresponds to the three basic physical units Cof mass. length and time) while accounting for the independent constraints on their possible rescalings.," This corresponds to the three basic physical units (of mass, length and time) while accounting for the independent constraints on their possible rescalings."381 Such resealings of the basic units are potentially relevant to many ditferent areas of research. such as plasma physics. astrophysics. cosmology. fluid dynamics or Earth and planetary sciences.," Such rescalings of the basic units are potentially relevant to many different areas of research, such as plasma physics, astrophysics, cosmology, fluid dynamics or Earth and planetary sciences."382 They can prove very useful in numerical studies of various physical systems. and save precious computational resources. especially in systematic numerical studies ofa arge parameter space.," They can prove very useful in numerical studies of various physical systems, and save precious computational resources, especially in systematic numerical studies of a large parameter space."383 The author thanks E. Nakar. F. van den Bosch. F. DeColle. T. Piran. O. Bromberg. E. Ramirez-Ruiz and the anonymous referee for useful discussions. suggestions or comments on the manuscript.," The author thanks E. Nakar, F. van den Bosch, F. DeColle, T. Piran, O. Bromberg, E. Ramirez-Ruiz and the anonymous referee for useful discussions, suggestions or comments on the manuscript."384 This research was supported by the ERC advanced research grant “GRBs”., This research was supported by the ERC advanced research grant “GRBs”.385confidence.,confidence.386 Lower ratios seem to be a characteristic of curichment at 5>2 (Finoguenov ct al., Lower ratios seem to be a characteristic of enrichment at $z>2$ (Finoguenov et al.387 2003). while siauulations sueecst that the WIITM. originates at 2<1 (Con Ostriker 1999).," 2003b), while simulations suggest that the WHIM originates at $z<1$ (Cen Ostriker 1999)."388 Wlile we would rather have more observational evidence on the dispersion of O to alpha clement ratios at different sites. we believe that this is a majorJ source of systelatics in interpreting the clement abuudauce of N-ray laments as a universal value.," While we would rather have more observational evidence on the dispersion of O to alpha element ratios at different sites, we believe that this is a major source of systematics in interpreting the element abundance of X-ray filaments as a universal value."389" To illustrate the point. we calculate the deusity of barvous traced by the OVT absorbers under two sets of assunptious,"," To illustrate the point, we calculate the density of baryons traced by the OVI absorbers under two sets of assumptions."390 Scaling the original value of O4(OQVI)=0013741 of Tripp ct al. (, Scaling the original value of $\Omega_b(OVI) = 0.0043h_{70}^{-1}$ of Tripp et al. (3912000) for ionization equilibrium implied by measurements of Mathlur et al. (,2000) for ionization equilibrium implied by measurements of Mathur et al. (3922003) and using the measurements of the O abundance reported here vields: The formal errorbar is 0.006. mostly froii the uucertainty iu the estimate for iouization.,"2003) and using the measurements of the O abundance reported here yields: The formal errorbar is 0.006, mostly from the uncertainty in the estimate for ionization."393 If. on the other hand. our measurements of Ne abundance are used with the Ne/O ratio for OVI absorbers frou: Nicastro et al. (," If, on the other hand, our measurements of Ne abundance are used with the Ne/O ratio for OVI absorbers from Nicastro et al. ("394"2002) then. Therefore the second set of assunptiouns must be invalid suce the total barvon deusity is Qtoral=0.039, leaving no room for other major components of local burxuvons 1 suchas Lv,Ly, absorbersabsorl (0.012=+0.0020.002) aud starst aud clusters of galaxies (~0.006: ο-ο,, Fiuogueuov et al.","2002) then, Therefore the second set of assumptions must be invalid since the total baryon density is $\Omega_b^{\rm total}=0.039$, leaving no room for other major components of local baryons such as $_\alpha$ absorbers $0.012\pm0.002$ ) and stars and clusters of galaxies $\sim0.006$; e.g., Finoguenov et al."395 2003b and references therein)., 2003b and references therein).396 O depletion outo dust eraius in the OVI absorbers. as suggestedby Nicastroct al. (," O depletion onto dust grains in the OVI absorbers, as suggested by Nicastro et al. ("3972002) as an explanation of the high Ne/O ratio. docs uot explain the unacceptably high barvou abundance iuplied w Eq. (,"2002) as an explanation of the high Ne/O ratio, does not explain the unacceptably high baryon abundance implied by Eq. ("3982). since the solar Ne/O ratio in our observations nav be simply explained by dust sputtering.,"2), since the solar Ne/O ratio in our observations may be simply explained by dust sputtering."399 The observational determination of scaling relatious vetween X-rav properties such as luninositv Ly. eas cluperature TZ. and eutropy is crucial in establishing he phvsieal properties of the ICAL," The observational determination of scaling relations between X-ray properties, such as luminosity $L_X$, gas temperature $T$, and entropy is crucial in establishing the physical properties of the ICM."400 The slopes of he LyT cud inasstemperature relations (e.g. Markevitch 1998: Finoenenoy et al, The slopes of the $L_X-T$ and mass–temperature relations (e.g. Markevitch 1998; Finoguenov et al.401 2001) aud the eas entropy level (e.g. Pouman et al., 2001) and the gas entropy level (e.g. Ponman et al.402 1999: Finoenenov et al., 1999; Finoguenov et al.403 2002) are all at variance with model predictions sed oon pure eravitational heating (INaiser 1986) and require the introduction of extra plivsics to describe the rermmodvnainics of the ICAL (e.g. Evrard Heury 1901: Kaiser 1991)., 2002) are all at variance with model predictions based on pure gravitational heating (Kaiser 1986) and require the introduction of extra physics to describe the thermodynamics of the ICM (e.g. Evrard Henry 1991; Kaiser 1991).404 An often discussed piece of extra physics is preheating of the barvons before they acerete outo ie cluster., An often discussed piece of extra physics is preheating of the baryons before they accrete onto the cluster.405 Most barvous that accrete onto clusters are nought to come from fikumeuts. so we now have au opportunity to compare the ποιοναο properties of 1e filament gas with that of group and cluster eas.," Most baryons that accrete onto clusters are thought to come from filaments, so we now have an opportunity to compare the thermodynamic properties of the filament gas with that of group and cluster gas."406 The (itropy of the N-vay cmitting filament is 150 keV eng. which could be reproduced by heating while falling outo a filament (c.g. Con Ostriker 1999).," The entropy of the X-ray emitting filament is 150 keV $^2$, which could be reproduced by heating while falling onto a filament (e.g. Cen Ostriker 1999)."407 Iu fact. estimating the expected Mach iuuber of the accretion shock when the filament euters the Coma cluster vields à value of Lb. similar to predictions of simmlations by Màiniati et al. (," In fact, estimating the expected Mach number of the accretion shock when the filament enters the Coma cluster yields a value of 4, similar to predictions of simulations by Miniati et al. ("4082000).,2000).409 Reeardless of the origin of the cutropy of the filamentary gas. its entropy is nmeh simaller than the 100 keV cm? implied by ASCA observations of the outskirts of eroups (Fiuoguenov ct al.," Regardless of the origin of the entropy of the filamentary gas, its entropy is much smaller than the 400 keV $^2$ implied by ASCA observations of the outskirts of groups (Finoguenov et al."410 2002). ruling out a universal preheating value.," 2002), ruling out a universal preheating value."411 We note that the euerevoO. of the oOeas (2422=0.36+0.02 keV/particle) is similar. although higher than the SNe energy associated with euricluueut of eas to the observed O abundance (0.22+0.03. keV/particle). so heating by galactic winds is not ruled out.," We note that the energy of the gas ${3\over2}kT=0.36\pm0.02$ keV/particle) is similar, although higher than the SNe energy associated with enrichment of gas to the observed O abundance $0.22\pm0.03$ keV/particle), so heating by galactic winds is not ruled out."412 Although. the temperature of the filament is presently a factor of 10 lower than the Coma virial temperature. as it falls into the cluster it will be shock heated. aud its final adiabat will be higher than iu the selfsimular TL (Dox Santos Doré 2002: Ponnuui et al.," Although, the temperature of the filament is presently a factor of 40 lower than the Coma virial temperature, as it falls into the cluster it will be shock heated, and its final adiabat will be higher than in the self-similar case (Dos Santos Doré 2002; Ponman et al."413 2003)., 2003).414 Since the mass of the fibunent is compirable to that of the Coma cluster. the combined object will also deviate from cluster scaling relatious.," Since the mass of the filament is comparable to that of the Coma cluster, the combined object will also deviate from cluster scaling relations."415 Observations indicate that the gas-to-dark matter distribution will uot be affected (Sauderson et al., Observations indicate that the gas-to-dark matter distribution will not be affected (Sanderson et al.416 2003). but the temperature is hieher for a giveu mass (Finoguenuov ct al.," 2003), but the temperature is higher for a given mass (Finoguenov et al."417 2001)., 2001).418" This process is probably not muniversal, since some groups o: galaxies have “shallow eas profiles. thus possibly poiutiug to adiabatic compression rather than shock heatiug of the prelieated gas. ax proposed by Tozzi Norman (2001)."," This process is probably not universal, since some groups of galaxies have shallow gas profiles, thus possibly pointing to adiabatic compression rather than shock heating of the preheated gas, as proposed by Tozzi Norman (2001)."419 If the structures reported here are oulv associated withi largearee clusters of galaxies.e@alaxics. theirir coutributioutiibutiou fο the barvou budget is negligible (0.1-14)).," If the structures reported here are only associated with large clusters of galaxies, their contribution to the baryon budget is negligible )."420. Of. greater importance is to investigate the accreting environment of the massive groups aud poor clusters that lave a significant cutry in the barvou budget (6560)., Of greater importance is to investigate the accreting environment of the massive groups and poor clusters that have a significant entry in the baryon budget ).421 Tlowever. carly curichiment epoch. suggested by low Ne/O ratio. makes X-ray fibunents a substautial entry iu the ictal budget at high redshifts.," However, early enrichment epoch, suggested by low Ne/O ratio, makes X-ray filaments a substantial entry in the metal budget at high redshifts."422 The thermodvuaiic state of the filamentary gas causes a global feedback effect on the embedded: galaxies by straugliug the eas accretion (Fiuoguenuov et al., The thermodynamic state of the filamentary gas causes a global feedback effect on the embedded galaxies by strangling the gas accretion (Finoguenov et al.423 20032: OL Beuson 2003)., 2003a; Oh Benson 2003).424 The resulting starformation will proceed by consumption of the previously accumulated eas. iu either quicscent mode as in the disk. or mereer-aincdiuced bursts leading to formation of the spheroid (Somerville ct al.," The resulting star-formation will proceed by consumption of the previously accumulated gas, in either quiescent mode as in the disk, or merger-induced bursts leading to formation of the spheroid (Somerville et al."425 2001)., 2001).426 Galaxy ierecrs are frequent inside galaxy groups (Nodama ct al., Galaxy mergers are frequent inside galaxy groups (Kodama et al.427 2001). but in a filament the infall of the eas will primarily be recorded iun the star-formation history of the disk (J&ennieutt et al.," 2001), but in a filament the infall of the gas will primarily be recorded in the star-formation history of the disk (Kennicutt et al."428 1991)., 1994).429 A relevant observation could therefore shed light on the feedback epoch. which is crucial i understanding the relation between the N-rav Glameuts aud OVI absorbers.," A relevant observation could therefore shed light on the feedback epoch, which is crucial in understanding the relation between the X-ray filaments and OVI absorbers."430 The recent Sloan Digital Sky Survey (SDSS) discovery of passive spirals. iu the same filament iu frout of Coma (Coto et al.," The recent Sloan Digital Sky Survey (SDSS) discovery of passive spirals, in the same filament in front of Coma (Goto et al."431 2003). is exactly what is expected from this strangulation process.," 2003), is exactly what is expected from this strangulation process."432 The existence of these passive spirals lends further support to the association of the soft X-ray excess with the Coma filament., The existence of these passive spirals lends further support to the association of the soft X-ray excess with the Coma filament.433 As passive spirals are starting to be found im the outskirts of may, As passive spirals are starting to be found in the outskirts of many434the Lamanu-Werner background. (Machaceketal.Abel2007:O'Shea&Nonuau 2008)..,"the Lyman-Werner background \citep{Mac01, Mac03, Yos03, Sus07, Wis07, O'S08}. ."435 The Lyinan-Werner background thus increases cooling times iu the centers of such halos., The Lyman-Werner background thus increases cooling times in the centers of such halos.436 Asa result. the minima niass of a star-forming halo increases with the Lyuiui-Werner backeround intensity.," As a result, the minimum mass of a star-forming halo increases with the Lyman-Werner background intensity."437 The Lxiuau-Werner backgrouud becomes less of an issue iu atomic line cooling halos as Lya cooling provides wuple amounts of free clectrous for Πο cooling. and they become seltshiclding to this raciatio- (O'Shea&Norman2008:SusaWiseAbeaa2008:Wise&Cen 2009).," The Lyman-Werner background becomes less of an issue in atomic line cooling halos as $\alpha$ cooling provides ample amounts of free electrons for ${\rm H}_{2}$ cooling, and they become self-shielding to this radiation \citep{O'S08, Sus08, Wis08, Wis09}."438. Tn the later epoch. dust ejected bv stars in ealaxies is effective to shield the Lyian-Werner backeroundC» and acts as an effective. catalyst for Il» molecule production ou the dust grains.," In the later epoch, dust ejected by stars in galaxies is effective to shield the Lyman-Werner background and acts as an effective catalyst for ${\rm H}_{2}$ molecule production on the dust grains."439 Iu smaunulatious with star formation inodels based ou nolecular lvdrogen (Robertson&IEuavtsov2008:(ποσαetal. 2009).. once the eas enriched up to Z~0.011Z.. the subsequent star formation aud enrichment of metal anc dust can be απο more accelerated.," In simulations with star formation models based on molecular hydrogen \citep{Rob08, Gne09}, once the gas enriched up to $Z\sim0.01-0.1\ {Z_{\odot}}$, the subsequent star formation and enrichment of metal and dust can be much more accelerated."440 Cuedietal.(2000) show that the transition from atomic to molecular hydrogen depends primarily on metallicity. asstunineg that the dust abundance is directly related to metallicity.," \citet{Gne09} show that the transition from atomic to molecular hydrogen depends primarily on metallicity, assuming that the dust abundance is directly related to metallicity."441 Dus plavs a crucial role iu the star formation: (1) molecular bydrogen is produced more efficiently ou dust erains than m gas plase. (i) dust shiclds dissociating UV. radiation. and (3) dust allows the formation of low-mass stars in low-1uetallicitv chviromlments. aud hence affects the initial mass function (IME) (Oxninkaietal.2005:Schneider 2010).," Dust plays a crucial role in the star formation: (i) molecular hydrogen is produced more efficiently on dust grains than in gas phase, (ii) dust shields dissociating UV radiation, and (iii) dust allows the formation of low-mass stars in low-metallicity environments, and hence affects the initial mass function (IMF) \citep{Omu05, Sch06, Sch10, Omu10}."442. Iu theoretical studies on the molecular abuudauce in the interstellar medium (ISM). dust abuudanuce i» often scaled with the metallicity and dust erain properties are assuned to be the same as iu the local ISAL," In theoretical studies on the molecular abundance in the interstellar medium (ISM), dust abundance is often scaled with the metallicity and dust grain properties are assumed to be the same as in the local ISM."443 However. the composition of dust is likely to be differcut in early galaxies.," However, the composition of dust is likely to be different in early galaxies."444 The observational evidence is that the dust extinction curves of the broad absorption line quasars at ;Dom Lare likely to be due to the type II SN (SN ID dust (Maiolinoetal.2001:Callerani 2010).," The observational evidence is that the dust extinction curves of the broad absorption line quasars at $z>4$ are likely to be due to the type II SN (SN II) dust \citep{Mai04, Gal10}."445. Since the lifetime of SN II progenitor is short. SN II can be the dominant production source of dust erünus in voune («1 Cor) galaxies.," Since the lifetime of SN II progenitor is short, SN II can be the dominant production source of dust grains in young $<1$ Gyr) galaxies."446 Primeval SNe produced by Population III stars (Brounetal.2008) may contribute the dust production (Nozawactal.2003:Schneideret2001).," Primeval SNe produced by Population III stars \citep{Bro03, Kit05, Wha08} may contribute the dust production \citep{Noz03, Sch04}."447. The winds of evolved low-mass stars contribute to dust formation considerably in nearby galaxies. but the cosmic time is uot long enough for such stars to evolve at hieh redshift (2=5) where all galaxies should have ages vounecr than z1 Civ.," The winds of evolved low-mass stars contribute to dust formation considerably in nearby galaxies, but the cosmic time is not long enough for such stars to evolve at high redshift $z>5$ ) where all galaxies should have ages younger than $\simeq 1$ Gyr."448 Contribution of dust production by low-1ass stars is not donünant iu such vouug galaxies., Contribution of dust production by low-mass stars is not dominant in such young galaxies.449 Iun addition. dust is destroved bv SN. shocks.," In addition, dust is destroyed by SN shocks."450 Thus. the modeling of dust evolution in galaxies requires an accurate treatineut of production and destruction of dust eraius together with star formation activities (Ilirashita&Ferrara2002).," Thus, the modeling of dust evolution in galaxies requires an accurate treatment of production and destruction of dust grains together with star formation activities \citep{Hir02}."451. Iun this paper. we investigate uot only the evolution of dust mass but also the time evolution of dust size distribution.," In this paper, we investigate not only the evolution of dust mass but also the time evolution of dust size distribution."452 The dust size distribution evolves rapidly because of the destruction by sputtering in the high-velocitv shocks driven bx SNe., The dust size distribution evolves rapidly because of the destruction by sputtering in the high-velocity shocks driven by SNe.453 Collision of the expauding SN cjecta with the surrounding ISM. creates a forward shock at the interface between the ejecta and the ISM (Nozawactal.2006).. and a reverse shock that penetrates into the ejecta (Bianchi&Schucideretal. 2010).," Collision of the expanding SN ejecta with the surrounding ISM creates a forward shock at the interface between the ejecta and the ISM \citep{Noz06}, and a reverse shock that penetrates into the ejecta \citep{Bia07, Noz07, Nat08, Sil10}."454. Since the erosion rate by sputtering does not stronely depeud on the erain size. s122ll erains are predoniünantlv destroved regardless of erain species.," Since the erosion rate by sputtering does not strongly depend on the grain size, small grains are predominantly destroyed regardless of grain species."455 Therefore. the fraction of small size erains relatively decreases with galaxy evolution.," Therefore, the fraction of small size grains relatively decreases with galaxy evolution."456 We focus on the effects of molecular hydrogen abundance ou the SER in the carly stage of galaxy evolution. talking iuto account molecular formation on dust. «nee IH» formation on dust surface is very effective (Iirashita&Ferrara2002:Cazaux&Spaans200 [).," We focus on the effects of molecular hydrogen abundance on the SFR in the early stage of galaxy evolution, taking into account molecular formation on dust, since ${\rm H}_{2}$ formation on dust surface is very effective \citep{Hir02, Caz04}."457. IDirashita&Ferrara(2002) slow that this effect causes an eublauceioeut of the SER by an order of magnitude on a timescale of 3/5 ealactic dynamical time., \citet{Hir02} show that this effect causes an enhancement of the SFR by an order of magnitude on a timescale of $3-5$ galactic dynamical time.458 Iowever. they assuued a single dust eraiu size (~1.03 pau).," However, they assumed a single dust grain size $\sim0.03\ \mu{\rm m}$ )."459 We adopt more accurate analytic forilac for theformation of molecular hydrogeu ou ¢ust eraius than Iirashita by usiic the results of dust size distribution by Nozawactal(2006.2007 )..," We adopt more accurate analytic formulae for theformation of molecular hydrogen on dust grains than \citet{Hir02} by using the results of dust size distribution by \citet{Noz06, Noz07}. ."460 This is the first stidv ongalaxy evolution considering dust size evolution for halo masses above 108? in the high-redshift (5«+ 10). whose interiors we expect to be roughly," This is the first study ongalaxy evolution considering dust size evolution for halo masses above $10^{8-9}$ in the high-redshift $5<z<10$ ), whose interiors we expect to be roughly"461as m each night images of the wide binaries 442758. 445072. HIP446657. HIP550602.,"as in each night images of the wide binaries 42758, 45072, 46657, 50602."462 The instrument. Is found to be stable within the individual nights in May 2010., The instrument is found to be stable within the individual nights in May 2010.463" In addition. to our K-band observations we also obtained images in the J-. and H-band to determine the infrared photometry of BB. The magnitude difference between BB and its primary is measured always after the subtraction of the PSF of the bright star in all NACO images. and is summarized in reftable,froro.."," In addition, to our $\rm K_{s}$ -band observations we also obtained images in the J-, and H-band to determine the infrared photometry of B. The magnitude difference between B and its primary is measured always after the subtraction of the PSF of the bright star in all NACO images, and is summarized in \\ref{table_photo}."464" As AA is saturated in our deep NACO images. taken in September 2009. only a lowerlimit for the difference in the K.-band could be derived (AK,>3.0+0.1 mmag)."," As A is saturated in our deep NACO images, taken in September 2009, only a lowerlimit for the magnitude-difference in the $\rm K_{s}$ -band could be derived $\Delta K_{s} > 5.0\pm0.1$ mag)."465 The determined limit agrees with the photometry of BB obtained in all other observing epochs. in which NACO's neutral density filter σι was used in the case that AA would have saturated the NACO detector.," The determined limit agrees with the photometry of B obtained in all other observing epochs, in which NACO's neutral density filter $\rm ND_{Short}$ was used in the case that A would have saturated the NACO detector."466" The photometric measurements from the individual observing epochs are all consistent with each other within their uncertainties,", The photometric measurements from the individual observing epochs are all consistent with each other within their uncertainties.467" The apparent magnitudes of BB and its primary can be derived with the obtained magnitude-differences. as well as the accurate photometry of the TTel system 6.856+0.021] mmag. H=6.486+0.049 mmag. K,=6.366+0.024HL mmag). which is listed in the 2MASS point source catalogue (?).."," The apparent magnitudes of B and its primary can be derived with the obtained magnitude-differences, as well as the accurate photometry of the Tel system $J = 6.856 \pm 0.021$ mag, $H = 6.486 \pm 0.049$ mag, $K_{s} = 6.366 \pm 0.024$ mag), which is listed in the 2MASS point source catalogue \citep{skrutskie2006}."468" Finally. the precise Hipparcos parallax of TTelNd d distance modulus E=3.48040.127 mmag. which is usec05 derive the absolute magnitudes of BB 0.]2mmag. Mj;=8.52+40.13 mmag. and My=82440.10 mmag). assuming that the NACO and 2MASS JHK, color systems are identical."," Finally, the precise Hipparcos parallax of Telyields a distance modulus $E=3.480\pm0.127$ mag, which is used to derive the absolute magnitudes of B $M_{J}=9.05\pm0.12$ mag, $M_{H}=8.52\pm0.13$ mag, and $M_{K_{s}}=8.24\pm0.10$ mag), assuming that the NACO and 2MASS $K_{s}$ color systems are identical."469" We obtained deep NACO observations of AA and its companion in September 2009 in the K,-band.", We obtained deep NACO observations of A and its companion in September 2009 in the $\rm K_{s}$ -band.470 The achieved detection limit of our NACO image with and without PSF subtraction is shown in reflimit together with the expected magnitudes of substellar objects with different masses at an assumed age of MMyr. derived with the ? evolutionary models and the well know1 distance of the TTel system.," The achieved detection limit of our NACO image with and without PSF subtraction is shown in \\ref{limit} together with the expected magnitudes of substellar objects with different masses at an assumed age of Myr, derived with the \cite{baraffe2003} evolutionary models and the well known distance of the Tel system."471 After PSF subtraction. all brown dwarf companions (mass>12 M4) are detectable in our NACO image beyond aaresec (or ~ AAU of projected separation) arounc AA up to about aaresee (~ AAU) at the outer edge of the field of view. fully covered by NACO's S13 optics (Jitter-width. taken into account).," After PSF subtraction, all brown dwarf companions $>12\,M_{Jup}$ ) are detectable in our NACO image beyond arcsec (or $\sim$ AU of projected separation) around A up to about arcsec $\sim$ AU) at the outer edge of the field of view, fully covered by NACO's S13 optics (jitter-width taken into account)."472" In the background noise limited region. beyond a separation of about aaresec (~ AAU). a sensitivity of K,=19.6 mmag ts reached i1 average. Which allows the detection of planetary mass objects down to a mass of about 2M,,,,, around AA. Beside BB. one further very funt (AK,> mmag) companion-candidate is detected in. our deep NACO image at sep=3.818+0.006 aarcsec. and PA= 0.117."," In the background noise limited region, beyond a separation of about arcsec $\sim$ AU), a sensitivity of $K_{s} = 19.6$ mag is reached in average, which allows the detection of planetary mass objects down to a mass of about $2\,M_{Jup}$ around A. Beside B, one further very faint $\Delta K_{s}>10.2$ mag) companion-candidate is detected in our deep NACO image at $sep = 3.818\pm0.006$ arcsec, and $PA=166.21\pm0.11^{\circ}$ ."473 This candidate was already detected by ?.. who proposed that it is most probably à background source (Epoch:," This candidate was already detected by \cite{chauvin2010}, , who proposed that it is most probably a background source (Epoch:"474but speeds of ~2 km/s are found already in the inner penumbra.,but speeds of $\sim 2$ km/s are found already in the inner penumbra.475 Phenomena strikingly similar to the overturning motion in the penumbral filaments presented in the previous section are seen in high-resolution observations of convection around the small magnetic elements that make up most of a young active region., Phenomena strikingly similar to the overturning motion in the penumbral filaments presented in the previous section are seen in high-resolution observations of convection around the small magnetic elements that make up most of a young active region.476" An example is shown in Fig. 4,,"," An example is shown in Fig. \ref{oslo},"477 taken on 10 May 2004 with the SST., taken on 10 May 2004 with the SST.478" The magnetic field in such elements reduces the gas pressure, so they are more transparent and appear as ‘dips’, or depressions in the observed surface of the Sun (Spruit 1976, 1977)."," The magnetic field in such elements reduces the gas pressure, so they are more transparent and appear as `dips', or depressions in the observed surface of the Sun (Spruit 1976, 1977)."479 This is particularly clear in observations near the limb of the Sun., This is particularly clear in observations near the limb of the Sun.480 The limb-side rim of such a dip is seen as a brightening while the proximal boundary is obscured., The limb-side rim of such a dip is seen as a brightening while the proximal boundary is obscured.481 Radiative cooling of gas surrounding the boundary increases its density; as a consequence the element is surrounded by convective downflows., Radiative cooling of gas surrounding the boundary increases its density; as a consequence the element is surrounded by convective downflows.482" Given sufficient spatial resolution, these flows can be observed directly in time sequences of images such as Fig. 4.."," Given sufficient spatial resolution, these flows can be observed directly in time sequences of images such as Fig. \ref{oslo}."483 The phenomenology seen in such observations has been reproduced in detail by radiative magnetohydrodynamic simulations (Carlsson et al., The phenomenology seen in such observations has been reproduced in detail by radiative magnetohydrodynamic simulations (Carlsson et al.484" 2004, Keller et al 2004, De Pontieu et al."," 2004, Keller et al 2004, De Pontieu et al."485" 2006, see also Steiner 2005)."," 2006, see also Steiner 2005)."486 We can thus be confident of the interpretation given above: we have a good understanding of what overturning convection along a magnetic boundary in the solar photosphere looks like., We can thus be confident of the interpretation given above: we have a good understanding of what overturning convection along a magnetic boundary in the solar photosphere looks like.487" The boiling, overturning impression given by the penumbral movie of Fig."," The boiling, overturning impression given by the penumbral movie of Fig."488 1 is similar to the flows seen on the limb side of the pores in Fig. 4.., \ref{stria} is similar to the flows seen on the limb side of the pores in Fig. \ref{oslo}.489" Apart from the overall impression, the time scales and length scales as well as the ‘striated’ substructure are common properties."," Apart from the overall impression, the time scales and length scales as well as the `striated' substructure are common properties."490 'The main difference is the orientation of the striation., The main difference is the orientation of the striation.491 In the magnetic structures in refoslo the striation is parallel to the downward flow; in the penumbral filament it is at an angle., In the magnetic structures in \\ref{oslo} the striation is parallel to the downward flow; in the penumbral filament it is at an angle.492 For isolated magnetic elements we know that the striation follows magnetic field lines: it is a corrugation of the surface bounding the magnetic structure from the surrounding convection zone. [, For isolated magnetic elements we know that the striation follows magnetic field lines: it is a corrugation of the surface bounding the magnetic structure from the surrounding convection zone. [493"This is demonstrated by comparison with the MHD simulations, DDe Pontieu et al.","This is demonstrated by comparison with the MHD simulations, De Pontieu et al."494 2006]., 2006].495" The striation in the penumbral filament, on the other hand, is inclined at angles expected for the field at such a position in the penumbra."," The striation in the penumbral filament, on the other hand, is inclined at angles expected for the field at such a position in the penumbra."496" The obvious interpretation is thus that the striation is a corrugation of the magnetic surface surrounding the filament, outlining the direction of the field lines."," The obvious interpretation is thus that the striation is a corrugation of the magnetic surface surrounding the filament, outlining the direction of the field lines."497" The downflow along the boundary, carrying the corrugation with it, causes an apparent outward motion of the striation."," The downflow along the boundary, carrying the corrugation with it, causes an apparent outward motion of the striation."498 It is likely that a real outward fluid motion along the gap also contributes to the motion of the striation., It is likely that a real outward fluid motion along the gap also contributes to the motion of the striation.499 The numerical simulations of Heinemann et al. (, The numerical simulations of Heinemann et al. (500"2007) show an outward flow in the gaps, along the boundary with the magnetic field.","2007) show an outward flow in the gaps, along the boundary with the magnetic field."501 Scharmer et al. (, Scharmer et al. (502"2008) discuss its origin,","2008) discuss its origin,"503visible at 10” from the center.,visible at $\arcsec$ from the center.504" Both from the VDP and from the RC of NGC 1427 there is evidence for kinematically distinct components at the inner 2"" and inside 10” from the center; NGC 1427 shows also anti-correlated wiggles in both the RC and the VDP.", Both from the VDP and from the RC of NGC 1427 there is evidence for kinematically distinct components at the inner $\arcsec$ and inside $\arcsec$ from the center; NGC 1427 shows also anti-correlated wiggles in both the RC and the VDP.505 In summary: it seems that more than half of the galaxies in the present sample are. at least from the kinematical point of view. misclassified S(A-B)Os.," In summary: it seems that more than half of the galaxies in the present sample are, at least from the kinematical point of view, misclassified S(A-B)0s."506" Morphological classification by visual inspection of images. apparently results in a dramatic over-estimate of the true number of ""dynamically hot’ stellar systems."," Morphological classification by visual inspection of images, apparently results in a dramatic over-estimate of the true number of `dynamically hot' stellar systems."507 The catalog of Ferguson (1989) lists 58 Fornax galaxies with 7 «15.0 mag. from the 14 listed as having morphological type E. only 3 turn out to be true elliptical galaxies in the classical sense of the word: indicating that these objects are in fact quite rare.," The catalog of Ferguson (1989) lists 58 Fornax galaxies with $B_T$$<$ 15.0 mag, from the 14 listed as having morphological type E, only 3 turn out to be true elliptical galaxies in the classical sense of the word; indicating that these objects are in fact quite rare."508 Most of the objects. moreover. show complex kinematical profiles. like kinematically distinct components. wiggles. and asymmetries.," Most of the objects, moreover, show complex kinematical profiles, like kinematically distinct components, wiggles, and asymmetries."509If a star is gravitationally microlensed by a lens system composed of two masses. the resulting light curve can dramatically deviate from the smooth and symmetric one of a single-lens event.,"If a star is gravitationally microlensed by a lens system composed of two masses, the resulting light curve can dramatically deviate from the smooth and symmetric one of a single-lens event."510 This deviation is caused by the formation of caustics for binary-lens systems., This deviation is caused by the formation of caustics for binary-lens systems.511 The caustics represent the source positions at which the lensing magnification of a point source becomes infinite., The caustics represent the source positions at which the lensing magnification of a point source becomes infinite.512 The set of caustics forms one. two. or three close curves each of which is composed of concave curves that meet at points.," The set of caustics forms one, two, or three close curves each of which is composed of concave curves that meet at points."513 By analyzing the light curve of a binary-lens event. it is possible to obtain information about the lens system because the structure of the caustic system and the resulting light curve vary depending on the mass ratio and the projected separation between the components of binary lenses.," By analyzing the light curve of a binary-lens event, it is possible to obtain information about the lens system because the structure of the caustic system and the resulting light curve vary depending on the mass ratio and the projected separation between the components of binary lenses."514 Since the pioneering work by Chang&Refsdal(1980. 1984).. binary lensing has been a subject of intense theoretical studies.," Since the pioneering work by \citet{chang80, chang84}, binary lensing has been a subject of intense theoretical studies."515 Schneider&Weiss(1986) made a comprehensive study of binary lenses in order to learn about caustics in quasar macrolensing., \citet{schneider86} made a comprehensive study of binary lenses in order to learn about caustics in quasar macrolensing.516 Witt(1990) developed a simple algorithm for finding caustics of binary lenses., \citet{witt90} developed a simple algorithm for finding caustics of binary lenses.517 Witt&Mao(1995) studied lensing magnification inside caustic and found that the minimum magnification when the source Is inside a caustic is greater than 3., \citet{witt95} studied lensing magnification inside caustic and found that the minimum magnification when the source is inside a caustic is greater than 3.518 Rhie(1997) found that the maximum number of images for multiple-lens systems., \citet{rhie97} found that the maximum number of images for multiple-lens systems.519 With the beginning of microlensing surveys. theoretical studies became even more active.," With the beginning of microlensing surveys, theoretical studies became even more active."520 Gaudi&Gould(1997) pointed out that microlensing is an efficient method to detect close binaries., \citet{gaudi97} pointed out that microlensing is an efficient method to detect close binaries.521 DiStefano&Perna(1997). mentioned. various channels of detecting binaries including repeating events., \citet{distefano97} mentioned various channels of detecting binaries including repeating events.522 Dominik(1999b) studied the lensing behavior in the extreme cases of binary separations and mass ratios., \citet{dominik99b} studied the lensing behavior in the extreme cases of binary separations and mass ratios.523 Dominik(1999a) and Albrowetal.(1999b) mentioned possible degeneracies in modeling light curves of binary-lens events., \citet{dominik99a} and \citet{albrow99b} mentioned possible degeneracies in modeling light curves of binary-lens events.524 Han.Chun.&Chang(1999) and Han(2001) studied the astrometric behavior of binary-lens events., \citet{han99} and \citet{han01} studied the astrometric behavior of binary-lens events.525 Bozza(2000.2001) derived analytic expressions for the location of causties and studied the motion of images of microlensed stars.," \citet{bozza00,bozza01} derived analytic expressions for the location of caustics and studied the motion of images of microlensed stars."526 investigated the photometric and astrometric behaviors m the region very close to caustics., investigated the photometric and astrometric behaviors in the region very close to caustics.527 Graff&(2002) devised a method to measure the mass of the system from the analysis of light curves of crossing events., \citet{graff02} devised a method to measure the mass of the binary-lens system from the analysis of light curves of caustic-crossing events.528" In addition to the theoretical studies. binary- events were actually detected from various. surveys (Udalskietal.1994,1998:Alcock1999:Alard.Mao&Cassanetal.2004:Jaroszynski2005. 2006)."," In addition to the theoretical studies, binary-lens events were actually detected from various surveys \citep{udalski94, udalski98, 529alcock99, alard95, afonso00, albrow99a, albrow00, albrow01, 530an02, smith02, albrow02, abe03, kubas05, jaroszynski04, cassan04, 531jaroszynski05, jaroszynski06}."532. With the active researches in. both. theoretical and observational fields. binary microlensing has developed into a useful tool to study stellar astrophysics.," With the active researches in both theoretical and observational fields, binary microlensing has developed into a useful tool to study stellar astrophysics."533 The most active field of application is the stellar atmosphere for which microlensing is used to probe detailed structures on the surface of source stars by using the high resolution of caustic-crossing events (Albrowetal.1999a.2001:Abe2003).," The most active field of application is the stellar atmosphere for which microlensing is used to probe detailed structures on the surface of source stars by using the high resolution of caustic-crossing events \citep{albrow99a, albrow01, 534abe03}."535. Microlensing can also be used to probe the distributions of binary companions of Galactic stars as functions of mass ratio and separation., Microlensing can also be used to probe the distributions of binary companions of Galactic stars as functions of mass ratio and separation.536 These binary distributions provide important observational constraints on theories of star formation., These binary distributions provide important observational constraints on theories of star formation.537 Since microlensing 1s sensitive to low-mass companions that are difficult to be detected by other methods. it is in principle possible to make complete distribution down to the lower mass limit of binary companions.," Since microlensing is sensitive to low-mass companions that are difficult to be detected by other methods, it is in principle possible to make complete distribution down to the lower mass limit of binary companions."538 Despite the importance. the progress of this application of binary lensing has been stagnant.," Despite the importance, the progress of this application of binary lensing has been stagnant."539 There are two main reasons for this., There are two main reasons for this.540 The first reason is caused by the difficulty in estimating the detection efficiency of binary-lens events., The first reason is caused by the difficulty in estimating the detection efficiency of binary-lens events.541 In previous lensing surveys. most binary-lens events were discovered through the channel of caustic-crossing events. in which the caustic crossings were accidently discovered from the sudden rise of the source star flux.," In previous lensing surveys, most binary-lens events were discovered through the channel of caustic-crossing events, in which the caustic crossings were accidently discovered from the sudden rise of the source star flux."542 Due to the haphazard nature of caustic crossings. it was difficult to estimate the detection efficiency that is essential for the statistical studies of binary companions.," Due to the haphazard nature of caustic crossings, it was difficult to estimate the detection efficiency that is essential for the statistical studies of binary companions."543 The second reason is that microlensing is mainly sensitive to binaries over a narrow range of projected separations., The second reason is that microlensing is mainly sensitive to binaries over a narrow range of projected separations.544 This limits especially, This limits especially545Once the state on the interface is determined. the fluxes can be computed and the conservative quantities can be updated.,"Once the state on the interface is determined, the fluxes can be computed and the conservative quantities can be updated."546 The gravitational potential is obtained though the classical algorithm used by Particle-Mesh codes., The gravitational potential is obtained though the classical algorithm used by Particle-Mesh codes.547 We solve Poisson’s equation with Fourter-transformations and Green's function (2)., We solve Poisson's equation with Fourier-transformations and Green's function \citep{Hockney88}.548 Then. the conservative quantities are updated with the gravitational source terms.," Then, the conservative quantities are updated with the gravitational source terms."549 To perform the needed Fourter-transformations we use the public available FFTW library (?).., To perform the needed Fourier-transformations we use the public available FFTW library \citep{FFTW}.550 The evolution of the number densities and the heating and cooling originate in the same physical processes and have similar timescales., The evolution of the number densities and the heating and cooling originate in the same physical processes and have similar timescales.551 It is therefore necessary to compute their evolution in à similar way., It is therefore necessary to compute their evolution in a similar way.552 In the IE case a solution to =;=0 can be found by iteration., In the IE case a solution to $\Xi_i = 0$ can be found by iteration.553 The situation is more difficult in the on-IE case., The situation is more difficult in the non-IE case.554 Here. the integration of the system of ordinary moaifferential equations 7==; is performed.," Here, the integration of the system of ordinary differential equations $\dot{n} = \Xi_i$ is performed."555 These are stiff ordinary differential equations. and therefore most codes use nplicit methods for their solution.," These are stiff ordinary differential equations, and therefore most codes use implicit methods for their solution."556 In our code. we use a Cifferent approach and adopt the C.eveloped in biochemical oceanography (?)..," In our code, we use a different approach and adopt the developed in biochemical oceanography \citep{Burchard03}."557" Although it is αxplicit it ensures the positivity of temperature and number ""Sensities and conserves total amount of hydrogen and helium.", Although it is explicit it ensures the positivity of temperature and number densities and conserves total amount of hydrogen and helium.558 The modified Euler-Patankar scheme reads: where pa is the production matrix contaming the rates producing species { from species Κ. while dj is the destruction matrix containing the rates that transform species / into species κ.," The modified Euler-Patankar scheme reads: where $p_{ik}$ is the production matrix containing the rates producing species $i$ from species $k$, while $d_{ik}$ is the destruction matrix containing the rates that transform species $i$ into species $k$."559 That implies pg=dj; and all diagonal coefficients are zero., That implies $p_{ik} = d_{ki}$ and all diagonal coefficients are zero.560 We obtain: The other components vanish., We obtain: The other components vanish.561 If we define Eq. (B9)), If we define Eq. \ref{eModpatankar}) )562 can be further performed to This ts an easy solvable system of linear equations., can be further performed to This is an easy solvable system of linear equations.563 Since the 2x block matrix for hydrogen and 3x matrix for helium are not coupled. this system can be solved for them independently.," Since the $2 \times 2$ block matrix for hydrogen and $3 \times 3$ matrix for helium are not coupled, this system can be solved for them independently."564 In the IE as well as in the non-IE case the update of the pressure is performed using original Patankar-Trick (2):: The algorithm for the thermal conduction ts carried out similar to the hydrodynamie scheme., In the IE as well as in the non-IE case the update of the pressure is performed using original Patankar-Trick \citep{Patankar80}: The algorithm for the thermal conduction is carried out similar to the hydrodynamic scheme.565 After the thermal fluxes between the cells are computed. those fluxes are used to update the energy density and modified entropy density.," After the thermal fluxes between the cells are computed, those fluxes are used to update the energy density and modified entropy density."566 Like the hydrodynamic scheme this is done in an unsplit fashion., Like the hydrodynamic scheme this is done in an unsplit fashion.567" In order to compute the thermal flux. first the temperature gradient is computed: where ἐν""+1/2 denotes the positionm of7 the interfacen7 and i, and ἐν+I the cell left and right of the interface."," In order to compute the thermal flux, first the temperature gradient is computed: where $i_x+1/2$ denotes the position of the interface and $i_x$ and $i_x+1$ the cell left and right of the interface."568" Then. the conduction coefficient « and the fraction of mean free path and temperature 2,/7 are computed in cell ἐν and ἐν+1 and then extrapolated to the interface 7,+1/2 by simple averaging."," Then, the conduction coefficient $\kappa$ and the fraction of mean free path and temperature $\lambda_e / T$ are computed in cell $i_x$ and $i_x+1$ and then extrapolated to the interface $i_x+1/2$ by simple averaging."569 The heat flux is then, The heat flux is then570"resolved at their mass resolution (2.8x 10°Mo), prohibiting a self-consistent treatment of subhaloes.","resolved at their mass resolution $2.8\times 10^8571\Ms$ ), prohibiting a self-consistent treatment of subhaloes."572" Consequently, they only include haloes above 1.6x10'°Mo in the conditional mass function."," Consequently, they only include haloes above $1.6\times10^{10}\Ms$ in the conditional mass function."573 ? also apply their analysis to an analytic Sheth-Tormen mass function obtained by ?.., \citeauthor{Moster-2009} also apply their analysis to an analytic Sheth-Tormen mass function obtained by \cite{Vale-2006}.574" In this non- model, a halo mass of 10!°Mo corresponds to a stellar mass of 1.9x10°Mo, more similar to the value of ?.."," In this non-parametric model, a halo mass of $10^{10}\Ms$ corresponds to a stellar mass of $1.9\times10^6\Ms$, more similar to the value of \cite{Guo-2010}."575" In Figure 4,, we plot the stellar mass — halo mass relation of ? for haloes between 10° and 10!7Mo."," In Figure \ref{M/L-Qi}, we plot the stellar mass – halo mass relation of \cite{Guo-2010} for haloes between $10^{9}$ and $10^{12}\Ms$."576 The solid section of the line shows the relation in the region directly derived from SDSS DR-7 data where the uncertainties are very small., The solid section of the line shows the relation in the region directly derived from SDSS DR-7 data where the uncertainties are very small.577" The dashed section denotes an extrapolation to stellar masses below 10°°Mo, assuming faint-end slope of a=—1.15 for the stellar mass function,a as reported by ?.."," The dashed section denotes an extrapolation to stellar masses below $10^{8.3}\Ms$ assuming a faint-end slope of $\alpha = -1.15$ for the stellar mass function, as reported by \cite{Li-2009}."578" Studies of the faint-end of the stellar mass function are either limited to nearby regions or galaxy clusters, or require corrections for incompleteness and, in the case of photometric redshifts, background subtraction, which introduce considerable uncertainties (e.g.?).."," Studies of the faint-end of the stellar mass function are either limited to nearby regions or galaxy clusters, or require corrections for incompleteness and, in the case of photometric redshifts, background subtraction, which introduce considerable uncertainties \citep[e.g.][]{Christlein-2009}."579" As a result, different values for oin the range of —1.1 to —1.6 are found in the recent literature (e.g.????).."," As a result, different values for $\alpha$in the range of $-1.1$ to $-1.6$ are found in the recent literature \citep[e.g.][]{Trentham-2005, Blanton-2005, Carrasco-2006,580 Baldry-2008}."581" The dark grey area in Figure 4 shows the effect of a steepening of the faint-end slope up to a=—1.58, the value reported by ?.."," The dark grey area in Figure \ref{M/L-Qi} shows the effect of a steepening of the faint-end slope up to $\alpha = -1.58$, the value reported by \cite{Baldry-2008}."582" While this has a strong effect on the lowest mass haloes, we note that it cannot account for the discrepancy we find in haloes of 10!°Mo."," While this has a strong effect on the lowest mass haloes, we note that it cannot account for the discrepancy we find in haloes of $10^{10} \Ms$."583" In order to fit the constraints of SDSS DR-7, the maximal dispersion at fixed halo mass is 0.2 dex in M,, indicated by the light-grey area."," In order to fit the constraints of SDSS DR-7, the maximal dispersion at fixed halo mass is 0.2 dex in $_\star$, indicated by the light-grey area."584" We overplot the results of our six simulations as red squares and add other z=0 predictions from the studies listed in Table 1,, correcting all halo masses for baryonic effects, as described below."," We overplot the results of our six simulations as red squares and add other $z=0$ predictions from the studies listed in Table \ref{table:other}, correcting all halo masses for baryonic effects, as described below."585 It is apparent that all these hydrodynamical simulations overproduce stellar mass for their respective halo mass by at least an order of magnitude., It is apparent that all these hydrodynamical simulations overproduce stellar mass for their respective halo mass by at least an order of magnitude.586" In Table 3,, we compare the properties of our six simulations to the abundance matching predictions."," In Table \ref{table:compare}, we compare the properties of our six simulations to the abundance matching predictions."587" We note that, due to the outflow of baryons, the total mass of our six haloes is almost a factor of 1—Q,/Qm smaller than the masses of the corresponding haloes from the pure dark matter simulation."," We note that, due to the outflow of baryons, the total mass of our six haloes is almost a factor of $1-\Omega_b/\Omega_m$ smaller than the masses of the corresponding haloes from the pure dark matter simulation."588 This effect is expected at such low star formation efficiency., This effect is expected at such low star formation efficiency.589" For consistency with ?,, we therefore use the (higher) peak masses of the pure dark matter simulations in deriving the stellar mass predicted for each of our haloes by the abundance matching argument."," For consistency with \cite{Guo-2010}, we therefore use the (higher) peak masses of the pure dark matter simulations in deriving the stellar mass predicted for each of our haloes by the abundance matching argument."590" For all galaxies listed in Table 1 whose peak halo mass cannot be defined or is not given, we increase the halo mass in Figure by 22/Qm~2096, the maximally expected correction."," For all galaxies listed in Table \ref{table:other} whose peak halo mass cannot be defined or is not given, we increase the halo mass in Figure \ref{M/L-Qi} by $\Omega_b/\Omega_m\sim20\%$, the maximally expected correction."591" Comparing the results of our simulations to the predictions, we find that the hydrodynamical simulations overproduce stellar mass by a median factor of ~ 50."," Comparing the results of our simulations to the predictions, we find that the hydrodynamical simulations overproduce stellar mass by a median factor of $\sim 50$ ."592" Alternatively, abundance matching predicts that galaxies of 10°°Mo, the median stellar mass produced in our hydrodynamical simulations, should reside in haloes with typical masses of ~4.5x10!°Mo, rather than 10'°Mo."," Alternatively, abundance matching predicts that galaxies of $10^{7.9}\Ms$, the median stellar mass produced in our hydrodynamical simulations, should reside in haloes with typical masses of $\sim 4.5\times10^{10}\Ms$, rather than $10^{10}\Ms$."593" If 10!?M, haloes really hosted galaxies with M,=10?M, a ACDM universe would overpredict their abundance by a factor of ~4."," If $10^{10}\Ms$ haloes really hosted galaxies with $M_\star=10^{7.9}\Ms$, a $\Lambda$ CDM universe would overpredict their abundance by a factor of $\sim 4$."594 This discrepancy is too large to be attributed solely to incompleteness in the observed stellar mass function., This discrepancy is too large to be attributed solely to incompleteness in the observed stellar mass function.595 ? have used the stellar mass — surface brightness relation of SDSS galaxies in order to estimate the completeness at the faint end., \cite{Baldry-2008} have used the stellar mass – surface brightness relation of SDSS galaxies in order to estimate the completeness at the faint end.596" Based on this analysis, ? estimate the completeness at 105?Mg to be well above 70%."," Based on this analysis, \cite{Li-2009}597 estimate the completeness at $10^{8.3}\Ms$ to be well above $70\%$."598" Following ?,, the uncertainty in the number of 10?M galaxies is much smaller than the discrepancy we report."," Following \citeauthor{Baldry-2008}, the uncertainty in the number of $10^{7.9}\Ms$ galaxies is much smaller than the discrepancy we report."599" The difference is also unlikely to be attributable to numerical errors in our hydrodynamical simulations, or to the specific parametrisation of star formation and feedbackin our model."," The difference is also unlikely to be attributable to numerical errors in our hydrodynamical simulations, or to the specific parametrisation of star formation and feedbackin our model."600" From Table 1,, it is clear that all other current hydrodynamical models,while succeeding in reproducing many of the observed features of individual"," From Table \ref{table:other}, , it is clear that all other current hydrodynamical models,while succeeding in reproducing many of the observed features of individual"601"High-z studies (as far as z2.4 ) have found a significant number of massive. passively evolving galaxies (stellar mass M..>I0""M, ) with relatively small effective radii Ες<2kpe (see.amongothers.Trujilloetal.2006;Cimatti2008;etal. 2009).. sometimes named galaxies (SDGs).","High-z studies (as far as $z\sim2.4$ ) have found a significant number of massive, passively evolving galaxies (stellar mass $\sm>10^{10}\rm{M_{\odot}}$ ) with relatively small effective radii $\re<2\rm{kpc}$ \citep[see, among602others,][]{trujillo06,cimatti08,vandokkum08,vanderwel09,saracco09}, sometimes named galaxies (SDGs)."603 The general claim by various authors is that local galaxies are three to six times larger in size when compared to high-z ones. at the same stellar mass.," The general claim by various authors is that local galaxies are three to six times larger in size when compared to high-z ones, at the same stellar mass."604 In addition. Trujilloetal.(2009) found a complete absence of massive. old and extremely compact galaxies in the local universe.," In addition, \citet{trujillo09} found a complete absence of massive, old and extremely compact galaxies in the local universe."605" However. Valentinuzzietal.(2010) (hereafter V10) have shown that of local cluster members in the WINGS sample with M..>3«10'M, and Xs;23\10°M..kpe have the same characteristies of the high-z SDGs reported in the literature by various authors."," However, \citet{valentinuzzi10} (hereafter V10) have shown that of local cluster members in the WINGS sample with $\sm>3\per10^{10}\msol$ and $\Sigma_{50}\geq3\per10^{9}\msol kpc^{-2}$ have the same characteristics of the high-z SDGs reported in the literature by various authors."606 In the same paper. the authors found that selecting galaxies with old stellar populations is equivalent to selecting the smaller ones. for a given stellar mass.," In the same paper, the authors found that selecting galaxies with old stellar populations is equivalent to selecting the smaller ones, for a given stellar mass."607 Since a large number of galaxies have stopped forming stars at relatively low redshift ἐς« 1.4). and these tend to be the largest. it is not valid to compare high-z passive galaxies with all low-z passive ones.," Since a large number of galaxies have stopped forming stars at relatively low redshift $z<1.4$ ), and these tend to be the largest, it is not valid to compare high-z passive galaxies with all low-z passive ones."608 To avoid selection effects when making comparisons with passive galaxies at high redshift. one needs to select locally those galaxies which at the cosmic time the high-z data correspond to.," To avoid selection effects when making comparisons with passive galaxies at high redshift, one needs to select locally those galaxies which at the cosmic time the high-z data correspond to."609 More recently. Tayloretal.(2009). revisited the search of SDGs in SDSS-DR7 and found a relatively small but significant number of SDGs.," More recently, \citet{taylor09} revisited the search of SDGs in SDSS-DR7 and found a relatively small but significant number of SDGs."610 Following the same criterion used in VIO. they find a fraction of SDGs.," Following the same criterion used in V10, they find a fraction of SDGs."611 The issue is much debated., The issue is much debated.612 Mancinietal.(2010). have analyzed a sample of 12 galaxies at 0.5<<<1.9 in the Cosmos field. finding masses and sizes compatible with the local SDSS ones.," \citet{mancini09} have analyzed a sample of 12 galaxies at $0.5<z<1.9$ in the Cosmos field, finding masses and sizes compatible with the local SDSS ones."613 Furthermore. by using a set of simulated early-type galaxies. they have shown that the low signal-to-noise of high-z images can cause measured effective-radii to be lower than the intrinsic. values.," Furthermore, by using a set of simulated early-type galaxies, they have shown that the low signal-to-noise of high-z images can cause measured effective-radii to be lower than the intrinsic values."614 In a recent paper vanDokkumetal.(2010) select galaxies with a constant number density at different cosmic times.," In a recent paper \citet{vandokkum10}615 select galaxies with a constant number density at different cosmic times."616 They use all galaxies instead of only passive ones. and find that galaxies have grown in size by a factor of from z—2 to z—-0.," They use all galaxies instead of only passive ones, and find that galaxies have grown in size by a factor of 4 from $z\sim2$ to $z\sim0$."617 Even more 4recently. while Szomoruetal.(2010) confirm the extreme compactness of a z21.9 galaxy with the HST-WFC3. Saraccoetal.(2010) show that the comoving number density of compact ETGs over the volume of about I0Mpe? sampled by the GOODS area between 0.9«z1.92 is compatible even with the local lower limits given in VIO.," Even more recently, while \citet{szomoru10} confirm the extreme compactness of a $z=1.9$ galaxy with the HST-WFC3, \citet{saracco10} show that the comoving number density of compact ETGs over the volume of about $4.4\per10^5\rm{Mpc}^3$ sampled by the GOODS area between $0.9<\rm{z}< 1.92$ is compatible even with the local lower limits given in V10."618 In this Letter we present the results of a search for SDGs in the ESO Distant Clusters Survey (EDISCS)) at z—0.7. and we report the comparison of the mass-size relation (MSR) with the same relation in WINGS clusters at z~0.," In this Letter we present the results of a search for SDGs in the ESO Distant Clusters Survey ) at $z\sim0.7$, and we report the comparison of the mass-size relation (MSR) with the same relation in WINGS clusters at $z\sim0$."619 We further discuss selection effects which may introduce a spurious size evolutionwith redshift if not properly taken into account., We further discuss selection effects which may introduce a spurious size evolutionwith redshift if not properly taken into account.620 The high-z cluster sample is extracted from EDisCS.. a multiwavelength photometric and spectroscopicsurvey of galaxies in 20 fields containing galaxy clusters at 0.4< (Whiteetal. 2005)...," The high-z cluster sample is extracted from , a multiwavelength photometric and spectroscopicsurvey of galaxies in 20 fields containing galaxy clusters at $0.4<z<1$ \citep[][]{white05}. ."621" We will use a sub-sample of 8which have HST-ACS images for high- size Measurements (Desaietal. 2007).. and cluster central velocity dispersions (0,44,2400km s!"," We will use a sub-sample of 8which have HST-ACS images for high-precision size measurements \citep[][]{desai07}, , and cluster central velocity dispersions $\sigma_{clus}\geq400\rm{km\;s^{-1}}$ ,"622In (his mass-traces-light analvsis. (he CI? parameter changes by a [factor of 3.10 (depending upon the fit used) between (he inner and outer regions of the M33 disk.,"In this mass-traces-light analysis, the $CP$ parameter changes by a factor of 3–10 (depending upon the fit used) between the inner and outer regions of the M33 disk."623 In this illustrative example the CP) behavior appears inconsistent with the MOND scenario., In this illustrative example the $CP(r)$ behavior appears inconsistent with the MOND scenario.624 The sense of the discrepancy. wilh CP? values less than one. corresponds to ji.>pep. so Chat matter appears to be overaccelerating in the radial direction more than in the vertical direction.," The sense of the discrepancy, with $CP$ values less than one, corresponds to $\mu_z>\mu_r$, so that matter appears to be overaccelerating in the radial direction more than in the vertical direction."625 The exponential scale length of the \133 disk emission depends upon the passband used {ο measure the surlace brightness. ranging from 1.56 kpe in the Ix band to 2.5 kpe in the V band.," The exponential scale length of the M33 disk emission depends upon the passband used to measure the surface brightness, ranging from 1.56 kpc in the K band to 2.5 kpc in the V band."626 Stepping back from the light-traces-mass approach. is interesting to explore what combinations of fy and 2) would produce a CP(r) closest to unity.," Stepping back from the light-traces-mass approach, is interesting to explore what combinations of $R_0$ and $z_0$ would produce a $CP(r)$ closest to unity."627 Allowing both Ay ancl τη as free parameters. with no constraints and with no assumption about (he galaxys niass-to-light ratio. the values that best mateh CP?=1 are Ry=5.4 kpc and 24=0.035 kpe.," Allowing both $R_0$ and $z_0$ as free parameters, with no constraints and with no assumption about the galaxy's mass-to-light ratio, the values that best match $CP=1$ are $R_0=5.4$ kpc and $z_0=0.035$ kpc."628 This corresponds (o a remarkably Chin disk. with a verlical scale heieht ol only 35 pe.," This corresponds to a remarkably thin disk, with a vertical scale height of only 35 pc."629 The CP(+) profile from this more general fit is shown in Figure 2., The $CP(r)$ profile from this more general fit is shown in Figure 2.630 This provides a better fit to the kinematic observations. but. CP still varies bv over a [actor of two across the [ace ol M33.," This provides a better fit to the kinematic observations, but $CP$ still varies by over a factor of two across the face of M33."631 Also. the value of 2)//2)=0.006 is over an order of magnitude less than typical aspect ratios.," Also, the value of $z_0/R_0=0.006$ is over an order of magnitude less than typical aspect ratios."632 Although we can achieve improved MOND-inspired fits to the kinematic data. these models imply strong racial aid vertical eradients in (he galaxys mass-to-light ratio.," Although we can achieve improved MOND-inspired fits to the kinematic data, these models imply strong radial and vertical gradients in the galaxy's mass-to-light ratio."633 This is al variance with the elegant what-vou-see-is-all-t here-isMOND scenario., This is at variance with the elegant what-you-see-is-all-there-is MOND scenario.634 Our objective is to propose a general techiiieque for testing the sell-consistency of MOND. using the existing M33 data as an illustrative example.," Our objective is to propose a general technique for testing the self-consistency of MOND, using the existing M33 data as an illustrative example."635 The vertical aud circular motions of a galaxy can be jointly used for Chis test., The vertical and circular motions of a galaxy can be jointly used for this test.636 Potential weaknesses in (he argument presented above include i) the assertion that the vertical scale height of galaxies is racius-independent. ii) modeling the galaxy. with the form shown in equation (1). and iii) the implicit assertion that either objects overaccelerate. or Chey dont.," Potential weaknesses in the argument presented above include i) the assertion that the vertical scale height of galaxies is radius-independent, ii) modeling the galaxy with the form shown in equation (1), and iii) the implicit assertion that either objects overaccelerate, or they don't."637 The first issue can be addressed with better observations and more statistics. and the second by a more comprehensive treatinent of the svslems kinematics.," The first issue can be addressed with better observations and more statistics, and the second by a more comprehensive treatment of the system's kinematics."638"The Yale code (Demarque&Percy1964;1992) uses as an outer boundary condition the empirically derived fit of KrishnaSwamy(1966) to the T'—7 relation for the Sun, € Eridani, and Gmb 1830.","The Yale code \citep{demarque,gdkp92} uses as an outer boundary condition the empirically derived fit of \cite{ks66} to the $T-\tau$ relation for the Sun, $\epsilon$ Eridani, and Gmb 1830."639" Empirical fits have the flaw that they are suspect if extrapolated; these stars are on the main sequence, and of G and K spectral type (G2V, K2V, and G8Vp, respectively)."," Empirical fits have the flaw that they are suspect if extrapolated; these stars are on the main sequence, and of G and K spectral type (G2V, K2V, and G8Vp, respectively)."640" Gmb 1830 is a halo star of 0.60M with a metalicity of about 0.1 of solar (AllendePrieto,etal.2000),, while ε Eridani is a solar metalicity star of about 0.85Mo."," Gmb 1830 is a halo star of $0.64\rm M_\odot$ with a metalicity of about 0.1 of solar \citep{apetal00}, while $\epsilon$ Eridani is a solar metalicity star of about $0.85\rm M_\odot$."641" If applied to stars of the same stage of evolution and the same abundance, such empirical boundary condidtions are at their best."," If applied to stars of the same stage of evolution and the same abundance, such empirical boundary condidtions are at their best."642 Unfortunately the “calibration” approach may hide mistakes in the assumed physics., Unfortunately the “calibration” approach may hide mistakes in the assumed physics.643" The Garching code (Schlatt]1996) was modified (Schlattl,Weiss&Ludwig1997) to use synthetic atmospheres fitted to the interior solution at optical depth (r— 20)."," The Garching code \citep{schlattl}644 was modified \citep{swl97} to use synthetic atmospheres fitted to the interior solution at optical depth $\tau = 20$ )."645" In addition a spatially varying mixing length was employed to reproduce the pressure- stratification calculated by 2D- models (Freytag,Ludwig,& 1996)..", In addition a spatially varying mixing length was employed to reproduce the pressure-temperature stratification calculated by 2D-hydrodynamic models \citep{fls96}. .646 T'his involved the interpolation, This involved the interpolation647belore il enters the gas subshock.,before it enters the gas subshock.648" S0 we use the subscripts “O°. ""I. and 72 to denote the conditions [ar upstream. immediate upstream and downstream of shock. respectively."," So we use the subscripts “0"", “1"", and “2"" to denote the conditions far upstream, immediate upstream and downstream of shock, respectively."649 Ol course. in the (est-particle limit. the distinction between [ar and immediate upstream quantities disappears. e.g.. py=f».," Of course, in the test-particle limit, the distinction between far and immediate upstream quantities disappears, e.g., $\rho_0=\rho_1$."650 In the limit of large AJ (0224) and large M4 (020). the maximum energv of CR protons can be approximated bv The CR proton spectrum limited by the shock agec» is expected to have a cutoff at around eDuas) (see Section 3.3 lor further discussion).," In the limit of large $M$ $\sigma \approx 4$ ) and large $M_A$ $\delta \approx 0$ ), the maximum energy of CR protons can be approximated by The CR proton spectrum limited by the shock age is expected to have a cutoff at around $\sim p_{\rm max}(t)$ (see Section 3.3 for further discussion)."651 As noted in Introduction. it seems natural to assume that ICMs and cluster outskirts contain pre-existing CRs.," As noted in Introduction, it seems natural to assume that ICMs and cluster outskirts contain pre-existing CRs."652 But their nature is not well constrained. except that P.S0. the pressure of CR protons is less that ~10% of the gas thermal pressure (e.g..Abdoet 2010).," But their nature is not well constrained, except that $P_c \la 0.1 P_g$, the pressure of CR protons is less that $\sim 10$ of the gas thermal pressure \citep[e.g.,][]{abdo10,ddcb10}."653. With pre-existing CRs ofspectrum fo(p) upstream of shock. the steady-state. test-particle solution of Equation (1)) for the downstream CR distribution can be written as where q is the test-particle power-law slope given in Equation (2)) (Drury.1983).," With pre-existing CRs ofspectrum $f_0(p)$ upstream of shock, the steady-state, test-particle solution of Equation \ref{diffcon}) ) for the downstream CR distribution can be written as where $q$ is the test-particle power-law slope given in Equation \ref{qtp}) ) \citep{dru83}."654. Here. Pinj Is Lhe lowest momentum boundary above which particles can cross the shock. the injection momentunm (see the next subsection).," Here, $p_{\rm inj}$ is the lowest momentum boundary above which particles can cross the shock, the injection momentum (see the next subsection)."655 Dv this delinition of pij. the CR distribution unction. fp=0 and fo=0 lor p<pi.," By this definition of $p_{\rm inj}$, the CR distribution function, $f_0=0$ and $f_2=0$ for $p<p_{\rm inj}$."656 The first term in the right-hand-side of Equation (6)) represents the re-accelerated population of pre-existing CRs. while the second term represents the population of CRs freshly injected at the shock and will be discussed in the rext subsection.," The first term in the right-hand-side of Equation \ref{drury}) ) represents the re-accelerated population of pre-existing CRs, while the second term represents the population of CRs freshly injected at the shock and will be discussed in the next subsection."657 We adopt a power-law form. fap)=fyc:G/pij). with the slope s=4— 5. as the nodel spectrum lor pre-existing CR protons.," We adopt a power-law form, $f_0(p)=f_{\rm pre}\cdot (p/p_{\rm inj})^{-s}$, with the slope $s = 4 - 5$ , as the model spectrum for pre-existing CR protons."658 If pre-existing CRs were generated at previous shocks. the slope of s=4—5 is achieved for M>V5 with 9=0 (see Equation (2))).," If pre-existing CRs were generated at previous shocks, the slope of $s = 4 - 5$ is achieved for $M \geq \sqrt{5}$ with $\delta = 0$ (see Equation \ref{qtp}) ))."659 On the other hand. if (hey are mainly the outcome of turbulent acceleration. the slope should be close los~4 (see.e.g..Chandran 2005)..," On the other hand, if they are mainly the outcome of turbulent acceleration, the slope should be close to$s \sim 4$ \citep[see, e.g.,][]{chan05}. ."660 Then. the spectrum of re-accelerated CRs is," Then, the spectrum of re-accelerated CRs is"661"flux ος.70.3TeV)~44-10I""phem7s! (Grindlavetal.1997).. what made Centaurus A the very first (although not confirmed) detected extragalactic source of the VILE radiation.","flux $S(\varepsilon_{\gamma} \geq 0.3 \, {\rm TeV}) \sim 4.4 \cdot662 10^{-11} \, {\rm ph \, cm^{-2} \, s^{-1}}$ \citep{gri75}, what made Centaurus A the very first (although not confirmed) detected extragalactic source of the VHE radiation."663 Recent upper limit suggests that this emission can be variable on a timescale of vears. in analogy to the low- and high-states of activity known from the TeV blazar observations ," Recent upper limit suggests that this emission can be variable on a timescale of years, in analogy to the low- and high-states of activity known from the TeV blazar observations \citep[but see also][for the X-ray664 variability of the large scale jet emission in M 87]{har97,har03}."665Existence of a hidden BL Lae core in the Centaurus A nucleus. as expected in a framework of unification scheme. was wiclely discussed over the last decade (Baileyetal.al. 2000).," Existence of a hidden BL Lac core in the Centaurus A nucleus, as expected in a framework of unification scheme, was widely discussed over the last decade \citep{bai86,mor91,haw93,pac96,ste98,cap00}."666. Most. recently. Chiabergeetal.(2001) reconstructed broad-band spectrum of Centaurus A nucleus. [rom radio to 5-rav. [requencies. and found spectacular similarities to the characteristic double-peaked blazar spectral energy distribution.," Most recently, \citet{chi01}667 reconstructed broad-band spectrum of Centaurus A nucleus, from radio to $\gamma$ -ray frequencies, and found spectacular similarities to the characteristic double-peaked blazar spectral energy distribution."668 The svuchrotron component of (his radiation was found to peak al far infra-red energy. range. Verte~107— Hz. with the observed Iuminosity ο...104101 ere/s. The Compton break energv was placed near ~01. MeV. with the observed. power comparable io (he svnchrotron one.," The synchrotron component of this radiation was found to peak at far infra-red energy range, $\nu_{bl, \, br} \sim 10^{12} - 10^{13}$ Hz, with the observed luminosity $[\nu L_{\nu}]_{bl, \, br} \sim 10^{41} - 10^{42}$ erg/s. The inverse-Compton break energy was placed near $\sim 0.1$ MeV, with the observed power comparable to the synchrotron one."669 Chiabergeetal. fitted the SSC! model to the multiwavelength Centaurus A nucleus emission. and found that all (except one) intrinsic parameters are similar to those of the low-Iuminous blazar sources.," \citeauthor{chi01} fitted the SSC model to the multiwavelength Centaurus A nucleus emission, and found that all (except one) intrinsic parameters are similar to those of the low-luminous blazar sources."670 The only difference. as compared to the‘typical’ BL Lac broad-band spectrum. was a small value of the required Doppler factor. dy1.6.," The only difference, as compared to the`typical' BL Lac broad-band spectrum, was a small value of the required Doppler factor, $\delta_{bl} \sim 1.6$."671 Chiabergeetal. interpreted their results as (hie evidence for the jet radial velocity structure al pc-scales. consisting of a fast central spine surrounded by a slower boundary laver (seealsoChiabergeetal.2000).," \citeauthor{chi01} interpreted their results as the evidence for the jet radial velocity structure at pc-scales, consisting of a fast central spine surrounded by a slower boundary layer \citep[see672 also][]{chi00}."673. Assiuming that the physical properties (i.e. electron enerev distribution. magnetic field intensity. etc) are the same in both jet components. the observed multiwavelength spectrum of the Centaurus A nucleus can then be regarded as a representation of a (vpical low-Iuminous blazar emission. but originating within the slower jet boundary laver and (therefore less beamed as compared to the ‘classical’ BL Lacs.," Assuming that the physical properties (i.e. electron energy distribution, magnetic field intensity, etc) are the same in both jet components, the observed multiwavelength spectrum of the Centaurus A nucleus can then be regarded as a representation of a typical low-luminous blazar emission, but originating within the slower jet boundary layer and therefore less beamed as compared to the `classical' BL Lacs."674" It is consistent with the jet inclination ~70"".", It is consistent with the jet inclination $\sim 70^0$.675" Most probably. Centaurus Aobserved at small angles to the jet axis would be therefore classified as LBL. with the observed luminosity LOY—10"" ere/s and with the observed break frequency ~LOM—1011 Hz."," Most probably, Centaurus Aobserved at small angles to the jet axis would be therefore classified as LBL, with the observed luminosity $\sim 10^{45} - 10^{46}$ erg/s and with the observed break frequency $\sim 10^{13} - 10^{14}$ Hz."676 Note. that in such a casethe Centaurus A nucleus is not expected to radiate at the VIIE range 2001).," Note, that in such a casethe Centaurus A nucleus is not expected to radiate at the VHE range \citep[cf.][]{bai01}."677". For the estimates below. we assume [|z/L,]y,ο~0.3. vy4400.01. Το10 and ὃμ~1.6."," For the estimates below, we assume $[\nu L_{\nu}]_{bl, \, 42} \sim 0.3$, $\nu_{bl, \,678 14} \sim 0.01$, $\Gamma_{bl} \sim 10$ and $\delta_{bl} \sim 1.6$."679 In order to diseuss (he 5-rav emission of the large scale jet in Centaurus A. let us consider its brightest part in N-ravs and at radio frequencies. the ensemble of the knots Al - At.," In order to discuss the $\gamma$ -ray emission of the large scale jet in Centaurus A, let us consider its brightest part in X-rays and at radio frequencies, the ensemble of the knots A1 - A4."680 The N-ray observations (Ixraftοἱal.2002) suggest Chat for this region A4~ 0.8. ppi0 Od B.1 O06 ay~1.5 and Ly~4-10 erg/s. The synchrotron break frequency is unknown. as there is no observation of the jet svnchrotron emission at LR/optical frequencies.," The X-ray observations \citep{kra02} suggest that for this region $R_{-1} \sim 0.8$ , $r_1 \sim 0.4$ , $B_{-4} \sim 0.6$ , $\alpha_X \sim 1.5$ and $L_X \sim 4 \cdot 10^{39}$ erg/s. The synchrotron break frequency is unknown, as there is no observation of the jet synchrotron emission at IR/optical frequencies."681 (Crawford&Kraft1956)..., \citep{1956ApJ...123...44C}.682 ~107—M. e.g.]|andreferencestherein|2008cIno.book.....B..," $\sim 10^{-5} - 10^{-4} \msun$ \\citep[see, e.g.][and references therein]{2008clno.book.....B}."683 (Warner2008) x107—109 (Truran&Livio1986).. (Gaposchkin1957).. 1992;DellaValle&Livio1998).. (Starrfield2005). (Anupama2008)..," \citep{2008clno.conf....1W} $\times\;10^{3}-10^{6}$ \citep{1986ApJ...308..721T}. \citep{1957gano.book.....G}, \citep{1992AJ....104..725W}. \citep{1990LNP...369...34D,1992A&A...266..232D,1998ApJ...506..818D}. \citep{1985ApJ...291..136S,2005ApJ...623..398Y}. \citep{2008ASPC..401...31A}."684 Recurrent nova systems have been sub-divided into three general sub-classes (Anupama2008) via a combination of the properties of the eruption and via the properties of the progenitor system whilst at quiescence: (hereafter the RS Oph-class) are observed to contain red giant secondaries and hence have much longer orbital periods (~ a year). and typically smaller outburst amplitudes than CNe.," Recurrent nova systems have been sub-divided into three general sub-classes \citep{2008ASPC..401...31A} via a combination of the properties of the eruption and via the properties of the progenitor system whilst at quiescence: (hereafter the RS Oph-class) are observed to contain red giant secondaries and hence have much longer orbital periods $\sim$ a year), and typically smaller outburst amplitudes than CNe."685 Their outbursts exhibit rapid declines from maximum. with large ejection velocities (34000kms! y.," Their outbursts exhibit rapid declines from maximum, with large ejection velocities $\ge 4000\;\mathrm{km\;s}^{-1}$ )."686 These systems show evidence of an interaction between the ejecta and material from the pre-existing red giant wind., These systems show evidence of an interaction between the ejecta and material from the pre-existing red giant wind.687 The ejected mass from these systems 1s typically two orders of magnitude less than that observed from CN systems (seepaperswithinEvansetal.2008)..syste, The ejected mass from these systems is typically two orders of magnitude less than that observed from CN systems \citep[see papers within][]{2008ASPC..401.....E}.688ms are observed to contain. evolved main sequence or sub-giant secondaries. with orbital periods closer to those of CNe (hours up to of order a day).," are observed to contain evolved main sequence or sub-giant secondaries, with orbital periods closer to those of CNe (hours up to of order a day)."689 They again exhibit rapid declines. being amongst the fastest declining novae observed. with very high ejection velocities (up to 10000km s7!).," They again exhibit rapid declines, being amongst the fastest declining novae observed, with very high ejection velocities (up to $10000\;\mathrm{km\;s}^{-1}$ )."690 Their post-outburst spectra resemble those of the He/N sub-class of CNe (Williams1992).., Their post-outburst spectra resemble those of the He/N sub-class of CNe \citep{1992AJ....104..725W}.691 These systems eject a similar mass of material as RS Oph systems., These systems eject a similar mass of material as RS Oph systems.692 Thesystems (also CI Aql and IM Nor) are much more akin to CNe., The (also CI Aql and IM Nor) are much more akin to CNe.693 They exhibit short orbital. periods. and spectroscopically resemble Fe II CNe (Williams1992).., They exhibit short orbital periods and spectroscopically resemble Fe II CNe \citep{1992AJ....104..725W}.694 Their optical decline rate classifies them as moderately fast or slow novae., Their optical decline rate classifies them as moderately fast or slow novae.695 The ejected mass in these systems Is consistent with the range observed in CNe (Μα107 Μ.Ο., The ejected mass in these systems is consistent with the range observed in CNe $\mathrm{M}_{\mathrm{ej}}\sim 10^{-5}\msun$ ).696 These systems are generally only distinguishable from CNe due to their shorter recurrence times. not by the properties of the progenitor system or the outburst.," These systems are generally only distinguishable from CNe due to their shorter recurrence times, not by the properties of the progenitor system or the outburst."697 The short inter-outburst time observed in RNe is likely due to some combination of a higher mass WD and an aecretion rate greater than the typical for CN systems., The short inter-outburst time observed in RNe is likely due to some combination of a higher mass WD and an accretion rate greater than the typical for CN systems.698 Indeed. both RS Oph and U Sco (amongst others from these classes) appear to have WDs close to the Chandrasekhar limit.," Indeed, both RS Oph and U Sco (amongst others from these classes) appear to have WDs close to the Chandrasekhar limit."699 A number of authors (seee.g.Hachisuetal.2007;Osborne2011: have indicated that the WD mass may be increasing over time and these systems have been proposed as a Type lasupernova (SN) progenitor candidate (seee.g.Ko- 2008)..," A number of authors \cite[see e.g.][]{2007ApJ...659L.153H,2011ApJ...727..124O,SumnerConf} have indicated that the WD mass may be increasing over time and these systems have been proposed as a TypeIa supernova (SN) progenitor candidate \citep[see e.g.][]{2008ASPC..401..150K}."700However.Mason(2011) reported that U Sco could contain an O-Ne WD. rather than a C-O WD. and hence may," .However,\citet{2011arXiv1107.4013M} reported that U Sco could contain an O-Ne WD, rather than a C-O WD, and hence may"701between z;2O.4 and z;=1.4.,between $z_i=0.4$ and $z_i=1.4$.702 Thus we include by default only tomographic measures for every fifth bin /. but all j>i. in the S/N. The absolute value of the S/N depends of course on how many power spectra are incorporated. but we are only interested 1n the ratio of S/N for the nulled datasets over the set of original power spectra.," Thus we include by default only tomographic measures for every fifth bin $i$ , but all $j>i$, in the S/N. The absolute value of the S/N depends of course on how many power spectra are incorporated, but we are only interested in the ratio of S/N for the nulled datasets over the set of original power spectra."703 Note that for every z; one can make use of N.—i power spectra Οἱ(0)., Note that for every $z_i$ one can make use of $N_z-i$ power spectra $Q^{(ij)}(\ell)$.704 The very same number of modes is available in the standard nulling approach although one mode is discarded to perform the actual nulling (for details2009)., The very same number of modes is available in the standard nulling approach although one mode is discarded to perform the actual nulling <cit.>[for details.705 Transformed auto-correlation power spectra with /=j do not enter the S/N. but by construction the P'MOL) do contribute to all Οἱ) via the ATI). Whereas in standard nulling auto-correlations are completely discarded.," Transformed auto-correlation power spectra with $i=j$ do not enter the S/N, but by construction the $P^{(ii)}(\ell)$ do contribute to all $Q^{(ij)}(\ell)$ via the $\Pi_Q^{(i)}(\ell)$, whereas in standard nulling auto-correlations are completely discarded."706 However. due to the dense redshift binning. we expect the amount of independent information contained in auto-correlation power spectra to be small.," However, due to the dense redshift binning, we expect the amount of independent information contained in auto-correlation power spectra to be small."707 We have given the resulting. ratios. of the S/N for the nulled data set over the S/N for the original one in Table5., We have given the resulting ratios of the S/N for the nulled data set over the S/N for the original one in Table.708 The considerable loss of information can be confirmed. the S/N for both nulling methods yielding less than 20% of the original S/N. We find that these numbers are very robust against changes in the number and values of redshift bins / included in the S/N by varying the size of steps in bin numbers / and the range of redshifts considered.," The considerable loss of information can be confirmed, the S/N for both nulling methods yielding less than $20\,\%$ of the original S/N. We find that these numbers are very robust against changes in the number and values of redshift bins $i$ included in the S/N by varying the size of steps in bin numbers $i$ and the range of redshifts considered."709 It is quite remarkable that the ratios for both nulling methods are very similar., It is quite remarkable that the ratios for both nulling methods are very similar.710 The slightly bigger number for the nulling as devised in this work could be related to the inclusion of auto-correlation power spectra. but is not very significant anyway.," The slightly bigger number for the nulling as devised in this work could be related to the inclusion of auto-correlation power spectra, but is not very significant anyway."711 In the standard nulling case the information loss 1s causec by discarding part of the signal. namely one mode per bi i whereas the variant suggested here features à signal that deviates by at most about 20% from the untransformed one.," In the standard nulling case the information loss is caused by discarding part of the signal, namely one mode per bin $i$ whereas the variant suggested here features a signal that deviates by at most about $20\,\%$ from the untransformed one."712 I the latter case the loss ts caused by an increase in the covariance due to the subtraction of signals in (33)., In the latter case the loss is caused by an increase in the covariance due to the subtraction of signals in ).713 We conjecture at this point that the agreement in the amount of informatior lost. 1 spite of the largely different mechanisms of the two methods. hints at a fundamental limit of how far GI and GG signals ca be distinguished by only relying on the redshift dependence of the two contributions.," We conjecture at this point that the agreement in the amount of information lost, in spite of the largely different mechanisms of the two methods, hints at a fundamental limit of how far GI and GG signals can be distinguished by only relying on the redshift dependence of the two contributions."714 In this paper we presented à method which extracts shear-ellipticity correlations (the GI signal) from a tomographie cosmic-shear data set., In this paper we presented a method which extracts shear-ellipticity correlations (the GI signal) from a tomographic cosmic-shear data set.715 The approach relies neither on models of intrinsic alignments nor on knowledge of the cosmological parameters that characterise the cosmic shear (GG) signal. making only use of the typical and well-understood redshift dependencies of both the GI and GG term.," The approach relies neither on models of intrinsic alignments nor on knowledge of the cosmological parameters that characterise the cosmic shear (GG) signal, making only use of the typical and well-understood redshift dependencies of both the GI and GG term."716" We derived constraints which a linear transformation of second-order cosmic shear measures has to fulfil in order to boost the GI signal and simultaneously suppress the lensing contribution,", We derived constraints which a linear transformation of second-order cosmic shear measures has to fulfil in order to boost the GI signal and simultaneously suppress the lensing contribution.717 We studied in depth a particular parametrisation of the weights entering this transformation and analysed the performance of the resulting GI boosting technique for three representative survey models., We studied in depth a particular parametrisation of the weights entering this transformation and analysed the performance of the resulting GI boosting technique for three representative survey models.718 Applying the GI boosting to future all-sky cosmic shear surveys. it should be possible to isolate the GI signal with subdominant biases due to a residual GG term. and with constraints that are comparable to current results from indirect measurements of shear-ellipticity correlations2010).," Applying the GI boosting to future all-sky cosmic shear surveys, it should be possible to isolate the GI signal with subdominant biases due to a residual GG term, and with constraints that are comparable to current results from indirect measurements of shear-ellipticity correlations."719" If one restricts the analysis to galaxies with photometric redshift information of good quality. i.e. a redshift scatter of not more than c(l+5) with cy,=0.03. one can achieve | o-errors on the GI signal amplitude A in the parametrisation of (27) of better than 0.2when varying only the amplitude. and a marginalised error of approximately 0.7 when fitting an additional redshift dependence."," If one restricts the analysis to galaxies with photometric redshift information of good quality, i.e. a redshift scatter of not more than $\sigma_{\rm ph}(1+z)$ with $\sigma_{\rm ph}=0.03$, one can achieve $1\,\sigma$ -errors on the GI signal amplitude $A$ in the parametrisation of ) of better than 0.2when varying only the amplitude, and a marginalised error of approximately 0.7 when fitting an additional redshift dependence."720A. , 721New clues ave emerging that long GRB are associated with supernovae (Galamaοἱal.Bloometal.1999:Kulkarni2000:Reichart 2001).,"New clues are emerging that long GRB are associated with supernovae \citep{gal98,blo99,kul00,rei01}."722. This is illustrated most recently bv oplical emissions lines in the late-time light-ecurve of the HETE-II burst GRB 030329 (Stanekοἱal.2003).. which are remarkably similar to those observed in GRDB930425/8N1993bw (Galamaetal.1993).," This is illustrated most recently by optical emissions lines in the late-time light-curve of the HETE-II burst GRB 030329 \citep{sta03}, which are remarkably similar to those observed in GRB980425/SN1998bw \citep{gal98}."723.. A GRB-supernova assocation provides important support for the collapsar model of GIDs. representing a violent death of evolved massive stars 1998).," A GRB-supernova assocation provides important support for the collapsar model of GRBs, representing a violent death of evolved massive stars \citep{woo93,pac98}."724. The short lifespan of tens of Myrs of massive stars implies that GRBs take place in star-orming regions (Pacevuski1998:Fruchterοἱal.1999).. and hence more broadly points towards an association to molecular clouds.," The short lifespan of tens of Myrs of massive stars implies that GRBs take place in star-forming regions \citep{pac98,fru99}, and hence more broadly points towards an association to molecular clouds."725 The event rate of GRBs per unit cosmological volume is hereby. expected (o be correlated (to the cosmic stau-Iormation rate (e.g.. Blain&Natarajan(2000):Bergeretal.(2002):ChouclhurySrianand (2002))).," The event rate of GRBs per unit cosmological volume is hereby expected to be correlated to the cosmic star-formation rate (e.g., \citet{bla00,ber03,cho02}) )."726 Because observations bv past and current experiments (see Table I) are f[lux-Iimited. the observed CIRD-event rate is strongly biased towards events at lower redshilts.," Because observations by past and current experiments (see Table I) are flux-limited, the observed GRB-event rate is strongly biased towards events at lower redshifts."727are constrained using recent observations of disc fractions in nearby clusters (Mamajek 2009).,are constrained using recent observations of disc fractions in nearby clusters (Mamajek 2009).728 We require a viscosity coefficient of approximately a=2.5x107? to match the observational constraints., We require a viscosity coefficient of approximately $\alpha = 2.5\times10^{-3}$ to match the observational constraints.729 OOur main conclusions can be briefly summarised as follows:, Our main conclusions can be briefly summarised as follows:730source average count rate). were then computed according to the method described in Vaughanetal.(1994).,"source average count rate), were then computed according to the method described in \citet{vaughan94}."731. In OBSI. upper limits at à level of30%..20%.. and were inferred in the ss. ss. and ss period range. respectively.," In OBS1, upper limits at a level of, and were inferred in the s, s, and s period range, respectively."732 In OBS2. we derived upper limits at a level of20%%..30%.. and for periods 1n the range 0.03-20 s. 20-50 s. and s. respectively.," In OBS2, we derived upper limits at a level of, and for periods in the range 0.03-20 s, 20-50 s, and 0.02-0.03 s, respectively."733 oobserved oon 2007 May 29. with the Epic-PN camera operating in full frame.," observed on 2007 May 29, with the Epic-PN camera operating in full frame."734 To identify the high background time intervals we followed the same technique described for (see Sect., To identify the high background time intervals we followed the same technique described for (see Sect.735 4.2. and Fig. 1))., \ref{sec:igrresults} and Fig. \ref{fig:backselection}) ).736 We extracted the Epic-PN lightcurve for the full field of view (FOV) in the 10-12 keV energy band. and set a threshold on the full-FOV count rate in this energy band of 0.45 cts/s. The total effective exposure time after the good time interval selection for wwas 26 ks.," We extracted the Epic-PN lightcurve for the full field of view (FOV) in the 10-12 keV energy band, and set a threshold on the full-FOV count rate in this energy band of 0.45 cts/s. The total effective exposure time after the good time interval selection for was 26 ks."737 From the lighteurve of the observation (Fig. 100).," From the lightcurve of the observation (Fig. \ref{fig:igrb}) ),"738 it is apparent that the variability in the quiescent state of this source was rather similar to that of Un particular. the lower panel of Fig.," it is apparent that the variability in the quiescent state of this source was rather similar to that of In particular, the lower panel of Fig."739 10. shows that the hardness ratio of increased with the source count rate., \ref{fig:igrb} shows that the hardness ratio of increased with the source count rate.740 Figure 11. shows the hardness-intensity diagram of oobtained with the same technique described m Sect. 4.1.., Figure \ref{fig:igrbhardness} shows the hardness-intensity diagram of obtained with the same technique described in Sect. \ref{sec:xteresults}.741 In this case. the scatter of the points is somehow less evident than in the case of παπά a linear fit to the data required a slope of 1.9-40.2.," In this case, the scatter of the points is somehow less evident than in the case of and a linear fit to the data required a slope of $\pm$ 0.2."742 To investigate the origin of the variability in the hardness ratio of we extracted three different spectra during the time intervals of the observation in which the source count rate was 70.2. 0.1-0.2. and «0.1 (hereafter spectra A. B. C).," To investigate the origin of the variability in the hardness ratio of we extracted three different spectra during the time intervals of the observation in which the source count rate was $>$ 0.2, 0.1-0.2, and $<$ 0.1 (hereafter spectra A, B, C)."743 A fit to these spectra with a simple absorbed BB or PL model provided unacceptable results am .5-5.0. d.o.£.228-44).," A fit to these spectra with a simple absorbed BB or PL model provided unacceptable results $\chi^2_{\rm red}$$\gtrsim$ 1.5-5.0, d.o.f.=28-44)."744" A CUTOFFPL model with a fixed £44,211 keV (see Sect. 1))", A CUTOFFPL model with a fixed $E_{\rm cut}$ =11 keV (see Sect. \ref{sec:intro}) )745 provided tighter fits to the three spectra (AZ 1.2-1.6. d.o.f=28-44).," provided tighter fits to the three spectra $\chi^2_{\rm red}$$\sim$ 1.2-1.6, d.o.f=28-44)."746 However. the - was still significantly larger than |. the value of the absorption column density measured from the spectra B and C was unreasonably low (compatible with zero). and some structures were apparent in the residuals from the fits at energies «2 keV (see Fig. 12).," However, the $\chi^2_{\rm red}$ was still significantly larger than 1, the value of the absorption column density measured from the spectra B and C was unreasonably low (compatible with zero), and some structures were apparent in the residuals from the fits at energies $<$ 2 keV (see Fig. \ref{fig:igrbcountrate}) )."747 A CUTOFFPL model with a free to vary ων improved only the fit to spectrum A (X2. /d.o.f21.03/39). whereas the results of the," A CUTOFFPL model with a free to vary $E_{\rm cut}$ improved only the fit to spectrum A $\chi^2_{\rm red}$ /d.o.f=1.03/39), whereas the results of the"748"resonant for a particle of a given cnere AB, (07mee ky. where hy,= 22r). one can refer to a qualitative discussion of energetic particle diffusion presented by Drury (1983)","resonant for a particle of a given energy, $\delta B_r$ $\delta B_r^2 / 8 \pi \approx F(k_r) 749\cdot k_r$ , where $k_r = 2 \pi / r_g$ ), one can refer to a qualitative discussion of energetic particle diffusion presented by Drury (1983)."750" With his sealing 5jx(0D,/D) and 5&1x(0D,./ D). the amplitude for resonance waves can. be evaluated as 6B,/BzRE."," With his scaling $\kappa_\| \propto (\delta B_r / B)^{-2}$ and $\kappa_\perp \propto (\delta B_r / B)^2$ , the amplitude for resonance waves can be evaluated as $\delta B_r / B \approx \aleph^{1/4}$."751" The respective values o£8—81/5 were derived in auxiliary simulations involving the spatially uniform. background magnetic field with the induction of 1.510.* ""T and particles with energies equal to the initial energy fy=2 MeV. ""Trajectories of a large number of particles were followed with the imposed. scattering process involving the momentum angular scattering. uniform. within a cone of half opening angle equal to 11 and with the cone axis directed. along the original momentum vector."," The respective values of $\aleph \equiv \kappa_\perp / \kappa_\|$ were derived in auxiliary simulations involving the spatially uniform background magnetic field with the induction of $1.5 \cdot 10^{-3}$ T and particles with energies equal to the initial energy $E_0 = 2$ MeV. Trajectories of a large number of particles were followed with the imposed scattering process involving the momentum angular scattering, uniform within a cone of half opening angle equal to $11^\circ$ and with the cone axis directed along the original momentum vector."752 The only parameter varving between the simulations was the time interval between successive scattering events. Af.," The only parameter varying between the simulations was the time interval between successive scattering events, $\Delta t$."753 The resulting cillusion cocllicicnts were derived. from growing particle dispersions along the background field (64) and along two orthogona axes perpendicular to the backeround field (= along the 1- or 2-axis)., The resulting diffusion coefficients were derived from growing particle dispersions along the background field $\kappa_\|$ ) and along two orthogonal axes perpendicular to the background field $\equiv$ along the $1$ - or $2$ -axis).754 The results of such computations are presented in Pig., The results of such computations are presented in Fig.755 2., 2.756 Presentation of two derived values ofa.fr) and 82/58 allows one to evaluate the accuracy of these computations., Presentation of two derived values of $\kappa_1 / \kappa_\|$ and $\kappa_2 / \kappa_\|$ allows one to evaluate the accuracy of these computations.757" The values used in the paper are fits to the asvmptotic QUox) value of 8=0.5(58,|we)fay."," The values used in the paper are fits to the asymptotic $(T \to \infty)$ value of $\aleph = 0.5 \, 758(\kappa_1 + \kappa_2) / \kappa_\|$."759 For a sequence of scattering tines M — 10P. 10. 7. 10. Land 10.7 we derive the respective values of N = 1 7.6:10.7. 6-107. anc 6-10.," For a sequence of scattering times $\Delta t$ = $10^{-6}$, $10^{-5}$ , $10^{-4}$ and $10^{-3}$ we derived the respective values of $\aleph$ = $1.2 \cdot 10^{-2}$, $6 \cdot 10^{-3}$, $6 \cdot 76010^{-5}$, and $6 \cdot 10^{-7}$."761 The results derived without applying any scattering are indicated by N=0., The results derived without applying any scattering are indicated by $\aleph = 0$.762 In order to provide qualitative evaluations of turbulence ellects in the volume of reconnecting magnetic Ποια. but considering it only as a factor introducing rancom motion component to particle trajectories. we performed simulations of energetic proton spectra with a varving amount of turbulence (= scattering).," In order to provide qualitative evaluations of turbulence effects in the volume of reconnecting magnetic field, but considering it only as a factor introducing random motion component to particle trajectories, we performed simulations of energetic proton spectra with a varying amount of turbulence $\equiv$ scattering)."763 As explained. above. this approach assumes the existence of short wave magnetic Ποιά perturbations to be present in the limited volume — the black rectangle in Fig.," As explained above, this approach assumes the existence of short wave magnetic field perturbations to be present in the limited volume – the black rectangle in Fig."764 1... near the central neutral point. but we do not consider the influence of the turbulence on the reconnection process.," 1 – near the central neutral point, but we do not consider the influence of the turbulence on the reconnection process."765 Thus it is a complementary approach to that using MIID moelling of the turbulent reconnection including wave perturbations from a narrow wave vector range. as discussed in section 1.," Thus it is a complementary approach to that using MHD modelling of the turbulent reconnection including wave perturbations from a narrow wave vector range, as discussed in section 1."766" We performed simulations of particle evolution starting ab the same ""injection energv. Ly=2 MeV. avoiding consideration of the real injection process at. much. lower energies (cf."," We performed simulations of particle evolution starting at the same `injection' energy $E_0 = 2$ MeV, avoiding consideration of the real injection process at much lower energies (cf."767 Miller et al., Miller et al.768 1997)., 1997).769 For each set. of. particles we derived. the spectrum. of particles escaping from the reconnection volume. as illustrated in Fig.," For each set of particles we derived the spectrum of particles escaping from the reconnection volume, as illustrated in Fig."770 3., 3.771 In the non-»erturbed: model (CS=0. curve A) protons can increase heir initial energy. by approximately 70%.," In the non-perturbed model $\aleph = 0$, curve A) protons can increase their initial energy by approximately $70$."772 One should note that the injected energetic particles can gain as well as oose energy., One should note that the injected energetic particles can gain as well as loose energy.773 Introducing trajectory perturbations results in substantial modification of the acceleration process (curves D. €. D. Iz in Fig.," Introducing trajectory perturbations results in substantial modification of the acceleration process (curves B, C, D, E in Fig."774 3)., 3).775 The spectrum energy. eut-olf shifts to ugher values and the spectrum becomes harder when the amount of scattering (turbulence amplitude) is increased., The spectrum energy cut-off shifts to higher values and the spectrum becomes harder when the amount of scattering (`turbulence amplitude') is increased.776 In our simulations the resulting Hat spectra extend. up to 50 MeV. for models with strong turbulence (Model D and 19). and a steeper part of the spectrum is recorded. at energies above LOO MeV. This behaviour results from. the act that the dilfusive component introduced in to particle rajectorics by the scattering enables some particles to stay in the reconnection region much longer and dilfuse back close to the null point from outside.," In our simulations the resulting flat spectra extend up to $50$ MeV for models with strong turbulence (Model D and E), and a steeper part of the spectrum is recorded at energies above $100$ MeV. This behaviour results from the fact that the diffusive component introduced in to particle trajectories by the scattering enables some particles to stay in the reconnection region much longer and diffuse back close to the null point from outside."777 As illustrated. this can lave a pronounced influence on the acceleration process by substantially increasing the particlemean energy eain aud »ovidine much larecr energies of individual particles.," As illustrated, this can have a pronounced influence on the acceleration process by substantially increasing the particlemean energy gain and providing much larger energies of individual particles."778 There, There779dark matter oudegree scales.,dark matter on scales.780" As with the weak leusiug of faint galaxies. dmaee distortions manifest on simall augular scales aro used to reconstruct the mass on a much larger scale,"," As with the weak lensing of faint galaxies, image distortions manifest on small angular scales are used to reconstruct the mass on a much larger scale."781 Mapping the dark matter distribution therefore requires high resolution. high signal-to-noise maps of the CMB auisotropics themselves.," Mapping the dark matter distribution therefore requires high resolution, high signal-to-noise maps of the CMB anisotropies themselves."782" Conversely, though a wide Held of at least several degrees on the side is required to nap the full extent of the structures expected. the statistic essentially high pass filters the input. CMB maps."," Conversely, though a wide field of at least several degrees on the side is required to map the full extent of the structures expected, the statistic essentially high pass filters the input CMB maps."783 A true nap that retaius correlations across these scales is not lCCOSSUIPY., A true map that retains correlations across these scales is not necessary.784 To see how au observing strategy might be optimized or napping the dark matter. let us consider the trade-offs between sky coverage. mstruneutal noise aud beau.," To see how an observing strategy might be optimized for mapping the dark matter, let us consider the trade-offs between sky coverage, instrumental noise and beam."785 Because this statistic isa quadratic function of the temperature Huctuation data. the balance differs from the usual case.," Because this statistic is a quadratic function of the temperature fluctuation data, the balance differs from the usual case."786 Iu Fig. L.," In Fig. \ref{fig:sensitivity},"787 we show the total signal-to-noise in the measurement of the deflection power spectrum: (πιο in quadrature over L) of an experiment as a function of these parameters., we show the total signal-to-noise in the measurement of the deflection power spectrum (summed in quadrature over $L$ ) of an experiment as a function of these parameters.788 We consider separately the case of noise variance from the Gaussian random primary auisotropies and detector noise alone aud combined with tle sample variance of the lensing Ποια»., We consider separately the case of noise variance from the Gaussian random primary anisotropies and detector noise alone and combined with the sample variance of the lensing fields.789⋅ When- the former: exceeds the latter. a high. sigual-.TUE ot; : structures ∖↴⋅⊳1c ↴sults," When the former exceeds the latter, a high signal-to-noise map of the structures results."790",Be≱∖⋈ (othisijo de; at oCoorax. statistic.map thethi characteristic sigual-to-noise CaliforIs Goldberg. features is nich. higher (see Fig. 1))."," Because this is an integrated statistic, the characteristic signal-to-noise for large-scale features is much higher (see Fig. \ref{fig:defl}) )."791 Ile. arethe steep Increaseinerease 1ni he signasienal ο...EN llu.Πας detector noise is reduced with the shallow increase asKaiser. sky. coverage 2 oQUgló2, Compare the steep increase in the signal-to-noise as the detector noise is reduced with the shallow increase with sky coverage of $f_{\rm sky}^{1/2}$.792" Upτ eU?maili 1/2 ©2↽10(1(10 Μοτο,(-Ixiox. x.observing tineof isf. best spent goiug deep10 rather Seljak. wide."," Up until $w^{-1/2} \sim 10$ $(10^{-6}$ -arcmin), observing time is best spent going deep rather than wide."793 Bevoud. this point.. the. iutriusie noise. variance. Reljak.teli by⋅ the primary CAIBj anisotropiesκ⋅ themselves.Tyson. Zaldarriaga. to dominate and saturate the signal-to-noise.," Beyond this point, the intrinsic noise variance provided by the primary CMB anisotropies themselves begins to dominate and saturate the signal-to-noise."794 If the Zaldarriaga. eoal is to produce a high signal-to-nolse nap of structures. heu gomme down tow17?1: (10. arcuin) can achieve substantially improved maps of the finer scale structures iu the map.," If the goal is to produce a high signal-to-noise map of structures, then going down to $w^{-1/2} \sim 1$ $(10^{-6}$ -arcmin) can achieve substantially improved maps of the finer scale structures in the map."795 Another crucial factor is the beam size., Another crucial factor is the beam size.796 To resolve the structures thatbest trace the lensing. a beam of o«B5 is required aud it is not uutilo~1'2 that the eains saturate.," To resolve the structures thatbest trace the lensing, a beam of $\sigma < 5'$ is required and it is not until $\sigma \sim 1'-2'$ that the gains saturate."797 If foregrounds are not removed from the map through their spatial coherence and/or frequency dependence then this balance cau shift to larecr aneular scales and more skv coverage., If foregrounds are not removed from the map through their spatial coherence and/or frequency dependence then this balance can shift to larger angular scales and more sky coverage.798" For the 1.5’. 10 (10.arcmin) baseline experiment. iuchisiou of Gaussian random noise from the Suuvaev-Zeldovich aud Vishuiac effects iu CT"" imply a relative degradation in sigual-to-noise of ~105€ and ~L4 (for 7=0.1) respectivelv aud so do not require substantial reoptimization."," For the $1.5'$, $10$ $(10^{-6}$ -arcmin) baseline experiment, inclusion of Gaussian random noise from the Sunyaev-Zel'dovich and Vishniac effects in $C_l^{\rm tot}$ imply a relative degradation in signal-to-noise of $\sim 10\%$ and $\sim 1\%$ (for $\tau=0.1$ ) respectively and so do not require substantial reoptimization."799 A high sigual-to-noise map of the dark matter in projection can also be used to pull out tracers of the larec-scale structure of the universe in other maps through cross-correlation., A high signal-to-noise map of the dark matter in projection can also be used to pull out tracers of the large-scale structure of the universe in other maps through cross-correlation.800 Examples include secondary. aulsotropies suc[um as the integrated. Sachs-Wolte aud Suuyyaecv-Zeldovich effects (Goldberg&Sperecl 1999: Seljak&Zaldarriaga 1998: Cooray&Thi 2000)., Examples include secondary anisotropies such as the integrated Sachs-Wolfe and yaev-Zel'dovich effects \cite{GolSpe99} 1999; \cite{SelZal98} 1998; \cite{CooHu00a} 2000).801 Oue cau show that the statistic employed here retains all of the information iu the full bispectin of the secoucdary-lensine-primary correlation and sois the optimal statistic to measure these correlations., One can show that the statistic employed here retains all of the information in the full bispectrum of the secondary-lensing-primary correlation and so is the optimal statistic to measure these correlations.802 ⊺↕↓↸∖∏↕↾↸∖↕⋅↴⇖∏∖∩↧↾∪↕⋅↸∖↸↾∪∐↴∖↴∏⋅⋯↾↾↾↕↓↸∖↸↧⋮↕∏∖⊽↕⊔⋮↕⊺↾↸∖↕⋅↕⊔⋮↕⋟: ⋅ ↕≯∪∐∐⋜↧∐⋅↖⊽↥⋅↸∖≺∣∏∏⋅↸∖⋜↧↴∖↴↕∐↻∏↑∐↸∖↻∪∖∏∖↥⋅↴∖↴↻↸∖↸⊳∏↴∐, The filters used to reconstruct the dark matter map formally require as input the power spectrum of the CMB lensing.803⊔∪↕⋟∏∐∖≼⊲⋀∖∐≩ ≀⇂∣↕⋮↗∠∎∪∣⋏↕↕↸∖∐↴∖↴↕∐∶↴⋁∙⊺∐↸∖↕↸∖∐↴∖↴↸∖≼⊔⊲⋀∖∐≧↻∪↖↖↽↸∖↥⋅↴∖↴↻↸∖↸⊳⊓⋅⋯⊔↖↖⇁↕∐∪↕≯ ≼⊳≺∏∐⋅↴∖↴↸∖↴⋈∖∐∐∖⋜↧↴∖↴↿∐⋅↸∖≼↧↑∪↸∖⊼≺∏∏↴∖↴↕↑↸∖↻↥⋅↸∖↸⊳↕↴∖↴↕∪∐↴, The lensed CMB power spectrum will of course be measured to exquisite precision by CMB satellites and by the input temperature map themselves.804⋝∙↖⇁≼⊲⋀∖∐≧↴∖↴⋜↧↑↸∖∐↕↑↸∖↴∖↴ ⋜⋯≺⊓⋝∙↖↽↑↕∐∖↕↕∏⋯↑↑↸∖∐∏⋉∖↥⋅⋜↧↿∐⋅↸∖∐↓⋜∏≻∐↸∖↕⊔↴∖↴↸∖↕↖⇁↸∖↴∖↴∙⊏∐∏≻↕∪⋅↖↽↕∐∶↴⋁ he lensed οΠΟ power spectrin in the filter or an otherwise slightly incorrect assuiptiou simply degrades the sigual-o-hoise by a correspoudingly siuiall amount but does not introduce spurious structures in the enusenible-averaged recovery., Employing the lensed CMB power spectrum in the filter or an otherwise slightly incorrect assumption simply degrades the signal-to-noise by a correspondingly small amount but does not introduce spurious structures in the ensemble-averaged recovery.805 They appear as a calibration error for tle mass nap., They appear as a calibration error for the mass map.806 Indeed in the context of a parameterized cosmology he unlensed CAB power spectrum may itself be reconstructed Your the observed spectrum., Indeed in the context of a parameterized cosmology the unlensed CMB power spectrum may itself be reconstructed from the observed spectrum.807 For a non-uniform survey econmetrv. with perhaps foreground-contanminated reeious renmnioved. more sophisticated techniques than the Fouricr-ransforiu flteriug scheme enploved here will have to © developed.," For a non-uniform survey geometry, with perhaps foreground-contaminated regions removed, more sophisticated techniques than the Fourier-transform filtering scheme employed here will have to be developed."808 These complications should uot preseut au insumuouutable obstacle to the goal of mapping the dark hatter iu projection at intermediate redshifts., These complications should not present an insurmountable obstacle to the goal of mapping the dark matter in projection at intermediate redshifts.809 Y acknowledge useful conversations with A.R. Cooray and M. Zaldarriaga as well as support your NASA NAG5-10810. DOE OJI aud au Alfred D. Sloan Foundation Fellowship.," I acknowledge useful conversations with A.R. Cooray and M. Zaldarriaga as well as support from NASA NAG5-10840, DOE OJI and an Alfred P. Sloan Foundation Fellowship."810Gamma-Ray Bursts (GRBs) are explosions which release roughly 10°! erg in the form of kinetic energy of highly relativistic material (Frail et al.,Gamma-Ray Bursts (GRBs) are explosions which release roughly $^{51}$ erg in the form of kinetic energy of highly relativistic material (Frail et al.811 2001. Panaitescu Kumar2001011.," 2001, Panaitescu Kumar."812.. Many GRBs appear to be highly non-spherical explosions. as evidenced by a nearly-achromatie break im the light-curve (e.g. Harrison et al.," Many GRBs appear to be highly non-spherical explosions, as evidenced by a nearly-achromatic break in the light-curve (e.g. Harrison et al."813 1999; Stanek et al., 1999; Stanek et al.814 1999)., 1999).815" Highly relativistic jets are ""visible"" when our line of sight is within the jet aperture (0,4,< Oy). otherwise. because of relativistic beaming of photons away from our line-of-sight. the object is too dim."," Highly relativistic jets are “visible” when our line of sight is within the jet aperture $\theta_{\rm obs}<\theta_0$ ), otherwise, because of relativistic beaming of photons away from our line-of-sight, the object is too dim."816 As the jet decelerates. the relativistic beaming becomes less severe and the emission from the jet becomes detectable to observers at larger viewing angles.," As the jet decelerates, the relativistic beaming becomes less severe and the emission from the jet becomes detectable to observers at larger viewing angles."817" In this Letter we study the afterglow light-curves for off-axis locations (0,7 0). focusing on observers lying outside of the initial jet opening angle (0,4,7 09)."," In this Letter we study the afterglow light-curves for off-axis locations $\theta_{\rm obs}>0$ ), focusing on observers lying outside of the initial jet opening angle $\theta_{\rm obs}>\theta_0$ )."818 Granot et al. (, Granot et al. (819"2001) have shown that the light curve seen by an observer located within the initial jet aperture (0,5, 0) is very similar to that for an on-axis observer (η.= 0).",2001) have shown that the light curve seen by an observer located within the initial jet aperture $\theta_{\rm obs}<\theta_0$ ) is very similar to that for an on-axis observer $\theta_{\rm obs}=0$ ).820 Dalal et al. (, Dalal et al. (8212002) and Rossi et al. (,2002) and Rossi et al. (8222002) have presented simple models to calculate the flux in this case.,2002) have presented simple models to calculate the flux in this case.823 We reanalyze these models in $22.1 and consider more realistic models in $22.2 822.3., We reanalyze these models in 2.1 and consider more realistic models in 2.2 2.3.824 Moderski. Sikora and Bulik (2000) have calculated off-axis light-curves with a more In ," Moderski, Sikora and Bulik (2000) have calculated off-axis light-curves with a more complex model, similar to that presented in 2.2."825"$33 we calculate the temporal evolution of the linear polarization for various @,,,.", In 3 we calculate the temporal evolution of the linear polarization for various $\theta_{\rm obs}$.826 In $44 we analyze the prospects of using the detection rate of orphan afterglows to estimate the collimation of GRB jets., In 4 we analyze the prospects of using the detection rate of orphan afterglows to estimate the collimation of GRB jets.827 In 855 we analyze the suggestion of Woosley. Eastman. Schmidt (1999) that a relativistic Jet emanating from the SN explosion and pointing away from us could explain the observations.," In 5 we analyze the suggestion of Woosley, Eastman, Schmidt (1999) that a relativistic jet emanating from the SN explosion and pointing away from us could explain the observations."828 In this section we calculate the afterglow light curves of jetted GRBs. as seen by observers at different viewing angles. Oop. Wat the symmetry axis of the jet.," In this section we calculate the afterglow light curves of jetted GRBs, as seen by observers at different viewing angles, $\theta_{\rm obs}$, w.r.t the symmetry axis of the jet."829 For simplicity. we consider only a jet propagating into a homogeneous medium.," For simplicity, we consider only a jet propagating into a homogeneous medium."830 In order to improve our understanding of the underlying physics and in order to check how general the results are. we explore three different models with an increasing level of complexity.," In order to improve our understanding of the underlying physics and in order to check how general the results are, we explore three different models with an increasing level of complexity."831 We begin with a simple model. where for 4).=0 the light curve follows the results of simple jet models (Rhoads 1999: Sari. Piran Halpern 1999. hereafter R-SPH99). and for Oy.20 the light curves are calculated assuming the emission is from a point source that moves along the jet axis.," We begin with a simple model, where for $\theta_{\rm obs}=0$ the light curve follows the results of simple jet models (Rhoads 1999; Sari, Piran Halpern 1999, hereafter R-SPH99), and for $\theta_{\rm obs}>0$ the light curves are calculated assuming the emission is from a point source that moves along the jet axis."832 The on-axis light curve exhibits a jet break at (R-SPH99): where £5» is the isotropic equivalentenergy in units of 107? erg. y is the ambient density inci° and : is the cosmological redshift of the source.," The on-axis light curve exhibits a jet break at (R-SPH99): where $E_{52}$ is the isotropic equivalentenergy in units of $10^{52}$ erg, $n_0$ is the ambient density in ${\rm cm}^{-3}$ and $z$ is the cosmological redshift of the source."833 Att<fia. Ενθω0) is taken from Sari. Piran and Narayan (1998). while at #>fj4 the temporal scalings of the break frequencies and peak flux change according to R-SPH99.," At $t<t_{\rm jet}$, $F_{\nu}(\theta_{\rm obs}=0)$ is taken from Sari, Piran and Narayan (1998), while at $t>t_{\rm jet}$ the temporal scalings of the break frequencies and peak flux change according to R-SPH99."834" The observed flux density from a point source Is where L'/, and 7 are the spectral luminosity and frequency in the local rest frame of the jet. 4| and d; are the angular and luminosity distances to the source. (LF)H3 is the Lorentz factor of the source and 0 is the angle between the direction of motion of the source and the direction to the observer in the observer frame (in our case 0.= 0)."," The observed flux density from a point source is where $L'_{\nu'}$ and $\nu'$ are the spectral luminosity and frequency in the local rest frame of the jet, $d_{A}$ and $d_{L}$ are the angular and luminosity distances to the source, $\gamma=(1-\beta^2)^{-1/2}$ is the Lorentz factor of the source and $\theta$ is the angle between the direction of motion of the source and the direction to the observer in the observer frame (in our case $\theta=\theta_{\rm obs}$ )."835 Since tUzmdtfdt=vfvυ-ἷ- Jeos0). where f and v are the observed time and frequency. owe obtain that," Since $t/t'\approx dt/dt'=\nu'/\nu=(1+z)\gamma(1-\beta\cos\theta)$ , where $t$ and $\nu$ are the observed time and frequency, we obtain that"836"Fitting two-dimensional Gaussians to the SMA images, leads to flux densities of 16.8+1.5 mJy and 8.52.0 mJy for MM1 and MM14, respectively.","Fitting two-dimensional Gaussians to the SMA images, leads to flux densities of $16.8\pm1.5$ mJy and $8.5\pm2.0$ mJy for MM1 and MM14, respectively."837" The MM14 detection is tentative since, as we shall see below, it could not be reliably identified with any significant counterpart at other wavelengths."," The MM14 detection is tentative since, as we shall see below, it could not be reliably identified with any significant counterpart at other wavelengths."838" The Gaussian fit indicates that both sources are unresolved with a maximum deconvolved FWHM size of 1.8""x1.0"" and 2.0""x0.6"", respectively, consistent with the sizes found for high-redshift SMGs, which are typically unresolved at ~2” resolution (Ionoetal.etal. 2009)."," The Gaussian fit indicates that both sources are unresolved with a maximum deconvolved FWHM size of $1.8\arcsec\times1.0\arcsec$ and $2.0\arcsec\times0.6\arcsec$, respectively, consistent with the sizes found for high-redshift SMGs, which are typically unresolved at $\sim2\arcsec$ resolution \citep{Iono2006,Younger2007, Wang2007,Younger2009}."839. This also yields from the flatness of the real visibility amplitudes as a function of the projected baseline length., This also yields from the flatness of the real visibility amplitudes as a function of the projected baseline length.840" The measured SMA position for MM1 is a(J2000)=1000""15.6125, 5(J2000)=+02°15’49.00”, with a positional error in theGaussian fit of 0.09"", while for MM14 it is a(J2000)=10""00™47.329°, 5(J2000)= --02?10'21.44"", with a positional error in the fit of 0.15”."," The measured SMA position for MM1 is $\alpha(\mathrm{J2000})=10^\mathrm{h}00^\mathrm{m}15.612^\mathrm{s}$, $\delta(\mathrm{J2000})=+02\degr15\arcmin49.00\arcsec$, with a positional error in theGaussian fit of $0.09\arcsec$, while for MM14 it is $\alpha(\mathrm{J2000})=10^\mathrm{h}00^\mathrm{m}47.329^\mathrm{s}$, $\delta(\mathrm{J2000})=+02\degr10\arcmin21.44\arcsec$ , with a positional error in the fit of $0.15\arcsec$."841" This positional accuracy in the fit is consistent with the one expected for the beam and S/N of the observations: 0.09""and 0.2""for MM1 and MM14, respectively."," This positional accuracy in the fit is consistent with the one expected for the beam and S/N of the observations: and for MM1 and MM14, respectively."842" From the comparison of the reference (Browneetal.1998) and measured (this work) positions of the test quasar J1008+063, we find a positional uncertainty of 0.18""."," From the comparison of the reference \citep{Browne1998} and measured (this work) positions of the test quasar $+$ 063, we find a positional uncertainty of $0.18\arcsec$."843" 'This, added in quadrature to the positional error in the Gaussian fit to the MM1 and MM14 images, gives a positional uncertainty of 0.2"" and 0.27"", respectively."," This, added in quadrature to the positional error in the Gaussian fit to the MM1 and MM14 images, gives a positional uncertainty of $0.2\arcsec$ and $0.27\arcsec$, respectively."844MM1. The SMA peak position coincides with the position of a ~3.50 radio peak (Fig. 1))., The SMA peak position coincides with the position of a $\sim3.5\sigma$ radio peak (Fig. \ref{fig:allphot}) ).845" A bright and elongated source with photometric redshift z—1.4 (bertetal.2009) is located at —2.1""north-west from the SMA position.", A bright and elongated source with photometric redshift $z=1.4$ \citep{Ilbert2009} is located at $\sim$ north-west from the SMA position.846" The radio peak lies within 0.3"" from the SMA position, however given the beam of the radio image (~ 2""), we do not discard that part of the emission comes from this bright optical source."," The radio peak lies within $0.3\arcsec$ from the SMA position, however given the beam of the radio image $\sim2\arcsec$ ), we do not discard that part of the emission comes from this bright optical source."847 From Fig., From Fig.848" 2 (left), we identify a very faint K-band source, located at z0.3"" from the SMA position, as the likely counterpart."," \ref{fig:closeup} (left), we identify a very faint $K$ -band source, located at $\approx0.3\arcsec$ from the SMA position, as the likely counterpart."849" The bright optical source strongly contaminates theSpitzer images, making it difficult to reliably measure the faint emission of MM1."," The bright optical source strongly contaminates the images, making it difficult to reliably measure the faint emission of MM1."850 We extracted photometry in the IRAC bands by subtracting this bright source based on the K-band image convolved with the IRAC PSF (Table 1))., We extracted photometry in the IRAC bands by subtracting this bright source based on the K-band image convolved with the IRAC PSF (Table \ref{table:1}) ).851 We do not attempt to extract photometry of this source in the 24 wm images., We do not attempt to extract photometry of this source in the 24 $\mu$ m images.852" No emission is detected at 70 and 160 um. The deep K-band images show two peaks, separated by about0.6"", or a physical scale of ~4.3 kpc at z~8 (Fig. 2))."," No emission is detected at 70 and 160 $\mu$ m. The deep $K$ -band images show two peaks, separated by about, or a physical scale of $\sim4.3$ kpc at $z\sim3$ (Fig. \ref{fig:closeup}) )."853" The fainter peak appears to be the one associated with the submm emission, suggesting a possible double system, similar to the case of the SMG AzTECII (Youngeretal.2009)."," The fainter peak appears to be the one associated with the submm emission, suggesting a possible double system, similar to the case of the SMG AzTEC11 \citep{Younger2009}."854.MM14. The radio maps do not show any peak close to the position of the SMA source down to a 3c level of 30 LJ y., The radio maps do not show any peak close to the position of the SMA source down to a $3\sigma$ level of 30 $\mu$ Jy.855" At ~1.2"" to the north of the SMA position we find a faint optical source that appears diffuse and faint in the K-band (Fig. 1)).", At $\sim1.2\arcsec$ to the north of the SMA position we find a faint optical source that appears diffuse and faint in the $K$ -band (Fig. \ref{fig:allphot}) ).856 This source has a likely photometric redshift of ~3.4 (Mobasheretal.2007)., This source has a likely photometric redshift of $\sim3.4$ \citep{Mobasher2007}.857". From Fig. 1,,"," From Fig. \ref{fig:allphot},"858" the northern optical source appears to be composed by several “clumps” that extend over ~1.5"", or 11 kpc at z~3.5."," the northern optical source appears to be composed by several “clumps” that extend over $\sim1.5\arcsec$, or $\sim11$ kpc at $z\sim3.5$."859" We also find a very faint K-band emission peak (c-3e in the smoothed image), located tto the south of the SMA position (Fig. 2))."," We also find a very faint $K$ -band emission peak $\sim$ $\sigma$ in the smoothed image), located to the south of the SMA position (Fig. \ref{fig:closeup}) )."860" This peak has ~2σ significance in the original K-band image (without smoothing; Fig. 1)),"," This peak has $\sim2\sigma$ significance in the original $K$ -band image (without smoothing; Fig. \ref{fig:allphot}) ),"861 implying the source is spatially extended., implying the source is spatially extended.862" Due to its proximity to the SMA position, it appears to be the most likely counterpart to the submm emission despite its faintness."," Due to its proximity to the SMA position, it appears to be the most likely counterpart to the submm emission despite its faintness."863" Hereafter, we refer to this source as MM14S (south), while for the northern optical source we refer as MM14N. However, since we could not reliably identify any significant multi-wavelength counterpart for this source and given the relatively low significance of the SMA detection, we label this source (MM14S) as a tentative detection."," Hereafter, we refer to this source as MM14S (south), while for the northern optical source we refer as MM14N. However, since we could not reliably identify any significant multi-wavelength counterpart for this source and given the relatively low significance of the SMA detection, we label this source (MM14S) as a tentative detection."864" The spatial configuration between MM14S and MMIAN could resemble a system, where the submm emission comesmerger/interaction from a highly obscured source (MM14S), but could also correspond toan extended galaxy with the submm emission located in an obscured spiral arm."," The spatial configuration between MM14S and MM14N could resemble a merger/interaction system, where the submm emission comes from a highly obscured source (MM14S), but could also correspond toan extended galaxy with the submm emission located in an obscured spiral arm."865" The offset between the MM14N and the submm position (MM14S) is 9 kpc, assuming z~3.5, similar to the case of the high-redshift SMG GN20 (Jonoetal. 2006),, where the submm and the optical peaks are separated by ~0.8”, or ~6 kpc."," The offset between the MM14N and the submm position (MM14S) is $\sim9$ kpc, assuming $z\sim3.5$, similar to the case of the high-redshift SMG GN20 \citep{Iono2006}, , where the submm and the optical peaks are separated by $\sim0.8\arcsec$, or $\sim6$ kpc."866" Based on the local density of sources with z>3, n=0.002 arcsec-?, we find that the probability that a z>3 optical source brighter than MM14N is located by chance within a distance of ffrom the SMA position is only P—0.996, thus supporting a physical association."," Based on the local density of sources with $z>3$, $n=0.002$ $^{-2}$, we find that the probability that a $z>3$ optical source brighter than MM14N is located by chance within a distance of from the SMA position is only $P=0.9\%$, thus supporting a physical association."867" photometry was performed with SExtractor Optical/IR(Bertin&Arnouts1996) in a aaperture, using the K-band images for detection."," Optical/IR photometry was performed with SExtractor \citep{Bertin1996} in a aperture, using the $K$ -band images for detection."868" None of our targets was detected in the Spitzer MIPS bands, and we thus provide 3e upper limits based on their local noise level within one beam."," None of our targets was detected in the MIPS bands, and we thus provide $3\sigma$ upper limits based on their local noise level within one beam."869" The measured flux densities at several wavelengths for MM1, MM14S and MM14N are listed in Table 1.."," The measured flux densities at several wavelengths for MM1, MM14S and MM14N are listed in Table \ref{table:1}. ."870 MMI and MM14S were not detected in the COSMOS catalogs (Capaketal.2007;Ilbert and thus there is no previous estimate for theirredshift.," MM1 and MM14S were not detected in the COSMOS catalogs \citep{Capak2007, Ilbert2009} and thus there is no previous estimate for theirredshift."8712009) Assuming that the correlation between the far-IR and, Assuming that the correlation between the far-IR and872specific predictions about how center ancl satellite galaxies of the same luminosity ciffer: this dillerence is the subject of Section. ??..,specific predictions about how center and satellite galaxies of the same luminosity differ; this difference is the subject of Section \ref{compareM2L}.873 These predictions can also be tested. by studying how stellar and total mass-to-light ratios depend on environment: how the luminosity function. of clusters (alter removing the BCC) depends on cluster richness: and how the amount of intracluster light depends on. cluster richness., These predictions can also be tested by studying how stellar and total mass-to-light ratios depend on environment; how the luminosity function of clusters (after removing the BCG) depends on cluster richness; and how the amount of intracluster light depends on cluster richness.874 The connections between these tests and the halo niodel are discussed in a final section which summarizes our findings., The connections between these tests and the halo model are discussed in a final section which summarizes our findings.875" Fhroughout. we assume a spatially Hat cosmology withQO, 20.3. Ag=1.Qo and ex=0.9. and we write the ILubble constant as Ly=1005 km | |."," Throughout, we assume a spatially flat cosmology with$\Omega_0=0.3$ , $\Lambda_0=1-\Omega_0$ and $\sigma_8=0.9$, and we write the Hubble constant as $H_0=100h$ km $^{-1}$ $^{-1}$."876 An Appenclix presents a few inconsistencies between the halo mocel of Zehavi et al. (, An Appendix presents a few inconsistencies between the halo model of Zehavi et al. (8772005) and the group catalog of Jerlind et al. (,2005) and the group catalog of Berlind et al. (8782006).,2006).879 Ht argues that while these may be due to Zehavi et al., It argues that while these may be due to Zehavi et al.880's assumption that ax=0.9. they are unlikely to invalidate our findings.,"'s assumption that $\sigma_8=0.9$, they are unlikely to invalidate our findings."881 The halo model decomposition provides a prescription for how the ealaxy population in a halo depends. on halo mass., The halo model decomposition provides a prescription for how the galaxy population in a halo depends on halo mass.882 In practice. halo mass is not an observable. so comparison of this prediction with the objects in à eroup catalog is not straightforward.," In practice, halo mass is not an observable, so comparison of this prediction with the objects in a group catalog is not straightforward."883 Llowever. the halo model decomposition can be re-written so that observable cquantities are predicted: these include the number density of groups containing IN galaxies more luminous than some threshold Luminosity. as well as the average Iuminosities of the central ancl satellite galaxies as a function. of NV.," However, the halo model decomposition can be re-written so that observable quantities are predicted: these include the number density of groups containing $N$ galaxies more luminous than some threshold luminosity, as well as the average luminosities of the central and satellite galaxies as a function of $N$."884 Specifically. and where dn(AID)/dÀAL is the halo mass function. (we use the parametrization given by Sheth Tormen 1999). and the distribution pCN|AZ) has mean with Noy drawn from a Poisson distribution (Zehavi et al.," Specifically, and where $dn(M)/dM$ is the halo mass function (we use the parametrization given by Sheth Tormen 1999), and the distribution $p(N|M)$ has mean with $N_{\rm sat}$ drawn from a Poisson distribution (Zehavi et al."885 2005)., 2005).886" ere AZ,CL)zz23Αμ). where μμ denotes the minimum mass required to host a galaxy of luminosity L or greater. and àz1."," Here $M_1(L)\approx 23\,M_{\rm min}(L)$, where $M_{\rm min}$ denotes the minimum mass required to host a galaxy of luminosity $L$ or greater, and $\alpha\approx 1$."887 Phe minimum mass scales with i;-band £ (our r-band is actually the SDSS r filter shifted to z=0.1. sometimes denoted. ULL 77r) as (Skibba et al.," The minimum mass scales with $r$ -band $L$ (our $r$ -band is actually the SDSS $r$ filter shifted to $z=0.1$, sometimes denoted $^{0.1}r$ ) as so (Skibba et al."888" 2006). assuming Al.,=4.76 (Blanton et al."," 2006), assuming $M_{\odot r}=4.76$ (Blanton et al."889 2003)., 2003).890 Note that the luminosity of the central object is predicted to increase linearly. with halo mass when AL107 TAL. but the increase is only logarithmic at larger Ad (also see Tinker et al.," Note that the luminosity of the central object is predicted to increase linearly with halo mass when $M\ll 10^{12}\,h^{-1}M_\odot$ , but the increase is only logarithmic at larger $M$ (also see Tinker et al."891 2005)., 2005).892 This is qualitatively consistent with the findings of Lin Mohr (2004). Yang et al. (," This is qualitatively consistent with the findings of Lin Mohr (2004), Yang et al. ("8932005b) and Cooray (2006).,2005b) and Cooray (2006).894 The mean satellite luminosity is given hy Figure 2 of Skibba et al. (, The mean satellite luminosity is given by Figure 2 of Skibba et al. (8952006) shows that this is a much weaker function of A than is Leon.,2006) shows that this is a much weaker function of $M$ than is $L_{\rm cen}$.896 To see why. notice that if a(L) were independent of L. then the mean satellite Iuminosity would. be independent of Al.," To see why, notice that if $\alpha(L)$ were independent of $L$, then the mean satellite luminosity would be independent of $M$."897 This suggests that the Z-dependenee of à reflects the mass dependence of satellite luminosities: the halo model prediction. tha satellite luminosities depend. only weakly on halo mass is a consequence of the fact that a is only weakly dependen on L., This suggests that the $L$ -dependence of $\alpha$ reflects the mass dependence of satellite luminosities: the halo model prediction that satellite luminosities depend only weakly on halo mass is a consequence of the fact that $\alpha$ is only weakly dependent on $L$ .898" ligure1 compares equation (3)) with the mean satellite luminosity in the M,19.9 eroup catalog of Berlind e al. (", Figure\ref{berlindLsat} compares equation \ref{LsatN}) ) with the mean satellite luminosity in the $M_r\le -19.9$ group catalog of Berlind et al. (8992006).,2006).900 This catalog is drawn from the SDSS Fourth Data Release (DR4. Adelman-MeCarthy ct al.," This catalog is drawn from the SDSS Fourth Data Release (DR4, Adelman-McCarthy et al."901 2006): i, 2006); it902"find clear trends in the detailed radio morphologies with the properties of the stellar populations. it is notable that all but one (36305) of the 7 CSS/GPS sources in our sample have nuclear spectra that are consistent with relatively voung ages for their YSP (js,0.1 Gyr).","find clear trends in the detailed radio morphologies with the properties of the stellar populations, it is notable that all but one (3C305) of the 7 CSS/GPS sources in our sample have nuclear spectra that are consistent with relatively young ages for their YSP $t_{ysp} < 0.1$ Gyr)."903 At optical wavelengths most of the objects in our sample of starburst radio galaxies show morphological peculiaritics compared with quiescent elliptical galaxies: 17 (S0%)) show tidal tails. fans. or highly. asvnimetric/clumpy outer envelopes at. relatively high surface. brightness. levels: 14 (67'4)) show dust. features: 5 (23:43) have double. nuclei or close companions within 15 kpe: and 20 (95%)) show one or more of these optical peculiarities.," At optical wavelengths most of the objects in our sample of starburst radio galaxies show morphological peculiarities compared with quiescent elliptical galaxies: 17 ) show tidal tails, fans, or highly asymmetric/clumpy outer envelopes at relatively high surface brightness levels; 14 ) show dust features; 5 ) have double nuclei or close companions within 15 kpc; and 20 ) show one or more of these optical peculiarities."904 This rate of incidence is much higher than in the general. population of massive elliptical galaxies observed: with similar surface brightness sensitivity (c.g.Malin&Carter1983).., This rate of incidence is much higher than in the general population of massive elliptical galaxies observed with similar surface brightness sensitivity \citep[e.g.][]{malin83b}.905 However. at this relatively erude level of morphological classification. a similar rate of morphological disturbance has recently been found in the general population of powerful 2J. racio ealaxies at intermediate recshilts (including non-starburst objects: Ranios Almeida et al.," However, at this relatively crude level of morphological classification, a similar rate of morphological disturbance has recently been found in the general population of powerful 2Jy radio galaxies at intermediate redshifts (including non-starburst objects: Ramos Almeida et al."906 2010)., 2010).907 The ages of the YSP detected in radio galaxies can provide Κων information about the order-of-events and the triggering of the AGNjet activity., The ages of the YSP detected in radio galaxies can provide key information about the order-of-events and the triggering of the AGN/jet activity.908 Therefore it is interesting to examine the distribution of luminositv-weighted YSP ages determined. from the two component fits to the optical spectra of the full sample of starburst radio. galaxies described. in section 2., Therefore it is interesting to examine the distribution of luminosity-weighted YSP ages determined from the two component fits to the optical spectra of the full sample of starburst radio galaxies described in section 2.909 The top panel of Figure 1. shows the cistribution of luminositv-welghted ages for the nuclear of the starburst radio galaxies., The top panel of Figure 1 shows the distribution of luminosity-weighted ages for the nuclear of the starburst radio galaxies.910 For comparison we also show the YSP age distribution for a complete sample of ULIItCGs with redshifts 2<0.13.— representing the extreme starburst population in the local Universe which have been modelled: using identical techniques by RodriguezZaurinctal.(2009)., For comparison we also show the YSP age distribution for a complete sample of ULIRGs with redshifts $z < 0.13$ – representing the extreme starburst population in the local Universe -- which have been modelled using identical techniques by \citet{zaurin09}.911. Note that. in some apertures of some starburst radio galaxies it proved. possible to mocel the optical spectra with YSP covering a wide range of ages.," Note that, in some apertures of some starburst radio galaxies it proved possible to model the optical spectra with YSP covering a wide range of ages."912 In such cases we have used the mean age over the range of models that provided. good fits., In such cases we have used the mean age over the range of models that provided good fits.913 Since the upper limiting ages in the latter group were often large (C16 vr). this will tend to skew the age distribution to larger ages.," Since the upper limiting ages in the latter group were often large $>$ 1Gyr), this will tend to skew the age distribution to larger ages."914 Several features are apparent [rom Table 2 and Figure, Several features are apparent from Table 2 and Figure 1.915Toexplain theX—polarizat,asymmetry parameters as916Toexplain theX—polarizati,asymmetry parameters as917Toexplain theX—polarizatio,asymmetry parameters as918Toexplain theX—polarization,asymmetry parameters as919Toexplain theX—polarization.,asymmetry parameters as920be dense. compact aud massive enough to be au eccentric disk progenitor. however they are probably too diffuse to account for the laree disk mass in M31 within a few parsecs of its black hole.,"be dense, compact and massive enough to be an eccentric disk progenitor, however they are probably too diffuse to account for the large disk mass in M31 within a few parsecs of its black hole."921 Dense bulges such as found i AL31 itself. aud iu lower huninosity ellipticals galaxies such as M32. are dense aud conrpact enough that they could be similar to progenitors for ΑΟκ and NGC 1186D's ecceutzic disks.," Dense bulges such as found in M31 itself, and in lower luminosity ellipticals galaxies such as M32, are dense and compact enough that they could be similar to progenitors for M31's and NGC 4486B's eccentric disks."922 Nuclear star clusters. such as found in M33. may also be deuse aud conrpact cnough to be progenitors.," Nuclear star clusters, such as found in M33, may also be dense and compact enough to be progenitors."923 Though the mass of AI3B3¢s cluster (a few uulliou A.) is too small to he a progenitor for MDs eccentric disk. the nuclear stellar clusters observed by (Bokerotal.2002) iu late-tvpe ealaxies have half light radii of order Spec. rauge in their estimated nmiasses from LO°105A... aud so could be xoesenitors for eccentric disks following disruption by a nassive black hole.," Though the mass of M33's cluster (a few million $M_\odot$ ) is too small to be a progenitor for M31's eccentric disk, the nuclear stellar clusters observed by \citep{boker2002}924 in late-type galaxies have half light radii of order 5pc, range in their estimated masses from $10^6-10^8 M_\odot$, and so could be progenitors for eccentric disks following disruption by a massive black hole."925 Because of the large mass of bulges and nuclear star clusters at simall radii. it would be easier ) account for the lieh masses of the two known eccentric aeisks by cisvupting them. thin possible by disrupting a elobular cluster.," Because of the large mass of bulges and nuclear star clusters at small radii, it would be easier to account for the high masses of the two known eccentric disks by disrupting them, than possible by disrupting a globular cluster."926 While the massive black hole in ΑΣ welt prevent a progenitor simular to M2 from forming i eccentric disk. unclear clusters such as found iu M33 can lack massive black holes iud so might provide better xoesenitor candidates.," While the massive black hole in M32 might prevent a progenitor similar to M32 from forming an eccentric disk, nuclear clusters such as found in M33 can lack massive black holes and so might provide better progenitor candidates."927 To date the high augular resolution of TST has resolved extremely high stellar densities or order 109A7.pe7 in only the nearest ealaxv bulges., To date the high angular resolution of HST has resolved extremely high stellar densities or order $10^6 M_\odot{\rm pc}^{-3}$ in only the nearest galaxy bulges.928 Until higher augular resolution observatious are available. we wil uot know if such high deusitv galaxy cores are COMMON.," Until higher angular resolution observations are available, we will not know if such high density galaxy cores are common."929 The two galaxies with double nuclei. M31 and NCC 115610. exhibit only moderate color variatious in their nuclei (Laueretal.1996.1998).. a situation that could be a natural consequence of a scenario that involves the mereing of galaxy bulges (proposed here). aud is more difficult to explain with a scenario that forms a vounecr disk iu situ (an iueredieut of the formation scenarios discussed by Baconetal.2001:Toma2002:TagaJacobs&Selawood1999}).," The two galaxies with double nuclei, M31 and NGC 4486B, exhibit only moderate color variations in their nuclei \citep{lauer96,lauer98}, a situation that could be a natural consequence of a scenario that involves the merging of galaxy bulges (proposed here), and is more difficult to explain with a scenario that forms a younger disk in situ (an ingredient of the formation scenarios discussed by \citealt{bacon,touma,taga,jacobs}) )."930 The scenario proposed here is based on a simple tidal disuption aremuent aud can be most quickly tested with N-body simmilations such as have heen carried out bv Merritt&Cruz(2002):Bekla(20002):ITollev-Bockelinanu&Richstone(2000).," The scenario proposed here is based on a simple tidal disruption argument and can be most quickly tested with N-body simulations such as have been carried out by \citet{merritt,bekki,holley}."931.. The simulations of Doekki(20002) established that the disruption of a cluster could. result in the formation of au eccentric disk. aud Merritt&Cruz(2002):EHTollevy-Dockeluiuun&Richstone(2000) have carried out simulations based on realistic galaxy profiles aud with massive black holes.," The simulations of \citet{bekki} established that the disruption of a cluster could result in the formation of an eccentric disk, and \citet{merritt,holley}932 have carried out simulations based on realistic galaxy profiles and with massive black holes."933 Hollev-Bockeliuaun&Rich-stone(2000) established that a spinning nuclear stellar disk can be a remnant., \citet{holley} established that a spinning nuclear stellar disk can be a remnant.934 It remains to be seen whether the merecr of two galaxy cores ean result in the creation of au eccentric stellar disk., It remains to be seen whether the merger of two galaxy cores can result in the creation of an eccentric stellar disk.935 We suspect that the mereer of a primary galaxy containing a very massive black hole with a secondary with accore-type or shallow central surface brielitucss profile. and significantly lower mass black hole. would be most likely to form: an ecceutric disk with N-body simulations.," We suspect that the merger of a primary galaxy containing a very massive black hole with a secondary with a `core-type' or shallow central surface brightness profile, and significantly lower mass black hole, would be most likely to form an eccentric disk with N-body simulations."936 For the core-tvpe galaxies. the break radius and density at this radius provide au equivaleut for the Nine or core radius and ceutral deusity used in Figure 1 and so cau be used to estimate the Bkelibood that the core can disrupt to form an eccentric disk.," For the core-type galaxies, the break radius and density at this radius provide an equivalent for the King or core radius and central density used in Figure 1 and so can be used to estimate the likelihood that the core can disrupt to form an eccentric disk."937 Tf the mereecr of galaxy bulges cau result in tle formation of an eccentric disk. then their formation would be a natural cousequence of licrarchical galaxy. formation. aud can also be used to probe the properties of the parcuts of ealaxies which coutain tho.," If the merger of galaxy bulges can result in the formation of an eccentric disk, then their formation would be a natural consequence of hierarchical galaxy formation, and can also be used to probe the properties of the parents of galaxies which contain them."938 This work was initiated by discussions with Joel Creenu and Bob Cortermuth in the class Astronomy 552 at the University of Rochester during the fall of 2002., This work was initiated by discussions with Joel Green and Rob Gutermuth in the class Astronomy 552 at the University of Rochester during the fall of 2002.939 We thank Chien Peng. Ari Laor and Eric Eisellem for helpful discussions and correspondence.," We thank Chien Peng, Ari Laor and Eric Emsellem for helpful discussions and correspondence."940generally to surveys of isotropic distributions of tracers with uncertain radial positions.,generally to surveys of isotropic distributions of tracers with uncertain radial positions.941" In summary, the presented method is a flexible and numerically efficient addition to the analysis toolbox for large scale galaxy surveys."," In summary, the presented method is a flexible and numerically efficient addition to the analysis toolbox for large scale galaxy surveys."942 It improves accuracy of galaxy redshifts and three dimensional density fields from photometric galaxy redshift surveys and therefore has the potential to add substantial value to their scientific output., It improves accuracy of galaxy redshifts and three dimensional density fields from photometric galaxy redshift surveys and therefore has the potential to add substantial value to their scientific output.943" We thank Francisco S. Kitaura, Torsten A. Enflin and Simon D. White for useful discussions and encouraging us to pursue the project described in this work."," We thank Francisco S. Kitaura, Torsten A. lin and Simon D. White for useful discussions and encouraging us to pursue the project described in this work."944" Further, we thank Cristiano Porciani for providing us with the simulated density field and Nina Roth for providing us with required reading routines and information on how to handle the simulation data."," Further, we thank Cristiano Porciani for providing us with the simulated density field and Nina Roth for providing us with required reading routines and information on how to handle the simulation data."945 Particular thanks go to Rainer Moll and Bjórrn M. Schiffer for useful discussions and, Particular thanks go to Rainer Moll and Björrn M. Schäffer for useful discussions and946shorter orbital periods. reducing the mass below the hydrogen burning limit at the minimum period. after which evolution proceeds slowly back to longer periods (Kolb1993:Kolb&Baratte 1999).,"shorter orbital periods, reducing the mass below the hydrogen burning limit at the minimum period, after which evolution proceeds slowly back to longer periods \citep{Kolb93aa,KolbBaraffe99mn}."947" Whilst a number of CV secondary stars with sub-stellar masses have been identified hear the minimum period (Littlefairetal.2006.2008).. there is yet no unimpeachable detection of the predicted ""post-bounce"" population."," Whilst a number of CV secondary stars with sub-stellar masses have been identified near the minimum period \citep{Littlefair+06sci,Littlefair+08mn}, there is yet no unimpeachable detection of the predicted “post-bounce” population."948 The expected characteristics of post-bounce CVs are a very low accretion rate. a low WD temperature. a very low secondary star mass. and a brown-dwarf secondary spectral type.," The expected characteristics of post-bounce CVs are a very low accretion rate, a low WD temperature, a very low secondary star mass, and a brown-dwarf secondary spectral type."949 The ability to differentiate between pre- and post-bounce CVs increases with longer orbital periods. because of the greater difference in secondary spectral type and mass transfer rate between the two types of systems.," The ability to differentiate between pre- and post-bounce CVs increases with longer orbital periods, because of the greater difference in secondary spectral type and mass transfer rate between the two types of systems."950 Among the SDSS CVs that have white-dwarf dominated optical spectra. JJ0039 exhibits currently the best credentials to be a post-bounce system. as it has an extremely late-type companion star (2L2) and an orbital period clearly beyond the mmin period spike.," Among the SDSS CVs that have white-dwarf dominated optical spectra, J0039 exhibits currently the best credentials to be a post-bounce system, as it has an extremely late-type companion star $\ga$ L2) and an orbital period clearly beyond the min period spike."951 The post-bounce nature of our object can be tested by near-infrared photometry. which would provide a stronger constraint on the spectral type of the companion star.," The post-bounce nature of our object can be tested by near-infrared photometry, which would provide a stronger constraint on the spectral type of the companion star."952 Doppler maps of the Ha. Il aand II eemission lines were computed using the maximum entropy method (Marsh&Horne1988)..," Doppler maps of the $\alpha$, I and I emission lines were computed using the maximum entropy method \citep{MarshHorne88mn}."953 We have overlaid a basic interpretation of JJ0039 onto the Doppler maps reftig:0039:map))., We have overlaid a basic interpretation of J0039 onto the Doppler maps \\ref{fig:0039:map}) ).954 The centre of mass of the system is shown with a cross. and the expected position of the surface of the secondary star m velocity space is shown with an unbroken line.," The centre of mass of the system is shown with a cross, and the expected position of the surface of the secondary star in velocity space is shown with an unbroken line."955 The dots and dotted lines indicate the velocity of the accretion stream and the Keplerian velocity of the disc along the path of the stream., The dots and dotted lines indicate the velocity of the accretion stream and the Keplerian velocity of the disc along the path of the stream.956 The emission characteristics apparent in the trailed spectra of JJ0039 translate into unusual features in the Doppler maps., The emission characteristics apparent in the trailed spectra of J0039 translate into unusual features in the Doppler maps.957 The first of these is the intense inner emission feature. which is clearly visible at Ha but totally absent in the II lines.," The first of these is the intense inner emission feature, which is clearly visible at $\alpha$ but totally absent in the I lines."958 The maps have been rotated to bring this feature onto the line passing through the centres of mass of the two stars. the standard configuration for Doppler maps.," The maps have been rotated to bring this feature onto the line passing through the centres of mass of the two stars, the standard configuration for Doppler maps."959 In the next section we consider and reject the possibility that the inner emission feature arises from the surface of either the WD or secondary star., In the next section we consider and reject the possibility that the inner emission feature arises from the surface of either the WD or secondary star.960 The Doppler maps bring out another extraordinary feature of 0039 which is less obvious in the data than the central S-wave., The Doppler maps bring out another extraordinary feature of J0039 which is less obvious in the data than the central S-wave.961 The outer disc in Ha appears to be extremely non-circular. given that circular motion leads to symmetry around the centre of mass of the WD. located just below the centre of mass of the system.," The outer disc in $\alpha$ appears to be extremely non-circular, given that circular motion leads to symmetry around the centre of mass of the WD, located just below the centre of mass of the system."962 The non-circularity is extreme: the bright region in the lower-right quadrant has a velocity a factor of two lower than that of the upper-left quadrant., The non-circularity is extreme: the bright region in the lower-right quadrant has a velocity a factor of two lower than that of the upper-left quadrant.963 A Keplerian velocity profile (V.ος/7'7) then implies that the outer disc varies in radius by a factor of four!, A Keplerian velocity profile $V \propto r^{-1/2}$ ) then implies that the outer disc varies in radius by a factor of four!964 The behaviour of the II lines ts very different and more symmetric. which suggests that the lower-right quadrant of Ha is in some way unusual.," The behaviour of the I lines is very different and more symmetric, which suggests that the lower-right quadrant of $\alpha$ is in some way unusual."965 We can only interpret this feature in the Doppler maps as evidence of non-Keplerian flow., We can only interpret this feature in the Doppler maps as evidence of non-Keplerian flow.966" The inner emission feature is unusual in normal CVs and reminiscent of the “central spike"" seen in some CCVn (ultracompact binary) stars. where it is ascribed to the WD CCom: Morales-Ruedaetal.2003))."," The inner emission feature is unusual in normal CVs and reminiscent of the “central spike” seen in some CVn (ultracompact binary) stars, where it is ascribed to the WD Com; \citealt{Morales+03aa}) )."967 To investigate this we developed a six-Gaussian model to fit the observed Ha: line profiles., To investigate this we developed a six-Gaussian model to fit the observed $\alpha$ line profiles.968 The two wide emission peaks from the accretion disc are each modelled with one wide and one narrow Gaussian. the central spike with a fifth Gaussian. and the bright spot with a sixth.," The two wide emission peaks from the accretion disc are each modelled with one wide and one narrow Gaussian, the central spike with a fifth Gaussian, and the bright spot with a sixth."969 Each Gaussian was allowed to vary sinusoidally in both radial velocity and brightness on the orbital period., Each Gaussian was allowed to vary sinusoidally in both radial velocity and brightness on the orbital period.970 The fit is plotted in reffig:0039:fitplot.., The fit is plotted in \\ref{fig:0039:fitplot}.971" We find a velocity amplitude of A,=202+3 ffor the central spike. which immediately rules out the CCVn explanation’ as it is too high to be associated with the WD."," We find a velocity amplitude of $K_{\rm spike} = 202 \pm 3$ for the central spike, which immediately rules out the CVn explanation' as it is too high to be associated with the WD."972 On the other hand it is much too low to be from the bright spot region on the accretion disc. which the Doppler maps show to have a velocity of aboutkms7!.," On the other hand it is much too low to be from the bright spot region on the accretion disc, which the Doppler maps show to have a velocity of about."973. The only stable feature of the system left is the secondary star. so we now consider this possibility.," The only stable feature of the system left is the secondary star, so we now consider this possibility."974 It is very unlikely that the central spike originates from the whole surface of the secondary. because Άρης is very low given that the velocity amplitude of the accretion dise emission peaks is Vap=631 !.," It is very unlikely that the central spike originates from the whole surface of the secondary, because $K_{\rm spike}$ is very low given that the velocity amplitude of the accretion disc emission peaks is $V_{\rm AD} = 631$ ."975. Consider the following relations: under the Rapassumption of Keplerian velocities., Consider the following relations: under the assumption of Keplerian velocities.976 The orbital angular frequency. Q. is given by where a and i are the orbital separation and inclination. Mwp and M» are the masses of the component stars. K> is the velocity amplitude of the centre of mass of the secondary star. and Rap is the radius of the outer accretion disc.," The orbital angular frequency, $\Omega$, is given by where $a$ and $i$ are the orbital separation and inclination, $M_{\rm WD}$ and $M_2$ are the masses of the component stars, $K_2$ is the velocity amplitude of the centre of mass of the secondary star, and $R_{\rm AD}$ is the radius of the outer accretion disc."977 From this we find which for the values quoted above gives where g=Ms/Mwp isthe mass ratio and a is. the semimajor axis., From this we find which for the values quoted above gives where $q = {M_2}/{M_{\rm WD}}$ isthe mass ratio and $a$ is the semimajor axis.978 This value can be compared with the minimum, This value can be compared with the minimum979core dynamo hypothesis suggested by |Charbonneau&MacGregor)(2001) because the core must create magnetic fields that are much stronger than equipartition values in order to reach to the surface.,core dynamo hypothesis suggested by \citet{char2001} because the core must create magnetic fields that are much stronger than equipartition values in order to reach to the surface.980 (1999) argues that a principle ingredient of dynamo operation in a star is rapid rotation., \citet{spruit1999} argues that a principle ingredient of dynamo operation in a star is rapid rotation.981 This is certainly available in massive stars., This is certainly available in massive stars.982" While the driving mechanism of magnetic field generation is based on hydrodynamical instabilities in solar type stars, similar instabilities in the radiative stars may be produced by the magnetic fields themselves."," While the driving mechanism of magnetic field generation is based on hydrodynamical instabilities in solar type stars, similar instabilities in the radiative stars may be produced by the magnetic fields themselves."983 Examples are the Parker and Tayler instabilities ∙∙ ," Examples are the Parker and Tayler instabilities \citep{parker1979, tayler1973}."984formulated a dynamo mechanism for a differentially rotating star in which Tayler instability replaces the role of convection in closing the field amplification loop.," \citet{spruit2002}985 formulated a dynamo mechanism for a differentially rotating star in which Tayler instability replaces the role of convection in closing the field amplification loop."986 The azimuthal component of the magnetic field grows until it reaches a critical strength by winding up an initially very small radial component in a non-convective zone., The azimuthal component of the magnetic field grows until it reaches a critical strength by winding up an initially very small radial component in a non-convective zone.987" At that point the Tayler instability operates on a very short time-scale, of the order of Alfvénn crossing time, to regenerate the radial field."," At that point the Tayler instability operates on a very short time-scale, of the order of Alfvénn crossing time, to regenerate the radial field."988 The result is a predominantly toroidal field and a closed dynamo loop., The result is a predominantly toroidal field and a closed dynamo loop.989 Recent numerical simulations by and showed that a stable configuration can be reached within a non-convective star on an Alfvénn time-scale from an arbitrary initial magnetic field., Recent numerical simulations by \citet{brait2004} and \citet{brait2006} showed that a stable configuration can be reached within a non-convective star on an Alfvénn time-scale from an arbitrary initial magnetic field.990 The Spruit-Tayler mechanism is not the only one that operates in non-convective material., The Spruit-Tayler mechanism is not the only one that operates in non-convective material.991 |Balbus&Hawley](1994) have proposed a magneto-rotational instability which works well for accretion discs without convection., \citet{balbus1994} have proposed a magneto-rotational instability which works well for accretion discs without convection.992 reffiggainer shows the internal structure of the gainer during the mass transfer for our system with initial masses of 5 and 3Mo.," \\ref{figgainer} shows the internal structure of the gainer during the mass transfer for our system with initial masses of $5$ and $3\,\rm{M}_{\odot}$."993 The gainer has a substantial convective core and an almost constant mass radiative envelope throughout the mass accretion., The gainer has a substantial convective core and an almost constant mass radiative envelope throughout the mass accretion.994" As pointed out, differential rotation in single stars provides a finite amount of energy for generating magnetic fields so we might expect that the dynamo to cease once the rotation profile has been smoothed out."," As \citet{spruit2002} pointed out, differential rotation in single stars provides a finite amount of energy for generating magnetic fields so we might expect that the dynamo to cease once the rotation profile has been smoothed out."995" In the case of our semi-detached binary stars with discs, the energy in differential rotation can be continuously supplied from the disc material which has high specific angular momentum relative to the star as we discussed in section BJ]."," In the case of our semi-detached binary stars with discs, the energy in differential rotation can be continuously supplied from the disc material which has high specific angular momentum relative to the star as we discussed in section \ref{models}."996" Hence, if a Spruit-Tayler type dynamo operates in this case, magnetic fields are regenerated as long as mass transfer continues."," Hence, if a Spruit-Tayler type dynamo operates in this case, magnetic fields are regenerated as long as mass transfer continues."997 According to our assumption that the wind is accelerated to the stellar escape velocity (equation [12)) and leaves the system at the, According to our assumption that the wind is accelerated to the stellar escape velocity (equation \ref{meq5}) ) and leaves the system at the998In the fireball model. Gamma-Ray Burst (CRB) afterglows are thought to be the result. of svnchrotron. radiation eencrated by electrons during the interaction of a strongly collimated relativistic jet [rom a compact source with its environment (for recent reviews. see Piran2005:Alészaros 2006)).,"In the fireball model, Gamma-Ray Burst (GRB) afterglows are thought to be the result of synchrotron radiation generated by electrons during the interaction of a strongly collimated relativistic jet from a compact source with its environment (for recent reviews, see \citealt{Piran2005, Meszaros2006}) )."999 Initially the resulting spectra and light curves have been modelled: using only the shock front. of a spherical explosion ancl a simple power law approximation for the svnchrotron radiation (e.g. Wijers.Rees&Aészaros1997:Alészáros&Rees1997:Sarietal.1998:Rhoacls 1999)).," Initially the resulting spectra and light curves have been modelled using only the shock front of a spherical explosion and a simple power law approximation for the synchrotron radiation (e.g. \citealt{Wijers1997, Meszaros1997, Sari1998, Rhoads1999}) )."1000 One or more spectral and temporal breaks were used to connect regimes with dillerent. power law slopes., One or more spectral and temporal breaks were used to connect regimes with different power law slopes.1001 For the dynamics the self similar approximation of a relativistic explosion was used (Blandford&Melxee1976)., For the dynamics the self similar approximation of a relativistic explosion was used \citep{Blandford1976}.1002.. These models have been refined. continuously., These models have been refined continuously.1003 More. details of the shock structure were included (e.g. Guanotetal.1999:Gruzinov&Waxman 1999)). more accurate formulae for the svnchrotron radiation were used (e.g. Wijers&Calama 1999)) and. efforts have been made to implement collimation using various analytical approximations to the jet structure and lateral spreacing behaviour (see Cranot2005.r for an overview).," More details of the shock structure were included (e.g. \citealt{Granot1999, Gruzinov1999}) ), more accurate formulae for the synchrotron radiation were used (e.g. \citealt{Wijers1999}) ) and efforts have been made to implement collimation using various analytical approximations to the jet structure and lateral spreading behaviour (see \citealt{Granot2005} for an overview)."1004 On top of that. there have been studies focussing on arrival time effects (c.g. Hluangetal. 2007)) and some numerical simulations (e.g. Salmonson2003:Ciranotetal.2001:Nakar& 2007)).," On top of that, there have been studies focussing on arrival time effects (e.g. \citealt{Huang2007}) ) and some numerical simulations (e.g. \citealt{Salmonson2003, Granot2001, Nakar2007}) )."1005 The aim of this paper is twofold., The aim of this paper is twofold.1006" ""The first aim is to introduce a new method to cerive light curves and spectra by post-processing relativistic hvdrodyvnamic (RILD) jet simulations of arbitrary dimension. properly taking into account all beaming ancl arrival time cllects. as well as the precise shape of the svnchrotron spectrum. and electron cooling (in this paper we will ignore self-absorption. although it can in principle be included in our method)."," The first aim is to introduce a new method to derive light curves and spectra by post-processing relativistic hydrodynamic (RHD) jet simulations of arbitrary dimension, properly taking into account all beaming and arrival time effects, as well as the precise shape of the synchrotron spectrum and electron cooling (in this paper we will ignore self-absorption, although it can in principle be included in our method)."1007 This is done in sections 2. ancl 3.., This is done in sections \ref{peak_section} and \ref{cooling_section}.1008 The second aim is to present a set of scaling coelTicients [or the slow-cooling case for a density profile p—po-(RIBI) [or general values of &., The second aim is to present a set of scaling coefficients for the slow-cooling case for a density profile $\rho = \rho_0 \cdot (R/R_0)^{-k}$ for general values of $k$.1009 Fits to alterglow data using & as a [ree fitting parameter have vielded: values markedly cillerent from both &=0 and &=2 (Starlingetal. 2007).. although with error bars not excluding either option.," Fits to afterglow data using $k$ as a free fitting parameter have yielded values markedly different from both $k=0$ and $k=2$ \citep{Starling2007}, although with error bars not excluding either option."1010 The scaling coellicients have been obtained. by application of our post-process code not to ai full. hydrocdsynamic simulation but to an emulation of this., The scaling coefficients have been obtained by application of our post-process code not to a full hydrodynamic simulation but to an emulation of this.1011 From the spherical Dlandford Melxee (BM) analytical solution for the blast wave for the impulsive energy injection scenario. snapshots containing the state of the [uid at given emission times were constructed. ancl stored to. provide the input for the post-xYocess code.," From the spherical Blandford McKee (BM) analytical solution for the blast wave for the impulsive energy injection scenario, snapshots containing the state of the fluid at given emission times were constructed and stored to provide the input for the post-process code."1012 The use of the BAL solution provides us with an opportunity to check the results and. the consistency. of he code in an environment where we already have a ot of analytical control and understanding., The use of the BM solution provides us with an opportunity to check the results and the consistency of the code in an environment where we already have a lot of analytical control and understanding.1013 Phe scaling cocllicients are presented. in section 4.., The scaling coefficients are presented in section \ref{coefficients_section}.1014 Thes. can be used w observers to obtain the physical parameters for the blast wave (c.g. explosion cnerey and cireumburst censity) from. he values for the peak flux ancl break frequencies that have xen Obtained from fits to the data., They can be used by observers to obtain the physical parameters for the blast wave (e.g. explosion energy and circumburst density) from the values for the peak flux and break frequencies that have been obtained from fits to the data.1015 Reacers interested only, Readers interested only1016photon index of the incident. power law spectrum with an exponential cutoll at fo: R= O25. where 9 is the solid angle subtended by the optically thick material: sp—cost. where @ is the angle between the line of sight and the normal vector of the optically thick laver: zd. the iron abundance of the optically thick material.,"photon index of the incident power law spectrum with an exponential cutoff at $E_c$ ; $R=\Omega/2\pi$ , where $\Omega$ is the solid angle subtended by the optically thick material; $\mu=cos\theta$, where $\theta$ is the angle between the line of sight and the normal vector of the optically thick layer; $A_{\rm Fe}$, the iron abundance of the optically thick material."1017 Element abundances besides iron are assumed to be the solar values., Element abundances besides iron are assumed to be the solar values.1018 In the following [itting. ££. is fixed at 200 Κον (practically a single power law in the observed range).," In the following fitting, $E_c$ is fixed at 200 keV (practically a single power law in the observed range)."1019 qi is fixed at 0.45 so that the model spectrum is closest to that averaged over all viewing angles as described in. \lagedziarz Zelziarski (1995)., $\mu$ is fixed at 0.45 so that the model spectrum is closest to that averaged over all viewing angles as described in Magdziarz Zdziarski (1995).1020 Combining with the thermal component and the line emission. the overall fitting model is given by where [ree parameters are shown in. parentheses.," Combining with the thermal component and the line emission, the overall fitting model is given by where free parameters are shown in parentheses."1021 The normalization factors of the rellection component. Iac. [or the and.ANTE spectra are left. [ree from each other for possible time variation of the AGN luminosity.," The normalization factors of the reflection component, $K_{\rm AGN}$, for the and spectra are left free from each other for possible time variation of the AGN luminosity."1022 The flux ratio between the Fe Ix-line. and the AGN continuum {νενοκ ds assumed to be constant., The flux ratio between the Fe K-line and the AGN continuum $K_l/K_{\rm AGN}$ is assumed to be constant.1023 ALL other parameters are also assumed to be the same between the two observations., All other parameters are also assumed to be the same between the two observations.1024 Another power-law with a photon index of 1.56 that represents the contamination sources is acdcdec to the model for the PCA and LIENTE spectrum., Another power-law with a photon index of 1.56 that represents the contamination sources is added to the model for the PCA and HEXTE spectrum.1025 As shown in Figure 7 and ‘Table 4. this mode can account for the 0.5200 keV wide-band spectrum satisfactorily.," As shown in Figure \ref{fig:reffit} and Table 4, this model can account for the 0.5–200 keV wide-band spectrum satisfactorily."1026 The lux of the contamination sources in theXE spectrum determined from the fit is in goo agreement with that obtained with the CIS within ~I0., The flux of the contamination sources in the spectrum determined from the fit is in good agreement with that obtained with the GIS within $\sim10\%$.1027 The two normalization. factors of the AGN componen obtained from the andRAND spectra respectively happened to be very close (AESTEfyMC29 991.26). as were the Fe Ix-line. intensities nearly equal in these two observations.," The two normalization factors of the AGN component obtained from the and spectra respectively happened to be very close $K^{\rm RXTE}/K^{\rm ASCA}$ =0.92–1.26), as were the Fe K-line intensities nearly equal in these two observations."1028 “Phe equivalent width: of the iron line with respect to the rellection continuum. is OS keV. which is à typical value for the Duorescence line associated. with the Compton-rellection.," The equivalent width of the iron line with respect to the reflection continuum is 0.8 keV, which is a typical value for the fluorescence line associated with the Compton-reflection."1029 Llowever. the best-fit photon index E of the incident AGN spectrum is. 1.2640.18. which is unusually small compared to the typical values for AGNs (e.g. Mushotzky. Done. Pounds 1993).," However, the best-fit photon index $\Gamma$ of the incident AGN spectrum is $\pm$ 0.13, which is unusually small compared to the typical values for AGNs (e.g. Mushotzky, Done, Pounds 1993)."1030 In this fit. the viewing angle cos@ was fixed at 0.45.," In this fit, the viewing angle $\mu = cos \theta$ was fixed at 0.45."1031 Even if we allow fi to vary (Table 4). photon index larger than 1.54 is not acceptable.," Even if we allow $\mu$ to vary (Table 4), photon index larger than 1.54 is not acceptable."1032 Phe intrinsic luminosity. of the AGN is estimated to be larger than 4.3..10°13 ergs/s. the value correspondingH to the maximum. solid angle. Le. 42=O25. of 1.0.," The intrinsic luminosity of the AGN is estimated to be larger than $4.3\times10^{43}$ ergs/s, the value corresponding to the maximum solid angle, i.e. $R=\Omega/2\pi$, of 1.0."1033 Although. the above vellection-only model gives a satisfactory fit to theANTE | data. the small photon index derived in 4.2 still remains to be problem.," Although, the above reflection-only model gives a satisfactory fit to the + data, the small photon index derived in 4.2 still remains to be problem."1034 As shown below. this is resolved by adding an absorbed AGN continuum that is transmitted through a thick absorber on the line of sight. (," As shown below, this is resolved by adding an absorbed AGN continuum that is transmitted through a thick absorber on the line of sight. ("1035Here we do not consider the extent of the absorber. hence we assume no scattering of X-rays into the line of sight.),"Here we do not consider the extent of the absorber, hence we assume no scattering of X-rays into the line of sight.)"1036 The transmitted ACGN component is given by where epi is theThomsonscattering cross-section. and ;Ngcy ds the hvdrogen-column density along line of sight.," The transmitted AGN component is given by where $\sigma_{\rm Th}$ is theThomsonscattering cross-section, and $N_{\rm H,AGN}$ is the hydrogen-column density along line of sight."1037 The attenuation by the Thomson scattering becomes, The attenuation by the Thomson scattering becomes1038This research was supported by the Agenzia Spaziale Italiana (ASI) and the Ministero dellIstruzione. Univversita e della Ricerca.,"This research was supported by the Agenzia Spaziale Italiana (ASI) and the Ministero dell'Istruzione, versità e della Ricerca."1039and 4.. the former cisplaving how they change with viewing angle v at fixed i. the latter how thev changee with accretion rate mmn at fixed J.,"and \ref{fig:light-curves-mdot}, the former displaying how they change with viewing angle $\vartheta$ at fixed $\dot m$, the latter how they change with accretion rate $\dot m$ at fixed $\vartheta$."1040 Changingexe inclination does relatively little io alter longe time-scale fluctuations. but can lead to differences on short time-scales.," Changing inclination does relatively little to alter long time-scale fluctuations, but can lead to differences on short time-scales."1041 On the other hand. changingoOe the opacity ean lead to substantial differences in the lighte eurve even while the viewinge angleex remains the same.," On the other hand, changing the opacity can lead to substantial differences in the light curve even while the viewing angle remains the same."1042 Remarkably. however. the exgross shape of the power spectrum is almost invariant to both sorts of changes: the best-fit power-law index is ~—2 [or all but the highest accretion rates and inclinations (Fig. 5)).," Remarkably, however, the gross shape of the power spectrum is almost invariant to both sorts of changes: the best-fit power-law index is $\simeq -2$ for all but the highest accretion rates and inclinations (Fig. \ref{fig:power-law-exponents-pspace}) )."1043 The strongest effects influencing the inclination dependence of variations are relativistic beaming and boosting. which become more important as the orbital velocity becomes larger and more nearly parallel to the outgoing geodesics.," The strongest effects influencing the inclination dependence of variations are relativistic beaming and boosting, which become more important as the orbital velocity becomes larger and more nearly parallel to the outgoing geodesics."1044 They therefore have the greatest. effect on radiation issuing from the smallest radii when viewed at high inclination., They therefore have the greatest effect on radiation issuing from the smallest radii when viewed at high inclination.1045 Because those same inner radii have the highest dynamical frequency. one might (then expect a boost in the hieh-lrequeney portion of the power spectrum αἱ large J.," Because those same inner radii have the highest dynamical frequency, one might then expect a boost in the high-frequency portion of the power spectrum at large $\vartheta$."1046 Ii relative terms. this does occuras we have seen. (he slope of the power spectrum depends only weakly on inclination. except when i» is «quite large (see further discussion later in this subsection).," In relative terms, this does occur—as we have seen, the slope of the power spectrum depends only weakly on inclination, except when $\dot m$ is quite large (see further discussion later in this subsection)."1047 Nonetheless. although the relative variance changes little with inclination. the absolute variance. as well as the absolute luminosity. does increase when (he disk becomes more edge-on. as has also been seen in previous calculations (??)..," Nonetheless, although the relative variance changes little with inclination, the absolute variance, as well as the absolute luminosity, does increase when the disk becomes more edge-on, as has also been seen in previous calculations \citep{AR03,2006ApJ...651.1031S}."1048 Because we explore only relative variability. (he absolute Iuminositvs proportionality lo 1» is irrelevant to our discussion.," Because we explore only relative variability, the absolute luminosity's proportionality to $\dot{m}$ is irrelevant to our discussion."1049 The accretion rate influences the light eurves in our caleulations only bv setting Che opacity scale., The accretion rate influences the light curves in our calculations only by setting the opacity scale.1050 The accretion rate is therefore degenerate with our choice of 7. and we can speak equivalently in (terms of accretion rate or optical depth.," The accretion rate is therefore degenerate with our choice of $\tau_\circ$, and we can speak equivalently in terms of accretion rate or optical depth."1051 When the opacity is dominated by electron scattering. the disk is completely transparent for accretion rates re=0.001 or lower.," When the opacity is dominated by electron scattering, the disk is completely transparent for accretion rates $\dot m = 0.001$ or lower."1052 Increasing rn» moves the photosphere Luther from the disks midplane. and emission from high latitudes becomes more dominant because our disk follows a nearly constant ///r prolile.," Increasing $\dot{m}$ moves the photosphere farther from the disk's midplane, and emission from high latitudes becomes more dominant because our disk follows a nearly constant $H/r$ profile."1053 At (ihe same time. increasing 1 leads to a relative suppression of light [rom outer radii because the disk surface density. aud hence its optical depth. increases rapidly oulwarcl.," At the same time, increasing $\dot m$ leads to a relative suppression of light from outer radii because the disk surface density, and hence its optical depth, increases rapidly outward."1054 For (his reason. the largest accretion rates select out [Inctuations from (he innermost ancl uppermost regions of the (bound) accretion low.," For this reason, the largest accretion rates select out fluctuations from the innermost and uppermost regions of the (bound) accretion flow."1055 This pruning of the coronal volume with increasing 7? is the most likely explanation for the [act that the relative variance of the light curves monotonically increases with accretion rale. [rom 0.04 at i»=0.001 to 0.09 at m=1.," This pruning of the coronal volume with increasing $\dot m$ is the most likely explanation for the fact that the relative variance of the light curves monotonically increases with accretion rate, from $0.04$ at $\dot{m}=0.001$ to $0.09$ at $\dot{m}=1$."1056 As the region above the photosphere shrinks in racial and vertical extent with rv. it contains fewer independently-fhictuating volumes. so that their summed emission has larger fractional fluctuations.," As the region above the photosphere shrinks in radial and vertical extent with $\dot{m}$ , it contains fewer independently-fluctuating volumes, so that their summed emission has larger fractional fluctuations."1057in giants (angular momeutui deposited in the core is retained or all angular iiomentum is in the convective envelope). aud internal augular moinentum trausport on the liorizontal brauch. (solid body rotation or local conservation of augular momeutuim between the glaut branch tip aud the horizontal branch).,"in giants (angular momentum deposited in the core is retained or all angular momentum is in the convective envelope), and internal angular momentum transport on the horizontal branch (solid body rotation or local conservation of angular momentum between the giant branch tip and the horizontal branch)."1058 In section 2. we outline the method we used to construct our stellar moclels.," In section 2, we outline the method we used to construct our stellar models."1059 We present the results in section 3. ancl discuss the implications in section L," We present the results in section 3, and discuss the implications in section 4."1060 A παν of our conclusions is given in section 5., A summary of our conclusions is given in section 5.1061 We used the Yale Rotating Evolution Code (YREC. see Sills.Piusonneault&Terudrup (1999))) o calculate a standard non-rotati[n]ο stellar model from the main sequence up the giant branch to the ieliuiu core flash.," We used the Yale Rotating Evolution Code (YREC, see \cite{SPT99}) ) to calculate a standard non-rotating stellar model from the main sequence up the giant branch to the helium core flash."1062 This model was chosen to have parameters appropriate for stars in. M13: M=0.8 L.. Z=0.0006 ([Fe/H]—-1.5) and Y=0.23.," This model was chosen to have parameters appropriate for stars in M13: M=0.8 $_{\odot}$, Z=0.0006 ([Fe/H]=-1.5) and Y=0.23."1063 The turnolf age of this star is LL7 Gyr., The turnoff age of this star is 14.7 Gyr.1064 The mixing eneth parameter. set by calibrating a solar model. was 1.7.," The mixing length parameter, set by calibrating a solar model, was 1.7."1065 We used OPAL opacities (Iglesias& [or temperatures greater than logT=LO. Alexauder&Ferguson(1991) opacities or lower temperatures. the Sala equation of state. and grey Exldington atmospheres.," We used OPAL opacities \citep{IR96} for temperatures greater than $\log T = 4.0$, \cite{AF94} opacities for lower temperatures, the Saha equation of state, and grey Eddington atmospheres."1066 The choice of he equation of state aud atmospheres was mace necessary by the rauge of evolutiouary stages that we are Investigatiug., The choice of the equation of state and atmospheres was made necessary by the range of evolutionary stages that we are investigating.1067 The more recent. aud more accurate. equatious of state (Rogers.Swenson.&1996:Saumon.Chabrier.&VanHorn1995) aud atmospheres (Allard&Hauschildt1995) uufortunately do uot yet exteud to the temperatures aud deusities required for stellar models near the tip of the giant branch.," The more recent, and more accurate, equations of state \citep{RSI96,SCV95} and atmospheres \citep{AH95} unfortunately do not yet extend to the temperatures and densities required for stellar models near the tip of the giant branch."1068 However. since this work is an initial study of rotational evolutiou iu these advanced phases. the qualitative results presented bere will not be affected by minor chauges in the position of the evolutionary track in the HR diagram.," However, since this work is an initial study of rotational evolution in these advanced phases, the qualitative results presented here will not be affected by minor changes in the position of the evolutionary track in the HR diagram."1069 Helioseisinology cau be used to infer the internal rotation profile of the Sun by observing the rotational splitting of solar p-miodes., Helioseismology can be used to infer the internal rotation profile of the Sun by observing the rotational splitting of solar p-modes.1070 The results imply that the Stu's radiative core is rotating as a solid body down to about #=0.22.. with some disagreement about deeper layers (Chaplinetal.al.1996:Corbardet 1998).," The results imply that the Sun's radiative core is rotating as a solid body down to about $R=0.2 R_{\sun}$, with some disagreement about deeper layers \citep{Chap99,Laz96,Cor98}."1071.. The angular velocity of the solar surface convection zone is dependent on latitude but not on radius (Thompsonetal.1996)., The angular velocity of the solar surface convection zone is dependent on latitude but not on radius \citep{T96}.1072. Old metal-poor stars do not have similar direct coustraints on their internal rotation. but the solar case is certaluly a eood first approximation.," Old metal-poor stars do not have similar direct constraints on their internal rotation, but the solar case is certainly a good first approximation."1073 We therefore assume solid body rotation throughout the interior of the ain sequence turnolf progenitor and examine whether it is possible to retain sufficient. angular momentum to explain the rapid observed horizontal brauch rotation rates., We therefore assume solid body rotation throughout the interior of the main sequence turnoff progenitor and examine whether it is possible to retain sufficient angular momentum to explain the rapid observed horizontal branch rotation rates.1074 Qur initial conditions therefore reduce to the total moment of inertia at the main sequence, Our initial conditions therefore reduce to the total moment of inertia at the main sequence1075"Finally, the power spectrum is averaged over all segments.","Finally, the power spectrum is averaged over all segments."1076 The power spectrum obtained with an artificial light curve is shown on figure 2.., The power spectrum obtained with an artificial light curve is shown on figure \ref{mc_fps}.1077 The artificial light curve was produced by summing three simulated components., The artificial light curve was produced by summing three simulated components.1078" The light curve of PKS 1830-211 shown on figure 1 does not exhibit any easily recognizable features, but has a rather random-like aspect."," The light curve of PKS 1830-211 shown on figure \ref{lc} does not exhibit any easily recognizable features, but has a rather random-like aspect."1079" The first component was thus simulated as a white noise, with a Poisson distribution."," The first component was thus simulated as a white noise, with a Poisson distribution."1080" It would be more realistic to use red noise instead of white noise but the latter is sufficient for most of our purposes, such as computing D,. The second component is obtained from the first by shifting the light curve with a 28 days time lag."," It would be more realistic to use red noise instead of white noise but the latter is sufficient for most of our purposes, such as computing $D_{a}.$ The second component is obtained from the first by shifting the light curve with a 28 days time lag."1081 The effect of differential magnification of the images has also been included., The effect of differential magnification of the images has also been included.1082 The background photon noise was taken into account by adding a third component with a Poisson distribution., The background photon noise was taken into account by adding a third component with a Poisson distribution.1083 The mean number of counts per 2 day bin for PKS is 5.42 counts., The mean number of counts per 2 day bin for PKS 1830-211 is 5.42 counts.1084 This value was used for the simulation of the artificial light curve., This value was used for the simulation of the artificial light curve.1085 The first and second component contribute of the simulated count rate and the rest is contributed by the noise component., The first and second component contribute of the simulated count rate and the rest is contributed by the noise component.1086" To get a simulated flux similar to the observed flux, the simulated count rate is divided by the average exposure from observations ( 2.8557107s cm’)."," To get a simulated flux similar to the observed flux, the simulated count rate is divided by the average exposure from observations ( $2.8557\ 10^{7}\ s\ cm^{2}$ )."1087" The methods of time delay determination use the power spectrum P, obtained as described in the previous section.", The methods of time delay determination use the power spectrum $P_{\nu}$ obtained as described in the previous section.1088" The simulated P, presented on figure 2 shows a very clear periodic pattern.", The simulated $P_{\nu}$ presented on figure \ref{mc_fps} shows a very clear periodic pattern.1089 From equation 1 we know that the period of the observed wobbles corresponds to inverse of the time delay between the images., From equation \ref{Powereq} we know that the period of the observed wobbles corresponds to inverse of the time delay between the images.1090" Our preferred approach was to calculate the double power spectrum D,.", Our preferred approach was to calculate the double power spectrum $D_{a}$.1091" As in section 3.2,, the power spectrum P, has to be prepared before undergoing a Fourier transform to the ""time delay"" domain."," As in section \ref{FPSsubs}, the power spectrum $P_{\nu}$ has to be prepared before undergoing a Fourier transform to the “time delay” domain."1092" The low frequency part (v«1/55day|!) of P, is cut off.", The low frequency part $\nu < 1/55 \mbox{day}^{-1}$ ) of $P_{\nu}$ is cut off.1093 This cut arises because of the large power observed low frequencies in the power spectrum of PKS 1830-211., This cut arises because of the large power observed low frequencies in the power spectrum of PKS 1830-211.1094" The high frequency part of the spectrum P, is also removed because the power at high frequency is small (it goes to O at the Nyquist frequency).", The high frequency part of the spectrum $P_{\nu}$ is also removed because the power at high frequency is small (it goes to 0 at the Nyquist frequency).1095" The calculation of D, proceeds like in section 3.2,, except that the P, data are bend to zero by multiplication with a cosine bell."," The calculation of $D_{a}$ proceeds like in section \ref{FPSsubs}, except that the $P_{\nu}$ data are bend to zero by multiplication with a cosine bell."1096" This eliminates spurious high frequencies, when zeros are added to the P, series."," This eliminates spurious high frequencies, when zeros are added to the $P_{\nu}$ series."1097" The D, distribution is estimated from 5 segments of the light curve.", The $D_{a}$ distribution is estimated from 5 segments of the light curve.1098" In every bin of the D, distribution, the estimated double power spectrum is given by the average over the 5 segments."," In every bin of the $D_{a}$ distribution, the estimated double power spectrum is given by the average over the 5 segments."1099" The errors bars on D, are estimated from the dispersion of bin values divided by 2 (since there are 5 segments).", The errors bars on $D_{a}$ are estimated from the dispersion of bin values divided by 2 (since there are 5 segments).1100" Due to the random nature of the sampling process, some of the error bars obtained are much smaller than the typical dispersion in the D, points."," Due to the random nature of the sampling process, some of the error bars obtained are much smaller than the typical dispersion in the $D_{a}$ points."1101" To take this into account, a small systematic error bar was added quadratically to all points."," To take this into account, a small systematic error bar was added quadratically to all points."1102 The result (with statistical error bars only) is presented on figure 3.., The result (with statistical error bars only) is presented on figure \ref{mc_sps}.1103" As described in section 3.2,, we simulated light curves with atime delay of 28 days."," As described in section \ref{FPSsubs}, we simulated light curves with a time delay of 28 days."1104" A peak is apparent near a time delay of 28 days on the D, distribution shown on figure 3..", A peak is apparent near a time delay of 28 days on the $D_{a}$ distribution shown on figure \ref{mc_sps}.1105 The points just outside the peak are compatible with a flat distribution., The points just outside the peak are compatible with a flat distribution.1106 Including also the points in the peak gives a distribution which is incompatible with a flat distribution at the 10 sigma level., Including also the points in the peak gives a distribution which is incompatible with a flat distribution at the 10 sigma level.1107 The parameters of the peak were determined by fitting the sum of a linear function for the background plus a Gaussian function for the signal., The parameters of the peak were determined by fitting the sum of a linear function for the background plus a Gaussian function for the signal.1108" In the case shown on figure 3,, the time delay estimated from D, is 27.94+0.61 days."," In the case shown on figure \ref{mc_sps}, the time delay estimated from $D_{a}$ is $27.94\pm0.61$ days."1109" As mentioned in section 3.1,, the usual approach for the time delay estimation is to compute the autocorrelation of the light curve."," As mentioned in section \ref{idea}, the usual approach for the time delay estimation is to compute the autocorrelation of the light curve."1110" The auto-covariance is obtained by taking the real part of the inverse Fourier transform of P,.", The auto-covariance is obtained by taking the real part of the inverse Fourier transform of $P_{\nu}$ .1111 The auto-covariance is normalized (divided by the value at zero time lag) to get the autocorrelation., The auto-covariance is normalized (divided by the value at zero time lag) to get the autocorrelation.1112 The autocorrelation function of an artificial light curve simulated as in section 3.2 is presented on figure 4.., The autocorrelation function of an artificial light curve simulated as in section \ref{FPSsubs} is presented on figure \ref{mc_ac}.1113 A peak with a significance of roughly 16 o is present at 27.85+0.14 days., A peak with a significance of roughly 16 $\sigma$ is present at $27.85\pm0.14$ days.1114 However the significance of this peak is overestimated since light curves are simulated with white noise instead of red noise., However the significance of this peak is overestimated since light curves are simulated with white noise instead of red noise.1115" The autocorrelation function of a light curve driven by red noise is given by e"", In the case of our simulated light curves, A=0, so that the peak is a little affected by the background of the AGN."," The autocorrelation function of a light curve driven by red noise is given by $e^{-a/ \lambda}.$ In the case of our simulated light curves, $\lambda = 0$, so that the peak is a little affected by the background of the AGN."1116" For the simulated light curves, both approaches of time delay determination give reasonable and compatible results."," For the simulated light curves, both approaches of time delay determination give reasonable and compatible results."1117 The results for real data were obtained with the same procedure as was presented for the simulated light curves., The results for real data were obtained with the same procedure as was presented for the simulated light curves.1118" Figure 8 shows the power spectrum P, calculated from the light curve of PKS 1830-211.", Figure \ref{pks1830_fps} shows the power spectrum $P_{\nu}$ calculated from the light curve of PKS 1830-211.1119 A periodic pattern is obvious onthe distribution of, A periodic pattern is obvious onthe distribution of1120many cases the distance estimates that we can clerive are quite Inprecise.,many cases the distance estimates that we can derive are quite imprecise.1121 T Leo. BZ UAla. D8490. SW δία. and V405 Peg have high-quality. parallax distance measurements ((Thorstensen 2003: Thorstensenetal.2006: Thorstensenctal. 2008:: ''horstensenetal. 2009)).," T Leo, BZ UMa, RBS490, SW UMa, and V405 Peg have high-quality parallax distance measurements \citealt{Thorstensen03}; ; \citealt{ThorstensenLepineShara06}; \citealt{ThorstensenLepineShara08}; \citealt{Thorstensen09}) )."1122 Other reliable estimates of CV distances are found. by photometric parallax. in cases where the white carl or the onor star ds detected in a way that makes it possible to iscntanele its [lux contribution from that of other light sources.," Other reliable estimates of CV distances are found by photometric parallax, in cases where the white dwarf or the donor star is detected in a way that makes it possible to disentangle its flux contribution from that of other light sources."1123 We use such estimates for PP Ari anc EXDra7., We use such estimates for TT Ari and EX.1124. TT Ari has a distance measurement based on the donor star Es»eetrum (Gansickeetal.1999:: this is also consistent with 1e distance derived from the white dwarf spectrum)., TT Ari has a distance measurement based on the donor star spectrum \citealt{GansickeSionBeuermann99}; this is also consistent with the distance derived from the white dwarf spectrum).1125 Based on the photometric parallax of the secondary. the distance to EX Dra is 240zope (see Shafter&Holland2003: Baptistaςal. 2000:: Pretoriusetal. 2007b:: we have revised. this to be slightly less conservative than the estimate we used previously).," Based on the photometric parallax of the secondary, the distance to EX Dra is $240^{+68}_{-52}\,\mathrm{pc}$ (see \citealt{ShafterHolland03}; \citealt{BaptistaCatalanCosta00}; \citealt{NEPrho}; we have revised this to be slightly less conservative than the estimate we used previously)."1126 There. are a few well-known. less. direct (ancl less reliable) methods of estimating distances to CVs.," There are a few well-known, less direct (and less reliable) methods of estimating distances to CVs."1127 We use methodsbased. on dwarf nova (DN) outburst. maximum (Warner1987: sec also Harrisonetal.2004 and Patterson 20112). the near-LR apparent brightness for svstems in whichthe donor star is not directly detected (the method of 1981.. but as prescribed by Ixnigee2006 and. Ixnigge 2011)). and the strength. of L5 emission lines 1984: see also Patterson 2011)).," We use methodsbased on dwarf nova (DN) outburst maximum \citealt{brian87}; see also \citealt{HarrisonJohnsonMcArthur04} and \citealt{Patterson11}) ), the near-IR apparent brightness for systems in whichthe donor star is not directly detected (the method of \citealt{Bailey81}, but as prescribed by \citealt{Knigge06} and \citealt{KBP11}) ), and the strength of $\beta$ emission lines \citealt{Patterson84}; see also \citealt{Patterson11}) )."1128" The relation between the absolute magnitude at DN outburst maximum and. 2, was most recently studied. by Patterson(2011).. who confirms that the scatter is relatively small. and that there are no large outliers."," The relation between the absolute magnitude at DN outburst maximum and $P_{orb}$ was most recently studied by \cite{Patterson11}, who confirms that the scatter is relatively small, and that there are no large outliers."1129 We therefore use this relation as Far as possible (for CC Sel. VW Livi. WA Ivi. SU UMa. PY PsA. WW. Cet. SDSS J1730. and EE Tuc).," We therefore use this relation as far as possible (for CC Scl, VW Hyi, WX Hyi, SU UMa, TY PsA, WW Cet, SDSS J1730, and EF Tuc)."1130 ]t should. be noted that SU UMa has a parallax distance estimate that agrees very well with the distance based. on outburst maximum. but which is less precise: we choose in this case to use the estimate based on outburst. rather than the parallax (see Phorstensen2003. and. Patterson 2011)).," It should be noted that SU UMa has a parallax distance estimate that agrees very well with the distance based on outburst maximum, but which is less precise; we choose in this case to use the estimate based on outburst, rather than the parallax (see \citealt{Thorstensen03} and \citealt{Patterson11}) )."1131 ‘Two systems. SDSS J1730 and EE Tuc. do not have orbital inclination measurements (although it is known that they are not eclipsing). and have less well determined. maximum oparent magnitudes. leading to more imprecise distance estimates from this method.," Two systems, SDSS J1730 and EF Tuc, do not have orbital inclination measurements (although it is known that they are not eclipsing), and have less well determined maximum apparent magnitudes, leading to more imprecise distance estimates from this method."1132 For RA J1831 we use the prescription of Ixnigee(2006) (as updated. by IxXnigeeetal. 901109)., For RX J1831 we use the prescription of \cite{Knigge06} (as updated by \citealt{KBP11}) ).1133 This is based. on a semi-empirical donor sequence for CVs. ancl the olfsets between this sequence and the absolute 444A. magnitudes m La sample of CVs with parallax distances.," This is based on a semi-empirical donor sequence for CVs, and the offsets between this sequence and the absolute $JHK$ magnitudes of a sample of CVs with parallax distances."1134 Apparent near-IR. magnitudes for RX JISA31 were obtained [rom the Two Micron All Sky Survey (2ALASS: Skrutskieetal. 2006))., Apparent near-IR magnitudes for RX J1831 were obtained from the Two Micron All Sky Survey (2MASS; \citealt{2mass}) ).1135 Finally. although there clearly exists an. empirical relation between MW(13) and the absolute magnitude of the disc. this relation contains large scatter (see Patterson2011. for an updated plot).," Finally, although there clearly exists an empirical relation between $EW(H\beta)$ and the absolute magnitude of the disc, this relation contains large scatter (see \citealt{Patterson11} for an updated plot)."1136 We therefore use it as à ast resort. in those four cases where the data required » the other two methods. are not available (LW Pic. IQ Iri. RA J1715. and 129111).," We therefore use it as a last resort, in those four cases where the data required by the other two methods are not available (TW Pic, IQ Eri, RX J1715, and RBS1411)."1137 For RN J1715. and tDS141I. we have no data to allow us to check. whether he absolute magnitudes we find are reasonable (other than hat RA J1715 is known to be a short-period CV. and that tDS1411I has an optical spectrum resembling that of a short-xeriod. CV).," For RX J1715 and RBS1411, we have no data to allow us to check whether the absolute magnitudes we find are reasonable (other than that RX J1715 is known to be a short-period CV, and that RBS1411 has an optical spectrum resembling that of a short-period CV)."1138 For the remaining 2 svstems. we find absolute magnitudes that are in reasonable agreement with what we would find from outhurst (in the case of LQ Evi). and the method. of Ixnigge (in the case of TW Pic). if we mace reasonable assumptions about orbitalperiod”.," For the remaining 2 systems, we find absolute magnitudes that are in reasonable agreement with what we would find from outburst (in the case of IQ Eri), and the method of Knigge (in the case of TW Pic), if we made reasonable assumptions about orbital."1139 Interstellar extinction is expected to be low for our systems. since they are at high Galactic latitude. and since most of them are quite nearby.," Interstellar extinction is expected to be low for our systems, since they are at high Galactic latitude, and since most of them are quite nearby."1140 For those systems. with distances below 200 pe. we neglect. interstellar extinction.," For those systems with distances below 200 pc, we neglect interstellar extinction."1141 For the more distant objects. we use chy estimates from Patterson(2011).. where available. and for a few more. we fine estimates in Bruch&Engel(1904).," For the more distant objects, we use $A_V$ estimates from \cite{Patterson11}, where available, and for a few more, we find estimates in \cite{BruchEngel94}."1142. In the cases where no more direct estimate of extinction is available. we use the model of Amores&Lépine(2005).. with a few iterations. so that the value we finally adopt in the distance caleulation is that given by the model at the estimated distance to the object.," In the cases where no more direct estimate of extinction is available, we use the model of \cite{AmoresLepine05}, with a few iterations, so that the value we finally adopt in the distance calculation is that given by the model at the estimated distance to the object."1143 Lo convert from visual extinction to extinction in the PALASS bands. we use ely=0282.1. ly=0.175... and eli=OLD (Cambrésyetal.2002).," To convert from visual extinction to extinction in the 2MASS bands, we use $A_J = 0.282 A_V$, $A_H=0.175 A_V$ , and $A_{K_S} = 0.112 A_V$ \citep{CambresyBeichmanJarrett02}."1144. We conservatively assume errors of in the extinction values., We conservatively assume errors of in the extinction values.1145 We then find the probability distribution. for the distance to each source. assuming Gaussian errors in all the input parameters (apparent. magnitudes. inclination. EW(123). extinction)," We then find the probability distribution for the distance to each source, assuming Gaussian errors in all the input parameters (apparent magnitudes, inclination, $EW(H\beta)$, extinction)."1146 The distances estimates. listed in column 3 of Table 1.. are in all cases the median. together with the 1-7 confidence interval corresponding to the 16th and S4th percentile points.," The distances estimates, listed in column 3 of Table \ref{tab:distances}, are in all cases the median, together with the $\sigma$ confidence interval corresponding to the 16th and 84th percentile points."1147 Distance estimates may suller from. two well-knownbiases. namelyMalmeuist (Malmeuist1924). and Lutz-Ixelker bias (Lutz&Ixelker 1973)..," Distance estimates may suffer from two well-knownbiases, namelyMalmquist \citep{Mbias} and Lutz-Kelker bias \citep{LKbias}. ."1148 These biases. the relation between them. and how to correct for them have been the subject of many papers Smith 2003)).," These biases, the relation between them, and how to correct for them have been the subject of many papers \\citealt{GonzalezFaber97}; ; \citealt{Smith03}) )."1149 Llere να will examine whether our clistance estimates could be biased., Here we will examine whether our distance estimates could be biased.1150"To constrain the slope of the BM down to the lowest masses in "" cluster we derive the ratio of verv low-mass stars (0.076 n- 0.1 AL.) to brown dwarls (0.02 -Ma 0.076 NL. ) in our survey.",To constrain the slope of the IMF down to the lowest masses in the cluster we derive the ratio of very low-mass stars (0.076 - 0.1 $_\odot$ ) to brown dwarfs (0.02 - 0.076 $_\odot$ ) in our survey.1151 We calculate this ratio to be R==0.230x0.20 assuming a (os. isochrone. with the errors computed due to Poisson statistics.," We calculate this ratio to be $R = 3/10 = 0.30 \pm 0.20$ assuming a 0.3 Myr isochrone, with the errors computed due to Poisson statistics."1152 For al Myr isochrone ralio increases to Ro = 5/8 — 0.625 dL- 0.356., For a 1 Myr isochrone this ratio increases to R = 5/8 = 0.625 $\pm$ 0.356.1153 Both cluster ages give5 ratios consistent with having been drawn from a Chabrier(2003) svstem IME. which gives a most likely ratio (mode) of Ro = 0.30.," Both cluster ages give ratios consistent with having been drawn from a \citet{ch03} system IMF, which gives a most likely ratio (mode) of R = 0.30."1154 This corresponds to a slope of dN/dM x FF over this range., This corresponds to a slope of dN/dM $\propto$ $^{-1.1}$ over this range.1155 For the older isochrone there are a larger number of low-mass stars but still more brown dwarls due to the hvdrogen burning limit shifting to a fainter magnitude for a higher cluster age., For the older isochrone there are a larger number of low-mass stars but still more brown dwarfs due to the hydrogen burning limit shifting to a fainter magnitude for a higher cluster age.1156 Both ratios are lower limits. since the low-mass bin has objects for which we do not have spectra and thus contamination by field stars may lead us to overestimate the number of brown chwarls relative to low mass stars in (he sample.," Both ratios are lower limits, since the low-mass bin has objects for which we do not have spectra and thus contamination by field stars may lead us to overestimate the number of brown dwarfs relative to low mass stars in the sample."1157 Above 0.076 AL. all objects but one have assigned spectral types which allow us (o assess their cluster membership., Above 0.076 $_\odot$ all objects but one have assigned spectral types which allow us to assess their cluster membership.1158 The object. without a spectral tvpe is ASRGa which is a previously identified cluster member (Aspinetal.1994). which we have resolved to be a binary., The object without a spectral type is ASR9a which is a previously identified cluster member \citep{as94} which we have resolved to be a binary.1159 Below 0.076 M. however. apart fron ASR 9b. there are [our objects without spectral tvpes. which could be possible field stars.," Below 0.076 $_\odot$ however, apart from ASR 9b, there are four objects without spectral types, which could be possible field stars."1160" Thus these ratios imply pn limits for the slope of the cluster mass spectrum belowQ.1 M. of a x Ld anda x» 0.55MM lor 0.3slope. Myr and 1 Myr isochrones respectively. where dN/dAl x M.P"" aad a = 2.35 is "," Thus these ratios imply upper limits for the slope of the cluster mass spectrum below 0.1 $_\odot$ of $\alpha$ $\leq$ 1.1 and $\alpha$ $\leq$ 0.55 for 0.3 Myr and 1 Myr isochrones respectively, where dN/dM $\propto$ $^{-\alpha}$ and $\alpha$ = 2.35 is the Salpeter slope."1161Where does our result stand with regard to comparable clusters and studies?, Where does our result stand with regard to comparable clusters and studies?1162 have explored the mass spectrum of NGC 1333 ms an extinction limited sample down to»0.04 AL. finding ralio of sub-stellar (0.04- 0.1 AL.) to stellar objects (0.1- 1 M.) to Rey= 1.11 +0.8/-0.4., \citet{wil03} have explored the mass spectrum of NGC 1333 using an extinction limited sample down to 0.04 $_\odot$ finding the ratio of sub-stellar (0.04 - 0.1 $_\odot$ ) to stellar objects (0.1 - 1 $_\odot$ ) to be $_{SS}$ = 1.11 +0.8/-0.4.1163(he; functionThey used this to estimate an upper limit for the slope of the lower endof the mass of a < 1.6., They used this to estimate an upper limit for the slope of the lower endof the mass function of $\alpha$ $\leq$ 1.6.1164 This compares well with slopes in the solar neighborhood below the hvdrogen-burning limit. whieh Reidetal.(1999). found tobe l <a «2.," This compares well with slopes in the solar neighborhood below the hydrogen-burning limit, which \citet{rei98} found to be 1 $<$ $\alpha$ $<$ 2."1165 Allenetal.(2005) have further attempted to constrain the shape of the field star IME below 0.1 AL. and found -0.6 <a < 0.6 with confidence and a best fit of o — 0.3., \citet{al05} have further attempted to constrain the shape of the field star IMF below 0.1 $_\odot$ and found -0.6 $<$ $\alpha$ $<$ 0.6 with confidence and a best fit of $\alpha$ = 0.3.1166 To derive a broader estimate of the cluster mass function we attempted to combine this survey with that of Wilkingetal.(2004) to make the cluster mass function more easily comparable to ratios published for other regions., To derive a broader estimate of the cluster mass function we attempted to combine this survey with that of \citet{wil03} to make the cluster mass function more easily comparable to ratios published for other regions.1167" We combined all objects between 0.1 - 1 AL. from veeetal.(2004) with an extinction limit of A, < 12.8” with the LIST objects between 0.03 - 0.1 AL. with an extinetion limit of A, < 21.1"". scaling the number of LIST objects bv ""ratios of (he survey areas. which is 26.3. as well as the extinctions. which is"," We combined all objects between 0.1 - 1 $_\odot$ from \citet{wil03} with an extinction limit of $_v$ $\leq$ $^m$ with the HST objects between 0.03 - 0.1 $_\odot$ with an extinction limit of $_v$ $\leq$ $^m$ , scaling the number of HST objects by the ratios of the survey areas, which is 26.3, as well as the extinctions, which is"1168In the context of stellar-mass compact objects. resolved. radio-emitting relativistic ejection events are typically associated. with periods of high rates of accretion and transitions in the state of the accretion flow (e.g. Fender. Belloni Gallo 20043.,"In the context of stellar-mass compact objects, resolved radio-emitting relativistic ejection events are typically associated with periods of high rates of accretion and transitions in the state of the accretion flow (e.g. Fender, Belloni Gallo 2004)."1169 The case of SGR 1806-20 is clearly rather different: the object is probably not accreting (Kouveliotou et al., The case of SGR 1806-20 is clearly rather different: the object is probably not accreting (Kouveliotou et al.1170 1998) and the apparent steady growth of the radio source is rather different from the jets associated with X-ray binaries. which typically have small (<107) opening angles (Miller-Jones. Fender Nakar 2005).," 1998) and the apparent steady growth of the radio source is rather different from the jets associated with X-ray binaries, which typically have small $\leq 10^{\circ}$ ) opening angles (Miller-Jones, Fender Nakar 2005)."1171 Several aspects of this behaviour may be associated with the probable lower bulk Lorentz factor of this event. L'acg~1.4 (Granot et al.," Several aspects of this behaviour may be associated with the probable lower bulk Lorentz factor of this event, $\Gamma_{\rm SGR} \sim 1.4$ (Granot et al."1172 2005: compare with Lo2 for X-ray binary jets)., 2005; compare with $\Gamma \geq 2$ for X-ray binary jets).1173 We can also compare this event with the jet-like outflows from isolated neutron stars such as the Crab (Hester et al., We can also compare this event with the jet-like outflows from isolated neutron stars such as the Crab (Hester et al.1174 2002). Vela (Pavlov et al.," 2002), Vela (Pavlov et al."1175 2003) and PSR Β1500-55 (DeLaney et al., 2003) and PSR B1509-58 (DeLaney et al.1176 2005)., 2005).1177" In these radio pulsars and SGR 1806-20 it seems that the the ""escape velocity principle’. in which outflows have velocities comparable to the escape velocity at their launch point (e.g. Livio 1999 and references therein) is maintained. while it is is blatantly violated by the jets from the accreting neutron stars Sco X-1 (Fomalont. Geldzahler Bradshaw 2001) and Circinus X-| (Fender et al."," In these radio pulsars and SGR 1806-20 it seems that the the 'escape velocity principle', in which outflows have velocities comparable to the escape velocity at their launch point (e.g. Livio 1999 and references therein) is maintained, while it is is blatantly violated by the jets from the accreting neutron stars Sco X-1 (Fomalont, Geldzahler Bradshaw 2001) and Circinus X-1 (Fender et al."1178 2004). which are much more relativistic. suggesting the necessity of a disc in forming the most relativistic flows.," 2004), which are much more relativistic, suggesting the necessity of a disc in forming the most relativistic flows."1179 Nevertheless. the radio source is still associated with the ejection of matter in a preferred direction in space. and probably the resultant in-situ particle acceleration.," Nevertheless, the radio source is still associated with the ejection of matter in a preferred direction in space, and probably the resultant in-situ particle acceleration."1180 The observed synchrotron emission is likely to have the highest surface brightness close to regions of particle acceleration. and it may be these regions which are producing the brightest regions of radio flux measured on the longest baselines by MERLIN and the VLBA.," The observed synchrotron emission is likely to have the highest surface brightness close to regions of particle acceleration, and it may be these regions which are producing the brightest regions of radio flux measured on the longest baselines by MERLIN and the VLBA."1181 Obvious sites for the particle acceleration are at the leading edge of the ejecta (external shocks). internal shocks distributed along the flow itself (easier to achieve the more collimated the initial flow was) and possibly at the site of the magnetar itself.," Obvious sites for the particle acceleration are at the leading edge of the ejecta (external shocks), internal shocks distributed along the flow itself (easier to achieve the more collimated the initial flow was) and possibly at the site of the magnetar itself."1182 In this scenario any radio emission associated with more diffuse components would be due to leptons which have diffused away from the particle acceleration site., In this scenario any radio emission associated with more diffuse components would be due to leptons which have diffused away from the particle acceleration site.1183 To conclude. we have observed at high angular resolution the early stages of the evolution of the radio counterpart to the giant flare of SGR 1806-20 on 2004 Dec 27.," To conclude, we have observed at high angular resolution the early stages of the evolution of the radio counterpart to the giant flare of SGR 1806-20 on 2004 Dec 27."1184 Despite many difficulties with analysing and interpreting the MERLIN and VLBA datasets. we tind evidence for significant substructure on angular scales =100 mas. associated with about of the total radio flux.," Despite many difficulties with analysing and interpreting the MERLIN and VLBA datasets, we find evidence for significant substructure on angular scales $\la 100$ mas, associated with about of the total radio flux."1185 The compact radio structure is likely to be associated with sites of particle acceleration. which may be external or internal shocks in the outflow. or somehow associated with the environment close to the magnetar itself.," The compact radio structure is likely to be associated with sites of particle acceleration, which may be external or internal shocks in the outflow, or somehow associated with the environment close to the magnetar itself."1186 MERLIN is a National Facility operated by the University of Manchester at Jodrell Bank Observatory on behalf of the UK Particle Physics and Astronomy Research Council., MERLIN is a National Facility operated by the University of Manchester at Jodrell Bank Observatory on behalf of the UK Particle Physics and Astronomy Research Council.1187 The US National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities. Inc. We thank the referee for detailed and constructive criticism.," The US National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. We thank the referee for detailed and constructive criticism."1188velocity V and. its. dispersion σι. in radial bins.,velocity $V$ and its dispersion $\sigma_V^{\phantom2}$ in radial bins.1189 The niiddle left. panels of Figs. 6-, The middle left panels of Figs. \ref{M12_kin}-1190" 9 the quantity (fo,jhe versus radius. for some of the remnants."," \ref{M13_kin} the quantity $\langle(V/\sigma^{\phantom2}_V)^2\rangle^{1/2}$ versus radius, for some of the remnants."1191 In all simulations. we find (AVfay2.1/22l for the voung population. indicating that this population forms a massive. rotationally. supported. dise.," In all simulations, we find $\langle(V/\sigma^{\phantom2}_V)^2\rangle^{1/2}>1$ for the young population, indicating that this population forms a massive, rotationally supported disc."1192 Ehe only exception. is simulation M12z. where (Ve27«] between radii 3 and Gkpe.," The only exception is simulation M12z, where $\langle(V/\sigma^{\phantom2}_V)^2\rangle^{1/2}<1$ between radii 3 and $6\,\rm kpc$."1193 As the top panel of Fig., As the top panel of Fig.1194 7 shows. this region corresponds to the discontinuitv between the inner disc and the counter- outer ring.," \ref{M12z_kin} shows, this region corresponds to the discontinuity between the inner disc and the counter-rotating outer ring."1195" Simulations M12. MlI2orb. MI2z. and MII all have {170,72«L indicating the presence of a “hot cise” supported by internal motions rather than rotation."," Simulations M12, M12orb, M12z, and M11 all have $\langle(V/\sigma^{\phantom2}_V)^2\rangle^{1/2}<1$, indicating the presence of a “hot disc” supported by internal motions rather than rotation."1196 Simulation MI3 has (Y07L7zmo] oat oradii r«προ and (AVYayo-Lat larger radii.," Simulation M13 has $\langle(V/\sigma^{\phantom2}_V)^2\rangle^{1/2}<1$ at radii $r<3\,{\rm kpc}$ and $\langle(V/\sigma^{\phantom2}_V)^2\rangle^{1/2}>1$ at larger radii."1197 Simulations AI290.. rMI2. and MIIO all have (VVfayyhooLE. indicating that the old population is also rotationally supported. but in all three cases the rotational support. 1s significantly smaller for the old. population. tvpically by a [actor of order 5.," Simulations M1290, rM12, and M110 all have $\langle(V/\sigma^{\phantom2}_V)^2\rangle^{1/2}>1$, indicating that the old population is also rotationally supported, but in all three cases the rotational support is significantly smaller for the old population, typically by a factor of order 5."1198 In the case of simulation rMI2. this result is consistent with the fact that retrograde orbits are less destructive than proegrade orbits.," In the case of simulation rM12, this result is consistent with the fact that retrograde orbits are less destructive than prograde orbits."1199 The middle right panels of Pigs. 6-, The middle right panels of Figs. \ref{M12_kin}-1200 9 show the velocity dispersion versus formation epoch. with the cash vertical lines indicating the starburst.," \ref{M13_kin} show the velocity dispersion versus formation epoch, with the dash vertical lines indicating the starburst."

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