ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 In this section. we perform a comparison between the eascous and stellar kinematical data we obtained for the sample galaxies with the velocity curves and velocity dispersion profiles available in literature in order to assess the accuracy and reliability of our measurements., In this section we perform a comparison between the gaseous and stellar kinematical data we obtained for the sample galaxies with the velocity curves and velocity dispersion profiles available in literature in order to assess the accuracy and reliability of our measurements.3 In most cases dillerences between. cüfferent authors are due to slit centring and positioning and to the dilferent. analysis techniques. or both (see Fisher 1997 for a discussion)," In most cases differences between different authors are due to slit centring and positioning and to the different analysis techniques, or both (see Fisher 1997 for a discussion)."4 As far as our sample galaxies are concerned. ionized gas velocity curves have been already. measured. along the major axis of NGC 2683. NGC 3200. NGC 3898. NGC 4419. and GC. 1331.," As far as our sample galaxies are concerned, ionized gas velocity curves have been already measured along the major axis of NGC 2683, NGC 3200, NGC 3898, NGC 4419, and NGC 7331."5 Apart from NGC 3898 presented in Pignatelli οἱ al. (, Apart from NGC 3898 presented in Pignatelli et al. (62001) the other cases are discussed here briellv aad shown in Fie. Al..,2001) the other cases are discussed here briefly and shown in Fig. \ref{fig:gascomparison}.7 The complex kinematics of this galaxy has OCH unveiled by Pompei TFerndrup (1999) who isolated two kinematically distinct gaseous Components giving rise to a ‘Heure-oLecight” velocity curve., The complex kinematics of this galaxy has been unveiled by Pompei Terndrup (1999) who isolated two kinematically distinct gaseous components giving rise to a `figure-of-eight' velocity curve.8 The fast and the slow-rotating components are unresolved in our spectrum as well as in hat of Barbon Capacetoli (1975)., The fast and the slow-rotating components are unresolved in our spectrum as well as in that of Barbon Capaccioli (1975).9" We therefore measured intermediate V,s and higher a's. The agreement between our aan that measured by Rubin et al. (", We therefore measured intermediate 's and higher 's. The agreement between our and that measured by Rubin et al. (101982) is excellent.,1982) is excellent.11 This is also true for Mathewson et al. (, This is also true for Mathewson et al. (121992) in the outer regions.,1992) in the outer regions.13 The shallower central eracient can be explained taking into account for their lower spatial resolution., The shallower central gradient can be explained taking into account for their lower spatial resolution.14 Our data closely matches those obtained. by previous authors., Our data closely matches those obtained by previous authors.15 This is not the case for only of the rrotation curves given by Sperancio et al. (, This is not the case for only of the rotation curves given by Sperandio et al. (161995).,1995).17 In this case their lower spatial resolution produces. the observed shallower central gradient but it can not account for the strong discrepaney we see at large radii on both sides., In this case their lower spatial resolution produces the observed shallower central gradient but it can not account for the strong discrepancy we see at large radii on both sides.18 Our Vs matches those by. Dottema (1999)., Our 's matches those by Bottema (1999).19 A difference in the heliocentric svstemic velocity and the cdillerent »osition anele of the slit (P.A.= 170°) may explain the shift he ccurve by Afanas'ev. SilChenko Zasov (1989).," A difference in the heliocentric systemic velocity and the different position angle of the slit $=170\dg$ ) may explain the shift the curve by Afanas'ev, Sil'Chenko Zasov (1989)."20 Alajor-axis stellar kinematics have been previously xiblished for NGC 224. NGC 470. NGC 712. NGC 2683. NGC 28A41. NGC 3031. NGC 3368. NGC 3810. NGC 3898. NGC 5854 and NGC 7331.," Major-axis stellar kinematics have been previously published for NGC 224, NGC 470, NGC 772, NGC 2683, NGC 2841, NGC 3031, NGC 3368, NGC 3810, NGC 3898, NGC 5854 and NGC 7331."21 They are compared with our data in Fig., They are compared with our data in Fig.22 except for the cases of NGC 772 and NGC 3898 which we analyzed in Pignatelli et al. (, \ref{fig:starcomparison_a} except for the cases of NGC 772 and NGC 3898 which we analyzed in Pignatelli et al. (232001).,2001).24 The cliserepaney observed along the NE axis between our cata and those by WKormendy (1988). ancl by Dressler and Richstone (1988) may be the result of an incorrect sky subtraction in our data., The discrepancy observed along the NE axis between our data and those by Kormendy (1988) and by Dressler and Richstone (1988) may be the result of an incorrect sky subtraction in our data.25 An overestimation of the sky level due to the large size of the galaxy covering all the slit area may produce the higher aand shift in wave actually measure., An overestimation of the sky level due to the large size of the galaxy covering all the slit area may produce the higher and shift in we actually measure.26 The s we measured are consistent with those of Lérraucleau et al. (, The 's we measured are consistent with those of Hérraudeau et al. (27"1999) while less satisfactory is. the comparison between our and theiro,.",1999) while less satisfactory is the comparison between our and their.28 In particular their values range between about 70 and 170+. whereas we measured S50 aat almost all raclii (probably due to a template mismatching elect).," In particular their values range between about $70$ and $170$, whereas we measured $\;\la50$ at almost all radii (probably due to a template mismatching effect)."29 We do not resolve the counter-rotating stellar components observed. bv. Pompei Terndrup (1999) because we have no enough spectral resolution and either a good S/N in our spectra., We do not resolve the counter-rotating stellar components observed by Pompei Terndrup (1999) because we have no enough spectral resolution and either a good S/N in our spectra.30 In the centre the vvalue we obtained is within the scatter of the other data sets. the same is true forσε.," In the centre the value we obtained is within the scatter of the other data sets, the same is true for."31 however further out from the nucleus our aand aare are somewhat lower than those found in literature., however further out from the nucleus our and are are somewhat lower than those found in literature.32 We measure the same eeracient as Bender. Saglia Gerhard. (1994) and Hérraudeau Simien (1998) in the inner |rx107.," We measure the same gradient as Bender, Saglia Gerhard (1994) and Hérraudeau Simien (1998) in the inner $|r|\la10''$."33 Further out our ccontinues to increase., Further out our continues to increase.34 The cdillerences between the three ssets are as large as 50. 80., The differences between the three sets are as large as $50$ $80$.35 In the same radial region our aagrees with the velocity dispersions hy Bender et al. (, In the same radial region our agrees with the velocity dispersions by Bender et al. (361994) but are about 50 flower than those by L¢érrauceau Simicn (1998).,1994) but are about $50$ lower than those by Hérraudeau Simien (1998).37 mmeasurements do coincide in the centre., measurements do coincide in the centre.38 Phese dillerences in aand aare due to the different instrumental setup used. for the iferent observations., These differences in and are due to the different instrumental setup used for the different observations.39 We used a very spatial resolution. so 10 velocity gradient we measure is more accurate than that of 16 other authors.," We used a very spatial resolution, so the velocity gradient we measure is more accurate than that of the other authors."40 The cdillerences in the values of )etween our measurements and those obtained by Lérraucdeau Simien (1998) are probably due to a template mismatching elfect Our major-axis kinematics are in good agreement with the literature., The differences in the values of between our measurements and those obtained by Hérraudeau Simien (1998) are probably due to a template mismatching effect Our major-axis kinematics are in good agreement with the literature.41 This is Fso true for the wwe measured along the minor axis of NGC 5854., This is also true for the we measured along the minor axis of NGC 5854.42 The eeracient nmieasured by llérraudeau Simimien (1998) is shallower than that by us and other authors., The gradient measured by Hérraudeau mien (1998) is shallower than that by us and other authors.43 We suggest. it may be due to a dilferent. position of the slit., We suggest it may be due to a different position of the slit.44 Our rraclial profile shows a faster decrease and at larger radii it is mareially consistent with that by Bower et al. (, Our radial profile shows a faster decrease and at larger radii it is marginally consistent with that by Bower et al. (451993).,1993).46 For some of the sample galaxies velocity fields for the cool gascous component have been obtained. using CO molecular lines and/or 22]-cm line and can be compared to our ionized-gas velocity Curves to have some insights into the inner-to-outer gas distribution and. motion., For some of the sample galaxies velocity fields for the cool gaseous component have been obtained using CO molecular lines and/or 21-cm line and can be compared to our ionized-gas velocity curves to have some insights into the inner-to-outer gas distribution and motion.47 The ddata by Broeils van Woerden (1994) show a symmetric outer rotation curve with no particular peculiarities., The data by Broeils van Woerden (1994) show a symmetric outer rotation curve with no particular peculiarities.48All these tools are provided in thesimulations...,All these tools are provided in the.49 The algorithm can be summarized as follows:, The algorithm can be summarized as follows:50ΗΝΗ sources is attributed to the temporal movement of the reconnection site as reported earlier by Masudaetal.(2001):Dogachev(2005):Zhouοἱ(2008).,"HXR sources is attributed to the temporal movement of the reconnection site as reported earlier by \citet{Masuda2001, Bogachev2005, Zhou2008}."51. From Figure 6.. it is evident that the ΗΝ sources were not very well correlated with the TFs curing the entire peak phase of the flare as compared to the I ribbons.," From Figure \ref{DiffMap}, it is evident that the HXR sources were not very well correlated with the TFs during the entire peak phase of the flare as compared to the H ribbons."52 Therefore. we infer (hat ΗΝ sources alone were not the cause or effect of the TFs.," Therefore, we infer that HXR sources alone were not the cause or effect of the TFs."53" This inference agrees with our earlier results obtained for the X10/2D Ware of 2003 October 29 (ALAO9),", This inference agrees with our earlier results obtained for the X10/2B flare of 2003 October 29 (MA09).54 Although the WLF ribbons were faintly observable in the WAL continuum animations. ihey are rather difficult to identify even in the diflerence images.," Although the WLF ribbons were faintly observable in the HMI continuum animations, they are rather difficult to identify even in the difference images."55 However. [rom the animations. the WLF ribbons appeared to be correlated with the TFs.," However, from the animations, the WLF ribbons appeared to be correlated with the TFs."56 This is further corroboratecl by the (he WLF intensity. magnetic and Doppler velocity profiles of Figure 5((botfom)).," This is further corroborated by the the WLF intensity, magnetic and Doppler velocity profiles of Figure \ref{STMap}( )."57 Qiu&Gary(2003). had reported that (i) the apparent sign reversal occurs in cool. strong-fiekl (21000 GG) regions within sunspot umbrae. Gi) locations of the anomaly are exactly co-aligned with the Chick-target IIXNR sources. and (11) the transient reversal fIux is (emporally correlated. with the IEXB. flix.," \citet{Qiu2003} had reported that (i) the apparent sign reversal occurs in cool, strong-field $>$ G) regions within sunspot umbrae, (ii) locations of the anomaly are exactly co-aligned with the thick-target HXR sources, and (iii) the transient reversal flux is temporally correlated with the HXR flux."58 Based on these results. thev proposed that at the flare kernels (he Ni absorption line profile is either temporarily turned into emission or significantly. broadened with a strong central reversal due to the non-thermal beam impact on the umbral atmosphere.," Based on these results, they proposed that at the flare kernels the Ni absorption line profile is either temporarily turned into emission or significantly broadened with a strong central reversal due to the non-thermal beam impact on the umbral atmosphere."59 However. our results for this X2.2 flare are not in full conformity with Qiu&Gary(2003) as we did not [ind a very. good association of LIAR. and TFs.," However, our results for this X2.2 flare are not in full conformity with \citet{Qiu2003} as we did not find a very good association of HXR and TFs."60 Therefore. the TFs observed curing the flare of 2011 February 15. and the X10/2D flare of 2003 October 29 reported in MÁO9. are not filly explained only bv the non-thermal process suggested in Qiu&Gary (2003)..," Therefore, the TFs observed during the flare of 2011 February 15, and the X10/2B flare of 2003 October 29 reported in MA09, are not fully explained only by the non-thermal process suggested in \citet{Qiu2003}. ."61 Earlier studies based on numerical models (Machadoetal.1980:Vernazza1981:Dine&Fang1989:Dingetal.2002:QiuGary2003) have shown that the flare associated transients may be attributed to a change in the spectral line profile.," Earlier studies based on numerical models \citep{Machado1980,62Vernazza1981, Ding1989, Ding2002, Qiu2003} have shown that the flare associated transients may be attributed to a change in the spectral line profile."63 IIowever. due to the non-availability of observational spectral data. (he transients could be examined using only ihe imaged data of the flares al various wavelengths and inferences were drawn based on (his indirect method.," However, due to the non-availability of observational spectral data, the transients could be examined using only the imaged data of the flares at various wavelengths and inferences were drawn based on this indirect method."64 We are now able to address (his issue using SDO/IIMI spectral observations., We are now able to address this issue using SDO/HMI spectral observations.65 The HAI observes the Sun in two circular polarizations al six wavelength positions (634.4.4103.2 and 4172.0 )) of the spectral line.," The HMI observes the Sun in two circular polarizations at six wavelength positions $\pm34.4, \pm103.2$ and $\pm172.0$ ) of the spectral line."66 Using these observations one can construct the line profile for any desired location of the full disk Sun., Using these observations one can construct the line profile for any desired location of the full disk Sun.67 The spectroscopic maging of LAI observations are described in a recent paper by (2011)., The spectroscopic imaging of HMI observations are described in a recent paper by\citet{MartinezOliveros2011}. .68momentum Component parallel to the relative motion between the projectile and the target. pr the perpendicular component. and. \/s the total energy in the center-of-mass system.,"momentum component parallel to the relative motion between the projectile and the target, $p_{T}$ the perpendicular component, and $\sqrt{s}$ the total energy in the center-of-mass system."69 This hypothesis has become a powerful tool in extrapolating low energy data to higher energies inaccessible by accelerators (Perl1974:Collins&Martin1984).," This hypothesis has become a powerful tool in extrapolating low energy data to higher energies inaccessible by accelerators \citep{TextBook1,TextBook2}."70. Fexaman proposed the parton model (Feviman1972). as a physical model realizing the scaling hypothesis.," Feynman proposed the parton model \citep{Feynman72}71 as a physical model realizing the scaling hypothesis."72 The parton model soon became the quark-parton model anc enhanced its predietabilitv., The parton model soon became the quark-parton model and enhanced its predictability.73 It is. however. the perturbative QCD by Altarelli and. Parisi (Altarelli that gave a broader foundation for caleulating the absolute cross-section ol complex final states.," It is, however, the perturbative QCD by Altarelli and Parisi \citep{pQCD} that gave a broader foundation for calculating the absolute cross-section of complex final states."74 On this basis. Anderson and collaborators started. in late 1970s. the developiiental work toward a widely used numerical simulation code for e€— collider experiments. the Lund model (Anderssonetal.1979.1980;Andersson1993).," On this basis, Anderson and collaborators started, in late 1970's, the developmental work toward a widely used numerical simulation code for $e^+e^-$ collider experiments, the Lund model \citep{LundModel1,LundModel2,LundModel3}."75. Another equally popular simulation code. Herwig. was wrillen a few vears later by Webber and Marchesini (Marchesini&Webber1984:198ta.b) on a dillerent algorithm known as (he Jet Caleulus (Ixonishietal.1978.1979)..," Another equally popular simulation code, Herwig, was written a few years later by Webber and Marchesini \citep{Herwig1,Herwig2,Herwig3} on a different algorithm known as the Jet Calculus \citep{JetCalculus1,JetCalculus2}."76 Pythia (Sjostrandetal.2001) is considered as an extension of the Lund model for high energv p-p and p-p interactions., Pythia \citep{Pythia62} is considered as an extension of the Lund model for high energy $p$ $p$ and $p$ $\bar{p}$ interactions.77 Herwig has also been extended to a similardirection (Corcellaetal.2002)., Herwig has also been extended to a similardirection \citep{Herwig65}.78. We note that simulation codes have been developed. for hadron-hadron. hadron-nucleus. neucleus-neucleus. and. nucleus interactions includingPIIOJET!.," We note that simulation codes have been developed for hadron-hadron, hadron-nucleus, neucleus-neucleus, and photon-nucleus interactions including."79. However they are not as widely used as Pythia and Ierwie in simulating high energy p-p interactions., However they are not as widely used as Pythia and Herwig in simulating high energy $p$ $p$ interactions.80 These simulation codes have evolved. cross-checkine mutually as well as against experimental data. and built up confidence in the computer-based simulation over 20 vears (see. eg.. Sjóstrand&Sev," These simulation codes have evolved, cross-checking mutually as well as against experimental data, and built up confidence in the computer-based simulation over 20 years (see, eg., \citet{Sjostrand99},"81imour(1999).. Richardson(2003) ancl references therein).," \citet{MrennaRichardson03}82 and references therein)."83 since both Pythia and Herwig are written on the perturbative QCD. the scaling is violated when a hard parton-parton interaction occurs.," Since both Pythia and Herwig are written on the perturbative QCD, the scaling is violated when a hard parton-parton interaction occurs."84 However (here are many more parton diagrams that violate the Fevnman sealing as will be discussed in Section 4., However there are many more parton diagrams that violate the Feynman scaling as will be discussed in Section 4.85 A set of such higher order terms have been added to Pythia recently (Sjostrand&Skanes2004)., A set of such higher order terms have been added to Pythia recently \citep{Sjostrand04}.86.. We use Pythia without such higher order terms as a reference model (model B) (hat will approximate. crudely. (he Feviman sealing model.," We use Pythia without such higher order terms as a reference model (model B) that will approximate, crudely, the Feynman scaling model."87 We warn. however. that Pythia without the higher order terms (our model D) aud (he scaling models such as Stephens&Baclhwar(1981). ancl eive different gammia-ray spectral shapes as has been shown in Fie.3 of Mori(1997).," We warn, however, that Pythia without the higher order terms (our model B) and the scaling models such as \citet{SB81} and \citet{Dermer86} give different gamma-ray spectral shapes as has been shown in Fig.3 of \citet{Mori97}."88. Table 2 tabulates the computer programs and the cross-section models used in (liis work., Table 2 tabulates the computer programs and the cross-section models used in this work.89 several corollary scaling laws have been derived [rom the quark-parlon model., Several corollary scaling laws have been derived from the quark-parton model.90 Of them. the best known ancl relevant to the present paper is the INNO scaling in the particle multiplicitv distribution (IXobaοἱal. 1972)..," Of them, the best known and relevant to the present paper is the KNO scaling in the particle multiplicity distribution \citep{KNO72}. ."91 According to the INNO sealing. the distribution," According to the KNO scaling, the distribution"92profiles and PSE's created using (Isvist 1997). covering a range of both core and tidal radii. (,"profiles and PSF's created using (Krist 1997), covering a range of both core and tidal radii. ("93For similar approaches to photometry ou partially resolved. elobular clusters. sec Codlhuair (1999) and = Holtziuau (1996).),"For similar approaches to photometry on partially resolved globular clusters, see \markcite{grillmair99} Grillmair (1999) and \markcite{holtzman96} Holtzman (1996).)"94 Tn central. high signal to noise (S/N>30) pixels. where errors in the model fitting become siguificaut compared to the noise. the fux is measured directly.," In central, high signal to noise $(S/N > 30)$ pixels, where errors in the model fitting become significant compared to the noise, the flux is measured directly."95 The flux outside these pixels is estimated using the best fit iocdel., The flux outside these pixels is estimated using the best fit model.96 The remaining catalog still coutams contaminating objects. particularly backeround galaxies.," The remaining catalog still contains contaminating objects, particularly background galaxies."97 The removal of objects with colors outside of the range 0.5<<V.T1.5 (where practically all globular clusters fall). highlw asviuuetrie objects; aud ducobjec where the best fitting model provided a poor reed ts4? ft significantly reduces the contiuuination.," The removal of objects with colors outside of the range $0.5 < V-I < 1.5$ (where practically all globular clusters fall), highly asymmetric objects, and objects where the best fitting model provided a poor reduced $\chi^{2}$ fit significantly reduces the contamination."98 For the study of the color distribution. we consider only ol with signals ereater than 3000 in each filter.," For the study of the color distribution, we consider only objects with signals greater than 3000 $^-$ in each filter."99 These eetbothobjects are significantly above the detection thresholdiu filters. aud the uucertiiutyv in the color of fainter objects due to counting statistics alone is significant.," These objects are significantly above the detection threshold in both filters, and the uncertainty in the color of fainter objects due to counting statistics alone is significant."100 The bright maguitude cutoff reduces the smoothing of the color distribution due to measurement error. ensures that the catalog is complete down to a well defined limit. and minimizes coutamination due to ronainiug background galaxies.," The bright magnitude cutoff reduces the smoothing of the color distribution due to measurement error, ensures that the catalog is complete down to a well defined limit, and minimizes contamination due to remaining background galaxies."101 In all data sets except NGC 12365. NGC L660. and NCC 1158. this limit is fainter than the expected peak of the GC magnitude distribution.," In all data sets except NGC 4365, NGC 4660, and NGC 4458, this limit is fainter than the expected peak of the GC magnitude distribution."102 The limitiu the M86 data set is close to the expected peak of the GC distribution., The limit in the M86 data set is close to the expected peak of the GC distribution.103 The procedure outlined by Holtziaan (1995) euided the conversion of the measured— flux iu theZ/ST filters to standard V. aud £ maguitudes., The procedure outlined by \markcite{holtzman95} Holtzman (1995) guided the conversion of the measured flux in the filters to standard $V$ and $I$ magnitudes.104 Figure 1l displavs the color distributions of cach galaxy., Figure \ref{figure:colordists} displays the color distributions of each galaxy.105 The lieht erey shaded. area shows the distribution using a traditional listogram., The light grey shaded area shows the distribution using a traditional histogram.106 The histogram is not the ideal representation of the data: bin sizes narrow enough to detect fine structure will also display significautf noise. and the choice of phase can also have a siguificaut effect on the appearance.," The histogram is not the ideal representation of the data; bin sizes narrow enough to detect fine structure will also display significant noise, and the choice of phase can also have a significant effect on the appearance."107 Simonoff (1996). describes aud colmpares a varicty of alternatives for estimating the nuderlving probability distribution. inchiding the variable width Epanechuikov kernel.," Simonoff (1996) describes and compares a variety of alternatives for estimating the underlying probability distribution, including the variable width Epanechnikov kernel."108 For αν given value. one of the simplest wars to measure the density of points at that value is to count the umber of points within some distance P of that value: where The appropriate choice of is a function both of the form of the underlying distribution aud the density of data points: smaller values of / are warranted when there are a larger umber of data points.," For any given value, one of the simplest ways to measure the density of points at that value is to count the number of points within some distance $h$ of that value: where The appropriate choice of $h$ is a function both of the form of the underlying distribution and the density of data points; smaller values of $h$ are warranted when there are a larger number of data points."109 Useof an munecessarily large value for / will result iu an overly 1000th estimate of f(r), Useof an unnecessarily large value for $h$ will result in an overly smooth estimate of $f(x)$.110 One can acconumnodate the varving density of data points by substituting AGe)=hy<flrs)2 for h.," One can accommodate the varying density of data points by substituting $h(x) = h_{\nu} \times111f(x_i)^{-\frac{1}{2}}$ for $h$."112"n Clearly. an estimate of flr) 1st be made to apply this method. but an iterative process beginning with a crude (ο,οι, uniform) estimate provides stable results in few iterations."," Clearly, an estimate of $f(x)$ must be made to apply this method, but an iterative process beginning with a crude (e.g., uniform) estimate provides stable results in few iterations."113 A second Huprovement that can be made is in the choice of the function A(u)., A second improvement that can be made is in the choice of the function $K(u)$ .114" It can be shown that an estimate made using the Epauechnikov kernel. ΠΕ the mean iuteerated square difference between fle) and f(r). provided that f"" is continuous. f,"" is square iutegrable. and A(«)z0 (Simonoff 1996)."," It can be shown that an estimate made using the Epanechnikov kernel, minimizes the mean integrated square difference between $f(x)$ and $\hat{f}(x)$, provided that $f^{\prime \prime}$ is continuous, $f^{\prime \prime \prime}$ is square integrable, and $K(u) \geq1150$ (Simonoff 1996)."116" Iu figure we present the color distributious using a siuuple histogram and approximations made using two values of reference kernel width. 5,."," In figure \ref{figure:colordists}, we present the color distributions using a simple histogram and approximations made using two values of reference kernel width, $h_\nu$."117 The thick line is the smoothing using a reference kerucl width that woul be optimal for a Gaussian distribution with a stand deviation equal to that of the data. and estimated using a constant kernel width.," The thick line is the smoothing using a reference kernel width that would be optimal for a Gaussian distribution with a standard deviation equal to that of the data, and estimated using a constant kernel width."118 This value will over-simooth the data when applied. with a variable kernel width iux fle)<1. particularly if the distribution is not. Cassia: features seen in this smoothing are very likely to be real.," This value will over-smooth the data when applied with a variable kernel width and $\hat{f}(x)<1$, particularly if the distribution is not Gaussian; features seen in this smoothing are very likely to be real."119 A Ikolinogorov-Suiruov (IN-S) test comparing this s1100tlie« distribution to the data confirms that it is significautlv over-moothed., A Kolmogorov-Smirnov (K-S) test comparing this smoothed distribution to the data confirms that it is significantly over-smoothed.120 The thin line shows the smoothing using a sernel width such that the sinoothed curve can be exchidec wea Is-S test at the Evol. eiviug an indication of what he true distribution may be.," The thin line shows the smoothing using a kernel width such that the smoothed curve can be excluded by a K-S test at the level, giving an indication of what the true distribution may be."121 Towever. features seen in this ine cannot be reeuarded as having been reliably detected.," However, features seen in this line cannot be reguarded as having been reliably detected."122 The KMM. aleorithm (Ashinan. Bird. Zepf 1991) xovides a statistical test for comparing the likelihood of the underlying distribution being a single or double Gaussian.," The KMM algorithm (Ashman, Bird, Zepf 1994) provides a statistical test for comparing the likelihood of the underlying distribution being a single or double Gaussian."123 The WAIN algorithm veturus a likelihood ratio est statistic. which is a measure of the iuprovemeut in the ft of a two Gaussian imodel over a single Gaussian one.," The KMM algorithm returns a likelihood ratio test statistic, which is a measure of the improvement in the fit of a two Gaussian model over a single Gaussian one."124 From this we calculate the p value. the xobabilitv of measuring this statistic from a siugle Gaussian distribution.," From this we calculate the $p$ value, the probability of measuring this statistic from a single Gaussian distribution."125 Low p values reject the hivpothesis hat the examined distribution resulted from sinele Gaussian distribution., Low $p$ values reject the hypothesis that the examined distribution resulted from single Gaussian distribution.126 They do uot necessarily reject other (possibly unimodal) models for the distiubution. jiowever.," They do not necessarily reject other (possibly unimodal) models for the distribution, however."127 Because tle presence of contaminating objects outside the main distribution significauth reduces the effectiveuess of the KMM. algorvitlin. we have removed objects with colors far from the main distribution (which are probably contaminating backeround galaxies) from our saluple before applying the IMM algoritlin to our data (see Ash 1991 for a more complete discussion of the effects of such a truucation).," Because the presence of contaminating objects outside the main distribution significantly reduces the effectiveness of the KMM algorithm, we have removed objects with colors far from the main distribution (which are probably contaminating background galaxies) from our sample before applying the KMM algorithm to our data (see Ashman 1994 for a more complete discussion of the effects of such a truncation)."128 Table 1 presents the various plivsical properties of eac[um ealaxy. including the absolute B magnitude (calculated using SBF distances and RC3 apparent magnitudes). BoV color. aud IIubble type: the Wo omaenitude cutoff and the total wmuber of clusters considered iu the color distribution: and the p value statistic and distributio- locations from the IKMM algorithin (αποο 1 aud mode 2).," Table \ref{table:data} presents the various physical properties of each galaxy, including the absolute $B$ magnitude (calculated using SBF distances and RC3 apparent magnitudes), $B-V$ color, and Hubble type; the $V$ magnitude cutoff and the total number of clusters considered in the color distribution; and the $p$ value statistic and distribution locations from the KMM algorithm (mode 1 and mode 2)."129 For four of the eight data sets where a reasonably large number of clusters have been detected (o> 100). two peaks are clearly ideuti&ableeven where the data are over-sinoothed.," For four of the eight data sets where a reasonably large number of clusters have been detected $(N > 100)$ , two peaks are clearly identifiableeven where the data are over-smoothed."130 Furthermore. m cach of these four cases the locations of the peaks are consistently near," Furthermore, in each of these four cases the locations of the peaks are consistently near"131Array (ATCA) at 4.8 and 6.2 GHz. for the bulk of 14-hour observing runs between 16 and 19 March 2004.,"Array (ATCA) at 4.8 and 6.2 GHz, for the bulk of 14-hour observing runs between 16 and 19 March 2004."132 The data were reduced in the standard fashion using the Μπας (e.g. Sault Killeen 2004) and AIPS (e.g.. Greisen 2005) software packages.," The data were reduced in the standard fashion using the Miriad (e.g., Sault Killeen 2004) and AIPS (e.g., Greisen 2005) software packages."133 The resulting images showed GX 339-4 to be a point source with no obvious extension. at a resolution of 6.1« 5.2/(4.8 GHz). and 5.7«4.9(6.2 GHz).," The resulting images showed GX $-$ 4 to be a point source with no obvious extension, at a resolution of $6.1\times1345.2$ (4.8 GHz), and $5.7\times 4.9$ (6.2 GHz)."135 The mean flux densities (referenced to the standard flux calibrator PKS B1934—638) were 5.30.05mJ (4.8 GHz) and 5.7£0.05mJy (6.2 GHz). where the error barsy reflect the rms noise in the images from individual days. and there is no sign of strong variability.," The mean flux densities (referenced to the standard flux calibrator PKS $-$ 638) were $5.3\pm 0.05~\rm mJy$ (4.8 GHz) and $5.7\pm 0.05~\rm136mJy$ (6.2 GHz), where the error bars reflect the rms noise in the images from individual days, and there is no sign of strong variability."137" In summary. ratio of radio flux to X-ray flux. the radio spectral index (a240.30.1. Sj,x""). and the lack of strong variability (on the order of 0.1 mJy from day to day). are all typical of radio emission in the low-hard state."," In summary, ratio of radio flux to X-ray flux, the radio spectral index $\alpha = +0.3\pm 0.1$, $S_\nu\propto\nu^\alpha$ ), and the lack of strong variability (on the order of 0.1 mJy from day to day), are all typical of radio emission in the low–hard state."138 Such radio emission is generally interpreted as the signature of a steady. compactjet (e.g.. Fender 2005).," Such radio emission is generally interpreted as the signature of a steady, compact jet (e.g., Fender 2005)."139 An inspection of theRXTE X-ray light curves revealed strong flaring. superimposed on a relatively stable base flux level.," An inspection of the X-ray light curves revealed strong flaring, superimposed on a relatively stable base flux level."140 The flares occurred on a time scale of a few tens of seconds and the flare maxima occasionally reached count rates close to eight times that of the base level., The flares occurred on a time scale of a few tens of seconds and the flare maxima occasionally reached count rates close to eight times that of the base level.141 Power spectra were created from the GoodXenon data (total energy band. 2-60 keV). with frequency ranges of 1287'-1024 Hz.," Power spectra were created from the GoodXenon data (total energy band, 2–60 keV), with frequency ranges of $128^{-1}$ –1024 Hz."142 The power spectra were normalized according to Belloni and Hasinger (1990) and Miyamoto et al. (, The power spectra were normalized according to Belloni and Hasinger (1990) and Miyamoto et al. (1431991). and the Poisson level was subtracted following the method described in Klein-Wolt et al. (,"1991), and the Poisson level was subtracted following the method described in Klein-Wolt et al. ("1442004).,2004).145 Two broad peaks could be identified in the power spectrum of each of theRXTE observations (a representative power spectrum is shown in Figure 1)., Two broad peaks could be identified in the power spectrum of each of the observations (a representative power spectrum is shown in Figure 1).146 One Lorentzian peaks around 0.05 Hz. corresponding to the strong flaring that is directly visible in the light curves. and à second. broader feature peaks around 2 Hz.," One Lorentzian peaks around 0.05 Hz, corresponding to the strong flaring that is directly visible in the light curves, and a second, broader feature peaks around 2 Hz."147 The low-frequency peak power could be fit well with one Lorentzian. with a Q-value (re. frequency divided by full-width-at-half-maximum) of —0.3 and a fractional rms amplitude of ~30%..," The low-frequency peak power could be fit well with one Lorentzian, with a Q-value (i.e. frequency divided by full-width-at-half-maximum) of $\sim$ 0.3 and a fractional rms amplitude of $\sim$."148 This feature can be identified with the break that is seen 1n the hard state power spectra of. e.g. Cyg X-1 (Belloni Hasinger 1990).," This feature can be identified with the break that is seen in the hard state power spectra of, e.g. Cyg X-1 (Belloni Hasinger 1990)."149 Two Lorentzians were needed to fit the feature at higher frequencies. peaking around 0.5 Hz (Q fixed to 0. rms%20%)) and 2.5 Hz (Qz0.15. rmsz256ty).," Two Lorentzians were needed to fit the feature at higher frequencies, peaking around 0.5 Hz (Q fixed to 0, $\approx$ ) and 2.5 Hz $\approx$ 0.15, $\approx$ )."150 The total strength of the variability in the 125. —64 Hz range is about47—515c., The total strength of the variability in the $128^{-1}$ –64 Hz range is about.151. The variability proporties in our observations are consistent with those of the canonical hard state., The variability proporties in our observations are consistent with those of the canonical hard state.152 We made a preliminary study of theRXTE PCU-2 and HEXTE-A spectra., We made a preliminary study of the PCU-2 and HEXTE-A spectra.153 The spectra were fit jointly within XSPEC. utilizing a constant to account for normalization differences.," The spectra were fit jointly within XSPEC, utilizing a constant to account for normalization differences."154" The continuum is well fit by a very simple model consisting of a power-law modified by absorption (using the ""phabs? model with Ny fixed at 4.0«102!atomsem. Miller et 22004a)."," The continuum is well fit by a very simple model consisting of a power-law modified by absorption (using the “phabs” model with $N_{H}$ fixed at $4.0\times15510^{21}~{\rm atoms}~{\rm cm}^{-2}$, Miller et 2004a)."156 Only a broad Fe Kev emission line (see Figure 2) prevents the simple power-law model from being a formally acceptable fit (\-/7= 385.7/76).," Only a broad Fe $\alpha$ emission line (see Figure 2) prevents the simple power-law model from being a formally acceptable fit $\chi^{2}/\nu =157385.7/76$ )."158 Using this continuum model. we measure a photon index of D=1.50(2). and a normalization of 0.2101)phem™s!Κεν at | keV. This corresponds to an unabsorbed flux of 5.33«1077!ergem™s! in the 3-100 keV band. or a luminosity of 4.1«10°!ergs! (or Ly<0.05 Lg) for a distance of 8 kpe.," Using this continuum model, we measure a photon index of $\Gamma = 1.50(2)$, and a normalization of $0.21(1)~{\rm ph}~{\rm159cm}^{-2}~{\rm s}^{-1}~{\rm keV}^{-1}$ at 1 keV. This corresponds to an unabsorbed flux of $5.33\times 10^{-9}~{\rm erg}~{\rm cm}^{-2}~{\rm160s}^{-1}$ in the 3–100 keV band, or a luminosity of $4.1\times16110^{37}~{\rm erg}~{\rm s}^{-1}$ (or $L_{X} \leq 0.05~L_{Edd}$ ) for a distance of 8 kpc."162 While there is some evidence for subtle curvature in the high energy spectrum that is consistent with disk reflection. it is too weak to be significant.," While there is some evidence for subtle curvature in the high energy spectrum that is consistent with disk reflection, it is too weak to be significant."163 Power-law models with an exponential high-energy cut-off and broken power-law models do not provide significant improvements to the continuum fit., Power-law models with an exponential high-energy cut-off and broken power-law models do not provide significant improvements to the continuum fit.164 A simple power-law fit in th 20-100 keV band gives an energy flux of 2.5«107?ergems7!. and a photon flux of 3.6«107phems7!.," A simple power-law fit in th 20–100 keV band gives an energy flux of $2.5\times 10^{-9}~{\rm erg}~{\rm cm}^{-2}~{\rm s}^{-1}$, and a photon flux of $3.6\times 10^{-2}~{\rm ph}~{\rm cm}^{-2}~{\rm s}^{-1}$."165 This places our simultaneous X-ray and radio flux measurements 1n the middle of the radio-X-ray flux correlation Corbel et ((2000) found to hold in the hard state of GX 339—4. and further indicates that we observed GX 339-4 in a standard low-hard state.," This places our simultaneous X-ray and radio flux measurements in the middle of the radio–X-ray flux correlation Corbel et (2000) found to hold in the low--hard state of GX $-$ 4, and further indicates that we observed GX $-$ 4 in a standard low–hard state."166 We next explored simple continuum fits to the Newton/EPIC-MOS spectra., We next explored simple continuum fits to the /EPIC-MOS spectra.167 We fit the four spectra (MOSI and MOS? from revolutions 782 and 783) jointly. allowing a normalizing constant to float between the spectra.," We fit the four spectra (MOS1 and MOS2 from revolutions 782 and 783) jointly, allowing a normalizing constant to float between the spectra."168 A simple power-law model like that which adequately described theRXTE spectra was unable to fit the continuum in the spectra. due to a strong soft flux excess.," A simple power-law model like that which adequately described the spectra was unable to fit the continuum in the spectra, due to a strong soft flux excess."169 The presence of a strong soft excess in the spectra does not represent a flaw in the performance or calibration of the instruments aboard either observatory., The presence of a strong soft excess in the spectra does not represent a flaw in the performance or calibration of the instruments aboard either observatory.170 Rather. the soft flux excess is merely not required in theRXTE band. due to its effective low-energy bound of 3 keV. When a low energy threshold of 3.0 keV is chosen to match that ofRXTE. a simple power-law model adequately describes the continuum in the spectra.," Rather, the soft flux excess is merely not required in the band, due to its effective low-energy bound of 3 keV. When a low energy threshold of 3.0 keV is chosen to match that of, a simple power-law model adequately describes the continuum in the spectra."171 Extending this fit down to 0.7 keV reveals that the soft excess is very significant below 2—3 keV in the spectra., Extending this fit down to 0.7 keV reveals that the soft excess is very significant below 2–3 keV in the spectra.172 This effect is illustrated in Figure 3., This effect is illustrated in Figure 3.173 For any reasonable continuum. model (a continuum consisting of one or two additive components. which can be strongly constrained by the data). fits reveal strong evidence for a relativistic iron line arising from the inner disk (see Figures 4. 5. and 6).," For any reasonable continuum model (a continuum consisting of one or two additive components, which can be strongly constrained by the data), fits reveal strong evidence for a relativistic iron line arising from the inner disk (see Figures 4, 5, and 6)."174 Studies of black hole X-ray binary outbursts with.RXTE have documented falling accretion disk flux and. apparet= temperature through the outburst decay (e.g.. Park et 22004: see also MeClintock Remillard 2005).," Studies of black hole X-ray binary outbursts with have documented falling accretion disk flux and apparent temperature through the outburst decay (e.g., Park et 2004; see also McClintock Remillard 2005)."175 Below a certain disk temperature and flux level. however.RXTE is simply unable to detect disk emission.," Below a certain disk temperature and flux level, however, is simply unable to detect disk emission."176 In plotting additive componer= fluxes measured across an outburst withRXTE. then. it 1ny not uncommon to see a sudden disappearance of the disk flux.," In plotting additive component fluxes measured across an outburst with, then, it is not uncommon to see a sudden disappearance of the disk flux."177 However. it 1s unlikely that disk emission simply turns off at this point.," However, it is unlikely that disk emission simply turns off at this point."178 It is also unlikely thatRXTE can provide robust constraints on the nature of the disk in low-temperature. low-flux phases.," It is also unlikely that can provide robust constraints on the nature of the disk in low-temperature, low-flux phases."179 It is most likely that the soft excess we have discovered with is due to emission from an optically-thin. geometrically-thick accretion disk. and that is much better-suited to such measurements.," It is most likely that the soft excess we have discovered with is due to emission from an optically-thin, geometrically-thick accretion disk, and that is much better-suited to such measurements."180 We explored a number of fits with different disk components and hard components. to demonstrate that the disk and disk line components truly arise from an accretion disk. and are not modeling artifacts.," We explored a number of fits with different disk components and hard components, to demonstrate that the disk and disk line components truly arise from an accretion disk, and are not modeling artifacts."181 We note that no fits to the Newton/EPIC-MOS spectra. by themselves or in combination with spectra. are formally acceptable.," We note that no fits to the /EPIC-MOS spectra, by themselves or in combination with spectra, are formally acceptable."182 This is due to the presence of residual instrumental response deficiencies near | keV and 2 keV. Similar response issues have been documented previously (e.g.. Miller et 22004b). and do not complicate efforts to obtain strong constraints on the nature of," This is due to the presence of residual instrumental response deficiencies near 1 keV and 2 keV. Similar response issues have been documented previously (e.g., Miller et 2004b), and do not complicate efforts to obtain strong constraints on the nature of"183disc during outburst. as suggested by Ogilvie (2001). or the spiral asymmetries themselves.,"disc during outburst, as suggested by Ogilvie (2001), or the spiral asymmetries themselves."184 Other features worth mentioning about the spectrum of U Gem are the bumps. structures seen to the blue ofA., Other features worth mentioning about the spectrum of U Gem are the bumpy structures seen to the blue of.185. Phese are seen in other spectra of this sample. c. WY Per. PY κο V516 €veg.," These are seen in other spectra of this sample, i.e. KT Per, TY Psc, V516 Cyg."186 These features are real and correspond to multiple and lines., These features are real and correspond to multiple and lines.187 Some of them have been marked in the spectrum. of U Gem for clarity., Some of them have been marked in the spectrum of U Gem for clarity.188"UAMa. ""These spectra are particularly noisy as these dwarf novae are still quite faint during outburst and. our standard. exposure time did: not achieve the intended: signal to noise.", These spectra are particularly noisy as these dwarf novae are still quite faint during outburst and our standard exposure time did not achieve the intended signal to noise.189 The signal-to-noise ratio of these spectra does not allow us to conclude whether lis present in emission or not but they clearly show Balmer lines in absorption. perhaps with central emission.," The signal-to-noise ratio of these spectra does not allow us to conclude whether is present in emission or not but they clearly show Balmer lines in absorption, perhaps with central emission."190 They probably resemble the spectra of RU Peg or V1159 Ori more than that of IP Peg., They probably resemble the spectra of RU Peg or V1159 Ori more than that of IP Peg.191ελα. This spectrum shows strong Balmer and lines in emission. with absorption cores (the opposite to what we have seen up to now)., This spectrum shows strong Balmer and lines in emission with absorption cores (the opposite to what we have seen up to now).192 There is strong emission in aand the Bowen blend., There is strong emission in and the Bowen blend.193 Although from the light curve we can see that our spectrum does not coincide with amateur observations. we are certain that LY UMa was in outburst when we observed it as its quiescent level is magnitude ~17.," Although from the light curve we can see that our spectrum does not coincide with amateur observations, we are certain that IY UMa was in outburst when we observed it as its quiescent level is magnitude $\sim$ 17."194 The rapid variations seen in the light curve are due to eclipses., The rapid variations seen in the light curve are due to eclipses.195" Out of the sample of CVs observed we find. apart. from IP Peg. 12 dwarf novae that show iin emission: SS Aur. LIL CAla. PU Crt. EAL Cye. SS (ναι EX Dra. U Gem. ΗΝ Peg. Glx Per. INT. Per. V893 Seo. LY UMa. and possibly 7 other systems were lis present but. very faint: FO And. W542 (νο BE Ori. TY νο, VZ Pyx. ER UAla. and SS UAL."," Out of the sample of CVs observed we find, apart from IP Peg, 12 dwarf novae that show in emission: SS Aur, HL CMa, TU Crt, EM Cyg, SS Cyg, EX Dra, U Gem, HX Peg, GK Per, KT Per, V893 Sco, IY UMa, and possibly 7 other systems were is present but very faint: FO And, V542 Cyg, BI Ori, TY Psc, VZ Pyx, ER UMa, and SS UMi."196 In this section. we look for correlations between the quantities we can measure in our spectra (1.0. EW. ENIM. outburst phase) and. Fundamental parameters of the dwarf novae. like their masses and orbital periods.," In this section we look for correlations between the quantities we can measure in our spectra (i.e. EW, FWHM, outburst phase) and fundamental parameters of the dwarf novae, like their masses and orbital periods."197 For high inclination cwarf novae. the ENIM of the lines scales as sin? (where / is the inclination of the svsteni).," For high inclination dwarf novae, the FWHM of the lines scales as $\sin i$ (where $i$ is the inclination of the system)."198 This is due to Doppler broadening of the lines., This is due to Doppler broadening of the lines.199 Ht is not clear that this is true for low inclination svstems., It is not clear that this is true for low inclination systems.200 At low inclinations other mechanisms may dominate over Doppler broadening. e.g. thermal broadening. intrinsic broadening.," At low inclinations other mechanisms may dominate over Doppler broadening, e.g. thermal broadening, intrinsic broadening."201 It is not possible to establish at what range of inclinations the ENIM of the lines is directly proportional to sin? because we are not capable of measuring sin? with any certainty [or systems that are not eclipsing.," It is not possible to establish at what range of inclinations the FWHM of the lines is directly proportional to $\sin202i$ because we are not capable of measuring $\sin i$ with any certainty for systems that are not eclipsing."203 Keeping this in mind we search for correlations between re FAVLIAL of the lines and their strength. as given by their EW.," Keeping this in mind we search for correlations between the FWHM of the lines and their strength, as given by their EW."204 Fig., Fig.205 9 shows the EPWLILM versus EW Lor ((top panel) and ((bottom panel)., \ref{res:ewfwhm1} shows the FWHM versus EW for (top panel) and (bottom panel).206 There is some indication of positive correlation. of =WHAT with EW., There is some indication of positive correlation of FWHM with EW.207 This apparent correlation would indicate at high inclination svstems (those with higher FWIIAI) garow stronger emission lines., This apparent correlation would indicate that high inclination systems (those with higher FWHM) show stronger emission lines.208 Ht is worth mentioning that iree of the systems where lis strong in emission during outburst. ancl where spiral garucture has been detected. ic. IP Pee. EX Dra and U Gem. are edge-on systems anc one expects radiative: transfer ellects to favour seeing emission in such cases.," It is worth mentioning that three of the systems where is strong in emission during outburst and where spiral structure has been detected, i.e. IP Peg, EX Dra and U Gem, are edge-on systems and one expects radiative transfer effects to favour seeing emission in such cases."209of the two stars that are just ~1 away.,of the two stars that are just $\sim 1\prpr$ away.210 Apart from some telluric features. no spectral lines were confidently observed.," Apart from some telluric features, no spectral lines were confidently observed."211 Nevertheless. the lack of strong emission lines. which would be visible even in a contaminated spectrum if wwere a sort of nearby active galaxy (e.gg.. a Seyfert or a FR-ID. is consistent with the usual interpretation of aas a source within the Galaxy.," Nevertheless, the lack of strong emission lines, which would be visible even in a contaminated spectrum if were a sort of nearby active galaxy g., a Seyfert or a FR-II), is consistent with the usual interpretation of as a source within the Galaxy."212 However. in this case. the eccentricity of the orbit of the star would need to be very high to fill its Roche lobe if a 18.45 d period were assumed (Rothsteinetal.20031: Smithetal. 20025).," However, in this case, the eccentricity of the orbit of the star would need to be very high to fill its Roche lobe if a 18.45 d period were assumed \cite{rothstein-02}; \cite{smith-02}) )."213 The problems raised by this meonsistency will require further attention to unveil the true physical scenario behind1758-258., The problems raised by this inconsistency will require further attention to unveil the true physical scenario behind.214. In the absence of conclusive spectroscopic. data. only broad-band photometry can place broad constraints on the physical nature of1758—258.," In the absence of conclusive spectroscopic data, only broad-band photometry can place broad constraints on the physical nature of."215. An interstellar extinction of Ay=8.4 mag was estimated following a similar approach to that of Predehl&Schmitt(1995) and considering a column density towards oof Ny=CL5£0.1)x107 em (Mereghettietal. 1997))., An interstellar extinction of $A_V \simeq 8.4$ mag was estimated following a similar approach to that of \cite{predehl-95} and considering a column density towards of $N_H \simeq (1.5 \pm 0.1) \times 10^{22}$ $^{-2}$ \cite{mereghetti-97}) ).216 We also computed the values Ay. Ay. and Ag using the relations reported by Rieke&Lebofsky(1955).," We also computed the values $A_K$, $A_I$, and $A_R$ using the relations reported by \cite{rieke-85}."217 Assuming a Galactic center distance of 8.5 kpe. dereddened magnitudes of the candidate counterpart to aare obtained.," Assuming a Galactic center distance of 8.5 kpc, dereddened magnitudes of the candidate counterpart to are obtained."218 The results of our final revised photometry are summarized in Table 2.., The results of our final revised photometry are summarized in Table \ref{table-magnitudes}.219 We searched for any possible variability of the proposed counterpart in the ESO archives., We searched for any possible variability of the proposed counterpart in the ESO archives.220" A total of 11 observing nights of data were available. obtained with VLT and the ISAAC instrument in the K;,-band."," A total of 11 observing nights of data were available, obtained with VLT and the ISAAC instrument in the $K_s$ –band."221 No variability was detected with amplitude larger than 40.5 mag on a timescale of weeks., No variability was detected with amplitude larger than $\pm 0.5$ mag on a timescale of weeks.222" The A, dereddened magnitude is roughly consistent with an early A-type main sequence star.", The $K_s$ dereddened magnitude is roughly consistent with an early A-type main sequence star.223 However. the corresponding colours (R—7)=-0.8 and (7—K)=«1.2 are inconsistent with this or any other spectral type.," However, the corresponding colours $(R-I) \simeq -0.8$ and $(I-K) \simeq +1.2$ are inconsistent with this or any other spectral type."224 In a Galactic context. this may be indicative of the optical/near-infrared Iluminosity. being dominated by a non-stellar component gg.. an accretion disk) as we would expect from a low-mass X-ray binary.," In a Galactic context, this may be indicative of the optical/near-infrared luminosity being dominated by a non-stellar component g., an accretion disk) as we would expect from a low-mass X-ray binary."225" On the other hand. we cannot rule out the possibility that this might be caused by the brighter star (K,=13.7). which ts located very close to our proposed candidate counterpart and may contaminate the photometry even after we have carefully tried to subtract its effects."," On the other hand, we cannot rule out the possibility that this might be caused by the brighter star $K_s \simeq 13.7$ ), which is located very close to our proposed candidate counterpart and may contaminate the photometry even after we have carefully tried to subtract its effects."226 Since a different extinction law may explain the discrepant colours. we computed them again following the conversions of near-infrared extinctions to Ay towards the nuclear bulge described by Goslingetal.(2009).," Since a different extinction law may explain the discrepant colours, we computed them again following the conversions of near-infrared extinctions to $A_V$ towards the nuclear bulge described by \cite{gosling-09}."227.. Despite the different form of the extinction law. the derived colours do not substantially change compared to those listed in Table 2..," Despite the different form of the extinction law, the derived colours do not substantially change compared to those listed in Table \ref{table-magnitudes}."228 Hence. our conclusion of contamination by either the nearby star or by à non-stellar component such as an aceretion disk remains unaltered.," Hence, our conclusion of contamination by either the nearby star or by a non-stellar component such as an accretion disk remains unaltered."229 Despite the challenge to interpret spectroscopic observations. the main contribution of this work has been the identification of a serious candidate to the optical/near-infrared counterpart of bbased on accurate astrometric coincidence.," Despite the challenge to interpret spectroscopic observations, the main contribution of this work has been the identification of a serious candidate to the optical/near-infrared counterpart of based on accurate astrometric coincidence."230 This opens the possibility of investigating the true nature of this source., This opens the possibility of investigating the true nature of this source.231 Additional spectroscopic observations with 5 m-class telescopes and adaptive optics at southern locations are required to confirm its Galactic (or extragalactic) origin and. in the former case. to more clearly classify its spectral type.," Additional spectroscopic observations with 8 m-class telescopes and adaptive optics at southern locations are required to confirm its Galactic (or extragalactic) origin and, in the former case, to more clearly classify its spectral type."232three Bootes sources in Table 4 without firm SDSS or IRS redshifts. source 3 is the only source whose IRS spectrum is consistent will a strong silicate emission source al z = 2.4.,"three Bootes sources in Table 4 without firm SDSS or IRS redshifts, source 3 is the only source whose IRS spectrum is consistent with a strong silicate emission source at z = 2.4."233 As seen in Figure 3. the rest [rune spectrum of this source shows an increasing continuum al c (hat is just as expected [ον (he onset of a strong silicate emission feature.," As seen in Figure 3, the rest frame spectrum of this source shows an increasing continuum at $\sim$ that is just as expected for the onset of a strong silicate emission feature."234 We note also in Figure 3 the close similarity of the rest-frame spectrum of source AGNS to Chat of source AGN21. a tvpe 1 QSO with a known SDSS redshift aid the most luminous source in our 10 mJv sample. as discussed below.," We note also in Figure 3 the close similarity of the rest-frame spectrum of source AGN3 to that of source AGN21, a type 1 QSO with a known SDSS redshift and the most luminous source in our 10 mJy sample, as discussed below."235 The MIPS fIux of source AGN3 (IIoucketal.2007) of 10.3 mJv is also in agreement with the fIux of 10.5 mJy plotted bv Brownοἱal.(2006)., The MIPS flux of source AGN3 \citep{hou07} of 10.3 mJy is also in agreement with the flux of 10.5 mJy plotted by \citet{bro06}.236. We conclude. therefore. that source AGN3 is the QSO al z = 2.4 identified bv (Brownetal.2006).. and we include this source in our average speclra.," We conclude, therefore, that source AGN3 is the QSO at z = 2.4 identified by \citep{bro06}, and we include this source in our average spectra."237 Each source in Tables 2-5 is individually interesting. and many comparisons could be made among various properties because extensive nmultüiwavelength: cata already exist. [or most of (hese objects.," Each source in Tables 2-5 is individually interesting, and many comparisons could be made among various properties because extensive multiwavelength data already exist for most of these objects."238 For the present. we are not undertaking such an overall multiwavelengtl analvsis except lor noting in Tables 3 and 5 (he general agreement. between optical and IRS spectral classifications.," For the present, we are not undertaking such an overall multiwavelength analysis except for noting in Tables 3 and 5 the general agreement between optical and IRS spectral classifications."239 The primary result we discuss here is the relation between nuc-infrared Iwuinositv and (he infrared spectral characteristics., The primary result we discuss here is the relation between mid-infrared luminosity and the infrared spectral characteristics.240 This result is crucial to understanding the nature of sources which are seen in survevs of the mid-infrared sky. and in using these surveys to determine evolutionary characteristics of starbursts and AGN.," This result is crucial to understanding the nature of sources which are seen in surveys of the mid-infrared sky, and in using these surveys to determine evolutionary characteristics of starbursts and AGN."241 This 10 mJy sample clearly shows that the most Iuminous sources are those with AGN characteristics (silicate features) rather than starburst characteristics (PAIL features)., This 10 mJy sample clearly shows that the most luminous sources are those with AGN characteristics (silicate features) rather than starburst characteristics (PAH features).242 In Figure 5. the redshifts and [luxes ave compared for sources with and without measurable PAILI features.," In Figure 5, the redshifts and fluxes are compared for sources with and without measurable PAH features."243 It is seen that. while the (his distributions are similar. the redshifts are generally much higher for the AGN. implvinge 0greater Iuminosities.," It is seen that, while the flux distributions are similar, the redshifts are generally much higher for the AGN, implying greater luminosities."244 This result is made clear in Figure 6 where luminosity distributions are shown., This result is made clear in Figure 6 where luminosity distributions are shown.245" Luminosities are compared using rest-Drame pL,(15jpm) inevess +. (", Luminosities are compared using rest-frame $\nu$ $_{\nu}$ $\mu$ m) in ergs $^{-1}$. (246"Log vL, (15jpm)(L. )) = log vL,(15pm)(eres 1) - 33.59.)",Log $\nu$ $_{\nu}$ $\mu$ ) = log $\nu$ $_{\nu}$ $\mu$ m)(ergs $^{-1}$ ) - 33.59.)247 As mentioned previously. a wavelength of is used for comparison of intrinsic Iuminosities because the continuum is a pure dust continuum. without contamination by PAI or emission line," As mentioned previously, a wavelength of is used for comparison of intrinsic luminosities because the continuum is a pure dust continuum, without contamination by PAH or emission line"248"In order to verify the possible presence of PWNe in the optical, we have over plotted the X-ray contours of the Chandra//ACIS images of J1357—6429 and J1048—5832 on the V —bandimages(Fig.","In order to verify the possible presence of PWNe in the optical, we have over plotted the X-ray contours of the /ACIS images of $-$ 6429 and $-$ 5832 on the $V$ -band images (Fig."2494)., 4).250"TheX —rayPWN eof 6429hasbeendiscoveredinarecent~ 59 ks /ACIS image (Lemoine-Goumard et 22011; Chang et 22011) and has an angular extent much larger than that of the compact PWN (S 4"") tentatively detected by ((2007) in an older ~33 ks Chandra//HRC data set.", The X-ray PWNe of $-$ 6429 has been discovered in a recent $\sim$ 59 ks /ACIS image (Lemoine-Goumard et 2011; Chang et 2011) and has an angular extent much larger than that of the compact PWN $\la 4\arcsec$ ) tentatively detected by (2007) in an older $\sim 33$ ks /HRC data set.251 We note that the proximity of the J1357—6429 position to the oocculting bars and the relative crowding of the field makes it very difficult to search for the optical counterpart of its X-ray PWN., We note that the proximity of the $-$ 6429 position to the occulting bars and the relative crowding of the field makes it very difficult to search for the optical counterpart of its X-ray PWN.252" In particular, the bright core of the PWN overlaps with the position of Stars A and B and it is partially masked by the occulting bars south of it."," In particular, the bright core of the PWN overlaps with the position of Stars A and B and it is partially masked by the occulting bars south of it."253" Due to the relatively high fluxes of Stars A and B with respect to that expected for a putative optical PWN, the uncertainty in the PSF subtraction residuals makes its detection improbable."," Due to the relatively high fluxes of Stars A and B with respect to that expected for a putative optical PWN, the uncertainty in the PSF subtraction residuals makes its detection improbable."254" At the same time, the faint PWN tail overlaps with several stars detected northeast of the pulsar's pposition (Fig."," At the same time, the faint PWN tail overlaps with several stars detected northeast of the pulsar's position (Fig."255" 4, left)."," 4, left)."256" Thus, any upper limit on the optical surface brightness of the PWN would be highly uncertain and hampered by the partially covered area."," Thus, any upper limit on the optical surface brightness of the PWN would be highly uncertain and hampered by the partially covered area."257" We note that a PWN around J1357—6429 has been detected at TeV energies by HESS (Abramowski et 2001), but its angular size is much larger than the entire ffield-of-view, by itself masked by ~50% by the occulting bars."," We note that a PWN around $-$ 6429 has been detected at TeV energies by HESS (Abramowski et 2001), but its angular size is much larger than the entire field–of–view, by itself masked by $\sim 50\%$ by the occulting bars."258" In the case of J1048—5832, the proximity of the pposition to one of the clumps belonging to the large molecular cloud complex detected in the field (Fig.4, right) makes it difficult to search for optical emission along the whole PWN, whose angular extent (6""x11""; Gonzalez et 22006) is partially covered by the clump."," In the case of $-$ 5832, the proximity of the position to one of the clumps belonging to the large molecular cloud complex detected in the field (Fig.4, right) makes it difficult to search for optical emission along the whole PWN, whose angular extent $6\arcsec \times 11\arcsec$; Gonzalez et 2006) is partially covered by the clump."259" In particular, the clump entirely covers the PWN tail, which extends southeast of the pulsar position."," In particular, the clump entirely covers the PWN tail, which extends southeast of the pulsar position."260" No extended optical emission is recognised close to the head of the PWN, where the clumps are sparser and smaller."," No extended optical emission is recognised close to the head of the PWN, where the clumps are sparser and smaller."261" As in the case of J1357—6429, any upper limit of the optical surface brightness of the PWN is hampered by the covered area."," As in the case of $-$ 6429, any upper limit of the optical surface brightness of the PWN is hampered by the covered area."262 We compared our optical flux upper limits in the V band with the pulsars’ rotational energy loss rates., We compared our optical flux upper limits in the $V$ band with the pulsars' rotational energy loss rates.263" For J1357—6429, our upper limit of V~27 corresponds to an optical luminosity upper limit Loy;~ 0.6-21.6x1079 erg s7!, for a distance d=2.4+0.6 kpc and for an interstellar extinction Ay=2.2*17, after accounting for their associated uncertainties."," For $-$ 6429, our upper limit of $V\sim 27$ corresponds to an optical luminosity upper limit $L_{opt} \sim 0.6$ $ 21.6 \times 10^{29}$ erg $^{-1}$, for a distance $d=2.4 \pm 0.6$ kpc and for an interstellar extinction $A_V = 2.2^{+1.7}_{-1.1}$, after accounting for their associated uncertainties."264 This implies an emission efficiency upper limit ror~ 0.2-7x1077., This implies an emission efficiency upper limit $\eta_{opt} \sim 0.2$ $7 \times 10^{-7}$.265" This value is at least a factor of 5 lower than the Crab pulsar and, possibly, closer to that of the Vela pulsar."," This value is at least a factor of 5 lower than the Crab pulsar and, possibly, closer to that of the Vela pulsar."266" On the other hand, for J1048—5832 our upper limit of V~27.6 implies (for d=2.7+0.35 kpc and Ay= 5723) upper limits of Lopt~ 0.4-12.5x1050 erg s~! and Noptv 1.8-62.5x1077."," On the other hand, for $-$ 5832 our upper limit of $V\sim 27.6$ implies (for $d=2.7\pm 0.35$ kpc and $A_V = 5^{+2.2}_{-1.1}$ ) upper limits of $L_{opt} \sim 0.4$ $12.5 \times 10^{30}$ erg $^{-1}$ and $\eta_{opt} \sim 1.8$ $62.5 \times 10^{-7}$."267" In principle, this does not rule out an optical emission efficiency comparable to that of the Crab pulsar, although the pulsar spin-down age (20.3 kyr) might suggest, also in this case, a Vela-like emission efficiency."," In principle, this does not rule out an optical emission efficiency comparable to that of the Crab pulsar, although the pulsar spin-down age (20.3 kyr) might suggest, also in this case, a Vela-like emission efficiency."268 An optical emission efficiency rop.S 1077-1079 has been measured also from the upper limit on the optical emission of, An optical emission efficiency $\eta_{opt} \la 10^{-7}$ $10^{-6}$ has been measured also from the upper limit on the optical emission of269Is (here evidence in the short-period comet population lor (he prevalence of splitting evenis creating multiple comets?,Is there evidence in the short-period comet population for the prevalence of splitting events creating multiple comets?270 As of 2004. ten of the 160 known short-period comets were known to have split. although some of (hese events were more akin to mass shedcding than splittàng events (hat produce persistent secondary nuclei (2)..," As of 2004, ten of the 160 known short-period comets were known to have split, although some of these events were more akin to mass shedding than splitting events that produce persistent secondary nuclei \citep{boehnhardt04}. ."271 ?. report the results of using Lyapunov indicators to look for break-up families in the JEC: population: they conclude that eroups of 10 or more comets sharing a common break-up event are not prevalent in the 123 JECS used in the investigation., \citet{tancredi00a} report the results of using Lyapunov indicators to look for break-up families in the JFC population; they conclude that groups of 10 or more comets sharing a common break-up event are not prevalent in the 123 JFCs used in the investigation.272 So while there are observations of splitting events and even pairs of comets (hat share a common origin (?).. there is no direct evidence of larger sets ol JFCs sharing a single progenitor.," So while there are observations of splitting events and even pairs of comets that share a common origin \citep{boehnhardt04}, there is no direct evidence of larger sets of JFCs sharing a single progenitor."273 This could be a selection ellect if the secondary nuclei produced by break-ups have shorter [ade times than the primary nucleus. (hereby becoming very diffieult to observe.," This could be a selection effect if the secondary nuclei produced by break-ups have shorter fade times than the primary nucleus, thereby becoming very difficult to observe."274 H could also be due to the small numbers of comets that have been extensively studied., It could also be due to the small numbers of comets that have been extensively studied.275 It also may be more difficult to trace back to break-ups that occurred earlier in a comet's history during encounters with planets other (han Jupiter., It also may be more difficult to trace back to break-ups that occurred earlier in a comet's history during encounters with planets other than Jupiter.276 A quantitative estimate of the elfect of tidal disruption on the supply rate of JFCs requires a careful calculation of the distribution of close encounter distances and knowledge of the physical strength. properties of the objects: we do not attempt such a calculation here., A quantitative estimate of the effect of tidal disruption on the supply rate of JFCs requires a careful calculation of the distribution of close encounter distances and knowledge of the physical strength properties of the objects; we do not attempt such a calculation here.277 For the purpose of illustration. we can estimate (he fraction of comets (hat are tidally disrupted as at least as large as (he Iraction of comets that will impact a giant planet during (heir liletimes: in order to break up. a comet must come within a lew planetary radii of the eiant planet (2).. so this is a reasonable approximation.," For the purpose of illustration, we can estimate the fraction of comets that are tidally disrupted as at least as large as the fraction of comets that will impact a giant planet during their lifetimes; in order to break up, a comet must come within a few planetary radii of the giant planet \citep{asphaug96}, so this is a reasonable approximation."278 ? estimate that of ecliptic comets will impact a giant planet., \citet{levison00} estimate that of ecliptic comets will impact a giant planet.279 Taking (he?) population estimate lor the scattered disk. the rate al which SDOs become JFCs. and the rate at which the JFCs need to be resupplied. the οἱ SDOs that experience tidal disruption would need to break into roughly 100—1000 fragments to account lor the discrepancy.," Taking the \citet{bernstein04} population estimate for the scattered disk, the rate at which SDOs become JFCs, and the rate at which the JFCs need to be resupplied, the of SDOs that experience tidal disruption would need to break into roughly $100-1000$ fragments to account for the discrepancy."280 A population that could offer elues about the efficiency of break-up events. and thus if the rate and extent of tidal disruption comes close to the required limit estimated above. is the Centaur population.," A population that could offer clues about the efficiency of break-up events, and thus if the rate and extent of tidal disruption comes close to the required limit estimated above, is the Centaur population."281 During their dynamical lifetime. Centaurs suffer many close encounters with the four outer planets.," During their dynamical lifetime, Centaurs suffer many close encounters with the four outer planets."282 ? analvzed the orbital evolution of 53 observed Centaurs and reported a total of ~8000 close planetary encounters over the dvnoamical lifetimes of the 53 objects., \citet{tiscareno03} analyzed the orbital evolution of 53 observed Centaurs and reported a total of $\sim 8000$ close planetary encounters over the dynamical lifetimes of the 53 objects.283 They also report that (422)% of their objects impacted a planet. which is in agreement with the ? estimate.," They also report that $(4\pm2)\%$ of their objects impacted a planet, which is in agreement with the \citet{levison00} estimate."284 If tidal break-up occurs lor a sienilicant Iraction of the Centaurs. then there are (wo ellects on the Centaur population: their numbers would be greater (han expected Irom the steady state dynamical models. ancl the size distribution of Centaurs would be steeper than the SDO source (having relatively larger number of small objects).," If tidal break-up occurs for a significant fraction of the Centaurs, then there are two effects on the Centaur population: their numbers would be greater than expected from the steady state dynamical models, and the size distribution of Centaurs would be steeper than the SDO source (having relatively larger number of small objects)."285 At present. the data on the sizes and total population of Centamrs is very. limited due to a lack of well-characterized surveys sensitive to Centaur detection.," At present, the data on the sizes and total population of Centaurs is very limited due to a lack of well-characterized surveys sensitive to Centaur detection."286 The power law index ol the size distribution is estimated to be about —4for objects larger than D~100 km, The power law index of the size distribution is estimated to be about $-4$for objects larger than $D\sim100$ km287The analyzed sample cousists of the 717 Lymau-break galaxies with appareut magnitude in the fields 30321. 20002.CDFa. CDEb.DSF2237a. DSF2237b. HDF. Q0201. Q0256. Q0302. Q0933. Q1122. 58À22a. S8A92b. and Westphal whose spectroscopic redshifts were published by Steidel et al. (,"The analyzed sample consists of the 747 Lyman-break galaxies with apparent magnitude $23.5<{\cal R}<25.5$ in the fields 3c324, b20902, CDFa, CDFb, DSF2237a, DSF2237b, HDF, Q0201, Q0256, Q0302, Q0933, Q1422, SSA22a, SSA22b, and Westphal whose spectroscopic redshifts were published by Steidel et al. ("2882003).,2003).289" The size of the observed fields varied butwas typically 9x9"".", The size of the observed fields varied butwas typically $9'\times 9'$.290 I caleulated the observed inunber of pairs with comoving radial separation Z«20f| Mpe in each field individually., I calculated the observed number of pairs with comoving radial separation $Z<20h^{-1}$ Mpc in each field individually.291 Sumaiuesover all fields. a total of Πως=2539 pairs were found with comoving racial separations in this range.," Summing over all fields, a total of $n_{\rm obs}=2539$ pairs were found with comoving radial separations in this range."292 Since the Lyimau-break techuiqueT selects galaxies over a broad rauge of redshifts 23 5023.7. Lapproximated the selection function P(2) as a Gaussian withmean redshift jj=3.0 and standard deviation o4= 0.1.," Since the Lyman-break technique selects galaxies over a broad range of redshifts $2.3\simlt z\simlt 3.7$ , I approximated the selection function $P(z)$ as a Gaussian with mean redshift $\mu=3.0$ and standard deviation $\sigma_{\rm sel}=0.4$ ."293 To calculate the expected utmmber of pairs with Z<20h+ Mpe iu the th field for a eiven value of ry. E iuserted this selection function into equation 1.. asstumect a correlation function slope of +=1.6. aud integrated nunerically over the fields solid augle 2.," To calculate the expected number of pairs with $Z<20h^{-1}$ Mpc in the $i$ th field for a given value of $r_0$, I inserted this selection function into equation \ref{eq:blain}, assumed a correlation function slope of $\gamma=1.6$, and integrated numerically over the field's solid angle $\Omega$."294 ] set the expected total number of pais Hosp(rg) equal to the stun of the expected nunber for each individual field., I set the expected total number of pairs $n_{\rm exp}(r_0)$ equal to the sum of the expected number for each individual field.295 A value of ry=11.6os1 Alpe was required for Nesp to equal ype. while ry=10.59| Mpe made àxp=Mobs—Hu. and ry=11.334.1 Mpe mace Nesp=obs+Hus> ," A value of $r_0=11.08h^{-1}$ Mpc was required for $n_{\rm exp}$ to equal $n_{\rm obs}$, while $r_0=10.82h^{-1}$ Mpc made $n_{\rm exp}=n_{\rm obs}-n^{1/2}_{\rm obs}$ and $r_0=11.33h^{-1}$ Mpc made $n_{\rm exp}=n_{\rm obs}+n^{1/2}_{\rm obs}$ ."296conclude that the correlation length. for Lyman-break galaxies is rp=11.1£0.25+ Mpe at the lo level., I conclude that the correlation length for Lyman-break galaxies is $r_0=11.1\pm 0.25h^{-1}$ Mpc at the $1\sigma$ level.297 As noted in the abstract. this estimate of ry is roughly 200 away from the value of Mpe measured by Adelberger et al. (," As noted in the abstract, this estimate of $r_0$ is roughly $\sigma$ away from the value of $r_0\simeq 4.0\pm 0.6h^{-1}$ Mpc measured by Adelberger et al. ("2982001).,2004).299 What went wrong?, What went wrong?300 Most of the error in the previous sections estimate of ri came from the inaccurate model of the redshift selection function., Most of the error in the previous section's estimate of $r_0$ came from the inaccurate model of the redshift selection function.301 Although it is not always acknowlecleed in analyses of this sort. asstuuuptious about the selection function have a critical effect on the results.," Although it is not always acknowledged in analyses of this sort, assumptions about the selection function have a critical effect on the results."302" Figure 1. shows tliat in the example of 2 the best-fit value of ri changes by more than an order of maguitude as the assumed width of the Catssian selection fuuction iucreases [rom OQ,=0.2 to o4= 0.5."," Figure \ref{fig:r0_vs_sigsel} shows that in the example of \ref{sec:awry}303 the best-fit value of $r_0$ changes by more than an order of magnitude as the assumed width of the Gaussian selection function increases from $\sigma_{\rm sel}=0.2$ to $\sigma_{\rm sel}=0.5$ ."304" If we had adopted the correct width o,—0.3 CAdelberger et al.", If we had adopted the correct width $\sigma_{\rm sel}=0.3$ (Adelberger et al.305" 2001) instead of oy0.1. we would have found ry=7.2 instead of ry=11.14! Mpe—siguilicautly closer to the true value ryLh! Νερο, "," 2004) instead of $\sigma_{\rm sel}=0.4$, we would have found $r_0=7.2$ instead of $r_0=11.1 h^{-1}$ Mpc—significantly closer to the true value $r_0\sim 4 h^{-1}$ Mpc."306Unfortunately analyses similar to the one in 2 are usually attempted when the sample size is extremely small. too small for 6544 to be determined empirically.," Unfortunately analyses similar to the one in \ref{sec:awry} are usually attempted when the sample size is extremely small, too small for $\sigma_{\rm sel}$ to be determined empirically."307 La this case it is difficult to kuow which to adopt among the possible values of rj suggested by plots similar toFigure 1.., In this case it is difficult to know which to adopt among the possible values of $r_0$ suggested by plots similar toFigure \ref{fig:r0_vs_sigsel}. .308 Although theoretical arguments mayprovide a reasonableestimate of the selection-Dunction shape. it seems sensible to reduce as far as possible tledepeudence of the auswer ou the asstuned shape.," Although theoretical arguments mayprovide a reasonableestimate of the selection-function shape, it seems sensible to reduce as far as possible thedependence of the answer on the assumed shape."309 Approximating the selection fuuction as a boxear with halfwidth L. equation 1 can be," Approximating the selection function as a boxcar with half-width$L$ , equation \ref{eq:blain} can be"310A precise observational characterization of the thermal structure of the intra-cluster medium (ICM) is of crucial relevance for at least two reasons.,A precise observational characterization of the thermal structure of the intra–cluster medium (ICM) is of crucial relevance for at least two reasons.311 On one hand. the ICM thermodynamics is determined not only by the gravitational accretion of gas into the dark matter (DM) potential. wells forming clusters. but also by energy feedback processes (.e.. from supernova explosions and active galactic nuclei). which took place during the cosmic history of the cluster assembly.," On one hand, the ICM thermodynamics is determined not only by the gravitational accretion of gas into the dark matter (DM) potential wells forming clusters, but also by energy feedback processes (i.e., from supernova explosions and active galactic nuclei), which took place during the cosmic history of the cluster assembly."312 On the other hand. a precise characterization of the temperature structure of clusters is highly relevant to infer the cluster masses. under the assumption of hydrostatic equilibrium. and. therefore. to calibrate clusters as precision tools for cosmological applications reviews).," On the other hand, a precise characterization of the temperature structure of clusters is highly relevant to infer the cluster masses, under the assumption of hydrostatic equilibrium, and, therefore, to calibrate clusters as precision tools for cosmological applications \citep[e.g., ][for313reviews]{2002ARA&A..40..539R,2005RvMP...77..207V,2006astro.ph..5575B}. ."314Wolf-ltavet stars are surrounded by dense. stellar winds eiving rise to [rec-[ree emission extending from LR. to racio wavelengths.,Wolf-Rayet stars are surrounded by dense stellar winds giving rise to free-free emission extending from IR to radio wavelengths.315" ""vpicallv. this emission is characterised hy a power-law spectrum of the form S;xοὖν with values of he spectral index à~[0.7|0.8. ancl radio brightness emperatures —107 dx. AX. small number of WIL stars rave radio emission that exhibits quite dillerent. properties: negative spectral indices ancl brightness temperatures ~10"" Ix or higher. properties that are characteristic of non-hermal emission."," Typically, this emission is characterised by a power-law spectrum of the form $S_\nu\propto \nu^{\alpha}$, with values of the spectral index $\alpha316\sim +0.7-+0.8$, and radio brightness temperatures $\sim10^4$ K. A small number of WR stars have radio emission that exhibits quite different properties: negative spectral indices and brightness temperatures $\sim10^6$ K or higher, properties that are characteristic of non-thermal emission."317 W1t1146 is a member of this group. which includes W1t1125. 1140 and. WIULI4T.," 146 is a member of this group, which includes 125, 140 and 147."318 The radio emission from WILII46 was first. resolved in high resolution observations with ALERLIN (Dougherty et al., The radio emission from 146 was first resolved in high resolution observations with MERLIN (Dougherty et al.319 1996. hereafter Paper D).," 1996, hereafter Paper I)."320 These 5-GllIz observations revealed. two components. Nz and $5. separated by ~120 milli-arcseconds. (mas).," These 5-GHz observations revealed two components, $_5$ and $_5$, separated by $\sim120$ milli-arcseconds (mas)."321 The [lux of Sz; was consistent with that estimated. from extrapolation of the Et-millimetre spectrum arising from the free-free emitting envelope around the WR. star., The flux of $_5$ was consistent with that estimated from extrapolation of the IR-millimetre spectrum arising from the free-free emitting envelope around the WR star.322 Ehe brightness temperature of Nz (~Lo? ly) identified the nature of the emission from this component as non-thermal., The brightness temperature of $_5$ $\sim10^6$ K) identified the nature of the emission from this component as non-thermal.323 An optical spectrum. showed evidence for absorption lines at. H9. and H5. which we attributed to an earlv-type companion to the WR star.," An optical spectrum showed evidence for absorption lines at $\delta$ and $\gamma$, which we attributed to an early-type companion to the WR star."324 Fhis led us to hypothesize in Paper E that the non-thermal emission arose from a population of relativistic electrons. accelerated in a wind-wind collision region where the wind of the Wh star and the companion interacted (e.g. Eichler Usov 1993).," This led us to hypothesize in Paper I that the non-thermal emission arose from a population of relativistic electrons, accelerated in a wind-wind collision region where the wind of the WR star and the companion interacted (e.g. Eichler Usov 1993)."325 To be consistent with such a model. we suggested the companion lay at the same position angle as Nz from S5. but slightly further away from the WR. star.," To be consistent with such a model, we suggested the companion lay at the same position angle as $_5$ from $_5$, but slightly further away from the WR star."326 The presence of a companion was confirmed in optical imaging with the Hubble Space Telescope (LIST) by Niemela et al. (, The presence of a companion was confirmed in optical imaging with the Hubble Space Telescope (HST) by Niemela et al. (3271998).,1998).328 They. observed two stars. WRI4GA and DB (hereafter So and Neo respectively). at the same position angle as the radio sources but separated by ~168 mas.," They observed two stars, WR146A and B (hereafter $_{\rm O}$ and $_{\rm O}$ respectively), at the same position angle as the radio sources but separated by $\sim 168$ mas."329 Under the assumption that the southern sources in both the UST and ALERLIN images are coincident. these observations place the non-thermal source between the two stellar images. stronely supporting wind-wind collision as the origin of the non-thermal emission.," Under the assumption that the southern sources in both the HST and MERLIN images are coincident, these observations place the non-thermal source between the two stellar images, strongly supporting wind-wind collision as the origin of the non-thermal emission."330 Hs position relative to the two stellar components (120 mas from So anc ~ 48 mas from No) is where the dynamical pressure of the two stellar winds is balanced., Its position relative to the two stellar components $\sim 120$ mas from $_O$ and $\sim$ 48 mas from $_O$ ) is where the dynamical pressure of the two stellar winds is balanced.331 This indicates that the momentum of Sos stellar wind is  0.1 times that of No., This indicates that the momentum of $_O$ 's stellar wind is $\sim$ 0.1 times that of $_O$.332 With the wind velocity of the WC star in WILII46 (~ 2900 kms J|. Eenens Williams 1904) being greater than that of a tvpical OB star. and the expectation that the mass-Ioss rate of à WR star would be greater than that of an OD star. this strongly supports," With the wind velocity of the WC star in 146 $\sim$ 2900 km $^{-1}$, Eenens Williams 1994) being greater than that of a typical OB star, and the expectation that the mass-loss rate of a WR star would be greater than that of an OB star, this strongly supports"333setups. the ex205119 tite was 600 seconds per star. except lor the[aintest (V13) stars for which the exposure lies were Lucreasec to as much as 1800 seconds.,"setups, the exposure time was $600$ seconds per star, except for thefaintest $V>13$ ) stars for which the exposure times were increased to as much as 1800 seconds."334 Dala weὁ extracted usiug he FIGARO echelle software (Tomaney McCarliv. private comunuication).," Data were extracted using the FIGARO echelle software (Tomaney McCarthy, private communication)."335 Waveleneth calibration was determined from a κ)+)QO-secoucd exposu‘e of a luip take1 at the beeinnine of each night., Wavelength calibration was determined from a 300-second exposure of a Th-Ar lamp taken at the beginning of each night.336 After each observation of a target star. a short (15 SeCOILLC) exposure of the arc lamο was taken at the same telescope position in order to remove iustrumiental lexure.," After each observation of a target star, a short (45 second) exposure of the arc lamp was taken at the same telescope position in order to remove instrumental flexure."337 The spectra were not flux calibrated., The spectra were not flux calibrated.338 Racial velocities were cetermiued by cross-correlation against reference M. clwarls frou Marcy Beuitz (1989 - MBS9)., Radial velocities were determined by cross-correlation against reference M dwarfs from Marcy Benitz (1989 - MB89).339 The latter velocities are accurate to better than 0.23 |a factor of five higher than the accuracy of our own observations (as cliscussed further below).," The latter velocities are accurate to better than 0.23 $^{-1}$, a factor of five higher than the accuracy of our own observations (as discussed further below)."340 For tle bright. early M dwaTs CI1052 0.5) we usedte standard eclielle FIGARO cross-correlation progr:un.," For the bright, early M dwarfs $>0.5$ ) we used the standard echelle FIGARO cross-correlation program."341 Each order was Cor‘elaed with the velocity standards. auc the average racial velocity (rom all tje orders was determied.," Each order was correlated with the velocity standards, and the average radial velocity from all the orders was determined."342 The arc lamp exposres. taken acl]acent to each program star observatjon. were also cross-cor'elaed. providing a cor'ectiou for flexire.," The arc lamp exposures, taken adjacent to each program star observation, were also cross-correlated, providing a correction for flexure."343 Tils proc‘ectre did not provide retable velocities for faint. late-type M cdwarls.," This procedure did not provide reliable velocities for faint, late-type M dwarfs."344 The lower at bιο wavelengths le toa leher potentia for bias from the effects of telluric absorption aud wight sk vliies., The lower signal-to-noise at blue wavelengths led to a higher potential for bias from the effects of telluric absorption and night sky lines.345 We were able ο obtain reasonable results for those stars by individually computing YOss-correlatio1 for each order aud comjniug those measwenueuts to find the inedian racli: ocity., We were able to obtain reasonable results for those stars by individually computing the cross-correlation for each order and combining those measurements to find the median radial velocity.346 This procedu‘e was used for all stars with TiOS<0.5», This procedure was used for all stars with $\le 0.5$.347 Figure 1. plots the rius cispersi yout the mean racia| velocity for all M «warls with at leas [our measurements., Figure \ref{fig-sigmav} plots the rms dispersion about the mean radial velocity for all M dwarfs with at least four measurements.348 The clistribijon suggests a typical internal accuracy of z5 1.5 , The distribution suggests a typical internal accuracy of $\lesssim$ 1.5 $^{-1}$.349We cat determie our external errors by comparisoi with previous hieh accuracy velocity stuclies of Ν dwarls., We can determine our external errors by comparison with previous high accuracy velocity studies of M dwarfs.350" The resdts are shown in Table 1.. where o,,y is the forial tcertainty of the reference sauple."," The results are shown in Table \ref{table-vcomp}, where $\sigma_{ref}$ is the formal uncertainty of the reference sample."351 We lote hat a comparison jetween Tokoviniu(1988.1992) ane 1950 (13 stars) eives an rms of only. Q.16 ? but a mean difference of 0.78 +. consistent. with the ollset derived Grom our obse‘vations. which are tied to the MBS89 system.," We note that a comparison between \citet{toko88,toko92} and MB89 (13 stars) gives an rms of only $0.46$ $^{-1}$ but a mean difference of 0.78 $^{-1}$, consistent with the offset derived from our observations, which are tied to the MB89 system."352 Similarly. adopt a velocity of LLL ! for the velocity standard GL 526. while MBS0) measure a velocity of 15.7 for his star.," Similarly, \citet{sh86} adopt a velocity of 14.1 $^{-1}$ for the velocity standard Gl 526, while MB89 measure a velocity of 15.7 $^{-1}$ for this star."353 Agai1. (die. olfset Is Cousistent with our meas'ement.," Again, the offset is consistent with our measurement."354" Finally. we list two comparlsous wiitt the recent ¢)bse‘vatious by Dellosse (1998) sitce the dominant contribution to the resicdtts comes [TrOld hree stars: Gl 206 (Vp,;2S.Okims bs 1). G165-008 (8.0: .N= —15.5) and GI 268.3B. (-6.0: .N= —8.1)."," Finally, we list two comparisons with the recent observations by Delfosse (1998) since the dominant contribution to the residuals comes from three stars: Gl 206 $_{Del} = 8.0$ $^{-1}$; $\Delta=V_{P60}-V_{Del}=9.2$ $^{-1}$ ), G165-008 (8.0; $\Delta=-15.5$ ) and Gl 268.3B (-6.0; $\Delta=-8.4$ )."355 All three stars are kiOWL binaries. while (165-008 is also a very rapid rotator (see further below).," All three stars are known binaries, while G165-008 is also a very rapid rotator (see further below)."356 In general. the compa‘TSO indicates that the velocities derived from our echelle spectra are accurate to 6«1.5 ," In general, the comparison indicates that the velocities derived from our echelle spectra are accurate to $\sigma < 1.5$ $^{-1}$ ."357We cau also examine the quality of the radial velocities [ound [rom our previous moderate resolution spectra., We can also examine the quality of the radial velocities found from our previous moderate resolution spectra.358 Based ou au external comparison with the MBS89 staucards. we estimated au," Based on an external comparison with the MB89 standards, we estimated an"359the ionization. time scales were slightly below equilibrium ionization conditions and there are indications for higher than solar abundances of S. Si. Fe and Ni.,"the ionization time scales were slightly below equilibrium ionization conditions and there are indications for higher than solar abundances of S, Si, Fe and Ni."360 In the fits with simple continuum models the values for the galactic absorption turned out to be Ny~0.5x107 em. ie.. smaller than the values found for itself perIl. Brinkmann et al.," In the fits with simple continuum models the values for the galactic absorption turned out to be $_{\rm H} \sim 0.5\times10^{22}$ $^{-2}$, i.e., smaller than the values found for itself I, Brinkmann et al."361 2005)., 2005).362 This extra absorption towards the central source might quite well be related to the “equatorial ruff” detected in the radio band (Blundell 2001)., This extra absorption towards the central source might quite well be related to the “equatorial ruff” detected in the radio band (Blundell 2001).363 However. if we add a low energy thermal model to the power law. the fitted absorption can reach values Ny~1077 em. similar to those of itself.," However, if we add a low energy thermal model to the power law, the fitted absorption can reach values $_{\rm H} \sim 10^{22}$ $^{-2}$, similar to those of itself."364 The exact value depends on the complex interplay between the normalization of a soft thermal model and the absorption in à relatively narrow soft energy band., The exact value depends on the complex interplay between the normalization of a soft thermal model and the absorption in a relatively narrow soft energy band.365 It is further affected by the choice of the background and partly on the instrument under discussion., It is further affected by the choice of the background and partly on the instrument under discussion.366 For both pointings we tried spectral fits to the regions away from the prominent features: te.. where the jet enters the field of view from the right of reffig:jetl-s-h.. and at east (left in reffig:rgb2)) of the ring-like terminal shock.," For both pointings we tried spectral fits to the regions away from the prominent features; i.e., where the jet enters the field of view from the right of \\ref{fig:jet1-s-h}, , and at east (left in \\ref{fig:rgb2}) ) of the ring-like terminal shock."367 For the latter the signal is very low but both a power law and thermal emission are required by the data., For the latter the signal is very low but both a power law and thermal emission are required by the data.368 The contribution of the power law component is rather high which might be due to the fact that the extended source covers the projection of the whole final outer shock region of W50., The contribution of the power law component is rather high which might be due to the fact that the extended source covers the projection of the whole final outer shock region of W50.369 The spectrum of the jet. entering the field of view from the right in reffig;jetl-s-h. is predominantly of power law origin. similar to that of the bright lenticular region.," The spectrum of the jet, entering the field of view from the right in \\ref{fig:jet1-s-h} is predominantly of power law origin, similar to that of the bright lenticular region."370 The addition of a thermal model does not improve the fit significantly. but cannot be ruled out either.," The addition of a thermal model does not improve the fit significantly, but cannot be ruled out either."371 Compared to previous observations we have been able to better constrain the spectral parameters of the eastern Jet with these XMM-Newton observations., Compared to previous observations we have been able to better constrain the spectral parameters of the eastern jet with these XMM-Newton observations.372 Using the bright lenticular structure. for the parameter estimates. we find from the fits to the data a number density of the thermally radiating particles of 0.2. <n. $0.7 em™.," Using the bright lenticular structure for the parameter estimates, we find from the fits to the data a number density of the thermally radiating particles of 0.2 $\la {\rm n_e} \la $ 0.7 $^{-3}$."373 This. and the following estimates are based on the assumption of constant density in the emission regions.," This, and the following estimates are based on the assumption of constant density in the emission regions."374 Clumping of the gas will lead to a over-estimation of the electron densities and lower the required total mass and energy of the gas., Clumping of the gas will lead to a over-estimation of the electron densities and lower the required total mass and energy of the gas.375 Additionally. the total volume of the emission region might be larger by a factor of a few than the chosen extraction regions for the fits.," Additionally, the total volume of the emission region might be larger by a factor of a few than the chosen extraction regions for the fits."376 Assuming cosmic abundances this thermally radiating gas has a cooling time scale of ~10 yr., Assuming cosmic abundances this thermally radiating gas has a cooling time scale of $\sim 10^7$ yr.377" The ellipsoidal (in 2-dimensional projection lenticular) emission region has a volume of ~6.5x10°) en. containing 2x10?"" particles with a total thermal energy content of 5x10? erg."," The ellipsoidal (in 2-dimensional projection lenticular) emission region has a volume of $\sim 6.5\times10^{57}$ $^3$, containing $2\times10^{57}$ particles with a total thermal energy content of $\times10^{48}$ erg."378 The kinetic outflow energy of the jets of are of the order of 10°?—101° ss! following early estimates and the numerical modeling of the jet emission (for example1991.. Brinkmann Kawai 2000).," The kinetic outflow energy of the jets of are of the order of $^{39}-10^{40}$ $^{-1}$ following early estimates and the numerical modeling of the jet emission (for example, Brinkmann Kawai 2000)."379 With its known outflow velocity of ~0.26ce a jet thus supplies about £2x104 particles per second into the remnant., With its known outflow velocity of $\sim$ c a jet thus supplies about $\la 2\times10^{44}$ particles per second into the remnant.380 While the energy input from the jets over a life time of the system of ~5x10! vr is obviously far exceeding the thermal energy content of the gas the number of thermal particles in. the remnant must be supplied by other means., While the energy input from the jets over a life time of the system of $\sim 5\times10^4$ yr is obviously far exceeding the thermal energy content of the gas the number of thermal particles in the remnant must be supplied by other means.381 If the mass loss rate of the primary of the binary system. estimated to be 2-3x107 M. yyr! (Begelman 1980. Fuchs 2006) operates over the life time of the system a total number of ~2x10?? particles would have been injected into the remnant. fully sufficient to account for the density of thermal particles in W50.," If the mass loss rate of the primary of the binary system, estimated to be $2 - 3 \times 10^{-4}$ $_\odot$ $^{-1}$ (Begelman 1980, Fuchs 2006) operates over the life time of the system a total number of $\sim 2\times10^{59}$ particles would have been injected into the remnant, fully sufficient to account for the density of thermal particles in W50."382 Thus it seems that the gas mass in the remnant Is supplied by the wind from the binary system whereas the energy comes predominantly from the out-flowing Jets., Thus it seems that the gas mass in the remnant is supplied by the wind from the binary system whereas the energy comes predominantly from the out-flowing jets.383 The X-ray luminosities from the outer jets represent in any case only a small fraction of the available energy supply by 4433: the 0.5-10 keV luminosity in the power law component of the bright emission is Ly2x107 ss7!; the total lummosity of the soft thermal emission might be up to a factor of 2-3 higher., The X-ray luminosities from the outer jets represent in any case only a small fraction of the available energy supply by 433: the $-$ 10 keV luminosity in the power law component of the bright emission is $_{pl} \ma \ 2\times10^{34}$ $^{-1}$; the total luminosity of the soft thermal emission might be up to a factor of $-$ 3 higher.384 Even if the total emission region is a few times larger than the region extracted for the fits. the total luminosity amounts only to 107—107+ of the kinetic energy of the Jets.," Even if the total emission region is a few times larger than the region extracted for the fits, the total luminosity amounts only to $^{-5} - 10^{-4}$ of the kinetic energy of the jets."385 Assuming equipartition between the energy in the magnetic field and the relativistic electrons. the deduced luminosity of the power law emission yields an estimate for the magnetic field strength of B ~2—4x10°° G (Watson 1983. Yamauchi 1994).," Assuming equipartition between the energy in the magnetic field and the relativistic electrons, the deduced luminosity of the power law emission yields an estimate for the magnetic field strength of B $\sim 2 - 4 \times 10^{-6}$ G (Watson 1983, Yamauchi 1994)."386" The number density of the relativistic electrons is ~4x1077 σπα, the total energy content in the magnetic field and the electrons is ~107?—107 erg."," The number density of the relativistic electrons is $\sim 4\times10^{-14}$ $^{-3}$, the total energy content in the magnetic field and the electrons is $\sim 10^{45} - 10^{47}$ erg."387 Thus. the relativistic electrons as well represent only a small fraction of the kinetic energy deposited by the jets into the remnant over its estimated life time.," Thus, the relativistic electrons as well represent only a small fraction of the kinetic energy deposited by the jets into the remnant over its estimated life time."388 The most challenging physical question is how the directed kinetic energy of the jet is transferred to the relativistic electrons and then into radiation., The most challenging physical question is how the directed kinetic energy of the jet is transferred to the relativistic electrons and then into radiation.389" The simple picture of the jet being decelerated by the collistor with the supernova shell (Murata Shibazaki 1996. Velázzquez Raga 2000) can hold only for the terminal shock in the outermost eastern ""ear""."," The simple picture of the jet being decelerated by the collision with the supernova shell (Murata Shibazaki 1996, Velázzquez Raga 2000) can hold only for the terminal shock in the outermost eastern “ear”."390 Most of the emission. however. occurs further in. about aaremin away from $8433 and the X-ray intensity profile along the jet axis indicates a gradual growth of the energy transfer rate. starting at ~6x10!’ em from 4433.," Most of the emission, however, occurs further in, about arcmin away from SS433 and the X-ray intensity profile along the jet axis indicates a gradual growth of the energy transfer rate, starting at $\sim 6\times10^{19}$ cm from 433."391" If there the precessing jet would still follow an undisturbed ballistic motion it would have formed a conical spring with a separation of >10""? em between the turns which are only ~1.5x10"" cm thick.", If there the precessing jet would still follow an undisturbed ballistic motion it would have formed a conical spring with a separation of $\ma 10^{17}$ cm between the turns which are only $\sim 1.5\times10^{15}$ cm thick.392" The radius of the ""spring"" at this distance. from would be about 2.5x10'? em. which is ~53/5 at the distance of kkpe for 4433."," The radius of the “spring” at this distance from would be about $\times10^{19}$ cm, which is $\sim 5\farcm5$ at the distance of kpc for 433."393 This ts certainly not observed which means that up to this distance a re-collimation of the jet must have already taken place., This is certainly not observed which means that up to this distance a re-collimation of the jet must have already taken place.394" Further. early 3-dimensional hydrodynamical simulations of the precessing jet (Brinkmann Mülller 1998) showed that already at distances <10"" em the jet develops instabilities which lead to a dispersion of the matter of the ordered flow."," Further, early 3-dimensional hydrodynamical simulations of the precessing jet (Brinkmann Mülller 1998) showed that already at distances $\la 10^{17}$ cm the jet develops instabilities which lead to a dispersion of the matter of the ordered flow."395 If thus thematerial of the, If thus thematerial of the396The Galactic sample comprises results from both aand sstudies.,The Galactic sample comprises results from both and studies.397 We note that iis so far limited to studies of the visual spectral region — therefore iis the most important ddiagnosties — while ((also) uses the ultraviolet regime., We note that is so far limited to studies of the visual spectral region – therefore is the most important diagnostics – while (also) uses the ultraviolet regime.398 In the latter approach the UV lines are given more weight in the mass-loss determination., In the latter approach the UV lines are given more weight in the mass-loss determination.399 In the case of weak winds (x1077 Myr) the ddeterminations rely almost exclusively on fits to 411548.1551 (2)..," In the case of weak winds $\lesssim 10^{-7} \msunyr$ ) the determinations rely almost exclusively on fits to $\lambda\lambda 1548,1551$ \citep{martins05b}."400" Figure | shows good agreement between aand sstudies for relatively high luminosities (logL,/L.«> 5.5). consequently high wind densities."," Figure \ref{fig:wlr-gal} shows good agreement between and studies for relatively high luminosities $\log \lstar/\lsun401\gtrsim 5.5$ ), consequently high wind densities."402 For lower luminosities. the UV analyses of the dwarf sample studied by ? show a systematic discrepancy with the average relations.," For lower luminosities, the UV analyses of the dwarf sample studied by \cite{martins05b} show a systematic discrepancy with the average relations."403 This is emphasised by the grey dashed line. which shows the average relation for these objects.," This is emphasised by the grey dashed line, which shows the average relation for these objects."404 The fit coefficients of this latter relation are also listed in Tab., The fit coefficients of this latter relation are also listed in Tab.405 3 and clearly signal a discrepency between UV based mass-loss determinations and theoretical expectations., \ref{tab:wlr-par} and clearly signal a discrepency between UV based mass-loss determinations and theoretical expectations.406" This 1s referred to as the ""weak wind problem"" (seee.g. ?)..", This is referred to as the “weak wind problem” \citep[see e.g.][]{bouret03}.407 We will discuss this further in Sect. 8.1.., We will discuss this further in Sect. \ref{sec:weakwinds}.408" The studies from which we have drawn the LMC sample are those of 2.. 22., ? and ?.."," The studies from which we have drawn the LMC sample are those of \cite{crowther02}, \cite{massey04, massey05}, \cite{evans04b} and \cite{mokiem07}."409 In Tab., In Tab.410 A2. the relevant atmospheric parameters are listed., \ref{tab:wind_par_lmc} the relevant atmospheric parameters are listed.411 Note that some of the objects in. this table have been analysed in more than one study., Note that some of the objects in this table have been analysed in more than one study.412 In those cases we adopted the results from studies using the automated fitting procedure developed by ?.., In those cases we adopted the results from studies using the automated fitting procedure developed by \cite{mokiem05}.413 If these were not available we preferred results from studies that used both the optical and UV spectral range over results that consider only the optical regime., If these were not available we preferred results from studies that used both the optical and UV spectral range over results that consider only the optical regime.414 For à number of stars analysed by ?.. no UV measurement of the wind velocity was available.," For a number of stars analysed by \cite{mokiem07}, no UV measurement of the wind velocity was available."415" Consequently. these authors estimated bby scaling the escape velocity at the stellar surface (0,9) with a constant factor of 2.6 (cf.?).."," Consequently, these authors estimated by scaling the escape velocity at the stellar surface ) with a constant factor of 2.6 \cite[cf.][]{lamers95}."416 To account for the metallicity dependence and to facilitate a comparison with theoretical predictions. we accordingly rescaled this uusing Eq.," To account for the metallicity dependence and to facilitate a comparison with theoretical predictions, we accordingly rescaled this using Eq."417 3 with Z=0.5Z. and n=0.13 (cf.2).," \ref{eq:vinf_z} with $Z = 0.5\,\zsun$ and $n = 0.13$ \citep[cf.][]{leitherer92}."418. In Tab., In Tab.419 A2 the rescaled values are given between brackets., \ref{tab:wind_par_lmc} the rescaled values are given between brackets.420 As aalso influences the density in the line forming region of wind sensitive lines (because of the requirement of mass continuity). also a resealing of wwas required.," As also influences the density in the line forming region of wind sensitive lines (because of the requirement of mass continuity), also a rescaling of was required."421 For this we used the wind-strength parameter that conserves the eequivalent width (?.. see also ? and ?).," For this we used the wind-strength parameter that conserves the equivalent width \citealt{schmutz89}, see also \citealt{puls96} and \citealt{dekoter97}) )."422 The combined effect of these re-scalings is a reduction of the modified-wind momentum by 0.08 dex., The combined effect of these re-scalings is a reduction of the modified-wind momentum by 0.08 dex.423 The distribution of the modified-wind momenta as a function of stellar luminosity for the LMC stars is shown in Fig., The distribution of the modified-wind momenta as a function of stellar luminosity for the LMC stars is shown in Fig.424 2 using the same symbols as in Fig. 1.., \ref{fig:wlr-lmc} using the same symbols as in Fig. \ref{fig:wlr-gal}.425 On the left-hand side of the figure we (again) only consider objects that have been analysed by ? using an automated fitting method., On the left-hand side of the figure we (again) only consider objects that have been analysed by \cite{mokiem07} using an automated fitting method.426The solid and dotted lines give the mean relations for uncorrected and clumping corrected rates.,The solid and dotted lines give the mean relations for uncorrected and clumping corrected rates.427 The correction applied was the, The correction applied was the428Dust lane early-type galaxies are those galaxies classified in Galaxy Zoo as earlv-tvpe. galaxies with dust. lane features.,Dust lane early-type galaxies are those galaxies classified in Galaxy Zoo as early-type galaxies with dust lane features.429 The classification procedure. and: construction of the dust lane sample are described in detail in a companion paper. L).," The classification procedure and construction of the dust lane sample are described in detail in a companion paper, ."430. In that paper. we showed that dust. lane early-type galaxies often exhibit: morphological disturbances. show signs of recent star formation and have stellar ages that are older than starburst carly types. but vounger than the overall early-tvpe population.," In that paper, we showed that dust lane early-type galaxies often exhibit morphological disturbances, show signs of recent star formation and have stellar ages that are older than starburst early types, but younger than the overall early-type population."431 We therefore argued that. these objects are starburst systems. and suggested that they might. arise from gas-rich minor mergers.," We therefore argued that these objects are starburst systems, and suggested that they might arise from gas-rich minor mergers."432 While intergalactic medium accretion is also a plausible mechanism. we ruled it out in this case due to the presence of large amounts of dust. and the disturbed: nature of most galaxies.," While intergalactic medium accretion is also a plausible mechanism, we ruled it out in this case due to the presence of large amounts of dust, and the disturbed nature of most galaxies."433be verified according to the linear instability growth theory.,be verified according to the linear instability growth theory.434 We use τι to denote the sound crossing time for the initial state., We use $\tau_s$ to denote the sound crossing time for the initial state.435 Figure 11. shows the time evolution of the field lines αἱ various stages in our MTI simulation., Figure \ref{fig11} shows the time evolution of the field lines at various stages in our MTI simulation.436 We study the AIT] growth rate by considering the acceleration of the fluid elements., We study the MTI growth rate by considering the acceleration of the fluid elements.437 The mean speed on the v direction for the f[Iuid should follow the exponential growth: where Όρος is the strength of the initial velocity perturbation applied. + denotes the growth rate in the linear regime.," The mean speed on the y direction for the fluid should follow the exponential growth: where $v_{per}$ is the strength of the initial velocity perturbation applied, $\gamma$ denotes the growth rate in the linear regime."438" We obtain the growth rate 5 by plotting Ino, against the evolution time and then measuring the local slope through a certain time span."," We obtain the growth rate $\gamma$ by plotting $\ln\,v_y$ against the evolution time and then measuring the local slope through a certain time span."439" The Inve, vs | curve is plotted in Figure 12((a). which shows a nice linear relation."," The $\ln\,v_y$ vs $t$ curve is plotted in Figure \ref{fig12}( (a), which shows a nice linear relation."440 We plot the growth rate against evolution time., We plot the growth rate against evolution time.441 It should be stable around the theoretical value 0.4 initially and then decrease sharply due to the nonlinear effect., It should be stable around the theoretical value $0.4$ initially and then decrease sharply due to the nonlinear effect.442 Figure 12((b)., Figure \ref{fig12}( (b).443 shows that the simulation meels our expectation Laily well., shows that the simulation meets our expectation fairly well.444 We also look at the energy. evolution in the linear regime., We also look at the energy evolution in the linear regime.445 The mean kinetic energy should first stay stable aud (hen enter into an exponential growing phase until it hits a cap al around /=200 which denotes the starting of the nonlinear phase., The mean kinetic energy should first stay stable and then enter into an exponential growing phase until it hits a cap at around $t=200$ which denotes the starting of the nonlinear phase.446 The evolution of magnetic energy should follow similar pattern as to the kinetic energv evolution. but lagged behind.," The evolution of magnetic energy should follow similar pattern as to the kinetic energy evolution, but lagged behind."447 In Figure 13.. we plot the time evolution of (he mean kinetic and magnetic energy evolutions.," In Figure \ref{fig13}, we plot the time evolution of the mean kinetic and magnetic energy evolutions."448 The results confirms the physical intuition «quite well., The results confirms the physical intuition quite well.449"transitions from the ground state to excited states of Ay and B, symmetry are dipole-allowed.",transitions from the ground state to excited states of $_{\text{u}}$ and $_{\text{u}}$ symmetry are dipole-allowed.450" For wavelengths shorter than 500 nm, the electronic excitation schemes of the various transitions are very similar for the neutral and the cation."," For wavelengths shorter than 500 nm, the electronic excitation schemes of the various transitions are very similar for the neutral and the cation."451 Computational differences mainly arise from the broader cation bands which are caused by the convolution procedure and the fact that the cation has several low-energy transitions unlike the neutral molecule., Computational differences mainly arise from the broader cation bands which are caused by the convolution procedure and the fact that the cation has several low-energy transitions unlike the neutral molecule.452" Above 500 nm the theoretical spectrum of the DBR cation is dominated by weak transitions where electrons are promoted to the semi-occupied orbital, e.g., Ds(Bu)-Do(B,z) at 673 nm, De(Bu)<-Do(Bz) at 613 nm, Ώε(Βι1) —Do(Bg) at 567 nm, and D1o(B&)-—Do(Bg) at 540 nm."," Above 500 nm the theoretical spectrum of the DBR cation is dominated by weak transitions where electrons are promoted to the semi-occupied orbital, e.g., $_5$ $_{\text{u}}$ $\leftarrow$ $_0$ $_{\text{g}}$ ) at 673 nm, $_6$ $_{\text{u}}$ $\leftarrow$ $_0$ $_{\text{g}}$ ) at 613 nm, $_8$ $_{\text{u}}$ $\leftarrow$ $_0$ $_{\text{g}}$ ) at 567 nm, and $_{10}$ $_{\text{u}}$ $\leftarrow$ $_0$ $_{\text{g}}$ ) at 540 nm."453" Two further dipole-allowed (B,) and two dipole-forbidden (Ag) transitions are predicted beyond 900 nm, outside of the accessible scanning range."," Two further dipole-allowed $_{\text{u}}$ ) and two dipole-forbidden $_{\text{g}}$ ) transitions are predicted beyond 900 nm, outside of the accessible scanning range."454 The symmetry-related selection rules that apply to the anion are somewhat different., The symmetry-related selection rules that apply to the anion are somewhat different.455" Due to its ground state, dipole-allowed transitions are only possible to Ag and Bg states."," Due to its ground state, dipole-allowed transitions are only possible to $_{\text{g}}$ and $_{\text{g}}$ states."456" Therefore, its calculated spectrum deviates more strongly from the spectra of the other two species."," Therefore, its calculated spectrum deviates more strongly from the spectra of the other two species."457" In view of the experimental spectrum of ionized DBR and the lack of strong absorption bands beyond 600 nm, we conclude that much less anions were formed than cations and we ascribe the measured spectrum solely to the DBR cation."," In view of the experimental spectrum of ionized DBR and the lack of strong absorption bands beyond 600 nm, we conclude that much less anions were formed than cations and we ascribe the measured spectrum solely to the DBR cation."458" Except for a sometimes wrong ordering of states, it can be seen that the applied TD-DFT method works fairly well in the case of the neutral molecule."," Except for a sometimes wrong ordering of states, it can be seen that the applied TD-DFT method works fairly well in the case of the neutral molecule."459" The transition, for instance, is predicted at 536 nm, while $1(B4)-So(Ag)the origin band is actually measured at 540 nm."," The $_{1}$ $_{\text{u}}$ $\leftarrow$ $_0$ $_{\text{g}}$ ) transition, for instance, is predicted at 536 nm, while the origin band is actually measured at 540 nm."460" Two close-lying bands, 52(By)<-So(Ag) and S4(B4)«—So(Ag), are calculated to be at 448 and 427 nm."," Two close-lying bands, $_{2}$ $_{\text{u}}$ $\leftarrow$ $_0$ $_{\text{g}}$ ) and $_{4}$ $_{\text{u}}$ $\leftarrow$ $_0$ $_{\text{g}}$ ), are calculated to be at 448 and 427 nm."461" The weaker one at 448 nm ($5), with observed origin at 434 nm, is responsible for the vibrational pattern on top of the broad band that can be seen in the experimental spectrum between(S4) 360 and 440 nm."," The weaker one at 448 nm $_{2}$ ), with observed origin at 434 nm, is responsible for the vibrational pattern on top of the broad band $_{4}$ ) that can be seen in the experimental spectrum between 360 and 440 nm."462" These two bands have their counterparts with similar band positions and strengths in the cationic molecule, where they appear broader and slightly red-shifted in the measurement."," These two bands have their counterparts with similar band positions and strengths in the cationic molecule, where they appear broader and slightly red-shifted in the measurement."463" To the red of these two bands, two weak and broad features (marked with * and **) are observed around 620 and 690 nmwhich could correspond to the Όιρς-Ὀρ and DgD. transitions."," To the red of these two bands, two weak and broad features (marked with $^{*}$ and $^{**}$ ) are observed around 620 and 690 nmwhich could correspond to the $_{10}$$\leftarrow$ $_0$ and $_{6}$$\leftarrow$ $_0$ transitions."464" In the wavelength range between 340 and 200 nm, more than 100 single electronic transitions are predicted by TD-DFT for the cation."," In the wavelength range between 340 and 200 nm, more than 100 single electronic transitions are predicted by TD-DFT for the cation."465 Roughly 45 of them have non-zero oscillator strengths and actually contribute to the observed broad a — 7«* structure peaking at ca., Roughly 45 of them have non-zero oscillator strengths and actually contribute to the observed broad $\pi$ – $\pi^{*}$ structure peaking at ca.466 215 nm., 215 nm.467" Except for minor peak shifts, this band system resembles a broadened version of the analogous a — 7* structure of the neutral precursor which essentially can be explained by similar excitation schemes of electronic C-type transitions for both molecules."," Except for minor peak shifts, this band system resembles a broadened version of the analogous $\pi$ – $\pi^{*}$ structure of the neutral precursor which essentially can be explained by similar excitation schemes of electronic C-type transitions for both molecules."468" Because of a stronger broadening for all UV bands, the bump peaking at 215 nm appears even more pronounced for the cation compared to the neutral."," Because of a stronger broadening for all UV bands, the bump peaking at 215 nm appears even more pronounced for the cation compared to the neutral."469 The spectroscopy of matrix-isolated neutral HBC is discussed in detail elsewhere ∙∙, The spectroscopy of matrix-isolated neutral HBC is discussed in detail elsewhere \citep{rouille09}.470" Because of its all-benzenoid structure, it is believed that HBC is more abundant in space compared to other similarly-sized PAHs (Troy&Schmidt|2006)."," Because of its all-benzenoid structure, it is believed that HBC is more abundant in space compared to other similarly-sized PAHs \citep{troy06}."471". The calculated spectrum of neutral HBC, obtained at the B3LYP / 6-31+G(d) level of theory, reveals a good match with the MIS measurements (see Figure |5)), both in terms of relative band strengths and positions."," The calculated spectrum of neutral HBC, obtained at the B3LYP / 6-31+G(d) level of theory, reveals a good match with the MIS measurements (see Figure \ref{fig4}) ), both in terms of relative band strengths and positions."472 Neutral HBC has a Dey ground state geometry., Neutral HBC has a $_{6\text{h}}$ ground state geometry.473" The intensity of its S4(E1y)<-So(Azg) transition, calculated to be at 364 nm, is actually distributed over a complicated vibrational pattern that involves a44 modes of vibration and vibrational excitations belonging to an energetically lower Bj, state, to which electronic transitions from the ground state are dipole-forbidden."," The intensity of its $_{4}$ $_{\text{1u}}$ $\leftarrow$ $_0$ $_{\text{1g}}$ ) transition, calculated to be at 364 nm, is actually distributed over a complicated vibrational pattern that involves $_{\text{1g}}$ modes of vibration and vibrational excitations belonging to an energetically lower $_{\text{1u}}$ state, to which electronic transitions from the ground state are dipole-forbidden."474" Also the weak transition, for which a peak of an undefined Si(Bou)+-So(Aig)vibrationally excited state has been measured at 434 nm, borrows some intensity from the S4(E1u) state. ("," Also the weak $_{1}$ $_{\text{2u}}$ $\leftarrow$ $_0$ $_{\text{1g}}$ ) transition, for which a peak of an undefined vibrationally excited state has been measured at 434 nm, borrows some intensity from the $_4$ $_{\text{1u}}$ ) state. ("475"Actually, the Ej, state could also be S3.","Actually, the $_{\text{1u}}$ state could also be $_{3}$."476" For details, see (2009)..)"," For details, see \citet{rouille09}. .)"477" Quite well reproduced by the calculation, further strong bands are located around 217.5 nm."," Quite well reproduced by the calculation, further strong bands are located around 217.5 nm."478 The spectroscopic interpretation of the spectrum of ionized HBC in solid Ne is more complicated., The spectroscopic interpretation of the spectrum of ionized HBC in solid Ne is more complicated.479" The degenerate ground states of the HBC cation and anion cause Jahn-Teller interaction, which effectively leads to a reduction of the ground state geometry from Da, to Don."," The degenerate ground states of the HBC cation and anion cause Jahn-Teller interaction, which effectively leads to a reduction of the ground state geometry from $_{6\text{h}}$ to $_{2\text{h}}$ ."480 This also complicates the assignment of measured absorption bands on the basis of DFT calculations as these methods can already fail to correctly predict the, This also complicates the assignment of measured absorption bands on the basis of DFT calculations as these methods can already fail to correctly predict the481recombination. perturbations of all scales are amplified. by gravity at an identical rate whilst. Linear theory. applies.,"recombination, perturbations of all scales are amplified by gravity at an identical rate whilst linear theory applies."482 This growth rate depends on the matter and dark energy components which drive the cosmic expansion HlIleath 1977: Hamilton 2001: Linder Jenkins 2003: Percival 2005)., This growth rate depends on the matter and dark energy components which drive the cosmic expansion Heath 1977; Hamilton 2001; Linder Jenkins 2003; Percival 2005).483 The growth of fluctuations enters a non-linear regime at progressively larger scales at lower redshifts: in today’s Universe. only perturbations with Fourier wavescales 0.15 Alpe+ evolve linearly to a good approximation Ssmith et 22003: Jeong Ixomatsu. 2006: McDonald 2007).," The growth of fluctuations enters a non-linear regime at progressively larger scales at lower redshifts: in today's Universe, only perturbations with Fourier wavescales $k < 0.1 \, h$ $^{-1}$ evolve linearly to a good approximation Smith et 2003; Jeong Komatsu 2006; McDonald 2007)."484 The clustering pattern of galaxies at different recishifts is related to the underlving density Uuctuations and may be used to test this model of structure formation., The clustering pattern of galaxies at different redshifts is related to the underlying density fluctuations and may be used to test this model of structure formation.485 The shape of the clustering power spectrum the relative amplitudes of large-scale ancl small-scale modes. depends on the composition of the early Universe and may. be used to extract information about the matter and. baryon fractions PLeemark et 22004a: Cole et 22005: Percival ct 220075)., The shape of the clustering power spectrum – the relative amplitudes of large-scale and small-scale modes – depends on the composition of the early Universe and may be used to extract information about the matter and baryon fractions Tegmark et 2004a; Cole et 2005; Percival et 2007b).486 The amplitude of the clustering power spectrum as a function. of redshift. together. with the pattern of redshift-space distortions induced. hy galaxy peculiar velocities. can be used to measure the growth rate of structure Ullamilton 1992: Hawkins et 22003: Guzzo ct lesOS: nmePercival White 2009).," The amplitude of the clustering power spectrum as a function of redshift, together with the pattern of redshift-space distortions induced by galaxy peculiar velocities, can be used to measure the growth rate of structure Hamilton 1992; Hawkins et 2003; Guzzo et 2008; Percival White 2009)."487 Lligher-order or topological ors of the density field. such as the hispeetrum or genus. can be applied: to test whether the initial conditions are consistent with scale-invariant Gaussian random perturbations generated by inflation GGott. Dickinson Alelott 1986: bry Scherrer 1994: Sefusatti Ixomatsu 2007 :Janmies. Lewis Colless 2007).," Higher-order or topological descriptors of the density field, such as the bispectrum or genus, can be applied to test whether the initial conditions are consistent with scale-invariant Gaussian random perturbations generated by inflation Gott, Dickinson Melott 1986; Fry Scherrer 1994; Sefusatti Komatsu 2007; James, Lewis Colless 2007)."488 The interpretation of the shape and. amplitude of the galaxy power spectrum is complicated: by several factors., The interpretation of the shape and amplitude of the galaxy power spectrum is complicated by several factors.489" Firstly. the manner in which galaxies trace the density field the ""galaxy bias? is in general a complex function of scale. dark matter halo mass. galaxy. type and redshift (Dekel Lahay 1999: ‘Toemark Bromiley 1999:: Wd οἱ 22005: Conway et 22005: Percival et 22007a: Smith. Scoecimarro Sheth 2007: Cresswell Percival 2009)."," Firstly, the manner in which galaxies trace the density field – the “galaxy bias” – is in general a complex function of scale, dark matter halo mass, galaxy type and redshift (Dekel Lahav 1999; Tegmark Bromley 1999; Wild et 2005; Conway et 2005; Percival et 2007a; Smith, Scoccimarro Sheth 2007; Cresswell Percival 2009)."490 However. the bias of galaxy fluctuations on sulliciently large scales (&<O.1h J| at 2= 0) appears to he well-described. by a simple. constant. of proportionality. whose value depends on galaxy type and luminosity. or. more fundamentally dark matter halo mass (Peacock Dodds 1994: Scherrer. Weinbere LOOS: Verde et 22002).," However, the bias of galaxy fluctuations on sufficiently large scales $k < 0.1 \,491h$ $^{-1}$ at $z=0$ ) appears to be well-described by a simple constant of proportionality whose value depends on galaxy type and luminosity, or more fundamentally dark matter halo mass (Peacock Dodds 1994; Scherrer Weinberg 1998; Verde et 2002)."492 Secondly. small-scale density perturbations eventually begin to evolve in a non-linear fashion requiring more complex modelling techniques such as higher-order verturbation theory or numerical A’-body simulations (Smith ct 22003: Jeong IWomatsu 2006: MeDonald 2007).," Secondly, small-scale density perturbations eventually begin to evolve in a non-linear fashion requiring more complex modelling techniques such as higher-order perturbation theory or numerical $N$ -body simulations (Smith et 2003; Jeong Komatsu 2006; McDonald 2007)."493 TFhirdlv. there is a practical challenge of acquiring galaxy survey data across a “fair sample” of the Universe (Toemark 1997).," Thirdly, there is a practical challenge of acquiring galaxy survey data across a “fair sample” of the Universe (Tegmark 1997)."494" For the large-scale. linear moces of clustering. which provide the most robust link to undoerlving heory. this sample must map a volume of the order 1 Cpe? using of the order 10"" galaxies."," For the large-scale linear modes of clustering, which provide the most robust link to underlying theory, this sample must map a volume of the order 1 $^3$ using of the order $10^5$ galaxies."495 These demands require nmulti-vear campaigns with eround-based telescopes utilizing 1uncreds of clear nights (Glazebrook Blake 2005)., These demands require multi-year campaigns with ground-based telescopes utilizing hundreds of clear nights (Glazebrook Blake 2005).496 Despite these challenges. a series. of galaxy τούς surveys have been undertaken to provide such datasets at redshifts τς ," Despite these challenges, a series of galaxy redshift surveys have been undertaken to provide such datasets at redshifts $z < 0.5$."497The state-of-the-art. projects which have mapped the “local” (2&0.1) Universe are the 2-degree Field Galaxy Redshilt Survey (20ECGLIU: Colless et 22001) and the Sloan Digital Sky Survey (SDSS: York et 22000).," The state-of-the-art projects which have mapped the “local” $z \approx4980.1$ ) Universe are the 2-degree Field Galaxy Redshift Survey (2dFGRS; Colless et 2001) and the Sloan Digital Sky Survey (SDSS; York et 2000)."499 The 2GRS obtained redshifts for 210° galaxies covering 1500 dee? in the period between 1997 and 2002., The 2dFGRS obtained redshifts for $2 \times 10^5$ galaxies covering 1500 $^2$ in the period between 1997 and 2002.500" The “main” spectroscopic survev of the SDSS gathered S10"" galaxy redshifts over SOOO deg? between the vears 2000 ancl 2005.", The “main” spectroscopic survey of the SDSS gathered $8 \times 10^5$ galaxy redshifts over 8000 $^2$ between the years 2000 and 2005.501 The SDSS project also included: observations of 1.107 Luminous Rec Galaxies (LRGs) reaching up to a redshift >=0.5 (Eisenstein οἱ 22001)., The SDSS project also included observations of $1 \times 10^5$ Luminous Red Galaxies (LRGs) reaching up to a redshift $z = 0.5$ (Eisenstein et 2001).502 These datasets have provided a rich source of information about the clustering of galaxies., These datasets have provided a rich source of information about the clustering of galaxies.503" For example. power spectra have been extracted "" M"" 2dECGIUS by Percival οἱ ((2001) and Cole οἱ ""nn""m: for the SDSS ""main"" galaxy sample by Pope et Teemark et ((2004a) and. Percival et. ((2007a): vn for the LRGs by Eisenstein et ((2005).UaLLuctsi (2006).Nuke Teemark et ((2006) ancl Percival et ((2007b)."," For example, power spectra have been extracted for the 2dFGRS by Percival et (2001) and Cole et (2005); for the SDSS “main” galaxy sample by Pope et (2004), Tegmark et (2004a) and Percival et (2007a); and for the LRGs by Eisenstein et (2005), Huetsi (2006), Tegmark et (2006) and Percival et (2007b)."504 sis of these surveys. in combination with the Cosmic Microwave Background: [luctuations. has confirmed that we inhabit a low-density Universe where matter today provides. only 2530% of the total energy. governing the large-scale dvnanües. with the rest located in a mysterious “dark energv component.," Analysis of these surveys, in combination with the Cosmic Microwave Background fluctuations, has confirmed that we inhabit a low-density Universe where matter today provides only $25-30\%$ of the total energy governing the large-scale dynamics, with the rest located in a mysterious “dark energy” component."505" In addition the barvonic fraction. of the matter is only 1520%. with the remainder composed of non-barvonic. cold. particles M nature is M unknown PPercival et 2206""EEE et m""22004h: ‘Toemark οἱ 22006: Komatsu et 22M""."," In addition the baryonic fraction of the matter is only $15-20\%$, with the remainder composed of non-baryonic, cold particles whose nature is currently unknown Percival et 2002; Tegmark et 2004b; Tegmark et 2006; Komatsu et 2009)."506'The pattern is also sensitive to the presence dark matter such as massive neutrinos. which comprise a small fraction of the energy budget (IZlgarov et 22002: Seljak et 22005)," The clustering pattern is also sensitive to the presence of hot dark matter such as massive neutrinos, which comprise a small fraction of the energy budget (Elgaroy et 2002; Seljak et 2005)."507" ‘These galaxy surveys also describe how the underlving density Ductuations are modulated by galaxy bias (Verde e 22002: Wild ct ""n005: Conway et 22005: Perciva ot 22007a: Cresswe Percival 2009).", These galaxy surveys also describe how the underlying density fluctuations are modulated by galaxy bias (Verde et 2002; Wild et 2005; Conway et 2005; Percival et 2007a; Cresswell Percival 2009).508 In this context the comparison of power spectrum measurements [ron the 2dCRS anc SDSS. which targeted. galaxy. populations selected. in. blue ancl red. optical wavebands: respectively. is of particular interest.," In this context the comparison of power spectrum measurements from the 2dFGRS and SDSS, which targeted galaxy populations selected in blue and red optical wavebands respectively, is of particular interest."509 When the dillering galaxy types in these surveys are assigned lincar bias factors. the resulting model fits to the linear-regime power spectra produce. best-fitting matter densities which are inconsistent at. the statistical level of 2o.," When the differing galaxy types in these surveys are assigned linear bias factors, the resulting model fits to the linear-regime power spectra produce best-fitting matter densities which are inconsistent at the statistical level of $2\sigma$."510 Careful treatment of. scale-dependent: and Iuminositv-dependent: galaxy Pins dcan potentially explain this discrepancy (Pereival ct War Sanchez Cole 2008)., Careful treatment of scale-dependent and luminosity-dependent galaxy bias can potentially explain this discrepancy (Percival et 2007a; Sanchez Cole 2008).511 ‘There are strong motivations for extending these laree-scale structure measurements to higher redshifts (27 0.5)., There are strong motivations for extending these large-scale structure measurements to higher redshifts $z > 0.5$ ).512 Fiustlv. the growth. of structure implies that the. linear regime of evolving perturbations extends to smaller scales at higher redshifts. enabling cleaner and more accurate model fits.," Firstly, the growth of structure implies that the linear regime of evolving perturbations extends to smaller scales at higher redshifts, enabling cleaner and more accurate model fits."513 Secondly. the shape of the survey cone allows access to significantly greater cosmic volumes at higher redshift. enabling more accurate determinations of the large-scale power spectrum amplitude.," Secondly, the shape of the survey cone allows access to significantly greater cosmic volumes at higher redshift, enabling more accurate determinations of the large-scale power spectrum amplitude."514 Thirdly. barvon oscillations in galaxy power spectra at clilferent redshifts may be used as a standard ruler to extract the cosmic distance-recdshift relation and infer the properties of dark energy (Blake Glazebrook 2003: Seo Eisenstein 2003: Hu Llaiman 2003).," Thirdly, baryon oscillations in galaxy power spectra at different redshifts may be used as a standard ruler to extract the cosmic distance-redshift relation and infer the properties of dark energy (Blake Glazebrook 2003; Seo Eisenstein 2003; Hu Haiman 2003)."515 Fourthly. measurements of the growth. of cosmic structure as a function of redshift increases. our. ability," Fourthly, measurements of the growth of cosmic structure as a function of redshift increases our ability"516CCD was binned by a factor of two in the spatial direction to give 512. 32 pixels. along the slit length.,CCD was binned by a factor of two in the spatial direction to give 512 $\times$ .32 pixels along the slit length.517 Each integration was debiased anc wavelength calibrated. to better. than 0.5kms. using Thorium.Argon spectra obtained between exposures., Each integration was debiased and wavelength calibrated to better than $0.5~{\rm km~s^{-1}}$ using Thorium–Argon spectra obtained between exposures.518 Data were obtained from five slightly overlapping east-west slit lengths to produce an elfective slit length of aboutτος., Data were obtained from five slightly overlapping east-west slit lengths to produce an effective slit length of about.519 Phe slit position is marked on 2., The slit position is marked on \ref{eso}.520 The data from each slit was reduced and the five were mosaiced together., The data from each slit was reduced and the five were mosaiced together.521 A negative gray-scale representation of a position-velocity (PV) array of Iline profiles is displaved in Figs 4 and 5.., A negative gray-scale representation of a position-velocity (PV) array of line profiles is displayed in Figs \ref{oiiifig1} and \ref{oiiifig2}.522 Data from the full effective slit length is displaved in ᾱ while 5 isthe section of the data [rom the eastern side of the ellective slit., Data from the full effective slit length is displayed in \ref{oiiifig1} while \ref{oiiifig2} is the section of the data from the eastern side of the effective slit.523 Phe bright vertical band is the spectrum of a star intersected by the slit which can be used as a reference point between the two figures., The bright vertical band is the spectrum of a star intersected by the slit which can be used as a reference point between the two figures.524 The following features can readilv be seen., The following features can readily be seen.525 Throughout the data at zero heliocentric racial velocity there is faint background comission., Throughout the data at zero heliocentric radial velocity there is faint background emission.526 Lhe bright eastern edge ofthe nebula begins at an ollset of around40”., The bright eastern edge of the nebula begins at an offset of around.527. The data here exhibit velocity. knots and small velocity loops that correspond to the complex ilaments readily seen in 2.., The data here exhibit velocity knots and small velocity loops that correspond to the complex filaments readily seen in \ref{eso}.528 With increasing olfsets. he line. profiles begin to split.," With increasing offsets, the line profiles begin to split."529 At olfsets of greater than about he profiles are no longer split and only a single faint component at positiveNM velocitiesM (up to 120.kms. 7) ljis esent., At offsets of greater than about the profiles are no longer split and only a single faint component at positive velocities (up to $\sim 120~{\rm km~s^{-1}}$ ) is present.530 The positive velocity component then approaches je systemic with increasing ollsct and we identify the bright eature at around. aas being the western edge seen in 2.., The positive velocity component then approaches the systemic with increasing offset and we identify the bright feature at around as being the western edge seen in \ref{eso}.531 There is a negative velocity component from olIsets of oonwards that we attribute to the irregular diffuse emission present towards the western side of the nebula ancl not associated with ROW 37., There is a negative velocity component from offsets of onwards that we attribute to the irregular diffuse emission present towards the western side of the nebula and not associated with RCW 37.532 The position-velocity arrays show a coherent velocity structure across the nebula., The position-velocity arrays show a coherent velocity structure across the nebula.533 An almost complete classical velocity. cllipse is clearly apparent., An almost complete classical velocity ellipse is clearly apparent.534 The morphology. of the nebula is reminiscent of an incomplete funnel (or tube) but could also be simply a curved. sheet of emission., The morphology of the nebula is reminiscent of an incomplete funnel (or tube) but could also be simply a curved sheet of emission.535 This is discussed below but. broadly speaking. the velocity data indicate gas that is expancling racially at about 100kms," This is discussed below but, broadly speaking, the velocity data indicate gas that is expanding radially at about $100~{\rm536km~s^{-1}}$."537 At the edge of the nebula. the motion is into the plane of the sky while towards the middle there is a velocity splitting between the near and lar side of the emitting eas that increases towards the middle of the nebula.," At the edge of the nebula, the motion is into the plane of the sky while towards the middle there is a velocity splitting between the near and far side of the emitting gas that increases towards the middle of the nebula."538 Eventually. the red-shifted emission disappears while that the blue-shifted emission returns to the svstenic.," Eventually, the red-shifted emission disappears while that the blue-shifted emission returns to the systemic."539 At this point there is background. emission (seen in 2)) that contributes at negative velocities., At this point there is background emission (seen in \ref{eso}) ) that contributes at negative velocities.540 In the HlaJ image in 2. ROW 37 exhibits a curved morphology but there is also a parallel line of emission to the west., In the IIIaJ image in \ref{eso} RCW 37 exhibits a curved morphology but there is also a parallel line of emission to the west.541 This led Redmanetal.(2000). to suggest that together with the eastern side. the structure may form. a tube/funnel for hot eas to be vented from the remnant.," This led \citet{redman.et.al00} to suggest that together with the eastern side, the structure may form a tube/funnel for hot gas to be vented from the remnant."542 Just such a structure is present in the Crab SNIt lesen&Staker1993)) ancl also in the more evolved remnant DEM 3da (Aleaburn1987)., Just such a structure is present in the Crab SNR \citealt{fesen&staker93}) ) and also in the more evolved remnant DEM 34a \citep{meaburn87}.543. The previous kinematic data were not sullicient to test. this possibility., The previous kinematic data were not sufficient to test this possibility.544 The new kinematic data across ROW 37 are nearly exactly those expected of a funnel of cireular cross-section undergoing racial expansion., The new kinematic data across RCW 37 are nearly exactly those expected of a funnel of circular cross-section undergoing radial expansion.545 llowever. for a funnel. there should. be a similar. velocity splitting from the western edge towards the central of the putative funnel as for the eastern edge and so the ionization of the funnel would have to be incomplete.," However, for a funnel, there should be a similar velocity splitting from the western edge towards the central of the putative funnel as for the eastern edge and so the ionization of the funnel would have to be incomplete."546 Another dilliculty with this interpretation is that such a funnel would be pointing to the centre of the voung SNR., Another difficulty with this interpretation is that such a funnel would be pointing to the centre of the young SNR.547 Also the soft LASS X-ray maps reveal a more extensive bow shaped feature and it is only the hard RASS N-rav component of this that is adjacent to ROW 37 (Aschenbach1998)., Also the soft RASS X-ray maps reveal a more extensive bow shaped feature and it is only the hard RASS X-ray component of this that is adjacent to RCW 37 \citep{aschenbach98}.548. A plausible alternative interpretation is that the nebula eas is in the form of a thin ‘wavy sheet (Hester1987). of emission which at the eastern side overlaps along the line of sight., A plausible alternative interpretation is that the nebula gas is in the form of a thin `wavy sheet' \citep{hester87} of emission which at the eastern side overlaps along the line of sight.549 At the western side the single thin sheet curves to become οσο on. forming the western edge.," At the western side the single thin sheet curves to become edge on, forming the western edge."550 Interestingly. whether the single sheet curves into or out of the plane of sky is ambiguous kinematically.," Interestingly, whether the single sheet curves into or out of the plane of sky is ambiguous kinematically."551 Ehe whole svstem appears to be unclergoing a bulk expansion generating double-peaked line profiles at the eastern side where the sheet overlaps itself., The whole system appears to be undergoing a bulk expansion generating double-peaked line profiles at the eastern side where the sheet overlaps itself.552 Reclmanetal.(2000). showed that ROW 37 ancl D/D' are spatially coincident but the RASS data (see 1)) were not of high enough resolution to allow further investigation and the unlikely possibility of a chance alignment could not » ruled. out., \citet{redman.et.al00} showed that RCW 37 and D/D' are spatially coincident but the RASS data (see \ref{esorass}) ) were not of high enough resolution to allow further investigation and the unlikely possibility of a chance alignment could not be ruled out.553 The new Chandra data of D/D' displayed in 3 show morphological similarities to the optical data (sce Plucinskyctal.2002. for an excellent image)., The new Chandra data of D/D' displayed in \ref{esochandra} show morphological similarities to the optical data (see \citealt{plucinsky.et.al02} for an excellent image).554 There is an edge to the X-ray emission from ΤΟ) that runs parallel o the bright optical edge of ROW 37 and the X-ray peak is close to the peak of the optical emission., There is an edge to the X-ray emission from D/D' that runs parallel to the bright optical edge of RCW 37 and the X-ray peak is close to the peak of the optical emission.555 A chance alignment can be ruled out in the light of this new data., A chance alignment can be ruled out in the light of this new data.556" Plucinskyetal.(2002) argue that the morphology of D/L) makes it unlikely wt the object is a discrete ""bullet of ejecta and favour a shock break-out model where a change in density ahead of w old. Vela SNR boundary has [ος to a localised clistortion in the shock-front.", \citet{plucinsky.et.al02} argue that the morphology of D/D' makes it unlikely that the object is a discrete `bullet' of ejecta and favour a shock break-out model where a change in density ahead of the old Vela SNR boundary has led to a localised distortion in the shock-front.557 More controversial is whether. as suggested by Redmanetal. (2000)... ROW :7 and D/D' are physically associated with.," More controversial is whether, as suggested by \citet{redman.et.al00}, RCW 37 and D/D' are physically associated with."558 They. argued. that ROW 37 and D/D' represent a venting of hot eas from the interior of the remnant to bevond the roughly circular shell as cdelimited in the X-rav., They argued that RCW 37 and D/D' represent a venting of hot gas from the interior of the remnant to beyond the roughly circular shell as delimited in the X-ray.559 This view οους from that of Slaneet.al.(2001a) and Plucinskyetal.(2002) who argue that the X-ray spectrum of D/D' shows enhanced abuncances of O and Ne and is thermal in contrast to the spectrum of the main remnant bocky which is nonthermal., This view differs from that of \citet{slane.et.al01b} and \citet{plucinsky.et.al02} who argue that the X-ray spectrum of D/D' shows enhanced abundances of O and Ne and is thermal in contrast to the spectrum of the main remnant body which is non-thermal.560 This led Slane to suggest that ROW 37 and D/D' are not associated with 0852., This led \citet{slane.et.al01b} to suggest that RCW 37 and D/D' are not associated with .5610-4622.. However. as," However, as"562 , 563potential dominates).,potential dominates).564 Iu particular. all of our models show an increasing temperature profile for rS300 pe.," In particular, all of our models show an increasing temperature profile for $r \lsim565300$ pc."566 Note however. that because the eas temperature in nearly all models is roughly virial (aud therefore traces the potential). such a temperature increase would not necessarily confirm the cooling flow to accretion flow transition.," Note however, that because the gas temperature in nearly all models is roughly virial (and therefore traces the potential), such a temperature increase would not necessarily confirm the cooling flow to accretion flow transition."567 It would merely show that the eas dynamics is domunated by a centrally condensed mass distribution (namely. the black hole).," It would merely show that the gas dynamics is dominated by a centrally condensed mass distribution (namely, the black hole)."568 The second prediction of our model is that the. N-ray surface brightness profile. while ceutrally peaked. should be suppressed with respect to that expected from a cooling flow without a central point mass.," The second prediction of our model is that the X-ray surface brightness profile, while centrally peaked, should be suppressed with respect to that expected from a cooling flow without a central point mass."569" This is because the transition from a cooling flow to au accretion flow eutails a decrease in radiative efficiency,", This is because the transition from a cooling flow to an accretion flow entails a decrease in radiative efficiency.570 Α suppressed N-rav surface brightness profile is. however. also the characteristic signature of a cooling flow with mass drop out.," A suppressed X-ray surface brightness profile is, however, also the characteristic signature of a cooling flow with mass drop out."571 At a müninnuu. our analysis indicates that significant care iust be taken in interpreting the N-rav surface brightuess profiles of elliptical galaxies on Xi1l kpe scales.," At a minimum, our analysis indicates that significant care must be taken in interpreting the X-ray surface brightness profiles of elliptical galaxies on $\lsim 1$ kpc scales."572 Standard analvsis techniques. based ou the assumption of a cooling flow. could incorrectly infer a racially decreasing aceretion rate when iu fact the aceretion is via a Bondi flow with coustaut AZ andit is the radiative efficiency that decreases.," Standard analysis techniques, based on the assumption of a cooling flow, could incorrectly infer a radially decreasing accretion rate when in fact the accretion is via a Bondi flow with constant $\dot M$ and it is the radiative efficiency that decreases."573 As shown in 833 (see Figs., As shown in 3 (see Figs.574 2 5). AM ds expected to be nearly coustaut ou the siuall scales of interest here since the trausitiou to a Doudi-like flow strouglv suppresses niass drop out duc to thermal iustabilitv.," 2 5), $\dot M$ is expected to be nearly constant on the small scales of interest here since the transition to a Bondi-like flow strongly suppresses mass drop out due to thermal instability."575 (νου an observed X-ray luminosity £y and sound speed ος. the true local accretion of the flow is cqgO urcaleulationsindicatethat tesol/fing is Likely to be 210 on z0.1 kpe scales in M87 so that accretion rates imforred asstinue a cooling flow (feumfur AfozmEyfe2) cau be underestinmates by up to an order of magnitude.," Given an observed X-ray luminosity $L_X$ and sound speed $c_s$, the true local accretion of the flow is M. Our calculations indicate that $t_{\rm cool}/t_{\rm inf}$ is likely to be $\gsim 10$ on $\approx 0.1$ kpc scales in M87 so that accretion rates inferred assuming a cooling flow $\tc \approx \ti$, $\dot M \approx576L_X/c^2_s$ ) can be underestimates by up to an order of magnitude."577 This is shown explicitly iu Figure 5 where we compare the true accretion rate for our baselime (=0.6) model of ALS? (solid line) with that which we would infer if we took the predicted X-ray surface brightuess aud temperature profiles and assunued a pure cooling flow (dotted line)., This is shown explicitly in Figure 5 where we compare the true accretion rate for our baseline $q = 0.6$ ) model of M87 (solid line) with that which we would infer if we took the predicted X-ray surface brightness and temperature profiles and assumed a pure cooling flow (dotted line).578 N-ray spectra inav break the degeneracy between a change in radiative efficiency and mass drop out., X-ray spectra may break the degeneracy between a change in radiative efficiency and mass drop out.579 The presence of co-spatial multi-temperature components in coolings flows is indicated by a detailed examination of their N-rav spectral lines (Canizares ct al., The presence of co-spatial multi-temperature components in coolings flows is indicated by a detailed examination of their X-ray spectral lines (Canizares et al.580 1979. 1982: AlDushotzkv et al.," 1979, 1982; Mushotzky et al."581 1981)., 1981).582 This is interpreted as evideuce for ns drop out in the cooling flow., This is interpreted as evidence for mass drop out in the cooling flow.583 Consequently. theabsence of evidence for such imulti-teniperature conrponeuts (or a decrease in their prominence). together with a suppression in the ταν surface brightuess at s12all radii. would provide cousiderable support for our model of the cooling flow to accretion flow trausition.," Consequently, the of evidence for such multi-temperature components (or a decrease in their prominence), together with a suppression in the X-ray surface brightness at small radii, would provide considerable support for our model of the cooling flow to accretion flow transition."584 We acknowledge support froii an NSF Graduate Research Fellowship (EQ) and NSF Cant 9820686 (RN)., We acknowledge support from an NSF Graduate Research Fellowship (EQ) and NSF Grant 9820686 (RN).585 We thauk the referee for useful conuuents which sienificantly improved this paper., We thank the referee for useful comments which significantly improved this paper.586these clrifts. making their omission from these simulations insignificant.,"these drifts, making their omission from these simulations insignificant."587 The simulated data are. calibrated: ancl reduced. from. time-line data to maps using a simple map-maker., The simulated data are calibrated and reduced from time-line data to maps using a simple map-maker.588 Maps at the three SPLUS bands. 250. 350 and pim are obtained. having Pull width half maximum beams sizes of 18. 25r and 36 arcseconds respectively.," Maps at the three SPIRE bands, 250, 350 and $\mu$ m are obtained, having full width half maximum beams sizes of 18, 25 and 36 arcseconds respectively."589 Synthetic maps of the planc-of-sky. intensity distribution of the three LIRDCs are produced. using the radiative transfer mocel., Synthetic maps of the plane-of-sky intensity distribution of the three IRDCs are produced using the radiative transfer model.590 The maps are produced at eight wavebancds (8. 15. 70. 160. 250. 350. 500. and 500 rn) that replicate the filter sets of recent telescope facilities.," The maps are produced at eight wavebands (8, 15, 70, 160, 250, 350, 500, and 500 $\mu$ m) that replicate the filter sets of recent telescope facilities."591 Phe 8 and 15 pm wavelengths match two bands from the MSX satellite (Price et al., The 8 and 15 $\mu$ m wavelengths match two bands from the MSX satellite (Price et al.592 2001)., 2001).593 The near infra-red δ jam is also found on Spizers LRAC camera (Lazio et al., The near infra-red 8 $\mu$ m is also found on 's IRAC camera (Fazio et al.594 2004)., 2004).595 The S jun filter can show strong emission from. PALL grains (Elagev et al., The 8 $\mu$ m filter can show strong emission from PAH grains (Flagey et al.596 2006)., 2006).597 The far-infrarecl bands at TO and 160 sam bands match approximately the TO and 160 sam bands of Spifzer's ALPS camera (lüeke et al., The far-infrared bands at 70 and 160 $\mu$ m bands match approximately the 70 and 160 $\mu$ m bands of 's MIPS camera (Rieke et al.598 2004). the N60 and NI160 bands of AKARL (Ixzwada et al.," 2004), the N60 and N160 bands of AKARI (Kawada et al."599 2007). and the TO and 160 bands of Herschefs. camera (Poglitsch et al.," 2007), and the 70 and 160 bands of 's camera (Poglitsch et al."600 2009. 2010).," 2009, 2010)."601 Phe submillimetre bands. at 250. 350. and 500 yam match approximately the filter set. of Zerschefs SPIRE (Grillin et al.," The submillimetre bands at 250, 350, and 500 $\mu$ m match approximately the filter set of 's SPIRE (Griffin et al."602 2009. 2010) camera and the BLAST balloon experiment (Pascale et al.," 2009, 2010) camera and the BLAST balloon experiment (Pascale et al."603 2008)., 2008).604 The 850 sna band matches approximately the longewavelength filter of SCUBA (Llollancl et al., The 850 $\mu$ m band matches approximately the long-wavelength filter of SCUBA (Holland et al.605 1999) and SCUBA? (Llollancl et al., 1999) and SCUBA2 (Holland et al.606 2006) on the ΑΟΔΕΗ., 2006) on the JCMT.607 The 500 sam band is also roughly. equivalent to SCUDA's and SCUBA2’s 450 im band (Llolland et al., The 500 $\mu$ m band is also roughly equivalent to SCUBA's and SCUBA2's 450 $\mu$ m band (Holland et al.608 1999: 2006)., 1999; 2006).609 Given a synthetic map of intensity it is) possible to simulate the observing process and. produce simulated observations that match the resolution and expected instrumental characteristic of the chosen camera., Given a synthetic map of intensity it is possible to simulate the observing process and produce simulated observations that match the resolution and expected instrumental characteristic of the chosen camera.610 As described in Section 4.. we have used the SPLRIE simulator ο produce simulated observations for the 250500 sam data.," As described in Section \ref{sec:spire}, we have used the SPIRE simulator to produce simulated observations for the 250–500 $\mu$ m data."611 Figure S shows the mocdel IRDCs before (blue colour able) and after (red colour table) they have been. processed into simulated observations., Figure 8 shows the model IRDCs before (blue colour table) and after (red colour table) they have been processed into simulated observations.612 Phe columns are labellec at the op with the wavelength: the rows are labelled on the right-yanid side with the description of the cloud., The columns are labelled at the top with the wavelength; the rows are labelled on the right-hand side with the description of the cloud.613 Lhe maps show a radius of 1.1 parsee around the centre of cach cloud., The maps show a radius of 1.1 parsec around the centre of each cloud.614 The Pixel size of the model cloud maps at all wavelengths is 0.019 xc (1.9 aresec) for the spherical and. Uattened cloud. and 1.028 (2.9 aresec) for the turbulent eloud.," The pixel size of the model cloud maps at all wavelengths is 0.019 pc (1.9 arcsec) for the spherical and flattened cloud, and 0.028 (2.9 arcsec) for the turbulent cloud."615 The pixel sizes of he 250. 350. ancl 500 jam maps are approximately a third of the SPIRE beam EWILMSs. corresponding to 0.058 pc (6 arcsec). 0.097 pe (10 aresec). ancl 0.116 pe (12 aresee) at 250. 3510. and 208 pam respectively.," The pixel sizes of the 250, 350, and 500 $\mu$ m maps are approximately a third of the SPIRE beam FWHMs, corresponding to 0.058 pc (6 arcsec), 0.097 pc (10 arcsec), and 0.116 pc (12 arcsec) at 250, 350, and 500 $\mu$ m respectively."616 Ehe 8- and 15-5 bands are not shown in Figure S. as they simply show up as dark clouds against a bright background.," The 8- and $\mu$ m bands are not shown in Figure 8, as they simply show up as dark clouds against a bright background."617 IRDCs have been identified in large numbers from infra- surveys (Simon ct al., IRDCs have been identified in large numbers from infra-red surveys (Simon et al.618 2006: Peretto Fuller 2000) as higher-mass and more distant. analogues to the optically dark clouds of gas ancl dust seen in silhouette. against a bright background in V-band surveys (c.g. Barnarel 1927: Lynds 1962)., 2006; Peretto Fuller 2009) as higher-mass and more distant analogues to the optically dark clouds of gas and dust seen in silhouette against a bright background in V-band surveys (e.g. Barnard 1927; Lynds 1962).619 Starting at the shortest wavelength in Figure S (00 pm) this extinction can be seen in the spherical a Hattenecl model clouds as a central dark patch., Starting at the shortest wavelength in Figure 8 (70 $\mu$ m) this extinction can be seen in the spherical and flattened model clouds as a central dark patch.620 The size of this patch decreases with increasing wavelength until 500 sana where it has either closed. up entirely or can no longer be resolved., The size of this patch decreases with increasing wavelength until 500 $\mu$ m where it has either closed up entirely or can no longer be resolved.621 We note that the size of the emitting region a 500 yam is approximately the same size as the dark region al 7O jum. The substructure of the turbulent eloud which is eviden in the model images is hardly visible in the simulated images, We note that the size of the emitting region at 500 $\mu$ m is approximately the same size as the dark region at 70 $\mu$ m. The substructure of the turbulent cloud which is evident in the model images is hardly visible in the simulated images622The search for the values of the cosmological parameters has occupied astronomers for almost à century.,The search for the values of the cosmological parameters has occupied astronomers for almost a century.623 Recently. a study of the light. curves of. local supernovac la has provided an accurate calibration of their. intrinsic luminosity (Παν et al.," Recently, a study of the light curves of local supernovae Ia has provided an accurate calibration of their intrinsic luminosity (Hamuy et al."624 1996: Riess et al., 1996; Riess et al.625 1998)., 1998).626 With such a standard candle in hand. the measurement of apparent supernovae brightnesses at high redshift allows the uncerlsing cosmological parameters to be determined.," With such a standard candle in hand, the measurement of apparent supernovae brightnesses at high redshift allows the underlying cosmological parameters to be determined."627 This has been the goal of two teams who have now discovered approaching one hundred supernovae out to a redshift. of 2o1.2 (Schmidt et al., This has been the goal of two teams who have now discovered approaching one hundred supernovae out to a redshift of $z\sim1.2$ (Schmidt et al.628 1998: Perlmutter ct al., 1998; Perlmutter et al.629 1999: Riess et al., 1999; Riess et al.630 2000)., 2000).631" The results of these studies suggest that we live in a universe which is dominated by a cosmological constant. with A,—0.7. with enough matter. ,,=0.3. to Hatten the overall topology. as seen in studies of the cosmic microwave background. (Melehiorri et al."," The results of these studies suggest that we live in a universe which is dominated by a cosmological constant, with $\Lambda_o=0.7$, with enough matter, $\Omega_o=0.3$, to flatten the overall topology, as seen in studies of the cosmic microwave background (Melchiorri et al."632 2000)., 2000).633 With the release of the cosmological supernovae results. a number of analyses of physical processes that could. also dim clistant supernovac. and therefore mimic a cosmological constant. were considered.," With the release of the cosmological supernovae results, a number of analyses of physical processes that could also dim distant supernovae, and therefore mimic a cosmological constant, were considered."634" ""These included. gravitational lensing (c.g. Céllérricr 2000: BerestrGnun. Goliath. Cioobar. Morrtsell 2000). clust (Votan Ixobavashi 1999: Croft. Davé.. Herne(quist. Ixatz 2000) and the evolution of supernova properties (Lóolllich. Nomoto. Umeda. Wheeler 2000): see Itiess. (2000) for a more complete description of these ellects."," These included gravitational lensing (e.g. Céllérrier 2000; Bergströmm, Goliath, Goobar, Mörrtsell 2000), dust (Totani Kobayashi 1999; Croft, Davé,, Hernquist, Katz 2000) and the evolution of supernova properties (Höfflich, Nomoto, Umeda, Wheeler 2000); see Riess (2000) for a more complete description of these effects."635 Recently. however. the discovery of à supernova at a redshift of z~1.7 has been announced: seehttp://oposite.," Recently, however, the discovery of a supernova at a redshift of $z\sim1.7$ has been announced; see."636stsci.edu/pubinfo/pr/2001/09. Located in the northern Hubble Deep Field (Willies et al., Located in the northern Hubble Deep Field (Williams et al.637 1996: Ferguson. Dickinson. Williams 2000). this supernova. designatedSN19971L. was identified via the comparison of exposures at dilfering epochs by CGilliland. Nugent. Phillips (1999).," 1996; Ferguson, Dickinson, Williams 2000), this supernova, designated, was identified via the comparison of exposures at differing epochs by Gilliland, Nugent, Phillips (1999)."638 While a publication. detailing. the supernova has vet to appear. the press-release announces that this svstem. with a photometric redshift of z=1.7+ 0.15. represents the most distant. supernova discovered. anc that it confirms the earlier. conclusions of a cosmologica constant dominated universe. as it is brighter than woule be expected in a simple matter dominated. universe.," While a publication detailing the supernova has yet to appear, the press-release announces that this system, with a photometric redshift of $z=1.7\pm0.15$ , represents the most distant supernova discovered and that it confirms the earlier conclusions of a cosmological constant dominated universe, as it is brighter than would be expected in a simple matter dominated universe."639 Such dimming and brightening. relative to matter dominatec cosmologies. is a peculiarity expected. in universes with a substantial cosmological constant. but is not consisten with the action of dust. gravitational lensing or supernova evolution.," Such dimming and brightening, relative to matter dominated cosmologies, is a peculiarity expected in universes with a substantial cosmological constant, but is not consistent with the action of dust, gravitational lensing or supernova evolution."640"place no significant constraint on the lensing flexion, and nearly all the parameter values are consistent with zero flexion within the error estimates derived from the parameter covariance matrix.","place no significant constraint on the lensing flexion, and nearly all the parameter values are consistent with zero flexion within the error estimates derived from the parameter covariance matrix."641" We choose to fix the shear, rather than fixing the ellipticity, because it is possible to select a specific shear model which is observationally motivated by additional data on the galaxy cluster in question."," We choose to fix the shear, rather than fixing the ellipticity, because it is possible to select a specific shear model which is observationally motivated by additional data on the galaxy cluster in question."642" The shear can be estimated from mass proxies (e.g. standard weak lensing shear analysis, X-ray temperature or luminosity, or optical richness) and the assumption of a standard mass profile (e.g., a non-singular isothermal sphere or NFW profile)."," The shear can be estimated from mass proxies (e.g. standard weak lensing shear analysis, X-ray temperature or luminosity, or optical richness) and the assumption of a standard mass profile (e.g., a non-singular isothermal sphere or NFW profile)."643 Significant departures from the input shear model would be measurable as departures from the expected distribution of ellipticity magnitudes and orientations in the lensed galaxies., Significant departures from the input shear model would be measurable as departures from the expected distribution of ellipticity magnitudes and orientations in the lensed galaxies.644" Flexion measurements are a natural addition to joint weak+strong lensing mass mapping methods, as flexion directly constrains the mass gradients."," Flexion measurements are a natural addition to joint weak+strong lensing mass mapping methods, as flexion directly constrains the mass gradients."645" Mass reconstruction formalisms, such as that of or the non-grid-based method of (2008). can be easily modified to utilize data which further constrains the lensing potential."," Mass reconstruction formalisms, such as that of or the non-grid-based method of , can be easily modified to utilize data which further constrains the lensing potential."646" As a less-sophisticated method which does not use direct shear estimates, an iterative process of integrating flexion measurements could be used to correct the assumed input shear model (and thus the mass model) for the effects of lens substructure."," As a less-sophisticated method which does not use direct shear estimates, an iterative process of integrating flexion measurements could be used to correct the assumed input shear model (and thus the mass model) for the effects of lens substructure."647" The resulting updated shear model could then be used as an input to the next iteration of flexion fitting, and the process repeated until the shear model converges."," The resulting updated shear model could then be used as an input to the next iteration of flexion fitting, and the process repeated until the shear model converges."648 This type of procedure would be a test of the self-consistency of the measured shear and flexion fields; however it is beyond the scope of this work., This type of procedure would be a test of the self-consistency of the measured shear and flexion fields; however it is beyond the scope of this work.649" The simulations we present in refsec:aimtest confirm that our basic approach to the shear/ellipticity degeneracy (fixing the shear and fitting for the ellipticity) is adequate for successfully measuring the lensing flexion, even when significant errors are present in the assumed shear field."," The simulations we present in \\ref{sec:aimtest} confirm that our basic approach to the shear/ellipticity degeneracy (fixing the shear and fitting for the ellipticity) is adequate for successfully measuring the lensing flexion, even when significant errors are present in the assumed shear field."650and northern ares are the limb-brightened edges of the bicones in the outer structure.,and northern arcs are the limb-brightened edges of the bicones in the outer structure.651 Such an interpretation is in line with the Helix nebula being a polv-polar planetary nebula being viewed pole-on., Such an interpretation is in line with the Helix nebula being a poly-polar planetary nebula being viewed pole-on.652 The edge-on polv-polar PN. NGC 2440. has an inner torus of II» emission and an outer bipolar nebula of Hs emission with axes of symmetry that are tilted with respect io one another (Latteretal.1995).," The edge-on poly-polar PN, NGC 2440, has an inner torus of $_2$ emission and an outer bipolar nebula of $_2$ emission with axes of symmetry that are tilted with respect to one another \citep{latter95}."653. Our NICMOS field positions appear to lie in some of the fainter or non-existent regions ol Ils enission as observed by Speckοἱal.(2002) which had less sensitivity (han our studs., Our NICMOS field positions appear to lie in some of the fainter or non-existent regions of $_2$ emission as observed by \cite{speck02} which had less sensitivity than our study.654 Positions 1 and 2 are located outside the southern edee of the inner disk in what appears to be a gap between the inner disk and outer structures., Positions 1 and 2 are located outside the southern edge of the inner disk in what appears to be a gap between the inner disk and outer structures.655 Position 3 lies to the soutliwest X the outer structure where no apparent Il» emission appears in the Il5 image by (2002)., Position 3 lies to the southwest of the outer structure where no apparent $_2$ emission appears in the $_2$ image by \cite{speck02}.656. Positions 4 and 5 are located even further away [rom previously detectable Ho» emission south of the nebula., Positions 4 and 5 are located even further away from previously detectable $_2$ emission south of the nebula.657 Positions 3. 4 and 5 also lie in regions where no III 21 cm line Mnission was detected bv Rodriguezetal.(2002) nor CO emission detected by 1999).," Positions 3, 4 and 5 also lie in regions where no HI 21 cm line emission was detected by \cite{rodriguez02} nor CO emission detected by \cite{young99}."658. The nmunber densitv of Il» knots and area filling factor of Hs emission decreases with increasing radius and is the lowest in positions 3. 4 ancl 5 (Figs. 12- 14)).," The number density of $_2$ knots and area filling factor of $_2$ emission decreases with increasing radius and is the lowest in positions 3, 4 and 5 (Figs. \ref{nicpos3}- \ref{nicpos5}) )."659" In the laree beams E these radio line observations (731 FFEWIIM for CO and —42"" FFEWIIM for HI 21 em). the intensitv of the neutral gas emission from these knots is beam diluted and falls below the detection limit of the radio observations."," In the large beams of these radio line observations $\sim$ FWHM for CO and $\sim$ FWHM for HI 21 cm), the intensity of the neutral gas emission from these knots is beam diluted and falls below the detection limit of the radio observations."660 Our observations clearly show that (he morphology of the molecular hydrogen emission is highly clumped in comparison to the ionized eas tracers., Our observations clearly show that the morphology of the molecular hydrogen emission is highly clumped in comparison to the ionized gas tracers.661 Figure 17. shows a multi-color image comparing the [OTI]. the Ho /[NII] and the Hs emission for position 1.," Figure \ref{nicpos1_color} shows a multi-color image comparing the [OIII], the $\alpha$ /[NII] and the $_2$ emission for position 1."662 The structure observed in this image is primarily due to the Ils emission clumps., The structure observed in this image is primarily due to the $_2$ emission clumps.663 Ii fact. the IH» emission inmges are striking by their lack of diffuse I» emission.," In fact, the $_2$ emission images are striking by their lack of diffuse $_2$ emission."664 Close inspection of the more intense reeions shows thev are composed of overlapping knots of Il» emission., Close inspection of the more intense regions shows they are composed of overlapping knots of $_2$ emission.665 Hence. we confirm the conclusion of Specketal.(2002) that the molecular hydrogen is confined to the high density knots such as seen in the optical by ODell&IHIandron(1996).," Hence, we confirm the conclusion of \cite{speck02} that the molecular hydrogen is confined to the high density knots such as seen in the optical by \cite{odell96}."666.. A similar conclusion was reached by Speckοἱal.(2003) for the Ringe Nebula based on comparison of high resolution eround-based Ils emission images to the optical LIST images., A similar conclusion was reached by \cite{speck03} for the Ring Nebula based on comparison of high resolution ground-based $_2$ emission images to the optical HST images.667 Thus in two evolved planetary nebulae. the Ielix aud the Ring Nebulae. the IH line emission is highlv structured. and confined to knots.," Thus in two evolved planetary nebulae, the Helix and the Ring Nebulae, the $_2$ line emission is highly structured and confined to knots."668 The near-IR ll» emission provides us with the highest angular resolution map of the neutral gas knots in the [Helix nebula., The near-IR $_2$ emission provides us with the highest angular resolution map of the neutral gas knots in the Helix nebula.669 Previous work has suggested that the knots contain, Previous work has suggested that the knots contain670"accretion rate AJ=105 M, HL assuming the protoplanet is at 5 AU from the central star (see Papaloizou Terquem 1999).","accretion rate ${\dot M} = 10^{-8}$ $_{\odot}$ $^{-1}$, assuming the protoplanet is at 5 AU from the central star (see Papaloizou Terquem 1999)."671" For rau,=10r. the eritical core mass is 36. 24. 16 and 10 for M,=10. 105. 10* and LO |, respectively."," For $r_{\rm atm}=10 r_c$, the critical core mass is 36, 24, 16 and 10 $_{\oplus}$ for $\dot{M}_c=10^{-5}$ , $10^{-6}$, $10^{-7}$ and $10^{-8}$ $_{\oplus}$ $^{-1}$, respectively."672" For ra=5r. the critical core mass is 55. 37. 25 and 16 for these values of M,"," For $r_{\rm atm}=5 r_c$, the critical core mass is 55, 37, 25 and 16 $_{\oplus}$ for these values of $\dot{M}_c$."673" We note that. if the core is at 5 AU from the central star. Pam=LOr,. and rau=Sr, represent about and0.7%... respectively. of (he Roche lobe radius of the protoplanet when its core reaches the eritieal mass."," We note that, if the core is at 5 AU from the central star, $r_{\rm atm}=10 r_c$ and $r_{\rm atm}=5 r_c$ represent about and, respectively, of the Roche lobe radius of the protoplanet when its core reaches the critical mass."674" For comparison. in a standard steady state disc model with a=107 and gas accretion ide AY=105 M. Fat 5 AU from the central star. the critical core mass of a protoplanet with ra=rp is 24. 15. 9 and 5 for M,=10 . 105. 10* and 105 tf. respectively,"," For comparison, in a standard steady state disc model with $\alpha=10^{-2}$ and gas accretion rate ${\dot M} =67510^{-8}$ $_{\odot}$ $^{-1}$, at 5 AU from the central star, the critical core mass of a protoplanet with $r_{\rm atm}=r_L$ is 24, 15, 9 and 5 $_{\oplus}$ for $\dot{M}_c=10^{-5}$ , $10^{-6}$, $10^{-7}$ and $10^{-8}$ $_{\oplus}$ $^{-1}$, respectively."676 These values are almost independent of the conditions in the nebula. and therefore do not change when A/ and α are varied.," These values are almost independent of the conditions in the nebula, and therefore do not change when ${\dot M}$ and $\alpha$ are varied."677" We see that the critical core mass increases when ray, decreases.", We see that the critical core mass increases when $r_{\rm atm}$ decreases.678 This is because the gas in the atmosphere has less (negative) gravitational energy when raj is smaller. i.e. il is more bound. and therelore. for a fixed core accretion Iuminositvy. it can be supported at equilibrium up to larger core masses.," This is because the gas in the atmosphere has less (negative) gravitational energy when $r_{\rm atm}$ is smaller, i.e. it is more bound, and therefore, for a fixed core accretion luminosity, it can be supported at equilibrium up to larger core masses."679 Also. the temperatures at the bottom of the atmosphere tend to be lower for smaller μμ. so that more mass can settle near the surface of the core. which also helps to increase the critical core mass.," Also, the temperatures at the bottom of the atmosphere tend to be lower for smaller $r_{\rm atm}$, so that more mass can settle near the surface of the core, which also helps to increase the critical core mass."680 Finally. because the surface of the atmosphere is snialler. radiative losses are smaller which helps supporting the atmosphere at equilibrium up {ο larger core masses.," Finally, because the surface of the atmosphere is smaller, radiative losses are smaller which helps supporting the atmosphere at equilibrium up to larger core masses."681" However. for a given core mass and core aceretion Iuminositv. the mass of the atmosphere decreases as rj), decreases."," However, for a given core mass and core accretion luminosity, the mass of the atmosphere decreases as $r_{\rm atm}$ decreases."682 In all the calculationsdisplaved on figure 2.. ry is smaller (han the Bondi radius rg and represents the largest radius (tlie static atimosphliere of the protoplanet can expand to.," In all the calculationsdisplayed on figure \ref{fig1}, , $r_L$ is smaller than the Bondi radius $r_B$ and represents the largest radius the static atmosphere of the protoplanet can expand to."683 If (he midplane temperature of the protoplanetary disc were larger. rj would become smaller than ry.," If the midplane temperature of the protoplanetary disc were larger, $r_B$ would become smaller than $r_L$."684" This is the case. for instance. lor protoplanets less massive (han 16 when the midplane temperature is 140 IN. which corresponds to a a disc model with a=107 andgas accretion rate M=107 M, 1 feat5 AU from the central star."," This is the case, for instance, for protoplanets less massive than 16$_{\oplus}$ when the midplane temperature is 140 K, which corresponds to a a disc model with $\alpha=10^{-2}$ andgas accretion rate ${\dot M} =68510^{-7}$ $_{\odot}$ $^{-1}$ , at5 AU from the central star."68615.,$\sim 75^{\circ}$.687 Assuming the observed feature to be the approaching plasmon. we can expect a lower limit on the observed proper motion to be Q.2/d(kpc) aresec lo," Assuming the observed feature to be the approaching plasmon, we can expect a lower limit on the observed proper motion to be $\geq 0.2/d$ (kpc) arcsec $^{-1}$."688 However. caution must be exercised in making these assumptions. in particular as the spectral index of the ejecta is not clear. and ejections rom GRO 1655-40 can reveal an intrinsically asvnunetric nature (Ποπο Rupen 1995).," However, caution must be exercised in making these assumptions, in particular as the spectral index of the ejecta is not clear, and ejections from GRO J1655-40 can reveal an intrinsically asymmetric nature (Hjellming Rupen 1995)."689 The lack of an observed jet-like structure to a resolution of 1 aresee in observations mace 313 days before ours (data from Spencer et al., The lack of an observed jet-like structure to a resolution of $\sim 1$ arcsec in observations made 313 days before ours (data from Spencer et al.690 1997). aces a lower limit on the velocity of the ejecta of (dfkpe) ems. J|.," 1997), places a lower limit on the velocity of the ejecta of $v \geq 6 \times 10^8 (d/kpc)$ cm $^{-1}$."691 Ata distance of 1.3 kpe this corresponds ο  0.03€. so even if not releivistic the outflow is clearly veh velocity (but at such a velocity it would. need to be intrinsically one-sided as relativistic beaming would not be important).," At a distance of 1.3 kpc this corresponds to $\sim 0.03$ c, so even if not relativistic the outflow is clearly high velocity (but at such a velocity it would need to be intrinsically one-sided as relativistic beaming would not be important)."692 Soft N-rav monitoring with the NTE ASAI during the time of our observations is shown in Vie 4., Soft X-ray monitoring with the XTE ASM during the time of our observations is shown in Fig 4.693 The source appears to be undergoing an X-ray outburst at the time of the observations. although the overall Dux level corresponds tooff. the lowest of the X-ray states (Nowak 1995. and private communication).," The source appears to be undergoing an X-ray outburst at the time of the observations, although the overall flux level corresponds to, the lowest of the X-ray states (Nowak 1995 and private communication)."694 A poorly-unelerstooc but clear relation between X-ray and radio behaviour has already been established for CIS 1915|105 and. GRO 1655-40. (Foster et al., A poorly-understood but clear relation between X-ray and radio behaviour has already been established for GRS 1915+105 and GRO J1655-40 (Foster et al.695 1996: Llarmon et al., 1996; Harmon et al.696 1995)., 1995).697 Given the time required to achieve the observed angular separation. if associated. with the outburst the ejection would have needed to occur around the beginning of the X-ray event. which may be consistent with the behaviour of CARS 1915|105.," Given the time required to achieve the observed angular separation, if associated with the outburst the ejection would have needed to occur around the beginning of the X-ray event, which may be consistent with the behaviour of GRS 1915+105."698 Note that Alivamioto Witamoto (1991) have already. predicted the existence of a jet in GX 339-4. however this was in order to explain its X-ray properties in the state.," Note that Miyamoto Kitamoto (1991) have already predicted the existence of a jet in GX 339-4, however this was in order to explain its X-ray properties in the state."699 GX 339-4 has become the latest black hole candidate X-rav binary to be detected as a variable racio source., GX 339-4 has become the latest black hole candidate X-ray binary to be detected as a variable radio source.700 Durouchoux et al. (, Durouchoux et al. (7011997) and Sood et al. (,1997) and Sood et al. (7021997) have already. discussed possible radio - X-ray correlations in the source. and. have compared it to Cygnus N-1. the most. famous persistent black hole candidate radio source.,"1997) have already discussed possible radio - X-ray correlations in the source, and have compared it to Cygnus X-1, the most famous persistent black hole candidate radio source."703 In four davs of racio observations with ATCA in high-resolution. configuration we have measured. the spectral energy. distribution of GX 339-4 from 22 - 3 em and mapped the region of the source on scales from arcmin to arcseconds., In four days of radio observations with ATCA in high-resolution configuration we have measured the spectral energy distribution of GX 339-4 from 22 - 3 cm and mapped the region of the source on scales from arcmin to arcseconds.704 We find a relatively at (a~10.2) radio spectrum for the emission. indicative of a compact absorbed. core.," We find a relatively flat $\alpha \sim +0.2$ ) radio spectrum for the emission, indicative of a compact absorbed core."705 Low-resolution mapping finds no evidence on arcmin-scales [for lobes., Low-resolution mapping finds no evidence on arcmin-scales for lobes.706 bow shocks or svnchrotron. nebulae such as those associated: with other radio-jet X-ray. binaries., bow shocks or synchrotron nebulae such as those associated with other radio-jet X-ray binaries.707 Alost intriguinely however we have presented. evidence for the existence of a jet-like structure in radio maps of GX 339-4., Most intriguingly however we have presented evidence for the existence of a jet-like structure in radio maps of GX 339-4.708 HL confirmed. this source becomes the first. persistent black-hole cancidate source to reveal à racio jet.," If confirmed, this source becomes the first persistent black-hole candidate source to reveal a radio jet."709 The importance of the detection of a jet. which is in all likelihood relativistic. from a non-transicnt black hole candidate N-rav binary cannot be understated.," The importance of the detection of a jet, which is in all likelihood relativistic, from a non-transient black hole candidate X-ray binary cannot be understated."710 Both GRS 19151105 and GRS 1655-40 are transient sources. and while displaying quas-recurrent behaviour in the 2-3 vears since their discovery. the lack of detection of these systems bv previous X-ray satellites (Lochner Whitlock 1992: Castro-Virado 1994: C'astro-Tirado. private communication) testifies to prolonged states below detectable levels.," Both GRS 1915+105 and GRS J1655-40 are transient sources, and while displaying quasi-recurrent behaviour in the 2-3 years since their discovery, the lack of detection of these systems by previous X-ray satellites (Lochner Whitlock 1992; Castro-Tirado 1994; Castro-Tirado, private communication) testifies to prolonged states below detectable levels."711 GX 339-4 on the other hand is a persistently: visible source. both at X-rays and (at least for past 18 months) in the radio. and may turn out to be one of our most valuable laboratories in the study of radio jets.," GX 339-4 on the other hand is a persistently visible source, both at X-rays and (at least for past $\sim 18$ months) in the radio, and may turn out to be one of our most valuable laboratories in the study of radio jets."712 We are happy to acknowledge: fruitful ancl stimulating discussions with Ravi Sood. Philippe Durouchoux. Mike Nowak. Alberto Castro-Viracdo. Bob Sault and Vince Alelntvre.," We are happy to acknowledge fruitful and stimulating discussions with Ravi Sood, Philippe Durouchoux, Mike Nowak, Alberto Castro-Tirado, Bob Sault and Vince McIntyre."713 We acknowledge quick-Iook results provided by the ASMZNTIS team., We acknowledge quick-look results provided by the ASM/XTE team.714of low mass ratio binaries. where the low-aimplitude signal can be detected by using data obtained during the lifetime of the mission.,"of low mass ratio binaries, where the low-amplitude signal can be detected by using data obtained during the lifetime of the mission."715 We also show that there are in facttee photometric signals induced by the beaming effect during eclipse. oue sensitive to the stars self rotation aud spin-orbit anele. while the other is not.," We also show that there are in fact photometric signals induced by the beaming effect during eclipse, one sensitive to the star's self rotation and spin-orbit angle, while the other is not."716 Both effects uced to be accounted for in order to correctly interpret the light curve aud estimate A., Both effects need to be accounted for in order to correctly interpret the light curve and estimate $\lambda$.717 We describe the two effects im aud give approximated analytic expressions for thei aplitucles., We describe the two effects in and give approximated analytic expressions for their amplitudes.718 Iu we present a numerical simulation of au echpsing binary composed of an F aud IL type stars., In we present a numerical simulation of an eclipsing binary composed of an F and K type stars.719 We discuss the results of the numerical simulation inL.. includiug the possibility of detection with data. and possible. degeneracies in the model.," We discuss the results of the numerical simulation in, including the possibility of detection with data, and possible degeneracies in the model."720 We sumnnarize our work in5., We summarize our work in.721. The PRAL effect results from the combination of two effects. the RAL effect aud the beaming effect. briieflv described in the following paragraphs.," The PRM effect results from the combination of two effects, the RM effect and the beaming effect, briefly described in the following paragraphs."722 During different phases of an eclipse. the eclipsing star blocks the light comme from different reeious of the eclipsed star surface. that have differentLm racial velocities (RVs) duc to the rotation of the eclipsed star.," During different phases of an eclipse, the eclipsing star blocks the light coming from different regions of the eclipsed star surface, that have different radial velocities (RVs) due to the rotation of the eclipsed star."723 The observed spectroscopic line profile is distorted and its center is shifted. resulting in the RM. RV igual.," The observed spectroscopic line profile is distorted and its center is shifted, resulting in the RM RV signal."724 The RAL RV curve shape depeuds primarily on the siv-projected angle between the eclipsed stars spin aud the systems orbital angular moment. A. the sky-projected rotational velocity of the eclipsed star. V;sin2. aud the secondary to primary radii ratio. r—RfFeu (eg.etal.2005:Caimeénez2006:Candi&Winn 2007).," The RM RV curve shape depends primarily on the sky-projected angle between the eclipsed star's spin and the system's orbital angular momentum, $\lambda$, the sky-projected rotational velocity of the eclipsed star, $V_{rot}\sin I$, and the secondary to primary radii ratio, $r \equiv R_s/R_p$ \citep[e.g.,][]{ohta05, gimenez06, gaudi07}."725. The beaming effect causes the observed flix of a light-cluitting object to varv with its RV variation., The beaming effect causes the observed flux of a light-emitting object to vary with its RV variation.726 When the objects RV varies periodically. as is the case im binary systelus. it iuduces a periodic sinusoidal variation iu the observed flux.," When the object's RV varies periodically, as is the case in binary systems, it induces a periodic sinusoidal variation in the observed flux."727 When the helt of the secondary can be ucelected (e.g...Alazeh&Faigler2010:Shporerctal. 2010).. the amplitude of such a photometric modulation. in relative flux. IS OpenLvfe. where A is the RV auplitude of the primary aud ο the speed of light.," When the light of the secondary can be neglected \citep[e.g.,][]{mazeh10, shporer10}, , the amplitude of such a photometric modulation, in relative flux, is $\alpha_{beam} 4 K/c$, where $K$ is the RV amplitude of the primary and $c$ the speed of light."728" The cocfücient Apnea, equals unity for bolometric light. aud for a finite baudpass its value depends on the targets spectrum aud the detector transmission curve."," The coefficient $\alpha_{beam}$ equals unity for bolometric light, and for a finite bandpass its value depends on the target's spectrum and the detector transmission curve."729" Since iu stellar biuaries the RV of both compoucuts modulates In opposite phase. the observed effect is the weighted difference of the individual beaming effect inplitudoes. weighted by their relative fluxes (Zuckerotal. 2007): Where 04,:,,,,5. IX. aud E, ave the primary beaming cocfücient. RV amplitude aud fux. respectively.s while Oheam.s We. and Fy are the corresponding quautitics for the secondary."," Since in stellar binaries the RV of both components modulates in opposite phase, the observed effect is the weighted difference of the individual beaming effect amplitudes, weighted by their relative fluxes \citep{zucker07}: : where $\alpha_{beam,p}$, $K_p$, and $F_p$ are the primary's beaming coefficient, RV amplitude and flux, respectively, while $\alpha_{beam,s}$, $K_s$, and $F_s$ are the corresponding quantities for the secondary."730 Several authors have already observed this effect. both from space οιοvanIxkerkwijketal.2010:al.2011) and from the eround (Sliporeretal.2010.. sce also Maxtedetal. 2000)).," Several authors have already observed this effect, both from space \cite[e.g.,][]{vankerkwijk10, mazeh10, bloemen11, carter11} and from the ground \citealt{shporer10}, see also \citealt{maxted00}) )."731 When we apply the beaming effect to the eclipsed star rotational velocity. we ect the photometric analog of the RAL effect which we refer to as the photometric RM effect. or PRM.," When we apply the beaming effect to the eclipsed star rotational velocity, we get the photometric analog of the RM effect which we refer to as the photometric RM effect, or PRM."732 Photoimetrically. the blue shifted photous cluitted from the stars lemiusphere rotating towards the observer make that hemisphere appear shehth brighter than the other. redshitted hemisphere. rotating away from the observer.," Photometrically, the blue shifted photons emitted from the star's hemisphere rotating towards the observer make that hemisphere appear slightly brighter than the other, redshifted hemisphere, rotating away from the observer."733 It is this apparent nou uniforii surface brightness that causes a photometric anomalous signal during eclipse., It is this apparent non uniform surface brightness that causes a photometric anomalous signal during eclipse.734 We adopt a coordinate system centered at the eclipsed star. and the Y axis directed towards the observer while the Y-Z plane contains the eclipsed star rotation axis.," We adopt a coordinate system centered at the eclipsed star, and the Y axis directed towards the observer while the Y-Z plane contains the eclipsed star rotation axis."735" Therefore. the variation in relative flux during primary eclipse does not depend ou the secondary position along the Y axis. but only on the position within the X-Z plane. aud can be described by: where 9 and Z(r.2) are the eclipsed star rotation rate and surface brightuess (not cousicerie the PRAL effect). respectively, and D is the dilution factor. accounting for light from the eclipsing star. so Af is the observed relative fux citference."," Therefore, the variation in relative flux during primary eclipse does not depend on the secondary position along the Y axis, but only on the position within the X-Z plane, and can be described by: where $\Omega$ and ${\cal I}(x,z)$ are the eclipsed star rotation rate and surface brightness (not considering the PRM effect), respectively, and ${\cal D}$ is the dilution factor, accounting for light from the eclipsing star, so $\Delta f$ is the observed relative flux difference."736 The integration includes the non eclipsed stellar surface and we assune fux of unity when the stars are out of eclipse., The integration includes the non eclipsed stellar surface and we assume flux of unity when the stars are out of eclipse.737 is simular to the corresponding equation for the spectroscopic RM effect (ce...Oltaetal.2005).. where the multiplicatiou between 9 aud .c gives the RV at position ντ).," is similar to the corresponding equation for the spectroscopic RM effect \citep[e.g.,][]{ohta05}, where the multiplication between $\Omega$ and $x$ gives the RV at position $x$ $z$ )."738 An order of magnitude estimate of the PRM amplitude Is: We caution that is only a rough estimate. aud Appar decreases for orbits with an inclination angle of (o90 deg.," An order of magnitude estimate of the PRM amplitude is: We caution that is only a rough estimate, and $A_{\rm PRM}$ decreases for orbits with an inclination angle of $i\ \textless\ 90$ deg."739 The primary assuniptious behind are that the eclipsing star is relatively small and faint compared to the eclipsed star., The primary assumptions behind are that the eclipsing star is relatively small and faint compared to the eclipsed star.740 The orbital beaming effect follows the Iseplerian notion of the two stars., The orbital beaming effect follows the Keplerian motion of the two stars.741 Therefore. at the time of conjunctions the orbital beunuing modulation is an almost completely linear variation with time. especially or a circulay orbit.," Therefore, at the time of conjunctions the orbital beaming modulation is an almost completely linear variation with time, especially for a circular orbit."742 When au eclipse occurs the observed ractional brightuess of the two stars changes leading o à variation in the weights iu1.. resulting in a deviation frou the orbital beaming liebt curve.," When an eclipse occurs the observed fractional brightness of the two stars changes, leading to a variation in the weights in, resulting in a deviation from the orbital beaming light curve."743 We refer o this deviation as the in-eclipse orbital beaming. or InOrD. The amplitude of this second. effect. depends on the variation of the eclipsed stars relative brightness. aud its RV variation divine eclipse.," We refer to this deviation as the in-eclipse orbital beaming, or InOrB. The amplitude of this second effect depends on the variation of the eclipsed star's relative brightness, and its RV variation during eclipse."744 The latter can be approximated iu the following wav. for a circular orbit.," The latter can be approximated in the following way, for a circular orbit."745"The RV iuuplitude of a star of massA4 with a binary colupanion of mass Mo is: where eds the orbital seni major axis. 2,4, the orbital period. aud / is the orbital inclination angle.","The RV amplitude of a star of mass$M_1$ with a binary companion of mass $M_2$ is: where $a$ is the orbital semi major axis, $P_{orb}$ the orbital period, and $i$ is the orbital inclination angle."746 The orbital, The orbital747the current tile and consequently increasing the number of assignments.,the current tile and consequently increasing the number of assignments.748 Our tests indicate that. over a larec number of positioners. situations like this happen with relevant frequeney so the draining algorithm achieves a sensibly better performance than other approaches. as we will show below.," Our tests indicate that, over a large number of positioners, situations like this happen with relevant frequency so the draining algorithm achieves a sensibly better performance than other approaches, as we will show below."749 Following this idea. it is rather straightforward. to identily the conllicting cases and formalize this method into an algorithm so that the optimal sequence of tiles is found.," Following this idea, it is rather straightforward to identify the conflicting cases and formalize this method into an algorithm so that the optimal sequence of tiles is found."750 In order to assess the performance of the draining algorithm. we have generated a set of 100 catalogs of randomly distributed targets for svstems with four different arget-to-positioner ratios. namely yo=0.5.1.3.5.," In order to assess the performance of the draining algorithm, we have generated a set of 100 catalogs of randomly distributed targets for systems with four different target-to-positioner ratios, namely $\eta = 0.5,1,3,5$."751 Note hat. as shown in Table 1.. the values of y=1 and y=5 correspond. to the two examples. considered. in his paper. Le. SIDE and BieBOSS. respectively.," Note that, as shown in Table \ref{tab:BB_SIDE}, the values of $\eta = 1$ and $\eta = 5$ correspond to the two examples considered in this paper, i.e. SIDE and BigBOSS, respectively."752 We iwe implemented both the draining algorithm ancl a simple approach where targets are randomly assigned. to xositioners., We have implemented both the draining algorithm and a simple approach where targets are randomly assigned to positioners.753 In. Table 2... we show the average total fraction of all targets assigned to positioners after cach of the first 10 tiles (cumulative fractions) using both these metho:wa or the target-to-positioner ratios considered.," In Table \ref{tab:random}, we show the average total fraction of all targets assigned to positioners after each of the first 10 tiles (cumulative fractions) using both these methods, for the target-to-positioner ratios considered."754 The tile at which SO of the total number of targets is successfully assigned to positioners has been highlighted for each 5g., The tile at which $80\%$ of the total number of targets is successfully assigned to positioners has been highlighted for each $\eta$.755 The number of tiles needed to reach this completeness. (that we have selected: arbitrarily) obviously increases with the target-to-positioner ratio. ranging from only 1-2 tiles for gx το αρ to 5 tiles for jj—5.," The number of tiles needed to reach this completeness (that we have selected arbitrarily) obviously increases with the target-to-positioner ratio, ranging from only 1-2 tiles for $\eta \leq 1$ to up to 5 tiles for $\eta=5$."756 At this point it is necessary to remind that the scope of this optimization is not to reduce drastically the average number of tiles needed. to achieve a certain completeness. but to increase the fraction of targets observed. in the same number of tiles.," At this point it is necessary to remind that the scope of this optimization is not to reduce drastically the average number of tiles needed to achieve a certain completeness, but to increase the fraction of targets observed in the same number of tiles."757 As we can see in Table 2.. the draining algorithm: presented. here increases the assignments in approximately 244 as compare to à greedy. procedure at the 80% completeness level.," As we can see in Table \ref{tab:random}, the draining algorithm presented here increases the assignments in approximately $2\%$ as compare to a greedy procedure at the $80 \%$ completeness level."758 Fie., Fig.759 4 also illustrates the performance of the draining algorithm as compared to a random assignment., \ref{fig:draining} also illustrates the performance of the draining algorithm as compared to a random assignment.760 Here. the dilference in the cumulative percentage of targets assigned with our optimized algorithm (Ayeu.) and with a random approach (fy...) is shown as a function of the number of tiles.," Here, the difference in the cumulative percentage of targets assigned with our optimized algorithm $F_{drain}$ ) and with a random approach $F_{rand}$ ) is shown as a function of the number of tiles."761 Fig., Fig.762 4 shows that the gain provided by this optimized method increases slightly with η. ranging from ~1.7% for p—0.5 to —2.5% for y=5.," \ref{fig:draining} shows that the gain provided by this optimized method increases slightly with $\eta$, ranging from $\sim 1.7\%$ for $\eta=0.5$ to $\sim 2.5\%$ for $\eta=5$."763 Note that. due to the nature of this optimization. the improvement occurs in the first few tiles.," Note that, due to the nature of this optimization, the improvement occurs in the first few tiles."764 In the following sections we will show how an improvement like this can have a strong elfect in the design of a An important issue related to the fiber assignment »ocess in this type of fiber-fed spectrographs is the so- fiber collision problem., In the following sections we will show how an improvement like this can have a strong effect in the design of a An important issue related to the fiber assignment process in this type of fiber-fed spectrographs is the so-called fiber collision problem.765" This concept was used to describe the fact that in the SDSS (7). fibers could not be "" ≻↓⋯⇍⋯⇂≼∼↓∪⊳∖∢⊾↓⋅↿↕⋜⋯⋅↱≻⋅↱≻⋜⋯∼⊳∖", This concept was used to describe the fact that in the SDSS \citep{York2000} fibers could not be placed closer than $55''$ arcsec.766⋖⊾≼⋱⊾↔↓≻∢⋅≼⇍⇂↓⋅∪⋏∙≟↓⋅⋜↧↓≻↓↥⊳∖⇂↓⋯↿⇂⋖⊾⋜∐⊔↓⋅⋖⋅ . ⋅ ⋜↧∐∣⋡∢⊾↓⋅↓≻∪≱∖⋠↓↿⊀↓∪⊔⊀↓⊔⋏∙≟↓⋅∪∣⋯↿⋜↧⊳∖↿↓⋯↿∠⇂∢⊾⊳∖≼⇍↓⋰↓∣⋈⋅∠⇂⊀↓⊔∺⋖⊾≼∼↿⊲↓∪⊔∶⊰ present a similar problem. as due to the physical size of the positioners. frequently two or more targets cannot x: Observed simultaneously. (1.0. in the same tile).," Spectrographs that feature a fiber positioning robot as that described in Section \ref{sec:robot} present a similar problem, as due to the physical size of the positioners, frequently two or more targets cannot be observed simultaneously (i.e. in the same tile)."767 The results shown in this work were obtained assumüng that »ositioners. have no physical size. hence neglecting the »xossibilitv of fiber collisions.," The results shown in this work were obtained assuming that positioners have no physical size, hence neglecting the possibility of fiber collisions."768 The typical number of collisions as a function of the target-to-positioner ratio. 7. will depend on the geometry of the svstem. Le. on the number ancl he size of the positioners.," The typical number of collisions as a function of the target-to-positioner ratio, $\eta$, will depend on the geometry of the system, i.e. on the number and the size of the positioners."769 “Lhe problem. however. can x: solved. naturally within the framework of the draining algorithm.," The problem, however, can be solved naturally within the framework of the draining algorithm."770 Fiber collisions will occur exclusively in common areas and this method is specifically designed to deal with objects in these regions conveniently. ancl to ensure that," Fiber collisions will occur exclusively in common areas and this method is specifically designed to deal with objects in these regions conveniently, and to ensure that"771were able to derive the following conclusions: In GRB external shocks that accelerate ions to Lorentz factors >;<>10°. inverse Compton cooling in the shock upstream hinders nonthermal electron acceleration to high energies.,"were able to derive the following conclusions: In GRB external shocks that accelerate ions to Lorentz factors $\gamma_i\gg 10^3$, inverse Compton cooling in the shock upstream hinders nonthermal electron acceleration to high energies."772 Because of this. nonthermal electrons do not penetrate as far into the shock upstream as the highest-energy nonthermal ions do.," Because of this, nonthermal electrons do not penetrate as far into the shock upstream as the highest-energy nonthermal ions do."773 Thus. à region exists in the shock upstream far from the shock transition at R~αἱο. but still behind the photon shell at R=cr. where return current flows to cancel the charge separation between the nonthermal electrons and tons.," Thus, a region exists in the shock upstream far from the shock transition at $R\sim ct[1-(8\Gamma^2)^{-1}]$, but still behind the photon shell at $R=ct$, where return current flows to cancel the charge separation between the nonthermal electrons and ions."774 As the return current flows across the weak pre-existing magnetic field of the shock upstream. the Ampeérre force accelerates the upstream plasma perpendicular to the direction of shock propagation.," As the return current flows across the weak pre-existing magnetic field of the shock upstream, the Ampèrre force accelerates the upstream plasma perpendicular to the direction of shock propagation."775 If the upstream field reverses on scales A«Κ/ΦΓ”. the transverse acceleration produces a nonlinear density contrast on the same scales.," If the upstream field reverses on scales $\lambda\ll R/8\Gamma^2$, the transverse acceleration produces a nonlinear density contrast on the same scales."776 If the pre-existing field is quasr-uniform (non-reversing). Bell's streaming instability will efficiently convert the quasi-uniform field into a reversing field during the light-crossing time of the shock precursor.," If the pre-existing field is quasi-uniform (non-reversing), Bell's streaming instability will efficiently convert the quasi-uniform field into a reversing field during the light-crossing time of the shock precursor."777 As the shock transition sweeps the resulting density clumps. the bulk kinetic energy of the blastwave is converted into vortical energy.," As the shock transition sweeps the resulting density clumps, the bulk kinetic energy of the blastwave is converted into vortical energy."778 The vortical eddies in the shock downstream turn over many times and amplify the magnetic field via a dynamo mechanism., The vortical eddies in the shock downstream turn over many times and amplify the magnetic field via a dynamo mechanism.779 For clumps of peak density contrast of about one. the vortical energy (Sironi&Goodman2007) and with it the magnetic energy density can be amplified to eg~ QD. where in GRB external shocks. [<few«100.," For clumps of peak density contrast of about one, the vortical energy \citep{Sironi:07} and with it the magnetic energy density can be amplified to $\epsilon_B \sim (3\Gamma)^{-1}$ , where in GRB external shocks, $\Gamma \lesssim \textrm{ few }\times100$."780 This is consistent with the observed GRB light curves and spectra., This is consistent with the observed GRB light curves and spectra.781 The generated magnetic field will be coherent on scales much larger than the plasma skin depth and will. as such. not be susceptible to rapid collisionless decay.," The generated magnetic field will be coherent on scales much larger than the plasma skin depth and will, as such, not be susceptible to rapid collisionless decay."782 Taken together. these results indicate that the microgauss magnetic field (ep~ 107) typical of the interstellar medium is sufficient to drive Bell’s mechanism in. ultrarelativistic GRB external. shocks and deliver nonlinear density inhomogeneities. to the shock transition.," Taken together, these results indicate that the microgauss magnetic field $\epsilon_B\sim10^{-9}$ ) typical of the interstellar medium is sufficient to drive Bell's mechanism in ultrarelativistic GRB external shocks and deliver nonlinear density inhomogeneities to the shock transition."783 We speculatively propose a structure for the shock precursor consisting of four concentric zones characterized by different forms of plasma self-organization., We speculatively propose a structure for the shock precursor consisting of four concentric zones characterized by different forms of plasma self-organization.784 First. the outermost region of the precursor 1s the region. populated by streaming. nonthermal protons but devoid of nonthermal electrons.," First, the outermost region of the precursor is the region populated by streaming, nonthermal protons but devoid of nonthermal electrons."785 There. the plasma develops non-linear density inhomogeneities.," There, the plasma develops non-linear density inhomogeneities."786 Second. a region that. still contains a return current but where the nonthermal particle precursor streaming through the shock upstream is susceptible to small-scale kinetic plasma instabilities.," Second, a region that still contains a return current but where the nonthermal particle precursor streaming through the shock upstream is susceptible to small-scale kinetic plasma instabilities."787 Third. a region containing the relatively low-energy nonthermal electrons that can be accelerated in the shock in spite of the inverse Compton cooling losses: in this region. the return current is absent.," Third, a region containing the relatively low-energy nonthermal electrons that can be accelerated in the shock in spite of the inverse Compton cooling losses; in this region, the return current is absent."788 Finally. the fourth region is the shock transition. itself. where kinetic instabilities and plasma waves facilitate plasma isotropization and establish the hydrodynamic jump.," Finally, the fourth region is the shock transition itself, where kinetic instabilities and plasma waves facilitate plasma isotropization and establish the hydrodynamic jump."789 The relative ordering of the second and the third region may vary., The relative ordering of the second and the third region may vary.790 We thank the anonymous referee for emphasizing uncertainties associated with the efficiency of the diffusive shock acceleration process in ultrarelativistic collisionless shocks. and acknowledge numerous invaluable discussions with Uri Keshet and Anatoly Spitkovsky.," We thank the anonymous referee for emphasizing uncertainties associated with the efficiency of the diffusive shock acceleration process in ultrarelativistic collisionless shocks, and acknowledge numerous invaluable discussions with Uri Keshet and Anatoly Spitkovsky."791 This research was supported by a Senior Research Fellowship from the Sherman Fairchild Foundation and NASA grant NNHOSZDAOOIN (to Ε.Ν.., This research was supported by a Senior Research Fellowship from the Sherman Fairchild Foundation and NASA grant NNH05ZDA001N (to E. N.).792"Although the phases of the PCM have strong correlations with those of the ILC map, the TOH foreground-cleaned map and the Wiener-filtered map, as shown in Fig.14,, there are undoubtedly deviations in phases between them, which is an indication of different morphology.","Although the phases of the PCM have strong correlations with those of the ILC map, the TOH foreground-cleaned map and the Wiener-filtered map, as shown in \ref{pcmilcxcorr}, there are undoubtedly deviations in phases between them, which is an indication of different morphology."793 The CMB map from the “blind” PCM method allows us to reconstruct the foregrounds for each band., The CMB map from the “blind” PCM method allows us to reconstruct the foregrounds for each band.794" In Fig.15 we show at the top the foreground map at the V band, a simple subtraction of the PCM from the V-band map."," In \ref{pcmforeground} we show at the top the foreground map at the V band, a simple subtraction of the PCM from the V-band map."795 In the middle panel we show the foreground map at the same band and the difference of these two panels is shown at the bottom., In the middle panel we show the foreground map at the same band and the difference of these two panels is shown at the bottom.796" As one can see from this Figure, an additional power of the foregrounds from the PCM subtraction than the foreground map is clearly shown in the third panel, in particular we can see strong contribution of the of the point-like sources residues along the Galactic plane which are detected and removed as foregrounds from the PCM subtraction."," As one can see from this Figure, an additional power of the foregrounds from the PCM subtraction than the foreground map is clearly shown in the third panel, in particular we can see strong contribution of the of the point-like sources residues along the Galactic plane which are detected and removed as foregrounds from the PCM subtraction."797" (?,, ?,, ?,, ?)). ?)), extremely(?,, ?,, ?,, 2, 2, 2, 2, ?)). ?,, ?)), (?).."," \citealt{Reipurth2001}, \citealt{Close2003}, \citealt{Siegler2005}, \citealt{Konopacky2007}) \citealt{Bate2009}) \citealt{PhanBao2006}, \citealt{Artigau2007}, \citealt{Caballero2007}, \citealt{Artigau2007}, \citealt{Law2008}, \citealt{Radigan2009}, \citealt{Zhang2010}, \citealt{Faherty2010}) \citealt{Close2003}, \citealt{Konopacky2007}) \citep{Kouwenhoven2010}."798 the higher-order multiplicity statistics of the systems may be different from that of systems with larger binding energies., the higher-order multiplicity statistics of the systems may be different from that of systems with larger binding energies.799" In addition to binding energy considerations for VLM stars, empirical limits on binary separation have also been found among higher-mass M-dwarfs: logamax=3.3Mitot+1.1 for total masses greater than 0.3Mo (?),, and for lower masses Aamax=1400M2, (?),, where My is the total system mass in solar masses and aga, is the maximum separation in AU."," In addition to binding energy considerations for VLM stars, empirical limits on binary separation have also been found among higher-mass M-dwarfs: $\rm \log a_{max} = 3.3 M_{tot} + 1.1$ for total masses greater than ${\rm M_{\odot}}$ \citep{Reid2001}, and for lower masses $\rm a_{max} = 1400 M_{tot}^{2}$ \citep{Burgasser2003}, where $\rm{M_{tot}}$ is the total system mass in solar masses and $\rm{a_{max}}$ is the maximum separation in AU."800" that violate these limits could be considered “unusual”, Systemsand may similarly have different multiplicity propertiesfrom themuchmorecommoncloseM-dwarfbinaries."," Systems that violate these limits could be considered “unusual”, and may similarly have different multiplicity propertiesfrom themuchmorecommoncloseM-dwarfbinaries."801The totalmasses ofsuchunusuallywide systems,The totalmasses ofsuchunusuallywide systems802"using the convolution kernel, and then a 2D Fourier transform can be used to recover the sky brightness distribution.","using the convolution kernel, and then a 2D Fourier transform can be used to recover the sky brightness distribution."803 This algorithm can be applied to the case of Faraday synthesis without modification., This algorithm can be applied to the case of Faraday synthesis without modification.804" It should also be possible to apply the A-projection algorithm of ?,, which corrects for direction-dependent beam effects in a manner similar to the w-projection algorithm."," It should also be possible to apply the A-projection algorithm of \citet{bhatnagar_aprojection_2008}, which corrects for direction-dependent beam effects in a manner similar to the $w$ -projection algorithm."805" To compare the 3D approach to polarization imaging with the traditional 2+1D approach, we have implemented a proof of concept 3D imaging and deconvolution software package calledfsimager."," To compare the 3D approach to polarization imaging with the traditional 2+1D approach, we have implemented a proof of concept 3D imaging and deconvolution software package called."806". For deconvolution, a 3D CLEAN algorithm has been implemented because it is by far the most common deconvolution method used in radio astronomical imaging, and with it we can make the most direct comparison between the two techniques."," For deconvolution, a 3D CLEAN algorithm has been implemented because it is by far the most common deconvolution method used in radio astronomical imaging, and with it we can make the most direct comparison between the two techniques."807" The CLEAN algorithm (?) is a non-linear, iterative deconvolution routine."," The CLEAN algorithm \citep{hogbom74} is a non-linear, iterative deconvolution routine."808 The algorithm makes the implicit assumption that the sky is composed of point sources distributed throughout a mostly blank field., The algorithm makes the implicit assumption that the sky is composed of point sources distributed throughout a mostly blank field.809" Over the last decades, it has been shown to work quite well even for fields that do not strictly meet this criterion."," Over the last decades, it has been shown to work quite well even for fields that do not strictly meet this criterion."810" In brief, the procedure calls for iteratively building up a model of the sky by locating the peak of the image, adding a point source to the model at the location of the peak and with some fraction of its strength, and subtracting from the image the new model point convolved with the dirty beam."," In brief, the procedure calls for iteratively building up a model of the sky by locating the peak of the image, adding a point source to the model at the location of the peak and with some fraction of its strength, and subtracting from the image the new model point convolved with the dirty beam."811" This is repeated until one can add no further flux to the sky model, i.e. when one is CLEANing the noise."," This is repeated until one can add no further flux to the sky model, i.e. when one is CLEANing the noise."812 A complete description of the 3D CLEAN algorithm that we have implemented is given in Appendix ??.., A complete description of the 3D CLEAN algorithm that we have implemented is given in Appendix \ref{sec:3DCLEAN}.813" Radio astronomical imaging relies heavily on Fourier transforms, and because the number of pixels in the 3D image of the Faraday spectrum is large, fast Fourier transforms (FFTs) are required for computational feasibility."," Radio astronomical imaging relies heavily on Fourier transforms, and because the number of pixels in the 3D image of the Faraday spectrum is large, fast Fourier transforms (FFTs) are required for computational feasibility."814" Visibility data is not collected on a regularly spaced grid in (u,v,A*)-space."," Visibility data is not collected on a regularly spaced grid in $(u,v,\lambda^{2})$ -space."815" To use the FFT algorithm, the data must be interpolated onto regularly spaced grid points prior to processing."," To use the FFT algorithm, the data must be interpolated onto regularly spaced grid points prior to processing."816 For this we employ a well known procedure known as that is used extensively in aperture synthesis imaging as well as in medical imaging., For this we employ a well known procedure known as that is used extensively in aperture synthesis imaging as well as in medical imaging.817" Specifically, we have implemented an algorithm described by ?.."," Specifically, we have implemented an algorithm described by \citet{beatty_gridding_2005}."818" In brief, we convolve the data with a Kaiser-Bessel window function (KBWF) and sample the result on a regular grid in (u,v,A*)-space."," In brief, we convolve the data with a Kaiser-Bessel window function (KBWF) and sample the result on a regular grid in $(u,v,\lambda^{2})$ -space."819" After this procedure, one is able to perform a FFT with the same result achieved by using a discrete Fourier transformation, to within an arbitrarily small accuracy."," After this procedure, one is able to perform a FFT with the same result achieved by using a discrete Fourier transformation, to within an arbitrarily small accuracy."820 The attenuation of the image plane caused by the convolution with the KBWF is corrected for by dividing the dirty image by the Fourier transform of the KBWF., The attenuation of the image plane caused by the convolution with the KBWF is corrected for by dividing the dirty image by the Fourier transform of the KBWF.821 There are a two parameters in the gridding procedure that affect precision at the cost of computational time., There are a two parameters in the gridding procedure that affect precision at the cost of computational time.822 One parameter describes the extent of the KBWF in visibility space., One parameter describes the extent of the KBWF in visibility space.823" The second parameter, the so-called oversampling ratio, is the factor by which the image plane should be enlarged in order to mitigate problems that occur at the edges of the image."," The second parameter, the so-called oversampling ratio, is the factor by which the image plane should be enlarged in order to mitigate problems that occur at the edges of the image."824" With the parameters that we have chosen, for the KBWF to extend over 6 pixels in each of u, v, and 22, and an oversampling ratio of 1.5, the results are the same as one would obtain with a discrete Fourier transformation (DFT) to within one part in 10,000."," With the parameters that we have chosen, for the KBWF to extend over 6 pixels in each of $u$, $v$, and $\lambda^{2}$, and an oversampling ratio of 1.5, the results are the same as one would obtain with a discrete Fourier transformation (DFT) to within one part in 10,000."825 In fact the dynamic range is only so limited near the edges of the image where the effects of the convolution with the KBWF are the most dramatic., In fact the dynamic range is only so limited near the edges of the image where the effects of the convolution with the KBWF are the most dramatic.826" Away from the edges of the image, the dynamic range is much higher."," Away from the edges of the image, the dynamic range is much higher."827" Overall, the dynamic range can easily be improved by changing the gridding parameters, but this is done at the expense of increased processing and memory requirements."," Overall, the dynamic range can easily be improved by changing the gridding parameters, but this is done at the expense of increased processing and memory requirements."828" We have implemented in Python, thus allowing for rapid development and testing, but resulting in overall poor performance."," We have implemented in Python, thus allowing for rapid development and testing, but resulting in overall poor performance."829" To improve the situation, we have optimized some sub-functions (particularly the gridding routines) using Cython and in the end the code performs admirably."," To improve the situation, we have optimized some sub-functions (particularly the gridding routines) using Cython and in the end the code performs admirably."830" We can load a 1GB data set, grid, image, and CLEAN a 16 megapixel image using 500 iterations in about 15 minutes on our 2.4 GHz Core 15 development machine with 8 GB of RAM."," We can load a 1GB data set, grid, image, and CLEAN a 16 megapixel image using 500 iterations in about 15 minutes on our 2.4 GHz Core i5 development machine with 8 GB of RAM."831 The most major limitation of the current version of the software is that all of the data resides in memory and this limits the size of the images that can be produced to the amount of memory that is available on the machine., The most major limitation of the current version of the software is that all of the data resides in memory and this limits the size of the images that can be produced to the amount of memory that is available on the machine.832" We have run all tests on a computer having 64 GB of memory, and are limited to producing image cubes that are 400 megapixels in size (about 750 pixels per side)."," We have run all tests on a computer having 64 GB of memory, and are limited to producing image cubes that are 400 megapixels in size (about 750 pixels per side)."833" This may be sufficient for imaging small fields of view, but when imaging data from a wide-field, high resolution instrument (e.g. LOFAR), this is inadequate."," This may be sufficient for imaging small fields of view, but when imaging data from a wide-field, high resolution instrument (e.g. LOFAR), this is inadequate."834" To compare the 3D and 2+1D approaches, we have produced a mock observation of a set of polarized point sources."," To compare the 3D and 2+1D approaches, we have produced a mock observation of a set of polarized point sources."835" In this section, we first describe the mock data, and then we describe the method that we use to image the data using the 2+1D"," In this section, we first describe the mock data, and then we describe the method that we use to image the data using the 2+1D"836We have presented a Monte-Carlo simulation of the Galactic-plane population of AISPs and corresponding predictions for the numbers of both racdio-quiet and radio-Ioud AISDPs that are detectable as 5-rav sources.,We have presented a Monte-Carlo simulation of the Galactic-plane population of MSPs and corresponding predictions for the numbers of both radio-quiet and radio-loud MSPs that are detectable as $\gamma$ -ray sources.837 In order to accomplish this. we made significant improvements in our population statistics Monte Carlo code by adding the more realistic description of the Galactic potential of Dehnen&Binney(1998) with a more accurate 5th order Cash-Karp Hunge-Ixutta trajectory integration routine (Pressetal.1992).. using improved all- threshold maps lor EGRET (Casandjian&Grenier2007) and GLAST (Grenier Casandjian. private communication). and including the Swinburne Intermediate Latitude radio survey (Edwardsοἱal.2001).," In order to accomplish this, we made significant improvements in our population statistics Monte Carlo code by adding the more realistic description of the Galactic potential of \citet{Dehnen98} with a more accurate 5th order Cash-Karp Runge-Kutta trajectory integration routine \citep{Press92}, using improved all-sky threshold maps for EGRET \citep{Casand07} and GLAST (Grenier Casandjian, private communication), and including the Swinburne Intermediate Latitude radio survey \citep{Edwards01}."838. We have moclified the intrinsic radio Iuminositv model of ACC to describe the total radio luminosity of both normal ancl MSPs., We have modified the intrinsic radio luminosity model of ACC to describe the total radio luminosity of both normal and MSPs.839 From our study of radio pulsars with thiree-peak profiles (Gonthieretal.2006.2007).. we find that the ratio of (he core-to-cone peak fluxes lor short period pulsars is much smaller for short period pulsars than the ratio predicted by ACC model.," From our study of radio pulsars with three-peak profiles \citep{Gon06,Gon07}, we find that the ratio of the core-to-cone peak fluxes for short period pulsars is much smaller for short period pulsars than the ratio predicted by ACC model."840 Although MSPs have on average larger pulse widths than NPs. (this resulting radio beam geometry model provides a reasonable agreement to the average pseudoluminosities ancl pulse widths at 1400 MIIz and pulse widths of both NPs and MSPs.," Although MSPs have on average larger pulse widths than NPs, this resulting radio beam geometry model provides a reasonable agreement to the average pseudoluminosities and pulse widths at 1400 MHz and pulse widths of both NPs and MSPs."841 We inelucle a 5-rav beam geometry and luminosity model of the curvature radiation from all open field lines within a pair-stirved polar cap model (Harding. (hat accounts for 5-ray. emission below the curvature radiation pair death line. which is applicable to MSPs.," We include a $\gamma$ -ray beam geometry and luminosity model of the curvature radiation from all open field lines within a pair-starved polar cap model \citep{Hard05} that accounts for $\gamma$ -ray emission below the curvature radiation pair death line, which is applicable to MSPs."842 These improvements in our computer code have allowed us to study the population statistics of radio and y-ray MSPs to complement our previous studies of NPs from the Galactie disk., These improvements in our computer code have allowed us to study the population statistics of radio and $\gamma$ -ray MSPs to complement our previous studies of NPs from the Galactic disk.843 As a first order study. we believe that we have improved the simulation bv including à beam geometry for MSPs ancl an intrinsic radio luminosity whose functional form allows for the description of the population statistics of normal pulsars.," As a first order study, we believe that we have improved the simulation by including a beam geometry for MSPs and an intrinsic radio luminosity whose functional form allows for the description of the population statistics of normal pulsars."844 The actual. beam geometry. of MSPs max (urn out to be significantly different. and require a different model Chan the one proposed here from the work of Ixijak&Gil(1998.2003).," The actual beam geometry of MSPs may turn out to be significantly different and require a different model than the one proposed here from the work of \citet{Kijak98,Kijak03}."845". The population statistics study is not sensitive enough to discriminate between beam geometry models as the average flux of the profile is the quantity (hat is compared to the 55,58 of the radio survevs.", The population statistics study is not sensitive enough to discriminate between beam geometry models as the average flux of the profile is the quantity that is compared to the $S_{min}$ s of the radio surveys.846 A detailed study including relativistie effects will be necessary along with --[unigh quality polarization data max enable establishment of systematic trends (hat allows Lor the development of an adequate beam model for MSPs., A detailed study including relativistic effects will be necessary along with high quality polarization data may enable establishment of systematic trends that allows for the development of an adequate beam model for MSPs.847 In this study. we do not attempt to describe the numerous MSPs within globular ]usters.," In this study, we do not attempt to describe the numerous MSPs within globular clusters."848 Limiting our study (ο the ASPs born in the Galactic disk. we treat. them as point parücles. evolving their location within the Galactic potential aud (heir spin-«down. alter spin-up by mass accretion [rom a binary companion star has ended.," Limiting our study to the MSPs born in the Galactic disk, we treat them as point particles, evolving their location within the Galactic potential and their spin-down, after spin-up by mass accretion from a binary companion star has ended."849 This group of old. short period pulsars with low magnetic fields are eiven radio and y-ray beam ancl bhuninositw characteristics and filtered through. a set of ten radio surveys and (he 5-rav. instruments," This group of old, short period pulsars with low magnetic fields are given radio and $\gamma$ -ray beam and luminosity characteristics and filtered through a set of ten radio surveys and the $\gamma$ -ray instruments"850undergo significant baryonic evolution alter reionization.,undergo significant baryonic evolution after reionization.851 The easiest way to suppress star formation in the lower mass non-lossils is to raise the filtering velocity., The easiest way to suppress star formation in the lower mass non-fossils is to raise the filtering velocity.852 As has already been discussed in Chapter 4. any non-fossil embedded in the WHIM (7T.—10? K) would have à eyes~LO km !," As has already been discussed in Chapter 4, any non-fossil embedded in the WHIM $T\sim10^5$ K) would have a $v_{filter}\sim40$ km $^{-1}$."853" However, the WHIM does not exist until =<1 (?).. leaving ~6 Gyr alter reionization when the non-lossils could have accreted gas and formed stars."," However, the WHIM does not exist until $z<1$ \citep{Smithetal:10}, leaving $\sim6$ Gyr after reionization when the non-fossils could have accreted gas and formed stars."854" Active galactic nuclei (AGN) eject enormous amounts of energy into their environs, heating the gas and raising the filtering velocity, but how [ar [rom the host galaxy the AGN 1s ellective at suppressing star formation in dwarts .and for how long is unclear."," Active galactic nuclei (AGN) eject enormous amounts of energy into their environs, heating the gas and raising the filtering velocity, but how far from the host galaxy the AGN is effective at suppressing star formation in dwarfs ,and for how long is unclear."855" In addition, we see a bright satellite problem around every large Local Volume galaxy."," In addition, we see a bright satellite problem around every large Local Volume galaxy."856" Is it reasonable to assume that, at some point in its evolution, every £L, galaxy hosted an AGN?"," Is it reasonable to assume that, at some point in its evolution, every $L_\ast$ galaxy hosted an AGN?"857 A final possibility is that reionization was extremely efficient at quenching star formation in 20—lO kms B halos and the were never able to build up enough gas [rom the post-reionization IGM to form additional stars., A final possibility is that reionization was extremely efficient at quenching star formation in $20-40$ km $^{-1}$ halos and the non-fossils were never able to build up enough gas from the post-reionization IGM to form additional stars.858" In summary, while the bright satellite problem can be ""solved"" for the primordial population alone, we sull need to account for the post-reionization evolution of the non-fossils."," In summary, while the bright satellite problem can be “solved” for the primordial population alone, we still need to account for the post-reionization evolution of the non-fossils."859" In order to maintain the agreement with observations, only 10% of the non-fossils can form significant stellar populations alter reionization."," In order to maintain the agreement with observations, only $\sim10\%$ of the non-fossils can form significant stellar populations after reionization."860 Determining how and if the other ~90'€ can be suppressed will tell us how much of a problem the bright satellite problem is., Determining how and if the other $\sim90\%$ can be suppressed will tell us how much of a problem the bright satellite problem is.861" The simulations presented in this paper were carried out using computing clusters administered by the Center for Theory and Computation of the Department of Astronomy at the University of Maryland ϱyorp). and the Office of Information Technology at the University of Maryland (""hpec)."," The simulations presented in this paper were carried out using computing clusters administered by the Center for Theory and Computation of the Department of Astronomy at the University of Maryland (""yorp""), and the Office of Information Technology at the University of Maryland (""hpcc"")."862 This research was supported by NASA grants NNXO7AHIOG and NNXIOAHIOG. The authors thank the anonymous referee [or constructive comments and feedback., This research was supported by NASA grants NNX07AH10G and NNX10AH10G. The authors thank the anonymous referee for constructive comments and feedback.863" Thanks Irom MSB and MR to Stacy McGaugh, Derek Richardson and Rosie Wyse lor helpful conversations and comments."," Thanks from MSB and MR to Stacy McGaugh, Derek Richardson and Rosie Wyse for helpful conversations and comments."864 MSB would like to thank Susan Lamb for discussions of dwarf dynamics and Evan Kirby and Beth Willman for discussions of modeling and observations., MSB would like to thank Susan Lamb for discussions of dwarf dynamics and Evan Kirby and Beth Willman for discussions of modeling and observations.865"is strongly dependent on rotation rate, mass and metallicity suggesting that it is essential to explore populations covering as wide a range as possible in order to test rotating models.","is strongly dependent on rotation rate, mass and metallicity suggesting that it is essential to explore populations covering as wide a range as possible in order to test rotating models."866" In order to compare the difference in the evolution of a star owing to the details of the model for convective angular momentum transport we now focus on cases 1, 4, 5 and 6."," In order to compare the difference in the evolution of a star owing to the details of the model for convective angular momentum transport we now focus on cases 1, 4, 5 and 6."867 Uniform specific angular momentum in the core causes more shear mixing near the core-envelope boundary than when the core is solid body rotating as shown in Fig. 10.., Uniform specific angular momentum in the core causes more shear mixing near the core-envelope boundary than when the core is solid body rotating as shown in Fig. \ref{convdist}.868 This results in higher luminosity stars with similar temperatures., This results in higher luminosity stars with similar temperatures.869" There is almost no difference between cases 4, 5 and 6 in the HR diagram."," There is almost no difference between cases 4, 5 and 6 in the HR diagram."870" When we compare the different models for convection in a Hunter diagram we see that cases 4, 5 and 6, which have uniform specific angular momentum throughout their convective zones, have significantly more enrichment for all masses and rotation rates than case 1."," When we compare the different models for convection in a Hunter diagram we see that cases 4, 5 and 6, which have uniform specific angular momentum throughout their convective zones, have significantly more enrichment for all masses and rotation rates than case 1."871 The difference is more pronounced for higher-mass rapid rotators (Fig. 11))., The difference is more pronounced for higher-mass rapid rotators (Fig. \ref{Nsol2}) ).872" However, we note that it is more difficult to distinguish between cases 4, 5 and 6."," However, we note that it is more difficult to distinguish between cases 4, 5 and 6."873" For the highest mass stars we do find some difference in the enrichment of nitrogen and helium-3 between the models but recall that there is a difference in Dcos, of four orders of magnitude between cases 5 and 6.", For the highest mass stars we do find some difference in the enrichment of nitrogen and helium-3 between the models but recall that there is a difference in $D_{\rm conv}$ of four orders of magnitude between cases 5 and 6.874 Given the small magnitude of the change in enrichment and structure over such a range of diffusion coefficients it seems unlikely that these tests can adequately distinguish between convective models., Given the small magnitude of the change in enrichment and structure over such a range of diffusion coefficients it seems unlikely that these tests can adequately distinguish between convective models.875" In addition, adjusting the calibration of case 1 could produce a very similar effect making it difficult even to distinguish between n=0 and n=2 models from observations."," In addition, adjusting the calibration of case 1 could produce a very similar effect making it difficult even to distinguish between $n=0$ and $n=2$ models from observations."876" At the same time though, it is interesting to note the significant change that modifying the core angular momentum distribution has had on the evolution of the surface composition."," At the same time though, it is interesting to note the significant change that modifying the core angular momentum distribution has had on the evolution of the surface composition."877The dynamical evolution of globular clusters has long been the subject of many theoretical studies. including a number of recent papers utilizing state of the art simulations (e.g.Makino2003.anclreferences therein)..,"The dynamical evolution of globular clusters has long been the subject of many theoretical studies, including a number of recent papers utilizing state of the art simulations \citep[e.g.][ and references878therein]{BM}."879 These studies find that mass loss due to (wo body relaxation anc (he resulting evaporation is (he primary mechanism lor the destruction of globular clusters., These studies find that mass loss due to two body relaxation and the resulting evaporation is the primary mechanism for the destruction of globular clusters.880 Onlv those clusters with disruption timescales similar to or less than a IIubble time will be significantly changed by Chis evolution over their lifetimes., Only those clusters with disruption timescales similar to or less than a Hubble time will be significantly changed by this evolution over their lifetimes.881 As evaporation causes clusters to lose mass at a fairly constant rate. the disruption timescale is directly related to the initial mass of the cluster.," As evaporation causes clusters to lose mass at a fairly constant rate, the disruption timescale is directly related to the initial mass of the cluster."882 Therefore. the clusters with the lowest initial masses should constrain the form of this evolution most stronelv.," Therefore, the clusters with the lowest initial masses should constrain the form of this evolution most strongly."883 These low mass clusters have lower luminosities. which makes (hem difficult to observe in other galaxies.," These low mass clusters have lower luminosities, which makes them difficult to observe in other galaxies."884 For the Milky Way. where finding lower huminositv clusters is not as diffieult. the small total nunmber of clusters prevents anv results [rom being statistically strong.," For the Milky Way, where finding lower luminosity clusters is not as difficult, the small total number of clusters prevents any results from being statistically strong."885 What is needed to provide constraints on the models of the ανασα] evolution of globular clusters is a system whieh has both large numbers. and observations that reach low masses with a high degree ol accuracy and reliability.," What is needed to provide constraints on the models of the dynamical evolution of globular clusters is a system which has both large numbers, and observations that reach low masses with a high degree of accuracy and reliability."886 In (his paper. we present results [rom new. very deep IIST images of AIST (hat achieves these 5goals of depth and large5 numbers of 5globular clusters.," In this paper, we present results from new, very deep HST images of M87 that achieves these goals of depth and large numbers of globular clusters."887 In 82. we present the data and explain the procedures used to measure (he elobular clusters in M87.," In 2, we present the data and explain the procedures used to measure the globular clusters in M87."888 We present our luminosity [function in 83. and compare it to other deep Iuminositv functions that have been previously published.," We present our luminosity function in 3, and compare it to other deep luminosity functions that have been previously published."889 We show our mass function. and show (he constraints it gives [or iheoretical models of 5globular cluster evolution in 84.," We show our mass function, and show the constraints it gives for theoretical models of globular cluster evolution in 4."890 Finally. we present our conclusions in $5.," Finally, we present our conclusions in 5."891The mechanism of forming nanoflares is the dissipation of current sheets arisen from tangential discontinuities in the continuously evolving corona (Levine 1974. Parker 1933).,"The mechanism of forming nanoflares is the dissipation of current sheets arisen from tangential discontinuities in the continuously evolving corona (Levine 1974, Parker 1988)."892II radio sources. although the one-sided jet with a kinetic power ~5V1-10!! erg/s displavs FR I morphology.,"II radio sources, although the one-sided jet with a kinetic power $\sim 5 \cdot 10^{44}$ erg/s displays FR I morphology."893 Detailed VLA and HIST studies (Direttaetal.199D.1999. revealed apparent superluninal motions of the jet components at distances up to a few iundreds parsecs from the active center. while VLBI observations measured much lower velocities al parsec scales.," Detailed VLA and HST studies \citep[respectively]{bir95,bir99} revealed apparent superluminal motions of the jet components at distances up to a few hundreds parsecs from the active center, while VLBI observations measured much lower velocities at parsec scales."894" This suggests a complex velocity structure of the M 87 jet. with vighly relativistic bulk velocities over all of its length (DL a few) and a relatively small jet inclination to the line of sight (6~30"":e.g..BicknellandDegelman1996)."," This suggests a complex velocity structure of the M 87 jet, with highly relativistic bulk velocities over all of its length $\Gamma \sim$ a few) and a relatively small jet inclination to the line of sight \citep[$\theta895 \sim 30^0$; e.g.,][]{bic96}."896. IR observations of the considered object (WhysongandAntonueci2001:Corbinetal.2002). give no evidence or the presence of an obscuring matter around the active center as expected for AGNs. consistently with a lack of the dusty nuclear torus or. eventually. with its small size (<50 pc).," IR observations of the considered object \citep{why01,cor02} give no evidence for the presence of an obscuring matter around the active center as expected for AGNs, consistently with a lack of the dusty nuclear torus or, eventually, with its small size $< 50$ pc)."897 Optical observations of the M 87 nuclear region revealed a small disc (9100 pe) of ionised gas with a LINER emission line spectrum. fuelling a supermassive central black hole (e.g..Macchettoetal.1997).," Optical observations of the M 87 nuclear region revealed a small disc $\sim 100$ pc) of ionised gas with a LINER emission line spectrum, fuelling a supermassive central black hole \citep[e.g.,][]{mac97}."898. The optical nuclear emission presents a smooth featureless continuum variable al (me scales of months and connected with an unresolved (<5 pc) central source (Isvetanovelal.1998)., The optical nuclear emission presents a smooth featureless continuum variable at time scales of months and connected with an unresolved $\leq 5$ pc) central source \citep{tsv98}.899. The large scale jet is verv prominent and highlv polarised in optical. what allows to perform its detailed racdio-to-optical spectroscopy and polarimetry (e.e..\leisenheimerοἱal.1996:SparksetPerlman1999.2001).," The large scale jet is very prominent and highly polarised in optical, what allows to perform its detailed radio-to-optical spectroscopy and polarimetry \citep[e.g.,][]{mei96,spa96,per99,per01}."900. At N-ravs the jet and the nucleus were early observed byROSAT satellite (e.g..Schreier 1982).," At X-rays the jet and the nucleus were early observed by satellite \citep[e.g.,][]{sch82}."901. These observations allowed (ο construct. broad-band radio-to-N-rav. spectrum ol the large scale jel emission (e.g..Direttaetal.1991).. to put. constraints on the X-ray nuclear radiation and its variability (Illarrisetal.1997) and. finally. to study interaction between the radio-emitting matter and the surrounding thermal gas within the extended M 8T halo (Doóhringeretal.1995.2001).," These observations allowed to construct broad-band radio-to-X-ray spectrum of the large scale jet emission \citep[e.g.,][]{bir91}, to put constraints on the X-ray nuclear radiation and its variability \citep{har97} and, finally, to study interaction between the radio-emitting matter and the surrounding thermal gas within the extended M 87 halo \citep{boh95,boh01}."902. Recently. the X-ray jet radiation was studied in more detail by (Marshalletal.2002;WilsonandYang2002:Harris2003).," Recently, the X-ray jet radiation was studied in more detail by \citep{mar02,wil02,har03}."903. Besicles several attempts in the past. till the last vear M. 87. was not detected in 5-rayvs. neither bvCGRO satellite (Sreekumarοἱal.1996). nor by ground-based detectors in the VIIE range.," Besides several attempts in the past, till the last year M 87 was not detected in $\gamma$ -rays, neither by satellite \citep{sre96} nor by ground-based detectors in the VHE range."904" Up to now. the existing upper limit on the TeV emission of the discussed object was Sle,>0221TeV)<L2-10""phem7s! (Weekesetal.1972)."," Up to now, the existing upper limit on the TeV emission of the discussed object was $S(\varepsilon_{\gamma} \geq 0.21 \, {\rm TeV}) < 1.2 \cdot 10^{-10} \, {\rm ph905 \, cm^{-2} \, s^{-1}}$ \citep{wee72}."906". However. recent. observations resulted in positive detection of the VIIE enission from the M 87 radio galaxy. wilh the observed this ος,>0.73TeV)~0.96-10.Pphem?s! (Aharonianοἱal. 2003).."," However, recent observations resulted in positive detection of the VHE emission from the M 87 radio galaxy, with the observed flux $S(\varepsilon_{\gamma} \geq 0.73 \, {\rm TeV}) \sim907 0.96 \cdot 10^{-12} \, {\rm ph \, cm^{-2} \, s^{-1}}$ \citep{aha03}. ."908 Similarly to the ease of Centaurus A. presence of a hidden blazar in the nucleus of M 87 was discussed previously by. e.g. Tsvetanovοἱal.(1993):Revnoldset(1999):ντοςandAntonucci(2001):Corbinetal. (2002).," Similarly to the case of Centaurus A, presence of a hidden blazar in the nucleus of M 87 was discussed previously by, e.g., \citet{tsv98,rey99,why01,cor02}."909. Llowever. contrary to Centaurus A. a spectrum of the discussed central source in the IR-00-UV lrequencies — and therefore parameters of the considered hidden blazar 1 poorly constrained.," However, contrary to Centaurus A, a broad-band spectrum of the discussed central source in the IR-to-UV frequencies – and therefore parameters of the considered hidden blazar – is poorly constrained."910 One may note. that the racdio-to-N-rav nuclear radiation is roughly similar to the large scale jet svnchrotron emission. with apo«l and αον>1 (Tsvetanovοἱal.1998:Bohringeret 2001)..," One may note, that the radio-to-X-ray nuclear radiation is roughly similar to the large scale jet synchrotron emission, with $\alpha_{RO} < 1$ and $\alpha_{OX} > 1$ \citep{tsv98,boh01}. ."911 Thisindicates.," Thisindicates,"912 ,})=r/ )].913We therefore also consider such a case., We therefore also consider such a case.914 In the following we discuss three cases., In the following we discuss three cases.915 The analytical expressions below are only valid for Eg.¢113)., The analytical expressions below are only valid for \ref{tau}) ).916" For the case of continuous photosphere models (Eq.[12]]). the analytical expressions for r.<r;, are more complicated. and we only present thenumerical results in Fig.1. where A’=L'cf, is used.(D:"," For the case of continuous photosphere models \ref{tau2}] ]), the analytical expressions for $r<r_{is}$ are more complicated, and we only present thenumerical results in Fig.1, where $\Delta'=\Gamma c t_v$ is used.:"917": Both the cutoff energy 7, (detined by τις)=Lat which energy the observed spectrum significantly deviates from the power-law extension of the low energy spectrum) and the threshold energy £75,,, (for £7) are above the break energy in the observed photon spectrum £77,,. be. £0),<£2,«EZ, Cor DEο«E)."," Both the cutoff energy $E_{\gamma c}^{\rm o}$ (defined by $\tau_{int}(E_{\gamma_c}^{\rm o})=1$ at which energy the observed spectrum significantly deviates from the power-law extension of the low energy spectrum) and the threshold energy $E_{\gamma_l,th}^{\rm o}$ (for $E_{\gamma c}^{\rm o}$ ) are above the break energy in the observed photon spectrum $E_{\gamma,br}^{\rm o}$, i.e. $E_{\gamma,br}^{\rm o}<E_{\gamma_l,th}^{\rm o}<E_{\gamma_c}^{\rm o}$ (or $E_{\gamma,br}'<E_{\gamma_l,th}'<E_{\gamma_c}'$ )."918" The expression for the optical depth is the simplest for this case (13)where FUE,2 with f?=fChe,2! has beenassumed for £2,>£7,,."," The expression for the optical depth is the simplest for this case where and $\frac{dN_{\gamma_l}^{\rm o}(E_{\gamma_{l}}^{\rm o})}{dE_{\gamma_{l}}^{\rm o}919dA}=f^{\rm o}_1{E_{\gamma_{l}}^{\rm o}}^{-\beta_2}$ with $f^{\rm o}_1=f^{\rm o}{E_{\gamma,br}^{\rm o}}^{\beta_2-\beta_1}$ has beenassumed for $E_{\gamma_l}^{\rm o}>E_{\gamma,br}^{\rm o}$."920 In the case of internal shocks the radius of prompt emission is r—L7e/2/(1|z) where /? is the observed variability time scale.," In the case of internal shocks the radius of prompt emission is $r=\Gamma^2 c921t_{v}^{\rm o}/(1+z)$ where $t_{v}^{\rm o}$ is the observed variability time scale."922" Substituting this expression of + in Eq.(13)) one gets 7,057,)XE?2 which is consistent with Lithwick&Sari(2001)."," Substituting this expression of $r$ in \ref{opt1}) ) one gets $\tau_{int}(E_{\gamma_h}^{\rm o})\propto \Gamma^{-2-2\beta_2}$, which is consistent with \citet{lithwick}."923" Our expression is more generic with r being a free(ID:: If the cutoff energy is still above the break energy. but the threshold energy for pair production is below the break energy. Le. (he,<ETS £2). the expression for internal optical depth is more complicated."," Our expression is more generic with $r$ being a free: If the cutoff energy is still above the break energy, but the threshold energy for pair production is below the break energy, i.e. $E_{\gamma_l,th}^{\rm o}<E_{\gamma,br}^{\rm o}<E_{\gamma_c}^{\rm o}$ ), the expression for internal optical depth is more complicated."924" Making use of Eq.(71). one gets for 7,= 1. where £7.,,” is the energy of the high energy photons that interact with the break-energy photons at the threshold condition. which is defined by £7.,,BU,=(:-)nm, c."," Making use of \ref{obs_f}) ), one gets with )^2 ) ] for $\beta_1 \neq 1$ , where $E_{\gamma_h,br}^{\rm o}$ is the energy of the high energy photons that interact with the break-energy photons at the threshold condition, which is defined by $E_{\gamma_h,br}^{\rm o} E_{\gamma,br}^{\rm o}=925\Big(\frac{\Gamma}{1+z}\Big)^2{m_e}^2c^4$ ."926" Equation (16)) can be reduced to 11 when 3,=4.", Equation \ref{A2}) ) can be reduced to \ref{A1}) ) when $\beta_1=\beta_2$.927" For 7,=1. τι does not depend on EL. and one has "," For $\beta_1=1$, $\tau_{int}$ does not depend on $\Gamma$, and one has )^2 ) )^2 ] ."928"In this case E is not needed to infer i. (IID:: In more extreme cases. usually with a low enough Lorentz factor. one couldhave the cutoff energy below the breakenergy. Le. Lj, ο."," In this case $\Gamma$ is not needed to infer $r$ : In more extreme cases, usually with a low enough Lorentz factor, one couldhave the cutoff energy below the breakenergy, i.e. $E_{\gamma_l,th}^{\rm o}<E_{\gamma_c}^{\rm o}<E_{\gamma,br}^{\rm o}$ ."929]t is known from observational cosmology that our universe is passing through a phase of acceleration.,It is known from observational cosmology that our universe is passing through a phase of acceleration.930 Unfortunately. the present phase of acceleration of the universe Is not clearly understood.," Unfortunately, the present phase of acceleration of the universe is not clearly understood."931 Standard Big Bang cosmology with perfect Iuid assumption fails to accommodate the observational fact., Standard Big Bang cosmology with perfect fluid assumption fails to accommodate the observational fact.932 llowever. an accelerating universe is permitted if a small cosmological constant (CA) be included. in the Einstein's &ravitv.," However, an accelerating universe is permitted if a small cosmological constant $\Lambda$ ) be included in the Einstein's gravity."933 There is. however. no satisfactory theory that explains the origin of A which is required to be unusually small.," There is, however, no satisfactory theory that explains the origin of $\Lambda$ which is required to be unusually small."934 Moreover. Standard. Bie Bane model. without a cosmological constant is inevitably pleagued with a time like singularity in the past.," Moreover, Standard Big Bang model without a cosmological constant is inevitably pleagued with a time like singularity in the past."935 The Bie Bang moclel is also found o be entanelec with some of the observational features which do not have explanation in the framework of perfect luicl model., The Big Bang model is also found to be entangled with some of the observational features which do not have explantion in the framework of perfect fluid model.936 Consequently an inflationary epoch in the early universe is required (Ciuth1981) to resolve the outstandinng issues in Cosmology., Consequently an inflationary epoch in the early universe is required \citep{alt4} to resolve the outstandinng issues in cosmology.937 Ht is not vet understood when and how he universe entered the phase., It is not yet understood when and how the universe entered the phase.938 However. the concept of inflation is taken up to build a consistent. scenario of the ealv universe.," However, the concept of inflation is taken up to build a consistent scenario of the ealy universe."939 Inllation may be realized in a semiclassical heory of eravity where one requires an additional inputs ike existence of a scalar. field which describes the matter in the universe., Inflation may be realized in a semiclassical theory of gravity where one requires an additional inputs like existence of a scalar field which describes the matter in the universe.940 An alternative approach is also followed where gravitational sector of the Einstein field. equation is mocified by including higher order terms in the Einstein-Llilbert action (Sotiriou2007)., An alternative approach is also followed where gravitational sector of the Einstein field equation is modified by including higher order terms in the Einstein-Hilbert action \citep{b19}.941. Jo address the present accelerating phase of the universe once again attempts are mace where theories with a mocification of the gravitational sector taking into account higher order terms that are relevant at the present energy scale are considered., To address the present accelerating phase of the universe once again attempts are made where theories with a modification of the gravitational sector taking into account higher order terms that are relevant at the present energy scale are considered.942 “Phere are other approaches generally adopted considering modification of the matter sector by including very cilferent kine of matter known as exotic matternamely. Chaplvgin. gas and its variations (Bento.Bertolami&Sen2002:‘Tupper&Viollier 2001).. models consisting one or more scalar field ancl tachyvon fields (Lyth2003)..," There are other approaches generally adopted considering modification of the matter sector by including very different kind of matter known as exotic matternamely, Chaplygin gas and its variations \citep{b3,b4}, models consisting one or more scalar field and tachyon fields \citep{b18}."943. While most of these models address dark energy. part of the universe. other models based: on non-equilibrium. thermodynamics and Boltzmann formulation. which co not require any dark energv (Zimdahletal.2001:Balakin2003:Lima.Silva&Santos 2008).. are also considered: suitable [or describing late universe.," While most of these models address dark energy part of the universe, other models based on non-equilibrium thermodynamics and Boltzmann formulation, which do not require any dark energy \citep{b15,b16,b17}, are also considered suitable for describing late universe."944 X. viable cosmological mocel should. accommodate an inflationary phase in the carly universe with a suitable accelerating phase at late time., A viable cosmological model should accommodate an inflationary phase in the early universe with a suitable accelerating phase at late time.945 An interesting area of cosmology is to consider models which are [ree from the initial singularity also., An interesting area of cosmology is to consider models which are free from the initial singularity also.946 Emiergent. Universe (EW) scenario is one of the well known choices in this field., Emergent Universe (EU) scenario is one of the well known choices in this field.947 EU models are proposed in different framework like Drans- theory (delCampo.Herrera&Labrana 2007).. brane world cosmology," EU models are proposed in different framework like Brans-Dicke theory \citep{b151}, , brane world cosmology"948the detection of a Y-type companion with an age < 2 Cir will be very rare.,the detection of a Y-type companion with an age $<$ 2 Gyr will be very rare.949 Therefore. relatively older svsteiis will make better targets to search for cool companions.," Therefore, relatively older systems will make better targets to search for cool companions."950" Brown dwarf secoudarics having masses larecr than 15 Aj, are more common than the lowest lass colpanious listed in Table 1 of Zuckerman&Song(2009) (sce Table 2 of samme paper).", Brown dwarf secondaries having masses larger than 15 $_{jup}$ are more common than the lowest mass companions listed in Table 1 of \cite{zuc09} (see Table 2 of same paper).951 These companions would have to be around stars older than 2 Chr in order to cool to the 500 I& effective temperature that might herald the onset of the Y-class., These companions would have to be around stars older than 2 Gyr in order to cool to the 500 K effective temperature that might herald the onset of the Y-class.952" According to the models of Dirafe (2003).. even brown dwarfs as old as 7 Cyr would lave to be less massive than +25 jj, to have cooled to 500 Ix. Therefore. Y-dwarts themselves must be relatively low-Wass."," According to the models of \cite{bar03}, even brown dwarfs as old as 7 Gyr would have to be less massive than $\sim$ 25 $_{jup}$ to have cooled to 500 K. Therefore, Y-dwarfs themselves must be relatively low-mass."953 We are interested in probing for Y-tvpo dawarts which are born with separations from their host star in the hundreds to thousands of AU rauge., We are interested in probing for Y-type dwarfs which are born with separations from their host star in the hundreds to thousands of AU range.954 It is for the above reasous that the targets selected for our proper motion colupanion search are those ucarby stars with ages > 2 Gar., It is for the above reasons that the targets selected for our proper motion companion search are those nearby stars with ages $>$ 2 Gyr.955 Our current list of 50 targets consists of stars from the Gliese catalog because these stars teud to be old CX» 100 My. Soneetal. 20033).," Our current list of 50 targets consists of stars from the Gliese catalog because these stars tend to be old $\gg$ 100 Myr, \citealt{song03}) )."956 Stars with the highest proper inotious (total proper motion = 650 mas/vr) were selected from this catalog because of Παςαπο considerations (see Section D)., Stars with the highest proper motions (total proper motion $\geq$ 650 mas/yr) were selected from this catalog because of instrumental considerations (see Section 4).957 Each poteutial target wasται cross-iuatelied with the ROSAT All-Sky Survey (RASS) with a search radius of 2° to check for N-rav cuaission as a possible indicator of age., Each potential target was cross-matched with the ROSAT All-Sky Survey (RASS) with a search radius of 2' to check for X-ray emission as a possible indicator of age.958 Of the targets in our sample. seven were found to have been detected ini X-rays.," Of the targets in our sample, seven were found to have been detected in X-rays."959 The X-rav hpuniünositv measured for cach still indicates an age at least as old as that of the IIvades (age 7600 Myr)., The X-ray luminosity measured for each still indicates an age at least as old as that of the Hyades (age $\sim$ 600 Myr).960 X-ray huninosity upper Πιν were caleulated for the remainder of our targets., X-ray luminosity upper limits were calculated for the remainder of our targets.961 Detectious and upper lanits for our tarects are shown in Figure 1., Detections and upper limits for our targets are shown in Figure 1.962 Additionally. space motions were calculated to verify that they do not fall within the voune star UVW defined by Zuckerman&Song(2001).," Additionally, space motions were calculated to verify that they do not fall within the young star UVW defined by \cite{zuc04}."963. These regions are areas of UWW space inhabited by voung (age = 100 Myr). nearby stars.," These regions are areas of UVW space inhabited by young (age $\lesssim$ 100 Myr), nearby stars."964 UVW space motions for our targets are plotted in Figure 2. which shows that the space motions of our targets are inconsistent with the space motions of nearby vouug stars.," UVW space motions for our targets are plotted in Figure 2, which shows that the space motions of our targets are inconsistent with the space motions of nearby young stars."965 Each target was also checked for auy measure ofbiuarity to exclude those with known conmpanious., Each target was also checked for any measure of binarity to exclude those with known companions.966 Om target list and current observation status are eiven in Table 1., Our target list and current observation status are given in Table 1.967 Parallax measurements are from the Gliese catalog., Parallax measurements are from the Gliese catalog.968 Bight ascension. declination. and J-naenitudes are from the Two Micron All Sky Survey (2\IASS).," Right ascension, declination, and J-magnitudes are from the Two Micron All Sky Survey (2MASS)."969 Spectral type aud proper motion are from he SIMDAD astronomical database., Spectral type and proper motion are from the SIMBAD astronomical database.970 Distributions of xoper motion and spectral type are shown in Figure 3., Distributions of proper motion and spectral type are shown in Figure 3.971 After the target list was created. we then checked cach target for CALEN near ultraviolet cuissiou as a »ossible additional indicator of age (Slikoluiketal.2011.. Rodvignezetal. 901111).," After the target list was created, we then checked each target for GALEX near ultraviolet emission as a possible additional indicator of age \citealt{shk11}, \citealt{rod11}) )."972 Twenty-cight of our targets iwl corresponding GALEN matches., Twenty-eight of our targets had corresponding GALEX matches.973 Comparison with voung stars (Zuckerman&Song200 1)). ITvadoes 1ienibers (obtained from the WEBDA open cluster database). aud he rest of the Cdeise catalog again iudicate that our saluple consists of an older population (Figure 1).," Comparison with young stars \citealt{zuc04}) ), Hyades members (obtained from the WEBDA open cluster database), and the rest of the Gleise catalog again indicate that our sample consists of an older population (Figure 4)."974 Observations for this survey beean in August of 2007 and we are still actively acquiring second epoch data for selected stars., Observations for this survey began in August of 2007 and we are still actively acquiring second epoch data for selected stars.975 This survey is beiug conducted witli the Cem camera (AIcLean et al., This survey is being conducted with the Gemini camera (McLean et al.976 1993) located on the Shane 3in Telescope at the Lick Observatory. Mt. ILhuuiltoun. CA.," 1993) located on the Shane 3m Telescope at the Lick Observatory, Mt. Hamilton, CA."977 The Lick Cemini camera is unique for our purposes with its combination of a wide field of view (37.39 and a coronagraplic spot., The Lick Gemini camera is unique for our purposes with its combination of a wide field of view $3'\times3'$ ) and a coronagraphic spot.978" Our observations of main sequence E-. Ge. Ίνον and M-tvpoe stars euiploy. this 5"" coronaeraphic spot to best suppress scattered light aud obtain παπα seusitivitv in the full field of view."," Our observations of main sequence F-, G-, K-, and M-type stars employ this 5” coronagraphic spot to best suppress scattered light and obtain maximum sensitivity in the full field of view."979 These observations vield a radial field of view of —907 and allow us to probe separations out to 900 AU at 10 pe and 1500 AU at 20 pe (distances to our targets range from 10 - 25 pc)., These observations yield a radial field of view of $\sim$ 90” and allow us to probe separations out to 900 AU at 10 pc and 1800 AU at 20 pc (distances to our targets range from 10 - 25 pc).980" While the smallest separations we can probe depend on the apparent brightuess of the target star. the typical smallest separatious to detect a source at 30 above the backerouud are ~ 10""."," While the smallest separations we can probe depend on the apparent brightness of the target star, the typical smallest separations to detect a source at $\sigma$ above the background are $\sim$ 10”."981 Based ou T dwarf spectra and theoretical models. the very low temperature objects we are seeking are auticipated to be more easily detected at J-baud rather than K-baud.," Based on T dwarf spectra and theoretical models, the very low temperature objects we are seeking are anticipated to be more easily detected at J-band rather than K-band."982 Therefore. all targets are being observed in Gemini J-baud imagiug.," Therefore, all targets are being observed in Gemini J-band imaging."983 With 30 miuutes of on-source integration time per object. we can (i good conditioux) achieve a Πιο J-band magnitude of 20 at the 6e detection level.," With 30 minutes of on-source integration time per object, we can (in good conditions) achieve a limiting J-band magnitude of 20 at the $\sigma$ detection level."984 Based on the Baraffe et al. (, Based on the Baraffe et al. (9852003) models. this ασπια lint is sufficient to detect companions as old as 5 Car withο temperatures down to 500 I& out to 15 pc. and companions with temperatures down to GOO Is out to 25 pe.,"2003) models, this magnitude limit is sufficient to detect companions as old as 5 Gyr with temperatures down to 500 K out to 15 pc, and companions with temperatures down to 600 K out to 25 pc."986 We search at two epochs for co-moving conipanious to old. high proper motion. main-sequence stars.," We search at two epochs for co-moving companions to old, high proper motion, main-sequence stars."987 Through the end of 2009. we have obtained first epoch images for 50 main sequence stars with spectral types frou late-F to michAL: second epoch imaging to similar cepths have been obtained for LL of these stars.," Through the end of 2009, we have obtained first epoch images for 50 main sequence stars with spectral types from late-F to mid-M; second epoch imaging to similar depths have been obtained for 41 of these stars."988 All target nuages were reduced with custom in-house IDL software routines., All target images were reduced with custom in-house IDL software routines.989 Science frames were reduced by performing skv subtraction. flat division. bad pixel masking. shifting. and averaging.," Science frames were reduced by performing sky subtraction, flat division, bad pixel masking, shifting, and averaging."990 Source extraction for this project was done using the IRAF routine DAOFIND., Source extraction for this project was done using the IRAF routine DAOFIND.991 Backeround 2MASS sources in each field cau be used to apply a world coordinate svsteni (ves) to cach inae., Background 2MASS sources in each field can be used to apply a world coordinate system (wcs) to each image.992 This is accomplished by matching pixel coordinates witli 2ATASS coordinates and using the IRAF task CCALAP., This is accomplished by matching pixel coordinates with 2MASS coordinates and using the IRAF task CCMAP.993" Ouce the transformation is found. a wes can be applied to the image with the iraf task CCSETWCS,"," Once the transformation is found, a wcs can be applied to the image with the iraf task CCSETWCS."994" Once a wes is applied to au ππασο, casing separatious and position aueles can be performed with the IDL routines geire.pro and posang.pro. both part of the IDL Astronomy Users Library."," Once a wcs is applied to an image, measuring separations and position angles can be performed with the IDL routines $gcirc.pro$ and $posang.pro$, both part of the IDL Astronomy User's Library."995 This process also allows us to calculate plate scale information for cach image., This process also allows us to calculate plate scale information for each image.996 We measure a GEMINI pixel scale of 0.707. per pixel for these observations., We measure a GEMINI pixel scale of 0.70” per pixel for these observations.997 The proper motion of a particular tarect can be measured and compared to any motions exhibited by stars in the surroundius field by tuagine the area around the target star at two epochs separated by a sufficient interval of time., The proper motion of a particular target can be measured and compared to any motions exhibited by stars in the surrounding field by imaging the area around the target star at two epochs separated by a sufficient interval of time.998 The IRAF task GEOMAP can create a general transformation between two sets of coordinates corresponding to sources in the same field at two different. epochs., The IRAF task GEOMAP can create a general transformation between two sets of coordinates corresponding to sources in the same field at two different epochs.999 GEOAIAP uses a polynomial fit to the sets of coordinates to account for translation. rotation. scaling. aud distortion (we use the default," GEOMAP uses a polynomial fit to the sets of coordinates to account for translation, rotation, scaling, and distortion (we use the default"1000or by a complex variable and its complex conjugate. and (hus whether one uses real basis vectors (implicitly 2-coblummn vectors (1.0) and (0.1) defined al one point on the caustic curve and the corresonding point on the critical curve) or zEz that are tangent aud normal vector fields on the caustic curve. we inevitablv deal with the same two degerees of Ireedom. namely the tangent component and normal component.,"or by a complex variable and its complex conjugate, and thus whether one uses real basis vectors (implicitly 2-column vectors $(1,0)$ and $(0,1)$ defined at one point on the caustic curve and the corresonding point on the critical curve) or $\pm E_\pm$ that are tangent and normal vector fields on the caustic curve, we inevitably deal with the same two degerees of freedom, namely the tangent component and normal component."1001 One of the obvious advantages of maximally utilizing (he quasi-analviie nature of (he quasi-analyic lens equations by emploving complex coordinate svstenis is (hat. we have explicit expressions of (he basis vector fields E., One of the obvious advantages of maximally utilizing the quasi-analytic nature of the quasi-analytic lens equations by employing complex coordinate systems is that we have explicit expressions of the basis vector fields $E_\pm$.1002 For example. we know how they change along the caustic curve parameterized bv jy half the phase angle of the &-lield: &ο... E =e’...," For example, we know how they change along the caustic curve parameterized by $\varphi$ half the phase angle of the $\kappa$ -field: $\kappa = |\kappa| \exp{i2\varphi}$."1003 E =ieή: dE —HEdz.. dE =F .(1)(," E_+ =, E_- = i; d E_+ = - E_-, d E_- = E_+. ("1004We note that the basis vector fields are not necessarily smooth evervswhere.),We note that the basis vector fields are not necessarily smooth everywhere.)1005 We do see a potential problem in the emphasis to have used real variables in because (hey are putng the focus in a worne place., We do see a potential problem in the emphasis to have used real variables in \citet{vertical} because they are putting the focus in a worng place.1006 IL it was a methodology to eenerale an undisclosed impression on the readers against our having consistently emploved the complex plane. it perhaps is a wronful deed.," If it was a methodology to generate an undisclosed impression on the readers against our having consistently employed the complex plane, it perhaps is a wronful deed."1007 IF Gaudi&Petters(2001) stated it because ibis simply true that they worked with real coordinates. the fault lies in their failure to clear the smoke and address the relevant issues: We will address the correct in the following. of course using complex coordinates (: for the image space and w for the source space) and the analvtie function. &-field.," If \citet{vertical} stated it because it is simply true that they worked with real coordinates, the fault lies in their failure to clear the smoke and address the relevant issues: We will address the correct in the following, of course using complex coordinates $z$ for the image space and $\omega$ for the source space) and the analytic function $\kappa$ -field."1008 As corollaries. the followings will be clear.," As corollaries, the followings will be clear."1009into Eq. (,into Eq. (101017) for =0.2 only.,"17) for $k = 0,2$ only."1011 This is because although we have used (he moment equations to obtain these results. the explicit assumption of an invariant powerlaw size distribution means that only the equations for the moments M.M» are needed (although see 3.2).," This is because although we have used the moment equations to obtain these results, the explicit assumption of an invariant powerlaw size distribution means that only the equations for the moments $M_0, M_2$ are needed (although see 3.2)."1012 This is nol (rue. however. for the implicit (and semi-implicit) assumption. where all the moments Afg.M4.Mà appear in the differential equations.," This is not true, however, for the implicit (and semi-implicit) assumption, where all the moments $M_0,M_1,M_2$ appear in the differential equations."1013 We see (hat there is excellent agreement between both approaches and (he numerical values obtained with the highest resolution case., We see that there is excellent agreement between both approaches and the numerical values obtained with the highest resolution case.1014 In fact. the agreement between the explicit and implicit assumptions is also quite good.," In fact, the agreement between the explicit and implicit assumptions is also quite good."1015 llowever. al this stage there has not been a ereat deal of growth (the largest particle size in the distribution has only grown to rp=11 cm in size bv (the end of the simulation for the explicit case).," However, at this stage there has not been a great deal of growth (the largest particle size in the distribution has only grown to $r_L = 11$ cm in size by the end of the simulation for the explicit case)."1016" Note Chat even though in the implicit case the C, are calculated only once. the estimate for the largest mass ny, for the evolving distribution f(m./) is still caleulated using Eq. ("," Note that even though in the implicit case the $C_k$ are calculated only once, the estimate for the largest mass $m_L$ for the evolving distribution $f(m,t)$ is still calculated using Eq. ("101727).,27).1018 At least in the case of minimal or slow growth. it appears that an implicit approach. or even periodic calculation of the C. may be sufficient.," At least in the case of minimal or slow growth, it appears that an implicit approach, or even periodic calculation of the $C_k$, may be sufficient."1019 Numerical glitches in the low resolution brute force case arise [rom the interpolation scheme for sampling the kernel., Numerical glitches in the low resolution brute force case arise from the interpolation scheme for sampling the kernel.1020 In particular. these elicthes are likely enhanced because the svslelatic relative velocities quickly approach zero [ον identical particle sizes (with the ellect much more prominent for larger particles. hence not appearing so much in Mo).," In particular, these glicthes are likely enhanced because the systematic relative velocities quickly approach zero for identical particle sizes (with the effect much more prominent for larger particles, hence not appearing so much in $M_0$ )."1021 The higher resolution case contains enough points to smooth out this effect., The higher resolution case contains enough points to smooth out this effect.1022 Note that Gn all simulations) the direct integration of the coagulation equation gives a constant. M4 as is (o be expected given that we found d.M4/di=0 in the derivation of the moment equations in the absence of sources and sinks: (his further validates the numerics of the brute force solution even for the complicated collisional kernel being utilized. ancl also provides a posteriori validation of our result that M4=constant from. e.g.. Eq. (," Note that (in all simulations) the direct integration of the coagulation equation gives a constant $M_1$ as is to be expected given that we found $dM_1/dt = 0$ in the derivation of the moment equations in the absence of sources and sinks; this further validates the numerics of the brute force solution even for the complicated collisional kernel being utilized, and also provides a posteriori validation of our result that $M_1=\rm{constant}$ from, e.g., Eq. ("10235). which further validates derivation of equations (24) and (25) which was based on svnuuetry of the kernel.,"5), which further validates derivation of equations (24) and (25) which was based on symmetry of the kernel."1024 Next. we explored cases in which the systematic velocities were set (o zero so that velocily differences between particles are due only to those induced by turbulence.," Next, we explored cases in which the systematic velocities were set to zero so that velocity differences between particles are due only to those induced by turbulence."1025 Depencine on the magnitude of the turbulence parameter a. these induced velocities can be either large or small relative to the svstematic velocities.," Depending on the magnitude of the turbulence parameter $\alpha$, these induced velocities can be either large or small relative to the systematic velocities."1026 To demonstrate. we ran cases lor three different values a=105.10.7. and LO7.," To demonstrate, we ran cases for three different values $\alpha = 10^{-6},10^{-5}$, and $10^{-4}$."1027 In the absence of anv mechanism to counter growth (e.g.. fragmentation). larger a translates to faster rates of growth (due to larger relative velocities).," In the absence of any mechanism to counter growth (e.g., fragmentation), larger $\alpha$ translates to faster rates of growth (due to larger relative velocities)."1028,.1029StraighUorward perturbative QCD (pQCD) and collinear [actorization approaches, The single-spin asymmetry was analyzed by the pQCD with the higher twist1030eye s 7. respectively).,"erg $^{-3}$ $^{-1}$, respectively)."1031 Some spikes are seen for Model 18 because the heating is oulv just matched bv the cooling. aud the balance is thus computationally delicate.," Some spikes are seen for Model 18 because the heating is only just matched by the cooling, and the balance is thus computationally delicate."1032 Boli iuodels show a vich chemistry. but there are sole plivsical and chemical ciffereuces.," Both models show a rich chemistry, but there are some physical and chemical differences."1033 For example. the iuportaut tracer ion ICO! is more abundant in Model l5: and the uolecules CN. ΠΟΝ and INC have a different priority order of abundance iu the two models. caused by the higher temperature in Model Ls.," For example, the important tracer ion $^{+}$ is more abundant in Model 18; and the molecules CN, HCN and HNC have a different priority order of abundance in the two models, caused by the higher temperature in Model 18."1034 The value of à is au nÓuportaut parameter both for the chemustry aud for the thermal balance., The value of $\zeta$ is an important parameter both for the chemistry and for the thermal balance.1035" The cases With highest à exiuunmed here are Models 6 aud. 7. with :«dOBs» 1,"," The cases with highest $\zeta$ examined here are Models 6 and 7, with $\zeta = 5\times 10^{-13}$ $^{-1}$."1036 The value of JJ is low dn both, The value of $H$ is low in both1037The mass distribution of close companions to Sun-like stars exhibits a clear deficit of brown dwarfs compared to planets and stellar binaries (?).,The mass distribution of close companions to Sun-like stars exhibits a clear deficit of brown dwarfs compared to planets and stellar binaries \citep{Grether:2006kx}.1038" With a frequency of less than 1 (?), brown-dwarf companions to solar-type stars at separations below 10 AU are much less common than planetary companions with a frequency of ~7 (e.g. ?)) and stellar binaries with a frequency of ~13 (??) at similar separations."," With a frequency of less than 1 \citep{Marcy:2000pb}, brown-dwarf companions to solar-type stars at separations below 10 AU are much less common than planetary companions with a frequency of $\sim$ 7 (e.g. \citealt{Udry:2007sf}) ) and stellar binaries with a frequency of $\sim$ 13 \citep{Duquennoy:1991kx, Halbwachs:2003kx} at similar separations."1039" Brown dwarfs are substellar objects, massive enough to burn deuterium but too light to permit hydrogen burning, which places them in the mass range of approximately 13—80 Jupiter masses (??).."," Brown dwarfs are substellar objects, massive enough to burn deuterium but too light to permit hydrogen burning, which places them in the mass range of approximately $13-80$ Jupiter masses \citep{Burrows:1997qe, Chabrier:2000kl}."1040" They therefore constitute objects at the transition between planets and stars, though the lower end of the brown-dwarf mass range overlaps with the one of massive planets (e.g. ?)), and the distinction between planets and brown dwarfs may require to trace the individual formation process."," They therefore constitute objects at the transition between planets and stars, though the lower end of the brown-dwarf mass range overlaps with the one of massive planets (e.g. \citealt{Luhman:2009oq}) ), and the distinction between planets and brown dwarfs may require to trace the individual formation process."1041" A comprehensive explanation for the formation of low-mass objects, covering the range of planets to very low-mass stars, remains to be found, although the progress in this direction is formidable as reported in the reviews of ?,, ? and ?.."," A comprehensive explanation for the formation of low-mass objects, covering the range of planets to very low-mass stars, remains to be found, although the progress in this direction is formidable as reported in the reviews of \cite{Whitworth:2007pi}, , \cite{Luhman:2007zm} and \cite{Burgasser:2007ix}."1042" Recently, a few companions with masses of 18—60 Jupiter masses (M;) were determined through astrometry (e.g. ??)) or discovered in transiting systems (e.g. ?,, Anderson et al,preparation,,"," Recently, a few companions with masses of $18-60$ Jupiter masses $M_J$ ) were determined through astrometry (e.g. \citealt{Martioli:2010kx, Benedict:2010ph}) ) or discovered in transiting systems (e.g. \citealt{Deleuil:2008it}, Anderson et al.,"1043" Bouchy et al., preparation))."," Bouchy et al., )."1044" Yet, most potential brown dwarf companions are discovered in radial velocity surveys (e.g. ?))"," Yet, most potential brown dwarf companions are discovered in radial velocity surveys (e.g. \citealt{Nidever:2002vn}) )."1045" In these high-precision programs, aiming at planet detection, they are easily spotted and characterised because of their large signatures, by far exceeding the radial velocity measurement precision (e.g. ??))."," In these high-precision programs, aiming at planet detection, they are easily spotted and characterised because of their large signatures, by far exceeding the radial velocity measurement precision (e.g. \citealt{Patel:2007ys, Bouchy:2009rt}) )."1046" However, radial-velocity measurements alone do not constrain the orbit inclination."," However, radial-velocity measurements alone do not constrain the orbit inclination."1047" Therefore, they can not reveal the companion mass, but yield a lower limit to it."," Therefore, they can not reveal the companion mass, but yield a lower limit to it."1048 Observations of complementary effects like the transit light-curve (?) or the astrometric motion of the host star are required to solve this ambiguity and to determine the companion mass., Observations of complementary effects like the transit light-curve \citep{Deleuil:2008it} or the astrometric motion of the host star are required to solve this ambiguity and to determine the companion mass.1049" High-precision astrometry with the Hubble space telescope (HST) has been used to find the masses of planetary companions discovered by radial velocity (?,, and references therein) and has demonstrated the power of astrometry to distinguish between planetary, brown-dwarf, or stellar companions."," High-precision astrometry with the Hubble space telescope ) has been used to find the masses of planetary companions discovered by radial velocity \citealt{Benedict:2010ph}, and references therein) and has demonstrated the power of astrometry to distinguish between planetary, brown-dwarf, or stellar companions."1050 Ground-based optical interferometers achieve the necessary precision to detect orbital motions of binary and multiple systems and to solve for the orbital parameters together with radial-velocity measurements (???)..," Ground-based optical interferometers achieve the necessary precision to detect orbital motions of binary and multiple systems and to solve for the orbital parameters together with radial-velocity measurements \citep{Hummel:1993rz, Muterspaugh:2006eu, Lane:2007sf}."1051" The astrometric detection of planetary orbits using IR-interferometry is the aim of the extrasolar-planet search with project(ESPRI, ?))."," The astrometric detection of planetary orbits using IR-interferometry is the aim of the extrasolar-planet search with project, \citealt{Launhardt2008}) )."1052" On a larger scale, the satellite (e.g. ?)) will advance the field of astrometric detection and characterisation of planetary systems, due to its outstanding measurement precision (?).."," On a larger scale, the satellite (e.g. \citealt{Lindegren:2010kx}) ) will advance the field of astrometric detection and characterisation of planetary systems, due to its outstanding measurement precision \citep{Casertano:2008th}."1053 Hipparcos astrometry has been extensively used to constrain the masses of sub-stellar and stellar companions in multiple systems (????)..," Hipparcos astrometry has been extensively used to constrain the masses of sub-stellar and stellar companions in multiple systems \citep{Perryman:1996vn, Pourbaix:2000sf, Zucker:2001ve, Torres:2007kx}. ."1054 ? used Hipparcos astrometry to analyse 30 extrasolar-planet candidates and concluded that half of these companions were rather brown of M dwarfs., \cite{Han:2001kx} used Hipparcos astrometry to analyse 30 extrasolar-planet candidates and concluded that half of these companions were rather brown of M dwarfs.1055" With the consequent rectification by ?,, showing that the results of ? had been biased by the fitting procedure, it became clear that the fitting of astrometric data has to be done very carefully, especially when the size of the orbital signature approaches the measurement precision of the instrument (?).."," With the consequent rectification by \cite{Pourbaix:2001rt}, showing that the results of \cite{Han:2001kx} had been biased by the fitting procedure, it became clear that the fitting of astrometric data has to be done very carefully, especially when the size of the orbital signature approaches the measurement precision of the instrument \citep{Pourbaix:2001qe}."1056 All of these past works used the original Hipparcos data (?).., All of these past works used the original Hipparcos data \citep{Perryman:1997kx}.1057" In 2007, the new reduction of the raw Hipparcos data (?) has been released, which represents a significant improvement in quality compared to the original data (?).."," In 2007, the new reduction of the raw Hipparcos data \citep{:2007kx} has been released, which represents a significant improvement in quality compared to the original data \citep{van-Leeuwen:2007yq}."1058 It also includes a revised version of the intermediate astrometric data ina new format that facilitates the search for the signature of orbital motion., It also includes a revised version of the intermediate astrometric data ina new format that facilitates the search for the signature of orbital motion.1059" We use the new Hipparcos reduction for our study, whichaims at determining the masses of companions"," We use the new Hipparcos reduction for our study, whichaims at determining the masses of companions"1060data).,data).1061" These clusters will be assigned correct ages with the standard method, but will be attracted to younger ages with the Bayesian method (with a positive extinction) because of the contrast in the model-density maps."," These clusters will be assigned correct ages with the standard method, but will be attracted to younger ages with the Bayesian method (with a positive extinction) because of the contrast in the model-density maps."1062" Finally, the rarer clusters with larger than typical V—J colours will be attracted to ages around 100 Myr (with a positive extinction), both with the standard and the Bayesian methods (features 7.b and 7.β)."," Finally, the rarer clusters with larger than typical $V-I$ colours will be attracted to ages around $100$ Myr (with a positive extinction), both with the standard and the Bayesian methods (features $7.b$ and $7.\beta$ )."1063" As noted earlier, underestimated ages lead to underestimated masses because stellar populations fade with time and extinction corrections do not quite compensate for this."," As noted earlier, underestimated ages lead to underestimated masses because stellar populations fade with time and extinction corrections do not quite compensate for this."1064" In our sample, many of the old clusters affected by the age artefacts get assigned masses near the lower limit (500 Μο) of our catalog (see Sect. [6.2))."," In our sample, many of the old clusters affected by the age artefacts get assigned masses near the lower limit $500$ $_\odot$ ) of our catalog (see Sect. \ref{sec:prospects}) )."1065" Outside the main age artefacts seen for old clusters (when extinction is a free parameter), the Bayesian methods recovers ages and masses similarly well whether or not the K band fluxes are included in the input data."," Outside the main age artefacts seen for old clusters (when extinction is a free parameter), the Bayesian methods recovers ages and masses similarly well whether or not the K band fluxes are included in the input data."1066" If we exclude objects lying in the features 7.a and 7.b as well as objects affected by the low-mass limit of our MC catalog, masses recovered with UBVI data sets are not significantly more dispersed (σ= 0.14) than those obtained with UBVIK data sets (c:= 0.13)."," If we exclude objects lying in the features $7.a$ and $7.b$ as well as objects affected by the low-mass limit of our MC catalog, masses recovered with UBVI data sets are not significantly more dispersed $\sigma = 0.14$ ) than those obtained with UBVIK data sets $\sigma = 0.13$ )."1067 Further aspects of photometric band-pass selection are discussed in Sect. [6.3]., Further aspects of photometric band-pass selection are discussed in Sect. \ref{sec:bandselection}.1068 Several decades have passed since the stochasticity of stellar populations was first mentioned asa serious issue., Several decades have passed since the stochasticity of stellar populations was first mentioned \citep{Barbaro1977} as a serious issue.1069" With powerful computers, stochasticity can now be taken into account explicitly when analysing the properties of unresolved populations."," With powerful computers, stochasticity can now be taken into account explicitly when analysing the properties of unresolved populations."1070" Considering stellar populations as stochastic requires some changes in habits, for instance because mass is not a simple scaling factor anymore: errors on absolute fluxes (e.g. due to uncertainties on distances) can affect estimated ages; and observations of only colours can provide some information on the mass."," Considering stellar populations as stochastic requires some changes in habits, for instance because mass is not a simple scaling factor anymore: errors on absolute fluxes (e.g. due to uncertainties on distances) can affect estimated ages; and observations of only colours can provide some information on the mass."1071" Clearly, more work is needed to explore the consequences of stochasticity more exhaustively."," Clearly, more work is needed to explore the consequences of stochasticity more exhaustively."1072" The analysis of the integrated light of small clusters with continuous population synthesis models produces strong age-dependent artefacts in the derived ages, and a broad distribution of random errors in the derived masses."," The analysis of the integrated light of small clusters with continuous population synthesis models produces strong age-dependent artefacts in the derived ages, and a broad distribution of random errors in the derived masses."1073 The good news is that there is no large systematic offset between estimated and real massesif the photometric data are of good qualityif observations that cannot find a statistically acceptable match among the continuous models are rejected., The good news is that there is no large systematic offset between estimated and real masses the photometric data are of good quality observations that cannot find a statistically acceptable match among the continuous models are rejected.1074" When the data have larger errors, fewer model fits are rejected."," When the data have larger errors, fewer model fits are rejected."1075" Then, a systematic trend appears in addition to the random errors: masses are underestimated on average."," Then, a systematic trend appears in addition to the random errors: masses are underestimated on average."1076 The value of the offset depends on the photometric pass-bands available and on the existence (or not) of independent information on extinction., The value of the offset depends on the photometric pass-bands available and on the existence (or not) of independent information on extinction.1077" The average error is of 0.3 dex for a sample of clusters of masses around 10° Μο observed in UBVIK, when extinction is treated as a free parameter."," The average error is of $0.3$ dex for a sample of clusters of masses around $10^3$ $_{\odot}$ observed in UBVIK, when extinction is treated as a free parameter."1078 The above means that mass distributions of large samples of clusters based on an analysis with continuous population synthesis models are probably not too strongly biased., The above means that mass distributions of large samples of clusters based on an analysis with continuous population synthesis models are probably not too strongly biased.1079" Several empirical determinations in the literature (seeandreferencestherein) favour M? mass distributions, and we used such a law as a prior in our Bayesian analysis."," Several empirical determinations in the literature \citep[see][and references therein]{Rafelski2005} favour $M^{-2}$ mass distributions, and we used such a law as a prior in our Bayesian analysis."1080" We find no immediate reason to apply a correction to this result, although a detailed investigation of each individual dataset in the literature would be worthwhile."," We find no immediate reason to apply a correction to this result, although a detailed investigation of each individual dataset in the literature would be worthwhile."1081" If, for instance, small masses are systematically underestimated by 0.3 dex while large masses are not, the power law index of the mass distribution would require a small"," If, for instance, small masses are systematically underestimated by $0.3$ dex while large masses are not, the power law index of the mass distribution would require a small."1082correctior]. Figure 9| shows the age-mass distribution obtained when UBVI data for our test sample of clusters is analysed with non-stochastic population synthesis models and no fit is rejected., Figure \ref{fig:AgeMassLum_UBVI} shows the age-mass distribution obtained when UBVI data for our test sample of clusters is analysed with non-stochastic population synthesis models and no fit is rejected.1083" While the properties of the test sample are smoothly distributed, the estimated properties are highly clustered."," While the properties of the test sample are smoothly distributed, the estimated properties are highly clustered."1084" The figure looks similar with UBVIK data, but we chose UBVI for comparison with the (UBVI+Ha)-based age-luminosity distribution of (more massive) Antennae clusters Whitmore] 2005)."," The figure looks similar with UBVIK data, but we chose UBVI for comparison with the $\alpha$ )-based age-luminosity distribution of (more massive) Antennae clusters \citep{Fall2005}."1085. The right panel of Fig., The right panel of Fig.1086" D| shows (dar,the derived& distribution in the age-luminosity plane, after conversion of the estimated masses into luminosities with the age-dependent mass-to-light ratio given by Péggase."," \ref{fig:AgeMassLum_UBVI} shows the derived distribution in the age-luminosity plane, after conversion of the estimated masses into luminosities with the age-dependent mass-to-light ratio given by Péggase."1087" In an observational context, such a figure would be truncated at low luminosity by some instrumental sensitivity limit."," In an observational context, such a figure would be truncated at low luminosity by some instrumental sensitivity limit."1088 The similarity between the distribution in Fig., The similarity between the distribution in Fig.1089 D] and that in Fig., \ref{fig:AgeMassLum_UBVI} and that in Fig.1090" 1 of Chandar,Whitmore| is striking, even more so [Fall,when one mentally& corrects for the sharp low-mass limit of our sample and our relative lack of young clusters."," $1$ of \cite{Fall2005} is striking, even more so when one mentally corrects for the sharp low-mass limit of our sample and our relative lack of young clusters."1091 Accumulations and gaps occur at essentially the same ages (differences can be traced back to the different sets of evolutionary tracks used by the authors)., Accumulations and gaps occur at essentially the same ages (differences can be traced back to the different sets of evolutionary tracks used by the authors).1092 We have discussed the origins of the artefacts in our test-sample age distribution in Sect. Af:, We have discussed the origins of the artefacts in our test-sample age distribution in Sect. \ref{sec:UBVIKphot}:1093" they arise because real, stochastic clusters of small masses are distributed over a wide range of colours, and can therefore fall quite far off on the line of continuous models when only extinction is available to alter their colours."," they arise because real, stochastic clusters of small masses are distributed over a wide range of colours, and can therefore fall quite far off on the line of continuous models when only extinction is available to alter their colours."1094" The clusters in the Antennae sample, however, are typically 50 times more luminous than the ones in our study."," The clusters in the Antennae sample, however, are typically 50 times more luminous than the ones in our study."1095 More massive clusters should lie closer to the lines of continuous models., More massive clusters should lie closer to the lines of continuous models.1096 Why then are these artefacts so strongly seen in the Antennae cluster distribution?, Why then are these artefacts so strongly seen in the Antennae cluster distribution?1097 Our interpretation is that the combined effects of observational errors and real extinction disperse the clusters enough in colour-space to produce a global derived age distribution that is similar to the distribution produced at lower masses by stochasticity., Our interpretation is that the combined effects of observational errors and real extinction disperse the clusters enough in colour-space to produce a global derived age distribution that is similar to the distribution produced at lower masses by stochasticity.1098" The input age distribution of the clusters in our test-sample (and in our main MC catalog of clusters) is constant in logarithmic age bins, and this produces derived age-luminosity distributions that are very similar to the ones in the literature."," The input age distribution of the clusters in our test-sample (and in our main MC catalog of clusters) is constant in logarithmic age bins, and this produces derived age-luminosity distributions that are very similar to the ones in the literature."1099" Our tentative conclusion is that the adopted age-distribution is, for the time being, an adequate prior for the Bayesian,"," Our tentative conclusion is that the adopted age-distribution is, for the time being, an adequate prior for the Bayesian,"1100at large radii (M. in. AL.ναiy the radius around which the ionization imstabilitv sets in is given by Ta mag °C Lawhere ry2300.,"at large radii $\dot M$, in $\mpy$ ), the radius around which the ionization instability sets in is given by r_A r_0 , where $r_0 \approx 300$."1101 Equations (3)) aud (3)) can be roughly reproduced analytically by fixing T—d05 ina Shakwwa-Suuvacy disk (thus isolating the portions of the disk where hydrogen starts beime partially ionized).," Equations \ref{sig}) ) and \ref{ra}) ) can be roughly reproduced analytically by fixing $T \sim110210^4$ K in a Shakura-Sunyaev disk (thus isolating the portions of the disk where hydrogen starts being partially ionized)."1103 It is also interesting to note that equations (3)) aud (3)) are applicable to DN and SXTs as well as ACN. with wy then ~10°. AT~109Muy.1oand ka10°.," It is also interesting to note that equations \ref{sig}) ) and \ref{ra}) ) are applicable to DN and SXTs as well as AGN, with $m_9$ then $\sim110410^{-9}$, $\dot M \sim 10^{-9} \mpy$, and $r_A \sim 10^5$."1105 Using the Sala equation for a solar metallicity gas. we fud that. in LTE. the ionization fraction at T4z:2000 Iv in the thermalhy uustable aunulus is (5105.* for MeL.10.19]ALay15 Substituting equations (3)) and (3)) iuto equatious (1)) aud (2)) we then find the values of Rea; iud Be iu the thermal limit evele (obtained at point A): RUM 10° 21pes aud Rey acd:31a:3.2107 2E EL us)!," Using the Saha equation for a solar metallicity gas, we find that, in LTE, the ionization fraction at $T_A \approx 2000$ K in the thermally unstable annulus is $x_e \equiv n_e/n_n \approx 10^{-6}-10^{-7}$ for $\dot M \ \epsilon \ [1,10^{-10}] \mpy$ Substituting equations \ref{sig}) ) and \ref{ra}) ) into equations \ref{rem}) ) and \ref{rea}) ) we then find the values of $Re_M$ and $Re_A$ in the thermal limit cycle (obtained at point A): Re_M 10^8 ) and Re_A 3 10^7 ) ) )."1106 For a given accretion rate. equations (5)) and (63) determine the coupling of the gas to the magnetic field in he annulus which is unstable to the ionization iustabilitv: lis aunulus lies at a radius given by equation (3)).," For a given accretion rate, equations \ref{remfinal}) ) and \ref{reafinal}) ) determine the coupling of the gas to the magnetic field in the annulus which is unstable to the ionization instability; this annulus lies at a radius given by equation \ref{ra}) )."1107 Note hat Rea; and Rey are incepeudeut of black hole mass at fixed M.," Note that $Re_M$ and $Re_A$ are independent of black hole mass at fixed $\dot1108M$."1109 Wall currents cau significautly modifv the dvuamics of low density. weakly-ionized disks (e.g... Wardle 1999: Balbus Terquem 2000).," Hall currents can significantly modify the dynamics of low density, weakly-ionized disks (e.g., Wardle 1999; Balbus Terquem 2000)."1110" Thei importance can be ueasured using the ion Wall parameter, 3)—wifspy. where w; is the jon cvelotron frequency."," Their importance can be measured using the ion Hall parameter, $\beta_i \equiv \omega_i/\gamma \rho_n$, where $\omega_i$ is the ion cyclotron frequency."1111 For 2;21 the aiubipolar diffusion lamit applies. while for 2;«1 Tall currents are important.," For $\beta_i \gg 1$ the ambipolar diffusion limit applies, while for $\beta_i \ll 1$ Hall currents are important."1112" Asstuning equipartitiou magnetic fields. we estimate J;zs0,34793(X/1000).4/2 in the uustable auuuli of interest."," Assuming equipartition magnetic fields, we estimate $\beta_i \approx11130.3 \dot M^{0.1} (\Sigma_0/1000)^{-1/2}$ in the unstable annuli of interest."1114 The role of Wall currents in nodifving MIID turbulence is deteriuued by Reycm Rey: since 3;~1d. Rey is a reasonable proxy for Regu: it Reyc1. then Reyc9 1. developed. aud Tall currents are uninuportaut.," The role of Hall currents in modifying MHD turbulence is determined by $Re_H \approx \beta_i Re_A$ ; since $\beta_i \sim 1$, $Re_A$ is a reasonable proxy for $Re_H$: if $Re_A \gg 1$, then $Re_H1115\gg 1$ , , and Hall currents are unimportant."1116 By contrast. if Rey~1 MIID turbulence is modified (aud Vall curreuts must be considered effects).," By contrast, if $Re_A \sim 1$ MHD turbulence is modified (and Hall currents must be considered )."1117" AIITD turbulence aud its associated augular 1no1ieutui transport are expected to be suppressed for Rea; audor Rey less than critical values =Rey, and Fc.", MHD turbulence and its associated angular momentum transport are expected to be suppressed for $Re_M$ and/or $Re_A$ less than critical values $\equiv Re_M^c$ and $Re_A^c$.1118" Niunerical siuulatious with explicit resistivity are cousisteut with Peg,m105 (Tawley et al.", Numerical simulations with explicit resistivity are consistent with $Re_M^c \approx 10^4$ (Hawley et al.1119 1996: Fleming et al., 1996; Fleming et al.1120" 2000). while sinmlatious of ion-neutral disks give e,=LOO (Tlawley Stone 19098: see also Mac Low et al."," 2000), while simulations of ion-neutral disks give $Re^c_A \approx 100$ (Hawley Stone 1998; see also Mac Low et al."1121 1995: 1995)., 1995; ).1122 Equatious (5)) and (6)) then show that there is au inportaut difference between accretion in DN aud SXNTs. where M~10?M.vrto and aecretion in huuinous AGN. where M—0.0L10AMvr31;," Equations \ref{remfinal}) ) and \ref{reafinal}) ) then show that there is an important difference between accretion in DN and SXTs, where $\dot M \sim 10^{-9} \mpy$, and accretion in luminous AGN, where $\dot1123M \sim 0.01-10 \mpy$."1124" As shown by CAL ReapSRey, πι DN aud SNTs."," As shown by GM, $Re_M \lsim Re_M^c$ in DN and SXTs."1125 ATID turbulence is thus suppressed on the “cold” branch of the thermal limit cvcle., MHD turbulence is thus suppressed on the “cold” branch of the thermal limit cycle.1126" By contrast. for reasonable AL in AGN. ReMoRey, aud ReycBe."," By contrast, for reasonable $\dot M$ in AGN, $Re_M \gg Re_M^c$ and $Re_A \gg Re_A^c$."1127 This nmuples that the disk is MIID-turbuleut throughout the thermal Bhnit cycle., This implies that the disk is MHD-turbulent throughout the thermal limit cycle.1128 Iu coutrast to DN aud SATs. the efficiency. of aueular moment transport should then be comparable ou the hot aud cold branches (Aco%ἁἉμω).," In contrast to DN and SXTs, the efficiency of angular momentum transport should then be comparable on the hot and cold branches $\alpha_{\rm cold} \approx \alpha_{\rm1129hot}$ )."1130 lu this case elobal time-depeudent calculations show that the thermal ionization instability is probably not a siguificaut source of time-dependent accretion in ACN: if leads to huuinositv “flickering.” rather than large amplitude outbursts analogous to DN and SATs (e.g. S11ak 198 Alineshige Shields 1990).," In this case global time-dependent calculations show that the thermal ionization instability is probably not a significant source of time-dependent accretion in AGN; it leads to luminosity “flickering,” rather than large amplitude outbursts analogous to DN and SXTs (e.g., Smak 1984; Mineshige Shields 1990)."1131 The analvsis preseuted does not. of course. preclude that accretion in ACN is highly time dependent: it does. however. sugeest that the thermal ionization instability. as applied to DN aud SATs. is not relevaut to AGN.," The analysis presented does not, of course, preclude that accretion in AGN is highly time dependent; it does, however, suggest that the thermal ionization instability, as applied to DN and SXTs, is not relevant to AGN."1132 Radiation-pressure induced thermal aud viscous iustabilities at simall radii may be an important source of time depeudence in AGN accretion disks (σαι Eardley 1971: Pian 1978)., Radiation-pressure induced thermal and viscous instabilities at small radii may be an important source of time dependence in AGN accretion disks (Lightman Eardley 1974; Piran 1978).1133 Another. less well explored. possibility lies in the iuterplav between MITD. (uuistable and eravitationally (un)stable portions of the accretion disk.," Another, less well explored, possibility lies in the interplay between MHD (un)stable and gravitationally (un)stable portions of the accretion disk."1134 We briefly address several of the relevant issuesbelow: much more theoretical work on these problems is ποσο., We briefly address several of the relevant issues; much more theoretical work on these problems is needed.1135 An obvious shortcoming of the argument in §33 is that it is local., An obvious shortcoming of the argument in 3 is that it is local.1136 We examined aunuli in thin accretion disks which are subject to the thermal ionization instability aud found that they are always ΑΠΟ turbulent so long as MPs107Moy|2, We examined annuli in thin accretion disks which are subject to the thermal ionization instability and found that they are always MHD turbulent so long as $\dot M \gg 10^{-7} \mpy$.1137 At πας somewhat larger than the thermally unstable region. however. the disk is everywhere stable. but on thecold brauch of the S-curve in Figure 1: if viscous dissipation is the only source of heating. the ceutral temperature in the disk eventually drops to «1000 Ix. Iu LTE the ionization fraction then becomes very πια aud AMID turbulence dies away.," At radii somewhat larger than the thermally unstable region, however, the disk is everywhere stable, but on the branch of the S-curve in Figure 1; if viscous dissipation is the only source of heating, the central temperature in the disk eventually drops to $\ll 1000$ K. In LTE the ionization fraction then becomes very small and MHD turbulence dies away."1138 A-ravs and cosnüc-cavs nw provide sufficient heating and/or nouthermal ionization to maintain imaguetic coupling in the disk at large radii., X-rays and cosmic-rays may provide sufficient heating and/or nonthermal ionization to maintain magnetic coupling in the disk at large radii.1139" Blaes Balbus (1991) estimated Rea,2 Laud Rey~l1 from cosmic-ray ionizationin the parsec scale cireuninnuclear disk in our Calaxy."," Blaes Balbus (1994) estimated $Re_M \gg 1$ and $Re_A1140\sim 1$ from cosmic-ray ionizationin the parsec scale circumnuclear disk in our Galaxy."1141 Simple estimates of N-ray ionization vield similar results., Simple estimates of X-ray ionization yield similar results.1142 As a concrete example. cousider the z0.1—0.25 pe lasingdiskaround the Af=3.6«10°AL. black hole in NGC 1258 (Mivoshi et al.," As a concrete example, consider the $\approx 0.1-0.25$ pc masingdiskaround the $M = 3.6 \times 10^7 M_\odot$ black hole in NGC 4258 (Miyoshi et al."1143 1995)., 1995).1144 Neuteld Maloney (1995: NM) proposed that the iiasing region is strongly iradiated by the ceutral X-ray source. due to a siguificaut," Neufeld Maloney (1995; NM) proposed that the masing region is strongly irradiated by the central X-ray source, due to a significant"1145 , 1146ihe mean value of the strength of VxB in the interaction region.,the mean value of the strength of $\curl \textbf{B}$ in the interaction region.1147 We observe that in the vertical and straight field case. |VxD| remains constant. but decreases to a fixed value for R>2 cases.," We observe that in the vertical and straight field case, $|\curl \textbf{B}|$ remains constant, but decreases to a fixed value for $R \geq 2$ cases."1148 This means the field in high 2 cases is straightened by (he stretching of the interaction region as seen in Figure 7((c)., This means the field in high $R$ cases is straightened by the stretching of the interaction region as seen in Figure \ref{fig07}( (c).1149 For the 2X1 cases. we see that |VxB| increases.," For the $R \leq 1$ cases, we see that $|\curl \textbf{B}|$ increases."1150 This rise is due (ο magnetic energv brought in via the cold mass flow ancl the creation of fine field structures (hat amplify Jj faster than dissipation caused by interface expansion., This rise is due to magnetic energy brought in via the cold mass flow and the creation of fine field structures that amplify $J_B$ faster than dissipation caused by interface expansion.1151 The local field distortion can be clearly demonstrated by studying the energy evolution of magnetic energv stored in different [iekl components., The local field distortion can be clearly demonstrated by studying the energy evolution of magnetic energy stored in different field components.1152 In. Figure 9((a). we plot the evolution of mean magnetic energy stored in the vertical field Bo2. compared with 2/2.," In Figure \ref{fig09}( (a), we plot the evolution of mean magnetic energy stored in the vertical field $\bar{B}_y^2/2$, compared with $\bar{B}_x^2/2$."1153 We note that the latter includes only the fInctuating contribution to the energy in the x field) that is. the contribution to the horizontal field that does not come from the global Meal component.," We note that the latter includes only the fluctuating contribution to the energy in the x field– that is, the contribution to the horizontal field that does not come from the global mean $x$ component."1154 From Figure 9((a). we observe that the LB energy decreases while the B? energy either increases or remains the same lor all cases.," From Figure \ref{fig09}( (a), we observe that the $B_y^2$ energy decreases while the $B_x^2$ energy either increases or remains the same for all cases."1155 The magnetic energv evolution can thus be viewed as a conversion of vertical field to horizontal field., The magnetic energy evolution can thus be viewed as a conversion of vertical field to horizontal field.1156 This conversion need not conserve the total magnetic energy of the local tangled field because of magnetic reconnection ancl because material advecting magnetic field can flow in and out of the interaction region., This conversion need not conserve the total magnetic energy of the local tangled field because of magnetic reconnection and because material advecting magnetic field can flow in and out of the interaction region.1157 By comparison. in the 2>1 cases. the thermal energy. and local magnetic energy can both decrease and add to the kinetic energy of the material surrounding the interface. because of the fast thermal diffusion enabled by. the strong global field.," By comparison, in the $R > 1$ cases, the thermal energy and local magnetic energy can both decrease and add to the kinetic energy of the material surrounding the interface, because of the fast thermal diffusion enabled by the strong global field."1158 The distortion of the local field loops can also be demonstrated by plotting the mean eccentricitv of the field loops., The distortion of the local field loops can also be demonstrated by plotting the mean eccentricity of the field loops.1159 In Figure 9((b). we plot the mean eccentricity evolution.," In Figure \ref{fig09}( (b), we plot the mean eccentricity evolution."1160 For, For1161correction from the center of light to the center of body is below 0.1 mas.,correction from the center of light to the center of body is below 0.1 mas.1162 In any. case. a data set that samples more deusely auy possible variatious iu the orbits of P2 aud PI on the £00-500-day timescales slould provide stroug coustraiuts ο1the masses of P2 and PL.," In any case, a data set that samples more densely any possible variations in the orbits of P2 and P1 on the $400$ $500$ -day timescales should provide strong constraints on the masses of P2 and P1."1163 There are no apparent ellects due to the respective proximity of P2 aud Pl to the [:1 anc 6:1 mean-motion comanensurabilTTes with Charon., There are no apparent effects due to the respective proximity of P2 and P1 to the high-order 4:1 and 6:1 mean-motion commensurabilities with Charon.1164" However. have p'oposed that P2 aud P!| may have been trapped iu the corotatiou resouauces at these Coniinensurajlities (ie.. those associated witl he resonance variable ©,—loo+3a~ for P2 and O.—OO,+9a, for P1) curing tie. tidal expation of Charou's orbit. if Charon formed with large orbial eccenricity [rom a giant iupact on Puto."," However, \citet{war06} have proposed that P2 and P1 may have been trapped in the corotation resonances at these commensurabilities (i.e., those associated with the resonance variable $\phi_c - 4\phi_21165+ 3\varpi_c$ for P2 and $\phi_c - 6\phi_1 + 5\varpi_c$ for P1) during the tidal expansion of Charon's orbit, if Charon formed with large orbital eccentricity from a giant impact on Pluto."1166 P2 aud P1 escaped from the corotation resonances whe 1C1aLolYs orbital eeceutriciyo was tidaly amped to very sinall. value., P2 and P1 escaped from the corotation resonances when Charon's orbital eccentricity was tidally damped to very small value.1167" Our analvsis shows that cotinued observations of tje Plilo system with HST (aud possibly rolud-YASECl adaptive optics) i the near fuure will allow""us to detect the nonu-Ixeplerian behaviors of the orbits of P2 and PI (in acdition totie. already deectec deviation from Ixepler's third law) and tothereby constraiu their 1jasses.", Our analysis shows that continued observations of the Pluto system with HST (and possibly ground-based adaptive optics) in the near future will allow us to detect the non-Keplerian behaviors of the orbits of P2 and P1 (in addition to the already detected deviation from Kepler's third law) and to thereby constrain their masses.1168 Muc1 more precise determination of the orbits and masses of P2 atd P1 will be possible as the New Horizous spacec‘all aj»proaches the Pluto system iu 2015., Much more precise determination of the orbits and masses of P2 and P1 will be possible as the New Horizons spacecraft approaches the Pluto system in 2015.1169 We thank Robin Canup aud Alan Stern for sencling i5 preints ou the uew satellites of Pluto., We thank Robin Canup and Alan Stern for sending us preprints on the new satellites of Pluto.1170 This research was supported in part by NASA erant NNCOSCINS8C., This research was supported in part by NASA grant NNG05GK58G.1171we assess whether or not there is evidence for an upper cutoff to the masses with which clusters in M33 can form.,we assess whether or not there is evidence for an upper cutoff to the masses with which clusters in M83 can form.1172 Curvature at the high end of the mass function would provide evidence for such a physical limit., Curvature at the high end of the mass function would provide evidence for such a physical limit.1173 Second. we determine whether there is evidence for the early disruption of lower mass clusters when compared with their higher mass counterparts.," Second, we determine whether there is evidence for the early disruption of lower mass clusters when compared with their higher mass counterparts."1174 Curvature or a flattening at the low end of the mass function would provide evidence Lor the mass-dependent disruption of the clusters., Curvature or a flattening at the low end of the mass function would provide evidence for the mass-dependent disruption of the clusters.1175 several recent papers have suggested that there is a cutoff at the hieh end of the mass function of relatively voung (7<fewx105 vr) clusters in some spiral galaxies. such as A[5I1. M83. NGC 6946 (e.g.. Gieles οἱ 22006: Larsen 2009).," Several recent papers have suggested that there is a cutoff at the high end of the mass function of relatively young $\tau \lea \mbox{few} \times 10^8$ yr) clusters in some spiral galaxies, such as M51, M83, NGC 6946 (e.g., Gieles et 2006; Larsen 2009)."1176 More recently. Portegies Zwart et ((2010) suggested that a cutoll Me:2x10AL. may be present in.all Milky Wavy-like spiral galaxies.," More recently, Portegies Zwart et (2010) suggested that a cutoff $M_C\approx2\times10^5~M_{\odot}$ may be present in Milky Way-like spiral galaxies."1177 A eutolf can typically be described bv a Sehechter funetion. OU)xMἹοκρί--M/Me) (eg. Burkert Smith 2000: Fall Zhang 2001: Jordan et 22007). where the imunber of massive clusters drops exponentially compared wilh (he number of lower mass clusters. i.e.. faster than a power law.," A cutoff can typically be described by a Schechter function, $\psi(M) \propto M^{\beta} \mbox{exp}(-M/M_C)$ (e.g., Burkert Smith 2000; Fall Zhang 2001; Jordan et 2007), where the number of massive clusters drops exponentially compared with the number of lower mass clusters, i.e., faster than a power law."1178 For example. Schechter functions with Ale=~1-22x10°M. provide significantly better fits than power laws at the high end of the mass function of old globular clusters (e.g.. Burkert Smith 2000: Fall Zhang 2001: Jordan et 22007).," For example, Schechter functions with $M_C\approx 1-2\times10^6~M_{\odot}$ provide significantly better fits than power laws at the high end of the mass function of old globular clusters (e.g., Burkert Smith 2000; Fall Zhang 2001; Jordan et 2007)."1179 We [found in Section 5.3 and in Figure 12. that a power law provides a good fit to (he mass function of clusters in M83 at different ages., We found in Section 5.3 and in Figure \ref{fig:mf} that a power law provides a good fit to the mass function of clusters in M83 at different ages.1180 A IX-5 test comparing the masses of clusters with M28xLO!M. with a power law of 4=—2.02 returns a P-value of 0.32. ie. a power law provides an acceptable fit to the upper end of the cluster mass function (note: a P-value <0.05 is tvpically indicative of an unacceptable fit).," A K-S test comparing the masses of clusters with $M \geq 8\times 10^4~M_{\odot}$ with a power law of $\beta=-2.02$ returns a $P$ -value of 0.32, i.e., a power law provides an acceptable fit to the upper end of the cluster mass function (note: a $P$ -value $< 0.05$ is typically indicative of an unacceptable fit)."1181 The upper panel of Figure 13 compares the observed mass function with three different values of Me: LO?M... 4x10° M... and 105M...," The upper panel of Figure 13 compares the observed mass function with three different values of $M_C$ : $10^5~M_{\odot}$, $4\times10^5~M_{\odot}$ , and $10^6~M_{\odot}$."1182 This figure suggests that values of Me: that are lower than zz10?M... do not provide a good match to the data., This figure suggests that values of $M_C$ that are lower than $\approx10^5~M_{\odot}$ do not provide a good match to the data.1183 This visual impression is confirmed by statistical tests., This visual impression is confirmed by statistical tests.1184 We are only able to place a lower-Iimit on Me. with all values Mec1x10?M. giving acceptable fits. ie.. within a confidence level. based on formal K-S tests.," We are only able to place a lower-limit on $M_C$, with all values $M_C > 1\times10^5~M_{\odot}$ giving acceptable fits, i.e., within a confidence level, based on formal K-S tests."1185 We conclude that. because a power law provides an acceptable fit. our data cdo nol require a Schechterfunctionto describe them.," We conclude that, because a power law provides an acceptable fit, our data do not require a Schechterfunctionto describe them."1186We find that the dusty wall produces a radial temperature inversion that is a thermal barrier for rapid tvpe I planetary migration.,We find that the dusty wall produces a radial temperature inversion that is a thermal barrier for rapid type I planetary migration.1187 Whereas the torque balance in the well coupled aclive zone forces planets to migrate inward. once thev encounter the radial thermal inversion region. the torque balance reverses. and they move oul of the region.," Whereas the torque balance in the well coupled active zone forces planets to migrate inward, once they encounter the radial thermal inversion region, the torque balance reverses, and they move out of the region."1188 Thus. planets are (rappecl there if they. originally migrate from the active region bevond the dead zones. or even if they formed close to the outer edge of the dead zone.," Thus, planets are trapped there if they originally migrate from the active region beyond the dead zones, or even if they formed close to the outer edge of the dead zone."1189 The astrophysical implications of this result are very. important since we have shown that dusty protoplanetary disks wilh dead zones possess an innate mechanism for strongly slowing planetary migration within them. provided that the corotation torque is saturated.," The astrophysical implications of this result are very important since we have shown that dusty protoplanetary disks with dead zones possess an innate mechanism for strongly slowing planetary migration within them, provided that the corotation torque is saturated."1190 While such a thermal barrier exists for any size of dead zone (IIP10). its effectiveness is probably most important for lower mass disks. as we now show.," While such a thermal barrier exists for any size of dead zone (HP10), its effectiveness is probably most important for lower mass disks, as we now show."1191 The density structure of disks evolves with time due to viscous evolution., The density structure of disks evolves with time due to viscous evolution.1192 MI'T09 found that the difference of a between the active and dead regions produces a steep density eradient at the boundary. and the location of their jump moves inward with time over the long (~ 10 Myr) viscous timescale of the dead zone., MPT09 found that the difference of $\alpha$ between the active and dead regions produces a steep density gradient at the boundary and the location of their jump moves inward with time over the long $\sim$ 10 Myr) viscous timescale of the dead zone.1193 This densitv gradient at the outer dead zone boundary. also plavs an important role in slowing down or stopping tvpe I migration. provided (hat planets migrate Irom larger disk radii.," This density gradient at the outer dead zone boundary also plays an important role in slowing down or stopping type I migration, provided that planets migrate from larger disk radii."1194" The inner torques become larger than (he outer ones in the density gradient region. resulüing in the reflection of mierating planets olf the density gradient. (AIPTO9),"," The inner torques become larger than the outer ones in the density gradient region, resulting in the reflection of migrating planets off the density gradient (MPT09)."1195" The relative importance of these two dead zone mechanisms is controlled by the ratio ol dust settling 74;8XV2yao and the viscous 7, limescales. where py is the bulk densitv of cust ancl e is the grain size of dust."," The relative importance of these two dead zone mechanisms is controlled by the ratio of dust settling $\tau_{set}\approx \Sigma / \sqrt{2\pi} \rho_d a \Omega_{Kep}$ and the viscous $\tau_{vis}$ timescales, where $\rho_d$ is the bulk density of dust and $a$ is the grain size of dust."1196 We find that the critical condition, We find that the critical condition1197Tu any case. UV optical color can be used to discriminate eenuine IACCs from the old GCs masquerading as LAGC's.,"In any case, $-$ optical color can be used to discriminate genuine IAGCs from the old GCs masquerading as IAGCs."1198 Figue 2 shows the V—I versus V diagrams., Figure 2 shows the $V-I$ versus $-V$ diagrams.1199 We compare our NGC 5128 suuple with those of the Allkv Way (crosses. Solu et al.," We compare our NGC 5128 sample with those of the Milky Way (crosses, Sohn et al."1200 2006) aud MD (open circles; Rev et al.," 2006) and M31 (open circles, Rey et al."

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