ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2" The SNR. for closure phase is given bv 1992a) In the photon-noise dominated regime (VV>x 1). the SNR for closure phase aud visibility scales as .NE?,"," The SNR for closure phase is given by \citep{tango80,shaocola92} as compared to that for visibility and phase, In the photon-noise dominated regime $NV^2\gg1$ ), the SNR for closure phase and visibility scales as $N^{1/2}$."3 However. for photon-starved sources. the SNR drops precipitously as >NY?) even worse than the xV scaling of the visibilily SNR.," However, for photon-starved sources, the SNR drops precipitously as $N^{3/2}$, even worse than the $\propto N$ scaling of the visibility SNR."4 Hence it is important to check whether microlensing sources will be photon-rich or photon-starvec., Hence it is important to check whether microlensing sources will be photon-rich or photon-starved.5 In the A-band (2.27) a 15th magnitude source produces 0.16 photons em7s+., In the $K$ -band $2.2 \mu$ m) a 15th magnitude source produces 0.16 photons ${\rm cm}^{-2}~{\rm s}^{-1}$.6 Thus we would expect an 8-m class telescope to collect 80.000 photons |.," Thus we would expect an 8-m class telescope to collect $\sim 80,000$ photons $^{-1}$ ."7 Assuming a coherence time 7= 20msec. and a tvpical photon elliciency of5%.. we have V=80>>10 per integration. safely in the photon rich regime when using modern low-noise detectors.," Assuming a coherence time $\tau_0=20$ msec, and a typical photon efficiency of, we have $N=80\gg1$ per integration, safely in the photon rich regime when using modern low-noise detectors."8 In the absence of svstematic errors a 3-element interferometer should achieve a closure pliase precision of 10.* radians in 250 seconds., In the absence of systematic errors a 3-element interferometer should achieve a closure phase precision of $10^{-3}$ radians in 250 seconds.9 However. it remains to be seen if such levels can be achieved.," However, it remains to be seen if such levels can be achieved."10 To date. closure phase measurements havebeen made in the optical and near-IR bv 2 groups.," To date, closure phase measurements havebeen made in the optical and near-IR by 2 groups."11 COAST achieves a closure phase precision of 2 degrees (Baldwinetal.1996).. while NPOL achieves phase drifts of ~10 degrees |. which can be calibrated to the level ol 1-4 degrees bv lookingal known single stars (hunmeletal. 1998)..," COAST achieves a closure phase precision of $\sim 2$ degrees \citep{baldwin96}, while NPOI achieves phase drifts of $\sim 10$ degrees $^{-1}$ , which can be calibrated to the level of 1-4 degrees by lookingat known single stars \citep{hummel98}. ."12 Recent progress in, Recent progress in13the thermal background compared to the conventional 2.2j/m K filter (Wainscoat Cowie 1992).,the thermal background compared to the conventional $\mu$ m K filter (Wainscoat Cowie 1992).14 The plate scales of the NICMOS3 and QUIRC cameras are 0737 pixel! and 071886 pixel-!. respectively.," The plate scales of the NICMOS3 and QUIRC cameras are $\farcs$ 37 $^{-1}$ and $\farcs$ 1886 $^{-1}$, respectively."15" For observations made prior to April 1993. separate nearby sky frames were obtained by moving the telescope 90 — 120"" away from the source position. and these sky frames were then combined to produce final median sky frames."," For observations made prior to April 1993, separate nearby sky frames were obtained by moving the telescope 90 – $\arcsec$ away from the source position, and these sky frames were then combined to produce final median sky frames."16 For the rest of the observations. sky frames were constructed by median filtering dithered object frames.," For the rest of the observations, sky frames were constructed by median filtering dithered object frames."17 Because the sky brightness changes rapidly. the median-filtered sky frames were rescaled to the sky values of each object frame before the sky subtraction.," Because the sky brightness changes rapidly, the median-filtered sky frames were rescaled to the sky values of each object frame before the sky subtraction."18 Prior to this subtraction. all hot pixels were eliminated from the distribution of pixel values in dark frames.," Prior to this subtraction, all hot pixels were eliminated from the distribution of pixel values in dark frames."19 The distribution of pixel values i5 expected to be Gaussian and if a pixel value lies above or below the 3c values. then we regarded it as hot.," The distribution of pixel values is expected to be Gaussian and if a pixel value lies above or below the $\sigma$ values, then we regarded it as hot."20 Dome flats were obtained at the beginning and end of each night by turning a lamp in the dome on and off., Dome flats were obtained at the beginning and end of each night by turning a lamp in the dome on and off.21 The dark-subtracted flats were obtained by subtracting the lamp-off flats from the lamp-on flats., The dark-subtracted flats were obtained by subtracting the lamp-off flats from the lamp-on flats.22 Flat-fielded images were then coadded after shifting in fractional pixel units with respect to the object center., Flat-fielded images were then coadded after shifting in fractional pixel units with respect to the object center.23 During this procedure we carefully inspected all of the image frames to see if any hot pixels remained near the target object., During this procedure we carefully inspected all of the image frames to see if any hot pixels remained near the target object.24 Any remaining hot pixels near the target were then replaced with the median value from all other frames at the same position., Any remaining hot pixels near the target were then replaced with the median value from all other frames at the same position.25 The final coadded images were calibrated from observations of infrared standard stars (Elias et., The final coadded images were calibrated from observations of infrared standard stars (Elias et.26 al., al.27 1982) using the PHOT or POLYPHOT packages in IRAF., 1982) using the PHOT or POLYPHOT packages in IRAF.28 Airmass corrections Were carried out using the same procedure as for the optical observations., Airmass corrections were carried out using the same procedure as for the optical observations.29 The near-infrared observations are summarized in Table I., The near-infrared observations are summarized in Table 1.30 The R and K' greyscale images and contour plots of the entire I-Jy sample of ULIGs are presented in Figure 1., The $R$ and $K^\prime$ greyscale images and contour plots of the entire 1-Jy sample of ULIGs are presented in Figure 1.31 It is immediately evident from this figure that nearly all of the objects in the I-Jy sample show signs of a strong tidal interaction/merger in. the form of distorted or double nuclei. tidal tails. bridges. and overlapping disks.," It is immediately evident from this figure that nearly all of the objects in the 1-Jy sample show signs of a strong tidal interaction/merger in the form of distorted or double nuclei, tidal tails, bridges, and overlapping disks."32 These results are qualitatively. consistent. with previous imaging surveys of ULIGs (e.g.. Sanders et al.," These results are qualitatively consistent with previous imaging surveys of ULIGs (e.g., Sanders et al."33 1988: Melnick Mirabel 1990; Murphy et al., 1988; Melnick Mirabel 1990; Murphy et al.34 1996; Clements et al., 1996; Clements et al.35 1996; although see Lawrence et al., 1996; although see Lawrence et al.36 1959: Zou et al., 1989; Zou et al.37 199]: Leech et al., 1991; Leech et al.38 1994)., 1994).39 Recent surveys with HST and adaptive optics systems have also confirmed these results (e.g.. Surace et al.," Recent surveys with HST and adaptive optics systems have also confirmed these results (e.g., Surace et al."40 1998; Zheng et al., 1998; Zheng et al.41 1999; Scoville et al., 1999; Scoville et al.42 2000: Borne et al., 2000; Borne et al.43 2000: Cui et al., 2000; Cui et al.44 2001: Farrah et al., 2001; Farrah et al.45 2001: Colina et al., 2001; Colina et al.46 2001: Bushouse et al., 2001; Bushouse et al.47" 2002: Surace Sanders 1999, 2000: Surace. Sanders. Evans 2000. 2001)."," 2002; Surace Sanders 1999, 2000; Surace, Sanders, Evans 2000, 2001)."48 Great care was used to determine which objects in the field are involved in tidal interactions and which ones are not (the description of this analysis is postponed until $3 in Paper ID., Great care was used to determine which objects in the field are involved in tidal interactions and which ones are not (the description of this analysis is postponed until 3 in Paper II).49 Faint tidal features and distortions are generally easier to detect in our R-band images., Faint tidal features and distortions are generally easier to detect in our $R$ -band images.50" Galaxies labeled ""G"" in Figure | indicates a nearby group member with no evidence of tidal interaction with the main galaxy.", Galaxies labeled “G” in Figure 1 indicates a nearby group member with no evidence of tidal interaction with the main galaxy.51 The group membership of these galaxies was individually determined using a series of spectroscopic observations with the Keck IL telescope., The group membership of these galaxies was individually determined using a series of spectroscopic observations with the Keck II telescope.52 These observations will be described in Paper HH along with the results from a quantitative analysis of the imaging data., These observations will be described in Paper II along with the results from a quantitative analysis of the imaging data.53 We have measured the positions of the main galactic nuclei from the R and K' images., We have measured the positions of the main galactic nuclei from the $R$ and $K^\prime$ images.54 To determine the position of each nucleus. we first retrieved the positions of 3 — 8 stars around the galaxy from the USNO-A1.0 catalog (Monet et al.," To determine the position of each nucleus, we first retrieved the positions of 3 – 8 stars around the galaxy from the USNO-A1.0 catalog (Monet et al."55 1996)., 1996).56 A plate solution was then derived using the IRAF task PLTSOL., A plate solution was then derived using the IRAF task PLTSOL.57 The typical positional error (7 2-0) is estimated to be less than 0035., The typical positional error $\sim$ $\sigma$ ) is estimated to be less than $\farcs$ 5.58 The positions of the nuclei are listed in the second and third columns of Table 2., The positions of the nuclei are listed in the second and third columns of Table 2.59" The median values of the positional offsets between the R and A"" nuclei is 0748. or 1.22 kpe if we convert areseconds into physical scale."," The median values of the positional offsets between the $R$ and $K^\prime$ nuclei is $\farcs$ 48, or 1.22 kpc if we convert arcseconds into physical scale."60 Using the optical spectral types derived from our optical spectroscopy (Veilleux et al., Using the optical spectral types derived from our optical spectroscopy (Veilleux et al.61 19993). we find that the median values of the offsets are 075] (1.3 κρο). 0759 (1.2 κρο). 0724 (1.3 kpe). and 0722 (0.9 kpe) for H II region-like. LINER. Seyfert 2. and Seyfert | galaxies. respectively.," 1999a), we find that the median values of the offsets are $\farcs$ 51 (1.3 kpc), $\farcs$ 59 (1.2 kpc), $\farcs$ 44 (1.3 kpc), and $\farcs$ 22 (0.9 kpc) for H II region-like, LINER, Seyfert 2, and Seyfert 1 galaxies, respectively."62 This marginally significant positional offset can be attributed to the wavelength-dependent effects of dust extinction along our line of sight., This marginally significant positional offset can be attributed to the wavelength-dependent effects of dust extinction along our line of sight.63 The smaller offset among Seyfert Is may indicate less dust extinction in these objects., The smaller offset among Seyfert 1s may indicate less dust extinction in these objects.64 Global and nuclear (4-kpe diameter) aperture photometry was performed for each galaxy in the sample., Global and nuclear (4-kpc diameter) aperture photometry was performed for each galaxy in the sample.65 The results of these measurements are listed in Table 3., The results of these measurements are listed in Table 3.66 Since the I-Jy sources are selected to have |b] > 30° (Kim Sanders 1998). the photometry presented in this paper has not been corrected for Galactic extinction.," Since the 1-Jy sources are selected to have $\vert67b \vert$ $>$ $^\circ$ (Kim Sanders 1998), the photometry presented in this paper has not been corrected for Galactic extinction."68 Figure 2 shows the distribution of the integrated (= nuclear + host) R and K' absolutemagnitudes of our sample galaxies., Figure 2 shows the distribution of the integrated (= nuclear + host) $R$ and $K^\prime$ absolutemagnitudes of our sample galaxies.69 The absolute magnitudes range from —20.| to —26.4 at R (mean =—-21.9 + 0.9. median 2 221.83) and from —23.7 to 229.3 at K' (mean = -25.3 + I.I. median = -25.2).," The absolute magnitudes range from –20.1 to –26.4 at $R$ (mean = –21.9 $\pm$ 0.9, median = –21.83) and from –23.7 to –29.3 at $K^\prime$ (mean = –25.3 $\pm$ 1.1, median = –25.2)."70 Using Mj 2 221.2 and Mj; 2 —24.1 foran L galaxy with Ho = 75 km s! Mpe! (see discussion at the end of $1 in Paper IL). these magnitudes are equivalent to ~ 0.4 — 120 (0.7 — 120) L at R (K). with means and medians around 2 (3) L.," Using $M_R$ = –21.2 and $M_{K^\prime}$ = –24.1 for an $L^\ast$ galaxy with $H_0$ = 75 km $^{-1}$ $^{-1}$ (see discussion at the end of 1 in Paper II), these magnitudes are equivalent to $\sim$ 0.4 – 120 (0.7 – 120) $L^\ast$ at $R$ $K^\prime$ ), with means and medians around 2 (3) $L^\ast$."71 Figure 3 shows the distribution of global and nuclear R—K' colors., Figure 3 shows the distribution of global and nuclear $R - K^\prime$ colors.72" The global R—A’ and nuclear (4-kpe diameter) K'), colors range from 2.15 to 5.28 and 3.18 to 6.81 with median values of 3.25 and 4.37. respectively."," The global $R - K^\prime$ and nuclear (4-kpc diameter) $(R -73K^\prime)_4$ colors range from 2.15 to 5.28 and 3.18 to 6.81 with median values of 3.25 and 4.37, respectively."74" There is a strong correlation between the global and nuclear A—K"" colors (not shown here): this correlation is expected since the nuclear color contributes significantly to the global color.", There is a strong correlation between the global and nuclear $R - K^\prime$ colors (not shown here); this correlation is expected since the nuclear color contributes significantly to the global color.75 These colors can be compared with those of normal galaxies using the photometric tables of de Vaucouleurs Longo (1988)., These colors can be compared with those of normal galaxies using the photometric tables of de Vaucouleurs Longo (1988).76 In their table. we find 14 galaxies (5 ellipticals. 9 spirals) which have Kron-Cousins R and near-infrared K and H magnitudes: for these objects we find a mean R—K' value of 2.62 + 0.34.," In their table, we find 14 galaxies (5 ellipticals, 9 spirals) which have Kron-Cousins R and near-infrared $K$ and $H$ magnitudes; for these objects we find a mean $R -77K^\prime$ value of 2.62 $\pm$ 0.34."78 The H magnitude was used to convert K to A’ magnitudes using the conversion formula K' K(0.220.039(H—K) from Wainscoat Cowie (1992)., The $H$ magnitude was used to convert $K$ to $K^\prime$ magnitudes using the conversion formula $K^\prime = K + (0.22 \pm 0.03) (H - K)$ from Wainscoat Cowie (1992).79 Dust extinction in the nuclei of ULIGs ts at least partially responsible for the redder colors of ULIGs relative to normal galaxies: dust emission at K may also be important in ULIGs., Dust extinction in the nuclei of ULIGs is at least partially responsible for the redder colors of ULIGs relative to normal galaxies; dust emission at $K^\prime$ may also be important in ULIGs.80 This issue ts discussed in more detail in Paper II., This issue is discussed in more detail in Paper II.81 We define the “compactness” of a galaxy as the ratio of nuclear (4-kpe diameter) to total luminosities., We define the “compactness” of a galaxy as the ratio of nuclear (4-kpc diameter) to total luminosities.82 Figures + shows the histograms of the R and K' compactness values., Figures 4 shows the histograms of the $R$ and $K^\prime$ compactness values.83" The R (K"") compactness ranges from 0.03 (0.10) to 0.53 (0.91) with a mean value of 145-0.09 (0.36+0.17) (1 σ).", The $R$ $K^\prime$ ) compactness ranges from 0.03 (0.10) to 0.53 (0.91) with a mean value of $\pm$ 0.09 $\pm$ 0.17) (1 $\sigma$ ).84 The ULIGs in our sample are therefore significantly more compact at A’ than at R. possibly a consequence of the lower extinction and stronger warm-dust emission at longer wavelengths.," The ULIGs in our sample are therefore significantly more compact at $K^\prime$ than at $R$ , possibly a consequence of the lower extinction and stronger warm-dust emission at longer wavelengths."85 The dependence of the compactness on the infrared and optical spectroscopic properties of the galaxies will be discussed in Paper II., The dependence of the compactness on the infrared and optical spectroscopic properties of the galaxies will be discussed in Paper II.86dominates the accuracy of (p.0) polarimetric analysis for sources with intrinsically low polarization. if observed with a sufficient nunber of optimally placed dither positions: observers need not be concerned by the IPRE.,"dominates the accuracy of $p,\theta$ ) polarimetric analysis for sources with intrinsically low polarization, if observed with a sufficient number of optimally placed dither positions; observers need not be concerned by the IPRF."87 Since observations through the three polarizers are not sinuultaneouslv obtained. temporal instabilities iu the MST|NICMOS PSF are still a concern and the effects are readily seen in Figures 2.. 5.. 6 aud 7..," Since observations through the three polarizers are not simultaneously obtained, temporal instabilities in the +NICMOS PSF are still a concern and the effects are readily seen in Figures \ref{fig:rad2}, , \ref{fig:deviants}, \ref{fig:oldcal} and \ref{fig:newcal}."88 Outside of au aperture of radius (07558. the PSF affects are seen to be alleviated.," Outside of an aperture of radius 58, the PSF affects are seen to be alleviated."89 Tuside this radius. the errors in p aud 0 rise rapidly aud it will be left to the discretion of the observer to weieh their required accuracy to the possible results of beani-depolauization.," Inside this radius, the errors in $p$ and $\theta$ rise rapidly and it will be left to the discretion of the observer to weigh their required accuracy to the possible results of beam-depolarization."90 Iu a nou-ideal imaging polarimeter. such as NICAIOS. it is essential to observe several polarimetric standards. at three well separated position angles through cach yolarizer. in order to full characterize the instrmucutal x)hudzation.," In a non-ideal imaging polarimeter, such as NICMOS, it is essential to observe several polarimetric standards, at three well separated position angles through each polarizer, in order to full characterize the instrumental polarization."91 The additional roll angles remove the nucertaimtics in the (unknown) parallel transmission coefficients and allow rotation of amy iustruucutal xlarization with respects to the equatorial frame., The additional roll angles remove the uncertainties in the (unknown) parallel transmission coefficients and allow rotation of any instrumental polarization with respects to the equatorial frame.92 Using lis technique we lave placed an upper linüt to the NIC2 iustruuieutal polarization of0., Using this technique we have placed an upper limit to the NIC2 instrumental polarization of.936%... With a known value for the Stokes £ parameter. the instrumenta xilarization ean be transformed iuto the Q.UC plane iux )o subtracted.," With a known value for the Stokes $I$ parameter, the instrumental polarization can be transformed into the $Q,U$ plane and be subtracted."94 New parallel trausiuission coefficieuts ca- hen be deteriuued nmuuercallv by comparing p ae Ó with that of the apriori well-detcermined calibratio- standards., New parallel transmission coefficients can then be determined numerically by comparing $p$ and $\theta$ with that of the apriori well-determined calibration standards.95" Following this approach we have determine he ty and f499 coefiicicuts to be 0,5832EO.00 Land 0:8271.00L respectively.", Following this approach we have determined the $t_0$ and $t_{120}$ coefficients to be $0.883\pm0.004$ and $0.837\pm0.004$ respectively.96 As with the previous calibrations of the NIC2 polariueter. we held τοι constant at 0.9667," As with the previous calibrations of the NIC2 polarimeter, we held $t_{240}$ constant at 0.9667."97" The tyy cocficient is consistent with the previous calibration. but our knowledge of ty has beeu improved. resulting iu a change in its previously determined value by ~-ο--0.554, "," The $t_{120}$ coefficient is consistent with the previous calibration, but our knowledge of $t_0$ has been improved, resulting in a change in its previously determined value by $\sim0.5\%$ ."98Such a small change in ty does not warrant the sis of previous NIC2 imagine polarimetry data of polarized (po>5%) targets. but is sjenificaut for targets with intrinsically low polarization fractions.," Such a small change in $t_0$ does not warrant the re-analysis of previous NIC2 imaging polarimetry data of polarized $p>5\%$ ) targets, but is significant for targets with intrinsically low polarization fractions."99 As we use 13 determinations of fj. we are able to assign leo uncertaiuties to the calibration coefficients.," As we use 13 determinations of $t_k$, we are able to assign $1\sigma$ uncertainties to the calibration coefficients."100 Propagating these uncertainties through the polarimetric analysis. we find that they dominate all other sources of error.," Propagating these uncertainties through the polarimetric analysis, we find that they dominate all other sources of error."101 Applying these adjusted values of f; to this (and the archived) calibration data. we fiud that NIC2 is now capable of confidently detecting polarizations at level of z1.0.," Applying these adjusted values of $t_k$ to this (and the archived) calibration data, we find that NIC2 is now capable of confidently detecting polarizations at a level of $\approx1.0\%$."102" The uncertainties associated with such measurements are £0.6% and c5"" in p aud 0. for sources at the zz1% level of intrinsic polarization."," The uncertainties associated with such measurements are $\pm0.6\%$ and $\pm15\degr$ in $p$ and $\theta$, for sources at the $\approx1\%$ level of intrinsic polarization."103 This is the first time that such a level of accuracy has heen achieved with the NICMOS polarization calibration., This is the first time that such a level of accuracy has been achieved with the NICMOS polarization calibration.104 This nuproved calibration opens a new domain for observational investigations withZLST bv cuabling very lieh precision polarmietry of iutrinsically very low polarization sources., This improved calibration opens a new domain for observational investigations with by enabling very high precision polarimetry of intrinsically very low polarization sources.105 We are erateful to the referee for their thorough reading of this mamuscript., We are grateful to the referee for their thorough reading of this manuscript.106" Support for Proposal umber ΠΡΤ(01052001 was provided by NASA through a erant from the-Α Space Telescope Science Institute. which is operated by the Association of Universities for Research in Astronomy. DIucorporated. uuder NASA contract NAS5S-26555,"," Support for Proposal number HST-GO-10839.01-A was provided by NASA through a grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Incorporated, under NASA contract NAS5-26555."107 For the NICT observations. the individual poiutiuegs for eac1 polarizer were not dithered around the 12 point pattern used for the NIC2 observations.," For the NIC1 observations, the individual pointings for each polarizer were not dithered around the 12 point pattern used for the NIC2 observations."108 However. the observations from cach separate polarizer were dithered so as to avoid persistence.," However, the observations from each separate polarizer were dithered so as to avoid persistence."109 The poiutings were also placed on an area of NICT where the quantum efficiency (QE) eracicuts are particularly shallow aud where the QE is reasonably high., The pointings were also placed on an area of NIC1 where the quantum efficiency (QE) gradients are particularly shallow and where the QE is reasonably high.110" TUs area was also sufficiently far from anv ""erottv pixels and sufficicutly far from the edge of the detector.", This area was also sufficiently far from any “grotty” pixels and sufficiently far from the edge of the detector.111 As there ive ouly single poiutiugs per polarizer. the data aalysis for the NICT data is less complicated than for the NIC2 case.," As there are only single pointings per polarizer, the data analysis for the NIC1 data is less complicated than for the NIC2 case."112 The extracted radial profiles frou: cach polarizer (and pointing} at cach roll angle are shown in Figure A9.., The extracted radial profiles from each polarizer (and pointing) at each roll angle are shown in Figure \ref{fig:rad1}.113 For these profiles we can only define the S/N using the ploton noise., For these profiles we can only define the S/N using the photon noise.114 As there are only single poiutiues in cach NIC1 polarizer. it is inipossibleto perform the iterative 20 clipping techuique employed for NIC2.," As there are only single pointings in each NIC1 polarizer, it is impossibleto perform the iterative $2\sigma$ clipping technique employed for NIC2."115 Therefore all NICT profiles must be included in the analvsis., Therefore all NIC1 profiles must be included in the analysis.116 Although there is no statistical way to tell if the profiles in Figure AQ are robust. we can at least see that all profiles are consistent with cach other.," Although there is no statistical way to tell if the profiles in Figure \ref{fig:rad1} are robust, we can at least see that all profiles are consistent with each other."117 This is likely due to the care taken in avoiding nucorrectable bad pixels., This is likely due to the care taken in avoiding uncorrectable bad pixels.118 At the radius of the 37 NICI dark Airy mininnun (given by an aperture with r=7.0 pixels. assuming a central wavelength of LO05¢an and a2.28lin aperture) the respective signal to noise ratios for VRale. VSS VIIL-132 aud IID331591 are 257. 180 ane 330 when averaged across the three polarizers.," At the radius of the $3^{\rm rd}$ NIC1 dark Airy minimum (given by an aperture with $r=7.0$ pixels, assuming a central wavelength of $1.05\micron$ and a2.281m aperture) the respective signal to noise ratios for VR84c, VSS VIII-13 and HD331891 are 257, 180 and 330 when averaged across the three polarizers."119 The theoretical NICT achievable accuracies are approxinatelv 1.5% with au uncertaintv of 0. e)Mi, The theoretical NIC1 achievable accuracies are approximately $1.5\%$ with an uncertainty of $\pm0.2\%$ and $1.0\pm0.3\%$.120 At1.21jm.. 2). give VB8SIc a polarization of 3.194 LIS+1° and VSS VIIT-13 a polarization of 2.21£0.3% at 96+|," At, \citet{1992ApJ...386..562W} give VR84c a polarization of $3.19\pm0.05\%$ at $118\pm1\degr$ and VSS VIII-13 a polarization of $2.21\pm0.3\%$ at $96\pm1\degr$."121 As there is no data for ΠΟΟΟΙ5ΟΙ at this wavelength we assume that this target is unpolarized., As there is no data for HD331891 at this wavelength we assume that this target is unpolarized.122 The polarizations and uucertaimties are carried through the Serkowski correction and are prescuted in Table 2.., The polarizations and uncertainties are carried through the Serkowski correction and are presented in Table \ref{tab:stand}.123 Except for the 20 clippiug. the NICT data was treated exactly like the NIC2 data.," Except for the $2\sigma$ clipping, the NIC1 data was treated exactly like the NIC2 data."124 The calibration data frou the nmltiple orieutations are preseuted in Table As, The calibration data from the multiple orientations are presented in Table \ref{tab:rollsnic1}.125 The NICT iustrumnental polarization was then determined to be L340.9%( at an oricutation of 151+418, The NIC1 instrumental polarization was then determined to be $1.3\pm0.9\%$ at an orientation of $151\pm18\degr$.126 This mstrneutal polarization was subtracted iu ((Q.U7) space aud the parallel transmission coefficients were re-derived on au orbit bv orbit basis.," This instrumental polarization was subtracted in $(Q,U)$ space and the parallel transmission coefficients were re-derived on an orbit by orbit basis."127 The cocfhicicuts. auduncertainties. that bring all the data consistent with the eround-based data are £459=0.57250.01 and toy=0.69 250.01.," The coefficients, anduncertainties, that bring all the data consistent with the ground-based data are $t_{120} = 0.57\pm0.01$ and $t_{240} = 0.69\pm0.01$ ."128 All the coefficieuts to be used in NICI polarimetric observations are shown inTable A9.., All the coefficients to be used in NIC1 polarimetric observations are shown inTable \ref{tab:n1coes}. .129 Applving these new calibration coefficieuts to, Applying these new calibration coefficients to1302001).,.131. We note that it is likely anv bursts during this observation were probably not recorded due to pile-up aud (o on-board/post-processing rejection of anomalous events., We note that it is likely any bursts during this observation were probably not recorded due to pile-up and to on-board/post-processing rejection of anomalous events.132 To accurately localize1806—20.. we measured its position in both ddatasets.," To accurately localize, we measured its position in both datasets."133 The measured positions from the (wo observations are consistent to 0704. suggesting that the stochastic position errors are minimal.," The measured positions from the two observations are consistent to $0\farcs04$, suggesting that the stochastic position errors are minimal."134 There may however be svstemaltic errors on the order of 1” due to overall uncertainties in the aaspect solutions., There may however be systematic errors on the order of $1\arcsec$ due to overall uncertainties in the aspect solutions.135 To correct for such errors we searched the images lor background sources (o0 use as position relerences., To correct for such errors we searched the images for background sources to use as position references.136 We [ound seven weak sources in the 5-ks image., We found seven weak sources in the 5-ks image.137 None had a match in the SIAIBAD database. but (wo sources (detected αἱ 25-0 confidence) were coincicent with stars.," None had a match in the SIMBAD database, but two sources (detected at $\sigma$ confidence) were coincident with stars."138 In the 31-ks image we found 11 sources. two of which had matches in the USNO-A2.0 catalog: one detected al 4-7 confidence that was also in the 5-ks image. the other detected al 2.5-0 confidence.," In the 31-ks image we found 11 sources, two of which had matches in the USNO-A2.0 catalog: one detected at $\sigma$ confidence that was also in the 5-ks image, the other detected at $\sigma$ confidence."139 We summarize the X-ray detected USNO starsin Table 2.., We summarize the X-ray detected USNO starsin Table \ref{tab:usno}.140 There are zz4.3USNOstarsavemin7 in this region. giving chance comcidence rates of ~0.154 between an imdividual X-ray source and a USNO star. supporting our identifications.," There are $\approx 4.3\mbox{ USNO stars arcmin}^{-2}$ in this region, giving chance coincidence rates of $\sim 0.1$ between an individual X-ray source and a USNO star, supporting our identifications."141 We are pursuing photometric and spectroscopic observations of these stars that should allow us (ο elassifv them and. verily these identifications (e.g.vandenBere&Verbunt.2001)., We are pursuing photometric and spectroscopic observations of these stars that should allow us to classify them and verify these identifications \citep[e.g.][]{vdbv01}.142. Using the USNO stars to derive offsets for the astrometry. we lind corrections of and Ad=075. consistent between both images and comparable in magnitude to the expected aspectuncertainties?.," Using the USNO stars to derive offsets for the astrometry, we find corrections of $\Delta \alpha=0\farcs4$ and $\Delta143 \delta=0\farcs5$, consistent between both images and comparable in magnitude to the expected aspect."144. We [ind a corrected position for oo[ egg=L808239232 and Os=—207243975., We find a corrected position for of $\alpha_{2000} = 18^{\rm h}08^{\rm m}39\fs32$ and $\delta_{2000} = -20\degr 24\arcmin 39\farcs5$.145 This position has rms uncertainties of 073 in each coordinate (from centroiding the X-ray. sources and intrinsic USNO uncertainties of Q/2: Deutsch 19993). but should be [ree [rom svstematic uncertainties.," This position has rms uncertainties of $0\farcs3$ in each coordinate (from centroiding the X-ray sources and intrinsic USNO uncertainties of $0\farcs2$ ; \citealt{d99}) ), but should be free from systematic uncertainties."146" This position agrees very well (within the 1-7 errorellipse) with the position determined [rom IPN measurements (Iurlevetal. 1999a).. and is 1420.5"" from the position ofthe nebula from Frailetal. (1997): see Figure 2.."," This position agrees very well (within the $\sigma$ errorellipse) with the position determined from IPN measurements \citep{hkc+99}, , and is $14\pm 0.5\arcsec$ from the position ofthe non-thermal nebula from \citet{fvk97}; ; see Figure \ref{fig:radio}. ."147a homogeneous medium of density 7=0.1:θα7. ,"a homogeneous medium of density $n = 0.1 148\div 0.4\, \cm3$."149We have also found that a wind-like medium cannot reproduce the steepness of the optical light-curve break. yielding an unacceptable best fit (47=127 for 69 df).," We have also found that a wind-like medium cannot reproduce the steepness of the optical light-curve break, yielding an unacceptable best fit $\chi^2 = 127$ for 69 df)."150" Por ahomogeneous external medium. equation (32)) shows that a,=0.92+0.18 for a uniform outflow. which is consistent with the observed index. thus a large structural parameter q is disfavored. otherwise the early decay would be too shallow."," For a external medium, equation \ref{ab1}) ) shows that $\alpha_1 = 0.92 \pm151 0.18$ for a uniform outflow, which is consistent with the observed index, thus a large structural parameter $q$ is disfavored, otherwise the early decay would be too shallow."152 Further. equation (33)) shows that. for a fireball. the post-break index e» cannot exceed 1.67+0.18. which is too small compared to that observed. thus a spreading Jet is required.," Further, equation \ref{ab2}) ) shows that, for a fireball, the post-break index $\alpha_2$ cannot exceed $1.67 \pm 1530.18$, which is too small compared to that observed, thus a spreading jet is required."154 In this case. equation (34)) leads to a post-break index à»=2.22+ 0.21. which is consistent with the measured index.," In this case, equation \ref{alfamax}) ) leads to a post-break index $\alpha_2 = 2.22 \pm 0.24$ , which is consistent with the measured index."155 The above conclusion that the pre-break light-curve index of the afterglow of GRB 990510 does not allow much structure in a spreading jet is illustrated in Figure 5. showing the 4? of the fits obtained for several combinations of the structural parameter 4 and jet core size-to-opening ratio 0Ομ. and for two particular observer locations: the jet axis and the jet edge.," The above conclusion that the pre-break light-curve index of the afterglow of GRB 990510 does not allow much structure in a spreading jet is illustrated in Figure 5, showing the $\chi^2$ of the fits obtained for several combinations of the structural parameter $q$ and jet core size-to-opening ratio $\theta_c/\Theta_0$, and for two particular observer locations: the jet axis and the jet edge."156 By decreasing the ϐ.Ομ ratio or increasing q. a stronger jet structure is enforced.," By decreasing the $\theta_c/\Theta_0$ ratio or increasing $q$, a stronger jet structure is enforced."157" As can be noticed. only Jets with 0.—0.2Oy for 4= Land.=0.3Oy for 4/72 provide acceptable fits (defined by a probability larger than 10%)). while fits as good as that provided by a uniform jet (A= 36) require that 0.£0309 ify— Land 0,£0.10, if4=2."," As can be noticed, only jets with $\theta_c \simg 0.2\, 158\Theta_0$ for $q=1$ and $\theta_c \simg 0.3\, \Theta_0$ for $q \geq 2$ provide acceptable fits (defined by a probability larger than ), while fits as good as that provided by a uniform jet $\chi^2 = 36$ ) require that $\theta_c \simg 0.3\,\Theta_0$ if $q=1$ and $\theta_c \simg 1590.4\,\Theta_0$ if $q=2$."160 Thus. for s=0. the afterglow of GRB 990510 is best explained by a structured jet with a variation of the energy per solid angle less than a factor 5 across the jet surface.," Thus, for $s=0$, the afterglow of GRB 990510 is best explained by a structured jet with a variation of the energy per solid angle less than a factor $\sim 5$ across the jet surface."161 The radio. optical and V-ray light-curves for the best fit obtained with à structured jet are shown in the left panel of Figure 6.," The radio, optical and $X$ -ray light-curves for the best fit obtained with a structured jet are shown in the left panel of Figure 6."162 We note that its parameters are similar to those for a uniform jet., We note that its parameters are similar to those for a uniform jet.163" For a external medium. equation (32)) gives a,=1.12d:0.18 for a uniform outflow. thus structure is required in this case to explain the slower decay observed at early time."," For a external medium, equation \ref{ab1}) ) gives $\alpha_1 = 1.42 \pm 0.18$ for a uniform outflow, thus structure is required in this case to explain the slower decay observed at early time."164 Equation. (33)) shows that a structured fireball yields a.— 1.92+0.1s. slightly smaller than the observed index. suggesting that collimation may also be required to accommodate the post-break decay of the this afterglow.," Equation \ref{ab2}) ) shows that a structured fireball yields $\alpha_2 \leq 1.92 \pm 0.18$ , slightly smaller than the observed index, suggesting that collimation may also be required to accommodate the post-break decay of the this afterglow."165 The right panel of Figure 6 shows the best fit obtained with a structured jet interacting with a wind medium., The right panel of Figure 6 shows the best fit obtained with a structured jet interacting with a wind medium.166 The jet structure improves the fit by A\?=23 relative to the best fit obtained with a uniform jet. which ts statistically significant.," The jet structure improves the fit by $\Delta \chi^2 = 23$ relative to the best fit obtained with a uniform jet, which is statistically significant."167 However. the optical light-curves steepen too slowly. overestimating the afterglow flux before and after the break and yielding 4?=LOL for 66 df.," However, the optical light-curves steepen too slowly, overestimating the afterglow flux before and after the break and yielding $\chi^2 = 104$ for 66 df."168 We conclude that a wind-like medium is not compatible with the observations of the 990510 afterglow even if the jet is endowed with structure., We conclude that a wind-like medium is not compatible with the observations of the 990510 afterglow even if the jet is endowed with structure.169" The A-band light-curve index of the 000301c afterglow increased froma,=0.70450.07 to»=2.[1:50.29 (Bhargavi Cowsik 2000). a sharp break occurring at £~| days (Figure 7)."," The $R$ -band light-curve index of the 000301c afterglow increased from $\alpha_1 = 0.70 170\pm 0.07$ to $\alpha_2 = 2.44 \pm 0.29$ (Bhargavi Cowsik 2000), a sharp break occurring at $t \sim 4$ days (Figure 7)."171" Jensen (2001) found that. at =3 days. the optical spectral slope is 4,=0.57+0.02 after correcting for the host reddening. determined from the curvature of the spectrum and assuming an SMC reddening law."," Jensen (2001) found that, at $t = 3$ days, the optical spectral slope is $\beta_o = 0.57 \pm 0.02$ after correcting for the host reddening, determined from the curvature of the spectrum and assuming an SMC reddening law."172 [X-ray observations were not made. thus the location of the cooling frequency is not constrained.," $X$ -ray observations were not made, thus the location of the cooling frequency is not constrained."173" If 7.Ὁ, then the pre-break light-curve index [32]J)o4=0.3623:0.03 for a uniform outflow would be too small compared with that observed.", If $\nu_c < \nu_o$ then the pre-break light-curve index ]) $\alpha_1 = 0.36 \pm 0.03$ for a uniform outflow would be too small compared with that observed.174" Therefore v,,<14. seems more likely for the 0002016 afterglow.", Therefore $\nu_o < \nu_c$ seems more likely for the 000301c afterglow.175 Given that structured jets interacting with a wind-like medium produce light-curves that are too smooth. we focus here only on a homogeneous circumburst medium.," Given that structured jets interacting with a wind-like medium produce light-curves that are too smooth, we focus here only on a homogeneous circumburst medium."176" For i4,<7, and a uniform fireball. equation (32)) yields a,=0.86+0.03. which is slightly larger than observed. thus a structured outflow is only marginally required. while equation (33)) leads toa. x1.61+0.03. which is well below the observed value. thus a jet is required."," For $\nu_o < \nu_c$ and a uniform fireball, equation \ref{ab1}) ) yields $\alpha_1 = 0.86 \pm 0.03$ , which is slightly larger than observed, thus a structured outflow is only marginally required, while equation \ref{ab2}) ) leads to $\alpha_2 \leq 1.61 \pm 0.03$, which is well below the observed value, thus a jet is required."177 Then. according to equation (34). e»=2.1Ed0.01. which is marginally compatible with the index measured by Bhargavi Cowsik (2000).," Then, according to equation \ref{alfamax}) ), $\alpha_2 = 2.14 \pm 0.04$, which is marginally compatible with the index measured by Bhargavi Cowsik (2000)."178 Other post-break asymptotic indices reported in the literature are larger (albeit more uncertain). which suggests that a jet model may have difficulties in explaining the steep post-break fall-off of the R-band light-curve ο 00020156.," Other post-break asymptotic indices reported in the literature are larger (albeit more uncertain), which suggests that a jet model may have difficulties in explaining the steep post-break fall-off of the $R$ -band light-curve of 000301c."179 In the framework of uniform jets. we have found (Panaitescu 2001) that this indeed the case: the best fit obtained for s=0 has 47=INO for 98 df and Ey~2«10?! ergs. Oy— ηcO.Olem7. pc2.5. failing to produce the observed steepening Aa1.71x0.30 when the jet edge becomes visible.," In the framework of uniform jets, we have found (Panaitescu 2001) that this indeed the case: the best fit obtained for $s=0$ has $\chi^2 = 480$ for 98 df and $E_0 \simeq 2 \times 10^{51}$ ergs, $\Theta_0 \simeq 3 \deg$ , $n \simeq 0.01\, \cm3$, $p \simeq 2.5$, failing to produce the observed steepening $\Delta \alpha \geq 1.74 \pm 0.30$ when the jet edge becomes visible."180 For this reason. we have investigated a jet model where the distribution of shock-accelerated electrons has à break. so that a sharp light-curve fall-off is seen after the passage through the optical of the synchrotron characteristic frequency corresponding to this break.," For this reason, we have investigated a jet model where the distribution of shock-accelerated electrons has a break, so that a sharp light-curve fall-off is seen after the passage through the optical of the synchrotron characteristic frequency corresponding to this break."181" Further indication that the distribution of injected electrons is not a pure power-law is provided by the discrepancy between the post-break light-curve indices at radio (a,=1.0+0.2) and optical frequencies. and also by the ἐν8 color change between 2 and 5 days after the burst (Rhoads Fruchter 2001). which implies a softening of the optical spectral slope Av,S0.5 that is too fast to be attributed to the passage of the cooling break."," Further indication that the distribution of injected electrons is not a pure power-law is provided by the discrepancy between the post-break light-curve indices at radio $\alpha_r 182= 1.0 \pm 0.2$ ) and optical frequencies, and also by the $K-R$ color change between 2 and 5 days after the burst (Rhoads Fruchter 2001), which implies a softening of the optical spectral slope $\Delta \beta_o \siml 0.5$ that is too fast to be attributed to the passage of the cooling break."183 The best fit obtained with the broken power-law injected electron distribution has V?=120 for 96 df. being marginally acceptable.," The best fit obtained with the broken power-law injected electron distribution has $\chi^2 = 120$ for 96 df, being marginally acceptable."184 Figure 7 assesses the ability of a structured jet to accommodate the sharp break of the 00052016 afterglow without recourse to a non-standard injected electron distribution., Figure 7 assesses the ability of a structured jet to accommodate the sharp break of the 000301c afterglow without recourse to a non-standard injected electron distribution.185 The new best fit has 47.=201 for 95 df. which is a substantial improvement in comparison. with the uniform jet model and à pure power-law electron distribution.," The new best fit has $\chi^2 = 204$ for 95 df, which is a substantial improvement in comparison with the uniform jet model and a pure power-law electron distribution."186 Nevertheless. the best fit obtained with a structured jet is not acceptable and. clearly. poorer than the uniform jet model with a broken power-law injected electron distribution.," Nevertheless, the best fit obtained with a structured jet is not acceptable and, clearly, poorer than the uniform jet model with a broken power-law injected electron distribution."187 It does not reproduced well the steep post-break decay of the R-band light-curve. and underestimates the 250 GHz emission., It does not reproduced well the steep post-break decay of the $R$ -band light-curve and underestimates the 250 GHz emission.188 We note that. for the best fit shown in Figure 7. the cooling frequency falls within the optical domain at a few days. a feature which ts required to explain the observed curvature of the optical spectrum (Jensen 2001).," We note that, for the best fit shown in Figure 7, the cooling frequency falls within the optical domain at a few days, a feature which is required to explain the observed curvature of the optical spectrum (Jensen 2001)."189 In the standard picture of uniform Jets. the measured pre- and post-break light-curve indices and the spectral slope offer an overconstramed problem. as. for a given type of external medium. all these quantities depend only on the exponent of the power-law distribution of shock-accelerated electrons.," In the standard picture of uniform jets, the measured pre- and post-break light-curve indices and the spectral slope offer an overconstrained problem, as, for a given type of external medium, all these quantities depend only on the exponent of the power-law distribution of shock-accelerated electrons."190 The angular structure of GRB jets and the observer location relative to the axis of the structured jet affects the pre-break index and. possibly. the post-break index also [27]]. Figures 2-4).," The angular structure of GRB jets and the observer location relative to the axis of the structured jet affects the pre-break index and, possibly, the post-break index also \ref{a2}] ], Figures 2–4)."191 For most well-observed afterglows. a uniform jet interacting with a homogeneous external medium provides good fits (Panaitescu Kumar 2002). indicating that the freedom allowed by the outflow structure is usually not," For most well-observed afterglows, a uniform jet interacting with a homogeneous external medium provides good fits (Panaitescu Kumar 2002), indicating that the freedom allowed by the outflow structure is usually not"1921.5 m Tilliughast reflector telescope at the EF. E. Whipple Observatory (FIWO) and CMOS lone-slit spectroscopy blue channel ou Coniui North.,1.5 m Tillinghast reflector telescope at the F. L. Whipple Observatory (FLWO) and GMOS long-slit spectroscopy blue channel on Gemini North.193 They are waveleneth-calibrated with standard packages. and are shown iu Figures 2 aud 3.," They are wavelength-calibrated with standard packages, and are shown in Figures 2 and 3."194 According to their spectra. they are all R2-tvpe stars.," According to their spectra, they are all K2-type stars."195 By comparing the region between 19005200 wwith FAST spectra of several K2 παποστας with different huninositv classes. we found all of them are @lauts (luminosity class IIE: Estimated unceutaiuties in huuinositv class are ILTV.," By comparing the region between $4900-5200$ with FAST spectra of several K2 standards with different luminosity classes, we found all of them are giants (luminosity class III; Estimated uncentainties in luminosity class are II-IV."196 Eunimosityv class T aud V are ruled out)., Luminosity class I and V are ruled out).197" We estimated moetallicities (TIO.340.3 for JOS30. and [Fe/UJ~0.940.1 for JO75 Land 1θτοῦ, by colparing with FAST spectra of several standard Ic eiut stars with kuown metallicities (Faber et al."," We estimated metallicities $\sim -0.3\pm0.3$ for J0830, and $\sim -0.9\pm0.4$ for J0754 and J0736, by comparing with FAST spectra of several standard K giant stars with known metalicities (Faber et al."198 1985)., 1985).199 We also found that JOSSO0 aud JO0751 do not show velocity changes within measurement errors (~8 Las). while JOT36 showed significant radial velocity changes in three different epochs. ie. 11+6 kin/s on Feb Ith. 18+6 kan/s on Feb 19th. and 22£6 kin/s on April Esth. 2009. and is then probably in a close biuarx.," We also found that J0830 and J0754 do not show velocity changes within measurement errors $\sim8$ km/s), while J0736 showed significant radial velocity changes in three different epochs, i.e. $11\pm6$ km/s on Feb 4th, $-18\pm6$ km/s on Feb 19th, and $22\pm6$ km/s on April 18th, 2009, and is then probably in a close binary."200 As shown in Figure 3. all three variables show Ca IT Ix and IT emission. lines in the absorption core. mdicatiug the presence of active chromospheres.," As shown in Figure 3, all three variables show Ca II K and H emission lines in the absorption core, indicating the presence of active chromospheres."201 Ca IT K and IL cussion lines are conuuon amone cool dwarf aud evolved stars. signaling the magnetic dvuanio activity iu chromospheres (ντα 1967: Soderblom 1982: Dupree Suuith 1995).," Ca II K and H emission lines are common among cool dwarf and evolved stars, signaling the magnetic dynamo activity in chromospheres (Kraft 1967; Soderblom 1983; Dupree Smith 1995)."202 Their fluxes correlate with stellar rotational volocities (sce Strassimieier et al., Their fluxes correlate with stellar rotational velocities (see Strassmeier et al.203 1991: Pasquini et al., 1994; Pasquini et al.204 2000 aud references therein)., 2000 and references therein).205 Followed Linsky et al. (, Followed Linsky et al. (2061979). assunune VR=thal for K2III stars (Cox 2000). we calculated the net. chromospheric loss iu the Is lines. which are logFUN)=6.35. 6.13 aud 5.98. iudicatius rotation velocities about 10 km/s. 25 kin/s and 16 κής (Strassuncier et al.,"1979), assuming $V-R=0.84$ for K2III stars (Cox 2000), we calculated the net chromospheric loss in the K lines, which are $\log \mathcal{F'}(K)=6.35$, 6.13 and 5.98, indicating rotation velocities about 40 km/s, 25 km/s and 16 km/s (Strassmeier et al."207 1991: the uncertainty is large though. about 0.5 dex). for Jü830. J075 band J07236. respectively.," 1994; the uncertainty is large though, about 0.5 dex), for J0830, J0754 and J0736, respectively."208 The plates we analyzed are centered. around the ope- cluster ALLL., The plates we analyzed are centered around the open cluster M44.209 The coverage decreases when the region 1SY. farther away from the ceuter of MEL, The coverage decreases when the region is farther away from the center of M44.210" There is roughly : 10« deg? region with good coverage νο, inore thaVER LOO scans).", There is roughly a $40\times40$ $^2$ region with good coverage (i.e. more than 100 scans).211 From Ἱνοριασαα photometry of a 3.2 deg? reeion near ALLL. we estimate there are about 1000-600 stars with 12DB-19.5 and 0.85cgyr<1.02 in this LO&10 dee? reeion.," From Keplercam photometry of a 3.2 $^2$ region near M44, we estimate there are about 4000-6000 stars with $12<B<13.5$ and $0.85<g-r<1.02$ in this $40\times40$ $^2$ region."212 If we assume that objects with 0.85<groc1.02 are I2IIT stars (Covey et al., If we assume that objects with $0.85<g-r<1.02$ are K2III stars (Covey et al.213 2007: Suuith et al., 2007; Smith et al.214 2002: note that some dwarfs aud supereiauts are also included. but there are many more eiauts than superelants. and at 12-13 maenitude. we are seciug more eqauts than dwarfs). then the eveut rate of such loue-term variables amoug IK2III stars is about 3/5000~0.06%.," 2002; note that some dwarfs and supergiants are also included, but there are many more giants than supergiants, and at 12-13 magnitude, we are seeing more giants than dwarfs), then the event rate of such long-term variables among K2III stars is about $3/5000\sim 0.06\%$."215 Table 1 lists the galactic coordinates. GSC2.5.2 D-R colors. GSC B. ASAS V aud 2MASS JIII maeuitiudes. [Fe/TI]. proper motions. radial velocities. distances. aud ealactic velocities for the three variables.," Table 1 lists the galactic coordinates, GSC2.3.2 B-R colors, GSC B, ASAS V and 2MASS JHK magnitudes, [Fe/H], proper motions, radial velocities, distances, and galactic velocities for the three variables."216 05020 aud J0751 have high proper motious (>10 mas/vr). while JOT36 has no proper motion within its error of 2 mas/vr.," J0830 and J0754 have high proper motions $>10$ mas/yr), while J0736 has no proper motion within its error of $2$ mas/yr."217 The 3 stars are about 500/—800 pe above the ealactic plane., The 3 stars are about $500-800$ pc above the galactic plane.218 JOS30 aud J0751L have velocities about 100 Em/s. while J0736 probably has smaller velocity <30 kms. Our spectra indicate metallicities —1 to 0.," J0830 and J0754 have velocities about 100 km/s, while J0736 probably has smaller velocity $<30$ km/s. Our spectra indicate metallicities $\sim -1$ to 0."219 They are most probably thick disk eiants|Fe/TII|- (Carollo et al., They are most probably thick disk giants (Carollo et al.220 2009)., 2009).221 The 2MASS ΠN color of 10500 is 0.27. which is redder than JK=0.01 expected for a K2 eiit (Covey ot al.," The 2MASS $H-K$ color of J0830 is 0.27, which is redder than $H-K=0.04$ expected for a K2 giant (Covey et al."222 2007)., 2007).223" Note that JOS30 also showed luge reddening in the 1970s and 1950s in our plates during its οπιπιο, as shown in Figure 1."," Note that J0830 also showed large reddening in the 1970s and 1980s in our plates during its dimming, as shown in Figure 1."224" As K2IITI stars with [Fe/II]-1 to 0, the 3 erratic variables could be ou the Red Caüaut Brauch (RGB). but not near the tip. on the Worizoutal Branch (IIB). or carly asviuptotic giant branch (ACB)."," As K2III stars with $\sim -1$ to 0, the 3 erratic variables could be on the Red Giant Branch (RGB), but not near the tip, on the Horizontal Branch (HB), or early asymptotic giant branch (AGB)."225 Timescales of 10-100 vear are too long to be pulsatious dviven by jouization (Perey 2007). or couvective lustabilities which have timescales iu the order of a vear for a IN eiaut (Prialuik 2000).," Timescales of 10-100 year are too long to be pulsations driven by ionization (Percy 2007), or convective instabilities which have timescales in the order of a year for a K giant (Prialnik 2000)."226 The lishteurves of these 3 erratic variables look somewhat like R Coronae Borealis (RCB) stars., The lightcurves of these 3 erratic variables look somewhat like R Coronae Borealis (RCB) stars.227 RCD stars are rare. hydrogen deficieut. carbou-rich supereiants which undergo large amplitude (3.S mae) facing eveuts lasting weeks to a few vears as dust condensates to block the light alone the Lue of sieht (Clavton 1996).," RCB stars are rare, hydrogen deficient, carbon-rich supergiants which undergo large amplitude $3-8$ mag) fading events lasting weeks to a few years as dust condensates to block the light along the line of sight (Clayton 1996)."228 Our variables share some of these typical RCB lishteurve features. and the liehteurve of JOSSO0 is sunilar to some hot (£7—20000 I RCB stars (De Miuco et al.," Our variables share some of these typical RCB lightcurve features, and the lightcurve of J0830 is similar to some hot $T\sim22920000$ K) RCB stars (De Marco et al."230 2002)., 2002).231 Dust obscuration eveuts have also been observed in some other carbon rich stars., Dust obscuration events have also been observed in some other carbon rich stars.232 Whütelock et al. (, Whitelock et al. (2332006) found about one-third of the Carbou-rich Miras and other AGB stars undergo dimming episodes.,2006) found about one-third of the Carbon-rich Miras and other AGB stars undergo dimming episodes.234" However. all of the three variables preseuted here are very different from normal RCD stars in the following aspects, and therefore are not RCB stays (or any other type of carbou-rich AGB stars): They are not post-ACB supereiants lise RCD stars (Alcock et al."," However, all of the three variables presented here are very different from normal RCB stars in the following aspects, and therefore are not RCB stars (or any other type of carbon-rich AGB stars): They are not post-AGB supergiants like RCB stars (Alcock et al."235 2001): mich cooler than most RCDs: have much longer variability timescales and mich smaller amplituces than average RCB stars: have no strong carbon absorption bands. aud have strong livdrogen absorption lines.," 2001); much cooler than most RCBs; have much longer variability timescales and much smaller amplitudes than average RCB stars; have no strong carbon absorption bands, and have strong hydrogen absorption lines."236 JO830 has weaker IIo absorption which nuüeht due to the chromospleric cluission iu the core. since the Ca IT cuission lines are," J0830 has weaker $\alpha$ absorption which might due to the chromospheric emission in the core, since the Ca II emission lines are"237reconstruction based on the (AL.21) diagram gives essentially the same results.,"reconstruction based on the $(M_V, B-V)$ diagram gives essentially the same results."238 A certain level of constant star formation activity can be seen. superimposed onto a strong. quasi-periodic component having a period close to 0.5 Gyr. as encoded in the positions of the observed stars in the CMD.," A certain level of constant star formation activity can be seen, superimposed onto a strong, quasi-periodic component having a period close to $0.5$ Gyr, as encoded in the positions of the observed stars in the CMD."239 The sharp feature seen towards §=3 Gye could be the beginning of a fifth evele. truncated. by the boundary condition S£AR(3)= 0.," The sharp feature seen towards $t=3$ Gyr could be the beginning of a fifth cycle, truncated by the boundary condition $SFR(3)=0$ ."240 We have performed. tests with synthetic CALDs having the same numbers of stars and magnitude limits as in Figure (4). and having a varicty of SZ.," We have performed tests with synthetic CMDs having the same numbers of stars and magnitude limits as in Figure (4), and having a variety of $SFR(t)$."241 The method cllicicntly diseriminates between constant and periodic input SEBIG). and correctly recovers features such as those found in the inferred. SEG) of Figure (4).," The method efficiently discriminates between constant and periodic input $SFR(t)$, and correctly recovers features such as those found in the inferred $SFR(t)$ of Figure (4)."242 We conclude that as far as the Padova isochrones at solar metallicity are representative of the observational properties of the stars in the CAIDs. the S£UU) of the solar neighbourhood over the last 3 Car has been that shown in Figure (4).," We conclude that as far as the Padova isochrones at solar metallicity are representative of the observational properties of the stars in the CMDs, the $SFR(t)$ of the solar neighbourhood over the last 3 Gyr has been that shown in Figure (4)."243 The unprecedented. time resolution of our S22 reconstruction makes it cillicult to compare with the results derived from chromospheric activity studies (Rocha-Pinto et al., The unprecedented time resolution of our $SFR$ reconstruction makes it difficult to compare with the results derived from chromospheric activity studies (Rocha-Pinto et al.244 1999). although qualitatively we do find the same activity at both 5 and above 2 Gyr. but not the decrease between 1 and 2 Gyr.," 1999), although qualitatively we do find the same activity at both 0.5 and above 2 Gyr, but not the decrease between 1 and 2 Gyr."245 One possible interpretation of a cvelic component. in he SEARO) of the solar neighbourhood. can be found. in he density wave hypothesis (Lin and Shu. 1964) for the »esence of spiral armis in late type galaxies.," One possible interpretation of a cyclic component in the $SFR(t)$ of the solar neighbourhood can be found in the density wave hypothesis (Lin and Shu, 1964) for the presence of spiral arms in late type galaxies."246 As the pattern speed and the circular. velocity. are in general dillerent. a eiven region of the disk (e.g. the solar neighbourhood) »eriodicallv crosses an arm region where the increased local eravitational potential might possibly trigger an episode of star formation.," As the pattern speed and the circular velocity are in general different, a given region of the disk (e.g. the solar neighbourhood), periodically crosses an arm region where the increased local gravitational potential might possibly trigger an episode of star formation."247 In the simplest. version of this scenario. we can take the pattern angular frequency. ον equal to twice the circular frequeney. O at the Suns position (Binney ‘Tremaine LOST). valid within a Hat rotation curve region.," In the simplest version of this scenario, we can take the pattern angular frequency $\Omega_p$ equal to twice the circular frequency $\Omega$ at the Sun's position (Binney Tremaine 1987), valid within a flat rotation curve region."248 The time interval Af between encounters with an arm at the solar neighbourhood will be given in general by that is. where m is the number of arms in the spiral pattern.," The time interval $\Delta t$ between encounters with an arm at the solar neighbourhood will be given in general by that is, where $m$ is the number of arms in the spiral pattern."249" The classical value of the pattern speed. Q,=0.50zc14.5 km s+ would imply that the interaction with a single arm (m= 1) would be enough to account for the observed. regularity. in the recent SER. history."," The classical value of the pattern speed, $\Omega_p = 0.5 \, \Omega \approx 14.5 $ km $^{-1}$ $^{-1}$ would imply that the interaction with a single arm $m=1$ ) would be enough to account for the observed regularity in the recent SFR history."250 However. more recent determinations tend to point to much larger values (e.g. Mishkurov et al.," However, more recent determinations tend to point to much larger values (e.g. Mishkurov et al."251" 1979. Avedisova 1989. Amaral and Léppine 1997) close to Q,~23.24 km s.+ "" which would then imply that the regularity present in the reconstructed SIG) would be consistent with a scenario where the interaction of the solar neighbourhood with à two-armed spiral pattern would have induced the star formation episodes we detect."," 1979, Avedisova 1989, Amaral and Léppine 1997) close to $\Omega_p \sim 23 - 24$ km $^{-1}$ $^{-1}$, which would then imply that the regularity present in the reconstructed $SFR(t)$ would be consistent with a scenario where the interaction of the solar neighbourhood with a two-armed spiral pattern would have induced the star formation episodes we detect."252 These arms are clearly. detected in. for instance. the distribution of free electrons in the galactic plane Clavlor ancl Cordes 1993).," These arms are clearly detected in, for instance, the distribution of free electrons in the galactic plane (Taylor and Cordes 1993)."253 This is reminiscent of the explanations put forward to account for the inhomogencities observed in the velocity distribution function. where well-defined branches associated with moving groups of cillerent ages (Chereul ct al.," This is reminiscent of the explanations put forward to account for the inhomogeneities observed in the velocity distribution function, where well-defined branches associated with moving groups of different ages (Chereul et al."254 1999. Skuljan et al.," 1999, Skuljan et al."255 1999. Asiain et al.," 1999, Asiain et al."256 1999) could perhaps be also associated with an interaction with spiral arm(s). although in this case the time scales are much smaller.," 1999) could perhaps be also associated with an interaction with spiral arm(s), although in this case the time scales are much smaller."257 Alternatively. if the solar neighbourhood. is closer to the corotation radius. the galactic bar could have triggered star formation in the solar neighbourhood with episodes separated by about 0.5 Cyr if the pattern speed of the bar is larger than about 40 lm + kpe+ (Dehnen 1999).," Alternatively, if the solar neighbourhood is closer to the corotation radius, the galactic bar could have triggered star formation in the solar neighbourhood with episodes separated by about 0.5 Gyr if the pattern speed of the bar is larger than about 40 km $^{-1}$ $^{-1}$ (Dehnen 1999)."258 Of course. other explanations are possible. for example the cloud formation. collision anc stellar feedback. mocels of Vazquez Scalo (1989) predict a phase of oscillatory SER) behaviour as à result. of a sclbreeulated star formation réggime.," Of course, other explanations are possible, for example the cloud formation, collision and stellar feedback models of Vazquez Scalo (1989) predict a phase of oscillatory $SFR(t)$ behaviour as a result of a self-regulated star formation réggime."259BS Close encounters with the MagellanicD Clouds have also been suggested to explain the intermittent nature of the SER on longer time scales (Itocha-Dinto et al., Close encounters with the Magellanic Clouds have also been suggested to explain the intermittent nature of the SFR on longer time scales (Rocha-Pinto et al.260 2000)., 2000).261 We have tested the ability of our method to accurateA distinguish oscillatory components in the S£IG) with tests such as those shown in Figures (1) and (2)., We have tested the ability of our method to accurately distinguish oscillatory components in the $SFR(t)$ with tests such as those shown in Figures (1) and (2).262 The oscillatory component in the case shown in Figure (1) is successfulA recovered. by the method., The oscillatory component in the case shown in Figure (1) is successfully recovered by the method.263 In the case shown in. Figure(2) however. although. the main features are also accurately recovered. a level of small amplitude Iuctuations spuriously appears.," In the case shown in Figure(2) however, although the main features are also accurately recovered, a level of small amplitude fluctuations spuriously appears."264 This last feature is of such a small level. that if a CAID where produced from the method answer of Figure ( having the same total number ofstars. each small [Ductuation would. produce a number of stars of order 1.," This last feature is of such a small level, that if a CMD where produced from the method answer of Figure (1) having the same total number of stars, each small fluctuation would produce a number of stars of order 1."265 Our answer shown in Figure (4) shows not only a large scale oscillatory component. but superimposed onto this. a certain level of small amplitude Iuctuations.," Our answer shown in Figure (4) shows not only a large scale oscillatory component, but superimposed onto this, a certain level of small amplitude fluctuations."266 Given the total number of stars present in our sample. we can not rule out the possibility. (quit. possibly in fact the case) that. these small [uctuations are numerical. as they are of amplitude similar to the ones discussed. appearing in Figure(2). and are actually buried within the error envelope.," Given the total number of stars present in our sample, we can not rule out the possibility (quit possibly in fact the case) that these small fluctuations are numerical, as they are of amplitude similar to the ones discussed appearing in Figure(2), and are actually buried within the error envelope."267 The main oscillatory component having a period of 0.5 Civr however. involves a sullicientIy large number of stars to be objectively icentifiect.," The main oscillatory component having a period of 0.5 Gyr however, involves a sufficiently large number of stars to be objectively identified."268 A larger and independent data set from which to derive SEHR) would be necessary in order to extend our results to a broader age range. and a more extensive region of the Galactic disk.," A larger and independent data set from which to derive $SFR(t)$ would be necessary in order to extend our results to a broader age range, and a more extensive region of the Galactic disk."269 Increasing the number of stars available for the LER: inversion procedure would also allow to recover finer features. and reduce the small numerical Ductuations discussed above.," Increasing the number of stars available for the HR inversion procedure would also allow to recover finer features, and reduce the small numerical fluctuations discussed above."270 In our Paper E we tested this method using synthetic CMDs produced. from known star formation histories. with which," In our Paper I we tested this method using synthetic CMDs produced from known star formation histories, with which"271shear anc thermally induced. convection are. included.,shear and thermally induced convection are included.272 Instead of considering. the full cise problem. with its particular density. ancl temperature structure. we use the shearing box approximation (?2?7?)..," Instead of considering the full disc problem, with its particular density and temperature structure, we use the shearing box approximation \citep{HGB95,B03,RU08}."273 As a simplification. we assume the (ow is incompressible and we introduce vertical garatification within the Boussinesq approximation (?)..," As a simplification, we assume the flow is incompressible and we introduce vertical stratification within the Boussinesq approximation \citep{SV60}."274 Although this approximation is not fully justified in a real disc. it allows us to explore the regime of strongly turbulent shearecl convection in a more controlled wav.," Although this approximation is not fully justified in a real disc, it allows us to explore the regime of strongly turbulent sheared convection in a more controlled way."275 In this letter we explore the wav turbulent convection transports angular momentum. but we do not include the generation. of an unstable temperature profile clue to viscous heating.," In this letter we explore the way turbulent convection transports angular momentum, but we do not include the generation of an unstable temperature profile due to viscous heating."276" Instead. we impose a ""background stratification profile as prescribed by the Boussinesq approximation."," Instead, we impose a `background' stratification profile as prescribed by the Boussinesq approximation."277" Pherefore. one has to keep in mind that convection is not generated scll-consistently in our model,"," Therefore, one has to keep in mind that convection is not generated self-consistently in our model."278 The shearing-box equations are found. by considering a Cartesian box centred at r=fy. rotating with the disc at angular velocity OQ=O(#y).," The shearing-box equations are found by considering a Cartesian box centred at $r=R_0$, rotating with the disc at angular velocity $\Omega=\Omega(R_0)$."279 Defining rRyτα and Ryo» yasin ?.. one obtains the following setof equations: where wi ids the total velocity. 6dpfp is the verturbation of the density logarithm (or entropy. as oessure perturbations are much smaller in the Boussinesc approximation). 7 is the kinematic viscosity ancl X is the hermal diffusivity.," Defining $r-R_0 \rightarrow x$ and $R_0\phi \rightarrow y$ as in \cite{HGB95}, one obtains the following setof equations: where $\bm{u}$ is the total velocity, $\theta\equiv \delta\rho/\rho$ is the perturbation of the density logarithm (or entropy, as pressure perturbations are much smaller in the Boussinesq approximation), $\nu$ is the kinematic viscosity and $\chi$ is the thermal diffusivity."280" In these equations.we have definec he mean shear 5— rO,Q. which is set to S=(8/2)0 for a Weplerian disc."," In these equations,we have defined the mean shear $S=-r\partial_r \Omega$ , which is set to $S=(3/2)\Omega$ for a Keplerian disc."281 The gencralisecl pressure IL is caleulated by. solving a Poisson equation derivec rom the incompressibiliiv condition., The generalised pressure $\Pi$ is calculated by solving a Poisson equation derived from the incompressibility condition.282 For dimensiona consistency. with the traditional. Boussinesq approach. we ave introduced a stratification length A=g/N7. where g is the vertical component of the gravity.," For dimensional consistency with the traditional Boussinesq approach, we have introduced a stratification length $\Lambda\equiv -g/N^2$, where $g$ is the vertical component of the gravity."283 Note. however. tha A disappears from the dynamical properties of this system of equations as one can renormalize the variables by defining #=X0.," Note, however, that $\Lambda$ disappears from the dynamical properties of this system of equations as one can renormalize the variables by defining $\theta'\equiv\Lambda \theta$."284 The stratification itself is controlled by the Vaisalla frequency iN. defined for a perfect gas by where 2 and p are the pressure and density. of the xickground equilibrium profile and 5 is the acliabatic index.," The stratification itself is controlled by the Brunt--V\""aiis\""all\""a frequency $N$, defined for a perfect gas by where $P$ and $\rho$ are the pressure and density of the background equilibrium profile and $\gamma$ is the adiabatic index."285 hysicallv. IN. corresponds to the oscillation frequency of a [uid particle displaced. vertically from itsequilibrium »osition.," Physically, $N$ corresponds to the oscillation frequency of a fluid particle displaced vertically from itsequilibrium position."286 When the low is convectively unstable. one has N?«0.," When the flow is convectively unstable, one has $N^2<0$."287 In our model. we assume Vo is constant. which ormallv corresponds to a local model in z.," In our model, we assume $N$ is constant, which formally corresponds to a local model in $z$."288 One can easily check that the velocity. field UOSrey is a steady solution of equations (1)) (2))., One can easily check that the velocity field $\bm{U}=-Sx\bm{e_y}$ is a steady solution of equations \ref{motiongeneral}) \ref{entropygeneral}) ).289 In the ollowing we consider the evolution of the perturbations v (not necessarily small) of this profile defined bv οστι— U., In the following we consider the evolution of the perturbations $\bm{v}$ (not necessarily small) of this profile defined by $\bm{v}=\bm{u}-\bm{U}$ .290 In the following. we use shearing-sheet boundary conditions (7) in the wr direction and. periodie boundary conditions in y.," In the following, we use shearing-sheet boundary conditions \citep{HGB95} in the $x$ direction and periodic boundary conditions in $y$."291" In the z direction. we use either frec-slip boundary conditions refwall)). imposing e;=60 and e,=One,0. or periodic boundary conditions refhomogeneous))D."," In the $z$ direction, we use either free-slip boundary conditions \\ref{wall}) ), imposing $v_z=\theta=0$ and $\partial_z v_x=\partial_z v_y=0$, or periodic boundary conditions )."292 Phe frec-4lip vertical boundary conditions correspond to a rigid wall with no tangential stress and a fixed temperature., The free-slip vertical boundary conditions correspond to a rigid wall with no tangential stress and a fixed temperature.293 Similar boundary conditions for the velocity. [field were used by ?.., Similar boundary conditions for the velocity field were used by \cite{C96}.294 ‘Lo simplify the analvsis of convection in shearec How. we will use three dimensionless numbers defined as follows: In the following. we will assume £27=1 for simplicity.," To simplify the analysis of convection in sheared flow, we will use three dimensionless numbers defined as follows: In the following, we will assume $Pr=1$ for simplicity."295 A more complete study including the elect of varving {ή will be the subject. of a subsequent. paper., A more complete study including the effect of varying $Pr$ will be the subject of a subsequent paper.296 The length. £L introduced. in these definitions is assumed to be a typical dimension of the box and should be of the order of the disc thickness., The length $L$ introduced in these definitions is assumed to be a typical dimension of the box and should be of the order of the disc thickness.297" In the following. we define £L as the smallest. box length with £L—L. in rebwall and L—L, in refhomogeneous.."," In the following, we define $L$ as the smallest box length with $L=L_z$ in \\ref{wall} and $L=L_x$ in \\ref{homogeneous}."298 When not explicitly. mentioned. the unit of time is the shear timescale S| which is equal to (3a)! orbital periods.," When not explicitly mentioned, the unit of time is the shear timescale $S^{-1}$ which is equal to $(3\pi)^{-1}$ orbital periods."299 In the following. all of our simulations are computed in the shear dominated regime (27< 1) which is expected. in disces.," In the following, all of our simulations are computed in the shear dominated regime $Ri<1$ ) which is expected in discs."300 By analogy with ?.. we define the dimensionlesstransport of angular momentum through the a-like coefficient à= L. 0) being a time and space average.," By analogy with \cite{SB96}, , we define the dimensionlesstransport of angular momentum through the $\alpha$ -like coefficient $\alpha \equiv \langle v_x v_y \rangle / S^2L^2$ , $\langle \cdot \rangle$ being a time and space average."301 Since S=| and L= lin all the simulations presented. below. we will simply write à=ορ) in our units.," Since $S=1$ and $L=1$ in all the simulations presented below, we will simply write $\alpha=\langle v_x v_y \rangle$ in our units."302 Alultiplving the y component of (1)) bv ορ. integrating over the volume of the box and using the boundary, Multiplying the $y$ component of \ref{motiongeneral}) ) by $v_y$ integrating over the volume of the box and using the boundary303in detail inAbdoetal.(201048). and in Marscheretal.(2010).,in detail in\citet{abd10a} and in \citet{mar10}.304.. A particularly large and isolated event was identified with start date 10 March. 2009 and stop date 9 April 2009 (Abdoetal.2010a).," A particularly large and isolated event was identified with start date 10 March, 2009 and stop date 9 April, 2009 \citep{abd10a}."305. The UAIRAO helt curves reveal that a radio baud total flux density flare commenced in early 20090 at which time both a --solved. linear polarization flare and an ordered swine in EVPA are apparent at 11.5 and 8.0 GIIz., The UMRAO light curves reveal that a radio band total flux density flare commenced in early 2009 at which time both a resolved linear polarization flare and an ordered swing in EVPA are apparent at 14.5 and 8.0 GHz.306" Because of the differences in variability time-scales iu the radio and 5-ay bands aud the expected time delays produced by selt-absorption in the cutting region. there are some uncertainties in associating specific eveuts across bands: an event with the signature of an oblique shock. however. ""uienbiguouslv occurred during this time period which iucludes the 5-rav. flare."," Because of the differences in variability time-scales in the radio and $\gamma$ -ray bands and the expected time delays produced by self-absorption in the emitting region, there are some uncertainties in associating specific events across bands; an event with the signature of an oblique shock, however, unambiguously occurred during this time period which includes the $\gamma$ -ray flare."307 Figure 2 shows the radio band data during the period 2008.0 through 2009.5 for the very active DE Lac object. OT Ost (1719|096). one of the three sources originally modeled using the trausverse shock formulation (ITughlies.Aller& 1991).," Figure \ref{fig2} shows the radio band data during the period 2008.0 through 2009.5 for the very active BL Lac object, OT 081 (1749+096), one of the three sources originally modeled using the transverse shock formulation \citep{hug91}."308. Several resolved events are apparent in both the total flux density aud fractional linear polarization light curves: an ordered swing in EWPA at LL5 GIIz occurred. foi August to December 2008 followed bv a shorter-duratioun ordered swine during January-February 2009., Several resolved events are apparent in both the total flux density and fractional linear polarization light curves; an ordered swing in EVPA at 14.5 GHz occurred from August to December 2008 followed by a shorter-duration ordered swing during January-February 2009.309 The Fermi light curve for this source ds included in the variability. study based on data frou the first vear of Fern operation (Abdoal. 2010b)., The Fermi light curve for this source is included in the variability study based on data from the first year of operation \citep{abd10b}.310. A verv huge flare in the οταν laud was in progress in August 2008. and a second fave which peaked in mid-March 2009 is also apparent in these data.," A very large flare in the $\gamma$ -ray band was in progress in August 2008, and a second flare which peaked in mid-March 2009 is also apparent in these data."311 Activity. including stroug faring. occurred iu both the +- rav and radio wavebands.," Activity, including strong flaring, occurred in both the $\gamma$ -ray and radio wavebands."312 Figure 5. shows both the 5-rav aud radio baud light curves for OJ 287., Figure \ref{fig3} shows both the $\gamma$ -ray and radio band light curves for OJ 287.313 In this source the signature of a shock temporally associated with the outburst observed bxFermi is clearly apparent., In this source the signature of a shock temporally associated with the outburst observed by is clearly apparent.314 The swing in EVPA through a Iuuited rauge of about 107 is consistent with the passage of an oblique shock., The swing in EVPA through a limited range of about $40\arcdeg$ is consistent with the passage of an oblique shock.315 All computations are performed in a box 61«61«600 cells in extent. with the axis of the jet parallel to the long axis. τν and polar angeles are measured in the usual seuse: 0 from the iz-direction. and o from the w-cdirection.," All computations are performed in a box $61\times61\times600$ cells in extent, with the axis of the jet parallel to the long axis, $z$, and polar angles are measured in the usual sense: $\theta$ from the $z$ -direction, and $\phi$ from the $x$ -direction."316 A simple conical form has been taken for the jet boundary as observations cannot constrain more couples. profiles explored over at mnost tens of jet radii., A simple conical form has been taken for the jet boundary as observations cannot constrain more complex profiles explored over at most tens of jet radii.317" The opening augle (pi) is determined by setting the jet radius to be rj, ou the inflow plane :=0. aud rji on the outflow plane DOtinax=600: angles are typically 127"," The opening angle $\mu$ ) is determined by setting the jet radius to be $r_{\rm lo}$ on the inflow plane $z=0,$ and $r_{\rm hi}$ on the outflow plane $z=z_{\rm max}=600$; angles are typically $1-2\arcdeg$."318" Quicscent flow values areestablished across the eutire domain. and then an apodiziug filter is. applied.. where p=(407.--|47) »\l/2.dis theradial. location. of à coll at some +. where the jet radius is τν and a, is à parameter that controls the flows boundary extent: dy is typically one cell."," Quiescent flow values areestablished across the entire domain, and then an apodizing filter is applied, where $\rho=\left(x^2+y^2\right)^{1/2}$ is the radial location of a cell at some $z$, where the jet radius is $r\left(z\right)$, and $a_w$ is a parameter that controls the flow's boundary extent; $a_w$ is typically one cell."319 Whether flows exhibit sienificant acceleration or deceleration remains coutroversial and indeed. might differ from) source to source.," Whether flows exhibit significant acceleration or deceleration remains controversial, and indeed, might differ from source to source."320 Deceleration has. been inferred for ER 1 radio galaxies (Laing1996:Lainectal.1999).. while a recent study of the BL Lac object OJ 287 finds that the flow remains highly relativistic o distances as high as hundreds of Kiloparsecs frou he nucleus (Mirscher&Jorstad2010).," Deceleration has been inferred for FR 1 radio galaxies \citep {lai96,321lai99}, while a recent study of the BL Lac object OJ 287 finds that the flow remains highly relativistic to distances as high as hundreds of kiloparsecs from the nucleus \citep{mj10}."322". In view of this uncertainty. aud the limited ΠΟΥ of jet radii explored. he quiescent fiow speed is taken as a constant specified yw αν Lorentz factor. σε: values are typically 2Ὁ, A diverging flow is then established. with stream Hines xwallel to the z-axis on axis. aud parallel to the flow voundary there."," In view of this uncertainty, and the limited number of jet radii explored, the quiescent flow speed is taken as a constant specified by its Lorentz factor, $\gamma_f$; values are typically $2-5.$ A diverging flow is then established, with stream lines parallel to the $z$ -axis on axis, and parallel to the flow boundary there."323 The magnetic field is constructed as described ii refinagnetic. and assumed to fall in streugth along the flow as r(:)2," The magnetic field is constructed as described in \\ref{magnetic}, and assumed to fall in strength along the flow as $r\left(z\right)^{-2}$."324 Leahy(1991). gives a good overview of he evolution of parameters in a diverging adiabatic flow. and it might be thought that a fall-off as r(+)H7 would ο appropriate for a flow of fixed speed. given that the default assmuption is that of a random field.," \citet{leahy91} gives a good overview of the evolution of parameters in a diverging adiabatic flow, and it might be thought that a fall-off as $r\left(z\right)^{-4/3}$ would be appropriate for a flow of fixed speed, given that the default assumption is that of a random field."325 However. hat assunues no coupling between the compoucuts. so hat the component perpendicular to the dow falls more slowly. driving the flow away from isotropic turbulence.," However, that assumes no coupling between the components, so that the component perpendicular to the flow falls more slowly, driving the flow away from isotropic turbulence."326 The asstunption of an isotropic raudom component at every location iu the quiesceut flow implies a turbulent driving that persists the leugth of the flow. transforming perpendicular iuto parallel field. which declines with the πα... dependence. and vice versa. coupling the decline of the perpendicular coupoueut to that of the parallel componcut.," The assumption of an isotropic random component at every location in the quiescent flow implies a turbulent driving that persists the length of the flow, transforming perpendicular into parallel field, which declines with the assumed $r\left(z\right)^{-2}$ dependence, and vice versa, coupling the decline of the perpendicular component to that of the parallel component."327 Further. the helical ordered field that is also explored. if generated frou a. turbulent conrponeut by a dissipative dvuanio process such as noted in refordered.. will then follow the same elobal treud.," Further, the helical ordered field that is also explored, if generated from a turbulent component by a dissipative dynamo process such as noted in \\ref{ordered}, will then follow the same global trend."328 The adopted dependence is thus a simplification. but reasonable given the other approximations.," The adopted dependence is thus a simplification, but reasonable given the other approximations."329 As discussed in the next section. the method used to geuerate a randonm field componoeut. the ad hoc scaling along the How. and the scaling of the relative streneths of random and ordered field) components. mcan that the field does not satisfy a self-consisteut maguetolivdrodvuaiic uodel for its generation. and ids not cdivergeuce-free.," As discussed in the next section, the method used to generate a random field component, the ad hoc scaling along the flow, and the scaling of the relative strengths of random and ordered field components, mean that the field does not satisfy a self-consistent magnetohydrodynamic model for its generation, and is not divergence-free."330 However. the aim is to coustruct a plausible magnetic fel topology with which to explore the properties of he emergent radiation. not a field to be evolved subject ο coustrauts to ensure conservation and/or preservation of the diverecuce-tree character of the field.," However, the aim is to construct a plausible magnetic field topology with which to explore the properties of the emergent radiation, not a field to be evolved subject to constraints to ensure conservation and/or preservation of the divergence-free character of the field."331 The flow is assiuned to be pervaded by a power law distribution of radiatiug particles. with density with the iudex à fixed.," The flow is assumed to be pervaded by a power law distribution of radiating particles, with density with the index $\delta$ fixed."332 Adiabatic gains and losses will not change the slope. svuchrotrou losses are ignore over the tens of jet radii propagation explored here. ane no allowance is made for Fermi acceleration at shocks. whose primary role will be toproduce a small number of particles radiating at frequencies above those probingthe quiescent enission.," Adiabatic gains and losses will not change the slope, synchrotron losses are ignored over the tens of jet radii propagation explored here, and no allowance is made for Fermi acceleration at shocks, whose primary role will be toproduce a small number of particles radiating at frequencies above those probingthe quiescent emission."333 The absolute scaling of the density is arbitrary. as functions of the density constant ry. are the magnetic field strength are absorbed into a fiducia optical depth. 7. which acts as a free parameter: see reftranster..," The absolute scaling of the density is arbitrary, as functions of the density constant $n_0$ , and the magnetic field strength are absorbed into a fiducial optical depth, $\tau$ , which acts as a free parameter; see \\ref{transfer}. ."334 The deusitv coustaut. vy. is taken to fal," The density constant, $n_0$ , is taken to fall"335 (e.g..?2??).. ?. ?..," \citep[e.g.,][]{1993Natur.364..421K, 1993Natur.364..423S, 2000ApJ...528L..17P,2002MNRAS.330..232C}."336 (e.g..2)). (e.g..222??).. ," \cite{kalogera_04} \citet{kalogera_04}. \citep[e.g.,][]{2006csxs.book..341V}) \citep[e.g.,][]{2001ApJ...557L..35A,2002ApJ...570..618D,2002ApJ...574L...5K,2003ApJ...595..743S, kim06}."337Ly>10?eress7!. Lx4«10°?ergss! (?).. (?).., $L_{\rm X} >10^{39} \ {\rm ergs\ s^{-1}}$ $L_{\rm X}\sim 4 \times 10^{39} {\ \rm ergs \ s^{-1}}$ \citep{2007Natur.445..183M}. \citep{2008ApJ...683L.139Z}.338 Ha/[O mass of 5-20M.. (2).., $\alpha$ mass of $5-20 M_\odot$ \citep{2009ApJ...705L.168G}.339 The ultraluminous X-ray source CXO J033831.8-352604 is associated with a globular cluster in the Fornax elliptical galaxy NGC 1399. with Ly>2«10ergss! (2)...," The ultraluminous X-ray source CXO J033831.8-352604 is associated with a globular cluster in the Fornax elliptical galaxy NGC 1399, with $L_{\rm X}\ga 2 \times 10^{39} {\rm ergs \ s^{-1}}$ \citep{2009arXiv0908.1115I}."340 This source shows strong [O III] emission lines (less broad: 0~70 km/s) and little or no hydrogen emission., This source shows strong [O III] emission lines (less broad; $\sigma\sim70$ km/s) and little or no hydrogen emission.341 It may be another black hole-white dwarf X-ray binary acereting near Eddington. although ? suggest a tidal disruption of a white dwarf by an intermediate mass black hole (MBH).," It may be another black hole-white dwarf X-ray binary accreting near Eddington, although \citet{2009arXiv0908.1115I} suggest a tidal disruption of a white dwarf by an intermediate mass black hole (IMBH)."342 How common are such systems?, How common are such systems?343 ?.KO6 found 8 such ULXs. with LyZ10ergss!. in 6173 globular clusters. wherethese GCs have an average mass of 6«10°M.," \citet[][K06]{kim06} found 8 such ULXs, with $L_{X}\ga 10^{39}\ {\rm ergs\ s^{-1}}$, in 6173 globular clusters, wherethese GCs have an average mass of $6\times 10^5 M_\odot$."344.. 3.HBOS found 2 such objects among 3782 eglobulars with total Ly~10°L.. (total mass M—3«10° M..., \citet[HB08]{2008ApJ...689..983H} found 2 such objects among 3782 globulars with total $L_V\sim10^9\ L_\odot$ (total mass $M \sim ~ 3\times10^9\ M_\odot$ ).345 These surveys suggest that GC ULXs are present at the rate of 2.0713.«10° and 7*P«107 per M... respectively. using Gehrels’ statistics at confidence (?)..," These surveys suggest that GC ULXs are present at the rate of $2.0^{+1.5}_{-1.0}\times 10^{-9}$ and $7^{+15}_{-6}\times 10^{-10}$ per $M_\odot$, respectively, using Gehrels' statistics at confidence \citep{1986ApJ...303..336G}."346 From the overlap in these numbers. we estimate that there is ~1 such object per 1-2«10?M... in GCs.," From the overlap in these numbers, we estimate that there is $\sim$ 1 such object per $1-2\times10^9\ M_\odot$ in GCs."347 These surveys were not completely independent. as several galaxies (including. NGC 1399) were contained in. both surveys.," These surveys were not completely independent, as several galaxies (including NGC 1399) were contained in both surveys."348 Some fraction of the observed globular ULXs may not be BH-WD systems. but accreting IMBHs.," Some fraction of the observed globular ULXs may not be BH-WD systems, but accreting IMBHs."349 The similarities between the two well-observed ULXs. discussed in ?.. suggest that they are either both BH-WD binaries or both acereting IMBHs.," The similarities between the two well-observed ULXs, discussed in \cite{2009arXiv0908.1115I}, suggest that they are either both BH-WD binaries or both accreting IMBHs."350 For this paper. we explore the consequences of the assumption that all globular cluster ULXs are BH-WD binaries. in. particular whether such numbers can be produced. and by what mechanisms.," For this paper, we explore the consequences of the assumption that all globular cluster ULXs are BH-WD binaries, in particular whether such numbers can be produced, and by what mechanisms."351 Let us consider now what this frequency implies for the formation rate of such systems per BH., Let us consider now what this frequency implies for the formation rate of such systems per BH.352 In globular clusters. roughly each 150-200 M... of currently remaining. stellar mass produced a BH in the past. where half of these BHs have masses above 10M.. (here. less cluster mass per BH is required in a metal-poor cluster).," In globular clusters, roughly each 150-200 $M_\odot$ of currently remaining stellar mass produced a BH in the past, where half of these BHs have masses above $10 M_\odot$ (here, less cluster mass per BH is required in a metal-poor cluster)."353 The retention fraction of BHs immediately after their formation. if supernova kicks are taken into account. is about30-40%.. for the escape velocity of 50 km/s (?).. ," The retention fraction of BHs immediately after their formation, if supernova kicks are taken into account, is about, for the escape velocity of 50 km/s \citep{2006ApJ...650..303B}. ."354We estimate therefore that. if no dynamical interactions between starsoccur.apresent dayaveragecluster inthe ? sample (6«10?M ..) would retain about 500-800 BHs," We estimate therefore that, if no dynamical interactions between starsoccur,apresent dayaverageclusterin the \cite{kim06} sample $6\times 10^5 M_\odot$ ) would retain about 500-800 BHs"355disces with small holes and large accretion rates. as our moclel does not reproduce such dises (Fig.,"discs with small holes and large accretion rates, as our model does not reproduce such discs (Fig."356 5)., 5).357 In this study. we developed a gas dise model which takes into account lavercd accretion and. photoevaporative winds induced by N-rays from the central stars.," In this study, we developed a gas disc model which takes into account layered accretion and photoevaporative winds induced by X-rays from the central stars."358 We found that a eap opens at à radius outside a poorlv-ionized. dead: zone. if the mass loss rate due to photoevaporation exceeds the mass accretion rate in the dead zone region.," We found that a gap opens at a radius outside a poorly-ionized dead zone, if the mass loss rate due to photoevaporation exceeds the mass accretion rate in the dead zone region."359 Since the dead zone survives even after the gap opens. high mass accretion onto the central star remains for a long time.," Since the dead zone survives even after the gap opens, high mass accretion onto the central star remains for a long time."360 We founc good agreements between modeled and observed. transition cliscs in regards to gap sizes ancl mass accretion rates., We found good agreements between modeled and observed transition discs in regards to gap sizes and mass accretion rates.361 However. our model shows clise masses (we take masses outside gaps) an order of magnitude smaller than those for the most massive observed: transition disces.," However, our model shows disc masses (we take masses outside gaps) an order of magnitude smaller than those for the most massive observed transition discs."362 This may indicate that the dust-to-gas ratios are large in the outer disces of observed transition disces while our mocel assumes a fixed dust opacity., This may indicate that the dust-to-gas ratios are large in the outer discs of observed transition discs while our model assumes a fixed dust opacity.363 We are erateful to anonymous reviewers for fruitful comments on our manuscript., We are grateful to anonymous reviewers for fruitful comments on our manuscript.364across the IBIS error circle suggesting incomplete coverage of this region by XMM.,across the IBIS error circle suggesting incomplete coverage of this region by XMM.365" 2MASS J00520059-7329255 lies 5.6"" away from the XRT position, marginally outside the error circle and consistent with the ROSAT HRI PSPC positions."," 2MASS J00520059-7329255 lies 5.6” away from the XRT position, marginally outside the error circle and consistent with the ROSAT HRI PSPC positions."366" This source is also known as [M2002] SMC 21983 (Massey 2002) and has B and V magnitudes of 15.18, typical of Be systems in the SMC."," This source is also known as [M2002] SMC 21983 (Massey 2002) and has B and V magnitudes of 15.18, typical of Be systems in the SMC."367" The source to the NW of 2MASS J00520059-1329255 is also in the Mssey catalogue (no: 21891) and has V=16.47 B-V=0.42 and is, again, a possible counterpart to a Be X-ray binary system."," The source to the NW of 2MASS J00520059-7329255 is also in the Mssey catalogue (no: 21891) and has V=16.47 B-V=0.42 and is, again, a possible counterpart to a Be X-ray binary system."368" However, its location well clear of all three error circles makes its association with the ROSAT and Swift objects much less likely."," However, its location well clear of all three error circles makes its association with the ROSAT and Swift objects much less likely."369 The OGLE light curve (see Figure 9)) of 2MASS J00520059-7329255 (OGLE III name SMC 103.4 33693) shows considerable variability on several timescales., The OGLE light curve (see Figure \ref{fig:00515ogle}) ) of 2MASS J00520059-7329255 (OGLE III name SMC 103.4 33693) shows considerable variability on several timescales.370" Despite this, timing analysis of the de-trended light curve yielded no significant periodicities."," Despite this, timing analysis of the de-trended light curve yielded no significant periodicities."371 A search of XTE monitoring observations performed on MJD54988 (just before the IBIS detection) and MJD54994 (during the outburst) found only a hint of a 8.29s pulse period in the MJD54994 data., A search of XTE monitoring observations performed on MJD54988 (just before the IBIS detection) and MJD54994 (during the outburst) found only a hint of a 8.29s pulse period in the MJD54994 data.372" Again, there is no robust way to associate this periodicity with IGR J00515-7328."," Again, there is no robust way to associate this periodicity with IGR J00515-7328."373" Overall, the detection of an X-ray source showing a high level of variability in flux between two epochs, and association with an optical counterpart which is typical of a Be star, suggests that IGR J00515-7328 is another high-mass X-ray binary system within the SMC."," Overall, the detection of an X-ray source showing a high level of variability in flux between two epochs, and association with an optical counterpart which is typical of a Be star, suggests that IGR J00515-7328 is another high-mass X-ray binary system within the SMC."374 SXP6.85 (= XTE J0103-728) underwent a large Type II outburst beginning on 2008 August 10 and the source was consistently seen in RXTE observations for the following 20 weeks (MJD54688 - 54830) and by INTEGRAL in the period MJD54790 - 54820., SXP6.85 (= XTE J0103-728) underwent a large Type II outburst beginning on 2008 August 10 and the source was consistently seen in RXTE observations for the following 20 weeks (MJD54688 - 54830) and by INTEGRAL in the period MJD54790 - 54820.375 Townsend et al (2010a) presented X-ray timing and spectroscopic analysis from the Rossi X-ray Timing Explorer (RXTE) and the INTEGRAL observatory., Townsend et al (2010a) presented X-ray timing and spectroscopic analysis from the Rossi X-ray Timing Explorer (RXTE) and the INTEGRAL observatory.376 À comparison with the Optical Gravitational Lensing Experiment (OGLE) III light curve of the Be counterpart showed the X-ray outbursts from this source to coincide with times of optical maximum., A comparison with the Optical Gravitational Lensing Experiment (OGLE) III light curve of the Be counterpart showed the X-ray outbursts from this source to coincide with times of optical maximum.377" A large outburst from a previously unknown source was seen by INTEGRAL starting MJD54989, lasting  20d and with a peak 3-10 keV luminosity of L,=7x10?""erg/s."," A large outburst from a previously unknown source was seen by INTEGRAL starting MJD54989, lasting $\sim$ 20d and with a peak 3–10 keV luminosity of $L_{x} = 7\times10^{37}erg/s$."378 A rapid follow-up observation using the Swift observatory refined the X-ray position and permitted the identification of an associated optical counterpart., A rapid follow-up observation using the Swift observatory refined the X-ray position and permitted the identification of an associated optical counterpart.379" Townsend et al (2010b) present X-ray and optical data on this proposed new Be/X-ray binary pulsar, IGR J01054-7253 = SXP11.5."," Townsend et al (2010b) present X-ray and optical data on this proposed new Be/X-ray binary pulsar, IGR J01054-7253 = SXP11.5."380 The optical counterpart was shown to be [M2002] SMC 59977 and OGLE III data on that source presented., The optical counterpart was shown to be [M2002] SMC 59977 and OGLE III data on that source presented.381" Following the discovery, RXTE began monitoring SXP11.5 approximately 3 time per week for the duration of the outburst (MJD — 55001 - 55063).These data revealed a clear pulse period of 11.48s (Corbet et al,"," Following the discovery, RXTE began monitoring SXP11.5 approximately 3 time per week for the duration of the outburst (MJD = 55001 - 55063).These data revealed a clear pulse period of 11.48s (Corbet et al.,"382 2009)., 2009).383" In addition, a strong Doppler modulation of the 11.48s pulse period was seen and interpreted as an accretion driven spin-up."," In addition, a strong Doppler modulation of the 11.48s pulse period was seen and interpreted as an accretion driven spin-up."384" Model fitting to these data allowed Townsend et al (2010b) to distinguish the spin-up rate from the orbital modulation and identify an orbital period of 36.3+0.4 days and an eccentricity of 0.28+0.03 (Townsend et al.,"," Model fitting to these data allowed Townsend et al (2010b) to distinguish the spin-up rate from the orbital modulation and identify an orbital period of $\pm$ 0.4 days and an eccentricity of $\pm$ 0.03 (Townsend et al.,"385 2009)., 2009).386 IBIS kkeV and JEM-X kkeV maps on time-scales varying between single revolutions up to five consecutive revolutions were searched for excesses which could indicate potential new sources in the SMC., IBIS keV and JEM-X keV maps on time-scales varying between single revolutions up to five consecutive revolutions were searched for excesses which could indicate potential new sources in the SMC.387 A list of candidates is supplied in Table ὃ and mapped on to the SMC in Figure 10.., A list of candidates is supplied in Table \ref{Tab:candidates} and mapped on to the SMC in Figure \ref{fig:tent}.388" With the large error circles on these objects, it is not yet possible to constrain the nature of these sources."," With the large error circles on these objects, it is not yet possible to constrain the nature of these sources."389necessary.,necessary.390 This helped us to reduce the number of calculated models by half., This helped us to reduce the number of calculated models by half.391" The radiative flux in a colour ο at the distance D from the star with radius R, is where the intensity /.(4.Q) at each surface point with spherical coordinates Q is obtained by means of interpolation between the intensities /.(4.eyo.és).δεν.£14) calculated from the erid of synthetic spectra (see Table 2)) as The transmissivity function (0) of à given filter ο of the Strómmgren photometric system is approximated for simplicity by a Gauss functiondetails)."," The radiative flux in a colour $c$ at the distance $D$ from the star with radius $R_*$ is where the intensity $I_c(\theta,\Omega)$ at each surface point with spherical coordinates $\Omega$ is obtained by means of interpolation between the intensities $I_c(\theta,\varepsilon_\text{He},\varepsilon_\text{Si},\varepsilon_\text{Cr},\varepsilon_\text{Fe})$ calculated from the grid of synthetic spectra (see Table \ref{esit}) ) as The transmissivity function $\Phi_c(\lambda)$ of a given filter $c$ of the Strömmgren photometric system is approximated for simplicity by a Gauss function."392 The magnitude difference is defined as where f. is calculated from Eq., The magnitude difference is defined as where $f_c$ is calculated from Eq.393 3. and f is the reference flux obtained under the condition that the mean magnitude difference over the rotational period ts zero., \ref{vyptok} and ${f_c^\mathrm{ref}}$ is the reference flux obtained under the condition that the mean magnitude difference over the rotational period is zero.394 Individual elements modify the temperature distribution. of model atmospheres by their bound-free and bound-bound transitions., Individual elements modify the temperature distribution of model atmospheres by their bound-free and bound-bound transitions.395 This can be seen in Fig. l..," This can be seen in Fig. \ref{tep},"396 where we compare the temperature distribution of model atmospheres for typical abundances found on the surface ofVir., where we compare the temperature distribution of model atmospheres for typical abundances found on the surface of.397" The free (caused by ionisation of helium and silicon) and bound-bound transitions (ine transition of chromium and tron) absorb the stellar radiation. consequently the temperature in. the continuum-forming region (Tr,=O.1— 1) increases with increasing abundance of these elements."," The bound-free (caused by ionisation of helium and silicon) and bound-bound transitions (line transition of chromium and iron) absorb the stellar radiation, consequently the temperature in the continuum-forming region $\tau_\text{ross}\approx0.1-1$ ) increases with increasing abundance of these elements."398 For silicon and iron the influence of abundance on the temperature is stronger. for chromium the influence is weaker. while for typical helium abundances found on the surface of tthe changes of temperature are only marginal.," For silicon and iron the influence of abundance on the temperature is stronger, for chromium the influence is weaker, while for typical helium abundances found on the surface of the changes of temperature are only marginal."399 In. atmospheres with overabundant helium. silicon. chromium or iron the enhanced opacity leads to the redistribution of the flux from the short-wavelength part of the spectrum to the longer wavelengths of the UV spectrum. and also to the visible spectral regions (see Fig. 2)).," In atmospheres with overabundant helium, silicon, chromium or iron the enhanced opacity leads to the redistribution of the flux from the short-wavelength part of the spectrum to the longer wavelengths of the UV spectrum, and also to the visible spectral regions (see Fig. \ref{prvtoky}) )."400 Consequently. the overabundant spots are bright in the uyby colours. and are dark in far-ultraviolet bands.," Consequently, the overabundant spots are bright in the $uvby$ colours, and are dark in far-ultraviolet bands."401 As already found by(2007).. helium can affect the flux distribution only if it significantly dominates over hydrogen. te. for ey.>0.9.," As already found by, helium can affect the flux distribution only if it significantly dominates over hydrogen, i.e. for $\varepsilon_\text{He}>0.5$."402 Consequently. for model atmospheres with underabundant helium the flux variations are only marginal.," Consequently, for model atmospheres with underabundant helium the flux variations are only marginal."403 Note also that the flux variations caused by silicon are most pronounced in the far-UV region witht«1600A..," Note also that the flux variations caused by silicon are most pronounced in the far-UV region with $\lambda<1600\,$."404 These flux changes can be detected as a change in the apparent magnitude., These flux changes can be detected as a change in the apparent magnitude.405 To demonstrate this. we plot (Fig. 3))," To demonstrate this, we plot (Fig. \ref{magtoky}) )"406 the relative magnitude difference defined as against wavelength., the relative magnitude difference defined as against wavelength.407" Here Hy is the reference flux calculated for slightly overabundant chemical composition (with ej,=—1.0. es;=—3.75. ες=—3.9. and εις= —4.4."," Here $H_\lambda^\text{ref}$ is the reference flux calculated for slightly overabundant chemical composition (with $\varepsilon_\text{He}=-1.0$, $\varepsilon_\text{Si}=-3.75$, $\varepsilon_\text{Cr}=-5.9$, and $\varepsilon_\text{Fe}=-4.4$ )."408 As can be seen in Fig. 3..," As can be seen in Fig. \ref{magtoky},"409 the absolute value of the relative magnitude difference decreases with increasing wavelength., the absolute value of the relative magnitude difference decreases with increasing wavelength.410 However. the behaviour of the flux calculated for modified helium is different.," However, the behaviour of the flux calculated for modified helium is different."411 The maxima of the relative brightness at the positions of the hydrogen lines (especially close to the Balmer, The maxima of the relative brightness at the positions of the hydrogen lines (especially close to the Balmer412"the GOO and Lincetal.(2009) ει scales well match. with an average dillerence 1ipg 13 IX (σ- 15 Ix). while the dilference with the temperatures ον A99 qpyv quit"" qg0? WN (a= 14 K).","the G09 and \citet{lind} $T_{eff}$ scales well match, with an average difference $T_{eff}^{GB}-T_{eff}^{Lind09}$ = –13 K $\sigma$ = 15 K), while the difference with the temperatures by A99 is $T_{eff}^{Alo}-T_{eff}^{Lind09}$ = –117 K $\sigma$ = 14 K)."413" the iron content is Vefl]o-2.08n dex (00.09 dex) with the"" CtO scale and -2.12 dex (σ--"" dex) with the (99 scale.", The iron content is [Fe/H]= -2.08 dex $\sigma$ =0.09 dex) with the G09 scale and -2.12 dex $\sigma$ =0.08 dex) with the A99 scale.414 find an average A(Li)-1.00NE dex (a= 0.09 dex) with the A99 scale and of dex (o 0.10dex) with the G09 scale., We find an average A(Li)=1.00 dex $\sigma$ = 0.09 dex) with the A99 scale and of A(Li)=1.09 dex $\sigma$ = 0.10 dex) with the G09 scale.415 ὃν interpolating in. Fe/1H] among the values of Tab., By interpolating in [Fe/H] among the values of Tab.416" 2. we derive an estimate for A(Li)), οἱ 2.33.2.42 dex with the model without ciffusion (A99 ancl CIO!) scales respectively) and 2.40.2.49 dex with the model with cdillusion."," 2, we derive an estimate for ${\rm A(Li)}_0$ of 2.33–2.42 dex with the model without diffusion (A99 and GH09 scales respectively) and 2.40–2.49 dex with the model with diffusion."417 Twenty-one HGD stars were observed with UVES within the ESO Large Program 65.L-0165 (Pl: Grunclahl)., 		 Twenty-one RGB stars were observed with UVES within the ESO Large Program 65.L-0165 (PI: Grundahl).418 Concerning the Li abundance. only the qualitative behaviour of the observed. EW's as a function of Vo magnitude was cliscussecl (Cruncdahletal.2002).. without the explicit determination of the Li abundance.," Concerning the Li abundance, only the qualitative behaviour of the observed EWs as a function of V magnitude was discussed \citep{grund}, without the explicit determination of the Li abundance."419 Here we consider the 12 stars fainter than the RGB bump. for whieh the Li line is clearly detectable.," Here we consider the 12 stars fainter than the RGB bump, for which the Li line is clearly detectable."420 We analyzed the obtained with the CD33 cross-disperser. deriving ha7;EU5; eanboth spectroscopicallv and photometrically. adopting 9 and (109 calibrations or the (JAo colour.," We analyzed the spectra obtained with the 3 cross-disperser, deriving $T_{eff}$ both spectroscopically and photometrically, adopting the A99 and G09 calibrations for the $(J-K)_0$ colour."421 Phe J and A; magnitudes are from he 2ALASS database. corrected for reddening using the E(DB-V) value by Ferraroetal.(1999).," The J and $K_s$ magnitudes are from the 2MASS database, corrected for reddening using the E(B-V) value by \citet{f99}."422.. Also for this cluster. we minimized the scatter in the final A(Li) values by emploving (Jho colours obtained projecting the position of cach star along the ROB [iducial line.," Also for this cluster, we minimized the scatter in the final A(Li) values by employing $(J-K)_0$ colours obtained projecting the position of each star along the RGB fiducial line."423" CGrundahlctal.(2002) derived. the Zip, for their argets by means of the A99 calibration lor the Strómmegren index.", \citet{grund} derived the $T_{eff}$ for their targets by means of the A99 calibration for the Strömmgren index.424 We find a reasonable consistency with our spectroscopic and. photometric Z;;; on the A99 scale(as or the case of field stars) with average dillerences 1oftSpeedi.∕pearlEU? ⊰↱⋟↓∖⊳≼∪∶↲≖⋅⊓↓∖⊐⋮⊔⊔⊔√⊻∕∣∣↝∕∣CU queetentuaES ol ⊰↓∖⇉⋅↱≻↓∖⊥⊐⊳ respectively.," We find a reasonable consistency with our spectroscopic and photometric $T_{eff}$ on the A99 scale (as for the case of field stars) with average differences $T_{eff}^{Spec}-T_{eff}^{Grundahl02}$ = –35 K $\sigma$ = 45 K) and $T_{eff}^{Alo}-T_{eff}^{Grundahl02}$ = --43 K $\sigma$ = 25 K), respectively."425" The olfset with the Zip, by ≺∪↸⋗↓∖ 155 quU] 65 Ix (a= 26 IK).", The offset with the $T_{eff}$ by G09 is of $T_{eff}^{GB}-T_{eff}^{Grundahl02}$ = +65 K $\sigma$ = 26 K).426 The average iron content is qeI= 1.68 dex (o6 =0.07 ex). when the spectroscopic temperatures are used. and illerent by only a few hundredths dex the Mric Tipp are adopted.," The average iron content is [Fe/H]= –1.68 dex $\sigma$ =0.07 dex), when the spectroscopic temperatures are used and different by only a few hundredths dex when the photometric $T_{eff}$ are adopted."427 The average A(Li) is ven0.83 licadex (a= 0.15 ex) with the spectroscopic temperatures the same abundance is obtained. with the scale. the G09 μαcale provides »Li)J= 0.98 dex. a= UB dex.," The average A(Li) is 0.83 dex $\sigma$ = 0.15 dex) with the spectroscopic temperatures (almost the same abundance is obtained with the A99 scale, while the G09 scale provides A(Li)= 0.93 dex, $\sigma$ = 0.15 dex)."428" vnThree stars isplay A(Li)~ -0.6 dex. lower by mi0.p0.4 ""x compared o the other stars in the sample."," Three stars display $\sim$ 0.5-0.6 dex, lower by $\sim$ 0.3-0.4 dex compared to the other stars in the sample."429 remaining 9 stars provide an average Li abundance X(Li)- 0.91 dex (a= 0.0% ex)., The remaining 9 stars provide an average Li abundance A(Li)= 0.91 dex $\sigma$ = 0.07 dex).430 The presence of these three Li-poor stars (alreadyiden-tifiedbyCiründahletal.2002) is probably ascribable to the lithium variation in the cluster. as testified by the Li-Na anticorrelation (Pasquinietal.2005). and. Li-O correlation (Shenetal.2010)," The presence of these three Li-poor stars \citep[already identified by][]{grund} is probably ascribable to the lithium variation in the cluster, as testified by the Li-Na anticorrelation \citep{pasquini05} and Li-O correlation \citep{shen} ."431ο These stars could belong to the second generation., These stars could belong to the second generation.432 ὃν employing the (Li) values Listed. in Tab., By employing the $\Delta$ (Li) values listed in Tab.433" 2. the models without and with the inclusion of the cliffusion provide estimates of 2.292.35. 2182.24 and 2.192.25 dex. by A(Li),adopting. respectively. the Zip, scale from (100. A99 and from the excitation equilibrium."," 2, the models without and with the inclusion of the diffusion provide ${\rm A(Li)}_0$ estimates of 2.29–2.35, 2.18–2.24 and 2.19--2.25 dex, by adopting, respectively, the $T_{eff}$ scale from GH09, A99 and from the excitation equilibrium."434" When we exclude the 3 Li-poor stars. the derived A(Li), increase by 0.08 dex"," When we exclude the 3 Li-poor stars, the derived ${\rm A(Li)}_0$ increase by 0.08 dex."435 We summarized briellv the results cliscussec in Mucciarellietal.(2011) about the metal-rich cluster MA. from the analysis of a sample of GLRAPEE spectra.," We summarized briefly the results discussed in \citet{muc} about the metal-rich cluster M4, from the analysis of a sample of GIRAFFE spectra."436 The dillerential reddening that affects the field. of view of MA makes uncertain the abundances derived. directly. by adopting the photometric τει due to the residual of the dillercntial reddening correction.," The differential reddening that affects the field of view of M4 makes uncertain the abundances derived directly by adopting the photometric $T_{eff}$ , due to the residual of the differential reddening correction."437 The atmospheric parameters for the RGB stars in the sample were therefore derived by projecting the position of cach star along the stellar isochrone the best fit. the observed. colour-magnitucde-diagram., The atmospheric parameters for the RGB stars in the sample were therefore derived by projecting the position of each star along the stellar isochrone the best fit the observed colour-magnitude-diagram.438" This Z;;r; scale is in nice agreement with the spectroscopic Loy, values inferred bv Marinoetal.(2008). for the stars in common.", This $T_{eff}$ scale is in nice agreement with the spectroscopic $T_{eff}$ values inferred by \citet{marino} for the stars in common.439 The NM Li abundance in lower RGB stars of MA A(Li)-0.92nen dex. that leads to (Liu 2.35 dex (models withou and 2.40 dex (models with cüllusion).," The derived Li abundance in lower RGB stars of M4 is A(Li)=0.92 dex, that leads to ${\rm A(Li)_0}$ =2.35 dex (models without diffusion) and 2.40 dex (models with diffusion)."440 We have discussed the use of Li abundances measured in Population HL lower RGB stars as an independent. reliable ancl robust. diagnostic of the initial Li abundance in the Galactic Lalo.," We have discussed the use of Li abundances measured in Population II lower RGB stars as an independent, reliable and robust diagnostic of the initial Li abundance in the Galactic Halo."441 Surface abundances in giant stars fainter than he RG3 bump are sensitive to the total Li content left at he end of th AIS phase. and are very weakly alfected. by atomic diffusion curing ALS.," Surface abundances in giant stars fainter than the RGB bump are sensitive to the total Li content left at the end of the MS phase, and are very weakly affected by atomic diffusion during MS."442 Also. the predicted. (Li) in hese objects is basically insensitive to the mixing length calibration. the precise stellar ages. initial He abuncdances. and realistic estimates of the overshooting extension below he Schwarzschilel boundary. of the convective envelope.," Also, the predicted A(Li) in these objects is basically insensitive to the mixing length calibration, the precise stellar ages, initial He abundances, and realistic estimates of the overshooting extension below the Schwarzschild boundary of the convective envelope."443 Chemical abundance measurements in giant stars also sugeest that anv additional clement transport along the tGB ds very likely ineflicient in this phase., Chemical abundance measurements in giant stars also suggest that any additional element transport along the RGB is very likely inefficient in this phase.444 Overall. our analysis reveals that the. predicted. Li. depletion A(Li) along the lower RGB is robust in terms of theoretical interpretation.," Overall, our analysis reveals that the predicted Li depletion $\Delta$ (Li) along the lower RGB is robust in terms of theoretical interpretation."445 The values of A(Li)o inferred from our sample of lower ROB Lalo field stars range from 2.28 (obtained with the A990 scale anc without the inclusion. of atomic. clilfusion) to 246 (when theGOO ει scale is used. together with modelsincluding atomic diffusion).," The values of ${\rm A(Li)_0}$ inferred from our sample of lower RGB Halo field stars range from 2.28 (obtained with the A99 scale and without the inclusion of atomic diffusion) to 2.46 (when the G09 $T_{eff}$ scale is used, together with models including atomic diffusion)."446 Inclusion of overshooting from the RGB convective boundary would increase. both limits by only 0.01 ον. while variations of age. initial Le abundance and mixing length parameter provide changes of a few hundredths of dex or less in terms of A(Li).," Inclusion of overshooting from the RGB convective boundary would increase both limits by only 0.01 dex, while variations of age, initial He abundance and mixing length parameter provide changes of a few hundredths of dex or less in terms of $\Delta$ (Li)."447" When a d,rp scale is adopted. the clleet of Lully cllicient atomic diffusion on the A(Lijy estimate is by at most. 0.07 dex."," When a $T_{eff}$ scale is adopted, the effect of fully efficient atomic diffusion on the ${\rm A(Li)_0}$ estimate is by at most 0.07 dex."448 The discrepancy with A(Li)u predicted. by BBN calculations thus remains. reconfirmed. by the robustness of our estimate.," The discrepancy with ${\rm A(Li)_0}$ predicted by BBN calculations thus remains, reconfirmed by the robustness of our estimate."449 Phe analysis performed. on. the lower ROB stars in three Galactic globular. clusters confirms similar values for A(Li)u. although in general the possible occurrence of scl-cnrichment processes in these objects has to be considered.," The analysis performed on the lower RGB stars in three Galactic globular clusters confirms similar values for ${\rm A(Li)_0}$ , although in general the possible occurrence of self-enrichment processes in these objects has to be considered."450 There are several discussions in the literature. about how to solve this discrepancy withBBN results., There are several discussions in the literature about how to solve this discrepancy withBBN results.451 Ideas involve à [first generation of stars that has processed, Ideas involve a first generation of stars that has processed452iuproved further aud models with Ομως=2.6)>0.1 should be detectable.,improved further and models with $\Omega_{\rm de}(z=2.6)>0.1$ should be detectable.453 Wile this is still not sufficiently accurate to measure dark energy directly for cosmological constaut model (ae= 1j QOenti~0.3. it will provide iuportaut constraints on the more ecucral models of dark cucrey such as the tracker models. where equation of state naturally increases in value at ligher redshifts.," While this is still not sufficiently accurate to measure dark energy directly for cosmological constant model $w=-1$ ) $\Omega_m \sim 0.3$, it will provide important constraints on the more general models of dark energy such as the tracker models, where equation of state naturally increases in value at higher redshifts."454the GALAXEV population synthesis code (Bruzual Charlot2003)) using a x? goodness-of-fit test.,the GALAXEV population synthesis code (Bruzual Charlot\cite{BC03}) ) using a $\chi^2$ goodness-of-fit test.455 We choose the BC03 models for their high-resolution templates which allow us to fit both broad-band photometry and spectra., We choose the BC03 models for their high-resolution templates which allow us to fit both broad-band photometry and spectra.456" Because of the low signal-to-noise ratio of the available FORS2 spectra (ranging from 5 to 6 at 8000 A)), we resort to stacking spectra of galaxies within the aforementioned stellar mass range separately for our cluster and field samples."," Because of the low signal-to-noise ratio of the available FORS2 spectra (ranging from 5 to 6 at 8000 ), we resort to stacking spectra of galaxies within the aforementioned stellar mass range separately for our cluster and field samples."457" Consequently, the photometric points are also co-added in the combined fit."," Consequently, the photometric points are also co-added in the combined fit."458" We assume a delayed exponential star formation history (SFH), which is similar to the one proposed by Sandage (1986)) and is more realistic than a simple exponentially declining SFH (Gavazzi et al. 2002)),"," We assume a delayed exponential star formation history (SFH), which is similar to the one proposed by Sandage \cite{Sandage86}) ) and is more realistic than a simple exponentially declining SFH (Gavazzi et al. \cite{Gavazzi02}) ),"459 parametrized by a time-scale Τ., parametrized by a time-scale $\tau$.460" Since we use both broad-band SEDs and spectroscopic features, we allow for more complex star formation histories."," Since we use both broad-band SEDs and spectroscopic features, we allow for more complex star formation histories."461" We expand the grid of models by adding secondary episodes of star formation after the main event parametrized by an instantaneous burst at time tyurstT of amplitude A, so that the star formation rate is expressed as : We consider age values, i.e. the time T after the onset of star formation, ranging from 200 Myr to 5 Gyr in increments of ~ 250 Myr."," We expand the grid of models by adding secondary episodes of star formation after the main event parametrized by an instantaneous burst at time $t_{burst} > \tau$ of amplitude $A$, so that the star formation rate is expressed as : We consider age values, i.e. the time $T$ after the onset of star formation, ranging from 200 Myr to 5 Gyr in increments of $\sim$ 250 Myr."462 The time-scale 7 ranges from 0 (corresponding to a simple stellar population) to 1 Gyr in increments of 0.1 Gyr., The time-scale $\tau$ ranges from 0 (corresponding to a simple stellar population) to 1 Gyr in increments of 0.1 Gyr.463" In the case of a secondary burst, tourst ranges from 1 to 4 Gyr in increments of 1 Gyr with amplitudes A of 0.1, 0.2 and 0.5, which correspond to 1/11, 1/6 and 1/3 of the final stellar mass respectively."," In the case of a secondary burst, $t_{burst}$ ranges from 1 to 4 Gyr in increments of 1 Gyr with amplitudes $A$ of 0.1, 0.2 and 0.5, which correspond to 1/11, 1/6 and 1/3 of the final stellar mass respectively."464" Thus, the grid (T7,tourst,A} contains 20x13x4x3+13x20=3380 models."," Thus, the grid $T,\tau,t_{burst},A$ contains $20\times13\times4\times3+13\times20=3380$ models."465 All models are computed at solar metallicity and are dust-free., All models are computed at solar metallicity and are dust-free.466 We will comment on this assumption later., We will comment on this assumption later.467" In Fig. 2,,"," In Fig. \ref{fig2},"468" left, we show a sample of our grid of star formation histories."," left, we show a sample of our grid of star formation histories."469" We first use this grid of models to fit the stacked SEDs, covering rest-frame wavelengths from 2000 to 2 um, which gives us a sub-grid of acceptable models within the confidence interval defined by x?<x2+16.25 (where x2 is the minimum x? solution) which corresponds to 3c for the 5 fitting parameters: age,7, tourst, A and stellar mass."," We first use this grid of models to fit the stacked SEDs, covering rest-frame wavelengths from 2000 to 2 $\mu$ m, which gives us a sub-grid of acceptable models within the confidence interval defined by $\chi^2 \leq \chi^2_0 + 16.25$ (where $\chi^2_0$ is the minimum $\chi^2$ solution) which corresponds to $\sigma$ for the 5 fitting parameters: $\tau$, $t_{burst}$, $A$ and stellar mass."470" Among this subsample of models, we select those which best fit the stacked spectral data, adopting the same 30 confidence level."," Among this subsample of models, we select those which best fit the stacked spectral data, adopting the same $\sigma$ confidence level."471" These solutions will be referred to as the “best fit models"" in the following.", These solutions will be referred to as the “best fit models” in the following.472" In Fig. 2,"," In Fig. \ref{fig2},"473" right, we show the projection of the 3c confidence levels of the fit on the stacked SEDs and spectra of the GOODS sample in the {T,r,tourst=O(noburst),A=0} plane."," right, we show the projection of the $\sigma$ confidence levels of the fit on the stacked SEDs and spectra of the GOODS sample in the $T,\tau,t_{burst}=0 {\rm (no burst)},A=0$ plane."474" In Fig. 3,,"," In Fig. \ref{fig3},"475" we show the SEDs and spectra of the best fitting models, with the stacked spectrophotometric data."," we show the SEDs and spectra of the best fitting models, with the stacked spectrophotometric data."476" The model spectra are smoothed to match the resolution of the GOODS and RDCS 1252 samples and cropped to a 500 iinterval centered on the 4000 bbreak, which roughly corresponds to the high S/N, well flux-calibrated part of the spectra in our sample."," The model spectra are smoothed to match the resolution of the GOODS and RDCS 1252 samples and cropped to a 500 interval centered on the 4000 break, which roughly corresponds to the high S/N, well flux-calibrated part of the spectra in our sample."477 This region also covers absorption features characteristic of young (e.g. Hs) and old (e.g. Call H&KK) stellar populations., This region also covers absorption features characteristic of young (e.g. $_{\delta}$ ) and old (e.g. CaII K) stellar populations.478" It includes the 4000 bbreak, a good age indicator with mild metallicity sensitivity (e.g. Poggianti Barbaro 1997)), and therefore removes part of the degeneracy inherent to our grid of star formation histories."," It includes the 4000 break, a good age indicator with mild metallicity sensitivity (e.g. Poggianti Barbaro \cite{Poggianti97}) ), and therefore removes part of the degeneracy inherent to our grid of star formation histories."479" By using this relatively narrow wavelength interval, possible distortions due to uncertain flux calibration on the red end of the spectra (Demarco et al. 2007))"," By using this relatively narrow wavelength interval, possible distortions due to uncertain flux calibration on the red end of the spectra (Demarco et al. \cite{Demarco07}) )"480 are also minimized., are also minimized.481" The BC03 models offer the choice of two initial mass functions (IMFs), Salpeter or Chabrier (2003)."," The BC03 models offer the choice of two initial mass functions (IMFs), Salpeter or Chabrier (2003)."482" The choice of the IMF has little effect on the shape of the compositespectrum for the considered age range (t < 5 Gyr), as the Salpeter and Chabrier IMFs are nearly identical above 1 Mo."," The choice of the IMF has little effect on the shape of the compositespectrum for the considered age range (t $\leq$ 5 Gyr), as the Salpeter and Chabrier IMFs are nearly identical above 1 $M_{\odot}$ ."483 We assume a Salpeter IMF for consistency with, We assume a Salpeter IMF for consistency with484"The scaled line profiles of the strongest, more isolated UV resonance lines in Eta Car are presented in Figure 7,, where the grey region shows the difference between the spectrum taken at @=10.820and at ϕ=10.995, corresponding to the excess absorption occurring across the spectroscopic event due to the high-velocity material in Eta Car.","The scaled line profiles of the strongest, more isolated UV resonance lines in Eta Car are presented in Figure \ref{highveluv1}, where the grey region shows the difference between the spectrum taken at $\phi=10.820$and at $\phi=10.995$, corresponding to the excess absorption occurring across the spectroscopic event due to the high-velocity material in Eta Car."485 The absorption components of the low-ionization and the high-ionization resonance lines behave quite differently across the 2003.5 event., The absorption components of the low-ionization and the high-ionization resonance lines behave quite differently across the 2003.5 event.486" Low-ionization resonance lines, such as 441334, 1335, 441526, 1533, andAlm 41671, show a gradual development of an absorption wing increasing from —500 to -900kms! between $=10.820 and ¢=10.984."," Low-ionization resonance lines, such as $\lambda\lambda$ 1334, 1335, $\lambda\lambda$ 1526, 1533, and $\lambda$ 1671, show a gradual development of an absorption wing increasing from $-500$ to $-900~\kms$ between $\phi=10.820$ and $\phi=10.984$."487" At $=10.995, the spectrum showsa significant increase in the strength of the absorption from —500 to —900kms'! (Fig. 7,,"," At $\phi=10.995$, the spectrum showsa significant increase in the strength of the absorption from $-500$ to $-900~\kms$ (Fig. \ref{highveluv1},"488" right panel), but the low-ionization UV resonance lines do not show evidence for high-velocity absorption from —1000 to --2000kms! before ϕ=11.0, as 410833 did just before $=12.0."," right panel), but the low-ionization UV resonance lines do not show evidence for high-velocity absorption from $-1000$ to $-2000~\kms$ before $\phi=11.0$, as $\lambda$ 10833 did just before $\phi=12.0$."489" The high-ionization ultraviolet resonance lines, andCiv, also show an increase in absorption from —500 to -900kms! before ¢=11.0, although, differently from the low-ionization lines, with most of the changes occurring between ¢=10.820 and ¢=10.984."," The high-ionization ultraviolet resonance lines, and, also show an increase in absorption from $-500$ to $-900~\kms$ before $\phi=11.0$, although, differently from the low-ionization lines, with most of the changes occurring between $\phi=10.820$ and $\phi=10.984$."490 More noticeable changes occurred after @=10.984., More noticeable changes occurred after $\phi=10.984$.491" High-velocity absorption from —1200 up to —2100kms! is seen in the high-ionization 441394, 1403 doublet and possibly in the 41548 line."," High-velocity absorption from $-1200$ up to $-2100~\kms$ is seen in the high-ionization $\lambda\lambda$ 1394, 1403 doublet and possibly in the $\lambda$ 1548 line."492" This high-velocity component becomes noticeably stronger between $=10.984 and ¢=10.995 (Fig. 7,,"," This high-velocity component becomes noticeably stronger between $\phi=10.984$ and $\phi=10.995$ (Fig. \ref{highveluv1},"493left panel).,left panel).494 The reality of the high-velocity absorption is confirmed by its presence in both of the doublet lines., The reality of the high-velocity absorption is confirmed by its presence in both of the doublet lines.495" The weaker 41550 line is severely blended with the stronger 41548 line, and it is impossible to unambiguously judge whether the high-velocity absorption is present in 41550 or not."," The weaker $\lambda$ 1550 line is severely blended with the stronger $\lambda$ 1548 line, and it is impossible to unambiguously judge whether the high-velocity absorption is present in $\lambda$ 1550 or not."496" Therefore, ultraviolet resonance lines from low-ionization species, such asSim 441527, 1533, 441334, 1335, andAlt 41671, show absorption up to —800kms!, possibly —1200kms7!, but the UV resonance lines from high-ionization species, specificallySiiv, show absorption from —1200 to -2100kms!.Thus, the high-velocity absorption originates from a region that is markedly more ionized than the windof Eta Car A. Analysis of optical singlet and triplet line profiles was done by Nielsenetal.(2007)."," Therefore, ultraviolet resonance lines from low-ionization species, such as $\lambda\lambda$ 1527, 1533, $\lambda\lambda$ 1334, 1335, and $\lambda$ 1671, show absorption up to $-800~\kms$, possibly $-1200~\kms$, but the UV resonance lines from high-ionization species, specifically, show absorption from $-1200$ to $-2100~\kms$.Thus, the high-velocity absorption originates from a region that is markedly more ionized than the windof Eta Car A. Analysis of optical singlet and triplet line profiles was done by \citet{nielsen07}."497. Profiles from the same observations are reproduced in Figure 8.., Profiles from the same observations are reproduced in Figure \ref{highvel_stis_hei}.498" A noticeable high-velocity absorption is apparent in the two triplet line profiles,Her 43888 and 45876, extending to —900, possibly —1000kms"", at @=10.995 (2003 Jul 05)."," A noticeable high-velocity absorption is apparent in the two triplet line profiles, $\lambda$ 3888 and $\lambda$ 5876, extending to $-900$ , possibly $-1000~\kms$, at $\phi=10.995$ (2003 Jul 05)."499" The profiles of singlet lines, such as 46680, show less pronounced absorptions up to —800kms! (note that ther 44714 line is much weaker and contaminated by m] 44702 emission), as noted by Nielsen (2005).."," The profiles of singlet lines, such as $\lambda$ 6680, show less pronounced absorptions up to $-800~\kms$ (note that the $\lambda$ 4714 line is much weaker and contaminated by ] $\lambda$ 4702 emission), as noted by \citet{nielsen05}. ."500 Stahletal.2005 also detected similar absorption up to —750kms! for 46680 from the polar spectrum reflected in the Homunculus., \citealt{stahl05} also detected similar absorption up to $-750~\kms$ for $\lambda$ 6680 from the polar spectrum reflected in the Homunculus.501 The optical depths of all of these optical linesare substantially less than even that of the Hei 420587 line., The optical depths of all of these optical linesare substantially less than even that of the $\lambda$ 20587 line.502"Hence, the likelihood of seeingabsorptions up to —2000kms! in the He optical lines is low.","Hence, the likelihood of seeingabsorptions up to $-2000~\kms$ in the optical lines is low."503determining the photoclissociation rate requires an estimate of the column density in order to take into account self shielding.,determining the photodissociation rate requires an estimate of the column density in order to take into account self shielding.504 As described in? we adopt a constant length of 35 pe to caleulate the column density. which is the average distance to a DO star in the Milky Way.," As described in \cite{Dobbs08} we adopt a constant length of 35 pc to calculate the column density, which is the average distance to a B0 star in the Milky Way."505 Given the LT» fraction fora particular particle. we determine the density used for this paper [rom n(I£)=n 20H). where n(4HE).n(H3S) and n are the number densities ofHi. Ho and the total number density.," Given the $\rm{H}_2$ fraction for a particular particle, we determine the density used for this paper from $n(H)=n-2n(H_2)$ where $n(H), n(H_2)$ and $n$ are the number densities of, $\rm{H}_2$ and the total number density."506 The evolution of the gas clise is described Lully in ? but we also provide a brief summary here., The evolution of the gas disc is described fully in \citet{DGCK08} but we also provide a brief summary here.507 As the disc evolves. the spiral pattern emerges and narrow spiral arms develop.," As the disc evolves, the spiral pattern emerges and narrow spiral arms develop."508 Most of the gas cools from the initial temperature of 7000 Ix. and typically 70% of the σας (and all the gas in the spiral armis) is «150 Ix. Clumps of cold gas accumulate into more massive clouds as they. pass through a spiral shock., Most of the gas cools from the initial temperature of 7000 K and typically 70 of the gas (and all the gas in the spiral arms) is $<150$ K. Clumps of cold gas accumulate into more massive clouds as they pass through a spiral shock.509 The molecular eas (which constitutes around. 30 of the total eas) Ties predominantly in the spiral arms. ancl tvpically forms from. the atomic medium. over time scales of order. 10 Myr.," The molecular gas (which constitutes around 30 of the total gas) lies predominantly in the spiral arms, and typically forms from the atomic medium over time scales of order 10 Myr."510 As dense clumps leave the spiral arms. they are shearecl into short spurs.," As dense clumps leave the spiral arms, they are sheared into short spurs."511 Some cold clumps. or spurs. ave able to survive between the arms. though they do not tend to contain much molecular gas.," Some cold clumps, or spurs, are able to survive between the arms, though they do not tend to contain much molecular gas."512 We do not have observational measurements of the proportions of warm and cold gas in external galaxies., We do not have observational measurements of the proportions of warm and cold gas in external galaxies.513 The fractions in our simulations are not dissimilar from the solar neighbourhood. the only region for which there is an observational indication of the fractions of cold and warm LL (?)..," The fractions in our simulations are not dissimilar from the solar neighbourhood, the only region for which there is an observational indication of the fractions of cold and warm HI \citep{Heiles2003}."514 In the absence ofobservational evidence to the contrary we can only assume that other nearby large spiral galaxies are not vastly different in terms of the amount of gas in different: phases., In the absence of observational evidence to the contrary we can only assume that other nearby large spiral galaxies are not vastly different in terms of the amount of gas in different phases.515 We run the simulation for a total of 320 Myr., We run the simulation for a total of 320 Myr.516 For the comparisons in this paper. we take the output at a time of 250 Myr. by which point the distribution of gas in cillerent phases. and the amount of molecular gas. has reached. a roughly steady state.," For the comparisons in this paper, we take the output at a time of 250 Myr, by which point the distribution of gas in different phases, and the amount of molecular gas, has reached a roughly steady state."517 We use the radiative transfer code (7). to generate synthetic observations., We use the radiative transfer code \citep{Harries00} to generate synthetic observations.518 is a gricl-based radiative transfer code that uses Adaptive Mesh Refinement (AMI) to provide variable spatial resolution., is a grid-based radiative transfer code that uses Adaptive Mesh Refinement (AMR) to provide variable spatial resolution.519 can perform radiative transfer calculations. using the Alonte Carlo method of ὃν. and can also generate spectral energy distributions. images and spectral cubes.," can perform radiative transfer calculations, using the Monte Carlo method of \cite{Lucy}, and can also generate spectral energy distributions, images and spectral cubes."520 “Phe code has frequently been applied: to. models. of stellar. clises and performs well in. benchmark. tests. even at high optical depths (?)..," The code has frequently been applied to models of stellar discs and performs well in benchmark tests, even at high optical depths \citep{pinte_2009}."521 To generate a synthetic data cube we first. need to convert from the particle representation of SPILL to the AMI grid. representation ofrorus., To generate a synthetic data cube we first need to convert from the particle representation of SPH to the AMR grid representation of.522 The AMD grid is constructed. using the octree method in which the eric initially comprises eight. cells (one octal) with two cells in each spatial dimension., The AMR grid is constructed using the octree method in which the grid initially comprises eight cells (one octal) with two cells in each spatial dimension.523 The eric is refined. by specifving a condition which determines when a cell is split into a further eight. cells., The grid is refined by specifying a condition which determines when a cell is split into a further eight cells.524 For this calculation the grid cells were split if the mass of the cell exceeded a eiven Limit (mass per cell init)., For this calculation the grid cells were split if the mass of the cell exceeded a given limit (mass per cell limit).525 A mass per cell limit gives higher spatial resolution in regions of high density. which is similar to the elfective spatial resolution of the SPLL method.," A mass per cell limit gives higher spatial resolution in regions of high density, which is similar to the effective spatial resolution of the SPH method."526" A maximum mass er cell o£ 2.5«10?"" & (1260 AL.) was used to split the grid. which resultec in an AALR grid comprising 678815 octals and 4151706 unique cells."," A maximum mass per cell of $2.5\times 10^{36}$ g (1260 $\rm{M}_{\odot}$ ) was used to split the grid, which resulted in an AMR grid comprising 678815 octals and 4751706 unique cells."527 This mass per cell limit corresponds o approximately 9 SPL particles per grid cell (for particles with an average atomic hydrogen fraction) and was chosen to give sullicient spatial resolution to represent the important eatures of the model galaxy. within the constraints of the available computer memory.," This mass per cell limit corresponds to approximately 9 SPH particles per grid cell (for particles with an average atomic hydrogen fraction) and was chosen to give sufficient spatial resolution to represent the important features of the model galaxy, within the constraints of the available computer memory."528 Should. a caleulation require ugher spatial resolution. the mass per cell limit can be decreased to give smaller cells in the AMI grid (?)..," Should a calculation require higher spatial resolution, the mass per cell limit can be decreased to give smaller cells in the AMR grid \citep{douglas_2010}."529 Once the grid structure has been generated density. emperature ancl velocity values are assigned. to cach cell using values from the SPILL particles. smoothed with an exponential kernel.," Once the grid structure has been generated density, temperature and velocity values are assigned to each cell using values from the SPH particles, smoothed with an exponential kernel."530 Construction of an AMI grid from SPILL xuticles. using this method. was tested. by 2? using an azimuthally svmmetric circumstellar cise benchmark.," Construction of an AMR grid from SPH particles, using this method, was tested by \cite{Acreman09} using an azimuthally symmetric circumstellar disc benchmark."531 In the case of a spiral galaxy it is also necessary (o represent accurately structure. such as spiral arms. clouds ancl spurs. which are not present in an azimuthally svmiumetric disc.," In the case of a spiral galaxy it is also necessary to represent accurately structure, such as spiral arms, clouds and spurs, which are not present in an azimuthally symmetric disc."532 We founc that the method of ? gave a good representation of structure within the dise ancl a good. representation of the total mass provided: one mioclification was mace., We found that the method of \cite{Acreman09} gave a good representation of structure within the disc and a good representation of the total mass provided one modification was made.533 The method. normalises density values by the sum of the SPL kernel weights. if the sum of the weights exceeds a specified threshold. in order to reduce noise in the interior of the distribution.," The method normalises density values by the sum of the SPH kernel weights, if the sum of the weights exceeds a specified threshold, in order to reduce noise in the interior of the distribution."534 ? normalise when the sum of the weights exceeds 0.3. but we found this value gave a total mass which was too Large. by 11 per cent. relative to the mass of the SPL particles.," \cite{Acreman09}535 normalise when the sum of the weights exceeds 0.3, but we found this value gave a total mass which was too large, by 11 per cent, relative to the mass of the SPH particles."536 Phe SPL to erid conversion was performed with a range of normalisation thresholds. in order to test the impact on the representation of the total mass. and the results are plotted in Fig. I..," The SPH to grid conversion was performed with a range of normalisation thresholds, in order to test the impact on the representation of the total mass, and the results are plotted in Fig. \ref{fig:mass_err_vs_norm}."537 A normalisation threshold of 0.5 gives à mass which is too small by only 0.3 per cent.so we use this value as the threshold above which the SPILL kernel smooth is normalised.," A normalisation threshold of 0.5 gives a mass which is too small by only $0.3$ per cent,so we use this value as the threshold above which the SPH kernel smooth is normalised."538solar units). and the degree of contact F.,"solar units), and the degree of contact $F$."539 Table 2. contains the corresponding results for the system with (hereafter system 2).," Table \ref{obs2}540 contains the corresponding results for the system with (hereafter system 2)."541 Larger values for « than those included in the tables lead to configurations which are either close to instability or unstable., Larger values for $a$ than those included in the tables lead to configurations which are either close to instability or unstable.542 This shows again that the sources of the circulation extend deep into the secondary's interior., This shows again that the sources of the circulation extend deep into the secondary's interior.543 Tables | and 2 show that the results for different circulation functions are in close agreement., Tables \ref{obs} and \ref{obs2} show that the results for different circulation functions are in close agreement.544 The function c4 with «=0.5 represents a limiting case (o6. has the smallest possible value)., The function $c_1$ with $a=0.5$ represents a limiting case $a$ has the smallest possible value).545 If the results for this function (first line in the tables) is omitted. the agreement becomes excellent.," If the results for this function (first line in the tables) is omitted, the agreement becomes excellent."546 We conclude that the choice of the circulation function. (in a broad range) is unimportant as far as observable quantities are concerned., We conclude that the choice of the circulation function (in a broad range) is unimportant as far as observable quantities are concerned.547 In other words. the invariance encountered in Sect.," In other words, the invariance encountered in Sect."548 2.2 extends in a close approximation to all observable properties., \ref{inv} extends in a close approximation to all observable properties.549 This invariance suggests the use of a standard circulation function., This invariance suggests the use of a standard circulation function.550 We decided to use the function ¢ with a=., We decided to use the function $c_2$ with $a=0$.551 Consider next the effects of uncertainties in the free parameters., Consider next the effects of uncertainties in the free parameters.552 Results for system |. obtained using the standard circulation function. are listed in Table 3.. which ts expectedto cover the range of possible variations of the parameters.," Results for system 1, obtained using the standard circulation function, are listed in Table \ref{obs1}, which is expectedto cover the range of possible variations of the parameters."553 Changes in α have little influence. in accordance with a result from Fig. 5..," Changes in $\alpha$ have little influence, in accordance with a result from Fig. \ref{fig5}."554 An decrease in the efficiency fg leads mainly to an increase II F'(as it might have been expected) and to a decrease in the primary’s luminosity., An decrease in the efficiency $f_{\rm E}$ leads mainly to an increase in $F$ (as it might have been expected) and to a decrease in the primary's luminosity.555 A change in the temperature difference affects all observable properties. particularly. the light ratio.," A change in the temperature difference affects all observable properties, particularly the light ratio."556 Since these effects are only moderate. an approximate treatment of contact binaries is possible using standard values of the free parameters.," Since these effects are only moderate, an approximate treatment of contact binaries is possible using standard values of the free parameters."557 When getting a first survey of contact configurations in Sect., When getting a first survey of contact configurations in Sect.558 3. we shall use the values given in Eq. (10).," \ref{surv}559 we shall use the values given in Eq. \ref{stand}) )."560 In a next step observational tests can be used to improve these standard values., In a next step observational tests can be used to improve these standard values.561 In particular. Table 3 shows that reliable observed values for F can be used to calibrate the efficiency.," In particular, Table \ref{obs1}562 shows that reliable observed values for $F$ can be used to calibrate the efficiency."563 This will be done in Sect. 4.., This will be done in Sect. \ref{test}.564 We shall first consider system 2 às a typical example for the internal structure of the components and for the influence of the choice of the circulation function., We shall first consider system 2 as a typical example for the internal structure of the components and for the influence of the choice of the circulation function.565 Figure 7 shows the luminosity in the secondary’s interior as the sum of the radiative luminosity and the circulation luminosity. (, Figure \ref{fig7} shows the luminosity in the secondary's interior as the sum of the radiative luminosity and the circulation luminosity. (566The increase of the luminosity 1n the envelope escapes notice in this diagram.),The increase of the luminosity in the envelope escapes notice in this diagram.)567 The standard circulation function is used., The standard circulation function is used.568 Figure 8 shows the circulation luminosity in the secondary’s interior for all circulation functions listed in Table 2.., Figure \ref{fig8} shows the circulation luminosity in the secondary's interior for all circulation functions listed in Table \ref{obs2}. .569 It is manifest that two classes of functions are used., It is manifest that two classes of functions are used.570 The curve for the function e4 with, The curve for the function $c_1$ with571goes exactly in the direction of moving the voung (12 Gr) isochrone towards the observed sequence.,goes exactly in the direction of moving the young $\approx$ 12 Gyr) isochrone towards the observed sequence.572 However. Salaris. Chielli Straniero (1993) ceuantifiel the effect of O (the most abundant element among the CNO group and Ne) overabundance over the TO Iuminositv: an O overabundance by a factor of 4 would increase the TO level by 98V.~0.07 mag.," However, Salaris, Chieffi Straniero (1993) quantified the effect of O (the most abundant element among the CNO group and Ne) overabundance over the TO luminosity: an O overabundance by a factor of 4 would increase the TO level by $\delta V \sim 0.07$ mag."573 An unlikely ο) overabundance of zz 20 would be necessary to move the 12 Gyr isochrone to the level of the observed TO., An unlikely O overabundance of $\approx$ 20 would be necessary to move the 12 Gyr isochrone to the level of the observed TO.574 Note that spectroscopic [O/Fe] measurements of a few RCB-a stars (see Fig., Note that spectroscopic [O/Fe] measurements of a few RGB-a stars (see Fig.575 5 in Origlia et al., 5 in Origlia et al.576 2003) indicate only marginal (if anv) O overabundance., 2003) indicate only marginal (if any) O overabundance.577 In sunumnary. i( seems impossible to reconcile the TO level of a young (12 Cyr) metal rich isochrone with the observed feature.," In summary, it seems impossible to reconcile the TO level of a young $\approx 12$ Gyr) metal rich isochrone with the observed feature."578 Accurate measurements of C.N.Ne and O abundances for a significant number of SGB-a stars are urgently needed to check for possible anomalies. which could play some role in characterizing the morphology aud (he position of the SGD-a. Moreover. additional modeling with a detailed fine-tuning among ΑΕΕ. CNO and Ne abundances could indeed improve the agreement between old (14-16 Gyr) isochrones and the observed SGD-a morphology.," Accurate measurements of C,N,Ne and O abundances for a significant number of SGB-a stars are urgently needed to check for possible anomalies, which could play some role in characterizing the morphology and the position of the SGB-a. Moreover, additional modeling with a detailed fine-tuning among [M/H], CNO and Ne abundances could indeed improve the agreement between old (14-16 Gyr) isochrones and the observed SGB-a morphology."579 A number of papers (Lee οἱ al., A number of papers (Lee et al.580 1999. Hughes Wallerstein 2000. Hilker Richtler 2000. Rev et al.," 1999, Hughes Wallerstein 2000, Hilker Richtler 2000, Rey et al."581 2003) aigue. [rom indirect evidences. that the age of the most metal rich stellar population in «Cen is significantly (Al~4 Gyr) vounger (hat the most metal poor one.," 2003) argue, from indirect evidences, that the age of the most metal rich stellar population in $\omega$ Cen is significantly $\Delta t \sim 4 $ Gyr) younger that the most metal poor one."582" Under the hypothesis that the SGD-a is related to the Πα, we demonstrated [rom the direct detection of the TO. that this anomalous. metal rich population cannot be vounger than (the most metal poor one."," Under the hypothesis that the SGB-a is related to the RGB-a, we demonstrated from the direct detection of the TO, that this anomalous, metal rich population cannot be younger than the most metal poor one."583 This evidence excludes the possibility that such a metal rich population be the latest product of the sell-enrichment process in w Cen (as suggested by Rev et al., This evidence excludes the possibility that such a metal rich population be the latest product of the self-enrichment process in $\omega$ Cen (as suggested by Rey et al.584 2003J) and references therein). while it would support ils extra-cluster origin (see Ferraro. Dellazzini. Pancino 2002).," 2003 and references therein), while it would support its extra-cluster origin (see Ferraro, Bellazzini, Pancino 2002)."585 In (he scenario proposed by Bekki Freeman (2003). ω Cen is the complex stellar relic of a nucleated dwarf galaxy that merged in a remote epoch with the Galaxy (see also Dinescu et al.," In the scenario proposed by Bekki Freeman (2003), $\omega$ Cen is the complex stellar relic of a nucleated dwarf galaxy that merged in a remote epoch with the Galaxy (see also Dinescu et al."586 1999: Majewski et al., 1999; Majewski et al.587 2000)., 2000).588 Populations with different metallicities would be the result of subsequent radial eas inflows into the main body of the parent clwarl galaxy., Populations with different metallicities would be the result of subsequent radial gas inflows into the main body of the parent dwarf galaxy.589 This scenario can reasonably account for the genuine w Cen sub-populations at [Fe/II|S—1.0., This scenario can reasonably account for the genuine $\omega$ Cen sub-populations at $\lesssim-1.0$.590" Conversely, ihe anomalous. metal rich. population could be a small stellar svstem (a elobular cluster?)"," Conversely, the anomalous, metal rich population could be a small stellar system (a globular cluster?)"591 accreted by (the main body of w Cen during the disrupting interaction with the Galaxy., accreted by the main body of $\omega$ Cen during the disrupting interaction with the Galaxy.592 The assumption that w Cen could host a satellite elobular cluster is not fullyhoc. since both the other two known disrupting svstems in the Galaxy. (the Sagittarius clwarl spheroidal Ibata et al.," The assumption that $\omega$ Cen could host a satellite globular cluster is not fully, since both the other two known disrupting systems in the Galaxy (the Sagittarius dwarf spheroidal – Ibata et al."593 1994 and the Canis Major dwarf galaxy Ibata et al., 1994 and the Canis Major dwarf galaxy – Ibata et al.594 2003) have their own globular cluster system., 2003) have their own globular cluster system.595 A number of alternative hypothesis about the nature of the SGB-a become possible if, A number of alternative hypothesis about the nature of the SGB-a become possible if596(zz 20).,"$\approx5972\sigma$ )."598 This is tentative evidence that red 2MASS QSOs are more often radio sources than optically selected QSOs., This is tentative evidence that red 2MASS QSOs are more often radio sources than optically selected QSOs.599 ? have identified reddened 2MASS QSOs by preselecting candidates in the FIRST radio survey.," \cite{Glikman2007}600 have identified reddened 2MASS QSOs by preselecting candidates in the FIRST radio survey."601 Their radio selected reddened sample represents a substantial fraction of the overall radio detected QSO population. up to 60 per cent.," Their radio selected reddened sample represents a substantial fraction of the overall radio detected QSO population, up to 60 per cent."602 This finding further supports an association between red QSOs and radio emission., This finding further supports an association between red QSOs and radio emission.603 We caution that 2MASS QSOs are more luminous. on average. in the A-band than the SDSS ones.," We caution that 2MASS QSOs are more luminous, on average, in the $K$ -band than the SDSS ones."604 This is demonstrated in Figure 7 plotting the Adj distribution of the two samples., This is demonstrated in Figure \ref{fig_mkdist} plotting the $M_K$ distribution of the two samples.605 Although the radio detection rate of SDSS QSOs does not appear to depend on Aly it might be possible that the somewhat different radio detection rates of the two samples are because of 2MASS QSOs are more luminous., Although the radio detection rate of SDSS QSOs does not appear to depend on $M_K$ it might be possible that the somewhat different radio detection rates of the two samples are because of 2MASS QSOs are more luminous.606 Larger samples of reddened QSOs are needed to further explore possible differences in their radio emission compared to optically selected samples., Larger samples of reddened QSOs are needed to further explore possible differences in their radio emission compared to optically selected samples.607 The fraction of reddened QSOs within the overall population is still under debate with different studies suggesting values from 15 0o over 50 per cent (e.g2222).," The fraction of reddened QSOs within the overall population is still under debate with different studies suggesting values from 15 to over 50 per cent \citep[e.g][]{Richards2002, Wilkes2002, White2003,608Glikman2004}."609 The difficulty in assessing this Taction is that one has to take into account the effect on dust in he detectability of reddened QSOs. which in effect means that at a given magnitude limit one detects only the most luminous reddened QSOS.," The difficulty in assessing this fraction is that one has to take into account the effect on dust in the detectability of reddened QSOs, which in effect means that at a given magnitude limit one detects only the most luminous reddened QSOs."610 In this section we take this effect into account by estimating he maximum volume. Vmax. that a source could be detected taking into account the dust reddening and its luminosity.," In this section we take this effect into account by estimating the maximum volume, Vmax, that a source could be detected taking into account the dust reddening and its luminosity."611 First however. we directly compare the surface density of he 2MASS QSOs with those of optically selected ones.," First however, we directly compare the surface density of the 2MASS QSOs with those of optically selected ones."612 In the orevious section we counted 638 QSOs in the SDSS-DR3 catalogue of ? with A.<14.5 mmag that fulfill the ? criteria.," In the previous section we counted 638 QSOs in the SDSS-DR3 catalogue of \cite{Schneider2005}613 with $K<14.5$ mag that fulfill the \cite{Richards2002} criteria."614 Using the spectroscopic area of SDSS-DR3. 3732deg. we estimate a sky density of O.17dee> for optically selected QSOs to A=14.5 mmag.," Using the spectroscopic area of SDSS-DR3, $\rm 3732 \, deg^2$, we estimate a sky density of $\rm 0.17\,deg^{-2}$ for optically selected QSOs to $K=14.5$ mag."615" In contrast. we find 10 reddened 2MASS QSOs in the 5282deg? of the photometric SDSS-DR3 catalogue. which corresponds to a surface density of 0.002deg7. 2ddex lower than optically selected QSOs,"," In contrast, we find 10 reddened 2MASS QSOs in the $\rm 5282\, deg^2$ of the photometric SDSS-DR3 catalogue, which corresponds to a surface density of $\rm 0.002\,deg^{-2}$, dex lower than optically selected QSOs."616 The reddened 2MASS QSOs selected here appear to be very rare and therefore insignificant. in terms of numbers. for the overall population of QSOs.," The reddened 2MASS QSOs selected here appear to be very rare and therefore insignificant, in terms of numbers, for the overall population of QSOs."617 However. as shown in Figure 7 reddened QSOS are more luminous and the SDSS QSOs and it is therefore not surprising they are rarer.," However, as shown in Figure \ref{fig_mkdist} reddened QSOS are more luminous and the SDSS QSOs and it is therefore not surprising they are rarer."618 We address this issue using the [/Wmax formalism (e.g.2) to estimate the A-band luminosity function of the 2MASS QSOs relative to that of the overall QSO population., We address this issue using the 1/Vmax formalism \citep[e.g.][]{Lilly1995} to estimate the $K$ -band luminosity function of the 2MASS QSOs relative to that of the overall QSO population.619 For each source with intrinsic absolute magnitude τι the maximum volume Vmax is estimated given the selection function of the sample. i.e. A«14.5mmag. &@A>4 and JA&2.," For each source with intrinsic absolute magnitude $M_K$ the maximum volume Vmax is estimated given the selection function of the sample, i.e. $K<14.5$ mag, $R-K>4$ and $J-K>2$."620 For the calculation of magnitudes. colours and. k-corrections we adopt the SDSS composite QSO SED (?). and redden it by SMC type dust (?) assuming the optical extinction. εν. listed in Table 3..," For the calculation of magnitudes, colours and k-corrections we adopt the SDSS composite QSO SED \citep{VandenBerk2001} and redden it by SMC type dust \citep{Pei1992} assuming the optical extinction, $A_V$, listed in Table \ref{tab_restframe}."621 We then sum the |/Vmax of each source in Ady: luminosity bins., We then sum the 1/Vmax of each source in $M_K$ luminosity bins.622 The same procedure is repeated for the optically selected SDSS QSOs with ÁNx14.5 mmag. assuming ον=0 for this population.," The same procedure is repeated for the optically selected SDSS QSOs with $K<14.5$ mag, assuming $A_V=0$ for this population."623 In order to minimise evolution effects and to avoid high redshift sources for which lensing artificially boosts the observed luminosity (e.g. III. we only consider 2MASS and SDSS QSOs with 1.," In order to minimise evolution effects and to avoid high redshift sources for which lensing artificially boosts the observed luminosity (e.g. 11), we only consider 2MASS and SDSS QSOs with $z<1$ ."624 The results are shown in the inset plot of Figure 7.. which plots as a function of Adj the ratio of the 2MASS sources luminosity function over the total luminosity function of both 2MASS and SDSS QSOs.," The results are shown in the inset plot of Figure \ref{fig_mkdist}, , which plots as a function of $M_K$ the ratio of the 2MASS sources luminosity function over the total luminosity function of both 2MASS and SDSS QSOs."625" The fraction of reddened QSOs is increasing from cz32 percentat Aj,=27.5 to about 12+S per cent of the overall population at Aj;=—29.5.", The fraction of reddened QSOs is increasing from $\approx 3\pm2$ per cent at $M_K=-27.5$ to about $12\pm8$ per cent of the overall population at $M_K=-29.5$.626 This is evidence that reddened QSOs become important at bright luminosities., This is evidence that reddened QSOs become important at bright luminosities.627 We caution that small number statistics are an issue in this calculation., We caution that small number statistics are an issue in this calculation.628 Larger reddened QSO samples at magnitudes fainter than the 2MASS A=14.5 limit are needed to further explore this trend and to provide a more reliable measure of the reddened QSO fraction., Larger reddened QSO samples at magnitudes fainter than the 2MASS $K=14.5$ limit are needed to further explore this trend and to provide a more reliable measure of the reddened QSO fraction.629 Efforts to identify QSOs in the the UKIRT Infrared Deep Sky Survey (UKIDSS. dyz:15 mmag) including dust reddened ones. have recently appeared in the literature (2).. although the source selection is very different to that presented here.," Efforts to identify QSOs in the the UKIRT Infrared Deep Sky Survey (UKIDSS, $K\approx18$ mag) including dust reddened ones, have recently appeared in the literature \citep{Maddox2008}, although the source selection is very different to that presented here."630 This paper combines photometric data from the largest optical and near-IR surveys. SDSS and 2MASS. to select QSOs with red. optical/near-IR colours. which are atypical to those of the traditional population of optically selected broad-line QSOs.," This paper combines photometric data from the largest optical and near-IR surveys, SDSS and 2MASS, to select QSOs with red optical/near-IR colours, which are atypical to those of the traditional population of optically selected broad-line QSOs."631 It is shown that the UV/optical SEDs of the red QSOs can be explained by moderate amounts of dust extinction. ely=1.83.2.," It is shown that the UV/optical SEDs of the red QSOs can be explained by moderate amounts of dust extinction, $A_V=1.3-3.2$."632 An open question is whether red QSOs can be explained by orientation arguments. and therefore are a subset of optically selected QSOs. or they represent a different stage of the life of QSOs.," An open question is whether red QSOs can be explained by orientation arguments, and therefore are a subset of optically selected QSOs, or they represent a different stage of the life of QSOs."633 On the latter point. there is a large volume of literature on the possible evolution link between starbursts. QSOs and spheroids.," On the latter point, there is a large volume of literature on the possible evolution link between starbursts, QSOs and spheroids."634 Both observations (e.g.22222222?) and numerical simulations of major mergers (e.g.222) support such an association.," Both observations \citep[e.g.][]{Sanders1988, Sanders1996, Clements2000,635Canalizo2001, Komossa2003, Alexander2005, Veilleux2006,636Schweitzer2006, Dasyra2007} and numerical simulations of major mergers \citep[e.g.][]{DiMatteo2005, Springel2005, Hopkins2006} support such an association."637 It is proposed in particular. that some mechanism. possibly mergers. drive gas efficiently to the centralgalaxy regions. thereby triggering powerful starbursts and black hole growth at a high accretion rate.," It is proposed in particular, that some mechanism, possibly mergers, drive gas efficiently to the centralgalaxy regions, thereby triggering powerful starbursts and black hole growth at a high accretion rate."638 During this stage both the central engine the star-forming regions are, During this stage both the central engine the star-forming regions are639LíLpas. so should include a range of intrinisic spectral slopes.,"$L/L_{Edd}$, so should include a range of intrinisic spectral slopes."640 The mean L/Li; for the Sevfert T's in the sample is higher than that for Sevíiert 2s. consistent with the steeper spectral slope inferred for the Sevfert I's being due to the intrinsic spectrum softening at higher {ρω," The mean $L/L_{Edd}$ for the Seyfert 1's in the sample is higher than that for Seyfert 2's, consistent with the steeper spectral slope inferred for the Seyfert 1's being due to the intrinsic spectrum softening at higher $L/L_{Edd}$."641 We stress that samples of Sevfert 1 and 2 AGN need to be matched on intrinsic properties such as L/Lg in order to explore dillerences in orientation., We stress that samples of Seyfert 1 and 2 AGN need to be matched on intrinsic properties such as $L/L_{Edd}$ in order to explore differences in orientation.642 We construct a moderately sized sample of local hard X-ray detected AGN., We construct a moderately sized sample of local hard X-ray detected AGN.643 These data. shown in Table 1 2. are taken from Malizia (2003 - BeppoS.AX)). Zdziarski (2000 - OSSE) and Beckmann (2006 - TEGRAL)). resulting in a total sample of 47 AGN: 23 Sevflert Ls and 24 Sevfert 2s.," These data, shown in Table 1 2, are taken from Malizia (2003 - ), Zdziarski (2000 - ) and Beckmann (2006 - ), resulting in a total sample of 47 AGN; 23 Seyfert 1s and 24 Seyfert 2s."644 There is always some ambiguity in assigning objects as type lor 2. firstly as there are optical intermediate types. and secondly as the absorption environment is complex.," There is always some ambiguity in assigning objects as type 1 or 2, firstly as there are optical intermediate types, and secondly as the absorption environment is complex."645 There is (Compton thin) molecular gas in the plane of the galaxy as well as the much smaller scale (and. possibly Compton hick) molecular torus (Miiolino Rieke 1995). and these wo obscuring structures are not aligned (Nagar Wilson 1999: Schmitt et al 2002).," There is (Compton thin) molecular gas in the plane of the galaxy as well as the much smaller scale (and possibly Compton thick) molecular torus (Maiolino Rieke 1995), and these two obscuring structures are not aligned (Nagar Wilson 1999; Schmitt et al 2002)."646 Thus a face on (type 1) nucleus can be obseured at. both optical and NXrav. wavelengths. cacing to a type 2 classification (e.g. NCC 5506: Nagar et al 2002).," Thus a face on (type 1) nucleus can be obscured at both optical and X–ray wavelengths, leading to a type 2 classification (e.g. NGC 5506: Nagar et al 2002)."647 Nonetheless. these classifications are those for which he dillerence in N-ray. spectral index is claimed. so this is he only sample definition we can use to explore whether accretion rate can be the reason for this dillerence.," Nonetheless, these classifications are those for which the difference in X-ray spectral index is claimed, so this is the only sample definition we can use to explore whether accretion rate can be the reason for this difference."648 The black hole masses for the objects in the sample are derived. primarily from stellar velocity dispersion. (21 objects) and reverberation mapping (15 objects)., The black hole masses for the objects in the sample are derived primarily from stellar velocity dispersion (21 objects) and reverberation mapping (15 objects).649 For the remaining 11 sources the black hole masses are inferred from, For the remaining 11 sources the black hole masses are inferred from650 ~500pc). (=0.1pe ?.. 7.. 2)). 0.1pe) (210pc) ?.. ?.. ?: 2 7? + 3% mir)x9 (oe. 73) ," $\sim 500 ~ \rm pc$ $\lesssim 0.1 ~ \rm pc$ \\citealt{motte1998:ophiuchus}, \citealt{johnstone2000:rho_ophiuchi}, \citealt{hatchell2005:perseus}, \citealt{enoch2007:cloud_comparison}) $0.1 ~ \rm pc$ $\gtrsim 10 ~ \rm pc$ \citealt{williams1994:clumpfind}, \citealt{cambresy1999:extinction}, \citealt{kirk2006:scuba-perseus}; \citealt{williams2000:pp_iv} \citet{larson1981:linewidth_size} $r$ $^{\rm rd}$ $m(r) \propto r^2$ (e.g., \citealt{mckee2007:review}) )."651This vlaw of coustant coluuu density”(with respect to scale. r) is now considered oue of the fundamental properties of molecular cloud structure (e.g. 7.. 7.. 7)).," This “law of constant column density”(with respect to scale, $r$ ) is now considered one of the fundamental properties of molecular cloud structure (e.g., \citealt{ballesteros-paredes2007:ppv}, \citealt{mckee2007:review}, \citealt{bergin2007:dense-core-review}) )."652 We do. however. not know whether this relation is still consistent with up-to-date cohuun density maps of molecular Part I of the present series (7) describes a new echnique to extract niass-size relations from cloud maps.," We do, however, not know whether this relation is still consistent with up-to-date column density maps of molecular Part I of the present series \citep{kauffmann2010:mass-size-i}653 describes a new technique to extract mass-size relations from cloud maps."654" It is based on ""deudrogranmis a tree-based segmenutation of cloud. structure (2)..."," It is based on “dendrograms”, a tree-based segmentation of cloud structure \citep{rosolowsky2008:dendrograms}."655 Tere.. we eiaiplov. this tecliuique o study the inoleculu clouds im Perseus. Taurus. Ophiuchus. Orion. aud the Pipe Nebula.," Here, we employ this technique to study the molecular clouds in Perseus, Taurus, Ophiuchus, Orion, and the Pipe Nebula."656 To illustrate he properties of more nasxve clouds. we also include data for two more cistaut clouds of high density (further hau 2kpe: 0.31 and The present paper sununuarizes the analysis method iu refsecinethod..," To illustrate the properties of more massive clouds, we also include data for two more distant clouds of high density (farther than $2 ~ \rm kpc$; $-$ 0.34 and $-$ The present paper summarizes the analysis method in \\ref{sec:method}."657 The main quantitative analysis of the aps ds presented in refsecisanuple-analvsis., The main quantitative analysis of the maps is presented in \\ref{sec:sample-analysis}.658 Section |. systelatizes the results aud interprets thei iu the context of our present knowledge of star formation regions., Section \ref{sec:interpretation} systematizes the results and interprets them in the context of our present knowledge of star formation regions.659 This discussion is supported by model calculations in Appendices A and D.., This discussion is supported by model calculations in Appendices \ref{sec-app:mass-size-models} and \ref{sec-app:polytropes}.660" We conclude with a sunny in τοκος ΜΙΑΝ,", We conclude with a summary in \\ref{sec:summary}.661 Qur basic analysis approach is stumarized in 22.1 of part L aud illustrated in 11 of the same paper.," Our basic analysis approach is summarized in 2.1 of part I, and illustrated in 1 of the same paper."662 Iu essence. starting from a set of local maxima. we contour a eiven coluun densitymap at all levels possible.," In essence, starting from a set of local maxima, we contour a given column densitymap at all levels possible."663"Forevery contour. we derive the cuclosed mass and area. A.Following theterminology of?7.. we define ""cloud fragments” im the maps as such regions euclosed by a","Forevery contour, we derive the enclosed mass and area, $A$.Following theterminology of\citet{peretto2009:irdc-catalogue},, we define “cloud fragments” in the maps as such regions enclosed by a"664chemical potentials differ by about because interactions do contribute.,chemical potentials differ by about because interactions do contribute.665 The pressure is most sensitive to the interactions., The pressure is most sensitive to the interactions.666 Dased on this intormation we estimate fig=1230+150 MeV. The Hagedorn temperature was already. determined in (he late 1960s and early LOTO's to be 100 MeV [29]..., Based on this information we estimate $\mu_0 = 1230 \pm 150$ MeV. The Hagedorn temperature was already determined in the late 1960's and early 1970's to be 160 MeV \cite{Hagedorn}.667 The critical temperature. no matter what order the transition is. ought to be slightly greater than this [30]..," The critical temperature, no matter what order the transition is, ought to be slightly greater than this \cite{excluded}."668 Data from heavy ion collisions al the SPS and RIIIC show that no hadrons have ever been observed wilh a temperature greater Chan about 160 to 170 MeV (ab very small chemical potential) [31].., Data from heavy ion collisions at the SPS and RHIC show that no hadrons have ever been observed with a temperature greater than about 160 to 170 MeV (at very small chemical potential) \cite{statmodels}.669 Current lattice QCD calculations agree that with the physical values of the light and strange quark masses. (he (vansilion is a rapid crossover al zero chemical potential.," Current lattice QCD calculations agree that with the physical values of the light and strange quark masses, the transition is a rapid crossover at zero chemical potential."670 However. thev disagree on the so-called critical temperature.," However, they disagree on the so-called critical temperature."671 One group [32]. puts it at. 150MeV while the other group [33]. puts it at 190 MeV. Part of the discrepancy mav be in exactly how this temperature is defined. but that is not entirely sufficient.," One group \cite{Fodor} puts it at 150MeV while the other group \cite{HotQCD} puts it at 190 MeV. Part of the discrepancy may be in exactly how this temperature is defined, but that is not entirely sufficient."672 Certainty. (o accurately determine (his temperature requires an accurate caleulation of the low temperature hadronic equation of state.," Certainly, to accurately determine this temperature requires an accurate calculation of the low temperature hadronic equation of state."673 But (his requires very line lattice spacing. since the lattice must first discern the structure of individual hadrons. and it requires a very. large lattice volume. since (he hadrons become widely separated al low temperature.," But this requires very fine lattice spacing, since the lattice must first discern the structure of individual hadrons, and it requires a very large lattice volume, since the hadrons become widely separated at low temperature."674 This is a difficult problem which may not be resolved for some time., This is a difficult problem which may not be resolved for some time.675 However. it seems safe to estimate Zi=170+20 MeV. The value of the temperature al the critical point is of course not known.," However, it seems safe to estimate $T_0 = 170 \pm 20$ MeV. The value of the temperature at the critical point is of course not known."676" Ilowever. it should lie on or very near to the curve of 7"" versus po under discussion."," However, it should lie on or very near to the curve of $T$ versus $\mu$ under discussion."677" Low then can we estimate (he pressure /7.. energy. densitv e... entropy density. si. and barvon density 2, al the critical point?"," How then can we estimate the pressure $P_c$ , energy density $\epsilon_c$, entropy density $s_c$, and baryon density $n_c$ at the critical point?"678 One obvious way is (o use the formulas fora perfect massless gas of gluons and Vy flavors of quarks evaluated at 7; and ji., One obvious way is to use the formulas fora perfect massless gas of gluons and $N_f$ flavors of quarks evaluated at $T_c$ and $\mu_c$.679 These formulas are (yr is the barvon chemical potential aud quarks have one third of (hat value): p —EE ZO Mui oye 7S oun 2j po ZENbier n= Ogn17qo 8, These formulas are $\mu$ is the baryon chemical potential and quarks have one third of that value): P = ( 16 + ) T^4 + ^2 T^2 + ^4 s = ( 16 + ) T^3 + ^2 Tn = T^2 + ^3 = 3P .680We note that. for consistency. all fluxes used in our study are designed to befliices. which do not require aperture corrections.,"We note that, for consistency, all fluxes used in our study are designed to be, which do not require aperture corrections."681 For this reason. we also choose not to include SDSS spectroscopic information available for these galaxies. which is restricted to the inner 3-arcsec diameter aperture sampled by the SDSS spectroscopic tibre aperture.," For this reason, we also choose not to include SDSS spectroscopic information available for these galaxies, which is restricted to the inner 3-arcsec diameter aperture sampled by the SDSS spectroscopic fibre aperture."682 At the low redshifts of our galaxies. this limited spatial sampling could severely bias estimates of the star formation rate and dust content (?)..," At the low redshifts of our galaxies, this limited spatial sampling could severely bias estimates of the star formation rate and dust content \citep{Kewley2005}."683 In addition. spectroscopic quantities pertaining fo a restricted central area cannot be compared directly with multi-wavelength photometric quantities describing the whole galaxy.," In addition, spectroscopic quantities pertaining to a restricted central area cannot be compared directly with multi-wavelength photometric quantities describing the whole galaxy."684 It is instructive to examine the typical infrared luminosity oof the galaxies in our sample., It is instructive to examine the typical infrared luminosity of the galaxies in our sample.685" For this purpose. we compute from the 60- and fflux densities A"" and £2°° using the empirical formula (2) where Here. dj, is the luminosity distance in m. A"" and £2°° are in Jy. and aand Lj are in W. We compute the correction factor η. to obtain ffrom Lyi in equation CL following the empirical prescription of ET ?.. which: depends on the 17""iot(£10υπ... ratio.: and assuming: a dust emissivity index 7=2."," For this purpose, we compute from the 60- and flux densities $F_\nu^{60}$ and $F_\nu^{100}$ using the empirical formula \citep{Helou1988}686 where Here, $d_\mathrm{L}$ is the luminosity distance in m, $F_\nu^{60}$ and $F_\nu^{100}$ are in Jy, and and $L_\mathrm{FIR}$ are in W. We compute the correction factor $F_c$ to obtain from $L_\mathrm{FIR}$ in equation \ref{Helou1988_1}) ) following the empirical prescription of \cite{Helou1988}, , which depends on the $F_{\nu}^{60}/F_{\nu}^{100}$ ratio, and assuming a dust emissivity index $\beta=2$."687 The resulting median correction for our sample is ;=1.35., The resulting median correction for our sample is $F_c=1.35$.688 In Fig. |..," In Fig. \ref{fig1},"689 we plot the total dust infrared luminosity ccomputed in this way as a function of redshift., we plot the total dust infrared luminosity computed in this way as a function of redshift.690" A large fraction of the galaxies in our sample (about 22 per cent) have Lj""1045 Le ", A large fraction of the galaxies in our sample (about 22 per cent) have $\ldust > 10^{11}$ .691Such galaxies are usually referred to as. luminous infrared galaxies’ (LIRGs)., Such galaxies are usually referred to as `luminous infrared galaxies' (LIRGs).692" About | per cent of the galaxies of our sample have Lj""1077Le."," About 1 per cent of the galaxies of our sample have $\ldust >69310^{12}$."694" These galaxies with extremely high infrared luminosities are usually referred to as ""ultra-Iuminous infrared galaxies"" (ULIRGs).", These galaxies with extremely high infrared luminosities are usually referred to as `ultra-luminous infrared galaxies' (ULIRGs).695 This type of galaxies has been the object of extensive studies (e.g. 222222).," This type of galaxies has been the object of extensive studies (e.g. \citealt{Soifer1987,Veilleux1995,Veilleux1999,Rigopoulou1999,Cao2006,Armus2007}) )."696 In the local universe. most ULIRGs are observed to be the results of interactions and mergers.," In the local universe, most ULIRGs are observed to be the results of interactions and mergers."697 Visual inspection of the SDSS optical images confirms that ULIRGS in our sample also have disturbed morphologies., Visual inspection of the SDSS optical images confirms that ULIRGS in our sample also have disturbed morphologies.698 In Fig. 2..," In Fig. \ref{fig:dust2},"699 we compare the properties of our sample with the overall properties of the SDSS star-forming galaxy sample., we compare the properties of our sample with the overall properties of the SDSS star-forming galaxy sample.700 Fig., Fig.701 2aa shows that galaxies in our sample tend to lie at lower redshifts han the bulk of SDSS star-forming galaxies., \ref{fig:dust2}a a shows that galaxies in our sample tend to lie at lower redshifts than the bulk of SDSS star-forming galaxies.702 This results from the required detection by low-sensitivity oobservations., This results from the required detection by low-sensitivity observations.703 Fig., Fig.704 2bb further shows that galaxies in our sample end to have typically redder g+ colours than SDSS star-forming galaxies., \ref{fig:dust2}b b further shows that galaxies in our sample tend to have typically redder $g-r$ colours than SDSS star-forming galaxies.705 This is most probably a consequence of the higher dust content of our galaxies. which makes them detectable by," This is most probably a consequence of the higher dust content of our galaxies, which makes them detectable by."706"/RAS.. In ""uet. ?.seetheirfigure19 point out that SDSS galaxies detected by ihave systematically higher dust attenuation than the average SDSS star-forming galaxy."," In fact, \citet[][ see their figure70719]{Obric2006} point out that SDSS galaxies detected by have systematically higher dust attenuation than the average SDSS star-forming galaxy."708" The difference in the distributions of r- band absolute magnitude M,. in Fig.", The difference in the distributions of $r$ -band absolute magnitude $_r$ in Fig.709 2ce is more subtle to interpret., \ref{fig:dust2}c c is more subtle to interpret.710 This is illustrated by Fig., This is illustrated by Fig.711" 2dd. where we plot M, in different redshift bins for both samples."," \ref{fig:dust2}d d, where we plot $_{r}$ in different redshift bins for both samples."712 At redshifts 2«0.12. galaxies in our sample are typically brighter than SDSS star-forming galaxies.," At redshifts $z<0.12$, galaxies in our sample are typically brighter than SDSS star-forming galaxies."713 This is because SDSS galaxies with intrinsically faint. +-band magnitudes are too faint in the infrared to be detected by/RAS., This is because SDSS galaxies with intrinsically faint $r$ -band magnitudes are too faint in the infrared to be detected by.714. At redshifts το0.12. the SDSS and ddetection limits both correspond to similarly bright galaxies.," At redshifts $z>0.12$, the SDSS and detection limits both correspond to similarly bright galaxies."715 In this Section. we use the simple model of ? to extract star formation histories and dust contents from the ultraviolet. optical and infrared observations of the galaxy sample described in Section 2..," In this Section, we use the simple model of \citet{daCunha2008}716 to extract star formation histories and dust contents from the ultraviolet, optical and infrared observations of the galaxy sample described in Section \ref{dust:sample}."717 We first briefly summarise the model., We first briefly summarise the model.718 Then. we describe the statistical approach used to derive median-likelihood estimates of physical parameters from the available data.," Then, we describe the statistical approach used to derive median-likelihood estimates of physical parameters from the available data."719 The simple. physically motivated model of ? allows us to interpret the mid- and far-infrared spectral energy distributions of galaxies consistently with the emission at ultraviolet. optical and near-infrared. wavelengths.," The simple, physically motivated model of \citet{daCunha2008}720 allows us to interpret the mid- and far-infrared spectral energy distributions of galaxies consistently with the emission at ultraviolet, optical and near-infrared wavelengths."721 We briefly recall the main features of this model., We briefly recall the main features of this model.722 We compute the emission by stars in galaxies using the latest version ofthe ? population synthesis code (Charlot Bruzual. in preparation).," We compute the emission by stars in galaxies using the latest version ofthe \citet{Bruzual2003} population synthesis code (Charlot Bruzual, in preparation)."723 This code prediets the spectral evolution of stellar populations in galaxies from far-ultraviolet to far-infrared wavelengths and at ages between |10° and 2107 yr.," This code predicts the spectral evolution of stellar populations in galaxies from far-ultraviolet to far-infrared wavelengths and at ages between $1\times10^5$ and $2\times10^{10}$ yr,"724The lower panel of Figure 3. shows the corresponding plots of fo(0).,The lower panel of Figure \ref{fig:2ndfandg} shows the corresponding plots of $f_0 (\t)$.725" We see that in every case. ensuriug regularity of w, on the downstream: axis."," We see that in every case, ensuring regularity of $u_r$ on the downstream axis."726 This couclijon was uot imposed a priori. but resulted aiomatically [rom integration of the governiug equations.," This condition was not imposed a priori, but resulted automatically from integration of the governing equations."727 Specilically. the coellicient of fj in equatio (35)) iucludes cot0. wlich diverges atQ.," Specifically, the coefficient of $f_0^\prime$ in equation \ref{eqn:secondr2}) ) includes ${\rm cot}\,\theta$, which diverges at."728". Since all the other terms in this equation remain finite on the axis. //,(0) is forced to zero."," Since all the other terms in this equation remain finite on the axis, $f_0^\prime (0)$ is forced to zero."729 Which of these solutions is the true outer [ow for gas that is accreting steadily onto the eravitating mass?, Which of these solutions is the true outer flow for gas that is accreting steadily onto the gravitating mass?730 In principle. one could auswer tus question by continuing each solution inward. to see if the flow smooty crosses the sonic surface. whereL.," In principle, one could answer this question by continuing each solution inward, to see if the flow smoothly crosses the sonic surface, where."731. We sha| not attempt such a calculation here., We shall not attempt such a calculation here.732 Instead. we will oxoceed by deter:iniug generically the mass accretion rate that is associated with each outer solution.," Instead, we will proceed by determining generically the mass accretion rate that is associated with each outer solution."733 Then. given the Bouclt prescription for this rate. we will indeed be able to select the physical soltion for each 3.," Then, given the Bondi prescription for this rate, we will indeed be able to select the physical solution for each $\beta$ ."734 One could. in principle. equate coellicients of r tr ὃν ete.," One could, in principle, equate coefficients of $r^{-4}$, $r^{-5}$ , etc.,"735 and thereby obtain the coupled equations linkine higher-order f- and g-variables., and thereby obtain the coupled equations linking higher-order $f$ - and $g$ -variables.736 We will uow demonstrate. however. that the first- auc secoud-order equatious just. presented are sullicient to establish the total accretion rate onto the mass.," We will now demonstrate, however, that the first- and second-order equations just presented are sufficient to establish the total accretion rate onto the mass."737 We will then relate. in Section 5 below. this infall rate to the desired frictiou force.," We will then relate, in Section \ref{sec:friction} below, this infall rate to the desired friction force."738 Refer again to Figure 1 aud inagine a sphere of radius r surrounding the mass., Refer again to Figure \ref{fig:coord} and imagine a sphere of radius $r$ surrounding the mass.739" Reverting temporarily to dlinensional variables. the mass accretion rate is where we have utilized equation (1)) connecting «, and 4."," Reverting temporarily to dimensional variables, the mass accretion rate is where we have utilized equation \ref{eqn:ur}) ) connecting $u_r$ and $\psi$."740 Recall that (rx) is actually a constant. independent of kc. and that we have set that coustaut to zero.," Recall that $\psi (r,\pi)$ is actually a constant, independent of $r$, and that we have set that constant to zero."741 We thus have To noudimensionalize this result. we irst⋅ set the fiducial⋅ mass accretion⋅ rate torz.," We thus have To nondimensionalize this result, we first set the fiducial mass accretion rate to."742. Alter using the expansion of ον from equation (13)). we obtain the noucdimeusioualequatiou Oneof our boundary couditious. eusuwiug reeularity of πρ on the downstreai axis. is tliat," After using the expansion of $\psi$ from equation \ref{eqn:psind}) ), we obtain the nondimensionalequation Oneof our boundary conditions, ensuring regularity of $u_\theta$ on the downstream axis, is that"743This approximation allows far quicker coniputatio- since. when the first moments have Όσοι tabulated. oulv single integrals are required whereas the exact conrputation requires double iutegrals.,"This approximation allows far quicker computation since, when the first moments have been tabulated, only single integrals are required whereas the exact computation requires double integrals."744" Πωπονα, th Fokker-Plauck approach used to model the evolutiou of particle aud photon distributions is valid only ic reeions of the incident energv space (My.py) for whicco the relative. energy exchauge in one scattering ds sinall: Ap(py.Ug)/po<<Ll and Ἀνίρυνι)<<1. respectively."," However, the Fokker-Planck approach used to model the evolution of particle and photon distributions is valid only in regions of the incident energy space $(\nu_0,p_0)$ for which the relative energy exchange in one scattering is small: $\Delta p (p_0,\nu_0) /p_0 << 1$ and $\Delta \nu (p_0,\nu_0) / \nu(\nu_0) << 1$, respectively."745 These coucitious will be presented iu a fortheomiug publication (Belmont2008)., These conditions will be presented in a forthcoming publication \citep{Belmont08}.746. Iun contrast to the Fokker-Planck approximation. the integral approach is exact analytically.," In contrast to the Fokker-Planck approximation, the integral approach is exact analytically."747 However. when used to compute the evolution nuimericallw. it leads to sole nunierical issues directly related to the use of linear evids (Navalshin&Aelia1998).," However, when used to compute the evolution numerically, it leads to some numerical issues directly related to the use of non-linear grids \citep{NM98}."748". With logarithmic grids. the cnerev bin size is larecr at high οποίον,"," With logarithmic grids, the energy bin size is larger at high energy."749 For example when. low euergv plotous are upe-scattered from high energy. particles. their relative enerev eain ds high. and these photons are scattered muuerically from low energy bius to higher energy bius.," For example when, low energy photons are up-scattered from high energy particles, their relative energy gain is high, and these photons are scattered numerically from low energy bins to higher energy bins."750 During this interaction. the particles lose ouly a simall fraction of their οποίον.," During this interaction, the particles lose only a small fraction of their energy."751 If the euergev bin size is too lege. these particles remain iu them original bin and muuerically. they do not lose energy.," If the energy bin size is too large, these particles remain in their original bin and numerically, they do not lose energy."752 The euergy balance is uot therefore exactly satisfied aud the error can propagate aud become large when the deusitv of low eucrgv plotous is also high., The energy balance is not therefore exactly satisfied and the error can propagate and become large when the density of low energy photons is also high.753 Although less relevant to most astrophysical situations. a sviunetrical problem appears when high cherey photons are scattered by low energy. particles.," Although less relevant to most astrophysical situations, a symmetrical problem appears when high energy photons are scattered by low energy particles."754" This uuuerical issue is not prescut in regions of the incident cherev space (pg.rg) for which the scattered distributions are far wider than the energv biu «Ίσα: Ar(py.ty)νο).2»1 aud Ap(pog.ig)/po.>>1 for the evolution of the photon and particle distributions respectively,"," This numerical issue is not present in regions of the incident energy space $(p_0,\nu_0)$ for which the scattered distributions are far wider than the energy bin size: $\Delta \nu (p_0,\nu_0) /\delta\nu(\nu_0) >> 1$ and $\Delta p (p_0,\nu_0) /p_0 >> 1$ for the evolution of the photon and particle distributions respectively."755 After selecting the ranges and resolution of the photon and particle euergv erids. these conditions constrain the region in which the integral approach is valid.," After selecting the ranges and resolution of the photon and particle energy grids, these conditions constrain the region in which the integral approach is valid."756 Fortunately. the regions for which the iuteeral aud the Fokker-Plauck approaches are validare in part complementary.," Fortunately, the regions for which the integral and the Fokker-Planck approaches are validare in part complementary."757 The code therefore combines the two e For tho particle evolution: Iun the inteeral approach. the integration over the photon distribution iu Eq.," The code therefore combines the two $\bullet$ For the particle evolution: In the integral approach, the integration over the photon distribution in Eq."758 9. is oulv. completed above a even photon euergv (py) that depeuds ou the incideut particle energy. whereas the iuteerals ou frequency in Eq.," \ref{compt_e_int} is only completed above a given photon energy $\nu_c(p_0)$ that depends on the incident particle energy, whereas the integrals on frequency in Eq."759 ll are completed up to 7. in the Fokker-Plauck approach., \ref{Ac_e} are completed up to $\nu_c$ in the Fokker-Planck approach.760" The total time evolution is then eiven by the sim of both contributions: ON,=(EN.dep|(ON,τομ”", The total time evolution is then given by the sum of both contributions: $\partial_t N_{e^\pm} = \left(\partial_t N_{e^\pm}\right)_{\rm{FP}} + \left(\partial_t N_{e^\pm}\right)_{\rm{Integral}}$.761 e For the photon evolution: A similar combination is used for the photon equation. with the definition of a critical particle momenta p(14) nuder which the FP approach is used aud above which the integral approach is used.," $\bullet$ For the photon evolution: A similar combination is used for the photon equation, with the definition of a critical particle momentum $p_c(\nu_0)$ under which the FP approach is used and above which the integral approach is used."762 If the wmmber of energy. bius per decade is too small. the validity domains for both caleulations may become independecut and the accuracy of the computation may decrease.," If the number of energy bins per decade is too small, the validity domains for both calculations may become independent and the accuracy of the computation may decrease."763 This will be true. however. oulv for simall regions of the exids for which there are few particles aud plotous. corresponding to very sinall errors.," This will be true, however, only for small regions of the grids for which there are few particles and photons, corresponding to very small errors."764 By combining the two approaches. we find cuipirically that an energy resolution of typically 10 euergy bius per decade provides errors that are stualler than other trumecation errors.," By combining the two approaches, we find empirically that an energy resolution of typically 10 energy bins per decade provides errors that are smaller than other truncation errors."765 As for Compton scattering. we describe the pair production and annihilation. for the case of isotropic distributions of particles and photons.," As for Compton scattering, we describe the pair production and annihilation for the case of isotropic distributions of particles and photons."766" Single photou-photon pair production and pair anuililation eveuts are characterized by the differeutial CYOSS sectious CO.QR.1»>p) which corresponds to the pair (d.c. electrons or positrons) momentum spectrum produced by the recombination of photous of frequencies 74 aud Óm. and oa(po.py>r). which correspouds to the cussion spectrin generated by the annihilation of one electron of mmomentiun p and one positron of momenta py. respectively,"," Single photon-photon pair production and pair annihilation events are characterized by the differential cross sections $\sigma_{\rm p}(\nu_1,\nu_2\rightarrow p)$ which corresponds to the pair (i.e. electrons or positrons) momentum spectrum produced by the recombination of photons of frequencies $\nu_1$ and $\nu_2$ , and $\sigma_{\rm{a}}(p_-,p_+\rightarrow\nu)$, which corresponds to the emission spectrum generated by the annihilation of one electron of momentum $p_-$ and one positron of momentum $p_+$ , respectively."767 Then. the evolution of the distributious is described by: where. asx for Compton scatterimg. the zeroth noment of both the annihilation Προςτι adipopp)=Lffoeop»pde and the pairxodueed. distribution of(7.12)=[στο»pp rave beenused?.," Then, the evolution of the distributions is described by: where, as for Compton scattering, the zeroth moment of both the annihilation spectrum $\sigma^{\rm{a}}_0(p_-,p_+) =1/2\int \sigma_{\rm{a}}(p_-,p_+\rightarrow \nu ) d\nu$ and the pair-produced distribution $\sigma^{\rm{p}}_0(\nu_1,\nu_2) = 2\int \sigma_{\rm{p}}(\nu_1,\nu_2\rightarrow p ) dp$ have been."768. The analytical expressions for pliotou-photon pair production aud pair annihilation correspoud o Eqs. (, The analytical expressions for photon-photon pair production and pair annihilation correspond to Eqs. (76921-29) of Bocttcher&Schlickeiser(1997) aud Eqs. (,24-29) of \citet{BS97} and Eqs. (770"23.33.55-58) of Sveusson (1982a).. respectively,","23,33,55-58) of \citet{Svensson82a}, , respectively."771 Iu contrast to Compton scattering. there are no mnerical problemsi computing cirectly the inteeral over the particle and photon distributions. even forlow resolution eris.," In contrast to Compton scattering, there are no numerical problemsin computing directly the integral over the particle and photon distributions, even forlow resolution grids."772(2T (\INushotzky C BBarecr IlIloruschenieier (Ff>25.5) £A 2<1.5 (Crawford BBarecr 21.5. ἐν=0.23) (2=01). (2=020.10) BBautz :=2.8: SSoucail BBarecr ILlvisou (BBautz SSimail. FFabian 1)). (CCrawtord FFabian ,$2-7$ \markcite{mushotzky00}M \markcite{giacconi01}G \markcite{barger01}B \markcite{horn01}H $I>23.5$ $I-K$ $z<1.5$ \markcite{crawford00}C \markcite{barger01}B $z>1.5$ $z=0.23$ $z=0.37$ $z=0.2-0.4$ \markcite{bautz00}B $z=1.060$ $z=2.8$ \markcite{soucail99}S \markcite{barger99}B \markcite{ivison98}I \markcite{bautz00}B \markcite{smail97}S \markcite{fabian00}F \ref{figimage}) \markcite{crawford00}C \markcite{fabian00}F 773"However, the visibility of chemical species in low-resolution reflection spectra also depends strongly on the spectral spectral distribution of the incident stellar radiation, i.e. on the type of central star.","However, the visibility of chemical species in low-resolution reflection spectra also depends strongly on the spectral spectral distribution of the incident stellar radiation, i.e. on the type of central star."774" The reflection spectrum of an Earth-like planet around the M-type, for example, displays no Os or O» feature owing to the lack of incident stellar radiation in the respective wavelength range."," The reflection spectrum of an Earth-like planet around the M-type, for example, displays no $\mathrm O_3$ or $\mathrm O_2$ feature owing to the lack of incident stellar radiation in the respective wavelength range."775 Only in case of the K-type star can the O4 Chappuis-band be seen directly in the resolution reflection spectra at high cloud coverages., Only in case of the K-type star can the $\mathrm O_3$ Chappuis-band be seen directly in the low-resolution reflection spectra at high cloud coverages.776" In contrast to the case of reflection spectra, the spectral planetary albedos enable molecular features to be detected, excluding the direct influence of the spectral distribution of the stellar radiation."," In contrast to the case of reflection spectra, the spectral planetary albedos enable molecular features to be detected, excluding the direct influence of the spectral distribution of the stellar radiation."777" In particular, we investigated the impact of multi-layered clouds for cloud cover combinations yielding global mean Earth surface temperatures of 288K for each stellar type."," In particular, we investigated the impact of multi-layered clouds for cloud cover combinations yielding global mean Earth surface temperatures of $288 \ \mathrm{K}$ for each stellar type."778" Owing to the large amount of low-level clouds necessary for this surface temperature, the absorption bands of Os and Ο2 are noticeable in the low-resolution spectral albedos for K and M-type star cases, whereas O3 is not detectable at low cloud coverages yielding mean Earth surface temperatures for F and G-type star spectra."," Owing to the large amount of low-level clouds necessary for this surface temperature, the absorption bands of $\mathrm O_3$ and $\mathrm O_2$ are noticeable in the low-resolution spectral albedos for K and M-type star cases, whereas $\mathrm O_3$ is not detectable at low cloud coverages yielding mean Earth surface temperatures for F and G-type star spectra."779" Owing to the much higher stellar luminosities compared to the reflected light from the planet, the ratios between the radiation fluxes of the planets to their respective central stars are quite low at clear sky conditions (from 107! (see?,andreferences"," Owing to the much higher stellar luminosities compared to the reflected light from the planet, the ratios between the radiation fluxes of the planets to their respective central stars are quite low at clear sky conditions (from $10^{-10}$ \citep[see][and references therein for more details]{Stam2008A&A}."780provides an excellent review on the subject of the SE properties iu galaxies. aud the depenudeucies on different factors such as the IIubble morphological type. preseuce of bars. interactions. and eas content. for both disks aud circeunnuclear regions.,"provides an excellent review on the subject of the SF properties in galaxies, and the dependencies on different factors such as the Hubble morphological type, presence of bars, interactions, and gas content, for both disks and circumnuclear regions."781 However. most previous works ou circunmnuclear SE properties were based on iuteerated properties rather than on the study of the properties of the individual regions.," However, most previous works on circumnuclear SF properties were based on integrated properties rather than on the study of the properties of the individual regions."782 We briefly sunumniiudze our main results. classed im three categories. below.," We briefly summarize our main results, classed in three categories, below."783 We find that the physical properties of individual circummnmclear regious. as represcuted bv typical regions (imnediau Io bdunünositv and size) aud by first ranked regions (the most Iuninous aud the largest regions). are not stronely cepeudent on the morphological ype of the host galaxy.," We find that the physical properties of individual circumnuclear regions, as represented by typical regions (median $\alpha$ luminosity and size) and by first ranked regions (the most luminous and the largest regions), are not strongly dependent on the morphological type of the host galaxy."784 Also. we find no relationship vetween the ΠΙΟ of eicumnuuclear regious per unit area and the morphological type.," Also, we find no relationship between the number of circumnuclear regions per unit area and the morphological type."785 The behavior of the physical properties of cireiunnumclear regions is in clear contrast with that of disk regions which teud to be arecr. brighter and more nuncrous (per uit area) for late ype spiral aud iegular galaxies (Ixeunnicutt 19858: IKEIT).," The behavior of the physical properties of circumnuclear regions is in clear contrast with that of disk regions which tend to be larger, brighter and more numerous (per unit area) for late type spiral and irregular galaxies (Kennicutt 1988; KEH)."786 Whereas the morphological type does not sec to  oue of the dominaut factors im deteriuniug the physical properties of the iudividual circiuunuuclear regions. it does influence the global cireuunuclear SE xoperties.," Whereas the morphological type does not seem to be one of the dominant factors in determining the physical properties of the individual circumnuclear regions, it does influence the global circumnuclear SF properties."787 The Ta luninosities over the central kpe (ouly owed uponu enuüsson from regious) are significautlv Chhanced in early-type (80/a.Sb) galaxies when conipare with late-tvpe galaxies, The $\alpha$ luminosities over the central kpc (only based upon emission from regions) are significantly enhanced in early-type (S0/a–Sb) galaxies when compared with late-type galaxies.788 This confiniis the findings of Bokker et al. (, This confirms the findings of Bökker et al. (7891999) for the average central surface Pan xiehtuesses region and diffuse cussion) over the field of view of the nuages. aud other studies base upon optical spectroscopy (c.g.. Πο et al.,"1999) for the average central surface $\alpha$ brightnesses region and diffuse emission) over the field of view of the images, and other studies based upon optical spectroscopy (e.g., Ho et al."790 L99Ta aux references there).," 1997a,b and references therein)."791 When the SFR per muit stellar mass are compared with the morphological type. the trem disappears because it is offset by a trend in the opposite direction. where earlier type galaxies teud to have more massive bulges than later type galaxies.," When the SFR per unit stellar mass are compared with the morphological type, the trend disappears because it is offset by a trend in the opposite direction, where earlier type galaxies tend to have more massive bulges than later type galaxies."792 A relation between the preseuce of a bar and the properties of the ciremuunuclear SF ois expected since bars are predicted to provide an cfiicicut nechauisui to transport eascousx imaterial from the disks of galaxies iuto the central regions. and as a consequence bars may trigecr the SF iu the circumauuelear regions of galaxies.," A relation between the presence of a bar and the properties of the circumnuclear SF is expected since bars are predicted to provide an efficient mechanism to transport gaseous material from the disks of galaxies into the central regions, and as a consequence bars may trigger the SF in the circumnuclear regions of galaxies."793 Tudeed. barred galaxies have cuhanced Πα buuinosities (anostlv occurmug in early type galaxies) aud SER per nuit stellar mass (or iuteerated pseudo equivalent width of Pan) over the ceutral 1 kpe area when compared to uubarred galaxies.," Indeed, barred galaxies have enhanced $\alpha$ luminosities (mostly occurring in early type galaxies) and SFR per unit stellar mass (or integrated pseudo equivalent width of $\alpha$ ) over the central 1 kpc area when compared to unbarred galaxies."794 Whereas the nuuber of regions per area or per unit stellar mass are not enhanced in barred with respect to non-barred galaxies. the first-ranked reeious (both iu ternis of diameter and bunuinositv) are on average more hnuuinous and larger in barred than iu uubaired ealaxies.," Whereas the number of regions per area or per unit stellar mass are not enhanced in barred with respect to non-barred galaxies, the first-ranked regions (both in terms of diameter and luminosity) are on average more luminous and larger in barred than in unbarred galaxies."795 This iu conjuction with results frou many other works provide further evidence that bars are cficicnut iu trieecring the SF in the central regions of ealaxies. although. as pointed out amone others by To et al. (," This in conjuction with results from many other works provide further evidence that bars are efficient in triggering the SF in the central regions of galaxies, although, as pointed out among others by Ho et al. ("79619975). the presence of a bar is neither a necessary nor a sufficient condition for SF to occur.,"1997b), the presence of a bar is neither a necessary nor a sufficient condition for SF to occur."797 We have analyzed the LFs aud inteeral diameter distributions of the cight ealaxies i our sample with oue iudred or nore cieunmuclear regions., We have analyzed the LFs and integral diameter distributions of the eight galaxies in our sample with one hundred or more circumnuclear regions.798 The LFs of he circumnmnuclear regions extend to Io. huninosities oflosL(lla) =38.3B8.8cresLowhereas iu galaxies with eulanced SF the LFs reach logL(Ila)=39.7eres|.," The LFs of the circumnuclear regions extend to $\alpha$ luminosities of $\log L({\rm H}\alpha) = 79938.3-38.8\,{\rm erg}\,{\rm800s}^{-1}$, whereas in galaxies with enhanced SF the LFs reach $\log L({\rm H}\alpha) = 39.7\,{\rm erg}\,{\rm801s}^{-1}$."802 We fitted power law slopes of the circumunuclear region LFs. of between a=2.5 anda Ξξντ values which are exactly within the range of slopes reported for spiral disks roni erouncd-based observations (¢c.e.. 1ΤΟΠ).," We fitted power law slopes of the circumnuclear region LFs, of between $\alpha=-2.3$ and $\alpha = -1.7$, values which are exactly within the range of slopes reported for spiral disks from ground-based observations (e.g., KEH)."803 This suggests hat the physical processes determine the massive SE in disks and cireununuclear resions must be common., This suggests that the physical processes determining the massive SF in disks and circumnuclear regions must be common.804 Although we can only ft slopes to the region LFs or a very Buited number of galaxies. we do coufiim the relation between LF slope aud galaxy type. with late type ealaxies showing shallower LEs.," Although we can only fit slopes to the region LFs for a very limited number of galaxies, we do confirm the relation between LF slope and galaxy type, with late type galaxies showing shallower LFs."805 The integral diameter distributions for these cight ealaxies are fitted with power laws whose indices are im arelatively good agreement with those predicted from the LF. assuming that the regions are iouization-bomnded. within a iecdimm of uniform density.," The integral diameter distributions for these eight galaxies are fitted with power laws whose indices are in a relatively good agreement with those predicted from the LF, assuming that the regions are ionization-bounded within a medium of uniform density."806 We fud. however. that the more commuouly used exponential fori provides fits of simular statistical significance.," We find, however, that the more commonly used exponential form provides fits of similar statistical significance."807 With the detailed analvsis of narrow baud IIo: aud Pan inages of spiral galaxies obtained with theZEST. we lave recently entered a new era in researcli on extragalactic regions (Pleuss et al.," With the detailed analysis of narrow band $\alpha$ and $\alpha$ images of spiral galaxies obtained with the, we have recently entered a new era in research on extragalactic regions (Pleuss et al."808 2000: Scoville et al., 2000; Scoville et al.809 2001: this paper)., 2001; this paper).810 One of the main conclusions from all these works is that although bleuding may affect results based on eround-based narrow-band nuaegius. one of the main paralcters describing statistical euseimbles of regious fromLST data. namely the slope of the LE. is still within the previously observed values.," One of the main conclusions from all these works is that although blending may affect results based on ground-based narrow-band imaging, one of the main parameters describing statistical ensembles of regions from data, namely the slope of the LF, is still within the previously observed values."811 The recent couchisious emereine from studies usingT imaging. which are based either ou partial imagine of the disk of one individual ealaxy. or. as in our case. on maging of the cireiunmnuclear parts oulv of a sample of spiral galaxies. will need to be confirmed by more extensive studies using high-resolution narrow-baud imaging. but contain iaportaut clues to the nuderling physical processes of massive SF iu galaxies.," The recent conclusions emerging from studies using imaging, which are based either on partial imaging of the disk of one individual galaxy, or, as in our case, on imaging of the circumnuclear parts only of a sample of spiral galaxies, will need to be confirmed by more extensive studies using high-resolution narrow-band imaging, but contain important clues to the underlying physical processes of massive SF in galaxies."812 We are grateful to an anonymous referee for useful conmunenuts that helped inprove the paper., We are grateful to an anonymous referee for useful comments that helped improve the paper.813 It is a pleasure to thank Dr. €. IT. Heller for providing us with the software. used to analyze the properties of the regions. and Drs.," It is a pleasure to thank Dr. C. H. Heller for providing us with the software, used to analyze the properties of the regions, and Drs."814 J.E. Beckman and A. Zurita for conmunents on an earlier version of the manuscript., J.E. Beckman and A. Zurita for comments on an earlier version of the manuscript.815 This research bas made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory. California Institute of Technology. under contract with the National Aeronautics and Space Achuimistration.," This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration."816Quasars and narrow-line radio galaxies (NLRGs) may be unified by orientation-dependent obscuration.,Quasars and narrow-line radio galaxies (NLRGs) may be unified by orientation-dependent obscuration.817 Raclio galaxies are thought to host quasar nuclei (hat are obscured by circummnuclear dusty tori aligned with the radio jets (Antonueci1984).., Radio galaxies are thought to host quasar nuclei that are obscured by circumnuclear dusty tori aligned with the radio jets \citep{ant84} .818 Unification of radio galaxies and quasars can therefore explain (he lack of quasars viewed al large angles to the radio axis (Barthel1989)., Unification of radio galaxies and quasars can therefore explain the lack of quasars viewed at large angles to the radio axis \citep{b89}.819. The percentage of high-redshift radio galaxies of the 3CRR FR I sample al 2> 0.5) would then indicate a torus covering Iraction of ~0.6., The percentage of high-redshift radio galaxies of the 3CRR FR II sample at $z>0.5$ ) would then indicate a torus covering fraction of $\sim 0.6$.820 IIowever. there appears to be a discrepancy between the redshift distributions of quasars and radio galaxies al 2< 0.5. with a [actor of ~4 more narrow-line radio galaxies than quasars (Singal1993).," However, there appears to be a discrepancy between the redshift distributions of quasars and radio galaxies at $z<0.5$ with a factor of $\sim 4$ more narrow-line radio galaxies than quasars \citep{s93}."821. Furthermore. (he median projected linear size of (hese “excess” radio ealaxies is smaller (han expected for quasars seen in the skv plane 2005).," Furthermore, the median projected linear size of these 'excess' radio galaxies is smaller than expected for quasars seen in the sky plane \citep{s93,w05}."822. The unification hypothesis may be mocilied to include a second population of lower luminosity. low-excitation FR. II radio galaxies (Wall&Jackson1997:Grimes.&Willott/| 2004).," The unification hypothesis may be modified to include a second population of lower luminosity, low-excitation FR II radio galaxies \citep{wj97,grw04}."823.. Alternatively. it has been arguedthat the torus covering fraction may increase will decreasing radio luminosity (Lawrence1991).," Alternatively, it has been arguedthat the torus covering fraction may increase with decreasing radio luminosity \citep{l91}."824. The unification hypothesis has been qualitatively confirmed by. spectropolarimetry. of radio galaxies. many of which have been shown to have highly polarized broad emission lines and blue continuum. scattered [rom material which has a direct. view of the active galactic nucleus (C*hmaitietal.1997:Cohen1999).," The unification hypothesis has been qualitatively confirmed by spectropolarimetry of radio galaxies, many of which have been shown to have highly polarized broad emission lines and blue continuum, scattered from material which has a direct view of the active galactic nucleus \citep{cdb97, cot99}."825.. Of particular note are the original discovery of highly polarized broad Ho from the hidden quasar nucleus in 3C 234 1984).. aud (he discovery of highly polarized broad Ha in the spectrum of the powerhu radio ealaxv Cygnus A (Oegleοἱal.1997).," Of particular note are the original discovery of highly polarized broad $\alpha$ from the hidden quasar nucleus in 3C 234 \citep{ant84}, and the discovery of highly polarized broad $\alpha$ in the spectrum of the powerful radio galaxy Cygnus A \citep{ocm97}."826. However. this method of detecting hidden cuasars relies on an appropriately placed scattering region to view the otherwise hidden nucleus.," However, this method of detecting hidden quasars relies on an appropriately placed scattering region to view the otherwise hidden nucleus."827 Such a region is not guaranteed to exist lor all radio galaxies. and thus spectropolarimetry can easily vield false negatives.," Such a region is not guaranteed to exist for all radio galaxies, and thus spectropolarimetry can easily yield false negatives."828 Polarimetry is also ineffective al determining the luminosity ol the hidden nucleus. since the scattering efficiency is usually unknown.," Polarimetry is also ineffective at determining the luminosity of the hidden nucleus, since the scattering efficiency is usually unknown."829 Another wav to seareh for hidden quasar nuclei is to observe radio galaxies in the mid-IR., Another way to search for hidden quasar nuclei is to observe radio galaxies in the mid-IR.830 If the unification hypothesis is correct. the dusty torus should serve as a crude calorimeter of ihe central engine (Meisenheimeretal.2001:Siebenmorgenοἱ2004:ΠαςWhvsong&Antonucei 2004).," If the unification hypothesis is correct, the dusty torus should serve as a crude calorimeter of the central engine \citep{mhm01,sfk04,hmb04,wa04}."831. Optical. UV. and. X-rav. photons [from the quasar nucleus are absorbed by dust in the torus and the energy. is re-emitted in the thermal infrared.," Optical, UV, and X-ray photons from the quasar nucleus are absorbed by dust in the torus and the energy is re-emitted in the thermal infrared."832 This explains why blue. UV color-selected quasars emit. of their Iuminositv in the Ih (Sandersetal1989:Haasοἱal.2000).," This explains why blue, UV color-selected quasars emit of their luminosity in the IR \citep{spn89,hmc00}."833. There appears to be no connection between the bulk of this IX emission and nonthermal radio emission. except in core-dominated radio sources such as blazars.," There appears to be no connection between the bulk of this IR emission and nonthermal radio emission, except in core-dominated radio sources such as blazars."834 Observations of matched 3CR quasars and radio galaxies by ISO indicate similar HR. luminosities.consistent with the unification picture 2004)...," Observations of matched 3CR quasars and radio galaxies by ISO indicate similar IR luminosities,consistent with the unification picture \citep{mhm01,hmb04}. ."835 Llowever. differences in 24 μπα 70 jan color max indicate that," However, differences in 24 $\mu$ m/ 70 $\mu$ m color may indicate that"836"outflow velocities of a few hundred kms~! by blastwave feedback, and slows down as it sweeps the ISM and halo material.","outflow velocities of a few hundred $\kms$ by blastwave feedback, and slows down as it sweeps the ISM and halo material."837" The peak velocity is comparable to those observed in high redshift LBGs (e,g.,Adelbergeretal.al. 2010)."," The peak velocity is comparable to those observed in high redshift LBGs \citep[e,g.,][]{Adelberger03,Veilleux05,Steidel10}."838". It is also comparable to the velocities adopted in various kinetic feedback models (e.g.,Springel&Hern- 2011)."," It is also comparable to the velocities adopted in various kinetic feedback models \citep[e.g.,][]{Springel03,Oppenheimer06,DallaVecchia08,Wiersma09,Choi11}."839". After reaching a peak value, the gas’ proper velocity declines rapidly, and particles are swept by the Hubble flow as they move farther from the center into the IGM."," After reaching a peak value, the gas' proper velocity declines rapidly, and particles are swept by the Hubble flow as they move farther from the center into the IGM."840 This behaviour is typical of all enriched gas particles., This behaviour is typical of all enriched gas particles.841" The rapid decline of the proper velocity is also seen in the kinetic feedback model of DallaVecchia&Schaye (2008),, where outflowing particles are allowed to interact hydrodyamically with the ISM, and pressure forces within the disk significantly decrease the wind speed."," The rapid decline of the proper velocity is also seen in the kinetic feedback model of \citet{DallaVecchia08}, where outflowing particles are allowed to interact hydrodyamically with the ISM, and pressure forces within the disk significantly decrease the wind speed."842" Observations of local starburst galaxies (e.g.,Schwartz&Martin2004;Rupkeetal.2005) have shown that outflow speeds are correlated with halo masses and star formation rates, and that the correlation flattens out for SFR»10Moyr! (Rupkeetal.2005)."," Observations of local starburst galaxies \citep[e.g.,][]{Schwartz04, Rupke05} have shown that outflow speeds are correlated with halo masses and star formation rates, and that the correlation flattens out for $>10\,\sfr$ \citep{Rupke05}."843". To investigate the existence of such relationship in the ErisMC simulation, we plot in the upper panel of Figure 15 the peak velocity of gas particles that become unbound after they are enriched in the main host, as a function of their enrichment redshift."," To investigate the existence of such relationship in the ErisMC simulation, we plot in the upper panel of Figure \ref{fig15} the peak velocity of gas particles that become unbound after they are enriched in the main host, as a function of their enrichment redshift."844" We choose the gas peak velocity as this is close to the flow speed when the wind is launched, and is relatively unaffected by interactions between the outflow and the ISM/gaseous"," We choose the gas peak velocity as this is close to the flow speed when the wind is launched, and is relatively unaffected by interactions between the outflow and the ISM/gaseous"845 256x256 1.., $\times$ \ref{si}.846 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup ," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ "847 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup ," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $"848 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup d," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d"849 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup d," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_"850 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup d," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{"851 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup d," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\"852 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup d," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\r"853 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup d," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm"854 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup d," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm "855 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup da," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm G"856 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daa," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Ga"857 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daau," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Gau"858 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daaus," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Gaus"859 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daauss," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Gauss"860 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daauss," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Gauss}"861 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daauss=," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Gauss}="862 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daauss=," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Gauss}= "863 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daauss=," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Gauss}= 864"865 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daauss=3," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Gauss}= 8663"867 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daauss=30," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Gauss}= 86830"869 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daauss=30," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Gauss}= 87030\"871 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daauss=30," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Gauss}= 87230\,"873 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daauss=30," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Gauss}= 87430\,{"875 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daauss=30," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Gauss}= 87630\,{\"877 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daauss=30," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Gauss}= 87830\,{\r"879 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daauss=30m," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Gauss}= 88030\,{\rm"881 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daauss=30m," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Gauss}= 88230\,{\rm "883 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daauss=30m," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Gauss}= 88430\,{\rm m"885 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daauss=30ma," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Gauss}= 88630\,{\rm ma"887 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daauss=30mas," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Gauss}= 88830\,{\rm mas"889 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daauss=30mas," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Gauss}= 89030\,{\rm mas}"891 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daauss=30mas," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Gauss}= 89230\,{\rm mas}\"893 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daauss=30mas," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Gauss}= 89430\,{\rm mas}\p"895 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daauss=30mas," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Gauss}= 89630\,{\rm mas}\pm"897 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daauss=30mas+," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Gauss}= 89830\,{\rm mas}\pm "899 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daauss=30mas+8," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Gauss}= 90030\,{\rm mas}\pm 8"901 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daauss=30mas+8," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Gauss}= 90230\,{\rm mas}\pm 8\"903 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daauss=30mas+8," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Gauss}= 90430\,{\rm mas}\pm 8\,"905 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daauss=30mas+8," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Gauss}= 90630\,{\rm mas}\pm 8\,{"907 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daauss=30mas+8," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Gauss}= 90830\,{\rm mas}\pm 8\,{\"909 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daauss=30mas+8," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Gauss}= 91030\,{\rm mas}\pm 8\,{\r"911 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daauss=30mas+8m," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Gauss}= 91230\,{\rm mas}\pm 8\,{\rm"913 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daauss=30mas+8m," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Gauss}= 91430\,{\rm mas}\pm 8\,{\rm "915 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daauss=30mas+8m," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Gauss}= 91630\,{\rm mas}\pm 8\,{\rm m"917 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daauss=30mas+8ma," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Gauss}= 91830\,{\rm mas}\pm 8\,{\rm ma"919 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daauss=30mas+8mas," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Gauss}= 92030\,{\rm mas}\pm 8\,{\rm mas"921 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daauss=30mas+8mas," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Gauss}= 92230\,{\rm mas}\pm 8\,{\rm mas}"923 x ~ (— um. 2 f.. f>0.7f. 2)). fc. daausdup daauss=30mas+8mas," $\times$ $\sim$ $=$ $\mu$ \ref{vis} $f_{\rm c}$ $f>0.7\,f_{\rm c}$ \ref{vis}) $f_{\rm c}$ $d_{\rm Gauss}$$d_{\rm UD}$ $d_{\rm Gauss}= 92430\,{\rm mas}\pm 8\,{\rm mas}$"925We use spherical coordinatization (r.0.6): jj and jj) are the spherical Bessel function aud its derivative: jj(AR)= 0.,"We use spherical coordinatization $(r,\theta , \phi )$ ; $j_1$ and $j_1'$ are the spherical Bessel function and its derivative; $j_1(kR)=0$ ."926 The magnetic field (2)) is the field of the minimal energy for a given helicity with a zero uormal component on the surface of the sphere of radius 2. The importance of helicity for the problem of stability is well known and explained in the next subsection (see AruoldaudIEIxhesin(1998). for discussion anc references).," The magnetic field \ref{mfield}) ) is the field of the minimal energy for a given helicity with a zero normal component on the surface of the sphere of radius $R$, The importance of helicity for the problem of stability is well known and explained in the next subsection (see \citet{arn} for discussion and references)."927 The free parameters of the initial coufiguration are tlie radius of the star Ze. the radius of the magnetized region A. the densities of the maguetized aud uumagnuetizedregions py and pe. aud the amplituce of the field By.," The free parameters of the initial configuration are the radius of the star $R_s$, the radius of the magnetized region $R$ , the densities of the magnetized and unmagnetizedregions $\rho _1$ and $\rho _2$, and the amplitude of the field $B_0$."928 To simplify the proof of stability we assume that the stratification is ↜∖⋃⋅∩∐∑≟↥⊽∖⇁⊳∖↕⋜↕∣≻↥≺↵⋅∕↗↓∶∕≥∖∕∖∕↗⊇⋅⋜↕∐≺⇂↕∐≺↵∐↕⋜↕∑≟∐≺↵⋃∢∙∐≺↵↥≺⊔⊳∖∖∖↽≺↵⋜↕↥⊆⋅∪∣↗↕∫↿≱−∕∖∕≥∖∕∖≵≩−∣⋅.," To simplify the proof of stability we assume that the stratification is strongly stable, $\rho_1\gg \rho_2$, and the magnetic field is weak, $G\rho _1^2R^2\gg B_0^2$."929 . ⋅ ⋅ ⋉⋅↽≻⋅↽≻∖⋅≻ Assume incompressibility aud ideal conductivity., Assume incompressibility and ideal conductivity.930 Then an equilibrium configuration is an extremmun of the total (gravitational plus magnetic) energy. under. incompressible cdeformations ol the star aud the maguetic field (comoving deusity coustant. maguetic field frozeu into the fIukl).," Then an equilibrium configuration is an extremum of the total (gravitational plus magnetic) energy under incompressible deformations of the star and the magnetic field (comoving density constant, magnetic field frozen into the fluid)."931 Stable equilibrium is the minunum of the energy. uncer incompressible clelormatious., Stable equilibrium is the minimum of the energy under incompressible deformations.932 The initial configuratiouOm is not an equilibrium. because the eeravitational euergvC is at a 1iinimui-— while the magnetic energy is not extremal.," The initial configuration is not an equilibrium, because the gravitational energy is at a minimum, while the magnetic energy is not extremal."933 The Ampere forcejxB does vanish inside the maguetized region due to (3))., The Ampere force ${\bf j} \times {\bf B}$ does vanish inside the magnetized region due to \ref{rot}) ).934 But there is a singular Ampere force on the boundary of the imaguetized region at r=2., But there is a singular Ampere force on the boundary of the magnetized region at $r=R$.935 This force acts in the clirection of deforminug the sphere into au oblate spheroicl., This force acts in the direction of deforming the sphere into an oblate spheroid.936 Cousider the set of all coufigious which can be obtained from (1..2)) by incompressible deformations.," Consider the set of all configurations which can be obtained from \ref{dens}, \ref{mfield}) ) by incompressible deformations."937 We will show that the miuimuurenergy coufiguration belongiug to the set is close to the initial configuration., We will show that the minimum-energy configuration belonging to the set is close to the initial configuration.938 Iu particular. the boundary of the magnetized region ofthe configuration is an aXisviumetric oblate spheroid close to a sphere (in the mean square deviation seuse).," In particular, the boundary of the magnetized region of the minimum-energy configuration is an axisymmetric oblate spheroid close to a sphere (in the mean square deviation sense)."939 The idea of the proof is straightforward., The idea of the proof is straightforward.940 A deformatiou of the star causes a deformation of the bouudary of the maguetized high-density region., A deformation of the star causes a deformation of the boundary of the magnetized high-density region.941" Let e(0.6) be the deviation of thedeformed boundary [rom the sphere: Forpy3» pa. the change of the gravitational energy dW, is afunctional of € ouly. after normalizing"," Let $\psi (\theta , \phi )$ be the deviation of thedeformed boundary from the sphere: For$\rho_1\gg \rho_2$ , the change of the gravitational energy $\delta W_g$ is afunctional of $\psi$ only, after normalizing"942a few simplifications can be made.,a few simplifications can be made.943" We can reduce the number of parameters by one if we transform the orientation and ellipticity parameters to their projected counterparts: Here q, and F, are the same parameters introduced earlier, and q=qy/q. is the projected axis ratio."," We can reduce the number of parameters by one if we transform the orientation and ellipticity parameters to their projected counterparts: Here $q_x$ and $F_z$ are the same parameters introduced earlier, and $q = q_y / 944q_x$ is the projected axis ratio."945" The parameter q, is the ratio of the projected major axis to the triaxial major axis of the halo.", The parameter $q_x$ is the ratio of the projected major axis to the triaxial major axis of the halo.946" It might be objected that we cannot perform this reduction since the characteristic density ó,, has an explicit dependence on the axis ratios a/c,b/c through the triaxial overdensity A, (see 5)."," It might be objected that we cannot perform this reduction since the characteristic density $\delta_{ce}$ has an explicit dependence on the axis ratios $a/c, b/c$ through the triaxial overdensity $\Delta_e$ (see $~\ref{delta_eq}$ )."947" However, this dependence simply scales the kappa profile and thus can be accounted for by redefining the F; parameter as F,=(c?Jab*]Af, where f is defined in eq. 8.."," However, this dependence simply scales the kappa profile and thus can be accounted for by redefining the $F_z$ parameter as $F_z = (c^2/ab)^{0.75}/ \sqrt{f}$, where $f$ is defined in eq. \ref{fgh_eq}."948 For simplicity we neglect scatter in the mass-luminosity relation and halo concentration., For simplicity we neglect scatter in the mass-luminosity relation and halo concentration.949 We will investigate later (see §??)) how the scatter might affect the calculation., We will investigate later (see \ref{sec:results}) ) how the scatter might affect the calculation.950" Another simplification can be made by first noting that the average image separation, in the absence of ellipticity, is very well approximated by ©~2Rg where Κε is the Einstein radius; or, in the units defined above, ©~2."," Another simplification can be made by first noting that the average image separation, in the absence of ellipticity, is very well approximated by $\Theta 951\approx 2 R_E$ where $R_E$ is the Einstein radius; or, in the units defined above, $\tilde\Theta \approx 2$."952" Introducing ellipticity changes the proportionality by a certain amount; however, c,, q,, F, and z simply scale the Einstein radius without significantly altering this relation."," Introducing ellipticity changes the proportionality by a certain amount; however, $c_e$, $q_x$, $F_z$ and $z$ simply scale the Einstein radius without significantly altering this relation."953" We find that the image separations resulting from the dark matter halo is fit well by the form, where M is the mass of the halo."," We find that the image separations resulting from the dark matter halo is fit well by the form, where $M$ is the mass of the halo."954" Likewise, the Hernquist component is well fit by Both models are conceived so that a(M)=2 when q=1."," Likewise, the Hernquist component is well fit by Both models are conceived so that $\alpha(M) = 2$ when $q = 1$."955" Finally, we model the total image separation © by a fitting function of the form The advantage of this approach is that, for a given image separation ©, we can easily find the total mass of the lens as a function of the other parameters, M(c,q,du.qx,F;), and likewise for dM/dO."," Finally, we model the total image separation $\tilde\Theta$ by a fitting function of the form The advantage of this approach is that, for a given image separation $\Theta$, we can easily find the total mass of the lens as a function of the other parameters, $M(c,q,q_H,q_x,F_z)$, and likewise for $dM/d\Theta$."956 This reduces the number of parameters by one., This reduces the number of parameters by one.957" Thus we are left with the following independent variables on which the cross sections depend: To simplify the analysis, rather than taking gy as an independent variable we will investigate two cases: first, we assume the ellipticities of galaxy and halo are strictly correlated; second, we assume different fixed values of qj."," Thus we are left with the following independent variables on which the cross sections depend: To simplify the analysis, rather than taking $q_H$ as an independent variable we will investigate two cases: first, we assume the ellipticities of galaxy and halo are strictly correlated; second, we assume different fixed values of $q_H$."958" Our motivation is that since the ellipticities of the adiabatically-contracted halos are still not well understood, the extent to which the ellipticities are correlated is unknown."," Our motivation is that since the ellipticities of the adiabatically-contracted halos are still not well understood, the extent to which the ellipticities are correlated is unknown."959 Undoubtedly the true distribution of ellipticities will lie somewhere between these two extreme cases., Undoubtedly the true distribution of ellipticities will lie somewhere between these two extreme cases.960" If we assume that q and 4η are completely uncorrelated, we can simplify the analysis by fixing gy at various values including its mean observed value."," If we assume that $q$ and $q_H$ are completely uncorrelated, we can simplify the analysis by fixing $q_H$ at various values including its mean observed value."961" Several studies have analyzed the isophotal shapes of E/SO galaxies in various surveys, the distribution of which is typically well fit by a Gaussian: dn/deeexp[-(e—e)/2€)], where e=(1-q2)/(0.+q;). ?. studied galaxies in the Coma cluster and found e;=0.26,Ae0.33, whereas ? studied 847 E/SO galaxies in SDSS and found &=0.22,Ae0.14."," Several studies have analyzed the isophotal shapes of E/S0 galaxies in various surveys, the distribution of which is typically well fit by a Gaussian: $dn / d\epsilon \propto exp[-(\epsilon-\epsilon_0)^2/2\Delta 962\epsilon^2]$, where $\epsilon = (1-q_H^2)/(1+q_H^2).$ \cite{keeton97} studied galaxies in the Coma cluster and found $\epsilon_0 = 0.26, \Delta \epsilon = 9630.33$, whereas \cite{hao06} studied 847 E/S0 galaxies in SDSS and found $\epsilon_0 = 0.22, \Delta \epsilon = 0.14$."964" The Coma distribution has a mean value at (4η)=0.67, which we will use for the uncorrelated case unless otherwise noted."," The Coma distribution has a mean value at $\langle q_H \rangle = 0.67$, which we will use for the uncorrelated case unless otherwise noted."965" On the other hand, if we make the simplifying assumption that q and 6η are strictly correlated, we can relate them directly by gy=q+Aq where Aq is a fixed increment (or simply qu=1.0 if g>1.0— Aq)."," On the other hand, if we make the simplifying assumption that $q$ and $q_H$ are strictly correlated, we can relate them directly by $q_H = q + \Delta q$ where $\Delta q$ is a fixed increment (or simply $q_H = 1.0$ if $q > 1.0 - \Delta q$ )."966" We will investigate both the correlated and uncorrelated cases, taking Aq=0.1 for the correlated case."," We will investigate both the correlated and uncorrelated cases, taking $\Delta q = 0.1$ for the correlated case."967 We will calculate dP/dO at specific values of z; these variables will be integrated over at the end., We will calculate $dP /d\Theta$ at specific values of $z$; these variables will be integrated over at the end.968" To do the integral we first calculate the values of o over a regular grid in the remaining three parameters (q,q,,F;) and then interpolate to find its value at any given point."," To do the integral we first calculate the values of $\sigma$ over a regular grid in the remaining three parameters $(q,q_x,F_z)$ and then interpolate to find its value at any given point."969" The interpolation is done by an N-dimensional analogue of bicubic interpolation, whereby the function values, its partial derivatives, and higher-order mixed partial derivatives are tabulated on a regular grid (the derivatives being calculated in this case by finite differencing across adjacent grid points)."," The interpolation is done by an N-dimensional analogue of bicubic interpolation, whereby the function values, its partial derivatives, and higher-order mixed partial derivatives are tabulated on a regular grid (the derivatives being calculated in this case by finite differencing across adjacent grid points)."970 The interpolating function is a cubic polynomial in the N variableswhose coefficients are uniquely determined by matching its values and derivatives to the tabulated values on the grid., The interpolating function is a cubic polynomial in the N variableswhose coefficients are uniquely determined by matching its values and derivatives to the tabulated values on the grid.971" Thus the resulting function is constrained to have the tabulated values on the grid, and also to vary smoothly from point to point. ("," Thus the resulting function is constrained to have the tabulated values on the grid, and also to vary smoothly from point to point. ("972"For a detailed derivation of the three-dimensional case, see ?..)","For a detailed derivation of the three-dimensional case, see \cite{lekien05}. .)"973" With o in hand, we integrate over the axis ratios and line-of-sight angles (which are the remaining lens parameters in eq. 2))"," With $\sigma$ in hand, we integrate over the axis ratios and line-of-sight angles (which are the remaining lens parameters in eq. \ref{eq:lens_parameters}) )"974" using the Vegas algorithm, and finally integrate over redshift to obtain the image separation distribution."," using the Vegas algorithm, and finally integrate over redshift to obtain the image separation distribution."975" Throughout this paper we plot the image separation distribution for a source placed at a redshift of z,= 2.0;", Throughout this paper we plot the image separation distribution for a source placed at a redshift of $z_s = 2.0$ ;976the outburst state is nios closely associated with large scale X-ray [lux variations.,the outburst state is most closely associated with large scale X-ray flux variations.977" ""he second. observation of Z Cam was made curing a (ransion to outburst ancl showed a dramatic decrease in the ccoun rate (see also 2)).", The second observation of Z Cam was made during a transition to outburst and showed a dramatic decrease in the count rate (see also \ncite{baskill01}) ).978 This is normal behaviour for dwarl novae., This is normal behaviour for dwarf novae.979 The observation of SS Cvg. made towards the end of an Ouburst. also shows a decreasing count rate reffig:ssevgaavsoxrav)). although in this case the variation OOS Lοι appear to be part of the outburst to quiescence ransiion.," The observation of SS Cyg, made towards the end of an outburst, also shows a decreasing count rate \\ref{fig:sscygaavsoxray}) ), although in this case the variation does not appear to be part of the outburst to quiescence transition."980 SU UMa was observed to be brightening during 1e second. half of the outburst. and its lightcurve is plotted in reffig:suumaaavsoxravy..," SU UMa was observed to be brightening during the second half of the outburst, and its lightcurve is plotted in \\ref{fig:suumaaavsoxray}."981 Phe only overall trend detected in a Leseent chvarl nova was in WAV Cet. which faded during --s I3hh observation.," The only overall trend detected in a quiescent dwarf nova was in WW Cet, which faded during its h observation."982 The, The983calibration uncertainties for the MOS at low energies).,calibration uncertainties for the MOS at low energies).984 We fitted the combined MOS and PN spectra using different models: initially a power-law. a blackbody and a combination of both. each modified by photoelectric absorption (wabs in XSPEC).," We fitted the combined MOS and PN spectra using different models: initially a power-law, a blackbody and a combination of both, each modified by photoelectric absorption (wabs in XSPEC)."985 The best-fit results are sunnmarized in Table 1.., The best-fit results are summarized in Table \ref{tab_spec}.986 The 4? values indicate that the spectrum is better represented by a thermal (blackbody) model. rather (han by an absorbed power-law.," The $\chi^{2}$ values indicate that the spectrum is better represented by a thermal (blackbody) model, rather than by an absorbed power-law."987 The additional power law component in the third (and fifth) fit is poorly constrained. ancl not required: by applying an F-test. we find an F-statistie of 1.6 and probability of 0.2.," The additional power law component in the third (and fifth) fit is poorly constrained, and not required: by applying an $F$ -test, we find an $F$ -statistic of 1.6 and probability of 0.2."988 The best-fit blackbody fit gives Ny=0.26x107 ? and TX=1.62x105 IK (where 7* is the blackbody temperature measured adEarth?: see Figure L.. first and second panels).," The best-fit blackbody fit gives $N_{H} = 0.26 \times 10^{22}$ $^{-2}$ and $T^\infty = 1.62 \times 10^6$ K (where $T^\infty$ is the blackbody temperature measured ad; see Figure \ref{fig_spec}, first and second panels)."989" We notice that. consistently. this value for the hydrogen column densitv is lower than the Galactic one in the source direction. which is Vy~0.84x1077 7. while the same argument can only be applied mareinally (within the lower limit of the error bars) to the value of Ny, inferred [rom the power-law fit."," We notice that, consistently, this value for the hydrogen column density is lower than the Galactic one in the source direction, which is $N_H \sim 0.84 \times 10^{22}$ $^{-2}$, while the same argument can only be applied marginally (within the lower limit of the error bars) to the value of $N_H$ inferred from the power-law fit."990" The radius of the emitting region. as derived [rom the blackbody fit using the Cordes&Lazio(2002) distance. is Roy,=1.66τρ kin."," The radius of the emitting region, as derived from the blackbody fit using the \citet{cor02} distance, is $R_{em}=1.66^{+0.59}_{-0.39}$ km."991 In order to attempt. a different representation of the thermal emission detected [romB23344+61.. we used a magnetized. pure IL atmospheric model (nsa in XSPEC. [or details see Pavlovetal. 1995)). by fixing the magnetic field al 2.—10! G. the value inferred. from (the radio timing measurements of the source.," In order to attempt a different representation of the thermal emission detected from, we used a magnetized, pure H atmospheric model (nsa in XSPEC, for details see \citealt{pav95}) ), by fixing the magnetic field at $B=10^{13}$ G, the value inferred from the radio timing measurements of the source."992" The neutron star mass and radius (neasured αἱ (he source) were fixed al AJ,=1.4M and R=10 km. respectively. although the spectral fit is not particularly sensitive (o (hese parameters (see [or an a posteriori estimate of the mass)."," The neutron star mass and radius (measured at the source) were fixed at $M_{ns}= 1.4 M\sun$ and $R=10$ km, respectively, although the spectral fit is not particularly sensitive to these parameters (see \\ref{disc} for an a posteriori estimate of the mass)."993" We found that (this model also provides an excellent representation of the pulsar spectrum. and the best-fit parameters are ? and T,=0.58xI0"" IX. where 775, is the effective temperature as measured ab Earth? (see Table 1))."," We found that this model also provides an excellent representation of the pulsar spectrum, and the best-fit parameters are $N_{H} = 0.42 \times 10^{22}$ $^{-2}$ and $T_{eff}^\infty = 0.58 \times 99410^{6}$ K, where $T_{eff}^\infty$ is the effective temperature as measured at $^2$ (see Table \ref{tab_spec}) )."995 However. this fit gives a pulsar distance of D=1.140.6 kpe. lower than (hat inferred from the value of the electron density (D=3.112 kpe. 2002)).," However, this fit gives a pulsar distance of $D=1.1\pm0.6$ kpc, lower than that inferred from the value of the electron density $D=3.1^{+0.2}_{-1.0}$ kpc, \citealt{cor02}) )."996 Although the pulsar distance and radius are poorly constrained by our data. we find that a better agreement can be reached by using the same atmospheric model anc fixing the neutron star radius at a slightly larger value of 13 kan.," Although the pulsar distance and radius are poorly constrained by our data, we find that a better agreement can be reached by using the same atmospheric model and fixing the neutron star radius at a slightly larger value of $13$ km."997" In this case. we find μις0.33x107? ? and T5,=0.65x10* IN (see Table 1 and Figure 1.. third and fourth panels)."," In this case, we find $N_{H}= 0.33\times 10^{22}$ $^{-2}$ and $T_{eff}^\infty= 0.65\times 99810^{6}$ K (see Table \ref{tab_spec} and Figure \ref{fig_spec}, third and fourth panels)."999 The distance resulting from this fit is D=3.241.7 kpe. which is consistent. with the electron density distance.," The distance resulting from this fit is $D=3.2\pm 1.7$ kpc, which is consistent with the electron density distance."1000 Finally. we verified (hat even when the thermal component is modeled by a neutron star atmosphere. an additional power law is not required (last fit in Table 1 ).," Finally, we verified that even when the thermal component is modeled by a neutron star atmosphere, an additional power law is not required (last fit in Table \ref{tab_spec}) )."100166574 (Lindt-Kriegetal.2008).. 22782 (Huntetal. 2008).. 33147 (Casasolaetal.2008a).. and 44579 (García-Burilloetal.2009).,"6574 \citep{lindt-krieg08}, 2782 \citep{leslie08}, 3147 \citep{vivi08a}, and 4579 \citep{santi09}."1002. The common feature shared by these galaxies is a slowly rotating stellar bar (or oval) with overlapping dynamical resonances (Casasolaetal.2008b) associated with kinematically decoupled inner bars or ovals., The common feature shared by these galaxies is a slowly rotating stellar bar (or oval) with overlapping dynamical resonances \citep{vivi08b} associated with kinematically decoupled inner bars or ovals.1003 Such resonances and kinematic decoupling are fostered by a large central mass concentration and high gas. fraction., Such resonances and kinematic decoupling are fostered by a large central mass concentration and high gas fraction.1004 us the unique potential NUGA galaxy with only one slowly rotating stellar bar., is the unique potential NUGA galaxy with only one slowly rotating stellar bar.1005 For3627.. this drives a molecular bar-like structure. apparently sufficient to transport the gas toward the AGN that. in a second step. could fuel directly the active nucleus.," For, this drives a molecular bar-like structure, apparently sufficient to transport the gas toward the AGN that, in a second step, could fuel directly the active nucleus."1006wilh those of νΙ2010. which suggest (hat each svstem may have evolved to ils present state through a process ol stable mass transler.,"with those of vK2010, which suggest that each system may have evolved to its present state through a process of stable mass transfer."1007 Our approach differs from theirs by using a different prescription for the radius of the donor star prior to envelope exhaustion., Our approach differs from theirs by using a different prescription for the radius of the donor star prior to envelope exhaustion.1008" Whereas vIN2010 used a formula for the radius which depends on only the core mass of the donor. our formula also incorporates the dependence on its equilibrium stellar mass M,. prior to the last phase of mass transfer."," Whereas vK2010 used a formula for the radius which depends on only the core mass of the donor, our formula also incorporates the dependence on its equilibrium stellar mass $M_\ast,$ prior to the last phase of mass transfer."1009 This has (wo effects., This has two effects.1010 First our approach tends to predict somewhat smaller values of the white dwarf mass., First our approach tends to predict somewhat smaller values of the white dwarf mass.1011 This will be tested through radial velocity measurements. and Equation (1) can be adjusted if needed. based on (he observations.," This will be tested through radial velocity measurements, and Equation (1) can be adjusted if needed, based on the observations."1012 Second. it allows thes period measurement to constrain both the white dwarf mass and the mass of the donor. thereby. providing useful input [or detailed evolutionary models.," Second, it allows the period measurement to constrain both the white dwarf mass and the mass of the donor, thereby providing useful input for detailed evolutionary models."1013 We also take seriously the possibility that the masses of IXOI-74b and IXOLI-SIb are in the brown dwarf range. so that (he formalism we and vIxX2010 have applied is not valid.," We also take seriously the possibility that the masses of KOI-74b and KOI-81b are in the brown dwarf range, so that the formalism we and vK2010 have applied is not valid."1014 We lind an interesting new evolutionary pathway., We find an interesting new evolutionary pathway.1015 In this case. there is a third body (hat pumps up the eccentricity of an inner binary.," In this case, there is a third body that pumps up the eccentricity of an inner binary."1016 Mass (transfer [rom (he primary to the secondary occurs at periastron. in analogy (o the mass transfer process in high-mass x-ray binaries.," Mass transfer from the primary to the secondary occurs at periastron, in analogy to the mass transfer process in high-mass x-ray binaries."1017 As the orbit evolves. eventually the primary experiences a dvnamical time scale instability al periastron. leading to a common envelope phase.," As the orbit evolves, eventually the primary experiences a dynamical time scale instability at periastron, leading to a common envelope phase."1018 During the common envelope. the orbit circularizes and (he core of the primary spirals closer to ils main-sequence companion. bul avoiding a merger.," During the common envelope, the orbit circularizes and the core of the primary spirals closer to its main-sequence companion, but avoiding a merger."1019 The signature that such an evolution has occurred is à white dwarf in a wider orbit (han expected had there been either stable mass transfer of a common envelope initiated rom a circular orbit., The signature that such an evolution has occurred is a white dwarf in a wider orbit than expected had there been either stable mass transfer of a common envelope initiated from a circular orbit.1020 We do not know if this scenario is needed to explain either IXOI-14 or IXOI-51. but i£ it occurs in nature.Kepler may find binaries (hat have evolved in this wav.," We do not know if this scenario is needed to explain either KOI-74 or KOI-81, but if it occurs in nature, may find binaries that have evolved in this way."1021 Whatever the nature of IXOI-74 and NOLS]. their discovery inspires us to compute the frequency of transits by white dwarls in binaries that have experienced mass transfer.," Whatever the nature of KOI-74 and KOI-81, their discovery inspires us to compute the frequency of transits by white dwarfs in binaries that have experienced mass transfer."1022 In many ol these cases. (he companion star has gained mass [rom the progenitor of the white dwarf and may be considered to be a field blue straggler.," In many of these cases, the companion star has gained mass from the progenitor of the white dwarf and may be considered to be a field blue straggler."1023 We have done a set of preliminary ealeulations io estimate the number of such white dwarls that transit stars in theAepler field., We have done a set of preliminary calculations to estimate the number of such white dwarfs that transit stars in the field.1024 Although our model may be viewed as a “lov model it allows us to parameterize the uncertainties involved in the complex physics needed to predict the details of the binary evolutions., Although our model may be viewed as a “toy model” it allows us to parameterize the uncertainties involved in the complex physics needed to predict the details of the binary evolutions.1025 We lind (hat. under a wide range of reasonable assumptions. roughly 0.0025—0.0075 of svstenis of the (wpe monitored byKepler should exhibit white dwarl transits.," We find that, under a wide range of reasonable assumptions, roughly $0.0025-0.0075$ of systems of the type monitored by should exhibit white dwarf transits."1026 It would be surprising if fewer than LOO transiting cdwarls were discovered byορίου. while it is possible (hat more than 1000 will be found.," It would be surprising if fewer than $100$ transiting s were discovered by, while it is possible that more than $1000$ will be found."1027 Furthermore. evidence of gravitational lensing is expected in 10—20% of the (transits: anti-Uransits may be observed in 1/3—1/2 of the cases in which there are lensing," Furthermore, evidence of gravitational lensing is expected in $10-20\%$ of the transits; anti-transits may be observed in $1/3-1/2$ of the cases in which there are lensing"1028"inside which embryos reach 103, within 10! vears (Equation (10))) is estimated to be much stnaller than AAU: a massive disk is likely to rnm gas ejut planets.","inside which embryos reach $10\,M_\oplus$ within $10^7$ years (Equation \ref{eq:crit_dis}) )) is estimated to be much smaller than AU; a massive disk is likely to form gas giant planets."1029" Embryos inside AAU of a ~ LOSAIAISN disk exceed final eiibryo masses Af, due to the accretion of small bodies drifting roni outside.", Embryos inside AU of a $\sim 10\times$ MMSN disk exceed final embryo masses $M_{\rm a}$ due to the accretion of small bodies drifting from outside.1030 Iu spite of such further erowth. Clubrvos starting from snall planetesinials ciunot reach the critical core mass ~10AL).," In spite of such further growth, embryos starting from small planetesimals cannot reach the critical core mass $\sim 10\,M_\oplus$."1031 Ii addition. urther erowth is insignificant bevoud AAT," In addition, further growth is insignificant beyond AU."1032", The foxiimlae for Mj aud e, suggest that initial anetesiaals with ry250. ΗΕ necessary or embryos to reach 1037, at SAAT in the LOS MMSN disk."," The formulae for $M_{\rm a}$ and $a_{\rm c}$ suggest that initial planetesimals with $r_0 \simeq 50$ km are necessary for embryos to reach $10\,M_\oplus$ at AU in the $10\times$ MMSN disk."1033 Iuaba et al. (, Inaba et al. (1034"2003) performed similar siaiulations incorporating collisional fagmcutation audeunblaucemoenut due to the embryos atmosphere aud showed a planetary core with AL>LOAD), could be produced around AAU with iny=L2«10! ee (ry=10 κα) for 10 MMSN,",2003) performed similar simulations incorporating collisional fragmentation and enhancement due to the embryo's atmosphere and showed a planetary core with $M>10M_\oplus$ could be produced around AU with $m_0 = 4.2 \times 10^{18}$ g $r_0=10$ km) for $10\times$ MMSN.1035" Ii our simulation. einibrvos cannot reach LOA), under this condition and larger planctesimals are uccessary to form. such massive eiibrvos bevoudAA."," In our simulation, embryos cannot reach $10M_\oplus$ under this condition and larger planetesimals are necessary to form such massive embryos beyond AU."1036 As Kobavashi&Tanaka(2010) discussed. Williams&Wether-il(1991) underestimated the total ejecta mass produced by ai single collision for crateriug: Iuaba et aadopted the fragmentation model simular to theirs that Wetherill&Stewart(1993) developed (sce Fig. 1)).," As \citet{kobayashi10} discussed, \citet{williams} underestimated the total ejecta mass produced by a single collision for cratering; Inaba et adopted the fragmentation model similar to theirs that \citet{wetherill93} developed (see Fig. \ref{fig:me}) )."1037 Erosive collisious shorten he depletion time of LOki-sized collision cascade by a factor of 15) (IXobavashi&Tanaka2010) and hence reduce final ονο nasses., Erosive collisions shorten the depletion time of 10km-sized collision cascade by a factor of 4–5 \citep{kobayashi10} and hence reduce final embryo masses.1038 As seen from Eqs. (21)), As seen from Eqs. \ref{eq:Mca}) )1039 and (36)). final enibrvo inasses AM. Ag dneroease with (Qj the results of Inaba et al.," and \ref{eq:Mfa}) ), final embryo masses $M_{\rm1040ca}$, $M_{\rm fa}$ increase with $Q_{\rm D}^*$; the results of Inaba et al."1041 correspond to enibryvo masses or higher Qp., correspond to embryo masses for higher $Q_{\rm D}^*$.1042 Although we aud Inaba et al., Although we and Inaba et al.1043 applied Qj provided by Deuz&Asplaug(1999).. ))rous bodies with r= LOkkin may have much ower (y (e.g.Stewart&Ecinhardt2009:Machi&Naluuura 2011).," applied $Q_{\rm D}^*$ provided by \citet{benz99}, porous bodies with $r \la 10$ km may have much lower $Q_{\rm D}^*$ \citep[e.g.,][]{stewart09,machii}."1044. For initial planetesimnals with radi 2 100Y1. (Qj of slightly larger bodies determines final embryo masses and ds ahuost entirely determined by the gravitational binding euergv: the uncertaiuty from their structure would be iinor.," For initial planetesimals with radii $\ga 100\,$ km, $Q_{\rm D}^*$ of slightly larger bodies determines final embryo masses and is almost entirely determined by the gravitational binding energy; the uncertainty from their structure would be minor."1045 Therefore. such large planctesimals arc possible to produce cores for gas giant plaucts.," Therefore, such large planetesimals are possible to produce cores for gas giant planets."1046 The iechanisius of planetcsimal formation are highlv debated but. despite intensive effort. remain fairly unknown.," The mechanisms of planetesimal formation are highly debated but, despite intensive effort, remain fairly unknown."1047 The formation through collisional coagulation in which dust smoothly erows to planctesimals with ry~1 kin face barriers: neter-sized objects should be lost to the ceutral star as a result of eas drag (Weideusclilline1977:Braunerctal.2008).. and further agelomeration of ci-ized objects upon collision is problematic because of collisional bouncing (Caittleretal.POLO:Zsoimetal.2010).," The formation through collisional coagulation in which dust smoothly grows to planetesimals with $r_0 \sim 1$ km face barriers: meter-sized objects should be lost to the central star as a result of gas drag \citep{weidenschilling77,brauer08}, and further agglomeration of cm-sized objects upon collision is problematic because of collisional bouncing \citep{guttler10,zsom10}."1048. Moreover. the electric repulsion may stop erowth of simaller objects (Okuzundü2009).," Moreover, the electric repulsion may stop growth of smaller objects \citep{okuzumi09}."1049. A new scenario that allows one to overcome the barriers has been proposccd recently: self-eravitv of small particles accumulating in turbulent structures of gaseous disks foris large ulauetesunals of the order of LOO kan (Jobhausenctal.2007:Cuzzict 2008).," A new scenario that allows one to overcome the barriers has been proposed recently: self-gravity of small particles accumulating in turbulent structures of gaseous disks forms large planetesimals of the order of $100$ km \citep{johansen07,cuzzi08}."1050. Not ouly do such large olaetesinuals produce plauetary cores excecediug he critical core mass to fori gas giant planets. hey may also be consisteut with properties of uir bodies in the solar system.," Not only do such large planetesimals produce planetary cores exceeding the critical core mass to form gas giant planets, they may also be consistent with properties of minor bodies in the solar system."1051 Tudeed. the initial planctesimals should be larger than Ian o reproduce the mass distribution of asteroids im he main belt (Morbidellictal.20091.," Indeed, the initial planetesimals should be larger than km to reproduce the mass distribution of asteroids in the main belt \citep{morbidelli09}."1052 For laree planctesimals. a final enmibryo lass een bv A is large enough to start core accretion. while enmibrvo erowth is slow.," For large planetesimals, a final embryo mass given by $M_{\rm ca}$ is large enough to start core accretion, while embryo growth is slow."1053" If the radial slope of surface density g=3/2 like the AIMSN aqnodel a massive disk with 104 MMSN is necessary for clubrves to reach the final mass around AAU,"," If the radial slope of surface density $q=3/2$ like the MMSN model, a massive disk with $10\times$ MMSN is necessary for embryos to reach the final mass around AU."1054 Towever. observations of protoplanctary disks inter thei relatively flatter radial distributions over several huudred AU (eg.Kitamuraetal. 2002).," However, observations of protoplanetary disks infer their relatively flatter radial distributions over several hundred AU \citep[e.g.,][]{kitamura02}."1055. Ii such a disk. dust eraius acctunulate iu au inner disk dueto radial dift during their growth. which increases the solid surface deusitv du the inner disk (Brauerctal.2008).," In such a disk, dust grains accumulate in an inner disk dueto radial drift during their growth, which increases the solid surface density in the inner disk \citep{brauer08}."1056.. The eubaucemenut of solid surface density accelerates embryo growth and hence enibrvos may achieve the critical core lass dn less massive disks., The enhancement of solid surface density accelerates embryo growth and hence embryos may achieve the critical core mass in less massive disks.1057 To fori gas giants via core accretion. rapid gas accretion outo a core with ~10 Earth masses iust occur prior to gas depletion.," To form gas giants via core accretion, rapid gas accretion onto a core with $\sim 10$ Earth masses must occur prior to gas depletion."1058 ETowever. these cores iügrate inwarddue to their exchange of angular ionmentun with the surrounding eas (CIvpoe I).," However, these cores migrate inwarddue to their exchange of angular momentum with the surrounding gas (Type I)."1059 From linear analvsis. the characteristic orbital decay time of Earth-anass cores at several AU in the MMSN model is about ΙΛ (Tanakaet 2002)..," From linear analysis, the characteristic orbital decay time of Earth-mass cores at several AU in the MMSN model is about Myr \citep{tanaka02}. ."1060 Several processes to delay the timescale of Type I migration have been poited out. for exaniple. disk surface density transitions (Masset 2006b).. iutriusic turbulence (Nelson& 2001).. and lydrodvuamic feedback," Several processes to delay the timescale of Type I migration have been pointed out, for example, disk surface density transitions \citep{masset06b}, , intrinsic turbulence \citep{nelson04}, , and hydrodynamic feedback"1061"We find that γι=—0.31 40.22, y=-0.06+ 0.22, and =0.41€0.14; s,=0.6240.04, 2=0.71+0.04, and s3=1.134:0.03.","We find that $\gamma_1=-0.31 \pm 0.22$ , $\gamma_2=-0.06\pm 0.22$ , and $\gamma_3=0.41 \pm 0.14$; $s_1=0.62\pm 0.04$, $s_2=0.71 \pm 0.04$, and $s_3=1.13\pm 0.03$."1062" That is, there is no evolution for the Mgta— Msoo relation, weak suggestion of evolution in Mia —MicM. and strong evidence of evolution in Micw-Msoo, which is manifested as an offset between the loci of fy for z«0.1 (solid squares) and z>0.1 (circles) clusters in Fig. 4.."," That is, there is no evolution for the $M_{\rm star}$ $M_{500}$ relation, weak suggestion of evolution in $M_{{\rm star}}$ $M_{{\rm ICM}}$, and strong evidence of evolution in $M_{\rm ICM}$ $M_{500}$ , which is manifested as an offset between the loci of $f_{\rm b}$ for $z<0.1$ (solid squares) and $z>0.1$ (circles) clusters in Fig. \ref{fig:fb}."1063" This is mainly due to the self-similar evolution (SSE) of the ICM, as noted first by V09 (see the discussion associated with Fig."," This is mainly due to the self-similar evolution (SSE) of the ICM, as noted first by V09 (see the discussion associated with Fig."1064 10 therein)., 10 therein).1065 Let us denote Micm« where &—$3—120.13 based on our data.," Let us denote $M_{\rm ICM} \propto M_{500}^{1+\kappa}$, where $\kappa \equiv s_3-1= 0.13$ based on our data."1066" Introducing Mis,the nonlinear mass scale, Mw; o(Mwi)D(z)=δεe1.69, where σ(Μ) is therms fluctuationsatisfying of linear power spectrum and D is the growth factor (Peebles1980),, we can expect the ICM mass fraction to be the same for systems of the same Mw. at different redshifts under the SSE."," Introducing the nonlinear mass scale, $M_{\rm NL}$, satisfying $\sigma(M_{\rm NL}) D(z)=\delta_c\approx 1.69$, where $\sigma(M)$ is the fluctuation of linear power spectrum and $D$ is the growth factor \citep[][]{peebles80}, we can expect the ICM mass fraction to be the same for systems of the same $M_{500}/M_{\rm NL}$ at different redshifts under the SSE."1067 It then follows that Msoo/Micm«Μορ, It then follows that $M_{\rm ICM} \propto M_{500}^{s_3}/M_{\rm NL}^{\kappa}$.1068" We note that Mw;(z) is consistent with (1-4-z)?? up to /MX,.z—0.4 or so.", We note that $M_{\rm NL}(z)^{-\kappa}$ is consistent with $(1+z)^{\gamma_3}$ up to $z\sim 0.4$ or so.1069" Indeed, with total mass scaled by Mw; the scatter reduces from to8%."," Indeed, with total mass scaled by $M_{\rm NL}$, the scatter reduces from to."1070. We have confirmed the consistency between the observed Micm—Ms00 evolution and the SSE expectation by repeating the above analysis using Msoo based on the Ty —Msoo relation of V09., We have confirmed the consistency between the observed $M_{\rm ICM}$ $M_{500}$ evolution and the SSE expectation by repeating the above analysis using $M_{500}$ based on the $T_X$ $M_{500}$ relation of V09.1071" Using all of the clusters we find that with a scatter of3196; Without strong evidence of evolution, for simplicity we take 5?=0 in Eqn."," Using all of the clusters we find that with a scatter of; Without strong evidence of evolution, for simplicity we take $\gamma_2 = 0$ in Eqn."1072 | and find that with a scatter of31%., \ref{eq:3eq} and find that with a scatter of.1073. The stellar mass-to-light ratio Y is the most important systematic uncertainty in our results., The stellar mass-to-light ratio $\Upsilon$ is the most important systematic uncertainty in our results.1074" We adopt the Kroupa IMF, as it gives Y at z~0 that is consistent with the SAURON measurements of nearby elliptical galaxies (Cappellarietal.2006)."," We adopt the Kroupa IMF, as it gives $\Upsilon$ at $z\sim 0$ that is consistent with the SAURON measurements of nearby elliptical galaxies \citep{cappellari06}."1075". Using the Salpeter (Chabrier) IMF, our Mar would be higher lower)."," Using the Salpeter (Chabrier) IMF, our $M_{\rm star}$ would be higher lower)."1076" Using a single value of Ύ for all galaxies in a cluster is admittedly too simplistic (Leauthaudetal.2011),, although we note the spread of Y in WI for galaxies of all types is smaller than in optical bands."," Using a single value of $\Upsilon$ for all galaxies in a cluster is admittedly too simplistic \citep{leauthaud11}, although we note the spread of $\Upsilon$ in W1 for galaxies of all types is smaller than in optical bands."1077" Furthermore, as galaxies in the M*+1 magnitude range contribute of the total light, our approach is reasonable, as long as Y is only a weak function of galaxy mass (and/or morphology)."," Furthermore, as galaxies in the $M^*\pm 1$ magnitude range contribute of the total light, our approach is reasonable, as long as $\Upsilon$ is only a weak function of galaxy mass (and/or morphology)."1078" Another systematic uncertainty stems from the relative mass calibration of the YyMoo relation at different redshifts, which is about between z=0 and z20.5 (V09)."," Another systematic uncertainty stems from the relative mass calibration of the $Y_X$ $M_{500}$ relation at different redshifts, which is about between $z=0$ and $z=0.5$ (V09)."1079" By boosting the total and ICM mass by for all clusters at z>0.45, we find that the exponents γι and y2 become more negative (both change by ~0.08), giving a weak hint of changing in the stellar mass content."," By boosting the total and ICM mass by for all clusters at $z>0.45$, we find that the exponents $\gamma_1$ and $\gamma_2$ become more negative (both change by $\sim 0.08$ ), giving a weak hint of changing in the stellar mass content."1080" If only using clusters at z«0.4, we would have found that Y2=—0.81+0.47 (c.f."," If only using clusters at $z<0.4$, we would have found that $\gamma_2=-0.81 \pm 0.47$ (c.f."1081 —0.06+0.22 when using the whole sample)., $-0.06\pm 0.22$ when using the whole sample).1082" That is, the 17 highest-z clusters have a substantial leverage on the determination of »."," That is, the 17 $z$ clusters have a substantial leverage on the determination of $\gamma_2$."1083 It is also these clusters that exhibit “brightening” of galaxies with respect to the BC model., It is also these clusters that exhibit “brightening” of galaxies with respect to the BC model.1084" Should we have adopted the measured m* based on these clusters (instead of using the BC model), which is equivalent to reducing Lj, and adopting a higher galactic stellar mass limit, we would have obtained »=—0.3640.24."," Should we have adopted the measured $m^*$ based on these clusters (instead of using the BC model), which is equivalent to reducing $L_{\rm tot}$ and adopting a higher galactic stellar mass limit, we would have obtained $\gamma_2=-0.36 \pm 0.24$."1085 We therefore acknowledge the possibility that our results may be driven by the behavior of these most massive clusters at z~0.5., We therefore acknowledge the possibility that our results may be driven by the behavior of these most massive clusters at $z\sim 0.5$.1086" Ideally we would use a large, volume-limited sample that may represent the average cluster properties better, which will be carried out in a future publication with the all-sky WISE data."," Ideally we would use a large, volume-limited sample that may represent the average cluster properties better, which will be carried out in a future publication with the all-sky WISE data."1087" Possible systematic effects aside, the apparent lack of redshift evolution in M;,—Msoo relation is consistent with the findings of G09 and LO6."," Possible systematic effects aside, the apparent lack of redshift evolution in $M_{\rm star}$ $M_{500}$ relation is consistent with the findings of G09 and L06."1088" In analyses that utilize fy to infer cosmological (e.g.,Allenetal.2004), the locally derived M;i,—Msoo parametersrelation is usually assumed to hold at higher redshifts."," In analyses that utilize $f_{\rm b}$ to infer cosmological parameters \citep[e.g.,][]{allen04}, the locally derived $M_{\rm star}$ $M_{500}$ relation is usually assumed to hold at higher redshifts."1089 Our result directly validates such an assmption., Our result directly validates such an assmption.1090" Our results suggest that, within rsoo, the gas and galaxy contents evolve in different ways; while gas mass grows according to the SSE fashion, the much largerscatterin Mgta— Msoo and Msta—Micm, as well as themuch-less-than-unity slopes in these scaling relations, suggest a more stochastic growth history, which likely involves tidal interactions to strip off material from galaxies (e.g., LO4, Conroyetal. 2007))."," Our results suggest that, within $r_{500}$, the gas and galaxy contents evolve in different ways; while gas mass grows according to the SSE fashion, the much largerscatterin $M_{\rm star}$ $M_{500}$ and $M_{\rm star}$ $M_{\rm ICM}$, as well as themuch-less-than-unity slopes in these scaling relations, suggest a more stochastic growth history, which likely involves tidal interactions to strip off material from galaxies (e.g., L04, \citealt{conroy07}) )."1091" In of this, it would be critical to constrain the evolution of lightthe stellar mass contained in the ICL."," In light of this, it would be critical to constrain the evolution of the stellar mass contained in the ICL."1092 The upcoming Subaru survey (Takada2010) will likely provide necessary data in this regard., The upcoming Subaru survey \citep{takada10} will likely provide necessary data in this regard.1093 It is equally important, It is equally important1094Factor Analvsis (FA) and Principal Component Analvsis (PCA) are powerful statistical methods in data analysis.,	Factor Analysis (FA) and Principal Component Analysis (PCA) are powerful statistical methods in data analysis.1095" Using PCA and FA Bagolyctal.(1998) cdemoustrated that the 9 variables typically neasured (Z5, and Τουdurations: 1). Pos5. and Pio», peak fluxes: Fy.Fo.Fs. and Fy fluences) for eanunia-rav oursts (CRBs). observed by the DATSE instruc onboard the Compton Camuna- Observatory and listed iu the Cirrent BATSE Catalog (Moeesanctal. 2001). cau be satistactorily represented by 3 hidden statistical variables."," Using PCA and FA \cite{bag98} demonstrated that the 9 variables typically measured $T_{50}$ and $T_{90}$durations; $P_{64},1096P_{256}$ , and $P_{1024}$ peak fluxes; ${\cal F}_1, {\cal F}_2, {\cal F}_3$, and ${\cal F}_4$ fluences) for gamma-ray bursts (GRBs), observed by the BATSE instrument onboard the Compton Gamma-Ray Observatory and listed in the Current BATSE Catalog \citep{mee01}, , can be satisfactorily represented by 3 hidden statistical variables."1097 Borgouovo&Djórussou(2006) (hereafter BBOG) studied the statistica properties of 197 long GRBs detected by BATSE., \cite{borbjor06} (hereafter BB06) studied the statistical properties of 197 long GRBs detected by BATSE.1098 They defined 10 statistical variables describing the tenipora and spectral properties of CRBs., They defined 10 statistical variables describing the temporal and spectral properties of GRBs.1099 By performing a PCA. they concluded that about 70% of the total variance in the parameters were explained bv the first 3 Principa Components (PCs).," By performing a PCA, they concluded that about 70 of the total variance in the parameters were explained by the first 3 Principal Components (PCs)."1100 The aim of this article is to procee ina similar way to BBOG by usine instead FA., The aim of this article is to proceed in a similar way to BB06 by using instead FA.1101 By solving the eigeuvalue problem of the correlation (covariance) πιατης. PCA trausforlus the observe variables iuto the same nuniber of uncorrelated variables (PCs).," 	By solving the eigenvalue problem of the correlation (covariance) matrix, PCA transforms the observed variables into the same number of uncorrelated variables (PCs)."1102" An essential ineredicnt of PCA is a distinction between the “important” and ""less important” variables by taking iuto account the maeuitude of the eigenvalues of the correlation (covariance) matrix.", An essential ingredient of PCA is a distinction between the “important” and “less important” variables by taking into account the magnitude of the eigenvalues of the correlation (covariance) matrix.1103 FA assumes that the observed variables can be deseribed by a near colmbination of hidden variables giveu by: wherex denotes an observed variable of dimension p. A is a niafrix of ps dinensious (i«o p). f represcuts a hidden variable of a dineusious.," FA assumes that the observed variables can be described by a linear combination of hidden variables given by: where${\bf x}$ denotes an observed variable of dimension $p$, ${\bf1104\Lambda}$ is a matrix of $p \times m$ dimensions $m<p$ ), $f$ represents a hidden variable of $m$ dimensions."1105 The components of A are called loadings. the factor f represents scores. aud 5 is a noise term.," The components of ${\bf \Lambda}$ are called loadings, the factor $f$ represents scores, and $\varepsilon$ is a noise term."1106 We caninter x from observatious while he quantities on the xight-haud-side of Eq., We caninfer ${\bf x}$ from observations while the quantities on the right-hand-side of Eq.1107 1. have to be computed by a suitable algoritlun., \ref{eq1} have to be computed by a suitable algorithm.1108 PCA expresses the x observed variable as a linear rausformationi of a hidden variable of the suuep dimension. whose components are uncorrelated.," 	PCA expresses the ${\bf x}$ observed variable as a linear transformation of a hidden variable of the same$p$ dimension, whose components are uncorrelated."1109 The raustormation natrix is set up from the cigeuvectors of he correlation uatrix of x., The transformation matrix is set up from the eigenvectors of the correlation matrix of ${\bf x}$.1110 By retainimg ouly the first mcop eigeuvecors. it cau be shownthat. the resultant raustormation matrix provides the best reproduction of x amoung those using onlv m-p componcuts.," By retaining only the first $m<p$ eigenvectors, it can be shownthat, the resultant transformation matrix provides the best reproduction of ${\bf x}$ among those using only $m < p$ components."1111 By retaining only the first nm)«p eiseuvectors. one receives a transformation matrix of dimensions p«m ancl anu expression ideutical to the first term ou the right side of Eq. 1..," By retaining only the first $m < p$ eigenvectors, one receives a transformation matrix of dimensions $p \times m$ and an expression identical to the first term on the right side of Eq. \ref{eq1}."1112 Due to this fact. the PCA is a default solution of FA iu many statistical packages (c.g.SPSS*:: for a detailed comparison of PCA aud FA. see Jolliffe (2002))).," Due to this fact, the PCA is a default solution of FA in many statistical packages (e.g.; for a detailed comparison of PCA and FA, see \cite{jo02}) )."1113 Although PCA is a default solution in many packages. FA has other algorithms as well.," Although PCA is a default solution in many packages, FA has other algorithms as well."1114 Iu our computations. we use the Maxinuum Likelihood (ML) method (for details sce Jolliffe (2002))).," In our computations, we use the Maximum Likelihood (ML) method (for details see \cite{jo02}) )."1115 We use the sample of 197 long CRBs in BBOG aud the 10 variables defined there., 	We use the sample of 197 long GRBs in BB06 and the 10 variables defined there.1116 Of the LO variables. Toy and F weretaken directly from the BATSE Catalog.," Of the 10 variables, $\td$ and $\fl$ weretaken directly from the BATSE Catalog."1117 The remaining & variables were calculated by BBOG., The remaining 8 variables were calculated by BB06.1118 Iu stunary. the 10 variables are the followine: duration time Toy. chussion tine 7539. autocorrelation unction (ACF) halfwidth +. variability V. eiission svaiuinetry Se. cross-fiction time lag 7j. the ratio of peak energies REREX. vk. fluencence F. V. peak peakeuevrgv.euergev Ey. Dan low frequency spectral iudex o.," In summary, the 10 variables are the following: duration time $\td$, emission time $\tem$, autocorrelation function (ACF) half-width $\tau$, variability $V$, emission symmetry $\SF$ , cross-correlationfunction time lag $\lag$ , the ratio of peak energies $\REpk$ , fluence $\fl$ , peak energy $\Epk$ , and low frequency spectral index $\alpha$ ."1119 Simce he variables have different diueusions in a siuular wav to BBOG we use the decimallogarithius, 	Since the variables have different dimensions in a similar way to BB06 we use the decimallogarithms1120There are two main properties which make the study of the Galactic globular clusters (GGC) particularly interesting: 1) each cluster (with possible rare exceptions) is made up by a single population of stars. all born at the same time. in the same place. and out of the same material: 2) GGC stars have the oldest measurable age in the Universe. and therefore we believe they are the oldest fossil records of the formation history of our Galaxy.,"There are two main properties which make the study of the Galactic globular clusters (GGC) particularly interesting: 1) each cluster (with possible rare exceptions) is made up by a single population of stars, all born at the same time, in the same place, and out of the same material; 2) GGC stars have the oldest measurable age in the Universe, and therefore we believe they are the oldest fossil records of the formation history of our Galaxy."1121 Among the many tools we have to investigate the properties of a stellar population. the color-magnitude diagrams (CMD) are the most powerful ones. as they allow to recover for each individual star its evolutionary phase. giving precious information on the age of the entire stellar system. its chemical content. and its distance.," Among the many tools we have to investigate the properties of a stellar population, the color-magnitude diagrams (CMD) are the most powerful ones, as they allow to recover for each individual star its evolutionary phase, giving precious information on the age of the entire stellar system, its chemical content, and its distance."1122 This information allows us to locate the system in the space. giving a base for the distance scale. study the formation histories of the Galaxy. and test our knowledge of stellar evolution models.," This information allows us to locate the system in the space, giving a base for the distance scale, study the formation histories of the Galaxy, and test our knowledge of stellar evolution models."1123 In particular. the study of a large sample of simple stellar systems. as the GGCs. provides important clues to the Milky Way formation history.," In particular, the study of a large sample of simple stellar systems, as the GGCs, provides important clues to the Milky Way formation history."1124 Recently. many studies on the relative ages of the GGCs have been presented with results at least controversial: while some authors find a notable age spread (~5 Gyrs) among the clusters. others find that the bulk of GGCs is coeval.," Recently, many studies on the relative ages of the GGCs have been presented with results at least controversial: while some authors find a notable age spread $\sim5$ Gyrs) among the clusters, others find that the bulk of GGCs is coeval."1125 This controversy is surely mainly due to the heterogeneity of the data used in each study. where the combination of photographic and/or CCD data from the early epochs of solid state detectors has been frequently used.," This controversy is surely mainly due to the heterogeneity of the data used in each study, where the combination of photographic and/or CCD data from the early epochs of solid state detectors has been frequently used."1126 For this reason. a survey of both southern and northern GGCs has been started two years ago by means of I-m class telescopes. i.e. the 9Iem European Southern Observatory (ESO) / Dutch telescope and the Im Isaac Newton Group (ING) / Jacobus Kapteyn telescope (JKT).," For this reason, a survey of both southern and northern GGCs has been started two years ago by means of 1-m class telescopes, i.e. the 91cm European Southern Observatory (ESO) / Dutch telescope and the 1m Isaac Newton Group (ING) / Jacobus Kapteyn telescope (JKT)."1127 We were able to collect the data for 52 of the 69 known GGCs with οM)x16.15., We were able to collect the data for 52 of the 69 known GGCs with $(m-M)_V\leq16.15$.1128 Thirty-nine have been observed with the Dutch telescope (data that are presented in this paper. hereafter Paper D. and the remaining ones with the JKT (the corresponding CMDs will be presented in à companion paper. Rosenberg et al. 2000..," Thirty-nine have been observed with the Dutch telescope (data that are presented in this paper, hereafter Paper I), and the remaining ones with the JKT (the corresponding CMDs will be presented in a companion paper, Rosenberg et al. \cite{rosenberg00},"1129 hereafter Paper ID., hereafter Paper II).1130 As a first exploitation of this new data base. we have conducted a GGC relative age investigation based on the best 34 CMDs of our catalog (Rosenberg et al. 1999..," As a first exploitation of this new data base, we have conducted a GGC relative age investigation based on the best 34 CMDs of our catalog (Rosenberg et al. \cite{rosenberg99},"1131 hereafter Paper III). showing that most of the GGCs have the same age.," hereafter Paper III), showing that most of the GGCs have the same age."1132 We have also used our data base to obtain a photometric metallicity ranking seale (Saviane et al. 2000..," We have also used our data base to obtain a photometric metallicity ranking scale (Saviane et al. \cite{saviane00},"1133 hereafter Paper IV). based on the red giant branch (RGB) morphology.," hereafter Paper IV), based on the red giant branch (RGB) morphology."1134 We measured a complete set of metallicity indices. based on the morphology and position of the RGB.," We measured a complete set of metallicity indices, based on the morphology and position of the RGB."1135 Using a grid of selected RGB fiducial points. we defined a function in the (WoP3. Mj. [Fe/H] space which is able to reproduce the whole set of GGC," Using a grid of selected RGB fiducial points, we defined a function in the $(V-I)_0$, $M_{\rm I}$, [Fe/H] space which is able to reproduce the whole set of GGC"1136"νου. ASCA observation of 6-30-15 to show hat neither the intensity nor profile of the iron line were ""unctions of the continuum lux.",ksec ASCA observation of $-$ 6-30-15 to show that neither the intensity nor profile of the iron line were functions of the continuum flux.1137 Finally. Fabian ct al. (," Finally, Fabian et al. ("11382002) and Fabian Vaughan (2003) examined the lone kksee) EPIC data of 6-30-15 in its normal state and found that the hard-band. cilference spectra were all well described by power-Iaw. forms.,2002) and Fabian Vaughan (2003) examined the long ksec) /EPIC data of $-$ 6-30-15 in its normal state and found that the hard-band difference spectra were all well described by power-law forms.1139 Using his fact. these authors decompose the EPIC-pn spectrum into an almost constant reflection dominated component and variable power-law component.," Using this fact, these authors decompose the EPIC-pn spectrum into an almost constant reflection dominated component and variable power-law component."1140 This is clearly dilferent. to he behaviour that we find during the Deep Minimum stato., This is clearly different to the behaviour that we find during the Deep Minimum state.1141 Finally. we cliscuss the implications of these results for theoretical models of the central engine.," Finally, we discuss the implications of these results for theoretical models of the central engine."1142 In this discussion. we shall assume that the hard-band X-ray spectral features arise from X-ray illumination of a flat accretion disk orbiting a rapicly-rotating black hole in the prograde sense in the 9=5/2 plane.," In this discussion, we shall assume that the hard-band X-ray spectral features arise from X-ray illumination of a flat accretion disk orbiting a rapidly-rotating black hole in the prograde sense in the $\theta=\pi/2$ plane."1143 We shall also assume that the steep emissivity profile of the inner disk is due to a violation ofthe standard zero-Lorque boundary condition ator=ru , We shall also assume that the steep emissivity profile of the inner disk is due to a violation of the standard zero-torque boundary condition at $r=r_{\rm ms}$.1144We must note that the physics of the inner. disk boundary is still very uncertain and the subject of current work and debate., We must note that the physics of the inner disk boundary is still very uncertain and the subject of current work and debate.1145 Phe motivation behind the PORQULED model of Section 3.4. was the presence of a magnetic connection between the inner disk ancl either the plunging region (A@ol Ixrolik 2000) or the rotating (stretched) event rorizon itself (Li 2002)., The motivation behind the TORQUED model of Section \ref{sec:physical_disk_models} was the presence of a magnetic connection between the inner disk and either the plunging region (Agol Krolik 2000) or the rotating (stretched) event horizon itself (Li 2002).1146 Lowever. all aspects of this scenario aave been challenged and. debated.," However, all aspects of this scenario have been challenged and debated."1147 Li (2003) analyzed the garucture of the magnetic field within the plunging region nd argued that the magnetic connection is too weak for the xunging region to influence the rest of the disk., Li (2003) analyzed the structure of the magnetic field within the plunging region and argued that the magnetic connection is too weak for the plunging region to influence the rest of the disk.1148 However. jese arguments are tempered. by the fact that it seenis o be rather casy to torque the disk with the plunging regions in simulated accretion disks (c.g... Lawley Ixrolik Wl: Revnolds Armitage 2002).," However, these arguments are tempered by the fact that it seems to be rather easy to torque the disk with the plunging regions in simulated accretion disks (e.g., Hawley Krolik 2001; Reynolds Armitage 2002)."1149 On a dillerent note. ovdlerloni Fabian (2003) have used the Alerloni (2003) σΠοσο for the energization of the disk corona to argue that 16 inner corona is strongly suppressed by disk torquing.," On a different note, Merloni Fabian (2003) have used the Merloni (2003) model for the energization of the disk corona to argue that the inner corona is strongly suppressed by disk torquing."1150 In other words. while the dissipation profile in a torqued disk can be very centrally concentrated. it might be hard to ranslate this into a centrally concentrated X-ray emission xutern.," In other words, while the dissipation profile in a torqued disk can be very centrally concentrated, it might be hard to translate this into a centrally concentrated X-ray emission pattern."1151 Instead. they suggest. that magnetic connections with the plunging region or rotating black hole energize he corona directly.," Instead, they suggest that magnetic connections with the plunging region or rotating black hole energize the corona directly."1152 A possible problem with this scenario is he requirement that the corona can transport the angular momentum released. by the plunging region or black hole., A possible problem with this scenario is the requirement that the corona can transport the angular momentum released by the plunging region or black hole.1153 Finally. Williams (2003) has challenged. the notion that magnetic fields are relevant for energizing the innermost disk.," Finally, Williams (2003) has challenged the notion that magnetic fields are relevant for energizing the innermost disk."1154 She shows that Penrose scattering processes (Penrose 1969: Williams 1995) can lead to a non-magnetic spin energy extraction mechanism., She shows that Penrose scattering processes (Penrose 1969; Williams 1995) can lead to a non-magnetic spin energy extraction mechanism.1155 Lt is bevond the scope of this (observational) paper to address these physical processes in any detail., It is beyond the scope of this (observational) paper to address these physical processes in any detail.1156 For now. we loosely refer to all of the above models ancl variants as “torquecl disk models”. and assume that some form of interaction with the plunging region or ergosphere of the black hole is energizing the inner disk/corona and producing the steep eniissivity profile seen in the observations.," For now, we loosely refer to all of the above models and variants as “torqued disk models”, and assume that some form of interaction with the plunging region or ergosphere of the black hole is energizing the inner disk/corona and producing the steep emissivity profile seen in the observations."1157 We can organize possible scenarios for Deep Minimum state ransitions by considering the three components of the X-rav continuum that might be relevant to inner disk X-ray rellection: (1) the normal aceretion-powered X-ray emission rom the corona of the accretion disk. (2) the torque-powered X-ray emission from the corona of the inner accretion disk. and (3) X-ray emission from a high Latitude source (maybe he base ofa Blandford-Znajek powered jet) near the black ole spin-axis (we shall refer to this as the jet-component. although this emitting material may not necessarily be moving rapidly).," We can organize possible scenarios for Deep Minimum state transitions by considering the three components of the X-ray continuum that might be relevant to inner disk X-ray reflection; (1) the normal accretion-powered X-ray emission from the corona of the accretion disk, (2) the torque-powered X-ray emission from the corona of the inner accretion disk, and (3) X-ray emission from a high latitude source (maybe the base of a Blandford-Znajek powered jet) near the black hole spin-axis (we shall refer to this as the jet-component, although this emitting material may not necessarily be moving rapidly)."1158 We can then elucidate three scenarios for normal/Deep-Minimum state changes in 6-80-15 by considering the dominance of these three X-ray continuum COonmrponelns., We can then elucidate three scenarios for normal/Deep-Minimum state changes in $-$ 6-30-15 by considering the dominance of these three X-ray continuum components.1159ratio of the intercoubination and Lforbicden emission to the resonance emission. G—(+f)/r. is consistent. with a purely recombining pasia: For andIN. where the lines are cleauly resolved. the measred ratio is C=LOLS for Viland L74-1.5 forIX... while the predicted ratios for an optically thin photoionized. plasma are LO and 3.7 respectively (calculated using HULLAC: Bar-Shaomοἱal. (1998))).,"ratio of the intercombination and forbidden emission to the resonance emission, $G=(i+f)/r$, is consistent with a purely recombining plasma; For and, where the lines are cleanly resolved, the measured ratio is $G=4.6 \pm 1.8$ for and $4.7 \pm 1.5$ for, while the predicted ratios for an optically thin photoionized plasma are $4.0$ and $3.7$ respectively (calculated using HULLAC; \citet{BarShalom}) )."1160 Tje series lies in tie middle of a complex instrumeutal absorption feature nakine it difficult to quantify the line ratios., The series lies in the middle of a complex instrumental absorption feature making it difficult to quantify the line ratios.1161 An enhanced intercombiuation line is often indicative of a hieh-cleusity plasma., An enhanced intercombination line is often indicative of a high-density plasma.1162 However. in fU. 1822-37. where here is a siguilicant UV flux (3x10.H eres/s/cm?from 1200106 100.A:19824). photoexcitation from the 2*9 level to he 222 level competes with the spoutateous decay of the 27S ine to the ground state.," However, in 4U $-$ 37, where there is a significant UV flux \citep[$3\times 10^{-11} from $1200$ to $6400\, {\rm \AA}$, photoexcitation from the $2^{3}S$ level to the $2^{3}P$ level competes with the spontaneous decay of the $2^{3}S$ line to the ground state."1163 Using the UV flux reported in Mason&Córdova(105211) we calculated he photoexcitation rate according o tlie procedure described iu Walietal.(2001)., Using the UV flux reported in \citet{MasonCordovaA} we calculated the photoexcitation rate according to the procedure described in \citet{Kahn2001}.1164. We calculated a dilution factor of 0.5 for the source [lux based ou the relative geometry of the corona aud je accretiou disk., We calculated a dilution factor of $\sim 0.8$ for the source flux based on the relative geometry of the corona and the accretion disk.1165" For aud we find the UV photoexcitation rate to be a factor of ~Lx10"" aud ~Lx10? larger than he rate of radiative decay.", For and we find the UV photoexcitation rate to be a factor of $\sim 4 \times 10^{6}$ and $\sim 4 \times 10^{5}$ larger than the rate of radiative decay.1166 The ratios it the He-like series are ierefore inseusitive to the plasina cenusity., The ratios in the He-like series are therefore insensitive to the plasma density.1167 These spectroscopic features can be used to locate aid describe the line emitting regions in IU 1822—37., These spectroscopic features can be used to locate and describe the line emitting regions in 4U $-$ 37.1168 The phase-depeudence of the recombination line inteisity and the lack of absorption features are consisteut wit1 euiission from au X-ray illumiinatec. «dtically thick region on the disk localized between biuary plases o=0.759 and ©=1.00.," The phase-dependence of the recombination line intensity and the lack of absorption features are consistent with emission from an X-ray illuminated, optically thick region on the disk localized between binary phases $\phi=0.75$ and $\phi=1.00$."1169 During phase ©=0.25 aud part of ó=0.50. we see emission lines from he X-ray illumiuated iuside edge of the jaterla.," During phase $\phi=0.25$ and part of $\phi=0.50$, we see emission lines from the X-ray illuminated inside edge of the material."1170 During phases ο=0.75 ald o=0.00 this emission regiou is essentially blocked (rom view., During phases $\phi=0.75$ and $\phi=0.00$ this emission region is essentially blocked from view.1171 This is illustrated in Figure 9.., This is illustrated in Figure \ref{FigCartoon}.1172 Tie inferred geometry is 1sensitive to our choice of phase bius., The inferred geometry is insensitive to our choice of phase bins.1173 Te obseved velocity structure in ile recombiuation lines is consistent with this scenario: emission lijes [roi iuaterial localized near ile edge of the disk at plase o=(82 will show very little velocity broaclening. but will appear Doppler-shifted by the vector sum of the orbital and Wepleriat velociies.," The observed velocity structure in the recombination lines is consistent with this scenario; emission lines from material localized near the edge of the disk at phase $\phi=0.85$ will show very little velocity broadening, but will appear Doppler-shifted by the vector sum of the orbital and Keplerian velocities."1174 At phase ó=0.25 ile lines will appear blue-shifted by epoppiec110Kkin/s and at dhase ὁ=0.50 blue-shifted. by Doppler~360kin/s.," At phase $\phi=0.25$ the lines will appear blue-shifted by $v_{\rm Doppler} \sim 140\, {\rm km/s}$ and at phase $\phi=0.50$ blue-shifted by $v_{\rm Doppler} \sim 360\, {\rm km/s}$."1175 The phase location of tle enission regiοι is consistent with the point of impact of the accretion stream and suggests that we are seelne lile emission from the bulge that Is expected to form iu the shock-heated. collidiug material (Lubow&Shu1976:Livioetal.," The phase location of the emission region is consistent with the point of impact of the accretion stream and suggests that we are seeing line emission from the bulge that is expected to form in the shock-heated, colliding material \citep{Shu,Livio}."11761986).. If the material is optically-thick. tie bulge is expected to extend above the disk aud downstream aloug the edge of the disk as it adiabatically cools (Armitage&Livio1998).," If the material is optically-thick, the bulge is expected to extend above the disk and downstream along the edge of the disk as it adiabatically cools \citep{ArmitageLivio}."1177. Viewed at bieh inclination angles. this would produce tle wide shallow cip observed in the HETGS lighteurves and in those from previous olservatLOLS.," Viewed at high inclination angles, this would produce the wide shallow dip observed in the HETGS lightcurves and in those from previous observations."1178 We can estimate the angular size of the material [rom the {lus iu the line emission by assuming, We can estimate the angular size of the material from the flux in the line emission by assuming1179"that alters the SiO emission within the region of the shock considered, such as an abundance effect, or from the presence of another shock, with a different velocity, within the telescope beam.","that alters the SiO emission within the region of the shock considered, such as an abundance effect, or from the presence of another shock, with a different velocity, within the telescope beam."1180" These possibilities are discussed in Subsection 3.3 but cannot be thoroughly investigated, given the large beam sizes associated with these transitions; they call for a more detailed study, with higher spatial resolution."," These possibilities are discussed in Subsection \ref{sub:mr} but cannot be thoroughly investigated, given the large beam sizes associated with these transitions; they call for a more detailed study, with higher spatial resolution."1181 The last step was to derive integrated intensities from these spectra., The last step was to derive integrated intensities from these spectra.1182" The results for the SiO knot, which is considered in our subsequent analysis, are shown in Table 4:: integrated intensities and associated r.m.s."," The results for the SiO knot, which is considered in our subsequent analysis, are shown in Table \ref{table4}: integrated intensities and associated r.m.s."1183 are given., are given.1184" The velocity interval over which the integration was made was [—10, 60] km s! for all three transitions."," The velocity interval over which the integration was made was $-$ 10, 60] km $^{-1}$ for all three transitions."1185" Again, the values inferred are consistent with results for other outflows, such as L1448 or L1157 (?)), for which the central source is also a young Class 0 proto-star with a similar bolometric luminosity (respectively, around 13.5, 11, and 1.5-3.5 Lo for BHR71, L1157, and L1448; see ?))."," Again, the values inferred are consistent with results for other outflows, such as L1448 or L1157 \citealt{Nisini07}) ), for which the central source is also a young Class 0 proto-star with a similar bolometric luminosity (respectively, around 13.5, 11, and 1.5–3.5 $_\odot$ for BHR71, L1157, and L1448; see \citealt{Neufeld09}) )."1186" In particular, the line profiles we observe for SiO (5-4), (6--5), and SiO(8-7) are remarkably similar to those of L1157-B1, peaking near the cloud velocity."," In particular, the line profiles we observe for SiO (5–4), (6--5), and SiO(8–7) are remarkably similar to those of L1157-B1, peaking near the cloud velocity."1187 The integrated intensities we inferred are also very close to those compiled for each knot of the L1157 bipolar outflow (?))., The integrated intensities we inferred are also very close to those compiled for each knot of the L1157 bipolar outflow \citealt{Nisini07}) ).1188 We derive emission-related quantities by means of a radiative transfer code used in combination with the shock models presented above., We derive emission-related quantities by means of a radiative transfer code used in combination with the shock models presented above.1189" The radiative transfer code is based on the LVG approximation, and has been described and used in G08a and GO8b."," The radiative transfer code is based on the LVG approximation, and has been described and used in G08a and G08b."1190" At each point of the shock model, it uses the computed parameters of relevance, such as the temperature, density, velocity gradient, and collision-partner density, to solve the equations of statistical equilibrium and calculate emission-related quantities, such as the level populations, optical depths, and local emissivities."," At each point of the shock model, it uses the computed parameters of relevance, such as the temperature, density, velocity gradient, and collision-partner density, to solve the equations of statistical equilibrium and calculate emission-related quantities, such as the level populations, optical depths, and local emissivities."1191" The set of equations is solved by means of a simple lambda-iteration, that stops when the relative difference between each of the level populations computed in two successive iterations drops below a convergence value of 107."," The set of equations is solved by means of a simple lambda-iteration, that stops when the relative difference between each of the level populations computed in two successive iterations drops below a convergence value of $^{-4}$."1192 The set of collisional rate coefficients for SiO with H» as a collision partner is simply scaled by the square root of the reduced mass ratio from the SiO-He rate coefficients calculated by ?.., The set of collisional rate coefficients for SiO with $_2$ as a collision partner is simply scaled by the square root of the reduced mass ratio from the SiO–He rate coefficients calculated by \citet{Dayou06}.1193 The ΤΝ code also provides the integrated intensity over the whole shock model for all transitions considered., The LVG code also provides the integrated intensity over the whole shock model for all transitions considered.1194 The silicon chemistry is extensively discussed in G08a and GO8b., The silicon chemistry is extensively discussed in G08a and G08b.1195" Regarding the initial distribution of silicon-bearing material, G08a made the assumption that Si is initially present exclusively in the grain cores, in the form of silicates, with a fractional abundance of 3.35x10 relative to total H. GO08b introduced an alternative scenario, in which the Si is partly in the grain mantles, in the form of SiO. Such an assumption was found to be necessary to fit both the SiO and"," Regarding the initial distribution of silicon-bearing material, G08a made the assumption that Si is initially present exclusively in the grain cores, in the form of silicates, with a fractional abundance of $3.35 \times 10^{-5}$ relative to total H. G08b introduced an alternative scenario, in which the Si is partly in the grain mantles, in the form of SiO. Such an assumption was found to be necessary to fit both the SiO and"1196with the instrument rotator operating to keep the FOV orientation fixed throughout the sequence.,with the instrument rotator operating to keep the FOV orientation fixed throughout the sequence.1197 In total. 38 30s exposures were obtained.," In total, 38 30s exposures were obtained."1198 These observations will be used in section G.4 for a comparison between ADI and classical observations., These observations will be used in section \ref{adivscla} for a comparison between ADI and classical observations.1199 The data reduction consists of flat. field) normalization. bad. pixel correction using a mediauir over surrounding pixels. and distortion correction using soltware provided by the Gemini Stall CIrujillo. private communication) and mocdilied to use the LDLinterpolate [function with cubic interpolation.," The data reduction consists of flat field normalization, bad pixel correction using a median over surrounding pixels, and distortion correction using software provided by the Gemini Staff (Trujillo, private communication) and modified to use the IDL function with cubic interpolation."1200 Images were then copied into larger blank images to ensure that no FOV was lost when shifting and rotating images., Images were then copied into larger blank images to ensure that no FOV was lost when shifting and rotating images.

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