ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 in either run), in either run).3 Only galaxies in. the magnitude range lí«r19.5 are used to avoid large galaxies with poorly detined centroids., Only galaxies in the magnitude range $17~<~r~<~19.5$ are used to avoid large galaxies with poorly defined centroids.4 For each object in the target run. the mean offsets in RA and Dec for the 100 such galaxies are calculated and added to the object position.," For each object in the target run, the mean offsets in RA and Dec for the 100 such galaxies are calculated and added to the object position."5 This procedure recalibrates the positions in the target run to the reference frame detined by the galaxies in the reference run., This procedure recalibrates the positions in the target run to the reference frame defined by the galaxies in the reference run.6 In Figure 5.. we show example mean offsets in RA and Dec for camera column | from runs 94 and 5918.," In Figure \ref{fig:ac}, we show example mean offsets in RA and Dec for camera column 1 from runs 94 and 5918."7 Notice that run 94. observed in 1998. requires larger mean offsets to correct for the mean proper motion of the UCAC calibration stars than run 5918. observed in 2005. since it is further away in time from when the reference run 5823 was observed in 2005.," Notice that run 94, observed in 1998, requires larger mean offsets to correct for the mean proper motion of the UCAC calibration stars than run 5918, observed in 2005, since it is further away in time from when the reference run 5823 was observed in 2005."8 After recalibrating the astrometry for all light-motion curves in the LMCC. we have recreated Figure ία) as. Figure +b) using the same sample of galaxies.," After recalibrating the astrometry for all light-motion curves in the LMCC, we have recreated Figure \ref{fig:astro_sysa}9 as Figure \ref{fig:astro_sysb} using the same sample of galaxies."10 The histograms of the galaxy proper motions in RA and Dec are now centred around ~Q mas yr indicating that galaxies are stationary in the recalibrated astrometric system of the LMCC., The histograms of the galaxy proper motions in RA and Dec are now centred around $\sim$ 0 mas $^{-1}$ indicating that galaxies are stationary in the recalibrated astrometric system of the LMCC.11 Also. the lower panels demonstrate that the RA dependence of the galaxy proper motions has been properly removed.," Also, the lower panels demonstrate that the RA dependence of the galaxy proper motions has been properly removed."12 There is also some evidence that the galaxy proper motion scatter has been improved., There is also some evidence that the galaxy proper motion scatter has been improved.13 The RMS deviation of the residuals about a fourth-degree polynomial fit in each of the bottom panels of Figure 4a) is 5.4 mas yr.+ for RA and 5.2 mas yr.+ for Dec. This may be compared to the improved RMS deviation of the proper motions in each of the bottom panels of Figure 4(b) at 4.8 mas yr for RA and 4.6 mas vr.! for Dec. The SDSS pipelines do not supply uncertainties on. the measured celestial coordinates in the tsObj files. and so we have determined a noise model describing how the astrometric noise behaves as a function of magnitude.," The RMS deviation of the residuals about a fourth-degree polynomial fit in each of the bottom panels of Figure \ref{fig:astro_sysa} is 5.4 mas $^{-1}$ for RA and 5.2 mas $^{-1}$ for Dec. This may be compared to the improved RMS deviation of the proper motions in each of the bottom panels of Figure \ref{fig:astro_sysb} at 4.8 mas $^{-1}$ for RA and 4.6 mas $^{-1}$ for Dec. The SDSS pipelines do not supply uncertainties on the measured celestial coordinates in the tsObj files, and so we have determined a noise model describing how the astrometric noise behaves as a function of magnitude."14 This was done by examining the distribution of coordinate RMS for objects in the LMCC., This was done by examining the distribution of coordinate RMS for objects in the LMCC.15 However. we found that the astrometric noise in the 2005 observing season was noticeably larger than in previous seasons. most likely due to the less stringent restrictions on observing conditions leading to a greater spread in PSF full-width half-maximum and object signal-to-noise.," However, we found that the astrometric noise in the 2005 observing season was noticeably larger than in previous seasons, most likely due to the less stringent restrictions on observing conditions leading to a greater spread in PSF full-width half-maximum and object signal-to-noise."16 To properly account for this. we determined separate noise models for the pre-2005 and 2005 observing seasons.," To properly account for this, we determined separate noise models for the pre-2005 and 2005 observing seasons."17 To determine the astrometric noise models. we select all PSF- objects 6) with at least 20 good epochs in + in each of the pre-2005 and 2005 observing seasons.," To determine the astrometric noise models, we select all PSF-like objects ) with at least 20 good epochs in $r$ in each of the pre-2005 and 2005 observing seasons."18 For these objects we derive the distribution of coordinate RMS deviations for 0.5 mag bins for both pre-2005 and 2005 data. and fit a peak and dispersion for each bin.," For these objects we derive the distribution of coordinate RMS deviations for 0.5 mag bins for both pre-2005 and 2005 data, and fit a peak and dispersion for each bin."19" In Figure θ(α).. we plot the peak RA RMS deviation for each magnitude bin versus + magnitude for pre-2005 data (filled circles) and 2005 data Copen circles: offset by 0.15 mag to the left for clarity),"," In Figure \ref{fig:rms_astro_a}, we plot the peak RA RMS deviation for each magnitude bin versus $r$ magnitude for pre-2005 data (filled circles) and 2005 data (open circles; offset by 0.15 mag to the left for clarity)."20 We obtain very similar results for the Dec coordinate., We obtain very similar results for the Dec coordinate.21 We tit the peak data as a function of magnitude mz via an exponential function of the form η)=1Dexp(CGn 18))where A. D and Care fitted parameters. and plot the fitted models in Figure 6(a) as continuous and dashed curves for pre-2005 and 2005 data. respectively.," We fit the peak data as a function of magnitude $m$ via an exponential function of the form $f(m)~=~A~+~B~\,\exp~(C~\,~(m~-~18))$ where $A$, $B$ and $C$ are fitted parameters, and plot the fitted models in Figure \ref{fig:rms_astro_a} as continuous and dashed curves for pre-2005 and 2005 data, respectively."22" The following equations represent our. final adopted astrometric noise model. based on the exponential model fits for both the RA and Dee coordinates: where e,(/) and o5(/) are the uncertainties on the measured celestial coordinates a(/) and 9(/). respectively. at time /. and em) represents the brightest PSF magnitude out of the tive photometric measurements at time /."," The following equations represent our final adopted astrometric noise model, based on the exponential model fits for both the RA and Dec coordinates: where $\sigma_{\alpha}(t)$ and $\sigma_{\delta}(t)$ are the uncertainties on the measured celestial coordinates $\alpha(t)$ and $\delta(t)$, respectively, at time $t$, and $m(t)$ represents the brightest PSF magnitude out of the five photometric measurements at time $t$."23 Evidence that this noise model is valid comes from the fact that the distribution of X7 per degree of freedom of the proper motion fit for the HLC (Section 3.1) is peaked at à value of —1.1., Evidence that this noise model is valid comes from the fact that the distribution of $\chi^{2}$ per degree of freedom of the proper motion fit for the HLC (Section 3.1) is peaked at a value of $\sim$ 1.1.24 Note that astrometric uncertainties are not given in the LMCC and should be obtained via Equation 1.., Note that astrometric uncertainties are not given in the LMCC and should be obtained via Equation \ref{eqn:sig_coord}.25 In Figure 6(b). we plot the results of the same coordinate RMS deviation analysis for. non-PSF-like objects 2) with at least 20 good epochs in r in each of the pre-2005 and 2005 observing seasons.," In Figure \ref{fig:rms_astro_b}, we plot the results of the same coordinate RMS deviation analysis for non-PSF-like objects ) with at least 20 good epochs in $r$ in each of the pre-2005 and 2005 observing seasons."26 It is clear from the plots in Figure 6 that we are achieving ~32 mas and ~35 mas RMS accuracy at r 18 mag for stars for pre-2005 and 2005 data. respectively. and ~35 mas and ~46 mas RMS accuracy at r~/8 mag for galaxies for pre-2005 and 2005 data. respectively.," It is clear from the plots in Figure \ref{fig:rms_astro} that we are achieving $\sim$ 32 mas and $\sim$ 35 mas RMS accuracy at $r\sim$ 18 mag for stars for pre-2005 and 2005 data, respectively, and $\sim$ 35 mas and $\sim$ 46 mas RMS accuracy at $r\sim$ 18 mag for galaxies for pre-2005 and 2005 data, respectively."27the South (see section 2)).. The detector edees remained parallel to the slit.,the South (see section \ref{objectives}) ).. The detector edges remained parallel to the slit.28 The observing procedure was as follows., The observing procedure was as follows.29 Using a direct image. the stars are brought to the approximate required position on the detector.," Using a direct image, the stars are brought to the approximate required position on the detector."30 A guide star is acquired and the slit brought iuto the beam at the exact position of he stars., A guide star is acquired and the slit brought into the beam at the exact position of the stars.31 Then the evista is inserted aud several sequences of observations lace., Then the grism is inserted and several sequences of observations made.32" Oue is defined as two exposures (1.2) at the same telescope position. followed by a telescope offset of 20"" iloug the slit and another wo exposures (3.1)."," One is defined as two exposures (1,2) at the same telescope position, followed by a telescope offset of $''$ along the slit and another two exposures (3,4)."33 The same sequence was then normally repeated with the ITI& filter., The same sequence was then normally repeated with the HK filter.34" This was continued for between three aud seven sequences iu each filter uutil it was noticed that the counts in the stars were decreasing due to a decentering of the slit with respect to the stars (which ranged from 0.6"" to 1.2” over two hours. despite the euidiug)."," This was continued for between three and seven sequences in each filter until it was noticed that the counts in the stars were decreasing due to a decentering of the slit with respect to the stars (which ranged from $''$ to $''$ over two hours, despite the guiding)."35 Then. without moving the telescope. eris or slit. the telescope come was moved across the field aud a series of dome flat fields obtained.," Then, without moving the telescope, grism or slit, the telescope dome was moved across the field and a series of dome flat fields obtained."36" Such a set of sequences coustitutes aeyele, This procedure was adopted iu order to obtain flat fields with as similar an optical path to the stars as possible aud to keep this path as constant as possible through muiuinual movement of the optical elements.", Such a set of sequences constitutes a. This procedure was adopted in order to obtain flat fields with as similar an optical path to the stars as possible and to keep this path as constant as possible through minimal movement of the optical elements.37 Each exposure used an integration time of 21min., Each exposure used an integration time of min.38 The readout time is essentially zero. so a single sequence took just over Suu.," The readout time is essentially zero, so a single sequence took just over min."39 Data were obtained on three cousecutivo niehts starting on 29 February 2000 (Table 3j)., Data were obtained on three consecutive nights starting on 29 February 2000 (Table \ref{obslog}) ).40" The seciug iu JII was usually 1.07 1.1"" but oceasioually as lieh as 2.07,", The seeing in JH was usually $''$ $''$ but occasionally as high as $''$.41 The weather was ecuerally very clear. but occasionally thin cius was present.," The weather was generally very clear, but occasionally thin cirrus was present."42 The data reduction and spectral extraction was mostly performed usingIRAF?., The data reduction and spectral extraction was mostly performed using.43. Careful processing is required to avoid biasing the data. so the procedure developed is described.," Careful processing is required to avoid biasing the data, so the procedure developed is described."44" The JII aud IIR spectra were treated separately,", The JH and HK spectra were treated separately.45 From the four tages (1.2.3.1) 1u a sequence. four were produced: a1.3. αι ο».f. c. This removes most of the sky backerouud uus the detector bias pattern.," From the four images (1,2,3,4) in a sequence, four were produced: $1-3$, $-$ a, $2-4$, $-$ c. This removes most of the sky background plus the detector bias pattern."46 These images were then fla fielded using the eud-of-cvcle dome flats described iu section 1.., These images were then flat fielded using the end-of-cycle dome flats described in section \ref{data}.47 These fats show absorption features due to the air in the circa nua optical pat[um οποσα Lump and detector., These flats show absorption features due to the air in the circa m optical path between lamp and detector.48 Towever. as the dispersion fiiction for the flats aud the science πασος is the same. this provides a valid flatiiclding of the detector iu the spatia direction to put the two dither positious (a.c and b.d) on the same plotometric scale.," However, as the dispersion function for the flats and the science images is the same, this provides a valid flatfielding of the detector in the spatial direction to put the two dither positions (a,c and b,d) on the same photometric scale."49 Simall shifts of the slit with respect to the detector in the waveleneth direction change the fat field value at each wavelength. but as this is the same change for both 2M11I1I5 and the reference star. it is not detrimental to spectrophotometry in the (that is. the ratio of these ος below).," Small shifts of the slit with respect to the detector in the wavelength direction change the flat field value at each wavelength, but as this is the same change for both 2M1145 and the reference star, it is not detrimental to spectrophotometry in the (that is, the ratio of these – see below)."50 Bad pixels (as identified from dark images) were removed from the flat-fieldec difference nuages bv Luearly interpolating over thei im the spatial direction., Bad pixels (as identified from dark images) were removed from the flat-fielded difference images by linearly interpolating over them in the spatial direction.51 These four iniages provide four indepeudeut spectra of cach of the arect and reference stars., These four images provide four independent spectra of each of the target and reference stars.52 The spectra were extracted using the onc-dinieusioual optimal extraction technique implemented in IRAES capsum’ task., The spectra were extracted using the one-dimensional optimal extraction technique implemented in IRAF's `apsum' task.53 As these Huages are skv subtracted. pixel cleaning tto remove cosnic τανκ) could not be used reliably within this package (but the effect of cosmic ravs was found to be iiiniual).," As these images are sky subtracted, pixel cleaning to remove cosmic rays) could not be used reliably within this package (but the effect of cosmic rays was found to be minimal)."54 A local sky subtraction at cach wavelength using the median value of regions on cach side of the spectrum was found, A local sky subtraction at each wavelength using the median value of regions on each side of the spectrum was found55(1991)]].,].56 lodels that track many abuxlauce 1jxtures with perfect self-cousisteucy. (πόδας tliat all ingredients from opacities to stellar isochrotres to stellar [fluxes would be produced with the same eleme jxtures) have not yet been »rocducec. but brave forays in this direction have been mace Clragereal.2000:Thomas.Marastou.&Beider2003).," Models that track many abundance mixtures with perfect self-consistency (meaning that all ingredients from opacities to stellar isochrones to stellar fluxes would be produced with the same element mixtures) have not yet been produced, but brave forays in this direction have been made \citep{trag00,tmb03}."57. For this paper we stay withthe iodes ol Worthey(199D)... atemeltec by the caleulatious of uousolar-mixture synthetic stellar c“ALCtlatious of Howasheltetal.(20022).. which are very similar to those of (he'eafter TB95).," For this paper we stay withthe scaled-solar models of \citet{w94}, augmented by the calculations of nonsolar-mixture synthetic stellar calculations of \citet{houda}, which are very similar to those of \citet{tb95} (hereafter TB95)."58 An Issle uncovered with the TB95 svuthetic fluxes should be mentioned bere., An issue uncovered with the TB95 synthetic fluxes should be mentioned here.59 Their carbo enlianceime owas 0.3 dex. sullicient to make the number abundance of carbou exceed that o“ONY geli.," Their carbon enhancement was 0.3 dex, sufficient to make the number abundance of carbon exceed that of oxygen."60 The large «lissociation ene‘oy of the CO molecule causes most of tlie carbon to be locked up i1 this molecile in oxvgen-richi stars. but in carbou-rieli stars Co Swan bands begiu to couiate the visible spectrum iu a uonllnear way. approximately as the square of the carbon abundace.," The large dissociation energy of the CO molecule causes most of the carbon to be locked up in this molecule in oxygen-rich stars, but in carbon-rich stars $_2$ Swan bands begin to dominate the visible spectrum in a nonlinear way, approximately as the square of the carbon abundance."61 The respouses [or carlon iu TB925's tables {. 5. aud 6 are therefore significantly overestimaed.," The responses for carbon in TB95's tables 4, 5, and 6 are therefore significantly overestimated."62 We double checked tLis conclusion with sets of syuhetic spectra küxly provided by A. IXoru. by M. Briley. aud also by E. Baron.," We double checked this conclusion with sets of synthetic spectra kindly provided by A. Korn, by M. Briley, and also by E. Baron."63 Tje Houdasheltetal.(2002) carbo1 responses were computed with a carbon enhance1ert of 0.15 «ex aud thus do 100 chauge the mic)ecular equilibrium very much., The \citet{houda} carbon responses were computed with a carbon enhancement of 0.15 dex and thus do not change the molecular equilibrium very much.64 In galaxy dat: ike those cousidered here. al»undance ratios can be estiiuated from scalecd-solar moclels by assumi that any ¢eviation betwee1 the model aud tje observations results [rom an individual element οιhancemen that acts like a1 overall abundauce increase. as seen. for instaiuce. in Worthey.Faber.&Couzalez(1992).," In galaxy data like those considered here, abundance ratios can be estimated from scaled-solar models by assuming that any deviation between the model and the observations results from an individual element enhancement that acts like an overall abundance increase, as seen, for instance, in \citet{wfg92}."65. This works ouly roughv. uas (1) the Lick/IDS iiclices cover many blended ines and tjerefore other syecies besides the dominau one contribute aid (2) abu anceljxt οςlanges the μονο isocione.," This works only roughly, as (1) the Lick/IDS indices cover many blended lines and therefore other species besides the dominant one contribute and (2) abundance mixture changes the underlying isochrone."66 Trageretal.(2000) and &Betder(2003) effectively calibrae agalust Iiie blends by using tle results of TB925. who exXlorecd the el‘ects o “elοuent ratio changes in the spect‘a ol three representative stars.," \citet{trag00} and \citet{tmb03}67 effectively calibrate against line blends by using the results of TB95, who explored the effects of element ratio changes in the spectra of three representative stars."68 The approach takeu here is essettialv the same as Trageretal.(2000) aud Thomas.Maraston.&Bender(2003).. except that wetie Houclasheltetal.(2002) Sj)ectra.," The approach taken here is essentially the same as \citet{trag00} and \citet{tmb03}, except that we use \citet{houda} spectra."69 Using the rus fit of model versis data (the Table 2. nuclear «ata polut) as a figure of merit. a best-[it age. ove‘all “metallicity” [N/H]. and aποτ mixture Vvere found.," Using the rms fit of model versus data (the Table \ref{tab2} nuclear data point) as a figure of merit, a best-fit age, overall “metallicity” [M/H], and abundance mixture were found."70 The best age is 1.75 Gyr. with [M/H]2-2-0.02.," The best age is 4.75 Gyr, with [M/H]=+0.02."71 Small abundance chaiges were sought siuultaneously to improve the fit., Small abundance changes were sought simultaneously to improve the fit.72 ΤΙe primary oues are [C'/MJ=+0.077. [N/M]—7—0.13. [Mg/M]——().18. and [Na/M]—--0.12.," The primary ones are [C/M]=+0.077, $-0.13$, $-0.18$, and [Na/M]=+0.12."73 These are relatively well measurecl. since they affect a variety of indices i La substantial way.," These are relatively well measured, since they affect a variety of indices in a substantial way."74 The sodium abuidauce. of course. could be spurious because of interstellar absorptiou in the Na D feature. UL the other measurements are good to roughly 0.02 dex. for wlich most of the uncertaiuty is lu he inodels. not the data.," The sodium abundance, of course, could be spurious because of interstellar absorption in the Na D feature, but the other measurements are good to roughly 0.02 dex, for which most of the uncertainty is in the models, not the data."75 Elements with much larger uncertainty jecause of the fact that they do 10 strongly impact the Lick/IDS indices are M]zz0. [Cr/M]z—0.15. and [Ti/M]z—0.2.," Elements with much larger uncertainty because of the fact that they do not strongly impact the Lick/IDS indices are $\approx 0$, $\approx -0.15$, and $\approx -0.2$."76 The indices that were used to find this solution (CN». Ca227. Fe1383. C»1663. les. Fe52T0. Fed335. FedLOG. Fe5709. Na D. aud all five Baliner indices) had a final rms Lit of 0.26 in units of the Wortheyetal.(1991) standard Lick/IDS errors.," The indices that were used to find this solution $_2$, Ca4227, Fe4383, $_2$ 4668, $_2$, Fe5270, Fe5335, Fe5406, Fe5709, Na D, and all five Balmer indices) had a final rms fit of 0.26 in units of the \citet{wor94} standard Lick/IDS errors."77" Including all indices raises he ris fit to Q.13.) in which the worst-fitting ones were Me, and TiO,."," Including all indices raises the rms fit to 0.43, in which the worst-fitting ones were $_1$ and $_1$ ."78 Both of these indices are, Both of these indices are79"our spectroscopy is biased towards the central regions. the E|A phenomenon iav be localized to 205316175 ""bulec: only with fully integrated. spectra cau we determine if the cutire galaxy is goiug through an E|A phase.","our spectroscopy is biased towards the central regions, the E+A phenomenon may be localized to 2053–1647's “bulge”; only with fully integrated spectra can we determine if the entire galaxy is going through an E+A phase."80 From the de Vaucouleurs bulge|exponcutial disk fits. we find the E|A’s are more likely to be bulee-dominated systems ((BYTa> than the average field ealaxy: of the E|A’s are bulec-doiinated compared to 30% of the field (?)..," From the de Vaucouleurs bulge+exponential disk fits, we find the E+A's are more likely to be bulge-dominated systems \citep[$(B/T)_{deV} than the average field galaxy: of the E+A's are bulge-dominated compared to $\sim30$ of the field \citep{simard:02}. ."81 Tuterestinely. both ? and? also find that nearby. post-starburst galaxies (2< 0.2) tend to be bulec-cominatec svstelus.," Interestingly, both \citet{quintero:04} and \citet{yang:04} also find that nearby post-starburst galaxies $z<0.2$ ) tend to be bulge-dominated systems."82 All the E|As have bright. centrally concentrated lelt profiles. simular to what ? find in their study of post-starburst galaxies in Coma.," All the E+A's have bright, centrally concentrated light profiles, similar to what \citet{caldwell:99} find in their study of post-starburst galaxies in Coma."83 From the suiooth light profiles of their E|Avs. 7. sugeested that the starburst preceding the E|A phase was probably an event localized in the ealaxy’s ceuter aud not due to. e... clumpy star-forming regions spread throughout a larger disk.," From the smooth light profiles of their E+A's, \citet{caldwell:99} suggested that the starburst preceding the E+A phase was probably an event localized in the galaxy's center and not due to, e.g., clumpy star-forming regions spread throughout a larger disk."84 However. removal of the 2D inodel from the E|A’s in our field sample shows that three (2053-115. 2053-1399. 2053-1617) lave chuupy. nou-axisviunetrie structure in addition to a bright central region (Fig. ??..," However, removal of the 2D model from the E+A's in our field sample shows that three (2053-415, 2053-1399, 2053-1647) have clumpy, non-axisymmetric structure in addition to a bright central region (Fig. \ref{gals},"85 right)., right).86 Uulike the E|A’s in Coma. our field E|A’s show both centralized bright regions and extended chuupy star formation.," Unlike the E+A's in Coma, our field E+A's show both centralized bright regions and extended, clumpy star formation."87" As noted in $11.3. the EA phenomenon may be associated primarily with the ""bulee component iu these systems."," As noted in 4.3, the E+A phenomenon may be associated primarily with the “bulge” component in these systems."88 Past studies of E|A’siu the nearby feld sugses he E|AÀ phenomenon is associated with galaxv-ealaxyv encounters (??.Z96)..," Past studies of E+A'sin the nearby field suggest the E+A phenomenon is associated with galaxy-galaxy encounters \citep[Z96]{liu:95,yang:04}."89 If the E|A phase was trigecrec oa recent interaction. we would expect the E|A’s to be norplologically disturbed because such features remain visible for the duration of the E|A phase (??)..," If the E+A phase was triggered by a recent interaction, we would expect the E+A's to be morphologically disturbed because such features remain visible for the duration of the E+A phase \citep{mihos:94a,mihos:94b}."90 We fine our of the fivefield E|]A's with WEPC2 imaging have elevated degrees of galaxy asviunetry (Ry29 0.05) and/or otal residuals C20.1:77): oue is even visually type as a iuerecr.," We find four of the fivefield E+A's with WFPC2 imaging have elevated degrees of galaxy asymmetry $R_A\geq0.05$ ) and/or total residuals \citep[$R_T\geq0.1$;][]{schade:96,tran:01}; one is even visually typed as a merger."91 These results are consistent with the E|A phase beige associated with ealaxv-galaxy interactions., These results are consistent with the E+A phase being associated with galaxy-galaxy interactions.92" Because internal velocity dispersion (0) is a useful tracer of the ealaxws total mass. we estimate 8,4; for the E]A’s that have (BOW). and structural paraincters nieasured from HST/WFEPC? imaging."," Because internal velocity dispersion $\sigma$ ) is a useful tracer of the galaxy's total mass, we estimate $\sigma_{est}$ for the E+A's that have $(B-V)_z$ and structural parameters measured from HST/WFPC2 imaging."93 As described iu 7. and TO03a. we can use colors to correct the mass-to-helt ratios of the galaxies and so estimate the internal velocity dispersions of these svsteiis.," As described in \citet{kelson:00c} and T03a, we can use colors to correct the mass-to-light ratios of the galaxies and so estimate the internal velocity dispersions of these systems."94 Iu this method. we essentially evolve the E|A’s by fading and reddening them until they Le on the color maguitude relation (CAIR) defined bv a passively evolving ealaxy population: here we use the CAIR normalized to the earlv-tvpe galaxies in MS1051 (2= 0.83).," In this method, we essentially evolve the E+A's by fading and reddening them until they lie on the color magnitude relation (CMR) defined by a passively evolving galaxy population; here we use the CMR normalized to the early-type galaxies in MS1054 $z=0.83$ )."95 We also correct the E|A’sfor siuple fading as deteriuned from the Fruudameameutal Plane (Aloe(AL/£)x|0.10::?).., We also correct the E+A'sfor simple fading as determined from the Fundamamental Plane \citep[$\Delta\log (M/L)\propto -0.40z$;][]{vandokkum:98a}.96 We find the field τιδι span a large rauge iu estimated internal velocity dispersion: 50ἙσιS220 (Table ??))., We find the field E+A's span a large range in estimated internal velocity dispersion: $50\lesssim\sigma_{est}\lesssim220$ (Table \ref{properties}) ).97" The two field E|A’s with the largest σι, are also the two highest redshift svstcus.", The two field E+A's with the largest $\sigma_{est}$ are also the two highest redshift systems.98 Tt may be that 1) the mass distribution of field E|A’s evolves with redshift and/or 2) the fraction of ficld E|A’s increases with redshift., It may be that 1) the mass distribution of field E+A's evolves with redshift and/or 2) the fraction of field E+A's increases with redshift.99 It is interesting to note that there are at least a few field E]A’s at τς0.13 with measured 620005 (?)., It is interesting to note that there are at least a few field E+A's at $z<0.13$ with measured $\sigma>200$ \citep{norton:01}.100 However. the current sanple sizes are too small to determine whether the field E|A dispersiou distributions differ between low aud intermecate redshifts.," However, the current sample sizes are too small to determine whether the field E+A dispersion distributions differ between low and intermediate redshifts."101 Z96 originally sugeested that most E|As lie in galaxy eroups because egalaxy-ealaxy interactions occur more frequeutly in groups than in the field., Z96 originally suggested that most E+A's lie in galaxy groups because galaxy-galaxy interactions occur more frequently in groups than in the field.102 Because the majority of field galaxies are in groups. we would expect that most of the E|A’s are also in eroups.," Because the majority of field galaxies are in groups, we would expect that most of the E+A's are also in groups."103 To test whether our E|Avs lie in euvironienuts simular to that of a typical field galaxy. we use our cutive feld redshift sample at 0.3<21 to estimate the average nunber of redshift ucighbors cach E|A has.," To test whether our E+A's lie in environments similar to that of a typical field galaxy, we use our entire field redshift sample at $0.3<z<1$ to estimate the average number of redshift neighbors each E+A has."104 Tere we consider a galaxy to be a neighbor if its redshift is within (ei);«500 Loofthe E1A and it is du the same field: the redshift distribution of galaxies near each E|A is shown in Fig. ??.., Here we consider a galaxy to be a neighbor if its redshift is within $(cz)_{rest}\leq500$ of the E+A and it is in the same field; the redshift distribution of galaxies near each E+A is shown in Fig. \ref{zhist_ea}.105 The average field E|A in our survey has 6.3c1.0 neighbors. a value cousisteut with the muuber of neighbors au average field galaxy has (1.9dE 0.1): here we asssunie a Poissonian distribution to estimate the errors.," The average field E+A in our survey has $6.3\pm1.0$ neighbors, a value consistent with the number of neighbors an average field galaxy has $4.9\pm0.1$ ); here we asssume a Poissonian distribution to estimate the errors."106 This indicates that like iost Ποια ealaxies. field E|As tend to lie in ealaxv groups even at intermeciate redshifts.," This indicates that like most field galaxies, field E+A's tend to lie in galaxy groups even at intermediate redshifts."107 Because the E|A galaxies are found in both the field and clusters at redshifts up to :~1l. they can place constraints on galaxv formation models.," Because the E+A galaxies are found in both the field and clusters at redshifts up to $z\sim1$, they can place constraints on galaxy formation models."108 Models must not only produce E|A’s but also how the E|A fraction varies with euvironmmnenut., Models must not only produce E+A's but also how the E+A fraction varies with environment.109 Tere we discuss in greater detail the importance of E|A galaxies and how they provide interesting constraints for galaxy evolution models., Here we discuss in greater detail the importance of E+A galaxies and how they provide interesting constraints for galaxy evolution models.110 Like E|A galaxies iu the nearby universe (Z96:7). the majority of E|Às at 2>0.3 are in the field/eroup environment.," Like E+A galaxies in the nearby universe \citep[Z96;][]{quintero:04}, the majority of E+A's at $z>0.3$ are in the field/group environment."111 Asstuine of galaxies are in clusters ?) and the E|A fraction in clusters aud the field is and respectively. we find GVrigaINquasi)~3.," Assuming of galaxies are in clusters \citep{gomez:03} and the E+A fraction in clusters and the field is and respectively, we find $(N_{field}/N_{cluster})\sim3$."112 However. the elevated E|A iu clusters iudicates environment does have au important role iu trigecring ot16 E|A phase.," However, the elevated E+A in clusters indicates environment does have an important role in triggering the E+A phase."113 Most likely additional cluster processes. Ase. galaxw harassment and/or iuteractions with a hot oeitracluster medium (22). can also trigeer an E|A phase.," Most likely additional cluster processes, e.g. galaxy harassment and/or interactions with a hot intracluster medium \citep{caldwell:99,poggianti:04}, can also trigger an E+A phase."114 To determine whether the E|A phase has an siguificaut role iu the conversion of oenüssion line galaxies iuto absorption Luc systems. we estinate the fraction of absorption line systems in the feld that have uudergoue an E|A phaseby 2= 0.," To determine whether the E+A phase has an significant role in the conversion of emission line galaxies into absorption line systems, we estimate the fraction of absorption line systems in the field that have undergone an E+A phaseby $z=0$ ."115 In our field sample of 2 ealaxies at θ<2«ld. we have 66 absorption line (OIT| 5A)) aud 151 emission line (JOT) 5A)) svsteiis.," In our field sample of 220 galaxies at $0.3<z<1$, we have 66 absorption line $<5$ ) and 154 emission line $\geq5$ ) systems."116 The field E|A fraction when considering only absorption lue galaxies ix ~ 94.., The field E+A fraction when considering only absorption line galaxies is $\sim9$ .117" Combining this fraction withthe elapsed. time between 2=0.3 and 2=1 (Aft=L3Cart: IH,=70 Mpe ον= 0.3. A= 0.7) and assuming the E|A phase is visible for 1.5 Cyr (??).. we"," Combining this fraction withthe elapsed time between $z=0.3$ and $z=1$ $\Delta t=4.3$Gyr; $H_0=70$ $^{-1}$ , $\Omega_M=0.3$ , $\Lambda=0.7$ ) and assuming the E+A phase is visible for 1.5 Gyr \citep{couch:87,barger:96}, , we"118Blue stragelersMD in globular clusters are thought to be created by stellar mergers.,Blue stragglers in globular clusters are thought to be created by stellar mergers.119 Such mergers can occur in two ways: through the spiraling in and merger of two components of a binary syste.," Such mergers can occur in two ways: through the spiraling in and merger of two components of a binary system,"120"to the shift in the preferred O,,, as the power spectrum data tend to prefer lower values of Qn.","to the shift in the preferred $\Om $, as the power spectrum data tend to prefer lower values of $\Omega_m$."121 Another interesting factor of this dark energy modeling is the effect that transitions at intermediate redshifts have in the allowed matter fluctuation amplitude - the og parameter., Another interesting factor of this dark energy modeling is the effect that transitions at intermediate redshifts have in the allowed matter fluctuation amplitude - the $\sigma_8$ parameter.122 Figure 5 presents a peculiar degeneracy between these parameters., Figure \ref{fig:sigma_at_1} presents a peculiar degeneracy between these parameters.123" This figure shows that for transitions occurring between a;~0.2 (z= 4) anda~0.6 (z= 0.6), the allowed matter amplitude og decreases linearly, meaning that transitions which occur at lower redshifts necessarily yield a lower value of c."," This figure shows that for transitions occurring between $a_t \approx 0.2$ $z_t=4$ ) and $a_t\approx 0.6$ $z_t=0.6$ ), the allowed matter amplitude $\sigma_8$ decreases linearly, meaning that transitions which occur at lower redshifts necessarily yield a lower value of $\sigma_8$."124" This is because a value of w close to 0 has the effect of inhibiting the growth of matter perturbations, as shown in Douspisetal.2003.."," This is because a value of $w$ close to $0$ has the effect of inhibiting the growth of matter perturbations, as shown in \cite{Douspis2003}."125" So, in the presence of a transition from a value of w close to 0, the overall amplitude of fluctuations (for a given CMB amplitude) is smaller at low redshifts."," So, in the presence of a transition from a value of $w$ close to 0, the overall amplitude of fluctuations (for a given CMB amplitude) is smaller at low redshifts."126 In principle the amplitude of matter fluctuations can be estimated from local cluster abundances., In principle the amplitude of matter fluctuations can be estimated from local cluster abundances.127" However, in practice the lack of reliable calibration of the mass temperature limits the use of this constraint (Pierpaolietal.2001;; Blanchard&Douspis 2005))."," However, in practice the lack of reliable calibration of the mass temperature limits the use of this constraint \cite{Pierpaoli}; \cite{ATM}) )."128" We have seen above that for a value of w, closer to O important changes in the predicted matter correlation function arise, which can improve the quality of the fit of the SDSS LRG data."," We have seen above that for a value of $w_+$ closer to 0 important changes in the predicted matter correlation function arise, which can improve the quality of the fit of the SDSS LRG data."129" We now check whether these models, which comprise transitions at low redshifts, may accommodate other observational data."," We now check whether these models, which comprise transitions at low redshifts, may accommodate other observational data."130" So, we determine the same combined constraints as done previously, but setting w,= —0.l."," So, we determine the same combined constraints as done previously, but setting $w_+=-0.1$."131" The obtained results for the other data combinations are summarized in Table 3 and in Fig. 6,"," The obtained results for the other data combinations are summarized in Table \ref{Table_wi01wf1} and in Fig. \ref{fig:Ol_at_wi01_wf1},"132" which shows the marginalized region contours in the Ώρ—a, parameter space.", which shows the marginalized region contours in the $\Omega_Q - a_t$ parameter space.133" For these models the allowed transition redshift space is reduced: models with Oo~0.75 (Q,,~ 0.25) and a,>0.5 (z;« 1) are excluded at the two sigma level.", For these models the allowed transition redshift space is reduced: models with $\Omega_Q\simeq0.75$ $\Omega_m\simeq0.25$ ) and $a_t>0.5$ $z_t<1$ ) are excluded at the two sigma level.134" This means that for these models the CMB data impose a stronger constraint, and the best fit model in middle panel of Fig."," This means that for these models the CMB data impose a stronger constraint, and the best fit model in middle panel of Fig."135" 2 with z,=0.5 becomes ruled out by the CMB.", \ref{fig:xi} with $z_t=0.5$ becomes ruled out by the CMB.136One may ponder how long a time base would be enough to distinguish between evolutionary period. changes. aud period changes caused by other cllects.,One may ponder how long a time base would be enough to distinguish between evolutionary period changes and period changes caused by other effects.137 Several ideas have been propounded to interpret the non-evolutionary period 'hanges. but none of them have been proven to be fully satisfactory vet.," Several ideas have been propounded to interpret the non-evolutionary period changes, but none of them have been proven to be fully satisfactory yet."138 Although the observed. large. non-evolutionary period 'hanges may frustrate the observer. there is a consent among researchers concerned that the mean value of the 'hange rates of large sample of RR Lyrac stars of a globular ‘Luster reflects athe trend of evolution consistently with the =nocdel calculation results of Lee(1991).," Although the observed large, non-evolutionary period changes may frustrate the observer, there is a consent among researchers concerned that the mean value of the period-change rates of a large sample of RR Lyrae stars of a globular cluster reflects the trend of evolution consistently with the model calculation results of \citet{le91}."139 One of the most thoroughly investigated globular ‘luster. as for the variable stars. is Messier 8 (as a recent gaucdy of the variables see e. Caccia.etal. (2005))).," One of the most thoroughly investigated globular cluster, as for the variable stars, is Messier 3 (as a recent study of the variables see e.g., \citet{ca05}) )."140 lt contains one of the largest RRO Lyrac populations., It contains one of the largest RR Lyrae populations.141 The atest investigation of the period-change behaviour of the th Lyrae stars in MS was made by Corwin&Carney (2001).., The latest investigation of the period-change behaviour of the RR Lyrae stars in M3 was made by \citet{co01}. .142 This period-change study utilized the ο6 data xublished. by Szeidl ας... 1973)) in combination with CCD observations obtained between 1990. and 1997.," This period-change study utilized the $O-C$ data published by \citeauthor{sz65} \citeyear{sz65}, \citeyear{sz73}) ) in combination with CCD observations obtained between 1990 and 1997."143 The ack of publishecl observational data from. between 1962 o 1990 mace the results. however. somewhat cubious or many of the variables.," The lack of published observational data from between 1962 to 1990 made the results, however, somewhat dubious for many of the variables."144 Since the archival. previously unpublished. Wonkoly photographic observations obtained in the vears between 19604 and 1989. fill this gap. ancl the new CCD photometry from 2009 extends the baseline of the observations by a decade over a century. a fresh hope arises to get a better insight into the period-change behaviour of cluster variables.," Since the archival, previously unpublished Konkoly photographic observations obtained in the years between 1964 and 1989 fill this gap, and the new CCD photometry from 2009 extends the baseline of the observations by a decade over a century, a fresh hope arises to get a better insight into the period-change behaviour of cluster variables."145 This provides the motivation for the present study., This provides the motivation for the present study.146 Since the pioneering work of Bailey(1913)... many photometric studies investigated. the properties of the variable star. population of M3.," Since the pioneering work of \citet{ba13}, many photometric studies investigated the properties of the variable star population of M3."147 As our aim is to carry out a study of period-change behaviour of the RRO Lyrac stars in. MS as complete as possible. all the measurable variables numbered from V1 to V203 have been on our List.," As our aim is to carry out a study of period-change behaviour of the RR Lyrae stars in M3 as complete as possible, all the measurable variables numbered from V1 to V203 have been on our list."148 Unfortunately. a number of stars. especially those discovere bv Müller.(1933) and Creenstein(1935)— are situatec in the crowded. central region and/or have close. brieh companion(s). therefore. their brightness measurements are unreliable and. useless in most cases.," Unfortunately, a number of stars, especially those discovered by \citet{mu33} and \citet{gr35} are situated in the crowded, central region and/or have close, bright companion(s), therefore, their brightness measurements are unreliable and useless in most cases."149 Variables numberec over V204 are too sparsely (if at all) observed: over. the past fifty vears for reliable period changes to be determined., Variables numbered over V204 are too sparsely (if at all) observed over the past fifty years for reliable period changes to be determined.150 Altogether. we have found 134 RR. Lyrae stars with extende enough data for a period-change analysis.," Altogether, we have found 134 RR Lyrae stars with extended enough data for a period-change analysis."151 Tables 1 and 2 summarize the photographic and CCD observations utilized in the present study., Tables \ref{pg} and \ref{ccd} summarize the photographic and CCD observations utilized in the present study.152 The code/reference. of the photometric data. the exposuse time/filters. the time interval of the observations. the number of variables observed. and the maximum number of data points in the dillerent datasets are given in the tables.," The code/reference of the photometric data, the exposuse time/filters, the time interval of the observations, the number of variables observed and the maximum number of data points in the different datasets are given in the tables."153 The brightness estimates of 17 stars. published. by Slavenas(1929).. which cannot be transformed to the magnitude scale. and the pge;s; observations of are not used in our analysis.," The brightness estimates of 17 stars published by \citet{sl29}, which cannot be transformed to the magnitude scale, and the $pg_{vis}$ observations of are not used in our analysis."154 These data are coincidental or very close in time to other observations. thus their omission has no ellect on the results.," These data are coincidental or very close in time to other observations, thus their omission has no effect on the results."155 Instead of light-curve data. only timines of the mid-point on the rising branch or times of maxima (OC' values) have been published. by Martin.(1942).. WKhevlo(1966). and Aleinunger (Wenzel1995).," Instead of light-curve data, only timings of the mid-point on the rising branch or times of maxima $O-C$ values) have been published by \citet{ma42}, \citet{kh66} and Meinunger \citep{we95}."156.. These cata cannot be utilized in our analysis., These data cannot be utilized in our analysis.157 The datasets obtained using the 60-em telescope of the Ixonkolx. Observatory. and the L-m telescope of the Hamburg Observatory published by Szeidl (1965... 1973)) are treated separately and are listed as datasets 7 and 15 in Table 1..," The datasets obtained using the 60-cm telescope of the Konkoly Observatory, and the 1-m telescope of the Hamburg Observatory published by \citeauthor{sz65} \citeyear{sz65}, \citeyear{sz73}) ) are treated separately and are listed as datasets 7 and 15 in Table \ref{pg}."158 The CCD era of the observations of M3 began in. 199t) (Carrettactal.1998). ancl continued. with the extended measurements of Corwin&Carney(2001) from 1992. 1993 and 1997. Waluznyctal.(1998) from 1996. Hartmanetal.(2005) from 19958. and Denkóetal.(2006). from 1998 and 1999.," The CCD era of the observations of M3 began in 1990 \citep{ca98} and continued with the extended measurements of \citet{co01} from 1992, 1993 and 1997, \citet{K98} from 1996, \citet{H05} from 1998, and \citet{be06} from 1998 and 1999."159 CCD datasets are referred by the abbreviations given in the second column of Table. 2.. hereafter.," CCD datasets are referred by the abbreviations given in the second column of Table \ref{ccd}, hereafter."160 Photographie observations of M3 with the telescopes of the Ixonkolv Observatory were obtained alter 1962. which data have not been published. previously.," Photographic observations of M3 with the telescopes of the Konkoly Observatory were obtained after 1962, which data have not been published previously."161 The exposures taken without filter with the 60-em telescope on two nights in 1964 and 1968. and with the Ln ROC telescope between 19761980 and 19881989 using 103aO plates are processed in the oesent work.," The exposures taken without filter with the 60-cm telescope on two nights in 1964 and 1968, and with the 1-m RCC telescope between 1976--1980 and 1988–1989 using 103aO plates are processed in the present work."162 The photographic plates were cigitalized using an Umax PowerLook 3000 [latbed. transparency. scanner., The photographic plates were digitalized using an Umax PowerLook 3000 flatbed transparency scanner.163 The ohotographic densities. of the variables ancl comparison stars were measured using standard. aperture. photometry xekages ofHAE., The photographic densities of the variables and comparison stars were measured using standard aperture photometry packages of.164 The brightness of the variables were measured using comparison stars selected. from. the shotographic standard sequence of Sandage(1953)., The brightness of the variables were measured using comparison stars selected from the photographic standard sequence of \citet{sa53}.165 CCD photometric data were obtained. with the 0.9- telescope of the Witt) Peak National Observatory on 1519 April 1999 using the Cassegrain imaging camera and μονΑλ Tektronix detector with δν. δν (24-1un pixels) and the extended ThuanGunn. vege? filter set.," CCD photometric data were obtained with the 0.9-m telescope of the Kitt Peak National Observatory on 15–19 April 1999 using the Cassegrain imaging camera and the ""T2KA"" Tektronix detector with $\times$ 2K $\micron$ pixels) and the extended Thuan–Gunn $uvgri$ filter set."166 The detector. olfered a field of view of approximately 24 aremin square., The detector offered a field of view of approximately 24 arcmin square.167 Data were reduced: using standard LAL processing procedures and photometric magnitudes. were measurecl using PSE fitting techniques., Data were reduced using standard IRAF processing procedures and photometric magnitudes were measured using PSF fitting techniques.168 From the 40 light curves evaluated. 39 are utilized as V161 does not have long enough photometric record to analyse its period changes.," From the 40 light curves evaluated, 39 are utilized as V161 does not have long enough photometric record to analyse its period changes."169 CCD observations of M3. were. performed. with the 60/90/180-cm Schmidt telescope αἲ the Piszkésstetó Mountain Station of the WKonkoly Observatory using a Photometries camera with a Ixodalk IN.XE-1600 1024 1500 chip between6 February and 13. May in 2009., CCD observations of M3 were performed with the 60/90/180-cm Schmidt telescope at the Piszkésstető Mountain Station of the Konkoly Observatory using a Photometrics camera with a Kodak KAF-1600 1024 $\times$ 1536 chip between6 February and 13 May in 2009.170 The field of view was Ίο 2S) with 1.0 pixel per aresce resolution., The field of view was 19' $\times$ 28' with $1.0$ pixel per arcsec resolution.171 The observations comprised four one-week long observing runs., The observations comprised four one-week long observing runs.172 In total. SOO and ~700 (ο frames were obtained.," In total, $\sim800$ and $\sim700$ $I_C$ frames were obtained."173 The frames were reduced. using standard LAL, The frames were reduced using standard IRAF174pertain primarily to the cooler gas component.,pertain primarily to the cooler gas component.175" We therefore turn to more detailed radiative transfer modeling of the position-switched (1,1), (2,2), (3,3), and (6,6) spectra taken towards the peak of NH3((3,3) emission (Figure 8)) and spectra averaged over the Core 2 region for a first look at the gas parameters towards Core 2."," We therefore turn to more detailed radiative transfer modeling of the position-switched (1,1), (2,2), (3,3), and (6,6) spectra taken towards the peak of $_3$ (3,3) emission (Figure \ref{fig:sample_spectra}) ) and spectra averaged over the Core 2 region for a first look at the gas parameters towards Core 2."176" The radiative transfer code,MOLLIE?,, can deal with arbitrary 3D geometries, but as a first step in obtaining the indicative properties of Core 2 in this paper, we modeled the emission as arising from a sphere with a constant temperature, density and non-thermal velocity component, taking the NHa spectra corrected for the Mopra aperture main beam efficiency of ma,=0.6."," The radiative transfer code, can deal with arbitrary 3D geometries, but as a first step in obtaining the indicative properties of Core 2 in this paper, we modeled the emission as arising from a sphere with a constant temperature, density and non-thermal velocity component, taking the $_3$ spectra corrected for the Mopra aperture main beam efficiency of $\eta_{\rm mb}=0.6$."177" The NHsa to He abundance ratio was fixed at 2x10? as in our earlier analyses, and a source radius of ppc (distance kkpc) was chosen based on the extent of the NHs ((3,3) intensity after a >0.18 KK cut."," The $\nhthree$ to $_2$ abundance ratio was fixed at $2\times10^{-8}$ as in our earlier analyses, and a source radius of pc (distance kpc) was chosen based on the extent of the $_3$ (3,3) intensity after a $\geq0.18$ K cut."178" Models were constructed with H2 densities, temperatures and non-thermal linewidths ranging from 10? to 10° cm33, 10 to 400 KK and 0.5 to 40kms, respectively."," Models were constructed with $_2$ densities, temperatures and non-thermal linewidths ranging from $10^3$ to $10^8$ 3, $10$ to $400$ K and $0.5$ to $40$, respectively."179" Radiative transfer modeling was then used to generate synthetic data cubes with a velocity resolution of for the NH3(1,1), (2,2), (3,3) and (6,6) emission."," Radiative transfer modeling was then used to generate synthetic data cubes with a velocity resolution of for the $\nhone$, (2,2), (3,3) and (6,6) emission."180" These were then convolved with 2D Gaussian profiles at a spatial scale corresponding to the 2"" FWHM of Mopra.", These were then convolved with 2D Gaussian profiles at a spatial scale corresponding to the $\arcmin$ FWHM of Mopra.181 The synthetic spectra at each transition were fit to the observed spectra (weighted by the signal-to-noise of each transition), The synthetic spectra at each transition were fit to the observed spectra (weighted by the signal-to-noise of each transition)182"As described inPanteretal.(2006a,b),, the MOPED algorithm has been used to extract star formation and metallicity histories of a magnitude limited sample (15.0€m,< 17.77) of about 300,000 galaxies drawn from the Third Data Release of the Sloan Digital Sky Survey DR3; Abazajianetal.","As described in\citet{PJHC06a,PJHC06b}, the MOPED algorithm has been used to extract star formation and metallicity histories of a magnitude limited sample $15.0 \le m_r \le 17.77$ ) of about 300,000 galaxies drawn from the Third Data Release of the Sloan Digital Sky Survey (SDSS DR3; \citet{SDSS-DR3}) )."183" We measured (SDSSmark correlations, using MOPED (2005))).attributes as the marks, in two smaller volume-limited catalogs extracted from the SDSS DR3."," We measured mark correlations, using MOPED attributes as the marks, in two smaller volume-limited catalogs extracted from the SDSS DR3."184" To facilitate future halo-model based interpretations of our measurements, these catalogs were chosen to approximately correspond to those studied by Zehavietal.(2005) and Skibbaetal. (2006):: a brighter catalog which spans M,«—21.5 for which 0.02«2<0.135, and one which includes fainter objects, ΛΜ;«—20, and so spans a smaller redshift range: 0.02<z0.071 (the associated apparent magnitude limit is conservative: m,< 17.5)."," To facilitate future halo-model based interpretations of our measurements, these catalogs were chosen to approximately correspond to those studied by \citet{Zehavi05} and \citet{SSCS06}: : a brighter catalog which spans $M_r<-21.5$ for which $0.02 < z < 0.135$, and one which includes fainter objects, $M_r<-20$, and so spans a smaller redshift range: $0.02 < z < 0.071$ (the associated apparent magnitude limit is conservative: $m_r \le 17.5$ )."185" Figure 1 shows the mark correlations in the two catalogs when r—band luminosity (top) and the MOPED-inferred mass-weighted age (bottom) are the marks with error bars show results for the fainter sample, (symbolsand lines without error bars are for the brighter sample)."," Figure \ref{fig:xiLumAge} shows the mark correlations in the two catalogs when $r-$ band luminosity (top) and the MOPED-inferred mass-weighted age (bottom) are the marks (symbols with error bars show results for the fainter sample, and lines without error bars are for the brighter sample)."186" So that the weights are dimensionless, the weight of each galaxy is normalized by the mean value for the population."," So that the weights are dimensionless, the weight of each galaxy is normalized by the mean value for the population."187 The notation WW/DD indicates that the mark statistic is the ratio of weighted pair counts to unweighted pair counts. (, The notation WW/DD indicates that the mark statistic is the ratio of weighted pair counts to unweighted pair counts. (188"In this notation, the traditional unweighted correlation function would be DD/RR, where RR is the number of unweighted pair counts in a random distribution.)","In this notation, the traditional unweighted correlation function would be DD/RR, where RR is the number of unweighted pair counts in a random distribution.)"189" Symbols with error bars show results for the fainter catalog, and lines without error bars are for the more luminous sample—we use a similar convention in all the figures which follow."," Symbols with error bars show results for the fainter catalog, and lines without error bars are for the more luminous sample—we use a similar convention in all the figures which follow."190" Error bars were estimated using the analytic expressions given in Shethetal. (2006), which Skibbaetal.(2006) have shown are similar to those from a jackknife analysis; they are similar for the two samples."," Error bars were estimated using the analytic expressions given in \citet{SCS06}, which \citet{SSCS06} have shown are similar to those from a jackknife analysis; they are similar for the two samples."191 The results of Skibba et al., The results of Skibba et al.192" also show that, while using redshift- rather than real-space distances tends to make WW/DD closer to unity on small scales, this is not a severe effect."," also show that, while using redshift- rather than real-space distances tends to make WW/DD closer to unity on small scales, this is not a severe effect."193" 'The top panel shows that close pairs of galaxies tend to be more luminous than average, consistent with previous mark correlation analyses of SDSS galaxies (Skibbaetal.2006)."," The top panel shows that close pairs of galaxies tend to be more luminous than average, consistent with previous mark correlation analyses of SDSS galaxies \citep{SSCS06}."194". Halo-model based analyses of the clustering of SDSS galaxies indicate that, on scales smaller than 1 Mpc, the pair counts are dominated by galaxies in massive haloes (Zehavietal.2005)."," Halo-model based analyses of the clustering of SDSS galaxies indicate that, on scales smaller than 1 Mpc, the pair counts are dominated by galaxies in massive haloes \citep{Zehavi05}."195". Thus, the top panel shows that galaxies in massive haloes are over-luminous."," Thus, the top panel shows that galaxies in massive haloes are over-luminous."196" The bottom panel shows that, in addition to being more luminous than average, close pairs tend to have older than average stellar populations."," The bottom panel shows that, in addition to being more luminous than average, close pairs tend to have older than average stellar populations."197 This suggests that the most massive halos host the oldest stellar populations., This suggests that the most massive halos host the oldest stellar populations.198 The scale dependence in the bottom panel is also qualitatively similar to that seen in semi-analytic galaxy formation models (Sheth2005;Shethetal.," The scale dependence in the bottom panel is also qualitatively similar to that seen in semi-analytic galaxy formation models \citep{sheth05, SCS06}."199" In the models, this happens because close pairs2006).. are dominated by galaxies in clusters, and cluster galaxies host the oldest stars."," In the models, this happens because close pairs are dominated by galaxies in clusters, and cluster galaxies host the oldest stars."200 This is consistent with the model interpretation mentioned above., This is consistent with the halo-model interpretation mentioned above.201 Figure 1 uses marks which are the result of integrating over the entire star formation history of each object., Figure \ref{fig:xiLumAge} uses marks which are the result of integrating over the entire star formation history of each object.202" One of the great virtues of the MOPED analysis is that it returns not just the mass-weighted age at the present time, but an estimate of the entire star formation history of an object."," One of the great virtues of the MOPED analysis is that it returns not just the mass-weighted age at the present time, but an estimate of the entire star formation history of an object."203" Thus, for each object, we have constructed estimates of the fraction of the current stellar mass which formed in each of eight bins in lookback time."," Thus, for each object, we have constructed estimates of the fraction of the current stellar mass which formed in each of eight bins in lookback time."204" Figure 2 shows the joint distribution of star formation fraction and metallicity in the fainter catalog, for each of the lookback time bins."," Figure \ref{fig:sffMet} shows the joint distribution of star formation fraction and metallicity in the fainter catalog, for each of the lookback time bins."205" In each panel, the marks have been normalized by the mean value in the bin."," In each panel, the marks have been normalized by the mean value in the bin."206"For instance, at the two largest lookback times, ((SFF),(Z/Z,))=(0.25,0.65) and (0.43, 0.77).","For instance, at the two largest lookback times, $(\langle {\rm SFF}\rangle, \langle {\rm Z/Z}_\odot\rangle) 207 = (0.25,0.65)$ and $(0.43,0.77)$ ."208" These numbers are (0.25,0.70) and (0.55,0.89) in the more luminous catalog."," These numbers are $(0.25,0.70)$ and $(0.55,0.89)$ in the more luminous catalog."209 The differences indicate that, The differences indicate that210The stability thresholds found from these simulations agree only qualitatively with the predictions (169). and (179).,The stability thresholds found from these simulations agree only qualitatively with the predictions \ref{eq:polfrac}) ) and \ref{eq:wright}) ).211 This probably has to do with effects not included in the analysis. such as the the toroidal geometry of the flux tube. the fact that the poloidal field lines are not eireular in the neighbourhood of the neutral line - in fact they are decidedly elliptical. and that the toroidal field falls off away from the neutral line.," This probably has to do with effects not included in the analysis, such as the the toroidal geometry of the flux tube, the fact that the poloidal field lines are not circular in the neighbourhood of the neutral line - in fact they are decidedly elliptical, and that the toroidal field falls off away from the neutral line."212 It is informative to think about this evolution into a new equilibrium in terms of the magnetic helicity. defined as [B ∆↙∣∖⋡∖↖∣↧∁⇂⊾∁∆↥⊰⋔∁∖⊽∁∁↾⋯⊾⇂↭↾∁⋂⊓⊔∣⋅⇀≓∖⊰↾∣↧∁∏∖∁∣↲∁∖⊽∩," It is informative to think about this evolution into a new equilibrium in terms of the magnetic helicity, defined as $\int {\mathbf B}\cdot{\mathbf A} dV$ where ${\mathbf A}$ is the vector potential."213∣∖⊽∁⊰∩⋂ a dynamical timescale. helicity is conserved and the field can be thought of as evolving into the lowest energy state for that value of helicity.," As the field evolves on a dynamical timescale, helicity is conserved and the field can be thought of as evolving into the lowest energy state for that value of helicity."214 Essentially. helicity can be thought of as the product of toroidal and poloidal fluxes. so that as we go to higher Lyfle ratios. the helicity falls. and below some threshold the lowest energy state is non-axisymmetric.," Essentially, helicity can be thought of as the product of toroidal and poloidal fluxes, so that as we go to higher $E_{\rm p}/E$ ratios, the helicity falls, and below some threshold the lowest energy state is non-axisymmetric."215 The initial equilibrium is essentially a twisted flux tube lying in a eircle around the equator, The initial equilibrium is essentially a twisted flux tube lying in a circle around the equator216(he atmospheric parameters and (he apparent magnitude following (2001).,the atmospheric parameters and the apparent magnitude following .217. The transversal velocity e of the star in kms| can then be caleulated using the simple formula ος=4.74dp. where the distance d is given in kpe and the proper motion je in mas.," The transversal velocity $v_{\rm t}$ of the star in ${\rm km\,s^{-1}}$ can then be calculated using the simple formula $v_{\rm t}=4.74d\mu$, where the distance $d$ is given in kpc and the proper motion $\mu$ in mas."218 The distance to the star is LSkpe and the transversal velocity ~150kms+ perfectly consistent with an evolved star in the thick disk or in the halo2011).," The distance to the star is $\simeq1.5\,{\rm kpc}$ and the transversal velocity $\simeq150\,{\rm km\,s^{-1}}$ perfectly consistent with an evolved star in the thick disk or in the halo."219. 222018—1916 has the highest v4;sin? ever measured for an sdD star., $-$ 1916 has the highest $v_{\rm rot}\sin{i}$ ever measured for an sdB star.220 All other single sdD stars analvsed so [ar have ejsini<lOkms!2009a).," All other single sdB stars analysed so far have $v_{\rm rot}\sin{i}<10\,{\rm km\,s^{-1}}$."221. In the following we discuss ancl exclude several possible explanations for this finding., In the following we discuss and exclude several possible explanations for this finding.222 Rotational velocities exceeding 100kms.+ are quite common among main sequence A and D stars.," Rotational velocities exceeding $100\,{\rm km\,s^{-1}}$ are quite common among main sequence A and B stars."223 Since the surlace gravity logg=4.77 is al the lower end of the hot subdwarl parameter range. (he star may be regarded as a inissclassifiecl massive main sequence star.," Since the surface gravity $\log{g}=4.77$ is at the lower end of the hot subdwarf parameter range, the star may be regarded as a missclassified massive main sequence star."224 This interpretation. however. can be ruled out because the surface gravity. is too high (see Figure 3)) and the helium abundance (1/10—solar) far to low.," This interpretation, however, can be ruled out because the surface gravity is too high (see Figure \ref{tefflogg}) ) and the helium abundance $1/10-$ solar) far to low."225 A double-lined binary consisting of two hot main sequence stars is another option., A double-lined binary consisting of two hot main sequence stars is another option.226 An unresolved. binary may explain the high measured surface gravity. which could be overestimated in this case.," An unresolved, double-lined binary may explain the high measured surface gravity, which could be overestimated in this case."227 ILowever. we cannot imagine a combination of main sequence stars. which would produce such an unusual spectrum.," However, we cannot imagine a combination of main sequence stars, which would produce such an unusual spectrum."228 Two kinds of sdD pulsators are known., Two kinds of sdB pulsators are known.229" The slow pulsations of the 110931IIHer stars (sdDV,) are not expected to influence the ine broadening significantly.", The slow pulsations of the Her stars $_{\rm s}$ ) are not expected to influence the line broadening significantly.230" In the case of the short-period pulsators Ulva (vpe. sdDV,). unresolved pulsations can severely affect the broadening of the lines aud therefore nimc higher c4,sin/."," In the case of the short-period pulsators Hya type, $_{\rm r}$ ), unresolved pulsations can severely affect the broadening of the lines and therefore mimic higher ${v_{\rm rot}\sin\,i}$."231 showed that this happens in the case of the ivbrid pulsator 0090100001., showed that this happens in the case of the hybrid pulsator 090100001.232 Unresolved. pulsations are also most likely responsible or the high c4sin/=39kms1 measured lor the hish-amplitude pulsator 1160520721999).," Unresolved pulsations are also most likely responsible for the high ${v_{\rm rot}\sin\,i}=39\,{\rm km\,s^{-1}}$ measured for the high-amplitude pulsator 1605+072."233. The five spectra of 222018—1916 have been taken with exposure times ranging from 900s to 1500s.," The five spectra of $-$ 1916 have been taken with exposure times ranging from $900\,{\rm s}$ to $1500\,{\rm s}$."234 The effective temperature of the sdD is consistent with the ones of pulsating sdDs., The effective temperature of the sdB is consistent with the ones of short-period pulsating sdBs.235" The tvpical pulsation periods of V, stars are of the order of a few minutes and therefore shorter (han the exposure times.", The typical pulsation periods of $_{\rm r}$ stars are of the order of a few minutes and therefore shorter than the exposure times.236 However. (he measured is so high that verv large photometric variations at periods of a lew minutes," However, the measured ${v_{\rm rot}\sin\,i}=163\,{\rm km\,s^{-1}}$ is so high that very large photometric variations at periods of a few minutes"237Prior to gap opening. gravitational interactions between planets and their surrounding gas disces act to elficienctly damp planetary cecentricity.,"Prior to gap opening, gravitational interactions between planets and their surrounding gas discs act to efficienctly damp planetary eccentricity."238 This damping implies that the formation of giant planets. via core aceretion leads to initially circular orbits. and that post-formation dvnanical ellects must be sought to explain the observed eccentricity distribution. of massive extrasolar planets 2006).," This damping implies that the formation of giant planets via core accretion leads to initially circular orbits, and that post-formation dynamical effects must be sought to explain the observed eccentricity distribution of massive extrasolar planets ."239 Dynamical instability in. multi-planet svstenis. leacing to orbit crossing and the ejection or merger of some of the planets. is one way to achieve this 1997).," Dynamical instability in multi-planet systems, leading to orbit crossing and the ejection or merger of some of the planets, is one way to achieve this ."240. Extensive experiments have shown that with realistic mass functions. the dvnamies of unstable tsvo-planet 20058).. three-planet 2008).. or richer systems can successfully reproduce the observed cecentricity distribution.," Extensive experiments have shown that with realistic mass functions, the dynamics of unstable two-planet , three-planet , or richer systems can successfully reproduce the observed eccentricity distribution."241 The good agreement between dynamical experiments ancl observations is somewhat surprising. as it is hard to cnvisage a Consistent scattering scenario in which gas disc interactions are not important.," The good agreement between dynamical experiments and observations is somewhat surprising, as it is hard to envisage a consistent scattering scenario in which gas disc interactions are not important."242 “Phe simplest model, The simplest model243Most X-ray binary pulsars (XBPs) are High Mass X-Ray Binaries (HMXRBs) in which a Neutron Star (NS) with a magnetic field B —1013 G aceretes matter from a high-mass early-type star. either an OB supergiant or a Be star.,"Most X–ray binary pulsars (XBPs) are High Mass X–Ray Binaries (HMXRBs) in which a Neutron Star (NS) with a magnetic field B $\sim 10^{12}$ G accretes matter from a high–mass early–type star, either an OB supergiant or a Be star."244 The X-ray spectra of both subgroups are generally described by a rather flat power law between 0.1 and 10 keV (photon index ~1) with a high-energy cutoff (?).., The X–ray spectra of both subgroups are generally described by a rather flat power law between 0.1 and 10 keV (photon index $\sim$ 1) with a high–energy cutoff \citep{Nagase02}.245 Several of the brightest XBPs (Ly~10°P eres +) have also à marked soft X-ray excess (222222?)..," Several of the brightest XBPs $L_{X} \sim 10^{37-38}$ erg $^{-1}$ ) have also a marked soft X–ray excess \citep{Ramsay+02,Paul+02,NaikPaul04,Yokogawa+00a,Kohno+00,Burderi+00,Manousakis+09}."246 A variety of simple models (both thermal and non-thermal) have been proposed to fit this feature., A variety of simple models (both thermal and non–thermal) have been proposed to fit this feature.247 Only in a few cases this low-energy component unambiguously showed coherent pulses. therefore the debate over its origin remains open.," Only in a few cases this low–energy component unambiguously showed coherent pulses, therefore the debate over its origin remains open."248 A large number of new pulsars in BeXRB systems has been discovered in the Small Magellanic Cloud. where the observations are unaffected by the high interstellar absorption along the Galactic plane (22222?)..," A large number of new pulsars in BeXRB systems has been discovered in the Small Magellanic Cloud, where the observations are unaffected by the high interstellar absorption along the Galactic plane \citep{Haberl&Sasaki00,Israel+00,Yokogawa+03,Macomb+03,Haberl+08,EgerHaberl08}."249 This allowed the detailed study of their X-ray spectra down to energies of a few hundred eV. leading to the detection of à marked soft excess in most pulsars. also in sources with relatively low luminosity erg 1j (227299).," This allowed the detailed study of their X–ray spectra down to energies of a few hundred eV, leading to the detection of a marked soft excess in most pulsars, also in sources with relatively low luminosity $L_{X} \sim 10^{35-36}$ erg $^{-1}$ ) \citep{Yokogawa+00b,Sasaki+03,Haberl&Pietsch04,Ueno+04,Majid+04,Haberl&Pietsch05}."250 Based on the these results. ? showed that a low-energy component should be visible in all X-ray pulsars that have sufficiently high flux and small absorption.," Based on the these results, \citet{Hickox+04} showed that a low–energy component should be visible in all X–ray pulsars that have sufficiently high flux and small absorption."251 In fact. most of the soft-excess sources are at small distances and/or away from the Galactic plane (most of them are in the Magellanie Clouds).," In fact, most of the soft–excess sources are at small distances and/or away from the Galactic plane (most of them are in the Magellanic Clouds)."252 This suggests that the presence of a soft spectral component could be à very common. if not an ubiquitous. feature intrinsic to X-ray pulsars.," This suggests that the presence of a soft spectral component could be a very common, if not an ubiquitous, feature intrinsic to X–ray pulsars."253 Different explanations for its origin have been proposed. depending on the source luminosity.," Different explanations for its origin have been proposed, depending on the source luminosity."254 When Ly>107 erg +. the luminosity and the shape of the soft component can be explained only by the presence of an optically-thick accretion disk. which reprocesses the hard coming from the neutron star at its inner edge.," When $L_{X} \ge 10^{38}$ erg $^{-1}$, the luminosity and the shape of the soft component can be explained only by the presence of an optically–thick accretion disk, which reprocesses the hard X--rays coming from the neutron star at its inner edge."255 In less luminous sources. with Ly<1079 erg +. the soft excess can be due to other processes. such as emission by photo-ionized or collisionally-heated diffuse gas or thermal emission from the surface of the neutron star.," In less luminous sources, with $L_{X} \le 10^{36}$ erg $^{-1}$, the soft excess can be due to other processes, such as emission by photo--ionized or collisionally–heated diffuse gas or thermal emission from the surface of the neutron star."256 Finally. in the sources of intermediate luminosity. either or both of these types of emission can be present.," Finally, in the sources of intermediate luminosity, either or both of these types of emission can be present."257 Recently. a clear thermal excess has been observed also in the cases of RX JO146.94+6121 (2) and 4U 03524309 (?).. which are two persistent Be pulsars.," Recently, a clear thermal excess has been observed also in the cases of RX J0146.9+6121 \citep{LaPalombaraMereghetti2006} and 4U 0352+309 \citep{LaPalombaraMereghetti2007}, which are two persistent Be pulsars."258 This is a specific class of binary pulsars characterized by low luminosity (Ly~Lo?!77 erg lj and long pulse period (?> 100 s): moreover. they show no transient behavior. since the source Juminosity varies at most of a factor ~ 10 (?)..," This is a specific class of binary pulsars characterized by low luminosity $L_{X} \sim 10^{34-35}$ erg $^{-1}$ ) and long pulse period $P >$ 100 s); moreover, they show no transient behavior, since the source luminosity varies at most of a factor $\sim$ 10 \citep{Negueruela98}."259 These properties suggest that the Be star orbits the NS in a wide and nearly circular orbit. continuously accreting material from the low-density outer regions of the circumstellar envelope.," These properties suggest that the Be star orbits the NS in a wide and nearly circular orbit, continuously accreting material from the low–density outer regions of the circumstellar envelope."260 This picture has been confirmed for 4U 03524309 by the discovery of an orbital period of 250.3 days (?).., This picture has been confirmed for 4U 0352+309 by the discovery of an orbital period of 250.3 days \citep{Delgado-Marti+2001}.261 The detection of the thermal excess in these two persistent pulsars was favoured by their small distance (d.< 2.5 kpc) and interstellar absorption (Nyy~1074 7)., The detection of the thermal excess in these two persistent pulsars was favoured by their small distance $d \le$ 2.5 kpc) and interstellar absorption $N_{\rm H} \sim 10^{21}$ $^{-2}$ ).262 It is interesting to investigate if other persistent Be binary pulsars are characterized by the same type of spectral feature. in order to check if it is à common property of this class of sources.," It is interesting to investigate if other persistent Be binary pulsars are characterized by the same type of spectral feature, in order to check if it is a common property of this class of sources."263 To this aim. we have observed with tthe Be/NS binary pulsarJ1037.5-5647.. identified with LS 1698. a BO III-Ve star at  5 kpe (?)..," To this aim, we have observed with the Be/NS binary pulsar, identified with LS 1698, a B0 III–Ve star at $\sim$ 5 kpc \citep{Motch+97}."264 This source is likely associated to the source 4U 1036-56 (?).. the source 3A 1036-565 (?) and the source 1M 1022-554 (?)..," This source is likely associated to the source 4U 1036-56 \citep{Forman+78}, , the source 3A 1036-565 \citep{Warwick+81} and the source 1M 1022-554 \citep{Markert+79}."265 Thanks to observations performed by the instrument on-boardRossiXTE.. ? performed the first detailed timing and spectral analysis. and discovered a pulsation with period P=860+2 s. The source spectrum could be described by a cut-off power law. with a low cut-off energy (4=1.7 keV) and a weak (equivalent width EQW ~ 65 eV) tron line at 6.5 keV: moreover. the estimated source luminosity (Lx~2«10°? erg +) was fully consistent with the luminosity level detected by the previous observations. and the light curve showed no large variability.," Thanks to observations performed by the instrument on–board, \citet{ReigRoche99} performed the first detailed timing and spectral analysis, and discovered a pulsation with period $P = 860 \pm 2$ s. The source spectrum could be described by a cut–off power law, with a low cut–off energy $E_{\rm cut} = 4.7$ keV) and a weak (equivalent width EQW $\simeq$ 65 eV) iron line at 6.5 keV; moreover, the estimated source luminosity $L_{\rm X} \simeq 2\times 10^{35}$ erg $^{-1}$ ) was fully consistent with the luminosity level detected by the previous observations, and the light curve showed no large variability."266 Therefore. lis a long-period. low-luminosity Be/NS XBP which has been detected every time it has been observed.," Therefore, is a long–period, low–luminosity Be/NS XBP which has been detected every time it has been observed."267 All these properties are typical of the persistent Be/NS pulsars. therefore ? suggested that lis a potential member of this class ofsources.," All these properties are typical of the persistent Be/NS pulsars, therefore \citet{ReigRoche99} suggested that is a potential member of this class ofsources."268the source is barely detected in the TE/ANSM. and the count rate often drops beow the 3-0 ASAL detection limit.,the source is barely detected in the /ASM and the count rate often drops below the $\sigma$ ASM detection limit.269 The lighteurve ancl hardness ratio shown in Fig., The lightcurve and hardness ratio shown in Fig.270 1 suggest that the source transited rom the LS to a lower Lux level. presumably an coll state zuter MJD 51330.," 1 suggest that the source transited from the LS to a lower flux level, presumably an `off' state after MJD 51330."271 PheAX liehteurves in the various energv bands do not show any evidence for variability on imescales from 100s to 5000s (the 3-7 upper limit on the semi-amplituce is ))., The lightcurves in the various energy bands do not show any evidence for variability on timescales from 100s to 5000s (the $\sigma$ upper limit on the semi-amplitude is ).272 We have also checked for the LS-like fast time (< 100 s) variability as seen typically in the LS of rlack hole X-ray binaries (see e.g. van der Ixlis 1995). but low counting statistics prevented us rom setting useful upper limits.," We have also checked for the LS-like fast time $<$ 100 s) variability as seen typically in the LS of black hole X-ray binaries (see e.g. van der Klis 1995), but low counting statistics prevented us from setting useful upper limits."273 The broad-band (0.850 keV) spectrum. of 33394 rom the LECS. MECS and PDS data is satisfactorily (AZ=1.09 for 56 degrees of freedom. (d.o.L))," The broad-band (0.8–50 keV) spectrum of 339–4 from the LECS, MECS and PDS data is satisfactorily $\chi^2_{\nu}=1.09$ for 56 degrees of freedom (d.o.f.))"274 fitted. by a single power-law plus absorption., fitted by a single power-law plus absorption.275 The best fit spectral parameters are summarized in Table 2 and the spectrum is shown in Fig., The best fit spectral parameters are summarized in Table 2 and the spectrum is shown in Fig.276 3., 3.277λ We do not sec any significant bo-l line. emission tween GA6.7. keV. with a confidence upper limit of 600 eV on the equivalent width.," We do not see any significant Fe-K line emission between 6.4–6.7 keV, with a confidence upper limit of $\sim 600$ eV on the equivalent width."278 We note that there is a residual in the LECS below 0.9 keV and this might be due to avery soft. black-bods component or line emission near the Ie-L complex (c.g. Vrtilek et al.," We note that there is a residual in the LECS below 0.9 keV and this might be due to a very soft black-body component or line emission near the Fe-L complex (e.g. Vrtilek et al.,"279 1988)., 1988).280 We have also fitted the spectrum. with single black-body and: bremsstrahlung models. but they are unacceptable (AZ. 2 2).," We have also fitted the spectrum with single black-body and bremsstrahlung models, but they are unacceptable $\chi^2_\nu$ $>$ 2)."281 In the optical. the source was seen at £=20.1+0.1 and V—19.2+001.," In the optical, the source was seen at $B=20.1\pm0.1$ and $V=19.2\pm0.1$."282 Our N-rav. (0.850. keV) and optical observations of 3339.4 took place during a very low intensity (212 keV) X-ray state. presumably the X-ray col. state (see Fig.," Our X-ray (0.8–50 keV) and optical observations of 339–4 took place during a very low intensity (2–12 keV) X-ray state, presumably the X-ray `off' state (see Fig."283 1)., 1).284 Comparing with andRATE observations obtained when the source was in a LS (Wilms et al., Comparing with and observations obtained when the source was in a LS (Wilms et al.285 L999: Belloni et al., 1999; Belloni et al.286 1999: see also Table E). the spectral index ancl neutral ivdrogen column are similar (a~L6. Ng~5.IO em7). it our observed lux o£2.2 10P erg 7s + (20 keV) is much lower by 23 orders of magnitude.," 1999; see also Table 1), the spectral index and neutral hydrogen column are similar $\alpha \sim 1.6$, $N_H \sim 5\times 10^{21}$ $^{-2}$ ), but our observed flux of $2.2\times 10^{-12}$ erg $^{-2}$ $^{-1}$ (2–10 keV) is much lower by 2–3 orders of magnitude."287 This confirms hat the source indeed changed to a very low luminosity state as indicated by the ZXTE/ASM cata., This confirms that the source indeed changed to a very low luminosity state as indicated by the /ASM data.288 Note that the observed column density is also Consistent with that derived rom optical reddening. Le. Na=(6.0+0.6)QU2 2? (see Zelziarski et al.," Note that the observed column density is also consistent with that derived from optical reddening, i.e. $N_H=(6.0\pm0.6)\times10^{21}$ $^{-2}$ (see Zdziarski et al."289 1998 for more detail)., 1998 for more detail).290 At a distance of 4 kpe. he observed soft X-ray {510 keV) lhiniinositv is 6.6107 erg +.," At a distance of 4 kpc, the observed soft X-ray (0.5–10 keV) luminosity is $6.6\times10^{33}$ erg $^{-1}$."291 LHovaisky et al. (, Ilovaisky et al. (29286) reporte an ol state seen byEXOSAT with a luminosity of 1.1;107 erg linthe 0.510 keV. band: our measurement is à factor of ~ 17 below that.,1986) reported an `off' state seen by with a luminosity of $1.1\times 10^{35}$ erg $^{-1}$ in the 0.5–10 keV band; our measurement is a factor of $\sim$ 17 below that.293 We also note that an upper limit was obtained by in 1993 of 5103 erg | (Asai et al., We also note that an upper limit was obtained by in 1993 of $5\times 10^{32}$ erg $^{-1}$ (Asai et al.294 1998). which suggests hat the source was in he voll state as well.," 1998), which suggests that the source was in the `off' state as well."295 In actelition. olan et al. (," In addition, Nolan et al. ("2961982) observed the source in the 12200 keV xui ancl claimed that one of the observations was in the ο state with a Lux level of 4.710 Loerg 2401; —cinthe 2050 keV band.,1982) observed the source in the 12–200 keV band and claimed that one of the observations was in the `off' state with a flux level of $4.7\times 10^{-10}$ erg $^{-2}$ $^{-1}$ in the 20–50 keV band.297 This luminosity is only comparable with he recent. TE/MIENTIE observations (Wilms et al., This luminosity is only comparable with the recent /HEXTE observations (Wilms et al.298 1999) in the LS. while our PDS observation indicates that the source was down to ~3.5.⋅1012 ere em Dod;in the same energy band.," 1999) in the LS, while our PDS observation indicates that the source was down to $\sim 3.5\times29910^{-12}$ erg $^{-2}$ $^{-1}$ in the same energy band."300 FPherefore. the Nolan ct al. (," Therefore, the Nolan et al. ("3011982) observation was actually not in the “oll” state.,1982) observation was actually not in the `off' state.302 We have obtained thefirs! firm detection of 3339.4 at low intensity up to 50 keV. In the optical. our observed. magnitude of V=19.2 and 44=20.1 are faint compared to the wide range of reported magnitudes: Dκ)21 (llovaisky 198 )and V—15.4 (Aloteh et al.," We have obtained the firm detection of 339–4 at low intensity up to 50 keV. In the optical, our observed magnitude of $V=19.2$ and $B=20.1$ are faint compared to the wide range of reported magnitudes: $B \gta 21$ (Ilovaisky 1981) and $V=15.4$ (Motch et al."303 1982)., 1982).304 Our result. is. however. comparable to the observations by Llovaisky (1981) ane Remillard and AMeClintock (1987). and this is the third. time that the B magnitude has been seen to fall to ~20.," Our result is, however, comparable to the observations by Ilovaisky (1981) and Remillard and McClintock (1987), and this is the third time that the $B$ magnitude has been seen to fall to $\sim 20$."305 The observed colour. D.V. is 0.9. which is also consistent with previous observations in dillerent X-ray states (Makishima et al.," The observed colour, $B-V$ is 0.9, which is also consistent with previous observations in different X-ray states (Makishima et al."306 1986: Hlovaisky ct al., 1986; Ilovaisky et al.307 1986: Corbet et al., 1986; Corbet et al.308 LOST)., 1987).309 We note that the optica and X-ray emission can be anti-correlated during state transitions (e.g. Motch et al., We note that the optical and X-ray emission can be anti-correlated during state transitions (e.g. Motch et al.310 1985: observations during LS to LIS transition)., 1985; observations during LS to HS transition).311" Our observations show that this may not be the case in the current ""oll state since both N-ray", Our observations show that this may not be the case in the current `off' state since both X-ray3122012).,.313". From this investigation we conclude that the decrease of LO""... due to iis noticeable only for very low mass progenitors, which reach low at early times, when r, is still potentially large."," From this investigation we conclude that the decrease of $\lcrit$ due to is noticeable only for very low mass progenitors, which reach low $\mdot$ at early times, when $\rnu$ is still potentially large."314" This would be Mpossible for a stiff equation of state of dense nuclear matter, which would keep r, high?."," This would be possible for a stiff equation of state of dense nuclear matter, which would keep $\rnu$ ."315. The reduction of |ae depends on the assumed neutrino energies and luminosities., The reduction of $\lcrit$ depends on the assumed neutrino energies and luminosities.316" So far, we have discussed the case favorable forCvO,, specifically (e,;8b,εν)=(13,15.5,20) MMeV and Ly,core=Lig,coreLvy,core."," So far, we have discussed the case favorable for, specifically $(\epsnue^{\rm i}, \epsnuebar^{\rm i}, \epsnux^{\rm i}) = (13,15.5,20)$ MeV and $\lcore = L_{\nuebar,{\rm core}} = L_{\nux,{\rm core}}$."317" Now we turn to neutrino energies and, luminosities that more closely approximate the results of the recent sophisticated calculations (e.g.Marek&Janka2009;Fischeretal.2010,2012),, namely (6,62,εν)=(11,13, MMeV and Ly,core= 2L,,.core, Shown with green 18)dotted lines in Figure 2.."," Now we turn to neutrino energies and luminosities that more closely approximate the results of the recent sophisticated calculations \citep[e.g.][]{marek09,fischer10,fischer12}, namely $(\epsnue^{\rm i},\epsnuebar,\epsnux^{\rm i}) = (11,13,18)$ MeV and $\lcore = L_{\nuebar,{\rm core}} = 2L_{\nux,{\rm core}}$ , shown with green dotted lines in Figure \ref{fig:fred}."318" We see that for these parameters, the bbecome apparent at approximately the same values of M,but the effect is much smaller."," We see that for these parameters, the become apparent at approximately the same values of $\mdot$,but the effect is much smaller."319" For M=1.2Mo and τν= 60kkm the maximum possible reduction of LOre is only about 10%, much smaller than ~40% for the equal luminosities and higher neutrino energies."," For $M=1.2\,\msun$ and $\rnu=60$ km the maximum possible reduction of $\lcrit$ is only about $10\%$, much smaller than $\sim 40\%$ for the equal luminosities and higher neutrino energies."320" Interestingly, unequal luminosities allow for a possibility of having freq>1."," Interestingly, unequal luminosities allow for a possibility of having $\fred > 1$."321" One case when this can happen is when ¢,,, is low enough, so that v, and v oscillate to vx, but there is very little v to oscillate back."," One case when this can happen is when $\phi_{\nux}$ is low enough, so that $\nue$ and $\nuebar$ oscillate to $\nux$, but there is very little $\nux$ to oscillate back."322" As a result, the luminosity in Νο and v decreases and ccan thus be detrimental for the explosion."," As a result, the luminosity in $\nue$ and $\nuebar$ decreases and can thus be detrimental for the explosion."323 We do not see frea>1 for any considered parameter combination., We do not see $\fred > 1$ for any considered parameter combination.324 Now we compare the eeffect to other physical effects that have been shown to decrease Lo ores , Now we compare the effect to other physical effects that have been shown to decrease $\lcrit$ .325"We have seen that the relative positions of rs, rsync and renq determine the effect of O."," We have seen that the relative positions of $\rs$, $\rsync$ and $\rend$ determine the effect of ."326". It is known that multi- effects like convection and SASI consistently increase shock radii (e.g.Burrowsetal.1995;Ohnishi2006;Iwakamihausetal.2010) and decrease Loore over the corresponding 1D value (Murphy&Burrows2008;Nordhausetal.2010;Suwa 2011),, as illustrated by the grey lines with dots in Figure 2.."," It is known that multi-dimensional effects like convection and SASI consistently increase shock radii \citep[e.g.][]{bhf95,ohnishi06,iwakami08,murphy08,marek09,nordhaus10} and decrease $\lcrit$ over the corresponding 1D value \citep{murphy08,nordhaus10,suwa10,hanke11}, as illustrated by the grey lines with dots in Figure \ref{fig:fred}."327 The common explanation is that multi-dimensional effects make the energy deposition of neutrinos more efficient by increasing the dwell time of the matter in the gain region (Murphy&Burrows2008;Nordhausetal.2010;Taki-wakietal.," The common explanation is that multi-dimensional effects make the energy deposition of neutrinos more efficient by increasing the dwell time of the matter in the gain region \citep{murphy08,nordhaus10,takiwaki12}. ."328" 2012).. In PaperL, we attempted to address this issue by adjusting the heating or cooling within the framework of our steady-state calculations."," In \citetalias{pejcha12}, we attempted to address this issue by adjusting the heating or cooling within the framework of our steady-state calculations."329" We found that both a decrease of cooling and an increase of heating make smaller and increase rg for a fixed L,,,core.", We found that both a decrease of cooling and an increase of heating make $\lcrit$ smaller and increase $\rs$ for a fixed $\lcore$.330" However, rg LOincreasesoeonly for the case of reduced cooling."," However, $\rscrit$ increasesonly for the case of reduced cooling."331" For this reason, based on inspection of simulation results, we suggested (but did not prove) that the decrease of Lo seen in multi-dimensional simulations is the result of less efficientore neutrino cooling instead of the commonly assumed increase in heating efficiency."," For this reason, based on inspection of simulation results, we suggested (but did not prove) that the decrease of $\lcrit$ seen in multi-dimensional simulations is the result of less efficient neutrino cooling instead of the commonly assumed increase in heating efficiency."332" This decreases Lgore by about 3096 compared to the fiducial case, similar to the difference in Lg observed by Nordhausetal.(2010),, as evidenced by the lower orethick grey line in Figure 2.."," This decreases $\lcrit$ by about $30\%$ compared to the fiducial case, similar to the difference in $\lcrit$ observed by \citet{nordhaus10}, as evidenced by the lower thick grey line in Figure \ref{fig:fred}."333 The blue dash-dotted line in Figure 2 (and in the left panel of Figure 1)) then shows Loore with aand reduced cooling., The blue dash-dotted line in Figure \ref{fig:fred} (and in the left panel of Figure \ref{fig:osc}) ) then shows $\lcrit$ with and reduced cooling.334" As expected, because of lower Loore and higher rs at fixed L,,,core, the effect of sstarts to be apparent for MX0.5Mos-!1 and reaches full strength for M<0.04Mcs~?."," As expected, because of lower $\lcrit$ and higher $\rs$ at fixed $\lcore$, the effect of starts to be apparent for $\mdot \lesssim 0.5\ \msun\ \invs$ and reaches full strength for $\mdot \lesssim 0.04\ \msun\ \invs$."335" At low M, the effect of bbecomes comparable to that of increasing the dimension of the simulation from 1D to 3D, but only for fairly large r, and small and for the less realistic energies and luminosities (red dashed Mlines)."," At low $\mdot$, the effect of becomes comparable to that of increasing the dimension of the simulation from 1D to 3D, but only for fairly large $\rnu$ and small $M$ and for the less realistic energies and luminosities (red dashed lines)."336" In PaperI we investigated the effect of a simple gray neutrino radiation transport on LOre dL,/dr4 0).", In \citetalias{pejcha12} we investigated the effect of a simple gray neutrino radiation transport on $\lcrit$ $\intd \lnu / \intd r \neq 0$ ).337 We found that including the neutrinos generated by the cooling of the accretion flow itself (the accretion luminosity) lowers Lore by 896 to 23% for the mass accretionrates between 0.01 and 2Mo ss!.," We found that including the neutrinos generated by the cooling of the accretion flow itself (the accretion luminosity) lowers $\lcrit$ by $8\%$ to $23\%$ for the mass accretionrates between $0.01$ and $2\,\msun$ $^{-1}$ ."338" However, the accretion luminosity was always a small fraction of Lgore and the PNS neutrino emission has to play the major role in reviving the stalled accretion shock."," However, the accretion luminosity was always a small fraction of $\lcrit$ and the PNS neutrino emission has to play the major role in reviving the stalled accretion shock."339 In Figure 2 we plot with a thick grey line frea that was obtained by including the accretion luminosity and we see that it is somewhat smallerthan the maximum effect from CvO., In Figure \ref{fig:fred} we plot with a thick grey line $\fred$ that was obtained by including the accretion luminosity and we see that it is somewhat smallerthan the maximum effect from .340". The effect of accretion luminosity is most prominent at high M and has similar importance at small M and small r,.", The effect of accretion luminosity is most prominent at high $\mdot$ and has similar importance at small $\mdot$ and small$\rnu$ .341 The effect of the accretion luminosity is comparable to going from 1D calculations to 2D in the calculations of Nordhaus (2010).., The effect of the accretion luminosity is comparable to going from 1D calculations to 2D in the calculations of \citet{nordhaus10}. .342 Throughoutthis Section wehave neglected the matter-suppression effects on iin order to obtain the maximum possible effect of oover abroad range of parameters., Throughoutthis Section wehave neglected the matter-suppression effects on in order to obtain the maximum possible effect of over abroad range of parameters.343 We found that, We found that344GOODS-N. region).,"GOODS-N, region)."345 In contrast. we find that the Farrahetal.2003. ULIRG sample has a median 7;=42bh when their photometry are fit with our grevbody. (see also Clementsetal. 2008)).," In contrast, we find that the \citealt{Farrah} ULIRG sample has a median $T_\mathrm{d}=42\,\mathrm{K}$ when their photometry are fit with our greybody (see also \citealt{Clements08}) )."346 Thus SMGs appear to have lower temperatures on average than local ULIIBCs. although bear in mind that local ULIRGs are selected. at GOyma which inherently introcluces a bias to selecting roller objects than submum observations would typically find.," Thus SMGs appear to have lower temperatures on average than local ULIRGs, although bear in mind that local ULIRGs are selected at $60\,\mathrm{\mu m}$ which inherently introduces a bias to selecting hotter objects than submm observations would typically find."347 The SED is integrated. to. estimate the bolometric luminosity of the SALG., The SED is integrated to estimate the bolometric luminosity of the SMG.348 Assuming that he FUR luminosity. is predominantly. powered. by star-formation (i.c. negligible contribution from an AGN). coming [rom ao starburst of less than LOOALAIwr. with a Salpeer(19595) initial," Assuming that the FIR luminosity is predominantly powered by star-formation (i.e. negligible contribution from an AGN), coming from a starburst of less than Myr, with a \citet{Salpeter55} initial"349"prescription for Mj and L/Lj4; use eppg and Lsyyy. which are derived [rom (or highly correlated. with) fo EWILIM ancl Mj: respectively, we perform two additional principal component analvses. one excluding //;5 EWIIM as an input variable and one excluding both Ho FWIHAI and Ady: as input variables.","prescription for $M_{BH}$ and $L/L_{Edd}$ use $v_{BLR}$ and $L_{5100}$, which are derived from (or highly correlated with) $H\beta$ FWHM and $M_V$ respectively, we perform two additional principal component analyses, one excluding $H\beta$ FWHM as an input variable and one excluding both $H\beta$ FWHM and $M_V$ as input variables."350" Note that. ο EWIIM but not M, figure prominently in (he first principal component. the one that we suspect is driven by. L/Lig."," Note that $H\beta$ FWHM but not $M_V$ figure prominently in the first principal component, the one that we suspect is driven by $L/L_{Edd}$."351 Table 2 gives the correlation coefliients among L/Lpag. Mg. and the (wo principal components of each of the three analyses.," Table 2 gives the correlation coefficients among $L/L_{Edd}$, $M_{BH}$, and the two principal components of each of the three analyses."352 It is clear Chat L/Lpj; is most highly correlated with PCI: correlation coefficients of 0.53. 0.45. and 0.45 are found for the three analvsis.," It is clear that $L/L_{Edd}$ is most highly correlated with PC1; correlation coefficients of 0.53, 0.45, and 0.45 are found for the three analysis."353 These correspond to chance probabilities less than0., These correspond to chance probabilities less than.3540154... Note also that {μμ is highly correlated. with both principal components., Note also that $M_{BH}$ is highly correlated with both principal components.355 The PG sample. although well defined. contains only a small nunber of radio-Ioud QSOs.," The PG sample, although well defined, contains only a small number of radio-loud QSOs."356 In order to work with a sample that will allow conclusions to be drawn about the differences between racio-quiet and radio-lIoud objects. we supplement (he DG92 measurements wilh two raclio-loud samples. 46 objects Irom Corbin(1997) and 29 additional objects Irom (1996).," In order to work with a sample that will allow conclusions to be drawn about the differences between radio-quiet and radio-loud objects, we supplement the BG92 measurements with two radio-loud samples, 46 objects from \citet{Corbin97} and 29 additional objects from \citet{Brotherton96}."357. A few of the objects from those samples in which the S/N was obviously poor. or in which [O IH] A5007 could not be accurately measured were excluded.," A few of the objects from those samples in which the S/N was obviously poor, or in which [O III] $\lambda$ 5007 could not be accurately measured were excluded."358 Measurements of (he emission-line parameters including the strengths of 19. |O ΗΕ A5007. and Fe II and the width. shape. shift. aud asvimmetry of f/f are. drawn [rom (hose papers.," Measurements of the emission-line parameters including the strengths of $H\beta$, [O III] $\lambda$ 5007, and Fe II and the width, shape, shift, and asymmetry of $H\beta$ are drawn from those papers."359" Continuum properties such as My. a,,. and log I. are drawn from those papers or references (herein."," Continuum properties such as $M_V$, $\alpha_{ox}$, and log R are drawn from those papers or references therein."360 In a few cases. we have updated (hese values or filled in missing values through searches of the more recent literature.," In a few cases, we have updated these values or filled in missing values through searches of the more recent literature."361 llavinge tabulated the known values for these 75 additional objects. the approach taken toward combining the samples was not to repeat the PCA with the entire dataset.," Having tabulated the known values for these 75 additional objects, the approach taken toward combining the samples was not to repeat the PCA with the entire dataset."362 Because the new objects represent very different selection criteria than the original PG sample. the variance in the total sample would be dominated by the differences between (he original UV-excess selected objects that are predominantly racdio-quiet ancl of lower luminosity aud the new racdio-selected objects that are at somewhat higher redshift and higher luminosity.," Because the new objects represent very different selection criteria than the original PG sample, the variance in the total sample would be dominated by the differences between the original UV-excess selected objects that are predominantly radio-quiet and of lower luminosity and the new radio-selected objects that are at somewhat higher redshift and higher luminosity."363 The goal of increasing the sample is to use the tools that have been derived [rom the PG analvsis to better understand what happens when the extent of parameter space is Increase., The goal of increasing the sample is to use the tools that have been derived from the PG analysis to better understand what happens when the extent of parameter space is increased.364 Therefore. (he projections of the new objects on the principal components derived in the previous section were evaluated. (using the coefficients eiven in Table 1) aud the new PCI vs. PC? diagram is shown in Figure 4.," Therefore, the projections of the new objects on the principal components derived in the previous section were evaluated (using the coefficients given in Table 1) and the new PC1 vs. PC2 diagram is shown in Figure 4."365 In evaluating (he new objects in terms of the original principal components. some of the," In evaluating the new objects in terms of the original principal components, some of the"366to thermal electrons in the CCD iuterferiug with the signal.,to thermal electrons in the CCD interfering with the signal.367 Most of this noise is in the high spatial frequency reeiue., Most of this noise is in the high spatial frequency regime.368 Iu order to get rid of this high frequency noise as wich as possible. a Wiener filter was used.," In order to get rid of this high frequency noise as much as possible, a Wiener filter was used."369 Applving the Wiener filter is esscutially the process of convolving the noise degraded image f(x) with the Wiener filter., Applying the Wiener filter is essentially the process of convolving the noise degraded image $I({\bf x})$ with the Wiener filter.370 The Wiener filter is applied in the frequency domain., The Wiener filter is applied in the frequency domain.371 Then the original nage spectrum Z(u) is estimated from the degraded image spectrum Z/(u) by simply iultiplviug the nuage spectimm with the Wiener filter W(u)., Then the original image spectrum ${I}({\bf u})$ is estimated from the degraded image spectrum $I^\prime({\bf u})$ by simply multiplying the image spectrum with the Wiener filter $W({\bf u})$.372 However. this will reduce the resolutiou iu the reconstructed image.," However, this will reduce the resolution in the reconstructed image."373 The advantage is the spurious higher frequency coutribution are eliminated., The advantage is the spurious higher frequency contribution are eliminated.374" The Wiener filter. in the frequency domain. has the following functional form: where. fu) is the Fourier transform of the point-spread-function.. (uu) the power spectrum of signal process. and 2,(u) the power spectrum of noise process."," The Wiener filter, in the frequency domain, has the following functional form: where, $H({\bf u})$ is the Fourier transform of the point-spread-function, $P_{s}({\bf u})$ the power spectrum of signal process, and $P_{n}({\bf u})$ the power spectrum of noise process."375" The term P,(u)/P.(u) can be interpreted as reciprocal of signal to noise ratio.", The term $P_{n}({\bf u})$ $P_{s}({\bf u})$ can be interpreted as reciprocal of signal to noise ratio.376 Iu our case. the noise is due to the CCD.," In our case, the noise is due to the CCD."377 We developed au IRAF-based algorithiu. where à Wiener parameter. e. is added to the PSF power spectra. in order to avoid zeros iu the PSF power spectimm that helps iu recoustructious with a few frames.," We developed an IRAF-based algorithm, where a Wiener parameter, $w$, is added to the PSF power spectrum in order to avoid zeros in the PSF power spectrum that helps in reconstructions with a few frames."378 The classic Weiner ülter that came out of the electronic information theory where diffractiou-limits do not mean much. is meant to deal with signal dependent coloured! noise.," The classic Weiner filter that came out of the electronic information theory where diffraction-limits do not mean much, is meant to deal with signal dependent 'coloured' noise."379 Ta practice. this term is usually just a constant. a noise coutrol parameter whose scale is estimated from the noise power spectrum.," In practice, this term is usually just a constant, a 'noise control parameter' whose scale is estimated from the noise power spectrum."380 In this case. it assumes that the uoise is white aud that one can estimate its scale in regions of the power spectrmm where the sigual is zero (outside the diffraction-liudt for an imagine svstem).," In this case, it assumes that the noise is white and that one can estimate its scale in regions of the power spectrum where the signal is zero (outside the diffraction-limit for an imaging system)."381 The expression for the Wiener filter simplifies to: where. wis the noise-variauce and termed as Wiener filter paramcter in the program.," The expression for the Wiener filter simplifies to: where, $w$ is the noise-variance and termed as Wiener filter parameter in the program."382 To get an optimally autocorrelated image. a judicious choice of the Wiener filter parameter is made according to the procedure described below: For a very wide range of Wiener filter parameter values. the autocorrelated inages are constructed.," To get an optimally autocorrelated image, a judicious choice of the Wiener filter parameter is made according to the procedure described below: For a very wide range of Wiener filter parameter values, the autocorrelated images are constructed."383 A sinall portion (16 X 16 pixels) of cach image. far from the ceutre. is sampled to find-out the standard deviation iu the iutensity," A small portion (16 X 16 pixels) of each image, far from the centre, is sampled to find-out the standard deviation in the intensity"384S101 and for the 0.50 aresce dise is 5.5«107.,$8\times10^4$ and for the 0.50 arcsec disc is $5.5\times10^4$.385 ΓΙ shows that for à Gaussian mask at the focus compared to a solid disc of comparable size. an undersized pupil stop further along the beam works to greater advantage in suppressing the final image.," This shows that for a Gaussian mask at the focus compared to a solid disc of comparable size, an undersized pupil stop further along the beam works to greater advantage in suppressing the final image."386 In terms of attenuation factors. the cllect of adding the Lyot stop (measured at LO pixels) with the Gaussian mask compared to no Lyot stop brings about a [actor of 16 drop in measured. CCD counts. for the 0.50 aresec disc this factor is only 4.6.," In terms of attenuation factors, the effect of adding the Lyot stop (measured at 10 pixels) with the Gaussian mask compared to no Lyot stop brings about a factor of 16 drop in measured CCD counts, for the 0.50 arcsec disc this factor is only 4.6."387 At GO pixels. for the Gaussian the [actor is 1.53 and for the 0.50 arcsec disc 1.75. approximately the same.," At 60 pixels, for the Gaussian the factor is 1.83 and for the 0.50 arcsec disc 1.75, approximately the same."388" The extra effectiveness of the Lyot stop with the Gaussian mask is therefore greatest. close in to the mask. with the ""Lyot factor’ dropping as the distance from the mask increases until it converges with the 0.50 aresec mask values."," The extra effectiveness of the Lyot stop with the Gaussian mask is therefore greatest close in to the mask, with the `Lyot factor' dropping as the distance from the mask increases until it converges with the 0.50 arcsec mask values."389 This trend is shown in Fig. 12.., This trend is shown in Fig. \ref{lyot_factor}.390 OSCA and its clectronies were shipped to La Palma at the beginning of May 2002 and it underwent first commissioning soon after., OSCA and its electronics were shipped to La Palma at the beginning of May 2002 and it underwent first commissioning soon after.391 Only two nights on-skv. were allocated for the OSCA commissioning so time was very limited., Only two nights on-sky were allocated for the OSCA commissioning so time was very limited.392 The first night was plagued by extremely bad. seeing throughout (5 aresee recorded at worst) and the AQ system could not be used., The first night was plagued by extremely bad seeing throughout (5 arcsec recorded at worst) and the AO system could not be used.393 Since the largest occulting mask in OSCA is 2.0 arcsec it was also not feasible to do any performance testing., Since the largest occulting mask in OSCA is 2.0 arcsec it was also not feasible to do any performance testing.394 The last night (24th May) saw very variable seeing over the course of the night and sky-location ancl the presence of high. cirrus cloud also caused problems on occasion., The last night (24th May) saw very variable seeing over the course of the night and sky-location and the presence of high cirrus cloud also caused problems on occasion.395 NAOAIL was used although centring objects on the OSCA occulting masks was cdillicult when the seeing was bad ancl OSCA performance was degraded., NAOMI was used although centring objects on the OSCA occulting masks was difficult when the seeing was bad and OSCA performance was degraded.396 “Phe average seeing was 1.5 arcsec. anc with the AO svstem an average corrected PSE width of 0.5 arcsec was obtained.," The average seeing was 1.5 arcsec, and with the AO system an average corrected PSF width of 0.5 arcsec was obtained."397 Fig., Fig.398 13. shows the suppression obtained. using OSCA in /I-band using the 2.0 aresec mask during these conditions., \ref{may_sup} shows the suppression obtained using OSCA in -band using the 2.0 arcsec mask during these conditions.399 From the graph it can » seen that just outside the edge of the occulting mask the Whoton count has been reduced. by a factor of 3.5., From the graph it can be seen that just outside the edge of the occulting mask the photon count has been reduced by a factor of 3.5.400 These values have already. been adjusted to account for the loss in hroughput due to the Lyot mask., These values have already been adjusted to account for the loss in throughput due to the Lyot mask.401 Attempts were made to observe science targets during he course of the night., Attempts were made to observe science targets during the course of the night.402 The objects were chosen. based on their need. for coronagraphie observations. be. features hat would not otherwise be casily observable and would demonstrate the benefits of using a coronagraph.," The objects were chosen based on their need for coronagraphic observations, i.e. features that would not otherwise be easily observable and would demonstrate the benefits of using a coronagraph."403 They also had to have a V-band. magnitude of less than 12 (i.e. xighter) due to the sensitivity of the NAOAIL wavelront sensor and be observable during the night at an altitude ereater than z=40°: below this the turbulence is generally ugher due to the high air-mass., They also had to have a -band magnitude of less than 12 (i.e. brighter) due to the sensitivity of the NAOMI wavefront sensor and be observable during the night at an altitude greater than $z=40^\circ$; below this the turbulence is generally higher due to the high air-mass.404 Additionally two possible subtraction stars were found lor cach target., Additionally two possible subtraction stars were found for each target.405 These were selected. to be as close to the target in. all. respects sky position. colour/spectral tvpe andV. magnitude.," These were selected to be as close to the target in all respects – sky position, colour/spectral type and magnitude."406 The attempt was to try and select. single. stars (no. known companions) with a LO aresec [field about them that. is [ree of any other (particularly. bright) stars., The attempt was to try and select single stars (no known companions) with a 10 arcsec field about them that is free of any other (particularly bright) stars.407 Finding good subtraction stars is dillicult as there are no comprehensive catalogues for this and information can be incomplete. or incorrect in the ones that are available. the ones discussed here were chosen with the aid of the SIEMDAD database.," Finding good subtraction stars is difficult as there are no comprehensive catalogues for this and information can be incomplete or incorrect in the ones that are available, the ones discussed here were chosen with the aid of the SIMBAD database."408 The reduced data for one of the commissioning targets 11D150451.AD revealed a faint detection. (sec bie. 14)), The reduced data for one of the commissioning targets – HD150451AB – revealed a faint detection (see Fig. \ref{obj15}) )409 of the recently identified cool white cdwarl companion 11D150451€' (Carson2005)., of the recently identified cool white dwarf companion HD150451C \citep{car05}.410. At the time a potential brown dwarf companion was suspected., At the time a potential brown dwarf companion was suspected.411 Since no Ποια rotations were performed. to confirm this was not an AO artefact and the signal to noise for the chwarl was extremely low. no specific conclusions could be made as of Alay 2002.," Since no field rotations were performed to confirm this was not an AO artefact and the signal to noise for the dwarf was extremely low, no specific conclusions could be made as of May 2002."412 The data collected over 2 vears by Carson(2005). has confirmed this to be a companion to LIDIS0451 and although initial data suggested the companion to be a AB.methane brown dwar. recent spectroscopic measurements favour a cool white dwarf classification.," The data collected over 2 years by \cite{car05}413 has confirmed this to be a companion to HD150451AB, and although initial data suggested the companion to be a methane brown dwarf, recent spectroscopic measurements favour a cool white dwarf classification."414 Sky frames were taken for all cata (every LO minutes inA and every 15 minutes in 7) to allow more accurate, Sky frames were taken for all data (every 10 minutes in and every 15 minutes in ) to allow more accurate415based on a sigma-clipping method.,based on a sigma-clipping method.416 The sequence of reduction stages alter spectra extraction and wavelength. calibration was as follows:, The sequence of reduction stages after spectra extraction and wavelength calibration was as follows:417"factor V(.M) from ?,, there are still uncertainties in the efficiency of acceleration as a function of Mach number.","factor $\Psi (\Mach)$ from \citet{Hoeft:2007aa}, there are still uncertainties in the efficiency of acceleration as a function of Mach number."418" However, exploration of the effects of these uncertainties are beyond the scope of this work."," However, exploration of the effects of these uncertainties are beyond the scope of this work."419 We also ignore the effects of re-accelerated y~200 electrons from radio galaxies., We also ignore the effects of re-accelerated $\gamma\sim200$ electrons from radio galaxies.420" To begin our study of projectionsradio relics, we first performed simple projections of the radio emission through the entire simulation volume."," To begin our study of radio relics, we first performed simple projections of the radio emission through the entire simulation volume."421" An example is shown in Figure 2 along with projections of density, temperature and Mach number."," An example is shown in Figure \ref{full-box-64} along with projections of density, temperature and Mach number."422" For quantities such as density, temperature and Mach number in an AMR simulation, we choose to weight each cell by a secondary quantity since a simple average along the line of sight for each cell would bias the most highly refined regions because of their increased number of cells."," For quantities such as density, temperature and Mach number in an AMR simulation, we choose to weight each cell by a secondary quantity since a simple average along the line of sight for each cell would bias the most highly refined regions because of their increased number of cells."423" Therefore, we choose to weight the density and temperature fields by cell mass, and the Mach number by the radio emission."," Therefore, we choose to weight the density and temperature fields by cell mass, and the Mach number by the radio emission."424" 'This has the effect of pulling out the values of density and temperature from the densest regions, and the shocks that contribute the most to the radio emission."," This has the effect of pulling out the values of density and temperature from the densest regions, and the shocks that contribute the most to the radio emission."425" For radio and X-ray fields, we project the emissivities [energy/time/volume] without a weight, leading to final values with units of [energy/time/area]."," For radio and X-ray fields, we project the emissivities [energy/time/volume] without a weight, leading to final values with units of [energy/time/area]."426" Mathematically, a weighted projection (here along the z-axis) is defined by:"," Mathematically, a weighted projection (here along the z-axis) is defined by:"427To determine the spin parameters forJ1346—0253.. we obtained phase-connected {imine solutions for vvr of X-ray timing data spanning 2000 January 31 (0 2005 July 27. and including 78 TOAs.,"To determine the spin parameters for, we obtained phase-connected timing solutions for yr of X-ray timing data spanning 2000 January 31 to 2005 July 27, and including 78 TOAs."428 The sampling of the observations over vvr includes several large eaps and that precludes a single phase-coherent timing solution for the entire interval., The sampling of the observations over yr includes several large gaps and that precludes a single phase-coherent timing solution for the entire interval.429 The first observations of the pulsar (which resulted in its discovery) occurred ~9 months prior to the commencement of regular monitoring observations. ancl so were not useful in our analvsis.," The first observations of the pulsar (which resulted in its discovery) occurred $\sim$ 9 months prior to the commencement of regular monitoring observations, and so were not useful in our phase-coherent analysis."430 The first coherent solution is valid over ALJD 51574-52837 vvir). while the second coherent solution is valid over MJD 52915-53578 (1.8vvr). as indicated in Figure L..," The first coherent solution is valid over MJD 51574-52837 yr), while the second coherent solution is valid over MJD 52915-53578 yr), as indicated in Figure \ref{fig:distribution}."431 We used our initial ephemeris (described in the previous section) to bootstrap a solution. valid over the vvr interval from MJD 51574-52837.," We used our initial ephemeris (described in the previous section) to bootstrap a phase-coherent solution, valid over the yr interval from MJD 51574-52837."432 This solution includes p. 7 and P. whose values ave given in Table 1.," This solution includes $\nu$, $\dot{\nu}$ and $\ddot{\nu}$, whose values are given in Table 1."433 In the process of phase connection. il became clear (hat a small gliteh occurred at MJD 52210410.," In the process of phase connection, it became clear that a small glitch occurred at MJD $\pm$ 10."434 Our measured glitch parameters are Av/v=2.5(2)xI0.? and az/r~9.3(1)x10.J|. as determined with the elitch fitting facility in TEMPO.," Our measured glitch parameters are $\Delta{\nu}/\nu = 2.5(2) \times43510^{-9}$ and $\Delta{\dot{\nu}}/{\dot{\nu}} \sim 9.3(1)\times 10^{-4}$, as determined with the glitch fitting facility in TEMPO."436 The relatively. wide spacing of data near the elite epoch prevent the detection of any. elitch recovery., The relatively wide spacing of data near the glitch epoch prevent the detection of any glitch recovery.437 In fact. it is possible that (he iniial frequency. jump was larger and recovered significantly before the following observation.," In fact, it is possible that the initial frequency jump was larger and recovered significantly before the following observation."438 Timing residuals after subtraction of our best-fit timing model. including the glitch. are shown in the top panel of Figure 3..," Timing residuals after subtraction of our best-fit timing model, including the glitch, are shown in the top panel of Figure \ref{fig:ephem1}."439 Note that svstematic trends remaining in the residuals are likely (he result of timing noise. common among voung pulsars. though unmocdelled elitch recovery may also contribute to the observed residuals.," Note that systematic trends remaining in the residuals are likely the result of timing noise, common among young pulsars, though unmodelled glitch recovery may also contribute to the observed residuals."440 Timing noise processes are known to contaminate measured spin parameters. hence it is twpically advisable to remove the svstematies from the residuals by filling additional Ireeuency derivatives until the residuals are consistent wilh Gaussian noise (e.g.Ixaspietal.1994).," Timing noise processes are known to contaminate measured spin parameters, hence it is typically advisable to remove the systematics from the residuals by fitting additional frequency derivatives until the residuals are consistent with Gaussian noise \cite[e.g.][]{kms+94}."441. For this pulsar. a total of eight frequency derivatives were recquired to obtain Gaussian distributed residuals.," For this pulsar, a total of eight frequency derivatives were required to obtain Gaussian distributed residuals."442 Timing residuals with all eight derivatives removed are shown in the bottom panel of Figure 3.., Timing residuals with all eight derivatives removed are shown in the bottom panel of Figure \ref{fig:ephem1}.443 Fitting additional Irequency derivatives improves the 4? from 2933 for 43 degrees of [reedom to 77 for 37 degrees of freedom., Fitting additional frequency derivatives improves the $\chi^2$ from 2933 for 43 degrees of freedom to 77 for 37 degrees of freedom.444 This \7 value indicates that the fit does not completely describe the data. however. tliis is not uncommon when fitüng timing noise. which is often not well described bv a polynomial.," This $\chi^2$ value indicates that the fit does not completely describe the data, however, this is not uncommon when fitting timing noise, which is often not well described by a polynomial."445 The braking index. resulting from this ‘whitened’ ünming solution. is 5»=2.64x:0.01.," The braking index, resulting from this `whitened' timing solution, is $n=2.64\pm 0.01$."446 Deterministic parameters (ie. not the hieher order derivatives that represent timing noise) as well as glitch parameters For (his timing solution are given in Table 1.., Deterministic spin-down parameters (i.e. not the higher order derivatives that represent timing noise) as well as glitch parameters for this timing solution are given in Table \ref{table:ephem}.447 Phase was lost over a 78-day gap in the data beginning at MJD 52837. made clear by the fact that a solution attempting to connect over this gap fails to predict the pulse frequency al previous epochs.," Phase was lost over a 78-day gap in the data beginning at MJD 52837, made clear by the fact that a solution attempting to connect over this gap fails to predict the pulse frequency at previous epochs."448 This loss of phase could be cue either to timing noise or another glitch., This loss of phase could be due either to timing noise or another glitch.449Because the peak accretion rate is likely to be super-Eddineton for almost the entire range of possible black hole masses. we expect (he peak disk Iuninosity to be close to the Eddington luminosity.,"Because the peak accretion rate is likely to be super-Eddington for almost the entire range of possible black hole masses, we expect the peak disk luminosity to be close to the Eddington luminosity."450 Unfortunately. however. the characteristic temperature of thermal . ≼∐⋟∖⊽↳↽↕⋅≀↧↴≼∐≀↧↴⊔∪∐≀↧↴↥⊔∐↲⊏≺⇂≼∐∐≸≟↥∪∐↥∏∐∐∐∪⋟∖⊽∐⋡∖↽↕⋟∖⊽↴∿↴↓⋗⋖↓∪∎⋅⇀⋃∐∣⊓⋅⋅↕∖⋅∐∐∐≺∢≀↧↴⊔∐≸≟⊔⋯↴↥⊔∐↲⋅⋅ ⋅ ⋅ ⋅ ↓↓⊽⋅⋅ ⋅ ∣↽≻∏∐↘↽∪↓⋟⊔∐↲∐≸≟↥∐∐↓≀↧↴⋡∖↽≼↲∐∐↲↕⋅≸≟≼↲↕∐⊔∐↲⊏↧⊺∖⊽⋅∖∖⇁↥∐↲↕⋅≼↲≺∐↕⋅≼↲≺∢↥∐∐↲≀↧⊔∖⊽⋯⋅≼↲∐∐↲↕∐," Unfortunately, however, the characteristic temperature of thermal disk radiation at the Eddington luminosity is $\sim 1 \times 10^6 M_{BH,6}^{-1/4}$ K, indicating that the bulk of the light may emerge in the EUV, where direct measurements are very difficult."451⋟∖⊽≀⋯↲∖⇁≼↲↕⋅⋡∖⇁≺∐∐∎↓≺∢∏∐⋅ Consequently. a bolometric correction that could well be O(10) or greater must be applied to anv observable measure of the disk luminosity.," Consequently, a bolometric correction that could well be $\sim O(10)$ or greater must be applied to any observable measure of the disk luminosity."452 Unfortunately. given our current limited understanding of disk spectra even when the accretion rate is sub-Ecddineton. not to mention potential dust extinction in the host galaxy. or possible reprocessing in a wind (Strubbe&Quataert2011).. à sizable uncertainty must be attached (o any such correction.," Unfortunately, given our current limited understanding of disk spectra even when the accretion rate is sub-Eddington, not to mention potential dust extinction in the host galaxy or possible reprocessing in a wind \citep{strubbe11}, a sizable uncertainty must be attached to any such correction."453 For this reason. we give higher priority (o the use of other observables.," For this reason, we give higher priority to the use of other observables."454 In our description of the time-dependence of (he jet and disk Iuminosities. the transition from super- to sub-Eddington behavior occurs earlier for (the disk than for the jet.," In our description of the time-dependence of the jet and disk luminosities, the transition from super- to sub-Eddington behavior occurs earlier for the disk than for the jet."455 The ralio of the accretion rates al these two timescales is ~jj. (he radiative efficiency of the disk in the trans-Ecddineton regime.," The ratio of the accretion rates at these two timescales is $\sim \eta$, the radiative efficiency of the disk in the trans-Eddington regime."456 Consequently. the ratio of these (wo timescales primarily constrains (he black hole spin. but not any of the other parameters.," Consequently, the ratio of these two timescales primarily constrains the black hole spin, but not any of the other parameters."457 For the other parameters. no additional information is gained bv using both timescales: either one will clo.," For the other parameters, no additional information is gained by using both timescales; either one will do."458 Suppose. then. that we choose to use the timescale at which the jet luminosity f[Iattens as a [function of time. jg.," Suppose, then, that we choose to use the timescale at which the jet luminosity flattens as a function of time, $t_{\rm jet}$."459 This Gmescale is (vpically a few (mes /jqa., This timescale is typically a few times $t_{\rm Edd}$.460" For generality. let the accretion rate scale with time as (///9)"". where n~5/3 is expected."," For generality, let the accretion rate scale with time as $(t/t_0)^{-n}$, where $n \simeq 5/3$ is expected."461 Then we find that where /i4 is likewise scaled in davs., Then we find that where $t_{\rm jet}$ is likewise scaled in days.462 Combining this timescale constraint. with the one based on the characteristic flare timescale. we may solve for the black hole mass and the penetration factor:," Combining this timescale constraint with the one based on the characteristic flare timescale, we may solve for the black hole mass and the penetration factor:"463respectively). anc 1e distribution around these peaks is rather narrow.,"respectively), and the distribution around these peaks is rather narrow."464 From the bottom panel of Fig., From the bottom panel of Fig.465 3. it is clear hat there is an exchange of momentum between the cloud and the corona. but. the corona acquires. momentum. when the gas is allowed to cool. as can be inferred from he heights of the peaks at Jo»10l.," \ref{fig:momhist} it is clear that there is an exchange of momentum between the cloud and the corona, but the corona acquires momentum when the gas is allowed to cool, as can be inferred from the heights of the peaks at $T > 10^6\K$."466 This can be »etter. uncerstooc -- Save recall how the mass of the eas is distributed. among the various phases., This can be better understood if we recall how the mass of the gas is distributed among the various phases.467 At the beginning. most of the gas is at the cloud and the corona initial emperatures. ancl only a small fraction of the total mass is at intermediate. temperatures.," At the beginning, most of the gas is at the cloud and the corona initial temperatures, and only a small fraction of the total mass is at intermediate temperatures."468 Phe momentum of the cloud is mostly transferred to this intermediate temperature component as a result of the mixing., The momentum of the cloud is mostly transferred to this intermediate temperature component as a result of the mixing.469 Because this gas is in the temperature range Z01.5107I. in which the cooling function reaches its maximum. it can cool very ellectivelv.," Because this gas is in the temperature range $T \simeq 1-5\times 10^5 \K$, in which the cooling function reaches its maximum, it can cool very effectively."470 The consequence of this cooling is a mass transfer from the corona towards the cold gas., The consequence of this cooling is a mass transfer from the corona towards the cold gas.471 Phe momentum removed from the cold cloud is thus retained by the cooling gas and never transferred to the coronal gas., The momentum removed from the cold cloud is thus retained by the cooling gas and never transferred to the coronal gas.472 I£ the cooling is not. present. the process of condensation of the mixed gas cannot occur," If the cooling is not present, the process of condensation of the mixed gas cannot occur"473have mostly been based on simulations of short duration.,have mostly been based on simulations of short duration.474" For example, presented a simulation that displayed spiral patterns for ~10 rotations, but the existence of some underlying long-lived wave is unclear because the pattern changed from snapshot to snapshot."," For example, \cite{ET93}475 presented a simulation that displayed spiral patterns for $\sim 10$ rotations, but the existence of some underlying long-lived wave is unclear because the pattern changed from snapshot to snapshot."476" Other claims are equally doubtful, as I show next."," Other claims are equally doubtful, as I show next."477" As (1994)hereafterDT94) and (1996,hereafterZ96) have presented evidence for long-lived spirals in the same model, I have chosen to try to reproduce their results here."," As \citet[][hereafter DT94]{DT94} and \citet[][hereafter Z96]{Zhan96}478 have presented evidence for long-lived spirals in the same model, I have chosen to try to reproduce their results here."479 I first summarize the model they employed and then report my own analysis of the similar results I obtain when I reproduce their simulations., I first summarize the model they employed and then report my own analysis of the similar results I obtain when I reproduce their simulations.480" DT94 adopted the disc surface density distribution (Rohlfs&Kreitschmann||1980) Here [να is the scale length of the outer exponential disc and M, is the disc mass."," DT94 adopted the disc surface density distribution \citep{RK80}481 Here $R_d$ is the scale length of the outer exponential disc and $M_d$ is the disc mass."482" DT94 and Z96 chose M,=0.5Mi, where M; is the total mass of the model, and employed two additional mass components to represent a central bulge and a halo, both of which exert the central attraction in the mid-plane of a razor-thin simple exponential disc."," DT94 and Z96 chose $M_d = 0.5M_t$, where $M_t$ is the total mass of the model, and employed two additional mass components to represent a central bulge and a halo, both of which exert the central attraction in the mid-plane of a razor-thin simple exponential disc."483" The masses and scale lengths were respectively 0.1Mi, 0.1R4 for the bulge and 0.4M;, 0.5R4 for the halo."," The masses and scale lengths were respectively $0.1M_t$, $0.1R_d$ for the bulge and $0.4M_t$, $0.5R_d$ for the halo."484 The rotation curve of this model is shown in Fig. [6].," The rotation curve of this model is shown in Fig. \ref{rotcZ},"485 which compares well with that shown in Fig., which compares well with that shown in Fig.486 1 of DT94., 1 of DT94.487 These authors set the initial velocities in the disc such that Q—1 at all radii., These authors set the initial velocities in the disc such that $Q=1$ at all radii.488" Here I recreate this model, and compute its evolution using essentially the same 2D polar grid code,but with a larger number of particles."," Here I recreate this model, and compute its evolution using essentially the same 2D polar grid code,but with a larger number of particles."489 The disc has N— 2M particles that move over a grid having 100x128 mesh points., The disc has $N=2$ M particles that move over a grid having $100 \times 128$ mesh points.490" As DT94 and Z96, I use a Plummer softening law with a length scale 0.15Ra to compute forces between particles."," As DT94 and Z96, I use a Plummer softening law with a length scale $0.15R_d$ to compute forces between particles."491" However, I adopt a more physically motivated set of units for which G—Mi;=Ra 1."," However, I adopt a more physically motivated set of units for which $G = M_t = R_d = 1$ ."492" For comparison with the previous results, it should be noted that R4—10 in their units, and one rotation period at R=2R4, which takes 27R/V.=18.5 of my time units (925 time steps), is 314 time steps in DT94 and 628 time steps in 796."," For comparison with the previous results, it should be noted that $R_d = 10$ in their units, and one rotation period at $R=2R_d$, which takes $2\pi R/V_c = 18.5$ of my time units (925 time steps), is 314 time steps in DT94 and 628 time steps in Z96."493 Fig., Fig.494"[7] shows the evolution computed here, which should be compared with that shown in Fig."," \ref{pntsZ} shows the evolution computed here, which should be compared with that shown in Fig."495 2 of Z96., 2 of Z96.496" Since the ten times larger number of particles used here lowers the seed amplitude, a little more evolution is needed for the spiral to grow."," Since the ten times larger number of particles used here lowers the seed amplitude, a little more evolution is needed for the spiral to grow."497" To make the closest possible comparison, I therefore show snapshots that are spaced at the same time interval, but are shifted later by a little over one disc rotation from the start."," To make the closest possible comparison, I therefore show snapshots that are spaced at the same time interval, but are shifted later by a little over one disc rotation from the start."498" The overall appearance is quite similar; a strong m=2 spiral is developing by time 72 and is perhaps more persistent than that in Zhang’s calculation, where the spiral has faded more by the last two times."," The overall appearance is quite similar; a strong $m=2$ spiral is developing by time 72 and is perhaps more persistent than that in Zhang's calculation, where the spiral has faded more by the last two times."499" Since DT94 and Z96 claim that the m—2 features are a long-lived spiral, I examine them more closely here."," Since DT94 and Z96 claim that the $m=2$ features are a long-lived spiral, I examine them more closely here."500 Fig., Fig.501 shows that in my simulation they appear to be the super-position of several waves having differing pattern speeds., \ref{spctZ} shows that in my simulation they appear to be the super-position of several waves having differing pattern speeds.502 This figure should be compared with Fig., This figure should be compared with Fig.503" 5 of DT94, which presents a similar analysis for their model."," 5 of DT94, which presents a similar analysis for their model."504" Although I employed 40 times the number of particles used by DT94, the power spectrum is still quite noisy."," Although I employed 40 times the number of particles used by DT94, the power spectrum is still quite noisy."505" However, the lowest panel has three or more horizontal ridges that are caused by coherent waves extending roughly from the tto a little outside the iin each case."," However, the lowest panel has three or more horizontal ridges that are caused by coherent waves extending roughly from the to a little outside the in each case."506" The lowest frequency peak, which is the farthest out in the disc, has the largest relative amplitude, which is simply a reflection of the fact that the disc surface density decreases outward."," The lowest frequency peak, which is the farthest out in the disc, has the largest relative amplitude, which is simply a reflection of the fact that the disc surface density decreases outward."507 Forming separate power spectra on the first and second halves of the evolution (top two panels of Fig. By , Forming separate power spectra on the first and second halves of the evolution (top two panels of Fig. \ref{spctZ}) )508"reveals that the separate patterns reach peak amplitude in sequential order, with the fastest rotator (mQ,= 0.42) developing and decaying first — there is no significant power at that frequency in the second half of the run."," reveals that the separate patterns reach peak amplitude in sequential order, with the fastest rotator $m\Omega_p=0.42$ ) developing and decaying first – there is no significant power at that frequency in the second half of the run."509 At least two waves co-exist at significant amplitude for most of the evolution., At least two waves co-exist at significant amplitude for most of the evolution.510" A least-squares fit to these data (Sellwood&Athanas- 1986), as well as toan expansion of the particle distribution in logarithmic spirals, finds at least four coherent waves with mf,~ 0.42, 0.30, 0.25 0.12, in"," A least-squares fit to these data \citep{SA86}, as well as toan expansion of the particle distribution in logarithmic spirals, finds at least four coherent waves with $m\Omega_p \simeq 0.42$ , 0.30, 0.25 0.12, in"511more like the training set. with the «distribution of weights representing the probability distribution of the training set and the relationship between the components of individual weights encoding correlations between parameters.,"more like the training set, with the distribution of weights representing the probability distribution of the training set and the relationship between the components of individual weights encoding correlations between parameters."512 Most. importantly. similar nodes get grouped together in the map.," Most importantly, similar nodes get grouped together in the map."513 This allows one to examine the parameter space topology. and ean be used to search for clusters within the parameter space of the training set. and thus provides a means of object classification.," This allows one to examine the parameter space topology, and can be used to search for clusters within the parameter space of the training set, and thus provides a means of object classification."514 In addition. the BMU of any new test galaxy (for example) contains the SOM's ‘best guess! of what that galaxy’s parameters should be. based on similar galaxies it has seen before.," In addition, the BMU of any new test galaxy (for example) contains the SOM's `best guess' of what that galaxy's parameters should be, based on similar galaxies it has seen before."515 In the case of incomplete data for à new test galaxy (for example a missing redshift). the BMU can provide a prediction for what that missing parameter should be.," In the case of incomplete data for a new test galaxy (for example a missing redshift), the BMU can provide a prediction for what that missing parameter should be."516 Thus. the SOM ean be a predictive tool.," Thus, the SOM can be a predictive tool."517 The process of learning occurs over a series of ;V iterations., The process of learning occurs over a series of $N$ iterations.518 At each iteration /. nodes compete to be the best match to a randomly selected training vector. with the BMU being rewarded by changing its weight vector in the direction of the training vector.," At each iteration $t$, nodes compete to be the best match to a randomly selected training vector, with the BMU being rewarded by changing its weight vector in the direction of the training vector."519 Crucially. nodes within some vicinity of the BMU ¢r« νι} are allowed to adapt. but to a lesser extent than the BMU.," Crucially, nodes within some vicinity of the BMU $r<r_{\rm BMU}$ ) are allowed to adapt, but to a lesser extent than the BMU."520 The effect is that nodes with similar properties end up grouped close to each other on the map., The effect is that nodes with similar properties end up grouped close to each other on the map.521 The adaptation is set by a learning handicap. called the ‘neighbourhood function’ /? that falls off with x. and decays with learning time.," The adaptation is set by a learning handicap, called the `neighbourhood function' $R$ that falls off with $r$, and decays with learning time."522 The exact form of the neighbourhood function. /?. is arbitrary. but a gaussian function is often chosen as a suitable form: where σ depends on time: Here 7 is a decay constant. usually chosen to be equal to the number of iterations. AV’.," The exact form of the neighbourhood function, $R$, is arbitrary, but a gaussian function is often chosen as a suitable form: where $\sigma$ depends on time: Here $\tau$ is a decay constant, usually chosen to be equal to the number of iterations, $N$."523 The region of influence around the BMU ον shrinks over time /. such that ever smaller regions of the SOM are allowed to adaptas//—V: where rjj is taken to be half of the size of the map.," The region of influence around the BMU $r_{\rm BMU}$ shrinks over time $t$, such that ever smaller regions of the SOM are allowed to adapt as $t\rightarrow N$: where $r^0_{\rm BMU}$ is taken to be half of the size of the map."524 Finally.aH nodes in the SOM have their learning handicapped over time. with an additional factor. The effect of these decaying learning rates and neighbourhood function is sequence of retinement. where the most dramatic and coarse organisation of nodes occurs early in the learning process. with subsequent steps fine-tuning the SOM on smaller scales and resolving more subtle topology in the data.," Finally, nodes in the SOM have their learning handicapped over time, with an additional factor, The effect of these decaying learning rates and neighbourhood function is sequence of refinement, where the most dramatic and coarse organisation of nodes occurs early in the learning process, with subsequent steps fine-tuning the SOM on smaller scales and resolving more subtle topology in the data."525 From the learning sequence described in 322.1. the algorithm itself can be summarised as follows: After many iterations. the SOM will evolve such that similar regions are geometrically close to each other on the map.," From the learning sequence described in 2.1, the algorithm itself can be summarised as follows: After many iterations, the SOM will evolve such that similar regions are geometrically close to each other on the map."526 Although the nodes of the SOM are distributed in à 2D grid. the boundaries of the grid are periodic. such that the 2D projection is effectively an unravelled toroid.," Although the nodes of the SOM are distributed in a 2D grid, the boundaries of the grid are periodic, such that the 2D projection is effectively an unravelled toroid."527" Wrapping the boundaries ensures that trained nodes are not ""pushed off” the boundaries of the map.", Wrapping the boundaries ensures that trained nodes are not `pushed off' the boundaries of the map.528 A plot of the 2D grid coloured by the value of the Pha eight of each node is called à component plane. and comparison of different component planes can be used to study relationships between parameters in the training set.," A plot of the 2D grid coloured by the value of the $i^{\rm th}$ weight of each node is called a component plane, and comparison of different component planes can be used to study relationships between parameters in the training set."529 Restricting the learning rate of the SOM as a function of time. and only allowing it to change in ever finer regions. ensures that the introduction of new training vectors retines the SOM. rather than obliterating the learning of previous iterations.," Restricting the learning rate of the SOM as a function of time, and only allowing it to change in ever finer regions, ensures that the introduction of new training vectors refines the SOM, rather than obliterating the learning of previous iterations."530 On this note. one requires the total learning time (i.e. how many training vectors are used in the learning) to sufficiently over-sample the input training set so that all training vectors are given a chance to contribute to the learning at different stages of refinement.," On this note, one requires the total learning time (i.e. how many training vectors are used in the learning) to sufficiently over-sample the input training set so that all training vectors are given a chance to contribute to the learning at different stages of refinement."531" Note that since the SOM is initialised randomly. and training vectors are selected randomly. SOMs trained on the same input set will not ""look"" identical. however the encoding of the map should be equivalent — all that matters is that similar nodes are close to each other (anc distant from dissimilar nodes) on the toroidal surface."," Note that since the SOM is initialised randomly, and training vectors are selected randomly, SOMs trained on the same input set will not `look' identical, however the encoding of the map should be equivalent – all that matters is that similar nodes are close to each other (and distant from dissimilar nodes) on the toroidal surface."532 The key characteristic of the self organisation is that it retains the ‘topology’ of the input training set. revealing correlations between inputs tha are not obvious.," The key characteristic of the self organisation is that it retains the `topology' of the input training set, revealing correlations between inputs that are not obvious."533 In fact. the SOM is often described as a form of non-linear principle component analysis.," In fact, the SOM is often described as a form of non-linear principle component analysis."534 Before we move to real world data. to demonstrate the concep of self-organisation. we consider a simple toy example.," Before we move to real world data, to demonstrate the concept of self-organisation, we consider a simple toy example."535" In this example. we have two ""populations"" which are simply represented as two gaussian distributions."," In this example, we have two `populations' which are simply represented as two gaussian distributions."536" We will label these as ""Red"" anc ‘Blue’.", We will label these as `Red' and `Blue'.537 Red and Blue have means of pi=1l. pene=1 and both have scales σ=0.5.," Red and Blue have means of $\mu_{\rm538Red}=1$, $\mu_{\rm Blue}=-1$ and both have scales $\sigma=0.5$."539 We now randomly draw 100000 samples from Red and Blue and consider these as our training se — simply a list of 200000 numbers., We now randomly draw 000 samples from Red and Blue and consider these as our training set – simply a list of 000 numbers.540 Can we use self-organisation to separate these two populations and predict whether a new tes value belongs to the Red or Blue population?, Can we use self-organisation to separate these two populations and predict whether a new test value belongs to the Red or Blue population?541 Of course. this is a trivial example. because we could have achieved the same resul by simply plotting a histogram of the paramater values. found the form of the toy distributions and therefore assign a probability to any new value to determine the likelihood that it belongs to Red or Blue.," Of course, this is a trivial example, because we could have achieved the same result by simply plotting a histogram of the paramater values, found the form of the toy distributions and therefore assign a probability to any new value to determine the likelihood that it belongs to Red or Blue."542 Still. this is a good demonstrative example.," Still, this is a good demonstrative example."543 We create a 20. node SOM. initialised with random weights selected uniformly from the 200000 member training set.," We create a $20\times20$ node SOM, initialised with random weights selected uniformly from the 000 member training set."544 We set-up the initial SOM parameters as described in $22.1. and allow the total number of iterations to be 2000000. thus," We set-up the initial SOM parameters as described in 2.1, and allow the total number of iterations to be 000, thus"545Fig.,Fig.546 1 indicates that. with a median distance of 98 pc. the current CAB sample contains relatively nearby systenis. which can be considered as being contained within the galactic thin disk.," 1 indicates that, with a median distance of 98 pc, the current CAB sample contains relatively nearby systems, which can be considered as being contained within the galactic thin disk."547 Thev can also be accepted. as almost homogencously distributed in all directions as they are seen from the Sun., They can also be accepted as almost homogeneously distributed in all directions as they are seen from the Sun.548 The high accuracy of the C. V. M velocities motivated us to investigate the elect of the dilferential galactic rotation to the C. V. MW. velocities.," The high accuracy of the $U$ , $V$, $W$ velocities motivated us to investigate the effect of the differential galactic rotation to the $U$, $V$, $W$ velocities."549 Phe ellect of the galactic cillerential rotation is proportional to the distance of stars from the Sun in the galactic plane. that is. the W velocities are not allected in the first approximation which assumes stars are on the galactic plane.," The effect of the galactic differential rotation is proportional to the distance of stars from the Sun in the galactic plane, that is, the W velocities are not affected in the first approximation which assumes stars are on the galactic plane."550 Since all of the systems are relatively nearby. the first. order correction described in. Alihalas Binney (1981) was announced to be smaller than the uncertainties of C and V by Eker (1992) for the 146 CAB which also exist in the present list.," Since all of the systems are relatively nearby, the first order correction described in Mihalas Binney (1981) was announced to be smaller than the uncertainties of $U$ and $V$ by Eker (1992) for the 146 CAB which also exist in the present list."551 Nevertheless. there was no harm in applving the correction even if it is negligible. as Eker (1992) explained.," Nevertheless, there was no harm in applying the correction even if it is negligible, as Eker (1992) explained."552 Since the largest uncertainty of the input data appears to be with the parallax measurements. the uncertainty of the distance contributes the most to the uncertainties of the C. V. WM velocities when compared to. the contributions of proper motions and radial velocities.," Since the largest uncertainty of the input data appears to be with the parallax measurements, the uncertainty of the distance contributes the most to the uncertainties of the $U$, $V$, $W$ velocities when compared to the contributions of proper motions and radial velocities."553 With the greatly. improved. astrometric data of Hipparcos which produces reliable parallax measurements up to 500 pc. the uncertainties in the (0.1.1) space motions are. greatly reduced. (nearly. five times) compared to the data used. by Eker (1992).," With the greatly improved astrometric data of Hipparcos which produces reliable parallax measurements up to 500 pc, the uncertainties in the $(U, V, W)$ space motions are greatly reduced (nearly five times) compared to the data used by Eker (1992)."554 Using the space distribution in .NX.Y plane in Fie.," Using the space distribution in $X, Y$ plane in Fig."555 1. the first order galactic dilferential correction contributions to the C and V. space motions were computed as described in Mihalas Binney (1981).," 1, the first order galactic differential correction contributions to the $U$ and $V$ space motions were computed as described in Mihalas Binney (1981)."556 Then. star by star. they were compared to the uncertainties of the C and V computed.," Then, star by star, they were compared to the uncertainties of the $U$ and $V$ computed."557 It was not unexpected to see 128 stars (54%) in our list with the elfect of galactie dillerential rotation being bigger than the uncertainty of C component of the space velocity., It was not unexpected to see 128 stars $54\%$ ) in our list with the effect of galactic differential rotation being bigger than the uncertainty of $U$ component of the space velocity.558 The effect on the V component is rather small. therefore. there are only three CAD with the ellect being bigger than the uncertainty of V.," The effect on the $V$ component is rather small, therefore, there are only three CAB with the effect being bigger than the uncertainty of $V$."559 Nevertheless. it seems evident that the first order galactic cillerential rotation correction is necessary [or most of the stars in our sample.," Nevertheless, it seems evident that the first order galactic differential rotation correction is necessary for most of the stars in our sample."560 Therefore. the first. order correction of galactic dilferential rotation was applied to all of the stars in the present sample.," Therefore, the first order correction of galactic differential rotation was applied to all of the stars in the present sample."561 The corrected C. V. MV are given in Table 2. together with the propagated standard οτο».," The corrected $U$, $V$, $W$ are given in Table 2, together with the propagated standard errors."562 The number of metal poor binaries in our sample was also determined. by using the kinematical parameter f=(1/800)0|2.517.3.5u7)4? suggested by Grenon (1987) and Bartkevicius et (1999).," The number of metal poor binaries in our sample was also determined by using the kinematical parameter ${\it f\/}=(1/300)(u^{2} + 2.5 v^{2}563+3.5 w^{2})^{1/2}$ suggested by Grenon (1987) and Bartkevicius et (1999)."564 LHlere. the worse velocities represent a space velocity with respect to the LSR.," Here, the $u, v, w$ velocities represent a space velocity with respect to the LSR."565 The (u.c.0). velocities are obtained by accding the velocity of the Sun with respect o the LS to the (0.1.MW) velocities of stars with respect o the Sun.," The $(u, v, w)$ velocities are obtained by adding the velocity of the Sun with respect to the LSR to the $(U, V, W)$ velocities of stars with respect to the Sun."566 The values of (VW).=(9.12.7) km/s (Alihalas Binney 1981) were used in this transformation.," The values of $(U, V, W)_{\odot}=(9, 12, 7)$ km/s (Mihalas Binney 1981) were used in this transformation."567 Statistically. the stars with f0.35 belong to the thin disc. the stars with O35<f.1.00 belong to the hick disc.," Statistically, the stars with ${\it f\/}\leq0.35$ belong to the thin disc, the stars with $0.35 < {\it f\/}\leq1.00$ belong to the thick disc."568 The stars with fl belong to the halo., The stars with $f>1$ belong to the halo.569 Consequently. the vast majority (92%) of our sample are hin clise stars.," Consequently, the vast majority $92\%$ ) of our sample are thin disc stars."570 Phe thick cisk stars are less composing about Ta of CAD in our sample., The thick disk stars are less composing about $7\%$ of CAB in our sample.571 Only one binary star. 1D149414 isa halo star according to its space motions (kinematically).," Only one binary star, HD149414 is a halo star according to its space motions (kinematically)."572 The spectroscopic metal abundance (m/1/]—L40 dex) of this star given by Latham et ((1988). confirms the classification based. on the kinematical criteria., The spectroscopic metal abundance $[m/H]=-1.40$ dex) of this star given by Latham et (1988) confirms the classification based on the kinematical criteria.573 ‘Phe Llipparcos parallax of this star gives the distance of 48 pe. so it appears to be a halo binary in the solar neighborhood.," The Hipparcos parallax of this star gives the distance of 48 pc, so it appears to be a halo binary in the solar neighborhood."574 This binary has a longperiod (133 days) and a eccentric orbit (Alavor Turon. 1982)., This binary has a longperiod (133 days) and a eccentric orbit (Mayor Turon 1982).575 Lt is interesting that Buser. Rong. Ixaraali (1099). and Siegel ct ((2002) found that the 6% of the solar neighborhood stars belong to the thick," It is interesting that Buser, Rong, Karaali (1999), and Siegel et (2002) found that the $6\%$ of the solar neighborhood stars belong to the thick"576material to fall into the star forming regions.,material to fall into the star forming regions.577 The low density tail increases since the cloud is freely expanding., The low density tail increases since the cloud is freely expanding.578 By 13 Myr. only Ho. We see that the majority of the gas has fallen to very low densities.," By 13 Myr, only $\sim 3 t_{cr}$, we see that the majority of the gas has fallen to very low densities."579 By this point it is unlikely that observations of such a cloud would reveal much in the way of molecular gas and would instead only be visible as HI., By this point it is unlikely that observations of such a cloud would reveal much in the way of molecular gas and would instead only be visible as HI.580 The cloud can now be assumed to be ‘dispersed’., The cloud can now be assumed to be `dispersed'.581 Even if the GMC fails to be a site of massive star formation. the dispersal would still occur on a timescale consistent with Elmegreen’s (2000) observations.," Even if the GMC fails to be a site of massive star formation, the dispersal would still occur on a timescale consistent with Elmegreen's (2000) observations."582 Note also from figure that the cloud contains cavities and dense regions of star formation., Note also from figure that the cloud contains cavities and dense regions of star formation.583 These are created in the simulation purely by the turbulence., These are created in the simulation purely by the turbulence.584 This type of structure in star forming clouds is often attributed to the effects of high mass stellar feedback. such as winds and supernovae. and is thought to be the trigger for star formation in the region (e.g. 2)) Instead. we realise that turbulence can mimick these effects.," This type of structure in star forming clouds is often attributed to the effects of high mass stellar feedback, such as winds and supernovae, and is thought to be the trigger for star formation in the region (e.g. \citealt{ElmegreenLada1977}) ) Instead, we realise that turbulence can mimick these effects."585 Furthermore the cavities in the simulation would be easily ionised by any high mass stars that form in the (2)., Furthermore the cavities in the simulation would be easily ionised by any high mass stars that form in the \citep{Daleetal2004}.586 We would then have a series of separated by a region of HII gas. just as is found in the classic picture of triggered star formation.," We would then have a series of separated by a region of HII gas, just as is found in the classic picture of triggered star formation."587 In this section we use some simple assumptions about the star formation that occurs in the to determine the numbers of high mass stars and the star formation efficiency that one might expect from the simulation., In this section we use some simple assumptions about the star formation that occurs in the to determine the numbers of high mass stars and the star formation efficiency that one might expect from the simulation.588 It is still beyond the capabilities of current computational resources to model the details of how individual stars form in a body of gas as large as a GMC., It is still beyond the capabilities of current computational resources to model the details of how individual stars form in a body of gas as large as a GMC.589 In the simulation presented here we cannot model any gas dynamics below the scale., In the simulation presented here we cannot model any gas dynamics below the scale.590 We can however give the reader a feel for the star formation that is present by using the results of previous simulations. along with some assumptions about the star formation efficiency and the form of the IMF.," We can however give the reader a feel for the star formation that is present by using the results of previous simulations, along with some assumptions about the star formation efficiency and the form of the IMF."591 It has been shown from numerical simulations that star formation occurs on roughly the local crossing time for the, It has been shown from numerical simulations that star formation occurs on roughly the local crossing time for the592"low O scales are strongly disfavored in both the scalar constraints (top panel) and the c,,,,; profile (bottom panel).",low O scales are strongly disfavored in both the scalar constraints (top panel) and the $c_{sound}$ profile (bottom panel).593" All of the models are discrepant at a statistically significant level in the c,,4 immediately below the surface convection zone.", All of the models are discrepant at a statistically significant level in the $c_{sound}$ immediately below the surface convection zone.594 We attribute this to the treatment of the mixing which is required to explain the low solar Li (Pinsonneault1997)., We attribute this to the treatment of the mixing which is required to explain the low solar Li \citep{Pinsonneault1997}.595". As in DPO6, we reduced the settling coefficient to account for the effect of rotational mixing from full evolutionary models (Richardetal.1996;Baheall2001)."," As in DP06, we reduced the settling coefficient to account for the effect of rotational mixing from full evolutionary models \citep{Richard1996, Bahcall2001}."596. However rotational mixing requires a more complete model so we don't use this feature as a diagnostic and defer such a topic to a subsequend paper., However rotational mixing requires a more complete model so we don't use this feature as a diagnostic and defer such a topic to a subsequend paper.597" Also illustrated in the bottom panel of Figure 3 (dashed line) is à model with low O (value from AGSS09) and high Ne (to satisfy the helioseismie contraints Rey and Y,,,) which is excluded at more than two o.", Also illustrated in the bottom panel of Figure 3 (dashed line) is a model with low O (value from AGSS09) and high Ne (to satisfy the helioseismic contraints $R_{CZ}$ and $Y_{surf}$ ) which is excluded at more than two $\sigma$.598 Helioseismology has proven to be a powerful means of inferring the solar composition., Helioseismology has proven to be a powerful means of inferring the solar composition.599" The depth of the surface convection zone and the initial helium abundance are very sensitive to the opacity of light and heavy metal respectively, and the errors in these model properties can be reliably quantified."," The depth of the surface convection zone and the initial helium abundance are very sensitive to the opacity of light and heavy metal respectively, and the errors in these model properties can be reliably quantified."600 Reproducing these seismic scalar features require a relatively high solar metallicity., Reproducing these seismic scalar features require a relatively high solar metallicity.601 If we combine these scalar constraints with reasonable priors about the relative abundances of CNONe (from the photosphere) and heavy elements (from meteorites) we can therefore infer a seismic solar mixture based primarily on stellar interiors physics., If we combine these scalar constraints with reasonable priors about the relative abundances of CNONe (from the photosphere) and heavy elements (from meteorites) we can therefore infer a seismic solar mixture based primarily on stellar interiors physics.602" Recent revisions to the input physics of the solar model - improvements in the nuclear reaction cross-sections, low temperature opacitics, and equation of state - yield a reference A(O) = 8.86 and A(Fe) = 7.50 which is the same as DP06."," Recent revisions to the input physics of the solar model - improvements in the nuclear reaction cross-sections, low temperature opacities, and equation of state - yield a reference A(O) = 8.86 and A(Fe) = 7.50 which is the same as DP06."603" However, the linkage between the thermal structure and the composition 1s indirect, which can lead to ambiguities in the interpretation of the strong constraints imposed by the measured solar thermal structure."," However, the linkage between the thermal structure and the composition is indirect, which can lead to ambiguities in the interpretation of the strong constraints imposed by the measured solar thermal structure."604" Fortunately, there is additional information encoded in the solar sound"," Fortunately, there is additional information encoded in the solar sound"605to ascertain what causes the misaliguiment between this structure iu the color iniage aud the immer bar.,to ascertain what causes the misalignment between this structure in the color image and the inner bar.606 Because of the preseuce of the spiral aris. the bulee|disk fits are not very good (Figs.," Because of the presence of the spiral arms, the bulge+disk fits are not very good (Figs."607 23f aud 22ο]., 23f and 23g).608 The K tage of this galaxy is quite ireeular (Fie., The K' image of this galaxy is quite irregular (Fig.609 21a): two armis with a flocculent appearance can be seen. but no bar.," 24a); two arms with a flocculent appearance can be seen, but no bar."610 The sharp-divided nuage does not show any strong feature (Fig., The sharp-divided image does not show any strong feature (Fig.611 21b)., 24b).612 On the other hand. the difference nuage reveals a beautiful spiral structure (Fie.," On the other hand, the difference image reveals a beautiful spiral structure (Fig."613 210). with a cieunnuclear ring. three rather closed spiral avis starting from the rine towards the north aud three other nore open spiral arms also starting from the rine but owards the south (Fig.," 24c), with a circumnuclear ring, three rather closed spiral arms starting from the ring towards the north and three other more open spiral arms also starting from the ring but towards the south (Fig."614 2le)., 24c).615 The € and PA variations with radius may reveal the oeseuce of a bar (Fie., The $\epsilon$ and PA variations with radius may reveal the presence of a bar (Fig.616 210): however. this feature docs iof appear very clearly in these plots aud we ouly have sole hints of a small thick bar in Fig.," 24e); however, this feature does not appear very clearly in these plots and we only have some hints of a small thick bar in Fig."617 21b. so we cannot © completely. certain of its detection.," 24b, so we cannot be completely certain of its detection."618 The bar aud spiral aris appear in the bulge|disk fits in J aud K as dips at about 12. 20 and 38 arcsec (Figs.," The bar and spiral arms appear in the bulge+disk fits in J and K' as bumps at about 12, 20 and 38 arcsec (Figs."619 2lf and 21g)., 24f and 24g).620 The J/IN image is quite smooth. with (1) somewhat redder at the ceuter (Fig.," The J/K' image is quite smooth, with (J-K') somewhat redder at the center (Fig."621 2ld)., 24d).622 The K image shows the bar. spiral aris aud a large weak external rine (Fig.," The K' image shows the bar, spiral arms and a large weak external ring (Fig."623 25a): the ceutral isophotes are twisted relative to the bar., 25a); the central isophotes are twisted relative to the bar.624 The shiiarp-cdividec Huaee seenis to slow a xnall structure in the ceuter at (Fig., The sharp-divided image seems to show a small structure in the center at (Fig.625 25h): the bar anc spiral aris are clearly secu., 25b); the bar and spiral arms are clearly seen.626 These structures appear even more stronglv in the differeuce nuage (Fie., These structures appear even more strongly in the difference image (Fig.627 256)., 25c).628 The e and PA variatious are also consisteut with the existence of two bars (Fig., The $\epsilon$ and PA variations are also consistent with the existence of two bars (Fig.629 250): however. it is difficult to sav if the small structure in the ceuter is really a siall bar within the bar because it is thick aud faint.," 25e); however, it is difficult to say if the small structure in the center is really a small bar within the bar because it is thick and faint."630 The bulge|disk fits are goo except in the bar aud spiral avin regions (Figs., The bulge+disk fits are good except in the bar and spiral arm regions (Figs.631 25f iux 25e)., 25f and 25g).632 The J/I nuage and the color eradieut are verv smooth. with a slightly redder uucleus (Fies.," The J/K' image and the color gradient are very smooth, with a slightly redder nucleus (Figs."633 25d aud 25h)., 25d and 25h).634 A inosaic of mages was obtained for this galaxy. so our data really eucoiipasses the entire object.," A mosaic of images was obtained for this galaxy, so our data really encompasses the entire object."635 The I& image shows a strong bar. aud weak flocculeut and asvauuetric spiral structure (Fie.," The K' image shows a strong bar, and weak flocculent and asymmetric spiral structure (Fig."636 26a). as confined bv the sharp-divided image (Fie.," 26a), as confirmed by the sharp-divided image (Fig."637 26b)., 26b).638 The bar and beeiunius of the spiral arms appear more clearly ou the difference inage (Fie., The bar and beginning of the spiral arms appear more clearly on the difference image (Fig.639 260)., 26c).640 Chapelou et al. (, Chapelon et al. (6411999) find a bar with and rsm 16 arcsec.,1999) find a bar with and $r\approx$ 16 arcsec.642 The bar that we nieasure is somewhat longer (Fie., The bar that we measure is somewhat longer (Fig.643 200). i agreement with Friedli ct al," 26e), in agreement with Friedli et al."644s (1996) result that bars are generally longer iu Iv than in R (see also NCC 3660).,'s (1996) result that bars are generally longer in K than in R (see also NGC 3660).645 The J/IV. colour nage is fairly s1000th (Fig., The J/K' colour image is fairly smooth (Fig.646 260)., 26d).647 The buleeo|disk fits clearly show the bar aud spiral arm regionso (Fies., The bulge+disk fits clearly show the bar and spiral arm regions (Figs.648 26f aud 268)., 26f and 26g).649 The K image shows a bar with somewhat peculiar slap edges: no evidence either for spiral arius or for a ring is seen. mi spite of the classification of this galaxy as RSBR2* (Fig.," The K' image shows a bar with somewhat peculiar sharp edges; no evidence either for spiral arms or for a ring is seen, in spite of the classification of this galaxy as RSBR2* (Fig."650 27a)., 27a).651 This iuauage is consistent with the smaller one obtained by de Jong vau der Ikiit (199D)., This image is consistent with the smaller one obtained by de Jong van der Kruit (1994).652 The peculiar aspect of the bar is confirmed by. the sharp-divided aud difference inages (Figs., The peculiar aspect of the bar is confirmed by the sharp-divided and difference images (Figs.653 27b aud 270). where the bar seeuis to be crossed by a dust lane.," 27b and 27c), where the bar seems to be crossed by a dust lane."654 In this case. the bar would be voung and star formation should be observable aloug it: we will therefore look for evidence for star formation iu our spectra.," In this case, the bar would be young and star formation should be observable along it; we will therefore look for evidence for star formation in our spectra."655 The difference image also shows evidence for bright spots towards the edges of the bar. specially towards the north (Fie.," The difference image also shows evidence for bright spots towards the edges of the bar, specially towards the north (Fig."656 27c) although this could be a star superimposed ou the galaxy. the fact that there is a fant southern counterpart tends to indicate that these regions iav both be in the galaxy.," 27c); although this could be a star superimposed on the galaxy, the fact that there is a faint southern counterpart tends to indicate that these regions may both be in the galaxy."657 The variations of e aud PA with radius (Fig., The variations of $\epsilon$ and PA with radius (Fig.658 270) give bar paraieters m agreement with de Joueg’s (1996) results., 27e) give bar parameters in agreement with de Jong's (1996) results.659 The bulee|disk model fits the profiles ταν nicely except in the region of the bar aud bright spots (Fies., The bulge+disk model fits the profiles very nicely except in the region of the bar and bright spots (Figs.660 27f and 27g)., 27f and 27g).661 The ον nuage and color geradieut are quite smooth throughout the galaxy. (Figs., The J/K' image and color gradient are quite smooth throughout the galaxy (Figs.662 27d and 27h)., 27d and 27h).663 A small bar is visible ou the R nuage. together with a spiral arii starting northward and another one wrapped towards the south cast (Fig.," A small bar is visible on the K' image, together with a spiral arm starting northward and another one wrapped towards the south east (Fig."664 28a)., 28a).665 Note that the center is displaced relatively to the centroid of the outer isophotes., Note that the center is displaced relatively to the centroid of the outer isophotes.666 The bar aud north spiral ina appear faintly on the sharp-divided image (Fig., The bar and north spiral arm appear faintly on the sharp-divided image (Fig.667 28b) aud much more clearly on the difference image (Fig., 28b) and much more clearly on the difference image (Fig.668 280)., 28c).669 The variations of e aud PA with radius (Fig., The variations of $\epsilon$ and PA with radius (Fig.670 280) show that the bar reaches a radiρα of 6 aresec (PA=120°))., 28e) show that the bar reaches a radius of 6 arcsec ).671 A larecr xw nw be present up to 15 aresee (PA=160°)): however. we cannot be certain tha it is a bar since the spiral arius seen to start at a «αλα radial distance than the edees of this structure.," A larger bar may be present up to 15 arcsec ); however, we cannot be certain that it is a bar since the spiral arms seem to start at a smaller radial distance than the edges of this structure."672 The bulge|disk model shows the strong contributio- ofthe bar aud spiral axis (Figs., The bulge+disk model shows the strong contribution of the bar and spiral arms (Figs.673 28f aud 28g)., 28f and 28g).674 The J/EK nuage is fairly smooth and becomes redder at the very ceuter (Figs., The J/K' image is fairly smooth and becomes redder at the very center (Figs.675o 28d and 28h)., 28d and 28h).676 We have observed a sample of 29 isolated spiral ealaxies: LS host an ACN (Seyfert { or Sevfert 2) and 11 are non-active galaxies., We have observed a sample of 29 isolated spiral galaxies: 18 host an AGN (Seyfert 1 or Seyfert 2) and 11 are non-active galaxies.677 We preseut here the infrared data in the J and I& bands. as well as the image analysis.," We present here the infrared data in the J and K' bands, as well as the image analysis."678 This, This679Gratton who derived solar gf values.,Gratton who derived solar $gf$ values.680 These two scales appear to be very similar: five lines in common give a mean cillerence log gfosou log gfessrwso = |0.06. dex with a standard error in the mean of 0.04 dex., These two scales appear to be very similar; five lines in common give a mean difference log $gf_{\rm GS90} -$ log $gf_{\rm CSSTW82}$ = +0.06 dex with a standard error in the mean of 0.04 dex.681 As this is significant only at the 1.56 level. it would be premature to adjust for it.," As this is significant only at the $\sigma$ level, it would be premature to adjust for it."682 Furthermore. by usingsolar gf. values. Sneden and Gratton have ellectively analysed their stars differentially with respect to the Sun. so changing the gf values would. alter the inferred. solar. abundance as well.," Furthermore, by using $gf$ values, Sneden and Gratton have effectively analysed their stars differentially with respect to the Sun, so changing the $gf$ values would alter the inferred solar abundance as well."683 We note. nevertheless. that even in their most metal-rich stars. Co/Fe] tends towards &0.05 at οΗ] = 0. which supports the view that their Co abundances are marginally. low.," We note, nevertheless, that even in their most metal-rich stars, [Co/Fe] tends towards $\simeq -0.05$ at [Fe/H] = 0, which supports the view that their Co abundances are marginally low."684 The problem (assuming there is one) may. perhaps be traced to differences in the assumptions in the solar model used for their solar analysis and those emploved in the other stellar caleulations., The problem (assuming there is one) may perhaps be traced to differences in the assumptions in the solar model used for their solar analysis and those employed in the other stellar calculations.685 We did. however. correct the three stars of Sneden Gratton alfected by the probable 0.47 dex error in the solar log gf value of the 4118 Line: see Norris. Ryan Beers (201) for details.," We did, however, correct the three stars of Sneden Gratton affected by the probable 0.47 dex error in the solar log $gf$ value of the 4118 line; see Norris, Ryan Beers (2001) for details."686 A comparison with the improved gf ναues of Nitz αἱ al. (, A comparison with the improved $gf$ values of Nitz et al. (6871999) conlirms the accuracy of the Carcdon et al.,1999) confirms the accuracy of the Cardon et al.688 scale: log ossqywess dog GISLoo = 0.02 dex and tossTwez ~ 0.08 dex., scale: log $gf_{\rm CSSTW82} -$ log $gf_{\rm NKWL99}$ = $-0.02$ dex and $\sigma_{\rm CSSTW82}$ $\simeq$ 0.08 dex.689 We are thus confident tha all stars are on a uniform. accurate gf scale.," We are thus confident that all stars are on a uniform, accurate $gf$ scale."690 This is quite an achievement since the stars span four orders of magnitude in abundance. and have been analysed. by several independent groups.," This is quite an achievement since the stars span four orders of magnitude in abundance, and have been analysed by several independent groups."691 As the DLA Co abundances are derived. [rom ionised ines whereas the stellar transitions are neutral. there is (in winciple) a possibility that the stellar ancl DLA abundance scales diller.," As the DLA Co abundances are derived from ionised lines whereas the stellar transitions are neutral, there is (in principle) a possibility that the stellar and DLA abundance scales differ."692 However. as the gf scales for both ionisation states are tied to modern lifetime measurements. we doubt hat clilferences exceed5-LO%.. or 0.02 0.04 dex.," However, as the $gf$ scales for both ionisation states are tied to modern lifetime measurements, we doubt that differences exceed, or 0.02 – 0.04 dex."693 Co | lines have extensive hyperfine structure which can alfect abundance measurements by up to several dex (oe. Itvan et al., Co I lines have extensive hyperfine structure which can affect abundance measurements by up to several $\times 0.1$ dex (e.g. Ryan et al.694 1996. Fie.," 1996, Fig."695 1)., 1).696 Phe stellar studies ci have all accounted for hyperfine structure. which was not always he case in earlier analyses.," The stellar studies cited have all accounted for hyperfine structure, which was not always the case in earlier analyses."697 Moreover. work by Pickering and. colleagues (1998 ancl priv.comm.)," Moreover, work by Pickering and colleagues (1998 and priv.comm.)"698 have confirmed. that he Co IL lines we have observed in the DLAs will not be »oacdened sulliciently to allect our results., have confirmed that the Co II lines we have observed in the DLAs will not be broadened sufficiently to affect our results.699 Both Co and Fe are primarily singly ionised. in he temperature range of the stars investigated. so the Co L measurements are of a minority state.," Both Co and Fe are primarily singly ionised in the temperature range of the stars investigated, so the Co I measurements are of a minority state."700 However. »ecause these elements have almost identical first ionisation »otentials. uncertainties in their temperatures or surface eravities will allect the ionisation degree of Co L just as much as for Fe 1. Representative errors in Co/Fc] που Ryan et al.," However, because these elements have almost identical first ionisation potentials, uncertainties in their temperatures or surface gravities will affect the ionisation degree of Co I just as much as for Fe I. Representative errors in [Co/Fe] — see Ryan et al."701 L996. Table 3 appear to be 20.05-0.10. dex (10) lor good S/N (—100) data. but can be ~0.2 dex for poorer data with S/N 2 30.," 1996, Table 3 — appear to be $\simeq$ 0.05-0.10 dex $\sigma$ ) for good S/N $\sim$ 100) data, but can be $\sim0.2$ dex for poorer data with S/N $\simeq$ 30."702 Lt is believed that the Lower S/N levels achieved in the first studies of the most. metal-poor stars may explain most of the spread in Co/Fc] seen in those stars. (, It is believed that the lower S/N levels achieved in the first studies of the most metal-poor stars may explain most of the spread in [Co/Fe] seen in those stars. (703See Norris ct al.,See Norris et al.704 2001 for much improved Co/VFe] measurements in such objects.), 2001 for much improved [Co/Fe] measurements in such objects.)705 The sellar data discussed. in the previous section are plottec in Figure 3. as a function of Fe/LH].," The stellar data discussed in the previous section are plotted in Figure 3, as a function of [Fe/H]."706 As discussed in the Introduction. Galactic stellar Co/EFe]. ratios. show distinc but. non-monotonic trends as a function of metallicity. which indicate key dillerences between the various stellar populations.," As discussed in the Introduction, Galactic stellar [Co/Fe] ratios show distinct — but non-monotonic — trends as a function of metallicity, which indicate key differences between the various stellar populations."707 The halo and. bulge data. for exanmnpie. at high and low metallicity. share great age and the highes €‘ofle ratios. whereas later-forming stars in the cisκ have progressively lower Co/Fc] ratios.," The halo and bulge data, for example, at high and low metallicity, share great age and the highest [Co/Fe] ratios, whereas later-forming stars in the disk have progressively lower [Co/Fe] ratios."708" In addition. the Co dete""lion in 199 Enn three upper limits are also. plotted. athough for the DLAs Zn/lM] is use as a metallicity indicator rather than Fe/H]."," In addition, the Co detection in $-$ 199 and three upper limits are also plotted, although for the DLAs [Zn/H] is used as a metallicity indicator rather than [Fe/H]."709 The frs determination of Co/Fe] = |0.31x0.05 in a DLA is Consistent wih the overabundance seen in. Galactic halo stars and the transition regime between the thick disk anc bulge at a metallicity consistent with the latter populations., The first determination of [Co/Fe] = $+0.31\pm0.05$ in a DLA is consistent with the overabundance seen in Galactic halo stars and the transition regime between the thick disk and bulge at a metallicity consistent with the latter populations.710 The poin rlotteck for 199 is he value determine [rom our Voigt profile fit although. as discussed in section 4. this may be a small overestimate if there is some blending of the blue components.," The point plotted for $-$ 199 is the value determined from our Voigt profile fit although, as discussed in section 4, this may be a small overestimate if there is some blending of the blue components."711 In addition. Co is also overabundan relative to Cr in 199. Co/Ci] = (0.23. again consisten with thick disk. moderately metal poor halo are metal-rich bulge stars.," In addition, Co is also overabundant relative to Cr in $-$ 199, [Co/Cr] = +0.23, again consistent with thick disk, moderately metal poor halo and metal-rich bulge stars."712 The trend of high Co/Fe] in metal-poor stars was [irs pointed out by MeWilliam et al. (, The trend of high [Co/Fe] in metal-poor stars was first pointed out by McWilliam et al. (7131995) ane confirmed. by Ryan et al. (,1995) and confirmed by Ryan et al. (7141996).,1996).715 ‘Phe observation that stellar Co/Fc] abundances are highest in the oldest. populations migh SUEgest that elevated: abundances arise. from the fastes evolving stars. Le. the most massive supernova (SN) progenitors.," The observation that stellar [Co/Fe] abundances are highest in the oldest populations might suggest that elevated abundances arise from the fastest evolving stars, i.e. the most massive supernova (SN) progenitors."716 However. halo star Co/Fe] values are. no uniformly high. and clearly vary as a function of metallicity.," However, halo star [Co/Fe] values are not uniformly high, and clearly vary as a function of metallicity."717 AleWilliam ct al. (, McWilliam et al. (7181995) suspected. that the trends: were due to a metallicity dependence of the vields of elements produced. in supernova (SN) nucleoswnthesis. while Rwan et al. (,"1995) suspected that the trends were due to a metallicity dependence of the yields of elements produced in supernova (SN) nucleosynthesis, while Ryan et al. ("7191996) noted that differences in the explosion energy,1996) noted that differences in the explosion energy720with MHs (Sect.,with MHs (Sect.721 2)., 2).722" Another possibility is that turbulence takes a small fraction of the energy released by the ""bubbles"" rising from the central AGN, and this can offset the cooling in most clusters McNamara Nulsen 2007)."," Another possibility is that turbulence takes a small fraction of the energy released by the “bubbles” rising from the central AGN, and this can offset the cooling in most clusters McNamara Nulsen 2007)."723 All 6 MH clusters indeed have an active radio galaxy at their center and 5 have cavities in the X-ray ICM., All 6 MH clusters indeed have an active radio galaxy at their center and 5 have cavities in the X-ray ICM.724" A detailed physical modeling of MHs in CCCs is beyond the scope of this letter, but we can derive some basic constraints here on their physical parameters."," A detailed physical modeling of MHs in CCCs is beyond the scope of this letter, but we can derive some basic constraints here on their physical parameters."725" We find that, although emitting a similar radio power, the radius of MHs is typically a factor ~4 smaller than that of GHs (see Fig. 2))."," We find that, although emitting a similar radio power, the radius of MHs is typically a factor $\approx 4$ smaller than that of GHs (see Fig. \ref{Fig.Lr_RH}) )."726 This implies a synchrotron emissivity for MHs ~50 times larger than that ofGHs?., This implies a synchrotron emissivity for MHs $\approx 50$ times larger than that of.727". Regardless of the origin of the emitting electrons, the ratio between the synchrotron emissivity of MHs (Zun) and of GH (gg) can be written as where nMP and Bun (ΠΟ and Box) are the number density of radio emitting electrons (at the energy needed to emit the observed synchrotron radiation) and the mean value of the magnetic field strength within the MH (GH), respectively, and α is the radio spectral index of the synchrotron spectrum, which is similar in GHs and MHs (a~1.1—1.3, Feretti Giovannini 2007)."," Regardless of the origin of the emitting electrons, the ratio between the synchrotron emissivity of MHs $\dot{\varepsilon}_{\rm MH}$ ) and of GH $\dot{\varepsilon}_{\rm GH}$ ) can be written as where $n_{\rm rel}^{\rm MH}$ and $B_{\rm MH}$ $n_{\rm728 rel}^{\rm GH}$ and $B_{\rm GH}$ ) are the number density of radio emitting electrons (at the energy needed to emit the observed synchrotron radiation) and the mean value of the magnetic field strength within the MH (GH), respectively, and $\alpha$ is the radio spectral index of the synchrotron spectrum, which is similar in GHs and MHs $\alpha\sim 1.1-1.3$, Feretti Giovannini 2007)."729 The measure of B in the ICM is quite problematic and different methods often give different estimates., The measure of $B$ in the ICM is quite problematic and different methods often give different estimates.730" Faraday rotation measure studies generally found a few to 10 wG in non-CCCs and ~10— 30uG in the central region of CCCs (Clarke 2004, Govoni Feretti 2004), whereas methods based on inverse Compton emission found from -0.1 to μα (Fusco-Femiano et al."," Faraday rotation measure studies generally found a few to 10 $\mu$ G in non-CCCs and $\sim10-30\,\mu$ G in the central region of CCCs (Clarke 2004, Govoni Feretti 2004), whereas methods based on inverse Compton emission found from $\sim 0.1$ to $\mu$ G (Fusco-Femiano et al."731 2004; Sanders et al., 2004; Sanders et al.732 2005)., 2005).733" There is, however, agreement on the fact that the magnetic field at the center of CCCs is larger than that on the Mpc scale in non-"," There is, however, agreement on the fact that the magnetic field at the center of CCCs is larger than that on the Mpc scale in non-CCCs."734 A suitable assumption for the ratio (Byu/Boxy) in Eq.1 (with Bug>> Boy) allows us to reproduce the observed ratio between the emissivities., A suitable assumption for the ratio $(B_{\rm MH}/B_{\rm GH})$ in \ref{Eq.1} (with $B_{\rm MH}>>B_{\rm GH}$ ) allows us to reproduce the observed ratio between the emissivities.735" However, the difference in terms of B cannot be the only cause of the large synchrotron emissivity in MHs."," However, the difference in terms of $B$ cannot be the only cause of the large synchrotron emissivity in MHs."736" Indeed a large B in CCCs produces a fast cooling of relativistic electrons due to synchrotron losses (that make nM! smaller), and this implies the important point that a very efficient mechanism of injection and/or acceleration of relativistic electrons should also be active in MHs."," Indeed a large $B$ in CCCs produces a fast cooling of relativistic electrons due to synchrotron losses (that make $n_{\rm rel}^{\rm MH}$ smaller), and this implies the important point that a very efficient mechanism of injection and/or acceleration of relativistic electrons should also be active in MHs."737" To quantify this point in a relevant case, we assume that electrons are re-accelerated sporadically by turbulence injected in the emitting region by some process."," To quantify this point in a relevant case, we assume that electrons are re-accelerated sporadically by turbulence injected in the emitting region by some process."738" Electrons are accelerated up to the energy where acceleration is balanced by losses, me.cyycy/B, where y is the acceleration efficiency and B=(B.+P?) accounts for the synchrotron and inverse Comptonlosses), and a corresponding break forms in the emitted synchrotron spectrum at vjος "," Electrons are accelerated up to the energy where acceleration is balanced by losses, $m_{\rm e} c^2 \gamma_{\rm b} \propto \chi/\beta$, where $\chi$ is the acceleration efficiency and $\beta=(B_{\rm cmb}^2 + B^2)$ accounts for the synchrotron and inverse Compton, and a corresponding break forms in the emitted synchrotron spectrum at $\nu_b \propto B \gamma_b^2$."739"Magnetosonic waves are proposed as possible sources of particleBy;,. acceleration in the ICM (Cassano Brunetti 2005; Brunetti Lazarian 2007);and in this case, following C07, the synchrotron emissivity (if the damping of turbulence is dominated by thermal electrons, for &e)/€n,<< 1) is where & (Getis the turbulence injection rate, &g/e the ratio between the energy density of relativistic and thermal particles, and T the cluster temperature."," Magnetosonic waves are proposed as possible sources of particle acceleration in the ICM (Cassano Brunetti 2005; Brunetti Lazarian 2007);and in this case, following C07, the synchrotron emissivity (if the damping of turbulence is dominated by thermal electrons, for $\epsilon_{\rm rel}/\epsilon_{\rm th} << 1$ ) is where $\dot{\varepsilon}_{\rm t}$ is the turbulence injection rate, $\epsilon_{\rm rel}/\epsilon_{\rm th}$ the ratio between the energy density of relativistic and thermal particles, and $T$ the cluster temperature."740" We consider the case in which GH and MH have νΜΗ=fv8"". and f=1 would imply that GH and MH have similar spectral index, in line with present observations."," We consider the case in which GH and MH have $\nu_{\rm b}^{\rm MH}= f\,\nu_{\rm b}^{\rm GH}$, and $f=1$ would imply that GH and MH have similar spectral index, in line with present observations."741 From Eqs., From Eqs.742" 35 and 36 in Cassano Brunetti (2005) (in the case &a/&n<< 1) &οBng(Tvs/B)! (ng is the thermal gas density) and assuming νΜΗ= fy8H, one can derive the ratio between the turbulence injection rate in"," 35 and 36 in Cassano Brunetti (2005) (in the case $\epsilon_{\rm rel}/\epsilon_{\rm th} << 1$ ) $\dot{\varepsilon_{\rm t}}\propto 743\beta\,n_{\rm th}(T\,\nu_{\rm b}/B)^{1/2}$ $n_{\rm th}$ is the thermal gas density) and assuming $\nu_{\rm b}^{\rm MH}= f\,\nu_{\rm b}^{\rm GH}$ , one can derive the ratio between the turbulence injection rate in"744starting the oligarchic growth stage (Ida&Ixokubo&Icla 1998).. with m the elfective planetesimal mass.,"starting the oligarchic growth stage \citep{b4,b15}, with m the effective planetesimal mass."745" The solid. aceretion rate for à core in the oligarchic erowth regimo. considering the particle-in-a-box approximation (Safronov1969) is where © is the Kepler frequency. Z2, anc M, are the planets radius ancl total mass (solid anc gas) and σ is the velocity cispersion which depends on the eccentricity of the planetesimals in the disc."," The solid accretion rate for a core in the oligarchic growth regime, considering the particle-in-a-box approximation \citep{b8} is where $\Omega$ is the Kepler frequency, $R_p$ and $M_t$ are the planet's radius and total mass (solid and gas) and $\sigma$ is the velocity dispersion which depends on the eccentricity of the planetesimals in the disc."746" Phomumesctal.(2003) obtain an expression for the rms eccentricity of the planetesimals when eravitational perturbation of the protoplanets are balanced by the dissipation due to the gas drag. which is where b is the orbital separation between the cnibrvos in Hill radius units. (b= 10). Cp is a dimensionless drag coefficient which is 21 and f, is the planetesimal bulk density."," \citet{b7} obtain an expression for the rms eccentricity of the planetesimals when gravitational perturbation of the protoplanets are balanced by the dissipation due to the gas drag, which is where $b$ is the orbital separation between the embryos in Hill radius units, $b=10$ ), $C_D$ is a dimensionless drag coefficient which is $\simeq 1$ and $\rho_m$ is the planetesimal bulk density."747" With this expression they foundthe next oligarchic-regime growth rate which includes the evolution of the planetesimal rms e and 7. where pay is the embryo bulk density. which is equal to the planetesimals density. then hereafter pay=pi,p."," With this expression they foundthe next oligarchic-regime growth rate which includes the evolution of the planetesimal rms $e$ and $i$, where $\rho_M$ is the embryo bulk density, which is equal to the planetesimals density, then hereafter $\rho_M=\rho_m=\rho$."748 The growth. of the cores terminate when the solid surface density in their feeding zones is zero. which is caused by a combination of these factors: the embrvos consume planetesimals on their feeding zones. the density of planetesimals is diminished by ejection (Phonesctal.2003:Ida&Lin2004) and the planetesimal migration caused by the gas drag ellect collaborate to empty this zone.," The growth of the cores terminate when the solid surface density in their feeding zones is zero, which is caused by a combination of these factors: the embryos consume planetesimals on their feeding zones, the density of planetesimals is diminished by ejection \citep{b7,b9} and the planetesimal migration caused by the gas drag effect collaborate to empty this zone."749 Once the core became massive enough to retain a gas envelope. the elfect of this atmospheric gas drag on the planetesimals inercases the collision cross section. of the protoplanet.," Once the core became massive enough to retain a gas envelope, the effect of this atmospheric gas drag on the planetesimals increases the collision cross section of the protoplanet."750 Fhis process was also taken into account in the niocel., This process was also taken into account in the model.751 When the core reaches the critical mass. the gas accretion process begins.," When the core reaches the critical mass, the gas accretion process begins."752 In this work only those embryos with very [ew gas are considered. because the process of collisions between gas giant is poorly understood.," In this work only those embryos with very few gas are considered, because the process of collisions between gas giant is poorly understood."753" For this reason we considered only those embryos with masses Al;<10 ,.", For this reason we considered only those embryos with masses $M_t<10M_{\oplus}$ .754" Nevertheless I will explain the gas accretion model considered. for those protoplanets which attain the critical mass necessary to start the gas accretion process. before reaching the LOAL,.", Nevertheless I will explain the gas accretion model considered for those protoplanets which attain the critical mass necessary to start the gas accretion process before reaching the $10M_{\oplus}$ .755" We assume that the critical mass necessary to start the gas aceretion process is given by This process occurs on a rate. where AM, is the mass of the surrounding envelope and Τι 15 its characteristic growth timo. this values were fitted from results obtained by Portieral.(2007) as is explained in Miguel&Brunini(2008)."," We assume that the critical mass necessary to start the gas accretion process is given by This process occurs on a rate, where $M_g$ is the mass of the surrounding envelope and $\tau_g$ is its characteristic growth time, this values were fitted from results obtained by \citet{b10} as is explained in \citet{b1}."756. Our model also includes the acquisition of spin angular momentum by the growing embryos due to the accretion of mass in the form of planetesimals., Our model also includes the acquisition of spin angular momentum by the growing embryos due to the accretion of mass in the form of planetesimals.757 Mutual impacts between embrvos contribute to the stochastic component. of the angular momentum., Mutual impacts between embryos contribute to the stochastic component of the angular momentum.758 On the other hand. aceretion of a large number of small planetesimals produces an ordered. spin angular momentum. which will be discuss in this section.," On the other hand, accretion of a large number of small planetesimals produces an ordered spin angular momentum, which will be discuss in this section."759 1n order to model the angular momentum accreted by the protoplanets due to the planetesimal mass accretion. we follow the work of Dones&Tremaine(1993)..," In order to model the angular momentum accreted by the protoplanets due to the planetesimal mass accretion, we follow the work of \citet{b34}."760 Their moctel depends on two parameters: In the oligarchic5 5growth regime.5 it is straightforward5 to demonstrate that the appropriate regime is that of high dispersion. and strong eravity (Dones&“Premaine 1993)..," Their model depends on two parameters: In the oligarchic growth regime, it is straightforward to demonstrate that the appropriate regime is that of high dispersion and strong gravity \citep{b34}."761 In this case. i£. we analyse the contribution of the small planetesimals. we would. found. that. the stochastic component is near one order ofmagnitude smaller. that the ordered. one.," In this case, if we analyse the contribution of the small planetesimals, we would found that the stochastic component is near one order ofmagnitude smaller that the ordered one."762 Pherefore..we add. to our model. only the ordered accretion of angular momentum duc to the planctesimal accretion.," Therefore,we add to our model, only the ordered accretion of angular momentum due to the planetesimal accretion."763 According to the appropriate three dimensional case of Dones&‘Tremaine(1993)... the > component of the angular momentum L due only to the ordered component isgiven by where and the velocity. dispersion is We assume that the SM eccentricity of planetesimals in the disc is the equilibrium value found by Thommoesetal. (2003).. which is given byequation 5..," According to the appropriate three dimensional case of \citet{b34}, the $z$ component of the angular momentum ${\bf L}$ due only to the ordered component isgiven by where and the velocity dispersion is We assume that the RSM eccentricity of planetesimals in the disc is the equilibrium value found by \citet{b7}, , which is given byequation \ref{em}. ."764 Introducing equations 11.. 12 and 5. in equation 10.. we obtain the expression for the ἐν component due to the accretion of planetesinials.," Introducing equations \ref{lamda}, , \ref{sigma} and \ref{em} in equation \ref{lz}, , we obtain the expression for the $L_z$ component due to the accretion of planetesimals,"765Exposure times for the optical frames were 300 sec for YALO images ancl 120 sec for Siromlo images.,Exposure times for the optical frames were 300 sec for YALO images and 120 sec for Stromlo images.766 For the infrared. 7 images of 90 sec each were obtained in A-band and 5 images of GO sec in Z-band.," For the infrared, 7 images of 90 sec each were obtained in $K$ -band and 5 images of 60 sec in $J$ -band."767 Each image was shifted via an internal mirror in right ascension or declination hy ~40 arcsec., Each image was shifted via an internal mirror in right ascension or declination by $\sim$ 40 arcsec.768 Optical data reduction. including bias subtraction and flat fielding. was performed using (he usual routines inIRAF.," Optical data reduction, including bias subtraction and flat fielding, was performed using the usual routines in."769 Photometry was perlormed using inIRAF., Photometry was performed using in.770 Calibration was derived by calculating the offsets [rom a secondary. star. the magnitude of which was measured previously (J. Orosz. private communication).," Calibration was derived by calculating the offsets from a secondary star, the magnitude of which was measured previously (J. Orosz, private communication)."771 The magnitudes were corrected [or airmass extinelion using coefficients taken from the CTIO table inIRAF., The magnitudes were corrected for airmass extinction using coefficients taken from the CTIO table in.772 Inlrared images were reduced using an in-houseIRAF script which flat fields (using dome flats). subtracts scaled sky images. shifts the images to a reference image (hen combines all images bv averaging them.," Infrared images were reduced using an in-house script which flat fields (using dome flats), subtracts scaled sky images, shifts the images to a reference image then combines all images by averaging them."773 Aperture photometry was perlormed using inIRAF., Aperture photometry was performed using in.774 Calibration was done using the primary standardPOL8T*.. observed on UT 2002 September 2.," Calibration was done using the primary standard, observed on UT 2002 September 2."775 Maegnitudes were corrected [ον airmass extinction using atmospheric extinction coelficients taken [rom Frogel (1993).., Magnitudes were corrected for airmass extinction using atmospheric extinction coefficients taken from \cite{fro98}. .776 Figure 1 shows B—.V—.[—.J— and K-band light eurves together with the RATE/ASAI light curve.," Figure \ref{fig:1543_alldata} shows $B-, V-, I-, J-$ and $K$ -band light curves together with the RXTE/ASM light curve."777 Due to the lack of data in the optical bands it is more difficult to make qualitative or quantitative comparisons to the X-ray. light curve., Due to the lack of data in the optical bands it is more difficult to make qualitative or quantitative comparisons to the X-ray light curve.778 Therefore. most of our analvsis of the outburst rise and peak deals with the IR bands.," Therefore, most of our analysis of the outburst rise and peak deals with the IR bands."779 The J-band light curve rises well before the RNTE/ASM flux becomes observable., The $J$ -band light curve rises well before the RXTE/ASM flux becomes observable.780 In Figure G6 we have plotted the RNTE/ASM data (top panel) and J-band data (bottom panel) for the period leading up to. and just after. the start of the outburst.," In Figure \ref{fig:rise} we have plotted the RXTE/ASM data (top panel) and $J$ -band data (bottom panel) for the period leading up to, and just after, the start of the outburst."781 The mean value of the quiescent data was found to be 15.13 mag for J-band and 0 counts/sec for the ASAI., The mean value of the quiescent data was found to be 15.13 mag for $J$ -band and 0 counts/sec for the ASM.782 These are indicated bv the dashed lines shown in Figure 6.., These are indicated by the dashed lines shown in Figure \ref{fig:rise}.783 To determine the start of the outburst we fitted the outburst part of the Leht curves with a linear least-squares fit., To determine the start of the outburst we fitted the outburst part of the light curves with a linear least-squares fit.784 For the X-ravs we fitted data between. MJD 52441.5- 5244.7 (four points)., For the X-rays we fitted data between MJD 52441.5- 52444.7 (four points).785 For the J-band, For the $J$ -band786azimuthal nature of magnetic fields. thus cnabline conduction and lowering the required AGN οπσον to accolmplish the CC to NCC transtormation.,"azimuthal nature of magnetic fields, thus enabling conduction and lowering the required AGN energy to accomplish the CC to NCC transformation."787 A detailed study of this process is clearly bevoud the scope of this paper (but see? for a simplified one-dimensional study of this effect on galaxy. groups ancl clusters)., A detailed study of this process is clearly beyond the scope of this paper (but see \citealt{guo09} for a simplified one-dimensional study of this effect on galaxy groups and clusters).788 We conducted a paraueter study of our model by performing a series of simulations with varied parameters as listed in Table 1., We conducted a parameter study of our model by performing a series of simulations with varied parameters as listed in Table 1.789 The resulting radial profiles of enission-weiehted spherically averaged eas eutropy at f=0.5 Cvr in these runs are shown iu Figure 6.., The resulting radial profiles of emission-weighted spherically averaged gas entropy at $t=0.5$ Gyr in these runs are shown in Figure \ref{plot6}.790" Iu run DI-D. the injected AGN energy is doubled (E,=6.3«10° cre). resulting iu much higher core eutropies at #=0.5 Gar."," In run D1-B, the injected AGN energy is doubled $E_{\rm agn}=6.3\times 10^{61}$ erg), resulting in much higher core entropies at $t=0.5$ Gyr."791 Varviug the initial abundance profile has a uceleible effect on cluster evolution.ue as shown iun ruus DI. D1-D. and D2. all of which show a very similar eutropy profile at £20.5 Cir.," Varying the initial abundance profile has a negligible effect on cluster evolution, as shown in runs D1, D1-D, and D2, all of which show a very similar entropy profile at $t=0.5$ Gyr."792 Obviously metallicity only affects the radiative cooling rate. which is not significant during the first one half Cor iu our simulations (shock heating increases the cooling time of thermal gas as well).," Obviously metallicity only affects the radiative cooling rate, which is not significant during the first one half Gyr in our simulations (shock heating increases the cooling time of thermal gas as well)."793 ILowever. the evolution of core eutropy does depend ou where the CRs are injected.," However, the evolution of core entropy does depend on where the CRs are injected."794 When the CRs are injected. at a larger radii 44=30 kpc in run DI-C. the cluster can not be heated to the NCC state. as clearly shown by the dot-short dashed line iu Figure 6..," When the CRs are injected at a larger radii $z_{\rm cav}=30$ kpc in run D1-C, the cluster can not be heated to the NCC state, as clearly shown by the dot-short dashed line in Figure \ref{plot6}."795 Iu this case. a pair of N-rav cavities are produced m opposite directions and do not merge at the cluster ceuter as iu run D1 (see 2 for more details of such a simulation in the cluster MS 0735.6|7121).," In this case, a pair of X-ray cavities are produced in opposite directions and do not merge at the cluster center as in run D1 (see \citealt{guo10} for more details of such a simulation in the cluster MS 0735.6+7421)."796 Even when the injected CR energv is doubled. the eas within the ceutral ~10- 20 kpc still can not be heated to high eutropies as iu run Dl.," Even when the injected CR energy is doubled, the gas within the central $\sim 10$ $20$ kpc still can not be heated to high entropies as in run D1."797 Since this very ceutral region in CC clusters is usually quite dense. it is very likely that ACNs often deposit quite a large fraction of energy directly iuto this region.," Since this very central region in CC clusters is usually quite dense, it is very likely that AGNs often deposit quite a large fraction of energy directly into this region."798 If so. powerful AGN outbursts can remove (ος as in run Di.," If so, powerful AGN outbursts can remove CCs as in run D1."799 In run DI-A. we assume that the CRs are injected into the ICAL continuously by a (jet) source moving out from the central ACN (amore specifically. τους increases from LO to 50 kpe at a constant speed within fau)," In run D1-A, we assume that the CRs are injected into the ICM continuously by a (jet) source moving out from the central AGN (more specifically, $z_{\rm cav}$ increases from $10$ to $50$ kpc at a constant speed within $t_{\rm agn}$ )."800 The resulting eutropy. profile at £=0.5 Cr (the short-dashed lue) clearly iudicates that the cluster is reated to the NCC state. aud. as expected. has ligher eutropies in the region ~10-50 kpc than iu run DI.," The resulting entropy profile at $t=0.5$ Gyr (the short-dashed line) clearly indicates that the cluster is heated to the NCC state, and, as expected, has higher entropies in the region $\sim10$ $50$ kpc than in run D1."801 It is of great interest to investigate what determines the »ositfion where ACN energy is deposited aud forms N-rav cavities., It is of great interest to investigate what determines the position where AGN energy is deposited and forms X-ray cavities.802 Incorporating the relevant plivsics. this may )e studied by higliesolutou jet simulations. which iav also reveal some important processes that may affect the cavity evolution aud that are not iceluded in our current simulations (e.g... ?:: ?2)).," Incorporating the relevant physics, this may be studied by high-resoluton jet simulations, which may also reveal some important processes that may affect the cavity evolution and that are not included in our current simulations (e.g., \citealt{sternberg07}; \citealt{sternberg08}) )."803 Fieure 7 shows ceutral slices of log (οσα7) at three epochs £=10. 100. 200 Myr in run DI-À. The injected CRs produce a low-density cavity. which is much iore elongated in the + direction than that in run DI.," Figure \ref{plot7} shows central slices of log $(n_{\rm e}/{\rm cm}^{-3})$ at three epochs $t=10$, $100$, $200$ Myr in run D1-A. The injected CRs produce a low-density cavity, which is much more elongated in the $z$ direction than that in run D1."804 As the cavity breaks up. its morphology resembles three pairs of N-rav cavities. as seen in the melt panel (f=200 Abvr)," As the cavity breaks up, its morphology resembles three pairs of X-ray cavities, as seen in the right panel $t=200$ Myr)."805" Such multiple pairs of ACN bubbles have been detected in the cluster Uvdra A (denoted as the ""Swiss-cheese-like” topology by ?)). which is currently hosting a very powerful ~1095 erg AGN outburst. probably transtormune that cluster to the NCC state."," Such multiple pairs of AGN bubbles have been detected in the cluster Hydra A (denoted as the ``Swiss-cheese-like"" topology by \citealt{wise07}) ), which is currently hosting a very powerful $\sim 10^{61}$ erg AGN outburst, probably transforming that cluster to the NCC state."806 This also sugecsts that the unmtiple pairs of ACN bubbles in Uvdra A are probably not an expression of the AGN duty cvele., This also suggests that the multiple pairs of AGN bubbles in Hydra A are probably not an expression of the AGN duty cycle.807 Teavy imetals observed iu the hot ICAL usine X- spectroscopy dudicate that in CC clusters the iron abundance profiles have ceutral peaks aud decline radially outward (27773.," Heavy metals observed in the hot ICM using X-ray spectroscopy indicate that in CC clusters the iron abundance profiles have central peaks and decline radially outward \citep{degrandi01, degrandi04, baldi07,leccardi08}."808 Tutercstinely. observatious reach coutracdictory results on the abundance profiles of NCC clusters.," Interestingly, observations reach contradictory results on the abundance profiles of NCC clusters."809 It has heen clauned by ο and ? that NCC clusters have a nearly uniform spatial distribution of auctals., It has been claimed by \citet{degrandi01} and \citet{degrandi04} that NCC clusters have a nearly uniform spatial distribution of metals.810 Iu contrast. observations bv 7? and ? indicate that the abundauce profiles of NCC clusters are very situilar to those of CC clusters. both showiug coutral peaks.," In contrast, observations by \citet{leccardi08} and \citet{sanderson09} indicate that the abundance profiles of NCC clusters are very similar to those of CC clusters, both showing central peaks."811 More receutlv. ?— fouud both types of NCC clusters in their cluster sample.," More recently, \citet{leccardi10} found both types of NCC clusters in their cluster sample."812 Iu this subsection. we investigate how the ceutrall-peaked. abuudauce profile evolve. when the CC cluster is transformed to the NCC state by ACN outbursts.," In this subsection, we investigate how the centrally-peaked abundance profile evolve when the CC cluster is transformed to the NCC state by AGN outbursts."813 We coustruct a plivsical scenario that can explain both observationally contradictory results on the NCC abuudance profiles., We construct a physical scenario that can explain both observationally contradictory results on the NCC abundance profiles.814 We first investigate the temporal evolution of the, We first investigate the temporal evolution of the815The resultaut xobuization across the line is cutirely in Stokes-Q when the observer's reference axes are aligned with hes viuinetrv axis of the star.,The resultant polarization across the line is entirely in Stokes-Q when the observer's reference axes are aligned with the symmetry axis of the star.816" Wilh £y=0.5. Figure 9 shows a plot of FF. for ii=2 (left) aud ""m=1l (right} at different viewing inclination angles of /=07.307.157.6VF. and 907 along the top panels."," With $E_1=0.5$, Figure \ref{figApp1} shows a plot of ${\cal F}_I^{\rm817sc}$ for $m=3$ (left) and $m=4$ (right) at different viewing inclination angles of $i=0^\circ, 30^\circ, 45^\circ, 60^\circ,$ and $90^\circ$ along the top panels."818 The profiles are jorinalized with respect to fje total enission produced if the line had been isotropically scattering., The profiles are normalized with respect to the total emission produced if the line had been isotropically scattering.819 A bottoni is the relative fractioial polarization q;—Qmfj or mn=3 andi =| for the same viewing inclitious.," At bottom is the relative fractional polarization $\qs={\cal F}_Q^{\rm sc}/{\cal F}_I^{\rm820sc}$ for $m=3$ and $m=4$ for the same viewing inclinations."821 Note that at the edees othe line. 473/7 for E4=0.5. iudepeudeut of the viewing inclination. a SONected under the poiut star approximation.," Note that at the edges of the line, $\qs = 3/7$ for $E_1=0.5$, independent of the viewing inclination, as expected under the point star approximation."822" The goal rere is to illustrate the polarimetric “οποιον,", The goal here is to illustrate the polarimetric “efficiency”.823 The actual measured fractional polarization would be uuch sinaller owing to dilution b ivect starlight., The actual measured fractional polarization would be much smaller owing to dilution by direct starlight.824 These efficicucty curves are relatively smooth functious of velocity shift., These efficiencty curves are relatively smooth functions of velocity shift.825 This smioothuess 1 partly due to the fact that dipole scattering is a fairly slowly varving function of location around the disk aud also because isovelocity loops sample a range of scatterimg angeles., This smoothness is partly due to the fact that dipole scattering is a fairly slowly varying function of location around the disk and also because isovelocity loops sample a range of scattering angles.826" For an axial maeuetic ficld with B=By(a)Z.. we have that c=0 aud 0,=i."," For an axial magnetic field with $\vec{B}=B_{\rm Z_\ast}(\varpi)\,827\hat{Z}_\ast$, we have that $\psis=0$ and $\thetas=i$."828 The scattering phase functions are quite simular to the zero field case. except that now the IIaule effect appears in factors in the functions C and D.," The scattering phase functions are quite similar to the zero field case, except that now the Hanle effect appears in factors in the functions $C$ and $D$."829 Using Paper IL the phase fictions are giveu by where where aud Solutions for the vector Stokes flux is no longer analytic.," Using Paper II, the phase functions are given by where where and Solutions for the vector Stokes flux is no longer analytic."830 With the IHaule effect. Fp40 except for B=0 or in the saturated lit.," With the Hanle effect, ${\cal F}_U \neq 0$ except for $B=0$ or in the saturated limit."831 Iu the latter case of by291 evervwhere. an analytic solution can be obtained. which Is given by Note that in this limut. the relative polarization becomes which is a constant across the profile and a function of viewing inclination only.," In the latter case of $b_0 \gg 1$ everywhere, an analytic solution can be obtained, which is given by Note that in this limit, the relative polarization becomes which is a constant across the profile and a function of viewing inclination only."832 This mcanus that the polarized profile is flat-topped., This means that the polarized profile is flat-topped.833 ‘Two prominent peaks are a characteristic feature of gamama-rav pulse shapes in the three brightest out of seven gamma-ray pulsars detected so far: Crab (PSR D0531|21). Vela (PSR. D0S33-45). and Geminga (0633|1746).," Two prominent peaks are a characteristic feature of gamma-ray pulse shapes in the three brightest out of seven gamma-ray pulsars detected so far: Crab (PSR B0531+21), Vela (PSR B0833-45), and Geminga (J0633+1746)."834 Phase separation between the two peaks is very large in each case. in the range between 0.4 and 0.5 (e.g. Fierro. Michelson Nolan 1998).," Phase separation between the two peaks is very large in each case, in the range between 0.4 and 0.5 (e.g. Fierro, Michelson Nolan 1998)."835 The separation. which we denote by AU was determined. with photons from the entire energy range o," The separation, which we denote by $\Delta^{\rm peak}$, was determined with photons from the entire energy range of."836tECRET.. Ixanbach. (1999) sugeested that the separation Apeak in Vela might be energy dependent., Kanbach \shortcite{kanbach} suggested that the separation $\Delta^{\rm peak}$ in Vela might be energy dependent.837 The effect: would be of the order of a lew percent or less., The effect would be of the order of a few percent or less.838" The plot of the phase separation against energy (Πο. of Ixanbach 1999) shows that AP""* decreases by about 5% over 20 energy intervals covering the range between ~50MeV. and ~9GeV.", The plot of the phase separation against energy (fig.2 of Kanbach 1999) shows that $\Delta^{\rm peak}$ decreases by about $5\%$ over 20 energy intervals covering the range between $\sim 50\MeV$ and $\sim 9\GeV$.839 The scatter of points is. however. large enough for this result stil to be consistent with the separation staving at à constan level of 0.43. especially when one rejects two energy intervals: of the lowest and the highest. value.," The scatter of points is, however, large enough for this result still to be consistent with the separation staying at a constant level of $0.43$, especially when one rejects two energy intervals: of the lowest and the highest value."840 Such ellects as suggested by Kanbach can be justifie qualitatively. at least within polar cap scenarios.," Such effects as suggested by Kanbach can be justified qualitatively, at least within polar cap scenarios."841" ""Their origin mav be dillerent at dillerent. οποίον ranges. aux their magnitude may. vary as well."," Their origin may be different at different energy ranges, and their magnitude may vary as well."842 For example. Miyazaki Takahara {JOT) found dramatic changes in. peak-to-peak phase separation due to magnetic absorption ellects in their attempts to mode the Crab pulse shapes.," For example, Miyazaki Takahara \shortcite{miyazaki} found dramatic changes in peak-to-peak phase separation due to magnetic absorption effects in their attempts to model the Crab pulse shapes."843 Their numerical calculations were performed. with low photon energy resolution for a model with homogeneous polar cap. and instant acceleration.," Their numerical calculations were performed with low photon energy resolution for a model with homogeneous polar cap, and instant acceleration."844 This new aspect of studying the LUE properties. of pulsars is potentially attractive., This new aspect of studying the HE properties of pulsars is potentially attractive.845 Phe problem of poor photon statistics should. become less essential with future, The problem of poor photon statistics should become less essential with future846those to category 2 stars.,those to category 2 stars.847 Belore final membership determination. we need to determine the expected radial velocity range for SAIC stars.," Before final membership determination, we need to determine the expected radial velocity range for SMC stars."848 As seen in Figure 4.. the radial velocity distribution of SAIC stars extends to ~240 kins | with one star at 300 kms +.," As seen in Figure \ref{fig:radVelRplot}, the radial velocity distribution of SMC stars extends to $\sim$ 240 km $^{-1}$ with one star at 300 km $^{-1}$."849 Since we are taking the radial velocity of the center of the SMC to be ~160 kms !|. given a Gaussian distribution. a reasonable lower limit would be ~80 kms !.," Since we are taking the radial velocity of the center of the SMC to be $\sim$ 160 km $^{-1}$, given a Gaussian distribution, a reasonable lower limit would be $\sim$ 80 km $^{-1}$."850 This value is consistent with the racial velocity histograms for our observed results and the Besancoon models for the Milky Way shown in Figure 5 lefl))where there appears to be a sharp drop in foreground stars above ~90 km s..., This value is consistent with the radial velocity histograms for our observed results and the Besançoon models for the Milky Way shown in Figure \ref{fig:histograms} )where there appears to be a sharp drop in foreground stars above $\sim$ 90 km $^{-1}$.851 These values. as well as our overall radial velocity results. are also consistent will previous finclings by Evans Howarth (2008) for SMC members.," These values, as well as our overall radial velocity results, are also consistent with previous findings by Evans Howarth (2008) for SMC members."852 Figure 5. )) shows their radial velocity results for 2500 O. D. A. F and G type stars in the SAIC.," Figure \ref{fig:histograms} ) shows their radial velocity results for $\sim$ 2500 O, B, A, F and G type stars in the SMC."853 This histogram again suggests that the number of SAIC stars drastically increases at à racial velocity value of 80 km 1 aud then drops olf at a value close to 240 kin, This histogram again suggests that the number of SMC stars drastically increases at a radial velocity value of $\sim$ 80 km $^{-1}$ and then drops off at a value close to 240 km $^{-1}$.854 The SMC is also rotating and thus stars on one side of the SAIC arent moving ad the same velocity as stars on the other side of the SAIC., The SMC is also rotating and thus stars on one side of the SMC aren't moving at the same velocity as stars on the other side of the SMC.855 As shown bv a study of the 9MC's Il] kinematics in Stanimirovié et ((2004). the northeast section and the wing both have svslematically higher velocities (han (he southwest section.," As shown by a study of the SMC's HI kinematics in Stanimirović et (2004), the northeast section and the wing both have systematically higher velocities than the southwest section."856 These values (vpically range between 80 kins | and 240 kins |., These values typically range between 80 km $^{-1}$ and 240 km $^{-1}$.857 Figure 6 shows how well our radial velocity results [it wilh (hese results., Figure \ref{fig:VelColor} shows how well our radial velocity results fit with these results.858 Generally we find hieher velocity stus in the northwest euadrant and the wing and lower velocity stars in the southwest., Generally we find higher velocity stars in the northwest quadrant and the wing and lower velocity stars in the southwest.859 However. we will also note that a smattering ol low velocity stars are mixed in with the high velocity stars and vice versa which futher underscores the inherent complexity of the SAIC kinematics.," However, we will also note that a smattering of low velocity stars are mixed in with the high velocity stars and vice versa which further underscores the inherent complexity of the SMC kinematics."860 Returning to the question of which velocity range to use for membership determination. both Figure 4.. Figure 5.. and Stanimirovié et ((2004) suggest that most SAIC members have velocities between the extremes of 80 and 240 km ," Returning to the question of which velocity range to use for membership determination, both Figure \ref{fig:radVelRplot}, Figure \ref{fig:histograms}, and Stanimirović et (2004) suggest that most SMC members have velocities between the extremes of 80 and 240 km $^{-1}$."861Based on Figure 4. we can conclude (hat stars with radial velocities higher than 135 kms ! are SMC supergiants and thus were assigned to category 1., Based on Figure \ref{fig:radVelRplot} we can conclude that stars with radial velocities higher than 135 km $^{-1}$ are SMC supergiants and thus were assigned to category 1.862 And. as discussed above. stars with radial velocities lower than 80 kins | are foreground stars and (hus were assigned lo category 3.," And, as discussed above, stars with radial velocities lower than 80 km $^{-1}$ are foreground stars and thus were assigned to category 3."863 We base our classilication of the 32 stars in the middle (with radial velocities between 80 km ! and 135 km !) on the OI ATTT4 abundances., We base our classification of the 32 stars in the middle (with radial velocities between 80 km $^{-1}$ and 135 km $^{-1}$ ) on the OI $\lambda$ 7774 abundances.864 Of these 32. 16 stars are hotter than log Z;;/223.172. aud thus are easy. (o classify based upon the OL A7774 line.," Of these 32, 16 stars are hotter than $\log T_{\rm eff}$ =3.72, and thus are easy to classify based upon the OI $\lambda$ 7774 line."865 Fourteen of these sixteen show the OI A7774 line. and are clearly SAIC supergiants. while two," Fourteen of these sixteen show the OI $\lambda$ 7774 line, and are clearly SMC supergiants, while two"866" and r, parameters (ancl therelore the slope) are constrained by the of the curve.",$\gamma$ and $r_t$ parameters (and therefore the slope) are constrained by the of the curve.867 Figure 3. shows the distribution of inferred mass density slopes derived using the LSB rotation curves and the best-fit > and ry parameters listed in Table 2 of H04., Figure \ref{fig:hayslope3} shows the distribution of inferred mass density slopes derived using the LSB rotation curves and the best-fit $\gamma$ and $r_t$ parameters listed in Table 2 of H04.868 The slopes for both r=ry and k&=Peony0.4 kpe are shown., The slopes for both $r=r_{\rm in}$ and $r=r_{\rm conv}=0.4$ kpc are shown.869 It is clear that the distributions are heavily biased towards shallow slopes aud very different from the values found in Che simulations al these radii (a<—1)., It is clear that the distributions are heavily biased towards shallow slopes and very different from the values found in the simulations at these radii $(\alpha \la -1)$.870" The small values of \24,4 derived in IL04 indicate that Eq. ("," The small values of $\chi^2_{\rm red, best}$ derived in H04 indicate that Eq. ("8711) fits the data well. ancl the problem is (hus not with the quality of the fits.,"1) fits the data well, and the problem is thus not with the quality of the fits."872 In Fig., In Fig.873" 3. is also indicated the distribution of slopes for the galaxies (hat H04 claim are consistent with CDM (their Group A with AZai4<L5 and V2,05< 15)."," \ref{fig:hayslope3} is also indicated the distribution of slopes for the galaxies that H04 claim are consistent with CDM (their Group A with $\chi^2_{\rm red,best} <1.5$ and $\chi^2_{\rm red,CDM} <8741.5$ )."875 This distribution is not markedly different from that of the entire sample., This distribution is not markedly different from that of the entire sample.876 From Fig., From Fig.877 9. one could thus conclude that the majority. of slopes are inconsistent with the CDM. prediction., \ref{fig:hayslope3} one could thus conclude that the majority of slopes are inconsistent with the CDM prediction.878 How can this be reconciled with the [104 conclusions?, How can this be reconciled with the H04 conclusions?879 As discussed above. LIO4 add an extra constraint to the 5-parameter. and argue that the resulting agreement with the range of 5-values shown by the simulations implies consistency wilh CDM.," As discussed above, H04 add an extra constraint to the $\gamma$ -parameter, and argue that the resulting agreement with the range of $\gamma$ -values shown by the simulations implies consistency with CDM."880 This point will be explored in more detail below. but one can already see here (hat this does not solve the problem of the discrepancy between observed and. simulated slopes.," This point will be explored in more detail below, but one can already see here that this does not solve the problem of the discrepancy between observed and simulated slopes."881 Consider the distribution of slopes of the subset of Group A for which τι=Natepu (aid both « 1.5). ie. galaxies for which the best fit is (apparently) already. consistent with CDM.," Consider the distribution of slopes of the subset of Group A for which $\chi^2_{\rm882red,best} = \chi^2_{\rm red,CDM}$ (and both $< 1.5$ ), i.e. galaxies for which the best fit is (apparently) already consistent with CDM."883 The distribution of slopes of (hiis sub-group is also plotted in Fig. 3.., The distribution of slopes of this sub-group is also plotted in Fig. \ref{fig:hayslope3}.884 The selection criteria for (his sub-eroup favour galaxies with sleeper slopes. and it should (hus come as no surprise that the dominant peak at à0 has disappeared.," The selection criteria for this sub-group favour galaxies with steeper slopes, and it should thus come as no surprise that the dominant peak at $\alpha \sim 0$ has disappeared."885 Nevertheless it is remarkable that the distributions are still dominated by slopes a7—1., Nevertheless it is remarkable that the distributions are still dominated by slopes $\alpha > -1$.886" The distribution using r—rj, peaks at a—0.25."," The distribution using $r =887r_{\rm in}$ peaks at $\alpha \sim -0.25$."888 The distribution using r=0.1 kpe peaks at a—0.5.," The distribution using $r =8890.4$ kpc peaks at $\alpha \sim -0.5$."890 As we are probing the slope at r=0.4 kpe and not in the centre. we should not expect all ISO haloes to have a [lal slope at this radius.," As we are probing the slope at $r=0.4$ kpc and not in the centre, we should not expect all ISO haloes to have a flat slope at this radius."891 The distribution of slopes found is consistent with that expected at r=0.4 kpc for an ensemble of pseudo-isothermal (ISO) halos with core-raclii between ~0.5 and ~5kpc?.., The distribution of slopes found is consistent with that expected at $r = 0.4$ kpc for an ensemble of pseudo-isothermal (ISO) halos with core-radii between $\sim 0.5$ and $\sim 5$.892 The decrease in mass-density at this radius is (hus much less steep than expected for a CDM halo., The decrease in mass-density at this radius is thus much less steep than expected for a CDM halo.893 The steepest slope expected for a realistic ISO halo econsistent with the smallest value He~0.5 kpc measured in real LSB galaxies: seeresults in deBlok&Bosma2002:MeGaughetal.2001:Swaters 2003)) is a~—0.3. with the large majority of ISO haloes having slopes less steep than that.," The steepest slope expected for a realistic ISO halo consistent with the smallest value $R_C \sim 0.5$ kpc measured in real LSB galaxies; seeresults in \citealt{dBB02, mcgaugh2001,swaters2003}) ) is $\alpha \sim -0.8$, with the large majority of ISO haloes having slopes less steep than that."894 The slopes measured in the 1104 simulations at i=0.4 kpe vary between ~—1 and ~ —1.3. firmly inconsistent with the observed distributions.," The slopes measured in the H04 simulations at $r = 0.4$ kpc vary between $\sim -1$ and $\sim -1.3$ , firmly inconsistent with the observed distributions."895For self-consistency. the jet must be reasonably beamecl ancl efficient. and the black hole must be spinning5 rapidly enough5 to make ⋅↜∕ία} not too small.,"For self-consistency, the jet must be reasonably beamed and efficient, and the black hole must be spinning rapidly enough to make $f(a/M)$ not too small."896" I Mt,<1. the hbeanune. jet efficiency. spin. etc."," If ${\cal M}_* < 1$, the beaming, jet efficiency, spin, etc."897 must be somewhat greater., must be somewhat greater.898 Although the available optical/UV observations are only very rough guides for further inlerence. (μον are consistent with these values.," Although the available optical/UV observations are only very rough guides for further inference, they are consistent with these values."899 Optical photomeltry suggests a steeply rising spectrum in the observed [rame between the g-band and the u-band 2011)., Optical photometry suggests a steeply rising spectrum in the observed frame between the $g^\prime$ -band and the $u$ -band \citep{cenko11}.900". The u-band flux on its own translates to a luminosity pL,o1.1xLOY eres !1 given the objects redshift (2= 1.18) and assuming a [lat cosmology with My=10 km ! /.", The $u$ -band flux on its own translates to a luminosity $\nu L_\nu \simeq 1.1 \times 10^{45}$ erg $^{-1}$ given the object's redshift $z=1.18$ ) and assuming a flat cosmology with $H_0 = 70$ km $^{-1}$ $^{-1}$.901 lE Liens 18 Eddington-limited and isotropic. this Iuminosity alone requires a black hole mass mqoxΙΑ.," If $L_{\rm therm}$ is Eddington-limited and isotropic, this luminosity alone requires a black hole mass $\gtrsim 7 \times 10^6 M_{\odot}$."902 However. the mass estimated in this fashion is proportional to the bolometric correction. and. as we have already noted. this may well be at least an order of magnituce.," However, the mass estimated in this fashion is proportional to the bolometric correction, and, as we have already noted, this may well be at least an order of magnitude."903 1 so. the mass required would be in the range just estimated on the basis of fy and /i4.," If so, the mass required would be in the range just estimated on the basis of $t_0$ and $t_{\rm jet}$ ."904 Lastly. we consider what information max be gleaned from the time-dependence of the optical/UV flux.," Lastly, we consider what information may be gleaned from the time-dependence of the optical/UV flux."905 Cenkoetal.(2011) report. g-band optical photometry taken within 10 d of the flares initiation and ~LO d. ~30 d. and ~40 d later.," \cite{cenko11} report $g^\prime$ -band optical photometry taken within 10 d of the flare's initiation and $\simeq 10$ d, $\simeq 30$ d, and $\simeq 40$ d later."906 They. also report. u- band magnitudes al ~10 d and ~40 d. In g'. there was no detectable dimming until 30 d alter the flare. but at 740 d. the latest time reported. the flix had diminished bv ~0.5 mag. ~40%.," They also report $u$ -band magnitudes at $\simeq 10$ d and $\simeq 40$ d. In $g^\prime$ , there was no detectable dimming until $\simeq 30$ d after the flare, but at $\simeq 40$ d, the latest time reported, the flux had diminished by $\simeq 0.5$ mag, $\simeq 40\%$."907 The u-band flux drops about 0.5 mag from ~10 d to 240 d. Thus. in rough terms. the optical/UV. luminosity appears to have varied very little over the first month or so. even though the X-ray luminosity fell by a [actor ~3: such behavior is in good agreement with our prediction that the disk output should remain steady while the jet power falls during the super-Edcdington phase.," The $u$ -band flux drops about 0.5 mag from $\simeq 10$ d to $\simeq 40$ d. Thus, in rough terms, the optical/UV luminosity appears to have varied very little over the first month or so, even though the X-ray luminosity fell by a factor $\sim 8$; such behavior is in good agreement with our prediction that the disk output should remain steady while the jet power falls during the super-Eddington phase."908 Η the drop between 30 d and 40 d marks the disk transition to sub-Edcdington behavior. the [actor »3 4 between that timescale and the possible timescale ol the jet transition is also consistent with our suggestion that theaccretion rate at the time of disk transition is a factor ~71greater than at the time of jet transition.," If the drop between 30 d and 40 d marks the disk transition to sub-Eddington behavior, the factor $\sim 3$ –4 between that timescale and the possible timescale of the jet transition is also consistent with our suggestion that theaccretion rate at the time of disk transition is a factor $\sim \eta^{-1}$greater than at the time of jet transition."909distant. galaxies.,distant galaxies.910 llowever. if (his is so. how does one understand these observations in the context of the classical Selimidt-IXennieutt scaling relations based on CO observations?," However, if this is so, how does one understand these observations in the context of the classical Schmidt-Kennicutt scaling relations based on CO observations?"911 These classical relations are often super linear and moreover. as Hleiderman et al. (," These classical relations are often super linear and moreover, as Heiderman et al. ("9122010) point out. they under predict the X554 in local regions bv factors of 17 - 50 (see also Evans et al.,"2010) point out, they under predict the $\Sigma_{SFR}$ in local regions by factors of 17 - 50 (see also Evans et al."913 2009)., 2009).914 In this paper we attempt to address (liis issue by re-examinine the extinction observations of local clouds to include low extinction material and re-examining the CO observations of the clouds studied by Gao and Solomon., In this paper we attempt to address this issue by re-examining the extinction observations of local clouds to include low extinction material and re-examining the CO observations of the clouds studied by Gao and Solomon.915 We show that all the observations can be understood within a self-consistent lramework im which the dillerences are primarily due to (he dense eas lractions that characterize the molecular gas being observed. supporting a hypothesis originally put lorwared by Gao and Solomon (2004).," We show that all the observations can be understood within a self-consistent framework in which the differences are primarily due to the dense gas fractions that characterize the molecular gas being observed, supporting a hypothesis originally put forward by Gao and Solomon (2004)."916 In Figure 1 we plot the relation between the (total) star lormation rate. SFR. and eas mass for the 11 clouds in the Paper I sunple.," In Figure 1 we plot the relation between the (total) star formation rate, SFR, and gas mass for the 11 clouds in the Paper I sample."917 The SFRs are [rom Table 2 of Paper ] and are the averaged rates over a limescale of 2 Mrs., The SFRs are from Table 2 of Paper I and are the averaged rates over a timescale of 2 Myrs.918 However. here we plot for each cloud. two different masses derived. [rom (he infrared extinction measurements.," However, here we plot for each cloud two different masses derived from the infrared extinction measurements."919 The filled circles represent cloud masses measured above an infrared (Ix-band) extinction threshold of 0.8 magnitudes and correspond to the dense gas masses CV pe.) of the clouds., The filled circles represent cloud masses measured above an infrared (K-band) extinction threshold of 0.8 magnitudes and correspond to the dense gas masses $M_{DG}$ ) of the clouds.920 The open circles represent cloud. masses measured above a lower inlrared extinction threshold of 0.1 magnitudes and correspond to the (total gaseous masses CALy¢;) of the clouds., The open circles represent cloud masses measured above a lower infrared extinction threshold of 0.1 magnitudes and correspond to the total gaseous masses $M_{TG}$ ) of the clouds.921 These latter masses should also approximately correspond to those that would be traced by CO emission. while the former masses approximately correspond to those that would be traced by Ην enussion.," These latter masses should also approximately correspond to those that would be traced by CO emission, while the former masses approximately correspond to those that would be traced by HCN emission."922 The parallel dashed lines represent a series of linear relations between SFR and mass., The parallel dashed lines represent a series of linear relations between SFR and mass.923 The top line is the best fit linear relation for the hieh extinction (dense gas) masses (following Paper I)., The top line is the best fit linear relation for the high extinction (dense gas) masses (following Paper I).924 The two lower lines are the same relation only shifted or scaled in the horizontal direction by one and two orders of magnitude in mass. respectively.," The two lower lines are the same relation only shifted or scaled in the horizontal direction by one and two orders of magnitude in mass, respectively."925 We can now express (he star formation scaling law for these clouds as: where Me; is molecular mass measured al a particular extinction threshold ancl corrected for thepresence of Helium and fpe; is the fraction of dense gas. i.e... Alpe=fpe Mc;.," We can now express the star formation scaling law for these clouds as: where $M_{G}$ is molecular mass measured at a particular extinction threshold and corrected for thepresence of Helium and $f_{DG}$ is the fraction of dense gas, i.e., $M_{DG} = f_{DG} M_G$ ."926 The, The927The new calibration of O star spectral types presented here with stellar evolution models provides a valuable new tool to derive O star masses. including initial and present-day masses. and includes an estimate of the errors.,"The new calibration of O star spectral types presented here with stellar evolution models provides a valuable new tool to derive O star masses, including initial and present-day masses, and includes an estimate of the errors."928 Furthermore. the minimal and maximal start and end ages for a given spectral class provide relevant information for statistical. studies of roughly solar-metallicity young stellar populations.," Furthermore, the minimal and maximal start and end ages for a given spectral class provide relevant information for statistical studies of roughly solar-metallicity young stellar populations."929 The relation derived here between spectral type and evolutionary Nass agrees very well with dynamical as well as spectroscopic Nass estimates for O stars from the literature and is therefore quite robust., The relation derived here between spectral type and evolutionary mass agrees very well with dynamical as well as spectroscopic mass estimates for O stars from the literature and is therefore quite robust.930 No systematic discrepancy between dynamical. nodel and spectroscopic mass estimates could be found.," No systematic discrepancy between dynamical, model and spectroscopic mass estimates could be found."931 Because there are still considerable error margins in the hew calibration. more observational and theoretical effort 1s necessary in order to improve on these.," Because there are still considerable error margins in the new calibration, more observational and theoretical effort is necessary in order to improve on these."932 Larger samples of O stars with homogeneously derived parameters and larger sets of evolutionary models with a broader range of initial conditions (to. metallieity. magnetic fields and. especially initial mass) would help to improve the calibration.," Larger samples of O stars with homogeneously derived parameters and larger sets of evolutionary models with a broader range of initial conditions $v_\mathrm{rot}$, metallicity, magnetic fields and, especially initial mass) would help to improve the calibration."933 Interestingly. seven out of nine stars located in the LMC in Figs.," Interestingly, seven out of nine stars located in the LMC in Figs."934 + and 6)) are below or at the lower end of the predicted evolutionary mass range., \ref{fig:comp_I} and \ref{fig:comp_V}) ) are below or at the lower end of the predicted evolutionary mass range.935 Even when considering an LMC metallicity grid and evolutionary models in Figs., Even when considering an LMC metallicity grid and evolutionary models in Figs.936 + to 6))., \ref{fig:comp_I} to \ref{fig:comp_V}) ).937 These systematically lower dynamie masses could have several reasons., These systematically lower dynamic masses could have several reasons.938 The influence of metallicity on the atmosphere and stellar models might be underestimated or these stars could be undetected contact systems instead of detached systems., The influence of metallicity on the atmosphere and stellar models might be underestimated or these stars could be undetected contact systems instead of detached systems.939 Or stars earlier than O6 in the LMC are systematically misclassified and should all be shifted by one spectral subtype towards later types., Or stars earlier than O6 in the LMC are systematically misclassified and should all be shifted by one spectral subtype towards later types.940 An additional startling fact are the low of the spectral type definitions for SMC metallicities and the resulting lower masses for early SMC O stars., An additional startling fact are the low of the spectral type definitions for SMC metallicities and the resulting lower masses for early SMC O stars.941 This is probably because of the lack of early O stars in the SMC study used here to calibrate the SMC spectral types., This is probably because of the lack of early O stars in the SMC study used here to calibrate the SMC spectral types.942 Yet these lower masses fit the eclipsing LMC (!), Yet these lower masses fit the eclipsing LMC (!)943 early O stars much better than the hot LMC spectral type definitions., early O stars much better than the hot LMC spectral type definitions.944 The other major source for uncertainties is massive binary evolution., The other major source for uncertainties is massive binary evolution.945 It is a major obstacle. especially for giant and supergiant systems with dynamical mass estimates.," It is a major obstacle, especially for giant and supergiant systems with dynamical mass estimates."946 These are generally short-period systems and the mereasing radii of giants and supergiants during their evolution make mass transfer highly likely., These are generally short-period systems and the increasing radii of giants and supergiants during their evolution make mass transfer highly likely.947 Whilst the modelling of the relevant processes has significantly improved in recent years(22???).. the huge parameter space of hitherto unknown initial conditions (mass ratio. eccentricity. period. orbital inclination) and the possibility of reaching the same final state from different initial ones makes a correction for binary. stellar evolutionary effects mostchallenging.," Whilst the modelling of the relevant processes has significantly improved in recent years, the huge parameter space of hitherto unknown initial conditions (mass ratio, eccentricity, period, orbital inclination) and the possibility of reaching the same final state from different initial ones makes a correction for binary stellar evolutionary effects mostchallenging."948thermally well coupled.,thermally well coupled.949 As a result. whatever anisotropies obtained by the N-wave heating would be wiped oul and all the ions would have isotropic kinetic temperature.," As a result, whatever anisotropies obtained by the N-wave heating would be wiped out and all the ions would have isotropic kinetic temperature."950 The process of the N-waves cannot explain the observed anisotropies. which also indicates that (he other mechanisms causing the anisotropic heating have to operate simultaneously.," The process of the N-waves cannot explain the observed anisotropies, which also indicates that the other mechanisms causing the anisotropic heating have to operate simultaneously."951 We thank Ix. Shibata. IX. Ohki. IX. Omukai. IX. Tomisaka. II. Saio. S. Nitta. S. Inutsuka. T. Nudoh. Y. Yoshii. T. IXajino. ancl A. Tobsaki as well as members of DTAP in NÀOJ for many valuable ancl critical comments ancl Y. Melean for improvement of presentation in this paper.," We thank K. Shibata, K. Ohki, K. Omukai, K. Tomisaka, H. Saio, S. Nitta, S. Inutsuka, T. Kudoh, Y. Yoshii, T. Kajino, and A. Tohsaki as well as members of DTAP in NAOJ for many valuable and critical comments and Y. Mclean for improvement of presentation in this paper."952 The author is supported by the JSPS Research Fellowship for Young Scientists. eranl 5936.," The author is supported by the JSPS Research Fellowship for Young Scientists, grant 5936."953BRuusc-EKutta scheme to advance the solutiou forward in fine.,Runge-Kutta scheme to advance the solution forward in time.954 The solution is stabilized agaiust nuunerical instabilities using additional artificial hwpoerdiffusive ternis. described in detail bv Cauut&Iorpi(2001).. Voeleretal.(2005). ancl Shelvagetal.(2008).," The solution is stabilized against numerical instabilities using additional artificial hyperdiffusive terms, described in detail by \cite{caunt}, , \cite{shelyag1} and \cite{shelyag3}."955.. The size of the computational domain used for the simulations is 12«12«L1 Min?. resolved by: 180&«100 erie cells providing a resolution of 25 km per erid cell.," The size of the computational domain used for the simulations is $12 \times 12 \times 1.4$ $^{3}$, resolved by $480 \times 480 \times 100$ grid cells providing a resolution of 25 km per grid cell."956 However. we emphasize that as a result of bywpercditfusivity. tle size of the sinallest structures produced in the sunulatious can be larger than a sinele exid cell.," However, we emphasize that as a result of hyperdiffusivity, the size of the smallest structures produced in the smulations can be larger than a single grid cell."957 Due to the dependence of the hvperdiffusivitv coefficieuts on the local solution. it ds not possible to elobally define a quantity. uiiquely represcuting the resolution.," Due to the dependence of the hyperdiffusivity coefficients on the local solution, it is not possible to globally define a quantity, uniquely representing the resolution."958 ILowever. a standard test. such as the strong (compression ratio 100) BRiecniauu shock tube (Sod1978). cau be used to provide an indication of the resolution.," However, a standard test, such as the strong (compression ratio 100) Riemann shock tube \cite[]{Sod78}, can be used to provide an indication of the resolution."959 The results of such tests for simular codes (.6. L-6-th order central difference spatial scheme aud hwperdiffusive sources) show that even for such an extreme case. the shock frout is diffused over 2-1 exid cells. depending ou the relative position of the shock ront with respect to the erid (Caunt IW&orpi. 2001: Shelvag et al..," The results of such tests for similar codes (i.e. 4-6-th order central difference spatial scheme and hyperdiffusive sources) show that even for such an extreme case, the shock front is diffused over 2-4 grid cells, depending on the relative position of the shock front with respect to the grid (Caunt Korpi, 2001; Shelyag et al.,"960 2008)., 2008).961 Consequently. the resolution of the code for this case is about 50-100 ki. a value similar to he resolution of the observations.," Consequently, the resolution of the code for this case is about 50-100 km, a value similar to the resolution of the observations."962 The side boundaries are periodic. the upper bouudarv is closed for vertical and stress-free horizoutal plasma motions. while the vottomn boundary is transparent.," The side boundaries are periodic, the upper boundary is closed for vertical and stress-free horizontal plasma motions, while the bottom boundary is transparent."963 The level corresponding o the visible solar surface is located approximately LOO ki below the upper boundary., The level corresponding to the visible solar surface is located approximately 400 km below the upper boundary.964 This setup allows us ο perform radiative diagnostics of C-band images. and directly compare them with the observations.," This setup allows us to perform radiative diagnostics of G-band images, and directly compare them with the observations."965 A detailed description of the method used is given in Shelvagoetal. (2001)., A detailed description of the method used is given in \cite{shelyag2}.966.. Were we provide a brief description of the X€X'OCOR, Here we provide a brief description of the process.967"S, For each of the light ravs corresponding to a vertical asina column in the simulation. we compute the LTE spectrmm in the 1295[315 range. which consists of 328 absorption lines. 239 of which are produced by CII uolecules."," For each of the light rays corresponding to a vertical plasma column in the simulation, we compute the LTE spectrum in the 4295–4315 range, which consists of 328 absorption lines, 239 of which are produced by CH molecules."968 The calculated spectrum is convolved with he C-band filter function., The calculated spectrum is convolved with the G-band filter function.969 The magnetic splitting of CII lines. and its influence ou CHband intensities. are suffüiiientlv simall for this effect to be neglected.," The magnetic splitting of CH lines, and its influence on G-band intensities, are sufficiently small for this effect to be neglected."970 G-xuid images obtained using this teclinique reproduce the dvuaiic and radiative properties of inagneto-convection. and show a large uuuber of C-band bright poiuts. corresponding to the heated. and partially evacuated. magnetic flux tubes seen in Figur 5..," G-band images obtained using this technique reproduce the dynamic and radiative properties of magneto-convection, and show a large number of G-band bright points, corresponding to the heated, and partially evacuated, magnetic flux tubes seen in Figure \ref{f1}."971 A series of 500 images were investigated. incorporating a total of 63312 AIBPs.," A series of 500 images were investigated, incorporating a total of 63312 MBPs."972 The MDBPs cover approximately of the solar surface with a variance between and across the time series., The MBPs cover approximately of the solar surface with a variance between and across the time series.973 Figure 8 displays he area distribution of MDPs. with their occurrence jorinalized to the mean nuniber detected across all bius.," Figure \ref{f4} displays the area distribution of MBPs, with their occurrence normalized to the mean number detected across all bins."974 The distribution was created by a sununation of [BPs across all iniages. iu 1 pixel bius.," The distribution was created by a summation of MBPs across all images, in 1 pixel bins."975" This technique may lead o the ""double counting” of MDBPs. some of which may wave louger lifetimes than others."," This technique may lead to the “double counting” of MBPs, some of which may have longer lifetimes than others."976 However. snapshots of single frames produce a simular distribution. with approxinatelv the same peak.," However, snapshots of single frames produce a similar distribution, with approximately the same peak."977 Therefore. this technique is equivalent to the sununation of multiple suapshot distributions. cach with similar parameters. resulting iu an overall identical distribution.," Therefore, this technique is equivalent to the summation of multiple snapshot distributions, each with similar parameters, resulting in an overall identical distribution."978 We therefore believe that auv double counting docs not pose a problem in our iuterpretation., We therefore believe that any double counting does not pose a problem in our interpretation.979 The nature of the distribution appears to conform with lognormal statistics., The nature of the distribution appears to conform with log-normal statistics.980 To confixii this. a loe-norimal probability deusitv fiction (PDF) of the form. where je and 6 are. respectively. the mean and standard deviation of lux. is fitted to the data.," To confirm this, a log-normal probability density function (PDF) of the form, where $\mu$ and $\sigma$ are, respectively, the mean and standard deviation of $\ln$ x, is fitted to the data."981 Values of =3.25 and 00.65 produce an excellent fit. shown by the over-plotted solid red line in Figure δι," Values of $\mu$ =3.25 and $\sigma$ =0.65 produce an excellent fit, shown by the over-plotted solid red line in Figure \ref{f4}."982" To quantity the eooduess of the fit. the 47 error statistic (Wall2003) of the form. where O; and £; are. respectively, the observed and expected frequencies. is utilized."," To quantify the goodness of the fit, the $\chi^2$ error statistic \cite[]{Wal03} of the form, where $O_{i}$ and $E_{i}$ are, respectively, the observed and expected frequencies, is utilized."983 The observe frequencies correspond. to the values obtained in the data. whilst the expected frequencies correspoud to the theoretical values set bv the loe-uornal fit.," The observed frequencies correspond to the values obtained in the data, whilst the expected frequencies correspond to the theoretical values set by the log-normal fit."984 Comparison of the real data with the fitted distribution reveals a conformity of aud coufirius the MIBP area distribution is well described by log-uorial statistics.," Comparison of the real data with the fitted distribution reveals a conformity of, and confirms the MBP area distribution is well described by log-normal statistics."985 The peak of the distribution occurs at an areca of 15000 Ln£C., The peak of the distribution occurs at an area of 45000 $^{2}$.986 Assuuiug a circular geometry. this corresponds to a diameter of 230 ki.," Assuming a circular geometry, this corresponds to a diameter of 230 km."987" While this estimate appears in gencral agreciuent with earlier works. there are a number of poiuts that need to be emphlasized.Utzetal.(2009) fud diameters of 218-18 kimi using a spatial sampling of 0.108"" + ou Hiuode SOT but this is dependent on the spatial samplue."," While this estimate appears in general agreement with earlier works, there are a number of points that need to be \cite{Utz09} find diameters of $\pm$ 48 km using a spatial sampling of $''$ $^{-1}$ on Hinode SOT but this is dependent on the spatial sampling."988" Reducing the spatial sampling to 0.051"" 3 gives a diameter of 166431 kin.", Reducing the spatial sampling to $''$ $^{-1}$ gives a diameter of $\pm$ 31 km.989 The latter value is in agreement with the results of Wiehretal(2001)., The latter value is in agreement with the results of \cite{Wie04}.990 Differences in the diameters may be explained by differences in the detection algorithms cuiploved., Differences in the diameters may be explained by differences in the detection algorithms employed.991 Wiehretal.(2001) cluplov the Multi Level Tracking (AILT) algorithiu which utilizes decreasing iuteusitv levels to identity aud separate objects., \cite{Wie04} employ the Multi Level Tracking (MLT) algorithm which utilizes decreasing intensity levels to identify and separate objects.992 MILT sets an initial uppermost intensity level., MLT sets an initial uppermost intensity level.993 Bright structures which exceed this threshold are tagecd., Bright structures which exceed this threshold are tagged.994 The intensity level is then lowered., The intensity level is then lowered.995 Pixels above the new intensity level. adjaceut to the structures identified iu the previous level. are added.," Pixels above the new intensity level, adjacent to the structures identified in the previous level, are added."996 New structures hat appear at this level are tageed separately., New structures that appear at this level are tagged separately.997 This repetitive procedure is terminated after a last extension oa final intensity level deemed adequate for represcutine he observed pattern., This repetitive procedure is terminated after a last extension to a final intensity level deemed adequate for representing the observed pattern.998 The structures are forced to (0 separated by 2 pixels ou all sides., The structures are forced to be separated by 2 pixels on all sides.999 The cuforced separation and the somewhat arbitrary final threshold evel. παν affect the dimensions of the MBPs measured Nw ondssdue diu οσο pixels.," The enforced separation and the somewhat arbitrary final threshold level, may affect the dimensions of the MBPs measured by missing dim edge pixels."1000 Utzetal.(2009). cuiplov a siluular repetitive intensity thresholding techuique to separate eranules aud MDPs., \cite{Utz09} employ a similar repetitive intensity thresholding technique to separate granules and MBPs.1001 They impose au upper and lower intensity boundary on the pixels of an object to determine its size., They impose an upper and lower intensity boundary on the pixels of an object to determine its size.1002 The upper boundarv is given bv the ανα intensity iu the object whilst the lower boundary is defined as the maxima miuus of the mean photospheric intensity., The upper boundary is given by the maximum intensity in the object whilst the lower boundary is defined as the maximum minus of the mean photospheric intensity.1003 Again these couditions may limit the final sizeof MBPs to the brightest pixels., Again these conditions may limit the final sizeof MBPs to the brightest pixels.1004 This effect may be exageeratedao at the highero spatial sampling., This effect may be exaggerated at the higher spatial sampling.1005Observations of neutron star low-mass X-ray binaries (NS LAINBs) with the Rossi X-ray. ‘Timing Explorer (RAPE:Dradtctal.1993). have led to two important. cliscoverics: Strong variability on millisecond. timescales in the X-ray light curves of these systems. the so-called kilohertz cuasi-periodic oscillations (kllzQPOs:vanderWisetal.1996a).. ane pulsations curing X-ray bursts. also known as burst oscillations (Strohmaverctal.1996a)..,"Observations of neutron star low-mass X-ray binaries (NS LMXBs) with the Rossi X-ray Timing Explorer \citep[RXTE;][]{bradt} have led to two important discoveries: Strong variability on millisecond timescales in the X-ray light curves of these systems, the so-called kilohertz quasi-periodic oscillations \citep[kHz QPOs;][]{vanderklis-scox-1-iauc}, and pulsations during X-ray bursts, also known as burst oscillations \citep{strohmayer-1728-iauc2}."1006 The kKIlz QPOs are relatively narrow peaks in the power density spectrum of NS LAINBs thatoften appear in pairs. at frequencies £j and vo>νι that change with time.," The kHz QPOs are relatively narrow peaks in the power density spectrum of NS LMXBs thatoften appear in pairs, at frequencies $\nu_1$ and $\nu_2 > \nu_1$ that change with time."1007 These QPOs are thought to rellect motion of matter at the inner edge of an accretion disk around the neutron star., These QPOs are thought to reflect motion of matter at the inner edge of an accretion disk around the neutron star.1008 Jurst oscillations are short-lived (7£5 108). almost coherent. pulsations seen at the rise and tail of X-ray bursts in NS LAINBs.," Burst oscillations are short-lived $\tau \simless 10$ s), almost coherent pulsations seen at the rise and tail of X-ray bursts in NS LMXBs."1009 The frequeney of these oscillations. 4). increases in the tail of the bursts to an asvinptotic value that is consistent with being the same in bursts separated bv more than a vear time (Strohmaveretal.1998)...," The frequency of these oscillations, $\nu_b$, increases in the tail of the bursts to an asymptotic value that is consistent with being the same in bursts separated by more than a year time \citep{strohmayer-longterm}."1010 This. and the fact that in the aceretion-powered milliseconcl X-rav pulsar CAMP) SAN JISOS.3658) burst. oscillations appear at the same frequeney as the pulsations seen during persistent. (non-burst). intervals. (Wijnandsetal.2003).. indicates that the frequency. of these burst. oscillations is equal to the spin frequeney of the NS. p.," This, and the fact that in the accretion-powered millisecond X-ray pulsar (AMP) SAX J1808.4–3658 burst oscillations appear at the same frequency as the pulsations seen during persistent (non-burst) intervals \citep{wijnands-1808}, indicates that the frequency of these burst oscillations is equal to the spin frequency of the NS, $\nu_s$."1011 Lt is commonly accepted that the spin of the neutron star is directly involved in the mechanism that produces the kllz QPOs., It is commonly accepted that the spin of the neutron star is directly involved in the mechanism that produces the kHz QPOs.1012 This consensus stems from the first. detection of kIIz QPOs and burst oscillations in the same source. the LAINB 4U 172834. very early on in the INTE mission.," This consensus stems from the first detection of kHz QPOs and burst oscillations in the same source, the LMXB 4U 1728–34, very early on in the RXTE mission."1013 While in dillerent observations the kllz QPOs appeared a different frequencies. οι in the range GOO500 Lz. anc vin the range 5001100 Lz. the frequency dillerence of the QPOs. when both were present. simultaneously. was consistent with being constant. Av—poνι&363 Hz. anc also consistent with the oscillations seen during bursts in this source at £y=363 Iz (Strohmaveretal.1996b).," While in different observations the kHz QPOs appeared at different frequencies, $\nu_1$ in the range $\sim 600 - 800$ Hz, and $\nu_2$ in the range $\sim 500 - 1100$ Hz, the frequency difference of the QPOs, when both were present simultaneously, was consistent with being constant, $\Delta \nu = \nu_2 - \nu_1 \approx 363$ Hz, and also consistent with the oscillations seen during bursts in this source at $\nu_b = 363$ Hz \citep{strohmayer-1728}."1014. This fittec with the suggestion (Strohmaveretal.19960). that a bea mechanism with the neutron star spin. was responsible for he kllz QPOs., This fitted with the suggestion \citep{strohmayer-1728-iauc1} that a beat mechanism with the neutron star spin was responsible for the kHz QPOs.1015 Further results on other sources (e...Foreetal.1997). appeared. to confirm this picture.," Further results on other sources \citep[e.g.,][]{ford-0614} appeared to confirm this picture."1016" A detailer model. the sonic-point model. proposed by Miller.Lamb.&""saltis(1998) explained the observed relation between the kz QPOs and the neutron star spin in terms of a bea xtween material orbiting at the inner edge of the disk with he Ixeplerian frequency at that racius. and the spin of the S."," A detailed model, the sonic-point model, proposed by \cite*{miller-1998} explained the observed relation between the kHz QPOs and the neutron star spin in terms of a beat between material orbiting at the inner edge of the disk with the Keplerian frequency at that radius, and the spin of the NS."1017 As soon as kIlz QPOs were discovered in 4U 163653 (vanderIxlisetal.1996b).— with a frequency. dillerence of Av=272411 Hz. and burst oscillations at a frequency m=581 Ue (Zhangetal.1996).. it became apparent that in this source Av was inconsistent with being equal to vy. but it was close to ο.," As soon as kHz QPOs were discovered in 4U 1636–53 \citep{vanderklis-1636-iauc} with a frequency difference of $\Delta \nu1018= 272 \pm 11$ Hz, and burst oscillations at a frequency $\nu_b = 581$ Hz \citep{zhang-1636-iauc}, it became apparent that in this source $\Delta1019\nu$ was inconsistent with being equal to $\nu_b$, but it was close to $\nu_b/2$ ."1020 This would have been the end of the sonic-point. model. unless in 4U 163653 the 581 Lz frequeney seen during X-ray bursts was the second harmonic of the NS spin frequenev. ον=2/5 vy. with ος=290.5 ," This would have been the end of the sonic-point model, unless in 4U 1636–53 the 581 Hz frequency seen during X-ray bursts was the second harmonic of the NS spin frequency, $\nu_b = 2 \times \nu_s$ , with $\nu_s = 290.5$ "1021"To evaluate 96;;. 1t follows from equation (?7)) that =o Zpy))(gbedolbbZ,)) — s(tbedol )(3bedolbbY,)) s(ibedol ) ]- since oz,z, vanishes in the unperturbed state.","To evaluate $\delta\sigma_{ij}$, it follows from equation \ref{sigij}) ) that = ) - ( ) ( ) ], since $\sigma_{\zb\zb}$ vanishes in the unperturbed state."1022 The terms in square brackets may be evaluated for the equilibrium field geometry. which we take to be — @+bbZ..$. Z.," The terms in square brackets may be evaluated for the equilibrium field geometry, which we take to be = +.$\bb{{\hat \phi}}$, $\bb{{\hat Z}}$,"1023 and R ave unil vectors in the indicated evlindrical directions. aud 9 is the angle between the magnetic field and the © axis.," and $\bb{{\hat R}}$ are unit vectors in the indicated cylindrical directions, and $\theta$ is the angle between the magnetic field and the $\phi$ axis."1024 The local magnetic field axes are then = =cos + bbZ..(18) = = -," The local magnetic field axes are then = = + , = = +"1025 The local magnetic field axes are then = =cos + bbZ..(18) = = -F," The local magnetic field axes are then = = + , = = +"1026After constructing the two samples of objects from each mock catalog. we can use standard correlation measurements and exploit the clustering of galaxies to recover the redshift distribution of the photometric sample.,"After constructing the two samples of objects from each mock catalog, we can use standard correlation measurements and exploit the clustering of galaxies to recover the redshift distribution of the photometric sample."1027" From here on. the spectroscopic sample. with. known observed redshifts. will be labeled ο, and the photometric sample. with redshifts assumed unknown. will be labelled ""p."," From here on, the spectroscopic sample, with known observed redshifts, will be labeled $s$ ', and the photometric sample, with redshifts assumed unknown, will be labelled $p$ '."1028 The most fundamental correlation measurements we use are the real space two-point correlation function and. the angular two-point correlation function., The most fundamental correlation measurements we use are the real space two-point correlation function and the angular two-point correlation function.1029 The real space two-point correlation function £(7) is à measure of the excess probability dP (above that for a random distribution) of finding a galaxy in a volume dV. at a separation + from another galaxy(?):: where 7 is the mean number density of the sample.," The real space two-point correlation function $\xi(r)$ is a measure of the excess probability $dP$ (above that for a random distribution) of finding a galaxy in a volume $dV$, at a separation $r$ from another \citep{1980lssu.book.....P}: where $n$ is the mean number density of the sample."1030" The angular two-point correlation function w(0) is a measure of the excess probability dP of finding a galaxy in a solid angle dO, at a separation ϐ on the sky from another galaxy (?) where X is the mean number of galaxies per steradian (1.e.. the surface density)."," The angular two-point correlation function $w(\theta)$ is a measure of the excess probability $dP$ of finding a galaxy in a solid angle $d\Omega$, at a separation $\theta$ on the sky from another galaxy \citep{1980lssu.book.....P} : where $\Sigma$ is the mean number of galaxies per steradian (i.e., the surface density)."1031" From the spectroscopic sample we measure the real space two-point autocorrelation function. Ca(rz) and from the photometric sample we measure the angular two-point autocorrelation function. wy),(@)."," From the spectroscopic sample we measure the real space two-point autocorrelation function, $\xi_{ss}(r,z)$, and from the photometric sample we measure the angular two-point autocorrelation function, $w_{pp}(\theta)$."1032 These measurements give information about the intrinsic clustering of the samples., These measurements give information about the intrinsic clustering of the samples.1033" We also measure the angular cross-ceorrelation function. between the spectroscopic and photometric sample. w,,(0.z). as a function of redshift."," We also measure the angular correlation function between the spectroscopic and photometric sample, $w_{sp}(\theta,z)$, as a function of redshift."1034 This is ameasure of the excess probability of finding a photometric object at an angular separation 7 from a spectroscopic object. completely analogous to wj.," This is a measure of the excess probability of finding a photometric object at an angular separation $\theta$ from a spectroscopic object, completely analogous to $w_{pp}$."1035" Modeling £(r) as a power law. £(r)=(rra). which is an accurate assumption from ~0.5 to ~20/7! comoving Mpe for both observed samples and those in the mock catalogs. we can determine a relation between the angular ccorrelation function w,,(0.z) and the redshift distribution."," Modeling $\xi(r)$ as a power law, $\xi(r)=(r/r_0)^{-\gamma}$, which is an accurate assumption from $\sim 0.5$ to $\sim 20 h^{-1}$ comoving Mpc for both observed samples and those in the mock catalogs, we can determine a relation between the angular correlation function $w_{sp}(\theta,z)$ and the redshift distribution."1036 Following the derivation in ?. (ef., Following the derivation in \cite{2008ApJ...684...88N} (cf.1037 eq., eq.1038" 4). where H(5)—F(1/2)E((5D/2)/LT(5/2) (where D(x) is the standard Gamma function). o,(z) is the probability distribution. function. of the redshift of an object in the photometric sample. D(z) is the angular size distance. anc l(z) is the comoving distance to redshift z."," 4), where $H(\gamma)=\Gamma(1/2)\Gamma((\gamma-1)/2)/\Gamma(\gamma/2)$ (where $\Gamma(x)$ is the standard Gamma function), $\phi_p(z)$ is the probability distribution function of the redshift of an object in the photometric sample, $D(z)$ is the angular size distance, and $l(z)$ is the comoving distance to redshift $z$."1039" Hence. to recover Ops) from w,,. we also must know the basic cosmology (to determine D(z) and d//dz). as well as the cross-ccorrelatiot parameters. 7,5 and 7,5."," Hence, to recover $\phi_p(z)$ from $w_{sp}$, we also must know the basic cosmology (to determine $D(z)$ and $dl/dz$ ), as well as the correlation parameters, $r_{0,sp}$ and $\gamma_{sp}$."1040 It has been shown that uncertainties in cosmological parameters have minimal effect on the recovery of oy(z)(?).., It has been shown that uncertainties in cosmological parameters have minimal effect on the recovery of $\phi_p(z)$ \citep{2008ApJ...684...88N}.1041" To determine the cross-ecorrelatioi parameters. we use the assumption of linear biasing. under which the cross-ccorrelation is. given. by the geometric mean of the autocorrelations of the two samples. £,,(7)=Γρ), ?"," To determine the correlation parameters, we use the assumption of linear biasing, under which the correlation is given by the geometric mean of the autocorrelations of the two samples, $\xi_{sp}(r)=(\xi_{ss}\xi_{pp})^{1/2}$ ."1042 Thus we need to measure the autocorrelation functions for each sample and determine their parameters. ry and .," Thus we need to measure the autocorrelation functions for each sample and determine their parameters, $r_0$ and $\gamma$ ."1043 We first need to determine. how the real space autocorrelation function. of the spectroscopic sample. C. evolves with redshift.," We first need to determine how the real space autocorrelation function of the spectroscopic sample, $\xi_{ss}$, evolves with redshift."1044 To do this we bin the spectroscopic objects in redshift and measure the two-point. correlation function as a function of projected separation. +. and line-of-sight separation. 7. for the objects in each bin.," To do this we bin the spectroscopic objects in redshift and measure the two-point correlation function as a function of projected separation, $r_p$, and line-of-sight separation, $\pi$, for the objects in each bin."1045" However. since it is affected by redshift-space distortions in the line of sight direction. it is difficult to measure the evolution of £r) accurately directly from the observed €(7,.7)."," However, since it is affected by redshift-space distortions in the line of sight direction, it is difficult to measure the evolution of $\xi_{ss}(r)$ accurately directly from the observed $\xi(r_p,\pi)$."1046" However. as we describe later. we can use £(r,.7) to derive the projected correlation function. wy,(r,). which is not significantly affected by redshift-space distortions."," However, as we describe later, we can use $\xi(r_p,\pi)$ to derive the projected correlation function, $w_p(r_p)$, which is not significantly affected by redshift-space distortions."1047 The evolution of the projected correlation function with redshift can be related to the evolution of £(7)., The evolution of the projected correlation function with redshift can be related to the evolution of $\xi(r)$.1048" To begin we measure ¢,, in bins of r, and 7. using the Landy Szalay estimator (2):: where DD. DR. and RR are the number of object pairs in each bin of r, and x — Le.. the number of cases where an object of type B is located a separation of r, and 7 away from an object of type A — considering pairs between objects in the data catalog and other objects in thedata catalog. between the data catalog and a random catalog. or within the random catalog. respectively; we will describe these catalogs in more"," To begin we measure $\xi_{ss}$ in bins of $r_p$ and $\pi$, using the Landy Szalay estimator \citep{1993ApJ...412...64L}: where DD, DR, and RR are the number of object pairs in each bin of $r_p$ and $\pi$ – i.e., the number of cases where an object of type B is located a separation of $r_p$ and $\pi$ away from an object of type A – considering pairs between objects in the data catalog and other objects in thedata catalog, between the data catalog and a random catalog, or within the random catalog, respectively; we will describe these catalogs in more"1049The gas distribution in each halo is calculated according to the prescription of (2005).,The gas distribution in each halo is calculated according to the prescription of \citet{OstrikerBB05}.1050. Gas is placed in hydrostatic equilibrium with the DM gravitational potential of the halo using a polvtropic equation of state., Gas is placed in hydrostatic equilibrium with the DM gravitational potential of the halo using a polytropic equation of state.1051 Pressure balance with infalling gas near the virial radius and energy conservation determine the (wo constants required for the polvtropic fit., Pressure balance with infalling gas near the virial radius and energy conservation determine the two constants required for the polytropic fit.1052 Two important processes alter (he eas energy., Two important processes alter the gas energy.1053 Star lormation removes low entropy gas: we fix the conversion of gas into stars al1054., Star formation removes low entropy gas; we fix the conversion of gas into stars at.1054.. This leaves the most important [ree parameter. which is the energy input into the cluster gas via feedback processes.," This leaves the most important free parameter, which is the energy input into the cluster gas via feedback processes."1055 We will show that with a reasonable amount of feedback it is possible to match X-ray. observations of hot cluster gas., We will show that with a reasonable amount of feedback it is possible to match X-ray observations of hot cluster gas.1056 In detail. a cubic mesh enclosing the particles is placed around (he halo. with the cell size twice the particle spline softening length. or /=32.55 !kpe.," In detail, a cubic mesh enclosing the particles is placed around the halo, with the cell size twice the particle spline softening length, or $l=32.55h^{-1}$ kpc."1057" The mass my, for each particle is placed on the mesh using the cloud-in-cell method. vielding the DM density. por. lor each cell |."," The mass $m_p$ for each particle is placed on the mesh using the cloud-in-cell method, yielding the DM density, $\rho_{{\rm D}k}$, for each cell $k$."1058 The gravitational potential on the mesh. o4. is computed from the density as in a standard Particle-Mesh code. but with a nonperiodic FFT.," The gravitational potential on the mesh, $\phi_k$, is computed from the density as in a standard Particle-Mesh code, but with a nonperiodic FFT."1059" The center of the cluster is defined as the cell with the lowest potential. 6)=MLN(o6,)."," The center of the cluster is defined as the cell with the lowest potential, $\phi_0=MIN(\phi_k)$."1060 The radii enclosing various overdensiües are calculated al (his point. (he outermost being (he virial radius. rj. enclosing (he overdensity expected [rom spherical tophat collapse. or 97 limes the critical density at z=0 for the cosmology used here (thisisachange[romOstrikeroverdensity200was used)..," The radii enclosing various overdensities are calculated at this point, the outermost being the virial radius, $r_{vir}$, enclosing the overdensity expected from spherical tophat collapse, or 97 times the critical density at $z=0$ for the cosmology used here \citep[this is a change from][where overdensity 200 was used]{OstrikerBB05}."1061 The velocity of the cluster as a whole is taken to be the mean velocily of (he 125 particles closest to the cluster center (or. for halos with fewer than 250 particles. the innermost half).," The velocity of the cluster as a whole is taken to be the mean velocity of the 125 particles closest to the cluster center (or, for halos with fewer than 250 particles, the innermost half)."1062 Particle velocities are moved to the rest [rame of the cluster. and then the kinetic energv. (XE) of each particle is placed on the grid in the same manner as the mass. vielding the IKE per unit volume Συ.," Particle velocities are moved to the rest frame of the cluster, and then the kinetic energy (KE) of each particle is placed on the grid in the same manner as the mass, yielding the KE per unit volume $\onehalf t_{{\rm D}k}$."1063" It is assumedhithat eus had the same distribution as the DM. with density fpi; and KE fip, (f= ΩΩ]."," It is assumed that gas originally had the same distribution as the DM, with density $f_c\rho_{{\rm D}k}$ and KE $f_c \onehalf t_{{\rm D}k}$ $f_c\equiv \Omega_b/\Omega_m$ )."1064" A “|certain amount of the gas mass. M, (described below). will have turned into stars: (his is presumably the most bound material. so cells are ranked by bindingS energvE o+5!DA i6. and then cells are checked off until the sum of the masses f.pp;D equals A."," A certain amount of the gas mass, $M_\star$ (described below), will have turned into stars; this is presumably the most bound material, so cells are ranked by binding energy $\phi_k+\onehalf t_{{\rm D}k}$ , and then cells are checked off until the sum of the masses $f_c\rho_{{\rm D}k}l^3$ equals $M_\star$ ."1065" The initial mass M, and energy. E, of the remaining gas are thus: where (he sum is over all cells inside r,;; except those marked ο for star formation.", The initial mass $M_g$ and energy $E_g$ of the remaining gas are thus: where the sum is over all cells inside $r_{vir}$ except those marked off for star formation.1066" Also. the gas surface pressure P, on thecluster exertedby surrounding material is estimated"," Also, the gas surface pressure $P_s$ on thecluster exertedby surrounding material is estimated"1067found in ?..,found in \citet{Rawlings:freezeout}.1068 This quantity depends on the relative abundance of dust erains compared to hydrogen nuclei. the physical properties of the grain as well as the species whose lreeze-oul is being considered. ancl electrostatic effects to take into account the fact that ionic species will Ireeze-out al a different rate to neutral species.," This quantity depends on the relative abundance of dust grains compared to hydrogen nuclei, the physical properties of the grain as well as the species whose freeze-out is being considered, and electrostatic effects to take into account the fact that ionic species will freeze-out at a different rate to neutral species."1069 Due to the presence of more (han one erain population in most svstenis. the grain. properties need (o be averaged over the grain size distribution.," Due to the presence of more than one grain population in most systems, the grain properties need to be averaged over the grain size distribution."1070 ? relate (his size distribution to the depletion coefficient. D which depends on the abundance of very small grains and on the metallicity.," \citet{Rawlings:freezeout} relate this size distribution to the depletion coefficient, $D$ which depends on the abundance of very small grains and on the metallicity."1071 Taking these assumptions into consideration. the freeze-oul timescale can be derived from the rate of [reeze-ont given by ?:: where ry is the molecular mass of (he species whose Ireeze-out is being considered ancl T is (he gas temperature.," Taking these assumptions into consideration, the freeze-out timescale can be derived from the rate of freeze-out given by \citet{Rawlings:freezeout}: where $m_{X}$ is the molecular mass of the species whose freeze-out is being considered and $T$ is the gas temperature."1072 Desorption is the process by which molecules in ices on the surface of dust grains. are returned {ο the ISM.," Desorption is the process by which molecules in ices on the surface of dust grains, are returned to the ISM."1073 The mechanism (through which heat is generated Lor this desorption. is still debated (?)..," The mechanism through which heat is generated for this desorption, is still debated \citep{Roberts:desorption}."1074 In this work. we consider onlv one mechanism for desorption. namely exolhermic reactions occurring on the erain surface.," In this work, we consider only one mechanism for desorption, namely exothermic reactions occurring on the grain surface."1075 More specifically. the liberation of energy from {ο Formation on dust grains results in a proportion of the frozen molecules on the dust erain being returned (o the gas phase.," More specifically, the liberation of energy from $H_2$ formation on dust grains results in a proportion of the frozen molecules on the dust grain being returned to the gas phase."1076 We calculate the desorption rate of CO which is the most abundant molecular species besides hvdrogen., We calculate the desorption rate of CO which is the most abundant molecular species besides hydrogen.1077 This rate is: The rate depends on (the metallicity which scales linearly with the dust (o gas ratio. the abundance of both molecular and atomic hydrogen. the temperature. 7 and the number ol CO molecules desorbed [or every {ο [ormed. .," This rate is: The rate depends on the metallicity which scales linearly with the dust to gas ratio, the abundance of both molecular and atomic hydrogen, the temperature, $T$ and the number of CO molecules desorbed for every $H_2$ formed, $\gamma$."1078 The coefficient 3x10n represents (he canonical //5 lormation rate in the Milkv. Way., The coefficient $3\times10^{-17}$ represents the canonical $H_2$ formation rate in the Milky Way.1079 From this expression. we can calculate a (vpical timescale associated wilh desorption:," From this expression, we can calculate a typical timescale associated with desorption:"1080opaque (r« 5).,opaque $\tau<5$ ).1081 However. larger values of R would imply even more massive clouds and lower densities.," However, larger values of $R$ would imply even more massive clouds and lower densities."1082 Thus we conclude that 1t is unlikely that the intrinsic ratio R is much larger than 0.5 except for the two clouds whose observed line ratio is larger than 2., Thus we conclude that it is unlikely that the intrinsic ratio $R$ is much larger than 0.5 except for the two clouds whose observed line ratio is larger than 2.1083 Similarly. for 520. the intrinsic ratio is expected to be smaller than 0.5.," Similarly, for s20, the intrinsic ratio is expected to be smaller than 0.5."1084 Molecular masses according to the integrated CO line brightness can be computed as follows: where the line intensity / refers to either the CO J21-0 or J=2-] line., Molecular masses according to the integrated CO line brightness can be computed as follows: where the line intensity $I$ refers to either the CO J=1-0 or J=2-1 line.1085 Cloud masses derived for à constant conversion factor Χου=2.8x I07em-7 Ko! are generally smaller than virial masses (except for one source in 515)., Cloud masses derived for a constant conversion factor $X_{CO}=2.8\times 10^{20}$ $^{-2}$ $^{-1}$ are generally smaller than virial masses (except for one source in s15).1086 Our estimated cluster masses (see Table +) are too small to account for the difference. even taking into account the incompleteness of the IMF.," Our estimated cluster masses (see Table 4) are too small to account for the difference, even taking into account the incompleteness of the IMF."1087" In the last column we give Xco. normalized to 10-"" cm K7!. as the value needed to have the CO-luminosity mass equal to virtal mass (we give the average between the values relative to the two CO lines): where the values of /.O.W refer to the CO line which has been used."," In the last column we give $X_{CO}$, normalized to $^{20}$ $^{-2}$ $^{-1}$, as the value needed to have the CO-luminosity mass equal to virial mass (we give the average between the values relative to the two CO lines): where the values of $I,\Theta, W$ refer to the CO line which has been used."1088 The large cloud sizes derived with this method for R=0.5 imply large cloud masses and very small star formatior efficiencies., The large cloud sizes derived with this method for $R=0.5$ imply large cloud masses and very small star formation efficiencies.1089 Gas densities are lower than expected for typical molecular cloud conditions (see Section 3.4 for à comparisor with Milky Way clouds)., Gas densities are lower than expected for typical molecular cloud conditions (see Section 3.4 for a comparison with Milky Way clouds).1090 We do not find a correlation between the cluster mass and the virial mass or between the ratio Μο ΜΙΑ ane the galactocentric radius (rp= —0.15)., We do not find a correlation between the cluster mass and the virial mass or between the ratio $_{vir}^{2-1}$ $_{vir}^{1-0}$ and the galactocentric radius $r_P=-0.15$ ).1091" For this model the CO-to-H» conversion factor, X¢o. does not correlate with galactocentric radius (rp= 0.34) but there is a correlation between Χορ and the cloud mass (rp= 0.92). shown m Figure 2."," For this model the $_2$ conversion factor, $X_{CO}$ , does not correlate with galactocentric radius $r_P=0.34$ ) but there is a correlation between $X_{CO}$ and the cloud mass $r_P=0.92$ ), shown in Figure 2."1092 This last correlation implies that X¢ increases for more massive clouds., This last correlation implies that $X_{CO}$ increases for more massive clouds.1093 Can this be justified?, Can this be justified?1094 The Χου value is expected to increase as the extinction through the cloud or the mean volume density decreases (??)..," The $X_{CO}$ value is expected to increase as the extinction through the cloud or the mean volume density decreases \citep{1988ApJ...325..389M,2010arXiv1003.1340G}."1095 Gas densities for this model decrease as clouds get more massive. which justify the observed trend.," Gas densities for this model decrease as clouds get more massive, which justify the observed trend."1096 Finally we find a marginal correlation between the cloud size and the CO linewidth. Do:W?. as it is observed in resolved molecular clouds and discussed in Section. 3.4 (rpz0.61. slope 1.940.6 for the J=1-0 line and rp=0.57 slope 1.9+0.7 for the J=2-1 line).," Finally we find a marginal correlation between the cloud size and the CO linewidth, $D\propto W^2$, as it is observed in resolved molecular clouds and discussed in Section 3.4 $r_P$ =0.61, slope $\pm$ 0.6 for the J=1-0 line and $r_P$ =0.57 slope $\pm$ 0.7 for the J=2-1 line)."1097 This method is heavily dependent on the assumption that clouds are located at the beam center. that coincides with the peak of the IR-24 eemission.," This method is heavily dependent on the assumption that clouds are located at the beam center, that coincides with the peak of the IR-24 emission."1098 Even though the molecular gas will likely follow the dust distribution. the peak of the mid-IR emission depends on the intensity of radiation field which is heating the grains.," Even though the molecular gas will likely follow the dust distribution, the peak of the mid-IR emission depends on the intensity of radiation field which is heating the grains."1099 So the molecular cloud might be offset with respect to the IR emission., So the molecular cloud might be offset with respect to the IR emission.1100 If cloud turbulent pressure equals the ISM ambient pressure given by hydrostatic equilibrium we can estimate the gas volume density of the cloud., If cloud turbulent pressure equals the ISM ambient pressure given by hydrostatic equilibrium we can estimate the gas volume density of the cloud.1101 This is m reality a lower limit since cloud cores can be denser and self gravitating. and the outer parts close to equilibrium with the surrounding ISM.," This is in reality a lower limit since cloud cores can be denser and self gravitating, and the outer parts close to equilibrium with the surrounding ISM."1102" From the minimum gas density we infer D"", the maximum cloud size. using the virial equation."," From the minimum gas density we infer $D^{max}$, the maximum cloud size, using the virial equation."1103 As we shall remark in Section 3.4. it might be that only part of the cloud is gravitationally bound and in virial equilibrium.," As we shall remark in Section 3.4, it might be that only part of the cloud is gravitationally bound and in virial equilibrium."1104" In this case the virial equation applies only for the higher density core with size D«Dres,", In this case the virial equation applies only for the higher density core with size $D<D^{max}$.1105 In Table 5 we give the resulting cloud parameters and below some details of this model., In Table 5 we give the resulting cloud parameters and below some details of this model.1106" We compute the ambient pressure (?) where X,, are the gas and stellar surface mass densities anc cy, are the velocity dispersion relative to gas and stellar disk."," We compute the ambient pressure as \citep{2003MNRAS.342..199C} where $\Sigma_{g,s}$ are the gas and stellar surface mass densities and $c_{g,s}$ are the velocity dispersion relative to gas and stellar disk."1107 The velocity dispersion of the gaseous disk Is 8 km s7!., The velocity dispersion of the gaseous disk is $c_g=8$ km $^{-1}$.1108 We shall use the local values of the HI column densities for the gas surface densities (WSRT data) and a scale height of the stellar disk zo=0.5 kpe for the stellar dispersion., We shall use the local values of the HI column densities for the gas surface densities (WSRT data) and a scale height of the stellar disk $z_0=0.5$ kpc for the stellar dispersion.1109 The stellar dispersion and surface density derived through the dynamical analysis of the rotation curve (?) reads: The ISM pressure in M33does not vary much radially since the gas surface density has a very large scale length., The stellar dispersion and surface density derived through the dynamical analysis of the rotation curve \citep{2003MNRAS.342..199C} reads: The ISM pressure in M33does not vary much radially since the gas surface density has a very large scale length.1110 However it, However it1111due to the dependency upon accretion rate is now superimposed on top of this trend.,due to the dependency upon accretion rate is now superimposed on top of this trend.1112" Our model is semi-analytic, not a real stellar evolution model, and therefore the sharpness in the variation is most likely artificial."," Our model is semi-analytic, not a real stellar evolution model, and therefore the sharpness in the variation is most likely artificial."1113" In reality, the protostar would only be able to respond to changes in the accretion rate according to its Kelvin-Helmholtz time."," In reality, the protostar would only be able to respond to changes in the accretion rate according to its Kelvin-Helmholtz time."1114" However, allowing the radius to vary along with the accretion rate decreases the variation in the luminosity, which is proportional to M/R., and hence this represents a conservative choice for our purposes."," However, allowing the radius to vary along with the accretion rate decreases the variation in the luminosity, which is proportional to $\dot{M}/R_*$, and hence this represents a conservative choice for our purposes."1115 10 also shows the accretion luminosity from the sink over the same period., \ref{sinkradius} also shows the accretion luminosity from the sink over the same period.1116 Initially the variation in the accretion rate dominates both the stellar radius and the luminosity., Initially the variation in the accretion rate dominates both the stellar radius and the luminosity.1117" However, over time the variation in the stellar radius becomes smaller as the star leaves the adiabatic phase and starts steadily contracting."," However, over time the variation in the stellar radius becomes smaller as the star leaves the adiabatic phase and starts steadily contracting."1118 During this later phase the actual mass of the star is no longer changing so rapidly and there is a clear trend in the radius., During this later phase the actual mass of the star is no longer changing so rapidly and there is a clear trend in the radius.1119" Consequently as LaceΜ.Μ/R«, the luminosity is no longer so noisy."," Consequently as $L_{acc}=GM_*\dot{M}/R_*$, the luminosity is no longer so noisy."1120" The effect of accretion luminosity feedback is a modifying factor affecting fragmentation in minihalos, rather than a dominant one."," The effect of accretion luminosity feedback is a modifying factor affecting fragmentation in minihalos, rather than a dominant one."1121" Inter-halo variability produces a greater variation in the number of fragments formed than feedback effects, and the number of fragments chiefly depended on the initial conditions of the halo which was being considered."," Inter-halo variability produces a greater variation in the number of fragments formed than feedback effects, and the number of fragments chiefly depended on the initial conditions of the halo which was being considered."1122 In halos in which a large number of, In halos in which a large number of1123at higher altitudes.,at higher altitudes.1124 We may consider our result às the first quantitative indication of such a decrease of the turbulent magnetic field strength with altitude., We may consider our result as the first quantitative indication of such a decrease of the turbulent magnetic field strength with altitude.1125 Further observations with a better spatial resolution should be performed to measure simultaneously the four Stokes parameters in the Ball line. in order to take advantage of both Hanle and Zeeman effects to obtain a complete view of the magnetic field structure.," Further observations with a better spatial resolution should be performed to measure simultaneously the four Stokes parameters in the BaII line, in order to take advantage of both Hanle and Zeeman effects to obtain a complete view of the magnetic field structure."1126 The observational data shown in this paper were obtained from a campaign performed at THEMIS S.L. operated on the island of Tenerife by CNRS-CNR in the Spanish Observatorio del Teide of the Instituto de Astrotisica de Canarias., The observational data shown in this paper were obtained from a campaign performed at THEMIS S.L. operated on the island of Tenerife by CNRS-CNR in the Spanish Observatorio del Teide of the Instituto de Astrofisica de Canarias.1127The gross spectral characteristics of the system can be derived from Figure 6.. where we show the field surrounding SNR lin four separate energy sub-bands.,"The gross spectral characteristics of the system can be derived from Figure \ref{fig_g320_bands}, where we show the field surrounding SNR in four separate energy sub-bands."1128 This set of images demonstrates that the northern ring of X-ray clumps coincident with hhave no detectable emission above —4 keV. while the PWN has significantly harder emission.," This set of images demonstrates that the northern ring of X-ray clumps coincident with have no detectable emission above $\sim$ 4 keV, while the PWN has significantly harder emission."1129 The pulsar is clearly the hardest source in the field. although this may largely be due to pile-up in its spectrum (see further discussion below).," The pulsar is clearly the hardest source in the field, although this may largely be due to pile-up in its spectrum (see further discussion below)."1130 These broad conclusions confirm the spectral decompositions made from and oobservations (Sewardetal.1983:: Tamuraetal. 1996))., These broad conclusions confirm the spectral decompositions made from and observations \cite{shmc83}; \cite{tkyb96}) ).1131 At the higher spatial resolution of the ddata. some new spectral features become apparent.," At the higher spatial resolution of the data, some new spectral features become apparent."1132 The 2.0-4.0 keV and 4.0-6.0 keV images in Figure 6 demonstrate that the PWN has an extended component coincident with the eclumps., The 2.0--4.0 keV and 4.0–6.0 keV images in Figure \ref{fig_g320_bands} demonstrate that the PWN has an extended component coincident with the clumps.1133 Furthermore. there is the suggestion from Figure 6 that the jet and outer are (features C and E respectively) have harder spectra than the overall PWN.," Furthermore, there is the suggestion from Figure \ref{fig_g320_bands} that the jet and outer arc (features C and E respectively) have harder spectra than the overall PWN."1134" Spectral fits show that the point-source seen at RA I5|]3""4]., Dee —S9°11/45” is heavily absorbed. with Ny~3<105: env? for simple thermal and non-thermal models."," Spectral fits show that the point-source seen at RA $15^{\rm h}13^{\rm m}41^{\rm s}$, Dec $-59^{\circ}11'45''$ is heavily absorbed, with $N_H \sim 3\times10^{22}$ $^{-2}$ for simple thermal and non-thermal models."1135 It therefore most likely represents an unrelated background source., It therefore most likely represents an unrelated background source.1136 The pulsar itself has a high X-ray flux and is expected to suffer from significant pile-up. in which multiple events urive on a given CCD pixel during a single frame.," The pulsar itself has a high X-ray flux and is expected to suffer from significant pile-up, in which multiple events arrive on a given CCD pixel during a single frame."1137 Indeed the spectrum of the pulsar has an excess of hard photons (presumably due to several lower-energy photons being recorded as a single event). and cannot be fit by any simple power-law model.," Indeed the spectrum of the pulsar has an excess of hard photons (presumably due to several lower-energy photons being recorded as a single event), and cannot be fit by any simple power-law model."1138" Assuming a foreground absorbing column Ny~1s107 en. a power-law spectrum with photon index P—1.4. and an unabsorbed flux f£,~6«1077 ere en? s! in the energy range 0.1—2.4 keV (Greiveldingeretal. 1995)). the pproposal planning predicts 50% pile-up. with a resulting detected count rate 0.16 cts s! over the energy range 0.5-10 keV. This in reasonable agreement with the value measured for the pulsar in Table 1.."," Assuming a foreground absorbing column $N_H1139\sim 1\times10^{22}$ $^{-2}$, a power-law spectrum with photon index $\Gamma \sim 1.4$, and an unabsorbed flux $f_x \sim11406\times10^{-12}$ erg $^{-2}$ $^{-1}$ in the energy range 0.1–2.4 keV \cite{gcm+95}) ), the proposal planning predicts $>$ pile-up, with a resulting detected count rate 0.16 cts $^{-1}$ over the energy range 0.5–10 keV. This in reasonable agreement with the value measured for the pulsar in Table \ref{tab_rates}."1141 We can determine the spectrum for the diffuse nebula surrounding the pulsar by extracting photon energies from the annular region shown in Figure 7.., We can determine the spectrum for the diffuse nebula surrounding the pulsar by extracting photon energies from the annular region shown in Figure \ref{fig_g320_regions}.1142" Measuring the spectrum for an extended source such as this is difficult because of radiation damage to the front-illuminatedCCDs.'"".. which has caused the response of each CCD to be a function of distance from the read-out nodes."," Measuring the spectrum for an extended source such as this is difficult because of radiation damage to the front-illuminated, which has caused the response of each CCD to be a function of distance from the read-out nodes."1143 To try and mitigate this effect. we extracted separate spectra for each of the four CCDs on which this diffuse emission falls. and generated response matrices and effective area curves for each CCD separately.," To try and mitigate this effect, we extracted separate spectra for each of the four CCDs on which this diffuse emission falls, and generated response matrices and effective area curves for each CCD separately."1144 We then fit these four spectra simultaneously over the entire usable energy range (0.5-10.0 keV). using a common value for all fit parameters except the normalization of each spectrum.," We then fit these four spectra simultaneously over the entire usable energy range (0.5–10.0 keV), using a common value for all fit parameters except the normalization of each spectrum."1145 These spectra. which between them represent a total of ~500000 photons. are shown in Figure 8..," These spectra, which between them represent a total of $\sim$ 000 photons, are shown in Figure \ref{fig_pwn_spec}."1146 While no significant spectral features are seen. some systematic residuals are still present. which we attribute to gain mismatches resulting from the aforementioned radiation damage.," While no significant spectral features are seen, some systematic residuals are still present, which we attribute to gain mismatches resulting from the aforementioned radiation damage."1147 The count rate from the diffuse nebula is very high (73 cts s! ). but this emission is spread over a very large area so that pile-up is negligible.," The count rate from the diffuse nebula is very high $\sim$ 3 cts $^{-1}$ ), but this emission is spread over a very large area so that pile-up is negligible."1148 We find that these data are well fitted by an absorbed power law., We find that these data are well fitted by an absorbed power law.1149 As listed in Table 2.. the best-fit spectral parameters are an absorbing column Ny=(9.540.3)«107! em and a photon index P=2.05+0.04.," As listed in Table \ref{tab_spec}, the best-fit spectral parameters are an absorbing column $N_H = (9.5\pm0.3)\times10^{21}$ $^{-2}$ and a photon index $\Gamma =2.05\pm0.04$."1150 We next consider the spectra of each of regions C and E and of features 1-5., We next consider the spectra of each of regions C and E and of features 1–5.1151 All these sources have à surface brightness far too low to produce pile-up in the detectors., All these sources have a surface brightness far too low to produce pile-up in the detectors.1152 We fit absorbed power laws to the data in each region over 0.5-10.0 keV. with the resulting spectral parameters listed in Table 2..," We fit absorbed power laws to the data in each region over 0.5–10.0 keV, with the resulting spectral parameters listed in Table \ref{tab_spec}."1153 With the exception of feature 2 (which has very few counts and correspondingly uncertain spectral parameters). the fitted values of Nj are all consistent with each other and with that for the diffuse PWN. while the resulting photon indices range between [z1.3 and Dz1.7.," With the exception of feature 2 (which has very few counts and correspondingly uncertain spectral parameters), the fitted values of $N_H$ are all consistent with each other and with that for the diffuse PWN, while the resulting photon indices range between $\Gamma \approx 1.3$ and $\Gamma \approx 1.7$."1154 These photon indices are all significantly flatter than that determined for the diffuse PWN., These photon indices are all significantly flatter than that determined for the diffuse PWN.1155 To more tightly constrain the photon index in these regions. we assume that they all have the same absorbing column as that determined for the diffuse nebula above. and thus fix Nj to 9.5«107! em™ corresponding to the power law fit to that source.," To more tightly constrain the photon index in these regions, we assume that they all have the same absorbing column as that determined for the diffuse nebula above, and thus fix $N_H$ to $9.5\times10^{21}$ $^{-2}$ corresponding to the power law fit to that source."1156 The resulting spectral fits confirm the flatter spectra for these regions when compared to the overall nebula., The resulting spectral fits confirm the flatter spectra for these regions when compared to the overall nebula.1157 Finally. we crudely fit à Raymond-Smith spectrum to the emission from feature 6. comeident with the star Muzzio 10.," Finally, we crudely fit a Raymond-Smith spectrum to the emission from feature 6, coincident with the star Muzzio 10."1158 The approximate spectral parameters are listed in Table 2.., The approximate spectral parameters are listed in Table \ref{tab_spec}.1159 The spectrum for the rregion is considerably more complex than for the PWN., The spectrum for the region is considerably more complex than for the PWN.1160" In Figure 9 we show a spectrum for the region shown in Figure 7.. enclosing the brightest clumps in ((sources NO. NI. N2. N3. ΝΟ, N6. N7 and Νδ in the designation of Brazier&Becker 1997))."," In Figure \ref{fig_clump_spec} we show a spectrum for the region shown in Figure \ref{fig_g320_regions}, enclosing the brightest clumps in (sources N0, N1, N2, N3, N5, N6, N7 and N8 in the designation of \cite{bb97}) )."1161 This spectrum is clearly dominated by emission lines., This spectrum is clearly dominated by emission lines.1162" We also show a crude fit to the data using a non-equilibrium tonization model with variable abundances (model ""vnei"" in XSPEC).", We also show a crude fit to the data using a non-equilibrium ionization model with variable abundances (model ” in XSPEC).1163 The fit ts poor (AZ/r2455/254= 1.91). but this is mainly due to large residuals in the Ne emission line at 0.9 keV. In particular. the continuum component of the spectrum of iis Well-accounted for. with little emission above 3-4 keV. While we defer a full and detailed treatment of these data to a subsequent paper. we think it clear from Figures 6 and 9. that we can rule out the possibility that cconsists of synchrotron-emitting clumps embedded in a diffuse thermal nebulae (as argued by G99). and that a model involving thermal clumps embedded in a diffuse synchrotron nebula (as proposed by Tamuraetal. 1996)) seems far more likely.," The fit is poor $\chi_\nu^2/\nu=455/254=1.91$ ), but this is mainly due to large residuals in the Ne emission line at 0.9 keV. In particular, the continuum component of the spectrum of is well-accounted for, with little emission above 3–4 keV. While we defer a full and detailed treatment of these data to a subsequent paper, we think it clear from Figures \ref{fig_g320_bands} and \ref{fig_clump_spec} that we can rule out the possibility that consists of synchrotron-emitting clumps embedded in a diffuse thermal nebulae (as argued by G99), and that a model involving thermal clumps embedded in a diffuse synchrotron nebula (as proposed by \cite{tkyb96}) ) seems far more likely."1164 It is immediately clear from the images presented here that the PWN surrounding PSR hhas a very complicated morphology. matched only by the," It is immediately clear from the images presented here that the PWN surrounding PSR has a very complicated morphology, matched only by the"1165shows two unfiltered points by ROTSEIIIb (Yost2005) and two other Π measures reported by Mirabaletal.(2005).. which we couverted to + assuuiug 0.3< (uo uncertainty was reported. so we assunied the systematic of 0.3 of the USNODIO. imagnuitudes. as they calibrated with a USNO01.0 field star).,"shows two unfiltered points by ROTSE–IIIb \citep{Yost05} and two other $R$ measures reported by \citet{Mirabal05}, , which we converted to $r'$ assuming $0.3<R-I<0.6$ (no uncertainty was reported, so we assumed the systematic of 0.3 of the USNO–B1.0 magnitudes, as they calibrated with a USNO–B1.0 field star)."1166 Iu particular. the latter poiuts sccm to confir the presence of the bump iu r’. despite the large uucertaiuties;," In particular, the latter points seem to confirm the presence of the bump in $r'$, despite the large uncertainties."1167 Durieetal.(2005) report unfiltered observations of the bun., \citet{Durig05} report unfiltered observations of the bump.1168 Since the couversion of unfiltered to standard magnitudes requires sole assunitious aud inplies large uucertainties. we are not as confident about the proper intercalibration of those converted magnitudes and our data as woe are at earlier epochs. when the decay is simply monotonic.," Since the conversion of unfiltered to standard magnitudes requires some assumptions and implies large uncertainties, we are not as confident about the proper intercalibration of those converted magnitudes and our data as we are at earlier epochs, when the decay is simply monotonic."1169 Therefore. lacking a comparison dataset of unfiltered data covering both the monotonic earlydecay and the bump. we have not included Duis data in Fig. 2..," Therefore, lacking a comparison dataset of unfiltered data covering both the monotonic earlydecay and the bump, we have not included \citet{Durig05} data in Fig. \ref{fig:LC}."1170 Following Lazzatietal(2002)... if we interpret the Dip as due to deusitv variatious of the ISAL this is possible oulv if the observation occured at a frequency vo=veo (let m) be the frequency of our optical bauds) below the cooling break 1η. aud above the peals svuchrotrou frequeney ii Min<<.," Following \citet{Lazzati02}, if we interpret the bump as due to density variations of the ISM, this is possible only if the observation occurred at a frequency $\nu=\nu_O$ (let $\nu_O$ be the frequency of our optical bands) below the cooling break $\nu_c$ and above the peak synchrotron frequency $\nu_m$: $\nu_m<\nu<\nu_c$."1171 In the following we consider the two cases of uniform ISAD and πια euvironuent. respectively.," In the following we consider the two cases of uniform ISM and wind environment, respectively."1172 Iu the case of uniform ISAL the expected powerlaw iudex of the light curve is à=ον Ἠι where p is the electron cnerev distribution iudex (Sanotal. 1998).," In the case of uniform ISM, the expected power–law index of the light curve is $\alpha=3(p-1)/4$ , where $p$ is the electron energy distribution index \citep{Sari98}."1173". Frou, our measure of a=1.2+0.1 we derive p=26401.", From our measure of $\alpha=1.2\pm0.1$ we derive $p=2.6\pm0.1$.1174 We also note that when Á. crosses the optical baud we should expect a steepening in the light curve of Aa=0.25., We also note that when $\nu_c$ crosses the optical band we should expect a steepening in the light curve of $\Delta\alpha=0.25$.1175" Since we do not find evidence for this before f<1 d. the only possibility is that ve<1, at least until £ —1 d. The energy spectrum at frequency Lg,OMκἩ isa power law with index s;=(p 1)/2. Le. —O840.05."," Since we do not find evidence for this before $t<1$ d, the only possibility is that $\nu_O<\nu_c$ at least until $t\sim$ 1 d. The energy spectrum at frequency $\nu_m<\nu<\nu_c$ is a power law with index $\beta=(p-1)/2$ , i.e. $\beta=0.8\pm0.05$."1176 Fieure 2 shows that this is consistent with our result., Figure \ref{fig:SED} shows that this is consistent with our result.1177 The cooling break 1 must lie between the optical baud ve and the Xrav Éxy: vyom.oy., The cooling break $\nu_c$ must lie between the optical band $\nu_O$ and the X–ray $\nu_X$ : $\nu_O<\nu_c<\nu_X$.1178 The powerlaw index of the spectra between τὰ. and vy is expected to be ἐν=pí21.30.05., The power–law index of the spectrum between $\nu_c$ and $\nu_X$ is expected to be $\beta_{cX}=p/2=1.3\pm0.05$.1179 The Nray powerlaw decay iudex. ay. is expected to be: αντον Wilt> ey) ay=(Bp2)/ Latter 7». has crossed the NXray band (7.< vy). thus experiencing a steepeuing of Aay=0.25.," The X–ray power–law decay index, $\alpha_X$, is expected to be: $\alpha_X=3(p-1)/4$ $\nu_c>\nu_X$ ), $\alpha_X=(3p-2)/4$ after $\nu_c$ has crossed the X–ray band $\nu_c<\nu_X$ ), thus experiencing a steepening of $\Delta\alpha_X=0.25$."1180 As this is expected to occur soon after the GRD. it is sensible to back-extrapolate the Xrav upper limit απήτο for most of the time ay=(3p.2)/1L.15.," As this is expected to occur soon after the GRB, it is sensible to back-extrapolate the X–ray upper limit assuming for most of the time $\alpha_X=(3p-2)/4=1.45$."1181 From Fig. 3..," From Fig. \ref{fig:SED},"1182 as long as we asstuue the validity of the Nray upper limut back-extrapolated to £—0.001 d assidue ay=1.15 (solid arrow]. we findthat the shallowest powerlaw index allowed between optical aud Nrays is joy>0.7.," as long as we assume the validity of the X–ray upper limit back-extrapolated to $t=0.004$ d assuming $\alpha_X=1.45$ (solid arrow), we findthat the shallowest power–law index allowed between optical and X–rays is $\beta_{OX}>0.7$."1183 Thus. this is consistent with a broken power law with powerlaw indices from 0.8 to 1.3.," Thus, this is consistent with a broken power law with power--law indices from $0.8$ to $1.3$."1184" Du παπα, we conclude that the case of a wuitorm ISM is fully cousisteut with our observations."," In summary, we conclude that the case of a uniform ISM is fully consistent with our observations."1185" Iu the case of wind cuvirommentand p<2 we ist use the relation a=(p|8)/8 by Dai&Cheng(2001) for vy,<r«nm. which vields p=1.6+0.8."," In the case of wind environmentand $p<2$ we must use the relation $\alpha=(p+8)/8$ by \citet{Dai01} for $\nu_m<\nu<\nu_c$, which yields $p=1.6\pm0.8$."1186 The case of p2 is incompatible with the data: from the relation a=(3p.Lf bx Chevalier&Li(1999) we derive a value of p=L9£0., The case of $p>2$ is incompatible with the data: from the relation $\alpha=(3p-1)/4$ by \citet{Chevalier99} we derive a value of $p=1.9\pm0.1$.1187" From 3.=(p1)/2 and oy= p/2. holding for v,,<17og and for VeyzMx. respectively. we derive: 4,j=0.340.L aud ay=O40.1."," From $\beta_{mc}=(p-1)/2$ and $\beta_{cX}=p/2$ , holding for $\nu_m<\nu<\nu_c$ and for $\nu_c<\nu<\nu_X$, respectively, we derive: $\beta_{mc}=0.3\pm0.4$ and $\beta_{cX}=0.8\pm0.4$."1188 Concerning the back-extrapolatiou of the Xταν upper limit. ày is expected to be: ay=(p|8)/8 (G4.=Py) αν=(p|6)/8 after i4. has crossed the Xrav band (7.<vy). thus experiencing a steepenius of Aay=025.," Concerning the back-extrapolation of the X–ray upper limit, $\alpha_X$ is expected to be: $\alpha_X=(p+8)/8$ $\nu_c>\nu_X$ ), $\alpha_X=(p+6)/8$ after $\nu_c$ has crossed the X--ray band $\nu_c<\nu_X$ ), thus experiencing a steepening of $\Delta\alpha_X=0.25$."1189 For the same reason as iu the previous case. it is reasonable to assume ay=(p|ο)1.95 for most of the tine.," For the same reason as in the previous case, it is reasonable to assume $\alpha_X=(p+6)/8=0.95$ for most of the time."1190 The cousequeut limit ou the spectrum ds Joyl.l (dashed arrow in Fig. 3))., The consequent limit on the spectrum is $\beta_{OX}>1.1$ (dashed arrow in Fig. \ref{fig:SED}) ).1191 This is colmpatible ouly with oy., This is compatible only with $\beta_{cX}$.1192" Furthermore. 1. should 6 very close to the optical bauds: this implies that duving our observation v, should cross the optical bauds. xoducig a slope change in the powerlaw decay of Aa=0.25, which is not observed."," Furthermore, $\nu_c$ should be very close to the optical bands: this implies that during our observation $\nu_c$ should cross the optical bands, producing a slope change in the power–law decay of $\Delta\alpha=0.25$, which is not observed."1193 If we assume. that US.vy for most of the time between tf=0.001 d and he epoch of the X.ray observation (1.33 d). we derive he Xrav upper luit assuunüug ay=(p|8)/81.2. vieldiug joyc0.9. which is not consistent with joy=jue=O2dEOLLL ," If we assume that $\nu_c>\nu_X$ for most of the time between $t=0.004$ d and the epoch of the X–ray observation $\sim1.33$ d), we derive the X–ray upper limit assuming $\alpha_X=(p+8)/8=1.2$, yielding $\beta_{OX}>0.9$, which is not consistent with $\beta_{OX}=\beta_{mc}=0.3\pm0.4$ ."1194Iu contrast to GRBs 990125 aud 021211. we fined uo evidence for a change iu the temporal slope within the first few uumutes of the onset of GRD 050502a. ruline out a transition from reverse to forward shock cnussion at this tine.," In contrast to GRBs 990123 and 021211, we find no evidence for a change in the temporal slope within the first few minutes of the onset of GRB 050502a, ruling out a transition from reverse to forward shock emission at this time."1195 In CRD 050502a the bump rises at ~6 nun after the CRB in the rest-frame. to be upared with 0.5 minu aud 2.7 nüu of GRB 990123 and CRB 021211. respectively. when the above transition between reverse and forward shocks is supposed to occur.," In GRB 050502a the bump rises at $\sim$ 6 min after the GRB in the rest-frame, to be compared with 0.5 min and 2.7 min of GRB 990123 and GRB 021211, respectively, when the above transition between reverse and forward shocks is supposed to occur."1196 Should GRB 050502a have exhibited a simular trausition. we should have detected it before the lauup.," Should GRB 050502a have exhibited a similar transition, we should have detected it before the bump."1197 We conclude that. despite the fact that a wind cuviromment cannot be ruled out. the wnitorm ISM with chumps in density seenis to better account for our observations.," We conclude that, despite the fact that a wind environment cannot be ruled out, the uniform ISM with clumps in density seems to better account for our observations."1198 The interpretation of the bumup as the result of a refreshed shock catching up with the afterelow front shock seeiis more problematic. even if it eiunot be ruled out.," The interpretation of the bump as the result of a refreshed shock catching up with the afterglow front shock seems more problematic, even if it cannot be ruled out."1199 Iu fact. according to the original refreshed-shocks scenario (simar&Piran2000:Caanotetal.2003).. we should expect that the duration. Af of the buuip is colmparable with its start time: At~f.," In fact, according to the original refreshed-shocks scenario \citep{Kumar00,Granot03}, we should expect that the duration $\Delta t$ of the bump is comparable with its start time: $\Delta t\approx t$."1200 In the case of CRB 050502a our measures aud those by Mirabaletal.(2005) show that. in spite of the uncertainty. Atzz0.2 d and fo0.02 d. Following Ruunar&Piran (2000).. the iupact between the two shells should produce a forward shock in the outer shell respousible for the bump aud a reverse shock propagating iu the inner shell.," In the case of GRB 050502a our measures and those by \citet{Mirabal05} show that, in spite of the uncertainty, $\Delta t\approx0.2$ d and $t\sim0.02$ d. Following \citet{Kumar00}, , the impact between the two shells should produce a forward shock in the outer shell responsible for the bump and a reverse shock propagating in the inner shell."

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