ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2" While the quality of the data above the spectral break in niu objects is nof very good. we note that often a roughly flat power fiux WF,x vy?) is secu. further strengthening this result."," While the quality of the data above the spectral break in many objects is not very good, we note that often a roughly flat power flux $\nu F_\nu \propto \nu^0$ ) is seen, further strengthening this result."3 While in recent vears significant progress in nuuderstanuding particle acceleration in —shock waves has been made. there is currently a discrepancy between the theoretical expectation of £j;<1 (e.g...Amato&Sironi&Spitkovsky2011) aud the phenomenological fittings indicating higher value of £j21 (6.5.Wijers&2001:Panaitescu&I&uniar2002:Markoffetαἱ. 2005).," While in recent years significant progress in understanding particle acceleration in shock waves has been made, there is currently a discrepancy between the theoretical expectation of $\xi_{pl} \ll 1$ \citep[e.g.,][]{AB05, Spit08, Caprioli+10, SS11} and the phenomenological fittings indicating higher value of $\xi_{pl} \simeq41$ \citep[e.g.,][]{WG99, FWK00, FW01, PK02, MNW05}."5 This discrepancy can perhaps be explained by the fact that the theory is not vet complete., This discrepancy can perhaps be explained by the fact that the theory is not yet complete.6 Since this topic is outside the scope of this work. we have explored the consequences for both scenarios.," Since this topic is outside the scope of this work, we have explored the consequences for both scenarios."7 Specifically we have demoustrated that in the alternate scenario in which most accelerated clectrous maiutain a Maxwellian distribution (μι< 1). good fits to the data can still be obtained.," Specifically, we have demonstrated that in the alternate scenario in which most accelerated electrons maintain a Maxwellian distribution $\xi_{pl} \ll 1$ ), good fits to the data can still be obtained."8 The high energy part of the spectra is explained by cussion frou particles at the peak of the Maswellian. although this scenario docs uot coustrain the value of the power-law index p.," The high energy part of the spectrum is explained by emission from particles at the peak of the Maxwellian, although this scenario does not constrain the value of the power-law index $p$."9 While we show here that a jet model is able to reproduce the XN-rav spectra. we note that possible contribution to the N-rav cussion may arise frou the inner parts of the disk (RIAF models).," While we show here that a jet model is able to reproduce the X-ray spectra, we note that possible contribution to the X-ray emission may arise from the inner parts of the disk (RIAF models)."10" Observationally there are some new results that hint at an interplay of the two processes as a function of the total huuinosity (Yuan&Cui2005:Russelletaf2010:Plotkinefal,2011:Caucdhie£αἱ.2011).. where RIAFs mav beein to dominate at the ligher hard state Iuninosities."," Observationally there are some new results that hint at an interplay of the two processes as a function of the total luminosity \citep{YC05,11 Russell+10, Plotkin+11, Gandhi+11}, where RIAFs may begin to dominate at the higher hard state luminosities."12" From a theoretical poiut of view. the conditions in the inner part of the inflow may be similar to the conditious in the imuer part of the outflow (seediscussioninMarkoffctal,2005)."," From a theoretical point of view, the conditions in the inner part of the inflow may be similar to the conditions in the inner part of the outflow \citep[see discussion in ][]{MNW05}."13. ence. a clear separation between the ier disk contribution and the immer jet contribution iav be dificult.," Hence, a clear separation between the inner disk contribution and the inner jet contribution may be difficult."14 Several methods may be used to separate the disk aud jet contributions., Several methods may be used to separate the disk and jet contributions.15 First. a clear connection between the N-ray emission aud the racio/NIR emission. which must have a jet origin. could provide evidence for jet dominated model. provided that the plysical conditions at both cussion sites (e.g. the maguetic field or the umuber of radiating particles) are matchecl.," First, a clear connection between the X-ray emission and the radio/NIR emission, which must have a jet origin, could provide evidence for jet dominated model, provided that the physical conditions at both emission sites (e.g., the magnetic field or the number of radiating particles) are matched."16 Such a connection already secs to be indicated by the observational papers cited above., Such a connection already seems to be indicated by the observational papers cited above.17 A second method is based on the requirement that the optical depth to scattering of the disk plotous needs to be not much larecr than wmnitv. otherwise the spectral shape of the disk will be altered.," A second method is based on the requirement that the optical depth to scattering of the disk photons needs to be not much larger than unity, otherwise the spectral shape of the disk will be altered."18 Thus. if the disk accretion fine is significautlv larger than ~r;/e. this could euable multiple Compton scatterings between the clectrous and the disk photons. which may introduce a differeut characteristic from inflow cimission.," Thus, if the disk accretion time is significantly larger than $\sim r_j/c$, this could enable multiple Compton scatterings between the electrons and the disk photons, which may introduce a different characteristic from inflow emission."19 À full reatinent of this idea is left for a future work., A full treatment of this idea is left for a future work.20 Finally. he best wav to discriminate between disk and jet uodels iiiv. be using N-rav polarization micasurements.," Finally, the best way to discriminate between disk and jet models may be using X-ray polarization measurements."21 Both svuchrotron emission aud non-saturated Compton scattering are liehly polarized. hence jet emission is expected to be polarized.," Both synchrotron emission and non-saturated Compton scattering are highly polarized, hence jet emission is expected to be polarized."22 Ou the other hand. in RIAF nodels the polarization signal is expected to be weaker. due to averaging of the svuchrotrou signal from different warts of the disk. as well as coutribution from frece-free cnussion frou the outer accretion flow.," On the other hand, in RIAF models the polarization signal is expected to be weaker, due to averaging of the synchrotron signal from different parts of the disk, as well as contribution from free-free emission from the outer accretion flow."23 We thus expect hat proposed future X-ray polarization missions. sich as he POLARTN uission (Costactal.2010) or theExplorer (GIMS) mission (Jahoda2010) may play a significant role in determining he relative contributions from the disks aud the jets im xoducimg the A-rav spectra.," We thus expect that proposed future X-ray polarization missions, such as the POLARIX mission \citep{Costa+10} or the (GEMS) mission \citep{Jahoda10} may play a significant role in determining the relative contributions from the disks and the jets in producing the X-ray spectra."24 We would like to thank Dipaukar Alaitra. Shuuulik Balbere. Ramesh Naravan. Jovrn Wiluis aud Picreioreio Casella for useful discussions aud comments.," We would like to thank Dipankar Maitra, Shmulik Balberg, Ramesh Narayan, Jörrn Wilms and Piergiorgio Casella for useful discussions and comments."25 A special thanks for Dipankar Mitra for providing us the reduced data from the 2000 outburst of NTE J11I8|£80 (trom Tynes ct al., A special thanks for Dipankar Maitra for providing us the reduced data from the 2000 outburst of XTE J1118+480 (from Hynes et al.26 2000)., 2000).27" SAD is grateful for support from a Netherlands Organization for Scieutific Research (NWO) Vidi Fellowship. aud the European Comunitys Seveutli Framework Progranuue (FP?/2007-2013) uuder eraut agreement nuuber ITN 215212. ""Black Tole Universe”."," SM is grateful for support from a Netherlands Organization for Scientific Research (NWO) Vidi Fellowship, and the European Community's Seventh Framework Programme (FP7/2007-2013) under grant agreement number ITN 215212, “Black Hole Universe”."28that portions of the image polarized in the vertical direction (in blue) now extend much farther above and below the disk.,that portions of the image polarized in the vertical direction (in blue) now extend much farther above and below the disk.29 And we shall see in figure 4 below that an important consequence of scattering is a general dilution of otherwise more strongly polarized X-ray emission., And we shall see in figure 4 below that an important consequence of scattering is a general dilution of otherwise more strongly polarized X-ray emission.30 Some of the most important results of our simulations are summarized in figure 4., Some of the most important results of our simulations are summarized in figure 4.31" With these, we can now begin to answer some of the questions posed in the introduction."," With these, we can now begin to answer some of the questions posed in the introduction."32" First of all, a broken power-law distribution of particles emitting synchrotron radiation from an energized ring at the marginally stable orbit produces a polarization fraction at infinity of up to ~15% (even more for inclination angles > 70°) when all the relevant general relativistic effects are taken into account."," First of all, a broken power-law distribution of particles emitting synchrotron radiation from an energized ring at the marginally stable orbit produces a polarization fraction at infinity of up to $\sim 15\%$ (even more for inclination angles $>70^\circ$ ) when all the relevant general relativistic effects are taken into account."33 Polarimetric measurements in the NIR reveal polarization fractions as high as 12%—25%., Polarimetric measurements in the NIR reveal polarization fractions as high as $12\%-25\%$.34 The geometry we have adopted here can therefore account for these observations without the need to induce linear polarization using more complicated procedures., The geometry we have adopted here can therefore account for these observations without the need to induce linear polarization using more complicated procedures.35" Detailed fits to the observations led to the idea that the X-rays may be due primarily to the same population of electrons producing the NIR emission, though synchrotron-cooled at higher energies."," Detailed fits to the observations led to the idea that the X-rays may be due primarily to the same population of electrons producing the NIR emission, though synchrotron-cooled at higher energies."36 The results of our simulations show that this remains a viable model even when all of the relativistic effects are taken into account., The results of our simulations show that this remains a viable model even when all of the relativistic effects are taken into account.37" Null geodesics (and parallel transport) are not energy dependent, so the polarization properties of the X-ray component echo those of the NIR."," Null geodesics (and parallel transport) are not energy dependent, so the polarization properties of the X-ray component echo those of the NIR."38" Therefore, a prediction of this model is that both the polarization fraction and position angle y of the X-rays should be similar to those of the infrared."," Therefore, a prediction of this model is that both the polarization fraction and position angle $\chi$ of the X-rays should be similar to those of the infrared."39" Panel (c) in figure 4 shows that y, defined by the expression lies somewhere between 85° and 90° for most inclination angles, except above ~70° where it can reach ~110° or more."," Panel (c) in figure 4 shows that $\chi$, defined by the expression lies somewhere between $85^\circ$ and $90^\circ$ for most inclination angles, except above $\sim 70^\circ$ where it can reach $\sim 110^\circ$ or more."40" These values of position angle are consistent with the fact that Εν dominates over F,, as one would expect when the extraordinarycomponent is much greater than the ordinary."," These values of position angle are consistent with the fact that $F_y$ dominates over $F_x$, as one would expect when the extraordinarycomponent is much greater than the ordinary."41" The increase in y with i is due to the increasing influence of redshift seen, e.g., in figure 2, which moves the core of the observed emission towards the left in these images."," The increase in $\chi$ with $i$ is due to the increasing influence of redshift seen, e.g., in figure 2, which moves the core of the observed emission towards the left in these images."42" Notice, however, that a different picture emerges for the X-ray characteristics when scattering is important."," Notice, however, that a different picture emerges for the X-ray characteristics when scattering is important."43 Panel (e) in figure 4 shows that the polarization fraction is smaller (typically smaller than 10%) when X-rays emerge from scattering., Panel (e) in figure 4 shows that the polarization fraction is smaller (typically smaller than $10\%$ ) when X-rays emerge from scattering.44" For many inclination angles, Π is actually closer to 0%."," For many inclination angles, $\Pi$ is actually closer to $0\%$."45" In addition, the position angle differs from that in Panel (c), by anywhere from ~5° to as much as 20°, depending on the inclination angle."," In addition, the position angle differs from that in Panel (c), by anywhere from $\sim 5^\circ$ to as much as $20^\circ$ , depending on the inclination angle."46We proceed to evaluate the constants through application of the boundary conditions.,We proceed to evaluate the constants through application of the boundary conditions.47 The requirement that gives Similarly. we haveQ.. viekliug It follows. from these last two relations. that Land0.," The requirement that gives Similarly, we have, yielding It follows, from these last two relations, that and."48. Finally. we have0.. from which we infer that0.," Finally, we have, from which we infer that."49. It may be verified that the boundary condition is then also satisfied., It may be verified that the boundary condition is then also satisfied.50 Iu suumuinary. the first-order density and stream Duuction perturbations are Notice that at both and s. implying that the density. prolile is fat (.e.. does uot have a cusp) on either the upstream or dowustreai axis.," In summary, the first-order density and stream function perturbations are Notice that at both and $\pi$, implying that the density profile is flat (i.e., does not have a cusp) on either the upstream or downstream axis."51 Our expression for g4 is consistent withIz the linear ceusity perturbation obtained by Dokuchaev(196 [).. Ruclerman&Spiegel(1971).. Hud Ostriker (1999)..," Our expression for $g_{-1}$ is consistent with the linear density perturbation obtained by \citet{d64}, , \citet{rs71}, and \citet{o99}. ."52 Notice that g(7/2) diverges as ? approaches unity. signifving the birth of the Mach cone.," Notice that $g_{-1}(\pi/2)$ diverges as $\b$ approaches unity, signifying the birth of the Mach cone."53 Our fj. in combination with g4. yields the linear. velocity comipouents given iu equatious (25) and (26) of Dokuchaev.(196£).," Our $f_1$, in combination with $g_{-1}$, yields the linear velocity components given in equations (25) and (26) of \citet{d64}."54. Figure 2. displays the streamlines curves) aud isodeusity contours ceurces) Lor the outer flow. includiug ouly the first-order perturbations.," Figure \ref{fig:1storder} displays the streamlines ) and isodensity contours ) for the outer flow, including only the first-order perturbations."55 The light. dotted circle marks the sonic radius.1L: the solution is only accurate well outside this sphere.," The light, dotted circle marks the sonic radius,; the solution is only accurate well outside this sphere."56 Notice how all curves aud contours are syiuuetric about the plane., Notice how all curves and contours are symmetric about the plane.57 The streatilites. in particular. show the [fluid veeriug toward the mass. but then turuing away again.," The streamlines, in particular, show the fluid veering toward the mass, but then turning away again."58 We canuot detect true accretion of mass or linear momenttun until we include the next higher-order perturbations., We cannot detect true accretion of mass or linear momentum until we include the next higher-order perturbations.59 We next equate coefficients of roE in both components of Euler's equation., We next equate coefficients of $r^{-3}$ in both components of Euler's equation.60 From the r- equation (15)). we obtain one relation between fyaud g 5:," From the $r$-component, equation \ref{eqn:eulerr}) ), we obtain one relation between $f_0$and $g_{-2}$ :"61ihe errors are much greater.,the errors are much greater.62 Another remarkable feature observed in this study is the correlation of the amplitude with the period., Another remarkable feature observed in this study is the correlation of the amplitude with the period.63 Using the instantaneous Irequencey. and amplitude derived by IIIT. the correlation between the evcle-averaged period aud the Hilbert amplitude in the most significant. IME (ος) was caleulated.," Using the instantaneous frequency and amplitude derived by HHT, the correlation between the cycle-averaged period and the Hilbert amplitude in the most significant IMF $c_5$ ) was calculated."64 The rank correlation coefficient is r=0.46 with a null hypothesis probability. value of 3.2x10.67. indicating a significant correlation between the period and the amplitude (see Figure 8)).," The rank correlation coefficient is $r=0.46$ with a null hypothesis probability value of $3.2\times10^{-6}$, indicating a significant correlation between the period and the amplitude (see Figure \ref{corr_mp_amp}) )."65 In order to obtain the correlation between Che period and amplitude in (he original data set. the rms amplitude of each evcle was calucalted.," In order to obtain the correlation between the period and amplitude in the original data set, the rms amplitude of each cycle was calucalted."66 The result shows that the period and the rms amplitude still show a significant correlation (r=0.32 with null hypothesis probability value of 1.4x10.7. see Figure 9)).," The result shows that the period and the rms amplitude still show a significant correlation $r=0.32$ with null hypothesis probability value of $1.4\times 10^{-3}$, see Figure \ref{corr_mp_rmsamp}) )."67 Although the correlation appears to change (o an anti-correlation after 2?=60 d. the number of eveles is too few to obtain a significant correlation for periods longer than ~60 d. Similar correlation is observed in (the superorbital modulation of Ler X-1 (Leahy&Tena2010:SULBovel2004).," Although the correlation appears to change to an anti-correlation after $P\gtrsim 60$ d, the number of cycles is too few to obtain a significant correlation for periods longer than $\sim60$ d. Similar correlation is observed in the superorbital modulation of Her X-1 \citep{Leahy2010, Still2004}."68. We have successfully performed IIILT-based. time-frequency analysis on the ASM light curve of SAIC X-1., We have successfully performed HHT-based time-frequency analysis on the ASM light curve of SMC X-1.69 The Hilbert spectrum manilesis variations in the instantaneous period of the superorbital modulation., The Hilbert spectrum manifests variations in the instantaneous period of the superorbital modulation.70 The instantaneous phase defined by HILL allows us to fold the light curve to derive a reasonable superorbital profile., The instantaneous phase defined by HHT allows us to fold the light curve to derive a reasonable superorbital profile.71 The time-Irequeney. information, The time-frequency information72These tests were applied to the six science stars in Table 1..,These tests were applied to the six science stars in Table \ref{targets}.73 All except 2M1145 failed at least one., All except 2M1145 failed at least one.74 From the results of the x? test we can setapproximate limits to the amount and timescale of intrinsic variability in these five stars at the epoch of the observations (Table 2))., From the results of the $\chi^2$ test we can set limits to the amount and timescale of intrinsic variability in these five stars at the epoch of the observations (Table \ref{limits}) ).75 For each star in this table (except 2M1145) there is no significant evidence P(x2) is » 00.01) for variability above lii on the timescale shown. (, For each star in this table (except 2M1145) there is no significant evidence ${\rm P}(\chi^2_s)$ is $>$ 0.01) for variability above $I_{\rm lim}$ on the timescale shown. (76This is not the same as saying that we are confident that there is no variability above li.,This is not the same as saying that we are confident that there is no variability above $I_{\rm lim}$.77" Moreover, larger variability on timescales to which we were not sensitive could be present.)"," Moreover, larger variability on timescales to which we were not sensitive could be present.)"78" Strictly, it is only possible to put a single magnitude limit on a given range of periods if the uncertainties (c,,) are the same for all t."," Strictly, it is only possible to put a single magnitude limit on a given range of periods if the uncertainties $\epsilon_{s,t}$ ) are the same for all $t$."79 This is not the case for our data due to changes in atmospheric conditions., This is not the case for our data due to changes in atmospheric conditions.80" Rather than defining different amplitude limits for different periods, we simply give an approximate limit for all periods."," Rather than defining different amplitude limits for different periods, we simply give an approximate limit for all periods."81 The upper limit period shown is the longest time base in our data., The upper limit period shown is the longest time base in our data.82" The shortest period is a sort of Nyquist period for the time series, and is slightly more than twice the shortest separation between frames."," The shortest period is a sort of Nyquist period for the time series, and is slightly more than twice the shortest separation between frames."83 We emphasise that these figures should not be viewed as strict magnitude/period sensitivity limits., We emphasise that these figures should not be viewed as strict magnitude/period sensitivity limits.84" 'The star 2M1145 passed all four tests for variability, and showed a significant (p« 10-4) peak in the periodogram at about 7 hours."," The star 2M1145 passed all four tests for variability, and showed a significant $p<10^{-4}$ ) peak in the periodogram at about 7 hours."85 The phased light curve is shown in Fig 1.., The phased light curve is shown in Fig \ref{phase}.86" To be sure that the detected period was not due to a reference star, we calculated the periodogram of the relative magnitudes of each reference star (relative to the other reference stars, as described above)."," To be sure that the detected period was not due to a reference star, we calculated the periodogram of the relative magnitudes of each reference star (relative to the other reference stars, as described above)."87 No reference star showed any even marginally significant peak., No reference star showed any even marginally significant peak.88" Additional checks on the variability detection in 2M1145 were made by using only a subset of the good reference stars in the reference set, and using slightly different aperture sizes in the original photometry."," Additional checks on the variability detection in 2M1145 were made by using only a subset of the good reference stars in the reference set, and using slightly different aperture sizes in the original photometry."89 In all cases significant variability was detected (according to the above four criteria) and the determined periods were the same to within1%., In all cases significant variability was detected (according to the above four criteria) and the determined periods were the same to within.90". The RMS (root mean squared) scatter of the relative magnitudes in Fig 1 is 0.038 mags, and the amplitude of a least-squares fit sinusoid (Axsin[wt+ $]) is 0.040 mags."," The RMS (root mean squared) scatter of the relative magnitudes in Fig \ref{phase} is 0.038 mags, and the amplitude of a least-squares fit sinusoid $A\times\sin[wt + \phi]$ ) is 0.040 mags."91" This latter value may be a slight overestimate of the amplitude of intrinsic variability on account of noise: the larger the aperture, the more noise in each measurement, and so the more likely it is that a larger amplitude is observed."," This latter value may be a slight overestimate of the amplitude of intrinsic variability on account of noise: the larger the aperture, the more noise in each measurement, and so the more likely it is that a larger amplitude is observed."92" This does not mean, however, that the detection is just due to noise, as with a much larger aperture the time series does not meet the variability criteria described above."," This does not mean, however, that the detection is just due to noise, as with a much larger aperture the time series does not meet the variability criteria described above."93" This problem with least-squares fitting could be overcome using more robust techniques, but we choose to acquire a more extensive data set before making an improved determination."," This problem with least-squares fitting could be overcome using more robust techniques, but we choose to acquire a more extensive data set before making an improved determination."94" Nonetheless, Fig 1 shows evidence of periodic variation beyond the size of the error bars."," Nonetheless, Fig \ref{phase} shows evidence of periodic variation beyond the size of the error bars."95 The most plausible explanation for the observed periodic variation in 2M1145 is a rotational modulation of the emitted flux., The most plausible explanation for the observed periodic variation in 2M1145 is a rotational modulation of the emitted flux.96" Assuming a radius of 0.1Mc; (Burrows et al. 1997)),"," Assuming a radius of $0.1 M_{\odot}$ (Burrows et al. \cite{burrows97}) ),"97" and rigid rotation, the period of 7.12 hours implies an equatorial rotation velocity of kkms-!."," and rigid rotation, the period of 7.12 hours implies an equatorial rotation velocity of $^{-1}$."98 This falls in the range of rotation speeds for 93 field M dwarfs measured by Delfosse et al. (1998)) (, This falls in the range of rotation speeds for 93 field M dwarfs measured by Delfosse et al. \cite{delfosse98}) ) (99"all except one with vsini in the range « kkms- 1), but is smaller than the range for 9 Pleiades M5-M6.5 dwarfs observed by Oppenheimer et al. (1997))","all except one with $v\sin i$ in the range $<$ $^{-1}$ ), but is smaller than the range for 9 Pleiades M5–M6.5 dwarfs observed by Oppenheimer et al. \cite{oppenheimer97}) )"100 (37€vsini«665 kkms- 1)., $\leq v\sin i \leq$ $^{-1}$ ).101" However, our data does not give unambiguous evidence for rotation at this speed."," However, our data does not give unambiguous evidence for rotation at this speed."102 All we can say for certain is that we have evidence for periodic variability which is not, All we can say for certain is that we have evidence for periodic variability which is not103"Tn this paper we focus on measurements of the aueular distributions of flarc-accelerated. protons and oo particles that impact ambient ο, ο. and ο ο through ineasurements of de-excitation lines from the recoiling nuclei;","In this paper we focus on measurements of the angular distributions of flare-accelerated protons and $\alpha$ particles that impact ambient $^{12}$ C, $^{16}$ O, and $^{20}$ Ne through measurements of de-excitation lines from the recoiling nuclei."104 We use spectral data from the σαταν spectrometer experiment., We use spectral data from the gamma-ray spectrometer experiment.105 Although the spectrometer has only imocerate spectral resolution it revealed ~L% red shifts for flares centered on the solar csk and ~3% dutfrimsc widths for al lice lines., Although the spectrometer has only moderate spectral resolution it revealed $\sim$ red shifts for flares centered on the solar disk and $\sim$ intrinsic widths for all three lines.106- We- also compare the °C2 liue observations with calculations for different assuned adelay distributions of interactiug and protons and à particles., We also compare the $^{12}$ C line observations with calculations for different assumed angular distributions of interacting and protons and $\alpha$ particles.107 The nuclear liue 1neasurements that we preseut were derived from 19 solar flares observed bvSALAL (Share&Murphy 1995).., The nuclear line measurements that we present were derived from 19 solar flares observed by \citep{share95}. .108 The eamiuua- spectrometer (Forrestctal.1980) Was exceptionally stable over its full 10 vear mission., The gamma-ray spectrometer \citep{forrest80} was exceptionally stable over its full $\sim$ 10 year mission.109 Tt was also well calibrated., It was also well calibrated.110 The cucrey calibration was determined using laboratory sources and was confined by observations of mushiftedt lines: he solar 0.511 MeV. (positron anuililation) aud 2.223 MeV. (neutron capture) lines (Share&Abuphny= 2000).. and the Lill MeV (HD. aud ?() and 6.13 MeV. (29O0)J lines from the Eartli's atinosphere (Share&Murphy2001).," The energy calibration was determined using laboratory sources and was confirmed by observations of unshifted lines: the solar 0.511 MeV (positron annihilation) and 2.223 MeV (neutron capture) lines \citep{share00}, and the 4.444 MeV $^{11}$ B and $^{12}$ C) and 6.13 MeV $^{16}$ O) lines from the Earth's atmosphere \citep{share01}."111. Based ou hese ueasuremenuts. we believe tha line energies are known to <3 keV. The iustrunieutal cnerey-resolutiou function was also deteriuned sine he laboratory calibrations and coufiiied by the sale flare and atmospheric line observations.," Based on these measurements, we believe that line energies are known to $\la$ 3 keV. The instrumental energy-resolution function was also determined using the laboratory calibrations and confirmed by the same flare and atmospheric line observations."112" The jiustruiuental resolution was (EWIIMD at L511 MeV. at 2.223 MeV, at Ll AIeV. and at 6.13 MeV. Share&Murphy.(2000) note that the neasured widths of de-excitation lines in the sti of the 19 flares were broader than predicted by heorv for an isotropic distribution of particles."," The instrumental resolution was (FWHM) at 0.511 MeV, at 2.223 MeV, at 4.44 MeV, and at 6.13 MeV. \citet{share00} noted that the measured widths of de-excitation lines in the sum of the 19 flares were broader than predicted by theory for an isotropic distribution of particles."113 Such broadening could occur if the interacting uticle distribution is auisotropic (thus producing Doppler-shitted lines) because spectra roni flares at various helioceutric angles were summed together., Such broadening could occur if the interacting particle distribution is anisotropic (thus producing Doppler-shifted lines) because spectra from flares at various heliocentric angles were summed together.114 We therefore sunm spectra into 4 eroups depending on the heliocentric angle of the flare., We therefore summed spectra into 5 groups depending on the heliocentric angle of the flare.115 The average angle aud uunuber of flares iu cach eroup are: 57. 1 (uufortunatelyv. this was a relatively weak flare): 307.23: 137.5: TL. οι 867. 5.," The average angle and number of flares in each group are: $^{\circ}$, 1 (unfortunately, this was a relatively weak flare); $^{\circ}$, 3; $^{\circ}$, 5; $^{\circ}$, 5; $^{\circ}$, 5."116" We plot count spectra in limited energy ranges around he Lil MeV ο 1Ο, 6.129 MeV. 1ο. and 1.631 MeV. 22Ne de-excitation lines for the five iclioceutric angles in Figures 3-5."," We plot count spectra in limited energy ranges around the 4.44 MeV $^{12}$ $^{11}$ B, 6.129 MeV $^{16}$ O, and 1.634 MeV $^{20}$ Ne de-excitation lines for the five heliocentric angles in Figures 3-5."117 We fit the count spectra with a power law aud a sinele Cassiashaped line with euergy. width. aud amplitude free ο vary.," We fit the count spectra with a power law and a single Gaussian-shaped line with energy, width, and amplitude free to vary."118 Solid lines through the data represent the vest fits., Solid lines through the data represent the best fits.119 For comparison. in Figure Ll we also ot the count spectra and fits for the thermal reutron capture line that is formed near rest aud should appear at 2.223 MeV. The vertical dotted ines are located at the rest cnergics of the nuclear ines.," For comparison, in Figure \ref{fig6} we also plot the count spectra and fits for the thermal neutron capture line that is formed near rest and should appear at 2.223 MeV. The vertical dotted lines are located at the rest energies of the nuclear lines."120 The centroid chereics of the ce-excitation ines appear to shift to lower energies for flares close to the ceuter of the solar disk., The centroid energies of the de-excitation lines appear to shift to lower energies for flares close to the center of the solar disk.121 We sununarize the results on line shifts iu Figure 15. where the best fit line energies and uucertainties for the three de-excitation lines aud the neutron capture line are dotted as a function of the cosine of heliocentric angle., We summarize the results on line shifts in Figure \ref{fig7} where the best fit line energies and uncertainties for the three de-excitation lines and the neutron capture line are plotted as a function of the cosine of heliocentric angle.122 The line cnereies and errors were derived by passing an incident photon spectrum. coutaining a power law and 22 lines from 0.3 to δ MeV. (Share&Afurpliy2001) through the iustriueut response function. ar lapping x: this yielded the same results as we obtained by simply fitting the counts spectrin with a power law aud single Gaussian over a restricted enerev range (see Fieures 3 - 5).," The line energies and errors were derived by passing an incident photon spectrum, containing a power law and 22 lines from 0.3 to 8 MeV \citep{share01} through the instrument response function, and mapping $\chi ^2$; this yielded the same results as we obtained by simply fitting the counts spectrum with a power law and single Gaussian over a restricted energy range (see Figures 3 - 5)."123 The HC. . ⊔⇂∪∙⋜⋯≼↧−∪⋀∖↸∖≼∐∖⊣∖⊼↸⊳↕↑⋜↧⊓∪∐↕∐∐∖↴∖↴ ona. ⋅⋅ ⋅ appear to be shifted to lower energies bv —1 near Sun center.," The $^{12}$ C, $^{16}$ O, and $^{20}$ Ne de-excitation lines appear to be shifted to lower energies by $\sim$ near Sun center."124 In contrast. the neutron capture line does not exhibit a siguificaut redshift C) at Sun ceuter.," In contrast, the neutron capture line does not exhibit a significant redshift $\la 0.1$ ) at Sun center."125 The hieher fitted energies C0.3% )) near the limb may be due to a coutribution from other lines. e.g. 78 and t4N that ibecome sjeuificaut with limb darkening ofthe 2.223 MeV capture line.," The higher fitted energies $\sim 0.3$ ) near the limb may be due to a contribution from other lines, e.g. $^{32}$ S and $^{14}$ N that become significant with limb darkening of the 2.223 MeV capture line."126" The statistical siguificance of the dine data πι Figures 5 was also adequate for us to independently ft for the Gaussian widths of the 11ο, 160, aud 29? No e-excitation lines for some of the helioceutric angles."," The statistical significance of the line data in Figures 3-5 was also adequate for us to independently fit for the Gaussian widths of the $^{12}$ C, $^{16}$ O, and $^{20}$ Ne de-excitation lines for some of the heliocentric angles."127 We once again fit the count spectra aud obtained the line widths aud uncertainties-. usingB D mapping., We once again fit the count spectra and obtained the line widths and uncertainties using $\chi ^2$ mapping.128: TJd1ο linewidths derived from these fits with sinoothly varvine 4? aps are plotted iu Figure 16 for the three lines., The linewidths derived from these fits with smoothly varying $\chi ^2$ maps are plotted in Figure \ref{fig8} for the three lines.129 There is no significant variation in the widths as a function of heliocentric angle., There is no significant variation in the widths as a function of heliocentric angle.130 The weighted means of the line widths (FWIIM) are 155 + 19 keV. 167," The weighted means of the line widths (FWHM) are 155 $\pm$ 19 keV, 167"131geometrical eross section. ary is larger that the polarization cross section (eq. A4)) when 2,geometrical cross section $\pi r_g^2$ is larger that the polarization cross section (eq. \ref{lange}) )132"4)z,|! (Og)À. a condition. generally satisfied by interstellar grains."," when r_g>24 , a condition generally satisfied by interstellar grains."133" The average momentum transfer cross section for collisions of spherical grains with neutral atoms or molecules is then = mr;óREN ""Ga. where Go(&) is given by eq. (16))"," The average momentum transfer cross section for collisions of spherical grains with neutral atoms or molecules is then = r_g^2 ), where $G_0(\xi)$ is given by eq. \ref{g0}) )"134 and 6 is a factor of order unity (the so-called Epstein coefficient) equal to unity if the neutrals impinging on the grain undergo specular reflections., and $\delta$ is a factor of order unity (the so-called Epstein coefficient) equal to unity if the neutrals impinging on the grain undergo specular reflections.135 For very subsonie drift velocity. this expression reduces to inno a result (PNderived by Epstein. (1924).," For very subsonic drift velocity, this expression reduces to r_g^2, a result derived by Epstein (1924)."136 Experiments with micron-size melamine-formaldehyde spheres show that ó=1.3 (Liu et al., Experiments with micron-size melamine-formaldehyde spheres show that $\delta\approx 1.3$ (Liu et al.137 2003)., 2003).138 Figure 20. shows the gram-neutral momentum transfer rate as a function of the relative drift velocity according to eq. (24)), Figure \ref{gn} shows the grain-neutral momentum transfer rate as a function of the relative drift velocity according to eq. \ref{hardspheres}) )139 with 6| compared with the approximations given by Drame Salpeter (1979). Nakano (1984). and Mouschovias Ciolek (1999).," with $\delta=1$ compared with the approximations given by Draine Salpeter (1979), Nakano (1984), and Mouschovias Ciolek (1999)."140 In this figure. the grain-neutral momentum transfer rate is normalized to the expression given by Mouschovias Ciolek (1999) in the low-drift limit. and the drift velocity i$ normalized to the mean thermal speed in the neutrals.," In this figure, the grain-neutral momentum transfer rate is normalized to the expression given by Mouschovias Ciolek (1999) in the low-drift limit, and the drift velocity is normalized to the mean thermal speed in the neutrals."141" Particles of charge Z«e can exchange momentum with particles of charge Z,e and density nm, via long-range Coulomb interactions.", Particles of charge $Z_{s^\prime} e$ can exchange momentum with particles of charge $Z_s e$ and density $n_s$ via long-range Coulomb interactions.142 In the standard Coulomb scattering theory (see e.g.. Chapman Cowling 1953). the momentum transfer cross section is given by Macon Ful. where is the Coulomb radius (the distance at which the electrostatic energy is of the order of the kinetic energy) at the relative velocity v. and Main. ημας are the minimum and maximum impact parameters of the collision.," In the standard Coulomb scattering theory (see e.g., Chapman Cowling 1953), the momentum transfer cross section is given by ) ], where is the Coulomb radius (the distance at which the electrostatic energy is of the order of the kinetic energy) at the relative velocity $v_{ss^\prime}$, and $r_{\rm min}$, $r_{\rm max}$ are the minimum and maximum impact parameters of the collision."143 Several different approaches have been taken to calculate (ji; and rj.," Several different approaches have been taken to calculate $r_{\rm min}$ and $r_{\rm144max}$."145 For the latter. the standard choice is the total Debye length in the plasma stp (Cohen et al.," For the latter, the standard choice is the total Debye length in the plasma $\lambda_{\rm D}$ (Cohen et al."146 1950). given by," 1950), given by"147or 300 davs.,or 300 days.148 The frequency residuals Av were obtained al the initial epoch of each interval relative to a third-order polynomial (1). including the mean parameters v. 7. ancl P defined over (he full interval 1979.2009. 1991.2009 or any other interval.," The frequency residuals $\Delta\nu$ were obtained at the initial epoch of each interval relative to a third-order polynomial (1), including the mean parameters $\nu$, $\dot\nu$, and $\ddot\nu$ defined over the full interval 1979–2009, 1991–2009 or any other interval."149 In 2009 November 5. the pulsar D09192-06 sullered a very large eliteh with the factional increase in (he rotation [frequency Av/v=1.3x10°.," In 2009 November 5, the pulsar B0919+06 suffered a very large glitch with the fractional increase in the rotation frequency $\Delta\nu/{\nu}=1.3 \times 10^{-6}$."150 This eliteh is comparable in size to the elitches observed in the Vela pulsar., This glitch is comparable in size to the glitches observed in the Vela pulsar.151 The eliteh was accompanied by a significant decrease in the frequency derivative Αν=-7x107., The glitch was accompanied by a significant decrease in the frequency derivative ${\Delta{\dot\nu}}/{\dot\nu}=-7 \times 10^{-3}$.152 A eliteh was detected during a series of daily observations. so the uncertaintv in determining the elitch epoch was within several hours. MJD 55139.8(1).," A glitch was detected during a series of daily observations, so the uncertainty in determining the glitch epoch was within several hours, MJD 55139.8(1)."153 Figure 1. shows the timing residuals relative to a simple i. 7 model fitted to the data before the glitch.," Figure \ref{glitch} shows the timing residuals relative to a simple $\nu$, $\dot\nu$ model fitted to the data before the glitch."154 The negative growth in the residuals due to this glitch corresponds (o a shift of the pulse in the observing window by ~ 109 ms/das., The negative growth in the residuals due to this glitch corresponds to a shift of the pulse in the observing window by $\sim$ 109 ms/day.155 The elitch parameters are given in Table 1.., The glitch parameters are given in Table \ref{glitchp}.156 Uncertainties in parentheses represent the formal standard deviation and refer to the last cligit (quoted., Uncertainties in parentheses represent the formal standard deviation and refer to the last digit quoted.157 The Luge glitch has occurred in a relatively old. pulsar with a characteristic age οἱ Tcbx10? νους., The large glitch has occurred in a relatively old pulsar with a characteristic age of $\tau\sim 5\times10^{5}$ years.158 This age is comparable to the age of PSR D03554-54 (7~5.6xLO? years) that experienced a giant glitch. with Av/y=4.4x10 in 1987 (Lyne1987)., This age is comparable to the age of PSR B0355+54 $\tau\sim 5.6\times10^{5}$ years) that experienced a giant glitch with $\Delta\nu/{\nu}=4.4 \times 10^{-6}$ in 1987 \citep{lyn87}.159. The timing observations of PSR BO919+06 over four months after the eliteh are not sufficient Lor the detailed research of the post-elitch behavior., The timing observations of PSR B0919+06 over four months after the glitch are not sufficient for the detailed research of the post-glitch behavior.160 Moreover. as will be shown in the following sections. (he rotation frequency of (his pulsar undergoes continuous. slow oscillations wilh the spacing of maxima ~ GOO davs.," Moreover, as will be shown in the following sections, the rotation frequency of this pulsar undergoes continuous, slow oscillations with the spacing of maxima $\sim$ 600 days."161 Further observations are needed (to establish a relationship between the large eliteh and this oscillatory behavior., Further observations are needed to establish a relationship between the large glitch and this oscillatory behavior.162 The timing behavior of PSR. DB0919--06 over the 30-vear interval [rom 1979 December io 2009 November before the large eliteh occurred is presented in Figure 2.., The timing behavior of PSR B0919+06 over the 30-year interval from 1979 December to 2009 November before the large glitch occurred is presented in Figure \ref{resid1}.163 A lour-vear data gap seen in the residuals between 1987 and 1990 insignificantly clistorts the information about the pulsars rotation., A four-year data gap seen in the residuals between 1987 and 1990 insignificantly distorts the information about the pulsar's rotation.164 An analvsis of the full data set showed that the timing behavior of PSR D09194-06 exhibits significant deviations from a deterministic spin-down low that indicates a presence, An analysis of the full data set showed that the timing behavior of PSR B0919+06 exhibits significant deviations from a deterministic spin-down low that indicates a presence165properties.,properties.166" Llowever. we have access to a statistically significant voung to intermecliate-ageresolved star cluster system, on our doorstep. notably in the Large. Magellanic Cloud. (LALC)."," However, we have access to a statistically significant young to intermediate-age star cluster system on our doorstep, notably in the Large Magellanic Cloud (LMC)."167 By combining&iuegraled properties. withresolved stellar population studies. the LMC cluster system olfers the unique chance to independently check the accuracy of age (ancl corresponding mass) determinations based. on broad-band spectral energy. distributions (SIZDs).," By combining properties with stellar population studies, the LMC cluster system offers the unique chance to independently check the accuracy of age (and corresponding mass) determinations based on broad-band spectral energy distributions (SEDs)."168 This is what we set out to do in this paper. based on the largest. most homogeneous and complete. set. of integrated LMC cluster photometry presently available.," This is what we set out to do in this paper, based on the largest, most homogeneous and complete set of integrated LMC cluster photometry presently available."169 With our new cluster age estimates. spanning ages from a few Myr up to LO Gyr. determined in an internally consistent fashion and with a firm handle on the associated: uncertainties. we now also have the largest. homogeneous sample of cluster masses with well-defined: uncertainties to date. which we use to explore the evolution of the CME.," With our new cluster age estimates, spanning ages from a few Myr up to 10 Gyr, determined in an internally consistent fashion and with a firm handle on the associated uncertainties, we now also have the largest, homogeneous sample of cluster masses with well-defined uncertainties to date, which we use to explore the evolution of the CMF."170 In Section 2. we discuss the details of the LMC cluster. sample we base. our analysis on. and explore the uncertainties associated with the age and| mass determinations.," In Section \ref{data.sec} we discuss the details of the LMC cluster sample we base our analysis on, and explore the uncertainties associated with the age and mass determinations."171 Section 3 discusses the formation and disruption history of the LMC star cluster sample., Section \ref{formdis.sec} discusses the formation and disruption history of the LMC star cluster sample.172 We use this as our basis for the interpretation of the LMC cluster mass distribution in terms of the initial and evolved distributions of cluster masses in Section 4.., We use this as our basis for the interpretation of the LMC cluster mass distribution in terms of the initial and evolved distributions of cluster masses in Section \ref{cmf.sec}.173 Finally. in Section 5 we summarise our results and conclusions.," Finally, in Section \ref{summary.sec} we summarise our results and conclusions."174" The basis for our detailed comparison of the age estimates for the LMC star cluster svstem is. provided. by (i) the UDVRI broacd-bancd SEDs of 11039. “Lous.based on Masseys (2002) CCD survey of the Melun (€ and(ii) M OCGLE-Ll data set (Udalski. Kubiak Szvmarisski 1997. ""and in particular their homogeneously determined: ages some G00 clusters. using colour-magnitude diagrams. (CMDs: Pietrzvsski Udalski 2000)."," The basis for our detailed comparison of the age estimates for the LMC star cluster system is provided by (i) the $UBVR$ broad-band SEDs of H03, based on Massey's (2002) CCD survey of the Magellanic Clouds, and (ii) the OGLE-II data set (Udalski, Kubiak Szymańsski 1997), and in particular their homogeneously determined ages for some 600 clusters, using colour-magnitude diagrams (CMDs; Pietrzyńsski Udalski 2000)."175 1103. determined. the ages for the individual LMC clusters by comparing their broad-band SEDs with a variety of cluster evolutionary models., H03 determined the ages for the individual LMC clusters by comparing their broad-band SEDs with a variety of cluster evolutionary models.176 Specifically. they used. the Starburst99 (Leitherer et al.," Specifically, they used the Starburst99 (Leitherer et al."177" 1999) with Z=0.00S lor ages up to 1 Give. while for older ages they used a combination of the CBY. colours of Se Sargent Dagnuolo(1973). theMN""(VI)e colours for. globular clusters from Reed (1985). the Charlot Bruzual (1991) simple stellar. population (S52P) models for the evolution of the V-band. luminosity in the age range from 1 to 10 Gyr."," 1999) with $Z = 0.008$ for ages up to 1 Gyr, while for older ages they used a combination of the $UBV$ colours of Searle, Sargent Bagnuolo (1973), the $(V-R)_{\rm C}$ colours for globular clusters from Reed (1985), and the Charlot Bruzual (1991) simple stellar population (SSP) models for the evolution of the $V$ -band luminosity in the age range from 1 to 10 Gyr."178 Thev then used a combination of two colour-colour diagrams. (D) vs. (BVi and (B Vives. (VR). to obtain their age estimates. by comparing the cluster positions to the model tracks in those diagrams.," They then used a combination of two colour-colour diagrams, $(U-B)$ vs. $(B-V)$ and $(B-V)$ vs. $(V-R)$, to obtain their age estimates, by comparing the cluster positions to the model tracks in those diagrams."179 The colours and. magnitudes of their sample. clusters were corrected. [for reddening using a blanket reddening of £(BV)20.13 mag for all clusters. where they adopted the extinction curve of Cardelli et al. ," The colours and magnitudes of their sample clusters were corrected for reddening using a blanket reddening of $E(B-V) = 0.13$ mag for all clusters, where they adopted the extinction curve of Cardelli et al. ["1801980: Ry—AlyE(B 1323440].,1989; $R_V \equiv A_V/E(B-V)= 3.10$ ].181 The Pietrzvsski Udalski (2000) ages are based on detailed: isochrone fits to the OGLE-IHLE colour-magnitucie data. using the Padova isochrones for Z= 0.008.," The Pietrzyńsski Udalski (2000) ages are based on detailed isochrone fits to the OGLE-II colour-magnitude data, using the Padova isochrones for $Z=0.008$ ."182 They dereddened: their photometry using the extinction. values for S4 LMC sublfields determined by Uclalski et al. (, They dereddened their photometry using the extinction values for 84 LMC subfields determined by Udalski et al. (1831999). ο.1)=0.143+0.020 mag.,"1999), $E(B-V) = 0.143 \pm 0.020$ mag."184 These extinction. values are based on Schlegel et al, These extinction values are based on Schlegel et al.185s {1998) reddening maps for the Galactic foreground extinction. on average (D.V)=0.075 mag. and their Z4;=3.24.,"'s (1998) reddening maps for the Galactic foreground extinction, on average $E(B-V)=0.075$ mag, and their $R_V = 3.24$."186 Finally. here we reanalvse the Alassey (2002) clata set. also assuming Z=0.008. for comparison purposes (although our analysis tool allows us to leave the metallicity as a [ree parameter: sce Section 2.2)).," Finally, here we reanalyse the Massey (2002) data set, also assuming $Z = 0.008$, for comparison purposes (although our analysis tool allows us to leave the metallicity as a free parameter; see Section \ref{degeneracies.sec}) )."187 For the total extinction towards the LAIC clusters. we assumed κV)=0.10 mag. using the €dtiattenuation . (6αἰκο 1997. 2001: Calzettieod ot al.," For the total extinction towards the LMC clusters, we assumed $E(B-V) = 0.10$ mag, using the Calzetti attenuation law (Calzetti 1997, 2001; Calzetti et al."188 : Leitherer οἱ al., 2000; Leitherer et al.189 2002) with #y=4.05, 2002) with $R_V = 4.05$.190" ‘This to EK(D.—V)mm=0.3 mag""n both the Cardelli et al. ("," This corresponds to $E(B-V) \simeq1910.13$ mag for both the Cardelli et al. ("1921989) and the Se al. (,1989) and the Schlegel et al. (193) extinction laws.,1998) extinction laws.194 In a series of recent papers. we developed a sophisticated tool for star cluster analvsis based. on broad-band SEDs. “AnalySED” which we testec extensively both internally (cle ας et al.," In a series of recent papers, we developed a sophisticated tool for star cluster analysis based on broad-band SEDs, “AnalySED”, which we tested extensively both internally (de Grijs et al."195 2003c.d: Anders et al.," 2003c,d; Anders et al."196 206H) and externally (cle ος et al., 2004) and externally (de Grijs et al.197 2005). using both theoretical ancl observed voung to intermediate-age.+ (/<3..I0(0 vr) star cluster SEDs. and the SSP models (να et al.," 2005), using both theoretical and observed young to intermediate-age $t \lesssim 3198\times 10^9$ yr) star cluster SEDs, and the SSP models (Kurth et al."199 1999: Schulz οἱ al., 1999; Schulz et al.200 2002)., 2002).201 We increased the accuracy lor vounger ages by the inclusion of an extensive set. of nebular emission lines. as well as gaseous continuum emission (Anders britze-," We increased the accuracy for younger ages by the inclusion of an extensive set of nebular emission lines, as well as gaseous continuum emission (Anders Fritze-v."202 Alvensleben: 2003), Alvensleben 2003).203 We concluded that the ages within a given cluster svstem can be determined to à very high accuracy depending on the specific combination of passbanels used. (Anclers et al., We concluded that the ages within a given cluster system can be determined to a very high accuracy depending on the specific combination of passbands used (Anders et al.204 2004)., 2004).205 Even when comparing the results of dillerent groups using the same data set; we can retrieve. prominent features in the cluster age distribution to within a=;Mlog(Xge/sr))x0.35 (de Crijs et al.," Even when comparing the results of different groups using the same data set, we can retrieve prominent features in the cluster age distribution to within $\sigma_t \equiv \Delta \langle \log( {\rm206Age / yr} ) \rangle \le 0.35$ (de Grijs et al."207 2005). which confirms that we understand the uncertainties associated with the use of our XnalvSED tool to à very high degree.," 2005), which confirms that we understand the uncertainties associated with the use of our AnalySED tool to a very high degree."208 The aim of this section is to compare our new age determinations with (i) those of 103 using the same cata set but a different approach. and. (ii) those of Pietrzyvüsski Udalski (200t) using the independent. (and presumably more accurate) method of CALD fitting.," The aim of this section is to compare our new age determinations with (i) those of H03 using the same data set but a different approach, and (ii) those of Pietrzyńsski Udalski (2000) using the independent (and presumably more accurate) method of CMD fitting."209 Vhis will allow us to set the tightest limits vet on the accuracy of age determinations based. on broad-band. SEDs. and therefore on the usefulness of such an approach in general.," This will allow us to set the tightest limits yet on the accuracy of age determinations based on broad-band SEDs, and therefore on the usefulness of such an approach in general."210 First. we compare the independently determined. ages of the clusters in common between the LIO3 and OCGLIZ-Η results.," First, we compare the independently determined ages of the clusters in common between the H03 and OGLE-II results."211 Fig., Fig.212 laa shows the distribution of the data points in the relevant parameter space. where the dashed line represents equality between both age estimates for a given cluster.," \ref{lmccf.fig}a a shows the distribution of the data points in the relevant parameter space, where the dashed line represents equality between both age estimates for a given cluster."213 It is immediately. clear that there is a systematic dillerence between the 1109 and OGLE-LL ages. the magnitude of which is a clear function of age.," It is immediately clear that there is a systematic difference between the H03 and OGLE-II ages, the magnitude of which is a clear function of age."214 The elfect is indeed. significant: a straightforward. linear regression results in a slope that is significantly dillerent. from unity. 1.47+=0.0," The effect is indeed significant; a straightforward linear regression results in a slope that is significantly different from unity, $1.47 \pm 0.07$."215 We will explore the origin of this svstematic clleet in Section 2.1. below.," We will explore the origin of this systematic effect in Section \ref{filters.sec}216 below."217 Lt is also clear that. in. units of logCXge/vr) the intrinsic scatter in the data points is somewhat greater at vounger ages: this is merely. an cllect of the poorer intrinsic age accuracy for older ages imposed bv the mocdels.," It is also clear that, in units of $\log(\mbox{Age/yr})$, the intrinsic scatter in the data points is somewhat greater at younger ages; this is merely an effect of the poorer intrinsic age accuracy for older ages imposed by the models."218 Secondly. we compare ourredetermined. ages to both those of OGLE-L and 103. in Figs.," Secondly, we compare ourredetermined ages to both those of OGLE-II and H03, in Figs."219 Ibb and c. respectively.," \ref{lmccf.fig}b b and c, respectively."220 We point out that because of the limiting Y -band magnitude, We point out that because of the limiting $V$ -band magnitude221The computer simulation was done at Columbia supercomputer αἱ NASA Ames Research Center.,The computer simulation was done at Columbia supercomputer at NASA Ames Research Center.222 Aw., A.v.223B.B. acknowledges support from Deutsche— Forschunesgemeinschalt (DPC) uncer the project MU 1020/6-3.,B.B. acknowledges support from Deutsche Forschungsgemeinschaft (DFG) under the project MU 1020/6-3.224 IZ.D. is supported by a LEW Marie. Curic Intra-European Fellowship under contract ALEUP-041569., E.D. is supported by a EU Marie Curie Intra-European Fellowship under contract MEIF-041569.225 Ally. acknowledges support of. NSE grant. AST-O4070702., A.K. acknowledges support of NSF grant AST-04070702.226 ALLL. acknowledges support from the DEG: under the project. Vo 5855/2., M.H. acknowledges support from the DFG under the project Vo 855/2.227have only one degree of freedom.,have only one degree of freedom.228 It depends for instance only on the eccentricity of the planetesimal e and of its longitude of periastron v with respect to that of the planet., It depends for instance only on the eccentricity of the planetesimal $e$ and of its longitude of periastron $\nu$ with respect to that of the planet.229" For any given fixedvalues for a and for the planet eccentricity ej, we can draw a phase portrait (i.e., level curves of Hamiltonian) of the dynamics in an (v,e) plane."," For any given fixedvalues for $a$ and for the planet eccentricity $e_p$, we can draw a phase portrait (i.e., level curves of Hamiltonian) of the dynamics in an $(\nu, e)$ plane."230" Two examples for e,0.1 and e,0.5 are shown in Fig. 8..", Two examples for $e_p=0.1$ and $e_p=0.5$ are shown in Fig. \ref{hsec}.231" They both correspond to a1.3a, (αρ is the semi-major axis of the planet).", They both correspond to $a=1.3a_p$ $a_p$ is the semi-major axis of the planet).232" The whole dynamical problem obviously simply scales with ap, so that a only needs to be given in units of αρ."," The whole dynamical problem obviously simply scales with $a_p$ , so that $a$ only needs to be given in units of $a_p$."233" The present case (a= 1.3ap) corresponds to a planetesimal orbiting outside the planet's orbit, like those we are simulating."," The present case $a=1.3a_p$ ) corresponds to a planetesimal orbiting outside the planet's orbit, like those we are simulating."234" Note also that the topology of the Hamiltonian is independent of the mass m, of the planet, because the non-constant part of Ho is proportional to m,."," Note also that the topology of the Hamiltonian is independent of the mass $m_p$ of the planet, because the non-constant part of $\mathcal{H}_0$ is proportional to $m_p$."235 Hence the plots in Fig., Hence the plots in Fig.236 8 hold for any planetary mass., \ref{hsec} hold for any planetary mass.237" The planetary mass m, only affects the speed at which the planetesimal moves along the Hamiltonian level curves (the speed is ος mp).", The planetary mass $m_p$ only affects the speed at which the planetesimal moves along the Hamiltonian level curves (the speed is $\propto m_p$ ).238 The plots in Fig., The plots in Fig.239" 8 hold for a=1.3a,, but for other values of a, we have similar plots."," \ref{hsec} hold for $a=1.3a_p$, but for other values of $a$, we have similar plots."240" Conversely, the shape of the phase portrait depends critically on ej."," Conversely, the shape of the phase portrait depends critically on $e_p$."241" We see that for a small ej, a planetesimal with a small initial e will keepe small for ever."," We see that for a small $e_p$ , a planetesimal with a small initial $e$ will keep$e$ small for ever."242" For a large ej however, any planetesimal with a small initial e will"," For a large $e_p$ however, any planetesimal with a small initial $e$ will"243Cluission of stars and starheated dust. aud allowine also for the presence of a dusty torusSun (AGN). using the method deseribed iu Fritz et votal. ,"emission of stars and star-heated dust, and allowing also for the presence of a dusty torus (AGN), using the method described in Fritz et al. ("244{6).,2006).245 In Fie., In Fig.246 5 we report an example of the SED fitting obtained for 9 represcutative objects. sclected among the 28 sources.," \ref{SED} we report an example of the resulting SED fitting obtained for 9 representative objects, selected among the 28 sources."247 The presence of an ACN is required iu mnost cases (25 out of 28) to reproduce the lau cluission. while its contribution to the 1000400] is always lower than5-10:4.. thus neeligible.," The presence of an AGN is required in most cases (25 out of 28) to reproduce the $\mu$ m emission, while its contribution to the $L[8-1000\mu m]$ is always lower than, thus negligible."248EIS None of the 16 galaxies observed by Chandra is detected (Elvis et al, None of the 16 galaxies observed by Chandra is detected (Elvis et al.249 2009). sugeestiug that the ACGNs are extremely obscured.," 2009), suggesting that the AGNs are extremely obscured."250" These objects are probably similar to the Fo A, cutting Compton thick QSO at .=2.5 from Ferugho et al. (", These objects are probably similar to the Fe $K_\alpha$ emitting Compton thick QSO at $z=2.5$ from Feruglio et al. (251"2011). that qualifies as a starburst ealaxy according fo our criterion,","2011), that qualifies as a starburst galaxy according to our criterion."252 Onlv 2 of our 28 sources fall in the AzTEC area (Scott ot al., Only 2 of our 28 sources fall in the AzTEC area (Scott et al.253 2008). and one of them is detected in the millimeter catalog.," 2008), and one of them is detected in the millimeter catalog."254 Fie., Fig.255 5 also re ACS-F775W cutouts for the example objects.," \ref{SED}256 also reports ACS-F775W cutouts for the example objects."257 À few portsobjects are consistent with advanced stage mcrecrs((double components on the f-haud ACS COSMOS nuage. Nockemocr. A.M. et al.," A few objects are consistent with advanced stage mergers (double components on the $I$ -band ACS COSMOS image, Koekemoer, A.M. et al."258 2007). others are quite compact (consistent with the analysis of Elbaz et al.," 2007), others are quite compact (consistent with the analysis of Elbaz et al."259 2011). whereas some remain undetected.," 2011), whereas some remain undetected."260 A more extended morphological analysis is postponed to a future paper (but see also Wuvts et al..," A more extended morphological analysis is postponed to a future paper (but see also Wuyts et al.,"261 20115)., 2011b).262 The redshiff range 1.5«:2.5 correspouds to a ~2 Car cosnüc time interval. lence our star-forming ealaxies have on average spent init ~1 Cor.," The redshift range $1.5<z<2.5$ corresponds to a $\sim2$ Gyr cosmic time interval, hence our star-forming galaxies have on average spent in it $\sim1$ Gyr."263 Therefore. the fact that only ~2% of the massive galaxies are off the main sequence implies that ou average cach galaxy speuds ~20 Myr in such a phase.," Therefore, the fact that only $\sim2$ of the massive galaxies are off the main sequence implies that on average each galaxy spends $\sim 20$ Myr in such a phase."264 This is actually much shorter than both the eas depletion timescale aud the (outer rotation) dynamical time in starburst ealaxics (Daddi ct al., This is actually much shorter than both the gas depletion timescale and the (outer rotation) dynamical time in starburst galaxies (Daddi et al.265 2010: Genzel et al., 2010; Genzel et al.266 2010)., 2010).267 This is also much shorter than the expected duration of the SFR-excess phase in imiergers based on muuerical simulations (e.g. di Matteo et al., This is also much shorter than the expected duration of the SFR-excess phase in mergers based on numerical simulations (e.g. di Matteo et al.268 2008. Martie et al.," 2008, Martig et al."269 2010). where the duration of the phase with SER in excess of 74 over the preanerger SER is of order of 200-300 Mer (Bournaucd et al.," 2010), where the duration of the phase with SFR in excess of $>4$ over the pre-merger SFR is of order of 200-300 Myr (Bournaud et al."270 2011)., 2011).271 Most likely this is because only a fraction of massive star-forming ealaxies undergoes uajor mergers duriug this time iuterval. and/or because uost mergers do not produce a substantial increase of he SFR (consistent with the simulations of di Matteo et al.," Most likely this is because only a fraction of massive star-forming galaxies undergoes major mergers during this time interval, and/or because most mergers do not produce a substantial increase of the SFR (consistent with the simulations of di Matteo et al."272 2008)., 2008).273 All in all our results quite clearly show that the ucrecr-enhanced SER phase:sare relatively unimniportaut or the formation of stars iu 2— galaxies. aud probably at all redshifts eiven that :~2 is known to be the “prime time for SMCs (Chapman et al.," All in all, our results quite clearly show that the merger-enhanced SFR phases are relatively unimportant for the formation of stars in $z\sim2$ galaxies, and probably at all redshifts given that $z\sim2$ is known to be the 'prime time' for SMGs (Chapman et al."274 2005). aud that lis is similar to what is observed iu the local Universe (e.g. the percentual contribution of starburst is very sinall. Sanders AGrabel. 1996).," 2005), and that this is similar to what is observed in the local Universe (e.g. the percentual contribution of starburst is very small, Sanders Mirabel, 1996)."275 Still. going through lis imergiue-driveu starburst plase may be a critical ghase for the transtormation of star-forming galaxies into passive cllipticals.," Still, going through this merging-driven starburst phase may be a critical phase for the transformation of star-forming galaxies into passive ellipticals."276 Deuce. we maintain that off galaxies are likely to be crucialevolution. objects for our nuderstauding galaxy formation aud," Hence, we maintain that off-sequence galaxies are likely to be crucial objects for our understanding galaxy formation and evolution."2771077) at a value of 2.0.,) at a value of 2.0.278 Note. that in most plots the intrinsic variance of the data is quite high.," Note, that in most plots the intrinsic variance of the data is quite high."279 The normalization of the power law changes only marginally and quite generally. the errors of the fitted parameters are larger when the source is bright and thus the relative contribution of the power law component smaller.," The normalization of the power law changes only marginally and quite generally, the errors of the fitted parameters are larger when the source is bright and thus the relative contribution of the power law component smaller."280 Changes of the flux are thus mainly caused by an increase of the optical depth of the scattering electrons combined with an increase of the normalization of the Comptonization component., Changes of the flux are thus mainly caused by an increase of the optical depth of the scattering electrons combined with an increase of the normalization of the Comptonization component.281 We repeated the fits. leaving the temperature of the scattering electrons free but fixed the optical depth to 1.8. The results are very similar to those of Fig. 7..," We repeated the fits, leaving the temperature of the scattering electrons free but fixed the optical depth to $\tau = 1.8.$ The results are very similar to those of Fig. \ref{figure:comppar}."282 The flux variations are in that case correlated linearly only with changes of the temperature of the scattering electrons over the range 3.9 keV KT 74 keV. The spectrum of0558-504. like that of other NLSI galaxies. can be fitted well by a combination of two compTT Comptonization models: one with low (~ 4.5 keV) temperature and moderate optical depths (tr~ 2.0) and a second. high temperature component with KT. 2 50 keV and low scattering depths (τς 0.7).," The flux variations are in that case correlated linearly only with changes of the temperature of the scattering electrons over the range 3.9 keV kT 7.4 keV. The spectrum of, like that of other NLS1 galaxies, can be fitted well by a combination of two compTT Comptonization models: one with low $\sim$ 4.5 keV) temperature and moderate optical depths $\tau \sim 2.0$ ) and a second, high temperature component with kT $\gta$ 50 keV and low scattering depths $\tau \lta$ 0.7)."283 A determination of exact parameters of the scatterer is not possible: from the high KT component only the low-energy power law can be seen in the XMM energy band and the measured slope is merely an indicator for a wide range of possible (KT.7) combinations (Titarchuk Lyubarssj 1995)., A determination of exact parameters of the scatterer is not possible: from the high kT component only the low-energy power law can be seen in the XMM energy band and the measured slope is merely an indicator for a wide range of possible $\tau$ ) combinations (Titarchuk Lyubarskij 1995).284 The low temperature component shows in. principle measurable characteristic changes of the spectral slope inside the PN energy band: however. the superposition of the two components and the position of the spectral break at rather high energies 25 keV) with low photon statistics leaves considerable uncertainties in the parameter determination as well.," The low temperature component shows in principle measurable characteristic changes of the spectral slope inside the PN energy band; however, the superposition of the two components and the position of the spectral break at rather high energies $\gta 5$ keV) with low photon statistics leaves considerable uncertainties in the parameter determination as well."285 Thus. this low-temperature component could be quite well replaced with a considerably hotter component with much smaller optical depth: the physical implications of this (less favored) combination will be discussed below.," Thus, this low-temperature component could be quite well replaced with a considerably hotter component with much smaller optical depth; the physical implications of this (less favored) combination will be discussed below."286 Nevertheless. the above envisaged two components. low kT and high 7 plus high KT and low r represent an appealing picture for the X-ray emission of NLSI galaxies.," Nevertheless, the above envisaged two components, low kT and high $\tau$ plus high kT and low $\tau$ represent an appealing picture for the X-ray emission of NLS1 galaxies."287 The high, The high288"Perrymanetal. 1997,, Hoegetal.1997)), BC is the bolometric correction (from Flower 1996)) and Ty is the effective temperature (from Boehm-Vitense1981)).","\citealt{1997A&A...323L..49P}, \citealt{1997A&A...323L..57H}) ), $BC$ is the bolometric correction (from \citealt{1996ApJ...469..355F}) ) and $T_{eff}$ is the effective temperature (from \citealt{1981ARA&A..19..295B}) )."289 In Fig., In Fig.290" 2 we also show the windows used to integrate the Mg line-core fluxes, which are 10 A--wide and are centred at 2795A."," \ref{fig.esp_b} we also show the windows used to integrate the Mg line-core fluxes, which are 10 -wide and are centred at 2795."291". The position and the width of these windows were chosen to guarantee that the contribution of the integrated flux is predominantly chromospheric, beyond the basal contribution."," The position and the width of these windows were chosen to guarantee that the contribution of the integrated flux is predominantly chromospheric, beyond the basal contribution."292" However, it can be seen in the figure that the Mg line-core emission can only be detected in stars of late spectral type, in which the level of phostospheric continuum is low."," However, it can be seen in the figure that the Mg line-core emission can only be detected in stars of late spectral type, in which the level of phostospheric continuum is low."293" Therefore, the Mg line-core fluxes derived from IUE low-resolution spectra could be only considered as an activity indicator in stars cooler than G3."," Therefore, the Mg line-core fluxes derived from IUE low-resolution spectra could be only considered as an activity indicator in stars cooler than G3."294" On the other hand, the ""IUE Newly Extracted Spectra"" (INES) system provides a spectrum for each high-resolution image, which is obtained by re-sampling the high-resolution spectrum into the low-resolution wavelength domain."," On the other hand, the “IUE Newly Extracted Spectra” (INES) system provides a spectrum for each high-resolution image, which is obtained by re-sampling the high-resolution spectrum into the low-resolution wavelength domain."295 The re-sampling has been performed so that the total flux is conserved., The re-sampling has been performed so that the total flux is conserved.296" However, the rebinned spectra have not been convolved with the low-resolution Point Spread Function (PSF) and, in consequence, have a better spectral resolution than low-dispersion spectra Riestraetal. 2000).."," However, the rebinned spectra have not been convolved with the low-resolution Point Spread Function (PSF) and, in consequence, have a better spectral resolution than low-dispersion spectra \citep{2000A&AS..141..343G}."297 In Fig., In Fig.298 3 we plot two quasi-simultaneous rebinned and low-dispersion spectra of the star HD 22049 (K2V)., \ref{fig.comp_a_b} we plot two quasi-simultaneous rebinned and low-dispersion spectra of the star HD 22049 (K2V).299 We can see that both spectra are similar but not equal., We can see that both spectra are similar but not equal.300" However, the Mg line-core fluxes integrated between 2790 and 2810 (dotted rectangle) on both spectra only differ by 1-2%.."," However, the Mg line-core fluxes integrated between 2790 and 2810 (dotted rectangle) on both spectra only differ by ."301" Therefore,in order to calculate"," Therefore,in order to calculate"302comprising a grid of phototonised absorbers based on the XS'TALHR code.,comprising a grid of photoionised absorbers based on the XSTAR code.303 These model absorbers cover a wide range of column density anc ionisation parameter £ (= Lfni?). with outllow (or inflow) velocities as a variable parameter.," These model absorbers cover a wide range of column density and ionisation parameter $\xi$ (= $L/nr^2$ ), with outflow (or inflow) velocities as a variable parameter."304 All abundant elements from € to Fe are included with the relative abundances as a variable input parameter., All abundant elements from C to Fe are included with the relative abundances as a variable input parameter.305 To limit processing time the NS'TTAIt models assume a fixed. width for each absorption line of 1000 km + EWIIM., To limit processing time the XSTAR models assume a fixed width for each absorption line of 1000 km $^{-1}$ FWHM.306" Civen the paucity of data from the sspectral analvsis we included. only. one absorbing column in the fit. assumed to fully cover the underlving continuum. recognising this would. probably ""average out the optimal parameters for ions as disparate. as FeXAWVI and NeX. Assuming solar abundances. a best-fit ionisation parameter of log£ of 3.70.2.with a column density of Ny=4LOen 7. was found to reproduce the observed absorption line strengths of FOXAVL SXVI and NeX. with a nett blueshift of O.15 (or —0.21c. in the AGN rest. frame)"," Given the paucity of data from the spectral analysis we included only one absorbing column in the fit, assumed to fully cover the underlying continuum, recognising this would probably `average out' the optimal parameters for ions as disparate as FeXXVI and NeX. Assuming solar abundances, a best-fit ionisation parameter of $\xi$ of $\pm$ 0.2,with a column density of $N_{H}=4\times10^{23}\rm{cm}^{-2}$ , was found to reproduce the observed absorption line strengths of FeXXVI, SXVI and NeX, with a nett blueshift of 0.15 (or $\sim$ 0.21c, in the AGN rest frame)."307" Apart from a minor contribution [rom ΕΟΝΧΜ, the main absorption lines produced by this highly ionised column were all of hvdrogenie ions."," Apart from a minor contribution from FeXXV, the main absorption lines produced by this highly ionised column were all of hydrogenic ions."308 An alternative fit. at an ionisation parameter of log£ = 3.2+0.15. was obtained by assuming line —entifications with Lle-like Fe. S and Ne.," An alternative fit, at an ionisation parameter of $\xi$ = $\pm$ 0.15, was obtained by assuming line identifications with He-like Fe, S and Ne."309 However. at this lower ionisation level. significant5 be L absorption1 lines are predicted in the 10-15 Anestrom band. which are not seen.," However, at this lower ionisation level, significant Fe L absorption lines are predicted in the 10-15 Angstrom band, which are not seen."310 We therefore conclude that the NSTADH fitting favours the high5 ionisation parameter solution. and an outllow velocity ∪⇂⋅∿∪⋡⇉≼⋱ ," We therefore conclude that the XSTAR fitting favours the high ionisation parameter solution, and an outflow velocity of $\sim$ 0.2c."311The oobservation of hhas revealed an X-ray. spectrum with intriguinely similar (albeit weaker) features to those recently reported for another bright. narrow line quasar PC1211|143 (Pounds 22003).," The observation of has revealed an X-ray spectrum with intriguingly similar (albeit weaker) features to those recently reported for another bright, narrow line quasar PG1211+143 (Pounds 2003)."312" ""Phe soft Meray excess reportecl ino previous observations is confirmed. being. somewhat ""hotter and less strong than for PGI2111148."," The soft X-ray excess reported in previous observations is confirmed, being somewhat `hotter' and less strong than for PG1211+143."313 Fe Ix. emission is again detected: and modelled by ai broad. but non-relativistic gaussian line.," Fe K emission is again detected and modelled by a broad, but non-relativistic gaussian line."314 Of most interest is finding further evidence of an absorption line structure. in both EPIC and GS data. indicating a high. column. high. ionisation absorber. outllowing at an even higher velocity (than found. for DOGI2111143) of —0.2c.," Of most interest is finding further evidence of an absorption line structure, in both EPIC and RGS data, indicating a high column, high ionisation absorber, outflowing at an even higher velocity (than found for PG1211+143) of $\sim$ 0.2c."315 We attribute the relatively faint absorption lines to the higher ionisation (lower opacity) of the outflow. despite the best-fit column density again being remarkably high.," We attribute the relatively faint absorption lines to the higher ionisation (lower opacity) of the outflow, despite the best-fit column density again being remarkably high."316 As for POGI211|143 we note that most of the uncertainty in the derived. column densities is on the upside. since partial covering and accounting for saturation in the relatively narrow line profiles would both increase the above values.," As for PG1211+143 we note that most of the uncertainty in the derived column densities is on the upside, since partial covering and accounting for saturation in the relatively narrow line profiles would both increase the above values."317 aacds to a growing list of AGN showing X-ray evidence for ugh velocity ionised. outllows. also including PG1211|143 (Pounds 2003). the ultra-Iuminous. quasar PDS456 (Reeves 22003) and the BAL quasar. ADM 08279|5255. reported to jwe strongly bluc-shifted resonance absorption lines of Fe XXV or XXVI by Chartas ((2002).," adds to a growing list of AGN showing X-ray evidence for high velocity ionised outflows, also including PG1211+143 (Pounds 2003), the ultra-luminous quasar PDS456 (Reeves 2003) and the BAL quasar, APM 08279+5255, reported to have strongly blue-shifted resonance absorption lines of Fe XXV or XXVI by Chartas (2002)."318 The most important. implication of finding such absorption in the hard. X-ray. band. is that. the required column densities are. higher (ef with those seen in the UV). and the mass and kinetic energv in the outllows are corresponcingly more significant.," The most important implication of finding such absorption in the hard X-ray band is that the required column densities are higher (cf with those seen in the UV), and the mass and kinetic energy in the outflows are correspondingly more significant."319 It appears that highly ionised. high velocity gas. capable of imparting Fe ly absorption features. may be a major component of (at least some) AGN that has. remained: undetected: prior to the iniproved sensitivity of observations in the 7.10 keV band.," It appears that highly ionised, high velocity gas, capable of imparting Fe K absorption features, may be a major component of (at least some) AGN that has remained undetected prior to the improved sensitivity of observations in the $\sim$ 7–10 keV band."320 As in the case of PGI211|143. the high column density of ionised matter in the line-of-sight to implies - for the simplest. assumption of a racial outflow - that the Dow will be optically thick at small racii.," As in the case of PG1211+143, the high column density of ionised matter in the line-of-sight to implies - for the simplest assumption of a radial outflow - that the flow will be optically thick at small radii."321 We show below that the hot ‘photosphere’ provides a major part of the cnerectically dominant thermal continuum (BBB) emission for349., We show below that the hot `photosphere' provides a major part of the energetically dominant thermal continuum (BBB) emission for.322. Other important implications of the observed high velocity outflow. which we assess below in terms of a physical model of winds from black holes accreting at or above the Ecldineton limit (xing and. Pounds. 2003: hereafter IXD03). are a significante mass loss and substantial kinetic energy associated with the outflow.," Other important implications of the observed high velocity outflow, which we assess below in terms of a physical model of winds from black holes accreting at or above the Eddington limit (King and Pounds 2003; hereafter KP03), are a significant mass loss and substantial kinetic energy associated with the outflow."323 As shown in the analvsis of PG@L211|143 (Pounds 22003). for a radial outflow with constant (coasting) speed v. occupying a solid angle of dab steradians. mass conservation implies the ου{μον is optically thick at a radius Z4. where," As shown in the analysis of PG1211+143 (Pounds 2003), for a radial outflow with constant (coasting) speed $v$, occupying a solid angle of $4\pi b$ steradians, mass conservation implies the outflow is optically thick at a radius $R_{\rm324ph}$ where"325The data were acquired at the Plateau de Bure Interferometer in May and July 2006 with 5 or 6 antennas.,The data were acquired at the Plateau de Bure Interferometer in May and July 2006 with 5 or 6 antennas.326 Table 1. summarizes the observed sightlines. observing dates. approximate quasar fluxes. integration times (the on-source time equivalent to having 6 antennas simultaneously observing). and the empirically-determined rms error in line/continuum ratio in the final. reduced spectra.," Table \ref{tab:obs} summarizes the observed sightlines, observing dates, approximate quasar fluxes, integration times (the on-source time equivalent to having 6 antennas simultaneously observing), and the empirically-determined rms error in line/continuum ratio in the final, reduced spectra."327 Six correlator bands of 20 MHz were concatenated to cover frequencies from 97600 to 97800 MHz (or a .150kms7! bandwidth) with a channel spacing of 39.06 kHz or 0.121 aand a channel width of 70 kHz.," Six correlator bands of 20 MHz were concatenated to cover frequencies from 97600 to 97800 MHz (or a $\sim 150\,\kms$ bandwidth) with a channel spacing of 39.06 kHz or 0.121 and a channel width of 70 kHz."328 Two additional correlator bands of 320 MHz were used to measure the 3 mm continuum over the 580 MHz instantaneous IF-bandwidth available with this generation of receivers., Two additional correlator bands of 320 MHz were used to measure the 3 mm continuum over the 580 MHz instantaneous IF-bandwidth available with this generation of receivers.329 The fluxes of the quasar continuum were determined relative to the primary flux calibrator used at Plateau de Bure. MWC349.," The fluxes of the quasar continuum were determined relative to the primary flux calibrator used at Plateau de Bure, MWC349."330 The resulting flux accuracy is -15%., The resulting flux accuracy is $\sim 15\%$.331 The data were processed inside the (Pety.2005)., The data were processed inside the \citep{pety05}.332 After a standard RF bandpass calibration. the time-dependent amplitude and phase gains were computed per baseline on the continuum data. assuming a point source.," After a standard RF bandpass calibration, the time-dependent amplitude and phase gains were computed per baseline on the continuum data, assuming a point source."333 Those gains were then applied to the line data taken simultaneously and spectra were computed as a weighted temporal average of the visibility amplitudes., Those gains were then applied to the line data taken simultaneously and spectra were computed as a weighted temporal average of the visibility amplitudes.334 Rest frequencies for the ttransitions (Table 2)) were taken from the NIST list of recommended rest frequencies. found online at http://physies.nist.gov/cgi-bin/micro/tableS/start.pl.," Rest frequencies for the transitions (Table \ref{tab:line}) ) were taken from the NIST list of recommended rest frequencies, found online at http://physics.nist.gov/cgi-bin/micro/table5/start.pl."335 Although the spectroscopic. constants have changed slightly. helpful energy level diagrams and related information for aare given by Lees(1973).. Nagaretal.(1979). and Fribergetal. (1988): Lees(1973) tabulates line strengths and spontaneous emission coefficients.," Although the spectroscopic constants have changed slightly, helpful energy level diagrams and related information for are given by \cite{Lees73}, \cite{NagKai+79} and \cite{FriHja+88}; \cite{Lees73}336 tabulates line strengths and spontaneous emission coefficients."337 As noted in Table 2.. we observed several J22&—ly transitions of A- and E-type aaround 96740 MHz.," As noted in Table \ref{tab:line}, we observed several $_{\rm K} - 1_{\rm K}$ transitions of A- and E-type around 96740 MHz."338 For tthe JO level of the K--1 ladder is absent owing to symmetry concerns and the 52.1—|_| transition is actually the state lline., For the J=0 level of the K=-1 ladder is absent owing to symmetry concerns and the $2_{-1} - 1_{-1}$ transition is actually the ground-state line.339" The fourth column of Table 2. gives the fraction of all A- or wwhich resides in the |, level of the various transitions when the rotational populations are in equilibrium with the 2.73 K cosmic microwave background.", The fourth column of Table \ref{tab:line} gives the fraction of all A- or which resides in the $_{\rm K}$ level of the various transitions when the rotational populations are in equilibrium with the 2.73 K cosmic microwave background.340 The total column density of iis the sum of all A- andE-CH;OH., The total column density of is the sum of all A- and.341. According to Lees(1973). the transitions observed are all of a-type. with. dipole moment of 0.885 D. leading to the spontaneous emission rates Az; shown in Table 2..," According to \cite{Lees73}, the transitions observed are all of a-type, with dipole moment of 0.885 D, leading to the spontaneous emission rates $_{21}$ shown in Table \ref{tab:line}."342 From standard formulae. given the assumed excitation and level populations. we may write for either the X=A or X=E configurations X-CH:OH)) =. where the observed optical depth integral over any of the οκ—I lines is expressed in aand values of qx are given in the last column of Table 2..," From standard formulae, given the assumed excitation and level populations, we may write for either the X=A or X=E configurations ) =, where the observed optical depth integral over any of the $_{\rm K} - 1_{\rm343 K}$ lines is expressed in and values of $_{\rm X}$ are given in the last column of Table \ref{tab:line}."344 We observed the J=5-4 HC;N and J=8-7 HCsN transitions at 45.4 and 21.3 GHz at the VLA on 2007 December 16-17 using a correlator setup with 128 channels of width 24.4 khz and 12.2 kHz. respectively (0.161 kms7!and 0.172 kms7!)).," We observed the J=5-4 $_3$ N and J=8-7 $_5$ N transitions at 45.4 and 21.3 GHz at the VLA on 2007 December 16-17 using a correlator setup with 128 channels of width 24.4 khz and 12.2 kHz, respectively (0.161 and 0.172 )."345 We bandpass calibrated and then observed the background sources fixedly without the need for other phase calibrators. given the strong emission and poimt-like nature of the sources (all of which are calibrators for other experiments).," We bandpass calibrated and then observed the background sources fixedly without the need for other phase calibrators, given the strong emission and point-like nature of the sources (all of which are calibrators for other experiments)."346 We usec reference pointing on all sources., We used reference pointing on all sources.347 After applying the bandpass calibration. we used the AIPS task UVLSD which forms anc averages line/continuum spectra during individual correlator integration intervals.," After applying the bandpass calibration, we used the AIPS task UVLSD which forms and averages line/continuum spectra during individual correlator integration intervals."348 The final spectra were then formed with vector averaging in the POSSM task and exported for reductiot and analysis., The final spectra were then formed with vector averaging in the POSSM task and exported for reduction and analysis.349 The fluxes of the background sources were not needed to form the absorption spectra and were not separately determined., The fluxes of the background sources were not needed to form the absorption spectra and were not separately determined.350 Although unforseen. it has not beer possible to correlate baselines with both VLA and eVLA antennas at the narrow IF bandwidths used in this work.," Although unforseen, it has not been possible to correlate baselines with both VLA and eVLA antennas at the narrow IF bandwidths used in this work."351 Given the makeup of the VLA during our observations. it was necessary to discard nearly half of the the baselines.," Given the makeup of the VLA during our observations, it was necessary to discard nearly half of the the baselines."352 Additionally. the Q-band HC3N observations were corrupted by an unexplained IF," Additionally, the Q-band $_3$ N observations were corrupted by an unexplained IF"353AGN is likely the dominant component.,AGN is likely the dominant component.354 These are consistent with our earlier results 2008)., These are consistent with our earlier results \citep{sajina08}.355". Note however. that using the above translation between Ls ancl Ly, implies starburst-only luminosities of z 107 eeven for MIPS16080 and MIPS223023. and consequently. SFRs of ~ //vr."," Note however, that using the above translation between $L_{3.3}$ and $L_{\rm{IR}}$ implies starburst-only luminosities of $\gs$ $10^{12}$ even for MIPS16080 and MIPS22303, and consequently SFRs of $\sim$ /yr."356 However. as discussed in 44.6. these features being of low signal-to-noise ratios and somewhat confused with the ice and WAC absorption features. are not particularly reliable.," However, as discussed in 4.6, these features being of low signal-to-noise ratios and somewhat confused with the ice and HAC absorption features, are not particularly reliable."357 The stacked spectrum shows that PAIL emission is likely present in (he majority of these sources. even excluding the {wo strone-PAIT sources.," The stacked spectrum shows that PAH emission is likely present in the majority of these sources, even excluding the two strong-PAH sources."358 The fact that stu-formation is present is further supported by the fact that although most of these sources are not individually detected in the far-IR. their stacked) 1.2mm (vest-lrame ~ pm)) flux is strongly detected at ~ mmJx. which is comparable to fainter (9554722. 32nmunJy) ΠΠ galaxies (Sajinaelal.2008).," The fact that star-formation is present is further supported by the fact that although most of these sources are not individually detected in the far-IR, their stacked 1.2mm (rest-frame $\sim$ ) flux is strongly detected at $\sim$ mJy which is comparable to fainter $S_{850}$ $\sim$ mJy) sub-mm galaxies \citep{sajina08}."359. These numbers suggests that SFRs on the order of msun//vr are feasible lor the bulk of the weak-PAII sample., These numbers suggests that SFRs on the order of /yr are feasible for the bulk of the weak-PAH sample.360 Although in itself significant. star-Iormation at Chis level is insullicient to dominate the bolometric Iuminosities of these SOULCeS.," Although in itself significant, star-formation at this level is insufficient to dominate the bolometric luminosities of these sources."361 Local ULIRGs show a high level of detectability of water ice absorption features., Local ULIRGs show a high level of detectability of water ice absorption features.362 For example the 46 sources in the AIKABI sample (ananishietal.2008) were selected out of the IRAS JJv sample merely on the basis of visibility to AINARI and are therefore unbiased with respect to the local IRAS ULIRG population as a whole., For example the 46 sources in the AKARI sample \citep{imanishi08} were selected out of the IRAS Jy sample merely on the basis of visibility to AKARI and are therefore unbiased with respect to the local IRAS ULIRG population as a whole.363 The [[eature was detected in 30/46 sources (65%.)). whereas the IHILAC! feature was only observed in 4 of the sources )).," The feature was detected in 30/46 sources ), whereas the HAC feature was only observed in 4 of the sources )."364 The presence of the IAC feature has been suggests as an indicator of AGN-dominance in the mic-IR (Risalitiοἱal.lmanishietal.2006a) and hence this low fraction is consistent with local ULIRGSs being predominantly starbursts.," The presence of the HAC feature has been suggests as an indicator of AGN-dominance in the mid-IR \citep{risaliti06,imanishi_ulirgs} and hence this low fraction is consistent with local ULIRGs being predominantly starbursts."365 To determine (he appropriate detectability for our sample we need to consider first that MIDPS8392 has too low a signal to noise in (his regime. and three other sources are of 2 z 11.8 which makes this leature too near the edge for reliable detections.," To determine the appropriate detectability for our sample we need to consider first that MIPS8392 has too low a signal to noise in this regime, and three other sources are of $z$ $\ls$ 1.8 which makes this feature too near the edge for reliable detections."366 This means that 3/7 (48%)) of our sample show the wwater ice absorption feature. (his is roughly comparable to the local ULIRGs given the «mall number of sources in our sample.," This means that 3/7 ) of our sample show the water ice absorption feature, this is roughly comparable to the local ULIRGs given the small number of sources in our sample."367 On the other hand (5/11) of the sources (45%)) show the ΗΗΑς: absorption feature. which fraction is significantly higher than observed for local ULIRGs (even accounting for the Poisson error in such a small sample).," On the other hand (5/11) of the sources ) show the HAC absorption feature, which fraction is significantly higher than observed for local ULIRGs (even accounting for the Poisson error in such a small sample)."368 However. the HAC feature can be practically difficult to detect in sources with strong," However, the HAC feature can be practically difficult to detect in sources with strong"369despitte this misalignment.,te this misalignment.370these two plots would. agree.,these two plots would agree.371 These. plots. confirm the conclusion drawn from the mean of the cilferences., These plots confirm the conclusion drawn from the mean of the differences.372 Even with the L1544w position included. the measured differences agree fairly well with the normal error. function. while if L1544w is excluded. the agreement is excellent.," Even with the L1544w position included, the measured differences agree fairly well with the normal error function, while if L1544w is excluded, the agreement is excellent."373 Hence. while the L1544w. position may. be anomalous as discussed originally by CLIT there is no statistically significant evidence for the MIP claim that the CLP assumption of a fairly uniform Ποιά direction for each cloud. is. invalid.," Hence, while the L1544w position may be anomalous – as discussed originally by CHT – there is no statistically significant evidence for the MT claim that the CHT assumption of a fairly uniform field direction for each cloud is invalid."374 The scatter in the differences is entirely attributable to the measurement uncertainties and not to any intrinsic scatter in the Bros., The scatter in the differences is entirely attributable to the measurement uncertainties and not to any intrinsic scatter in the $B_{LOS}$.375 Even i£ the L1544. cloud. were excluded from the CLIP analysis. the CLIT conclusion that these cores were not formed by ambipolar diffusion remains valid.," Even if the L1544 cloud were excluded from the CHT analysis, the CHT conclusion that these cores were not formed by ambipolar diffusion remains valid."376" ALT give an example of possible measurements of 10 μα and 14 eG. each with uncertainty 0.1 eG. and note that the mean ολους from each value by 2 µας, not the 0.07 pC given by propagation of errors."," MT give an example of possible measurements of 10 $\mu$ G and 14 $\mu$ G, each with uncertainty 0.1 $\mu$ G, and note that the mean differs from each value by 2 $\mu$ G, not the 0.07 $\mu$ G given by propagation of errors."377 However. these 1000 ancl 1HQc examples are not germane to the CLEE case of roughly 1.26 measurements.," However, these $100\sigma$ and $140\sigma$ examples are not germane to the CHT case of roughly $1-2\sigma$ measurements."378 Moreover. CLL did not. average the four envelope results for each cloud and obtain the uncertainty by error propagation: they synthesized a toroidal beam to sample the envelopes and obtained the uncertainties directly from the single envelope D;os measurement for each cloud.," Moreover, CHT did not average the four envelope results for each cloud and obtain the uncertainty by error propagation; they synthesized a toroidal beam to sample the envelopes and obtained the uncertainties directly from the single envelope $B_{LOS}$ measurement for each cloud."379 ALT argue that an arbitrarily twisted field morphology. (see the cartoon. shown in MT. Figure. 1) must. be. included in the analysis for R., MT argue that an arbitrarily twisted field morphology (see the cartoon shown in MT Figure 1) must be included in the analysis for ${\cal R}$.380 Although we have argued above that the data do not require that such a morphology is present. let us follow AVP ancl assume that it is.," Although we have argued above that the data do not require that such a morphology is present, let us follow MT and assume that it is."381 The MIT analysis of the CLIT data should. then be consistent with this proposed model of the field morphology — that is. that the angle @ between the core and envelope fields are arbitrarily large.," The MT analysis of the CHT data should then be consistent with this proposed model of the field morphology – that is, that the angle $\theta$ between the core and envelope fields are arbitrarily large."382 But then the ME analysisκο is internally inconsistent with this model., But then the MT analysis is internally inconsistent with this model.383 CIID defined R in order to eliminate the unknown angle 8 between the field direction and the line of sight: CIEE assumed that between he core and the envelope of a cloud those directions. are he same (except for minor differences in the @ that. do not significantly alfect the analysis. see discussion in CLIT).," CHT defined ${\cal R}$ in order to eliminate the unknown angle $\theta$ between the field direction and the line of sight; CHT assumed that between the core and the envelope of a cloud those directions are the same (except for minor differences in the $\theta$ that do not significantly affect the analysis, see discussion in CHT)."384 That assumption allowed the unknown angle @ between the ield and the line of sight. which enters as cos&. to drop out. of the ratio R (see Equations 1 and 2).," That assumption allowed the unknown angle $\theta$ between the field and the line of sight, which enters as $cos~\theta$, to drop out of the ratio ${\cal R}$ (see Equations 1 and 2)."385 1 the 6s for he four envelope positions and the core of cach cloud vary ereatly. as suggested in MT Figure 1. then 6s do not drop out of R.," If the $\theta$ s for the four envelope positions and the core of each cloud vary greatly, as suggested in MT Figure 1, then $\theta$ s do not drop out of ${\cal R}$."386 For a self-consistent NIE. analysis. each of the ive different @s (core ancl four. envelope) would. have to »f explicitly. included. in the expression for RR.," For a self-consistent MT analysis, each of the five different $\theta$ s (core and four envelope) would have to be explicitly included in the expression for ${\cal R}$."387 However. ALT do not do so: such an expression would have the five unknown 6s and could not be evaluated.," However, MT do not do so; such an expression would have the five unknown $\theta$ s and could not be evaluated."388 Instead. MT. use our expression for Ro with the cos 6s missing.," Instead, MT use our expression for ${\cal R}$ with the $cos~\theta$ s missing."389 ME stated that they were only allowing for cdillerent in over the four envelope positions. not for cilferent directions 8.," MT stated that they were only allowing for different in over the four envelope positions, not for different directions $\theta$."390 But this assumption is completely. inconsistent. with the astrophysical motivation of strongly twisted field lines (NITE ligure l and discussion) that they give for rejecting the CIPD analysis and substituting their own., But this assumption is completely inconsistent with the astrophysical motivation of strongly twisted field lines (MT Figure 1 and discussion) that they give for rejecting the CHT analysis and substituting their own.391 MT. olfer. no astrophysical explanation for fields at the envelope positions varving significantly in strength. ancl perhaps even. being antiparallel while the angle @ remains invariant., MT offer no astrophysical explanation for fields at the envelope positions varying significantly in strength and perhaps even being antiparallel while the angle $\theta$ remains invariant.392 The ME analysis is therefore not self-consistent. and cannot be used to analvze the CLIT data.," The MT analysis is therefore not self-consistent, and cannot be used to analyze the CHT data."393 Even within the framework of the MT analysis. it appears that the uncertainty in the Rs is overestimatecd.," Even within the framework of the MT analysis, it appears that the uncertainty in the ${\cal R}s$ is overestimated."394 ALTE considered the variation of the measured Dios as one component of the uncertainty. and. then added as a second component the measurement uncertainties.," MT considered the variation of the measured $B_{LOS}$ as one component of the uncertainty, and then added as a second component the measurement uncertainties."395 Llowever. as we showed above. the variation in the measured Dios is consistent with being due to the measurement uncertainties ancl not to a real variation.," However, as we showed above, the variation in the measured $B_{LOS}$ is consistent with being due to the measurement uncertainties and not to a real variation."396 MNT appear to be doubly counting the uncertainties., MT appear to be doubly counting the uncertainties.397 CILE. concluded that their. measurements of the ratios of AL/® between envelopes and. cores did not agree with the wedietion of the ambipolar diffusion mocdel., CHT concluded that their measurements of the ratios of $M/\Phi$ between envelopes and cores did not agree with the prediction of the ambipolar diffusion model.398 Here we have shown that the CLIT analysis is internally self. consistent: heir conclusions are valid within the framework of the assumptions they made., Here we have shown that the CHT analysis is internally self consistent; their conclusions are valid within the framework of the assumptions they made.399 The valicity of the APP paper rests on (wo pillars: (1) that the CLP data analysis ποσοστο is unambiguously inconsistent with the data itself. and (2) that MT. have a superior analysis technique.," The validity of the MT paper rests on two pillars: (1) that the CHT data analysis procedure is unambiguously inconsistent with the data itself, and (2) that MT have a superior analysis technique."400 We jwe demonstrated. that neither of these pillars of their oper is correct., We have demonstrated that neither of these pillars of their paper is correct.401 The conclusions of Crutcher.Hakobian&‘Trolancdl(2009). therefore stand the observed. variations of Md from envelope to core are not. Consistent with he prediction of the ambipolar diffusion driven theory of star formation., The conclusions of \cite{CHT} therefore stand – the observed variations of $M/\Phi$ from envelope to core are not consistent with the prediction of the ambipolar diffusion driven theory of star formation.402 This conclusion does not. of course. rule out the possibility that there are structures in magnetic i¢lcl morphology near dark cloud. cores: higher resolution and higher sensitivity observations would be necessary to investigate this possibility.," This conclusion does not, of course, rule out the possibility that there are structures in magnetic field morphology near dark cloud cores; higher resolution and higher sensitivity observations would be necessary to investigate this possibility."403 The approach of CIET to test the ambipolar cilfusion driven model of star formation by measuring the change in M/« between envelope and core is a powerful one that should be further exploited. since it reduces. uncertainties in actual values of magnetic field. direction. and. mass estimates by taking ratios.," The approach of CHT to test the ambipolar diffusion driven model of star formation by measuring the change in $M/\Phi$ between envelope and core is a powerful one that should be further exploited, since it reduces uncertainties in actual values of magnetic field direction and mass estimates by taking ratios."404 Unfortunately. such experiments will require very large amounts of telescope time.," Unfortunately, such experiments will require very large amounts of telescope time."405 Llowever. use of the eVLA for OLL Zeeman mapping anc ALALA for CN Zeeman mapping may make it possible to extend this technique to smaller. scales without requiring such large assignments of telescope tine.," However, use of the eVLA for OH Zeeman mapping and ALMA for CN Zeeman mapping may make it possible to extend this technique to smaller scales without requiring such large assignments of telescope time."406 This work is partially supported by the NSE under grants AST 0307642. 0606822 ancl 0908841.," This work is partially supported by the NSF under grants AST 0307642, 0606822 and 0908841."407"The results are given in Table 3, where the fourth and fifth column allows a comparison with Table 1.","The results are given in Table 3, where the fourth and fifth column allows a comparison with Table 1."408 Only small differences about few per cent are present between the best-fit values for b; and 6» in Table 1 and the new results for the best-fit value of c in Table 3., Only small differences about few per cent are present between the best-fit values for $b_1$ and $b_2$ in Table 1 and the new results for the best-fit value of $c$ in Table 3.409" Apart from the discrepancies already shown in Figure 3, we also note that the slope in the density profiles from the simulations tends to be shallower as compared to our approximation starting around 8 virial radii."," Apart from the discrepancies already shown in Figure 3, we also note that the slope in the density profiles from the simulations tends to be shallower as compared to our approximation starting around 8 virial radii."410 We therefore address the issue of the range of validity of our approximation., We therefore address the issue of the range of validity of our approximation.411" In order to study this, we will use a density profile which extends up to nearly 30 virial radii (see Fig."," In order to study this, we will use a density profile which extends up to nearly 30 virial radii (see Fig."412 7)., 7).413 At these very large distances we are able to analyse the asymptotic behaviour of both numerical and approximated density profiles., At these very large distances we are able to analyse the asymptotic behaviour of both numerical and approximated density profiles.414" To this aim, it is more useful to use the function y—(p/p)s since we can study its oblique asymptote."," To this aim, it is more useful to use the function $y=(\rho/\bar{\rho}) \ s$ since we can study its oblique asymptote."415 If we multiply Eq. (12)), If we multiply Eq. \ref{eq:ourmodel}) )416 by s we obtain that the asymptotic behaviour is: The leading term at large distances corresponds to the, by $s$ we obtain that the asymptotic behaviour is: The leading term at large distances corresponds to the417The anomalous X-ray pulsars (ANPs) ancl Soft. Ciamma Repeaters (SC:Rs) have spin down properties indicative of magnetic fields of ~LO!0 G which places then at the high end of the neutron star Ποια distribution.,"The anomalous X-ray pulsars (AXPs) and Soft Gamma Repeaters (SGRs) have spin down properties indicative of magnetic fields of $\sim 10^{14-15}\,$ G which places them at the high end of the neutron star field distribution."418 The source of the cquiescent X-ray luminosity in both the SCGlIts and the ANPs is unclear. but it is generally. believed that it is associated with the decay of some component of the magnetic field.," The source of the quiescent X-ray luminosity in both the SGRs and the AXPs is unclear, but it is generally believed that it is associated with the decay of some component of the magnetic field."419 The standard model of Duncan&Thompson(1992) ASSUDICS that the fickls are generated at. the time of formation of the neutron star by an ellicient àw dynamo that operates at low Rosshy numbers ancl requires milliscconcl birth periods., The standard model of \citet{Duncan92} assumes that the fields are generated at the time of formation of the neutron star by an efficient $\alpha- \omega$ dynamo that operates at low Rossby numbers and requires millisecond birth periods.420" Neutron stars born with initial periods £5 are predicted to generate large scale magnetic fields of 3104G(Lms/1I,) under optimum. concditions. which is more than adequate to explain the fields. in magnoetars."," Neutron stars born with initial periods $P_i$ are predicted to generate large scale magnetic fields of $3\times 10^{17}\,{\rm G}\left421({1\,\rm ms/P_i}\right)$ under optimum conditions, which is more than adequate to explain the fields in magnetars."422 A consequence of the rapid. initial spin predicted: for these models is that the supernova explosions that create the magnetars are expected to be an order of magnitude more energetic than ordinary core-collapse supernovae. if one makes the standard assumption that angular momentum is lost by magnetic braking and not by gravitational radiation or due to emission in a jet.," A consequence of the rapid initial spin predicted for these models is that the supernova explosions that create the magnetars are expected to be an order of magnitude more energetic than ordinary core-collapse supernovae, if one makes the standard assumption that angular momentum is lost by magnetic braking and not by gravitational radiation or due to emission in a jet."423 However. the energeties of some well studied supernova remnants associated with magnetars. appear to suggest that their formation may not always be," However, the energetics of some well studied supernova remnants associated with magnetars, appear to suggest that their formation may not always be"424noisy. and the catalogued (8—V) values of straggler candidates B283374 and B309015 turned out to be entirely inconsistent with their spectra. suggesting that those objects were either misidentified or very tightly blended.,"noisy, and the catalogued $(B-V)$ values of straggler candidates B283374 and B309015 turned out to be entirely inconsistent with their spectra, suggesting that those objects were either misidentified or very tightly blended."425 As a result. our sample shrunk to 19 photometric variables and 55 straggler candidates listed in Table Al..," As a result, our sample shrunk to 19 photometric variables and 55 straggler candidates listed in Table \ref{tab:object_list}."426 For each of them we obtained ten reduced spectra., For each of them we obtained ten reduced spectra.427 Three examples of the spectra are shown in Fig. 1.., Three examples of the spectra are shown in Fig. \ref{fig:example_spectra}.428 As detailed below. the information about our objects was mainly extracted from Hj.," As detailed below, the information about our objects was mainly extracted from $_\beta$."429 The average S/N at Hy was for all objects larger than 20., The average S/N at $_\beta$ was for all objects larger than 20.430 Out of the total of 740 spectra only a few had S/N « 20., Out of the total of 740 spectra only a few had S/N $<20$ .431 A broad spectroscopic survey of w Cen down to V=16.5 mag conducted by vanLoonetal.(2007) at a resolution R «2000 enabled us to verify the quality of the reduced spectra by a direct comparison.," A broad spectroscopic survey of $\omega$ Cen down to $V=16.5$ mag conducted by \citet{vl07}432 at a resolution $R\sim$ 2000 enabled us to verify the quality of the reduced spectra by a direct comparison."433 Among 15 of our variables and straggler candidates with V.<16.5 we found four in common with their sample., Among 15 of our variables and straggler candidates with $V<16.5$ we found four in common with their sample.434 In all four cases the agreement was good — an example is shown in Fig. 2.., In all four cases the agreement was good – an example is shown in Fig. \ref{fig:spectra_comparison}.435 Note that the nominal spectral range of VIMOS in the setup used for our observations starts at 4100 wwhile the spectra of vanLoonetal.(2007) extend from 3840 tto 4940A.. so that the range covered by both surveys is only 840 llong.," Note that the nominal spectral range of VIMOS in the setup used for our observations starts at 4100 while the spectra of \citet{vl07} extend from 3840 to 4940, so that the range covered by both surveys is only 840 long."436 The actual spectral range recorded by VIMOS depends on the location of the slit on the mask., The actual spectral range recorded by VIMOS depends on the location of the slit on the mask.437 In our data common to al slits was the region between 4700 and 5600 which in many spectra contained practically no lines except Hy and magnesium triplet at 5167.32. 5172.68 and 3183.60 (un the hottest objects even the latter was practically undetectable).," In our data common to al slits was the region between 4700 and 5600 which in many spectra contained practically no lines except $_\beta$ and magnesium triplet at 5167.32, 5172.68 and 5183.60 (in the hottest objects even the latter was practically undetectable)."438" The sodium doublet at 5889.95 and 5895.92 ffell beyond the red end of 11 spectra. and H, was visible in just 13 spectra."," The sodium doublet at 5889.95 and 5895.92 fell beyond the red end of 11 spectra, and $_\alpha$ was visible in just 13 spectra."439 As one can see. the material for radial velocity measurements was highly diverse.," As one can see, the material for radial velocity measurements was highly diverse."440 Moreover. the accuracy of wavelength calibration rapidly deteriorated below 4500A.. where only two lamp lines (He 4471.48 and He 4026.19 À)) were available.," Moreover, the accuracy of wavelength calibration rapidly deteriorated below 4500, where only two lamp lines (He 4471.48 and He 4026.19 ) were available."441 Keeping this in mind and aiming to make our survey as uniform as possible. we decided to base the measurements on Hy fitting. using other means for checkup only.," Keeping this in mind and aiming to make our survey as uniform as possible, we decided to base the measurements on $_\beta$ fitting, using other means for checkup only."442 The velocity was measured with the help of the IRAF task SPLOT by fitting Voigt profiles to Hj., The velocity was measured with the help of the IRAF task SPLOT by fitting Voigt profiles to ${_\beta}$.443 Wherever possible. it was also measured the same way from Mg and Na lines.," Wherever possible, it was also measured the same way from Mg and Na lines."444 For each line the object's velocity was calculated as a mean where N«x10 is the number of fitted spectra. and the corresponding rms deviation was found.," For each line the object's velocity was calculated as a mean where $N\le10$ is the number of fitted spectra, and the corresponding rms deviation was found."445 In the following. velocities and rms deviations are subseripted with the symbol of the element from which they are obtained: e.g. vy or cw.," In the following, velocities and rms deviations are subscripted with the symbol of the element from which they are obtained; e.g. $\bar{v}_{\rm H}$ or $\sigma_{\rm Na}$ ."446" The results of sodium-based measurements are further differentiated by indices referring to the origin of the line: e.g. vy; and vy, are velocities obtained. respectively. from interstellar and stellar component of the line."," The results of sodium-based measurements are further differentiated by indices referring to the origin of the line; e.g. $\bar{v}_{\rm Na,i}$ and $\bar{v}_{\rm Na,s}$ are velocities obtained, respectively, from interstellar and stellar component of the line."447 We also attempted to measure thevelocities with the help of the IRAF task FXCOR., We also attempted to measure thevelocities with the help of the IRAF task FXCOR.448 The measuring procedureconsisted of the following steps:, The measuring procedureconsisted of the following steps:449to its irregularities these values cannot be measured with the same degree of precision as for mode A. The B mode characteristically persists for less than 25 Ρι.,to its irregularities these values cannot be measured with the same degree of precision as for mode A. The B mode characteristically persists for less than 25 $P_1$.450" The third “drift” mode, C, displays three roughly stationary subpulse drift bands (P3/P»cz 0), with the components’ relative intensities being variable."," The third “drift” mode, C, displays three roughly stationary subpulse drift bands $P_3$ $P_2\approx 0$ ), with the components' relative intensities being variable."451 Mode C manifests itself in a complex variety of ways: most often the intensities of the three components are approximately equal to each another; see Fig. 4.., Mode C manifests itself in a complex variety of ways: most often the intensities of the three components are approximately equal to each another; see Fig. \ref{colourPS}.452" However, one or two of the components intermittently either turns off or notably weakens relative to the other two; every combination of the three constituent components was observed."," However, one or two of the components intermittently either turns off or notably weakens relative to the other two; every combination of the three constituent components was observed."453" The P5 value for mode is similar to that of mode A, taking into account the presenceC or absence of its three constituent features."," The $P_2$ value for mode C is similar to that of mode A, taking into account the presence or absence of its three constituent features."454 It is possible that the nearly vertical drift bands in mode C result from a near stoppage of carousel rotation; it is also possible that this is an effect of aliasing., It is possible that the nearly vertical drift bands in mode C result from a near stoppage of carousel rotation; it is also possible that this is an effect of aliasing.455" Because of the other similarities between modes A and C, it is likely that this “stopping” happens during what is otherwise known as mode A. The difference between modes A and is therefore only the carousel motion, not the fundamentalC subpulse structure."," Because of the other similarities between modes A and C, it is likely that this “stopping” happens during what is otherwise known as mode A. The difference between modes A and C is therefore only the carousel motion, not the fundamental subpulse structure."456" This dynamic accounts for the varying number of subpulses observed in mode C. In mode A, as the subpulses drift across the pulse window, anywhere between 1 and 3 may be seen depending on the modulationphase—1.e.,, see Fig. 6.."," This dynamic accounts for the varying number of subpulses observed in mode C. In mode A, as the subpulses drift across the pulse window, anywhere between 1 and 3 may be seen depending on the modulation, see Fig. \ref{modeA_modfold}."457" In mode C short bursts and nulls alternate quasiperiodically with each burst or null lasting some 10 Pi or so, and switching back and forth up to 10 times."," In mode C short bursts and nulls alternate quasiperiodically with each burst or null lasting some 10 $P_1$ or so, and switching back and forth up to 10 times."458" The length of these segments is very comparable to the P3 of mode A. Deich ffirst referred to mode D as ""chaotic""—that is, displaying little perceptible order in its subpulses."," The length of these segments is very comparable to the $P_3$ of mode A. Deich first referred to mode D as “chaotic”—that is, displaying little perceptible order in its subpulses."459" Our investigation has uncovered slightly different story for mode D. The mode-D emission doesa not usually span the entire pulse window, see Fig. 4.."," Our investigation has uncovered a slightly different story for mode D. The mode-D emission does not usually span the entire pulse window, see Fig. \ref{colourPS}."460" While its sparse subpulses are overshadowed by the bright and ordered ones of modes A, B and C, they appear to consistently have an underlying characteristic structure."," While its sparse subpulses are overshadowed by the bright and ordered ones of modes A, B and C, they appear to consistently have an underlying characteristic structure."461" Mode D's brightest subpulses appear approximately every 5-10 P, on the leading edge of its substantially narrower emission window.", Mode D's brightest subpulses appear approximately every 5–10 $P_1$ on the leading edge of its substantially narrower emission window.462 This withdrawal of emission in the profile wings is unique to mode D. Figure 5 gives partial polarized profiles for each of the four modes at L and P band., This withdrawal of emission in the profile wings is unique to mode D. Figure \ref{modalprofiles} gives partial polarized profiles for each of the four modes at L and P band.463 The profiles have different total power and total linear forms in the different modes., The profiles have different total power and total linear forms in the different modes.464 Most evident are their different modal widths in each of the bands., Most evident are their different modal widths in each of the bands.465 Mode A has the broadest modal profiles; see Figure 5(a).., Mode A has the broadest modal profiles; see Figure \ref{modeA}.466" Its L-band profile displays a nearly uniform distribution of linear power across the pulse window, showing only small dips that correspond to the subpulse separation."," Its L-band profile displays a nearly uniform distribution of linear power across the pulse window, showing only small dips that correspond to the subpulse separation."467" Its leading edge is marked by a distinct shoulder at both L and P band, also visible in the linear power, a feature hardly seen in any of the other modes at L band."," Its leading edge is marked by a distinct shoulder at both L and P band, also visible in the linear power, a feature hardly seen in any of the other modes at L band."468 The bright central subpulses in mode A display a linear power distribution that indicates there are in fact two distinct features that lead the central peak., The bright central subpulses in mode A display a linear power distribution that indicates there are in fact two distinct features that lead the central peak.469" They can be identified at both bands, though the second one is weaker at P band, nevertheless distinguishing itself as a unique feature."," They can be identified at both bands, though the second one is weaker at P band, nevertheless distinguishing itself as a unique feature."470" Also in both bands, the trailing subpulse features are brighter and more clearly defined than the leading ones."," Also in both bands, the trailing subpulse features are brighter and more clearly defined than the leading ones."471 The mode-B profiles display a slightly narrower FWHM than in mode A; see Table 2 and Fig. 2.., The mode-B profiles display a slightly narrower FWHM than in mode A; see Table \ref{modes} and Fig. \ref{modes}.472 The leading feature in mode A’s profile is clearly visible in mode B at P band but is very weak at L band; see Figure 5(b).., The leading feature in mode A's profile is clearly visible in mode B at P band but is very weak at L band; see Figure \ref{modeB}.473" At L band, the central peak of mode B occurs ~6° eearlier than in mode A; at P band the peaks of the two modes occur in the same location."," At L band, the central peak of mode B occurs $\sim$ earlier than in mode A; at P band the peaks of the two modes occur in the same location."474" The trailing feature in mode B is poorly defined, however this is likely due to the dense drift bands blurring the intensity distribution between the leading and trailing features, rather than a decrease of subpulse intensity."," The trailing feature in mode B is poorly defined, however this is likely due to the dense drift bands blurring the intensity distribution between the leading and trailing features, rather than a decrease of subpulse intensity."475 Mode C displays a FWHM width nearly as broad as that of mode A; see Table 2.., Mode C displays a FWHM width nearly as broad as that of mode A; see Table \ref{modes}.476" There is more evidence for the leading feature in the linear power distribution of mode C than in mode B. As in mode B, the central peak in mode C at L band is shifted eearlier relative to the peak in mode A, whereas at P band they occur at the same longitude."," There is more evidence for the leading feature in the linear power distribution of mode C than in mode B. As in mode B, the central peak in mode C at L band is shifted earlier relative to the peak in mode A, whereas at P band they occur at the same longitude."477 The trailing component is very well defined in mode in the profiles of both bands., The trailing component is very well defined in mode C in the profiles of both bands.478 Mode displays a significantlyC narrower profile at L band comparedD to the other modes., Mode D displays a significantly narrower profile at L band compared to the other modes.479" As in mode B, its leading component is very poorly defined at L band, though there is some evidence for it in the linear power distribution."," As in mode B, its leading component is very poorly defined at L band, though there is some evidence for it in the linear power distribution."480" At L band, the central peak of mode D is shifted approximately ccompared to that of mode A. At L band, the trailing feature is slightly more distinct in mode D than in mode B, though it remains weak."," At L band, the central peak of mode D is shifted approximately compared to that of mode A. At L band, the trailing feature is slightly more distinct in mode D than in mode B, though it remains weak."481 The trailing feature at P band is well defined., The trailing feature at P band is well defined.482" Mode changes are often punctuated by nulls, with two distinct exceptions: First, a small proportion of mode"," Mode changes are often punctuated by nulls, with two distinct exceptions: First, a small proportion of mode"483al.,al.484 2009a. b).," 2009a, b)."485 These observations. as well as those of substructures in clusters (e.g.. Forman Jones 1990: Briel οἱ al.," These observations, as well as those of substructures in clusters (e.g., Forman Jones 1990; Briel et al."486 1991: Escalera et al., 1991; Escalera et al.487 1994). strongly suggest that a significant fraction of clusters might have experienced merger events.," 1994), strongly suggest that a significant fraction of clusters might have experienced merger events."488 There are also observations which suggest that. cluster merging affects the global star formation in cluster member galaxies (e.g.. Caldwell et al.," There are also observations which suggest that cluster merging affects the global star formation in cluster member galaxies (e.g., Caldwell et al."489 1993: Caldwell Rose 1997: Miller et al., 1993; Caldwell Rose 1997; Miller et al.490 2003: Ferrari et al., 2003; Ferrari et al.491 2005)., 2005).492 These observations beg the kev question as to how and why some merging clusters show larger fractions of starburst and. post-starburst galaxies (han others (e.g.. Caldwell Rose 1997. Owen et al.," These observations beg the key question as to how and why some merging clusters show larger fractions of starburst and post-starburst galaxies than others (e.g., Caldwell Rose 1997, Owen et al."493 2005)., 2005).494 From a theoretical viewpoint. it is unclear whether and how cluster merging can significantly change (he number fractions of starburst ancl poststarburst galaxies.," From a theoretical viewpoint, it is unclear whether and how cluster merging can significantly change the number fractions of starburst and poststarburst galaxies."495 Bekki (1999) showed that the ime-dependent. Gdal fields of merging groups and clusters of galaxies can trigger secondary starbursts in their member galaxies and thus change the number [fractions of these galaxies., Bekki (1999) showed that the time-dependent tidal fields of merging groups and clusters of galaxies can trigger secondary starbursts in their member galaxies and thus change the number fractions of these galaxies.496 Fujita et al. (, Fujita et al. (4971999) showed that the star formation rates of galaxies curing a major cluster merger can decrease because of ram-pressure stripping of (he interstellar gas inilially within the galaxies.,1999) showed that the star formation rates of galaxies during a major cluster merger can decrease because of ram-pressure stripping of the interstellar gas initially within the galaxies.498 As such. the fractions of blue. actively star-lorming galaxies can decrease ancl (hen the fractions of poststarburst galaxies can increase.," As such, the fractions of blue, actively star-forming galaxies can decrease and then the fractions of poststarburst galaxies can increase."499 Recent numerical simulations have shown (hat strong ram pressure from the ICAI can significantly increase {he star formation rates in cluster galaxies (Bekki Couch. 2003: INronberger οἱ al., Recent numerical simulations have shown that strong ram pressure from the ICM can significantly increase the star formation rates in cluster galaxies (Bekki Couch 2003; Kronberger et al.500 2008)., 2008).501 Therefore. it is timely. (o revisit the question as to whether the rapidly evolving state of the ICM within a merging cluster can significantly change the number fractions of starburst and poststarburst galaxies.," Therefore, it is timely to revisit the question as to whether the rapidly evolving state of the ICM within a merging cluster can significantly change the number fractions of starburst and poststarburst galaxies."502 The purpose of this Letter is to thus show. for the first Gime. that cluster merging has the potential lo (rigeer star formation among a significant Traction of the meniber ealaxiesway: this “svuchronized” activity might be an important clue to better understanding and discriminating merger-driven galaxy evolution in cluster galaxy populations.," The purpose of this Letter is to thus show, for the first time, that cluster merging has the potential to trigger star formation among a significant fraction of the member galaxies: this “synchronized” activity might be an important clue to better understanding and discriminating merger-driven galaxy evolution in cluster galaxy populations."503 We investigate the orbital evolution of cluster member galaxies and the external pressure of the ICM surrounding the galaxies during the cluster merging phase. in order (o determine how such a dynamical event might influence the star formation histories of cluster populations.," We investigate the orbital evolution of cluster member galaxies and the external pressure of the ICM surrounding the galaxies during the cluster merging phase, in order to determine how such a dynamical event might influence the star formation histories of cluster populations."504 Our previous simulations showed that if the pressure of the ICAL becomes sullicientlv high. it can Wigeer the collapse of giant molecular clouds (GAICs) and hence bursts of star Formation in galaxies (Bekki Couch 2003: see also INronberger οἱ al.," Our previous simulations showed that if the pressure of the ICM becomes sufficiently high, it can trigger the collapse of giant molecular clouds (GMCs) and hence bursts of star formation in galaxies (Bekki Couch 2003; see also Kronberger et al."505 2008 Lor ranrpressure-induced star formation)., 2008 for ram-pressure-induced star formation).506" We thus adopt a model in which the star formation rates Οἱ galaxies in merging clusters are sienilicantlv increased if (he pressure (P2) of the ICM surrounding the galaxies exceeds the internal pressure of the GMCS,", We thus adopt a model in which the star formation rates of galaxies in merging clusters are significantly increased if the pressure $P$ ) of the ICM surrounding the galaxies exceeds the internal pressure of the GMCs.507satisfactory [or point sources. it breaks down for extended sources.,"satisfactory for point sources, it breaks down for extended sources."508" This is seen even for the conceptually simplest lens model. the point mass or Schwarzschild lens. which produces increasingly ""arcv images for extended: sources at small impact parameters to the lens."," This is seen even for the conceptually simplest lens model, the point mass or Schwarzschild lens, which produces increasingly “arcy” images for extended sources at small impact parameters to the lens."509" In order to account for the effects of gradients in the shear ancl convergence. a second-order Tavlor expansion of the eravitational field is required: approach of Bacon ct al.(2006)...the tensor termi. Dj), is associated with two additional lensing distortion terms ὃν further defining Σι|(Fo and G=6,|(Go. we note that the components of first (F) and second (G) Dlexion can be written: The components of first and second Hexion only require a subset of the tensor components. 2;;,. and do not depend On knowledge of Dyin. Du. Doo or Da."," In order to account for the effects of gradients in the shear and convergence, a second-order Taylor expansion of the gravitational field is required: Following the approach of \citet{bacon06}, the tensor term, $D_{ijk}$, is associated with two additional lensing distortion terms By further defining ${\cal F}={\cal F}_{1}+i{\cal F}_{2}$ and ${\cal G}={\cal G}_{1}+i{\cal G}_{2}$, we note that the components of first ${\cal F}$ ) and second ${\cal G}$ ) flexion can be written: The components of first and second flexion only require a subset of the tensor components, $D_{ijk}$, and do not depend on knowledge of $D_{112}$, $D_{121}$, $D_{212}$ or $D_{221}$."510 The relevance of this is cliscussecl in Section 3.3.., The relevance of this is discussed in Section \ref{sct:quant}. .511 For a circularly symmetric mass profile. the deflection angle 15 5. and the projected mass. A. is for surface density. X(|£D.," For a circularly symmetric mass profile, the deflection angle is where $\vert \xi \vert = \sqrt{\xi_1^2 + \xi_2^2 }$, and the projected mass, $M$, is for surface density, $\Sigma(\vert \xi \vert)$."512 This enables us to re-write equation (1)) as with critical surface density Defining the function we can now express the shear. convergence and first and second Hexion with their explicit. dependence on physical coordinates and surface mass density (see Paper E for full details): In this section. we describe how the rav-bundle method can be used as a numerical means of estimating [lexion along a given line-o[-5sight.," This enables us to re-write equation \ref{eqn:tle}) ) as with critical surface density Defining the function we can now express the shear, convergence and first and second flexion with their explicit dependence on physical coordinates and surface mass density (see Paper I for full details): In this section, we describe how the ray-bundle method can be used as a numerical means of estimating flexion along a given line-of-sight."513 We use the Schwarzschilcl lens model (hereafter. SL). as it provides us with simple analytic solutions for all of the relevant lensing properties.," We use the Schwarzschild lens model (hereafter, SL), as it provides us with simple analytic solutions for all of the relevant lensing properties."514 Llowever. since the SL has zero first flexion everywhere except at the origin. we emphasise the recovery of second Iexion with the RBAL whilst demonstrating that results remain consistent with zero first flexion.," However, since the SL has zero first flexion everywhere except at the origin, we emphasise the recovery of second flexion with the RBM, whilst demonstrating that results remain consistent with zero first flexion."515 We consider both backwards (lens plane to souree plane) and forwards (source plane to lens plane) rav-bundle propagation. as this separately allows us to constrain the appropriate bundle radius to use ancl to quantify the extent of the Hexion zone.," We consider both backwards (lens plane to source plane) and forwards (source plane to lens plane) ray-bundle propagation, as this separately allows us to constrain the appropriate bundle radius to use and to quantify the extent of the flexion zone."516 While knowledge of an image location uniquely defines he source location. in general. equation (1)) is not casily invertible to give. all image locations for a given source »oxition.," While knowledge of an image location uniquely defines the source location, in general, equation \ref{eqn:tle}) ) is not easily invertible to give all image locations for a given source position."517 While brute force” solution. methods can be used. (ee. Paczviisski 1986). the main alternative is to use inverse ràv-tracing in its direct form. as was introduce » dxavser.s Refsdal Stabell (1986). and. Schneider. Weiss (1986:1987). or in its hierachical tree-cocle form (Wounmnbsganss 1990:1000).," While “brute force” solution methods can be used (e.g. Paczyńsski 1986), the main alternative is to use inverse ray-tracing in its direct form, as was introduced by Kayser, Refsdal Stabell (1986) and Schneider Weiss (1986;1987), or in its hierachical tree-code form (Wambsganss 1990;1999)."518 Llere. light ravs are projectec xickwards from the observer. through the lens plane to the source plane. which is represented by a two-dimensional gri of source pixels.," Here, light rays are projected backwards from the observer, through the lens plane to the source plane, which is represented by a two-dimensional grid of source pixels."519 The dellection of each light rav is caleulatec with equation (1))., The deflection of each light ray is calculated with equation \ref{eqn:tle}) ).520 While rav-tracing methods are extremely well-suitec to studying statistical lensing cllects (e.g. the creation of magnification maps for studying probabilities of high magnification events in quasar microlensing). they are less well-suited for studying lensing effects along a given line-ol-sight.," While ray-tracing methods are extremely well-suited to studying statistical lensing effects (e.g. the creation of magnification maps for studying probabilities of high magnification events in quasar microlensing), they are less well-suited for studying lensing effects along a given line-of-sight."521 LE it were possible to write down an explicit analytic [orm for the null ecodesie equation. of general. relativity [or an arbitrary mass (ie. lens) distribution. the optical scalar equations (Sachs 1961: Dyer Roecler 1974). could be used to measure the changing shape of a (small) bundle of light rays as it propagates from the source to the observer.," If it were possible to write down an explicit analytic form for the null geodesic equation of general relativity for an arbitrary mass (i.e. lens) distribution, the optical scalar equations (Sachs 1961; Dyer Roeder 1974) could be used to measure the changing shape of a (small) bundle of light rays as it propagates from the source to the observer."522 Unfortunately. specifie solutions only exist for a. limited number of cases. such as light propogation in Swiss Cheese “inhomogeneous” Cosmologicalmodels (Llarper 1991). so an alternative approach is recquirecd.," Unfortunately, specific solutions only exist for a limited number of cases, such as light propogation in Swiss Cheese “inhomogeneous” cosmologicalmodels (Harper 1991), so an alternative approach is required."523The Orion A molecular cloud (L1641) is the nearest. giant molecular cloud (6GMC) containing the nearest regions of massive star-formation.,The Orion A molecular cloud (L1641) is the nearest giant molecular cloud (GMC) containing the nearest regions of massive star-formation.524 Because of its proximity it sullers little galactic extinction. and has been studied in [ar greater detail than other comparale regions in the Galaxy.," Because of its proximity it suffers little galactic extinction, and has been studied in far greater detail than other comparable regions in the Galaxy."525" The most recent formation of hichm:ws stars in the Orkü GMC is within the DecklinNeugebauerWleinmannLow (DN/IXL) region. about arcmin Northwest) from. the ""Trapezium star 65 Ori C. T""he explosive nature of this event is emonstrated dramatically by the infrared H2 and. FL] images of Allen Burton (09:3) and more recently Ixaifu et al. ("," The most recent formation of high–mass stars in the Orion GMC is within the Becklin–Neugebauer–Kleinmann–Low (BN/KL) region, about 1 arcmin Northwest from the Trapezium star $\theta^{1}$ Ori C. The explosive nature of this event is demonstrated dramatically by the infrared $_{2}$ and [FeII] images of Allen Burton (1993) and more recently Kaifu et al. ("5262000).,2000).527" ‘Bullets’ of matter are being ejected at huncdreds ofkms* to forma bipolar cone of molecular ""fingers! whose axis is perpendicular to the hot core traced by NIL; emission (Wilson ct al.", `Bullets' of matter are being ejected at hundreds of km $^{-1}$ to form a bipolar cone of molecular `fingers' whose axis is perpendicular to the hot core traced by $_{3}$ emission (Wilson et al.528 2000)., 2000).529 These ‘fingers’ are tipped by Llerbigaro (LULL) objects whose shocked. gas is visible at optica wavelengths(see Graham. Meaburn Redman 2003 for a recent association of these phenomena).," These `fingers' are tipped by Herbig--Haro (HH) objects whose shocked gas is visible at optical wavelengths (see Graham, Meaburn Redman 2003 for a recent association of these phenomena)."530 At radio and millimetre. wavelengths there are at leas two molecular outllows. one associated with the optical an near-infrarecl features just. described. ancl a second. Iow- outflow. first. detected through proper motions of ILO masers (Genzel et al.," At radio and millimetre wavelengths there are at least two molecular outflows, one associated with the optical and near-infrared features just described, and a second low-velocity outflow first detected through proper motions of $_{2}$ O masers (Genzel et al."531 1981)., 1981).532 The powerful. infrarec source LRe2 was originally thought to be the source. of the outllow. but more recent observations. in. particular of SiO masers (e.g. Greenhill et al.," The powerful infrared source IRc2 was originally thought to be the source of the outflow, but more recent observations, in particular of SiO masers (e.g. Greenhill et al."533 1998). suggest that raclio continuum source bof Alenten Reid(1995) is the more likely outflow source.," 1998), suggest that radio continuum source I of Menten Reid (1995) is the more likely outflow source."534 Source L is significantly olfset (hy ~0755) to the South of Mer., Source I is significantly offset (by $\sim$ 5) to the South of IRc2.535 Source Land the radio counterpart to BN have proper, Source I and the radio counterpart to BN have proper536"list the uused in our final sample, the host galaxy coordinates, the redshift of theSN,, the host galaxy stellar mass and mass-weighted age, the ccolor and stretch parameters, and the HR.","list the used in our final sample, the host galaxy coordinates, the redshift of the, the host galaxy stellar mass and mass-weighted age, the color and stretch parameters, and the HR."537 A complete list of the ffrom years two and three of the SSupernova Survey along with photometry and other associated data will be published inprep., A complete list of the from years two and three of the Supernova Survey along with photometry and other associated data will be published in.538". 'To determine if adding UV and near-IR photometry to optical data improves constraints on physical properties of our host galaxies, we examine the sample of 71 ggalaxies that have matches in both aand ((after all cuts are made)."," To determine if adding UV and near-IR photometry to optical data improves constraints on physical properties of our host galaxies, we examine the sample of 71 galaxies that have matches in both and (after all cuts are made)."539" We find that while adding aand ddata to the oobservations does not significantly change our resulting host masses, it does reduce the average uncertainties in the mass estimates (see Figure where the average uncertainty here is the mean of 1)),the upper and lower lo uncertainties."," We find that while adding and data to the observations does not significantly change our resulting host masses, it does reduce the average uncertainties in the mass estimates (see Figure \ref{figMassErrvz}) ), where the average uncertainty here is the mean of the upper and lower $1 \sigma$ uncertainties."540" The uncertainty in mass increases with redshift because the photometric errors increase with redshift, but adding UV and near-IR data reduces these uncertainties in mass overall by1796."," The uncertainty in mass increases with redshift because the photometric errors increase with redshift, but adding UV and near-IR data reduces these uncertainties in mass overall by."541. The addition of UV and near-IR data widens the range of the host age distribution while also reducing the average uncertainty in age on the whole by Figure 2))., The addition of UV and near-IR data widens the range of the host age distribution while also reducing the average uncertainty in age on the whole by (see Figure \ref{figHistAge}) ).542 Figure 3 shows a plot of (seemass-weighted average age versus the stellar mass of our of host , Figure \ref{figAgevMass} shows a plot of mass-weighted average age versus the stellar mass of our sample of host galaxies.543"T'he distribution exhibits the expected sampletrend that, in galaxies.general, the most massive galaxies are also the oldest."," The distribution exhibits the expected trend that, in general, the most massive galaxies are also the oldest."544" However, there appears to be an absence of low-mass old galaxies."," However, there appears to be an absence of low-mass old galaxies."545" 'This may be due to several factors, one of which is that for a given mass, older galaxies will be harder to detect by bbecause they are fainter in the optical due to a dearth of young, bright stars."," This may be due to several factors, one of which is that for a given mass, older galaxies will be harder to detect by because they are fainter in the optical due to a dearth of young, bright stars."546" This absence of small, old galaxies may also be due to the fact that these galaxies likely have a low SFR per unit mass and therefore do not produce many Type Ia events (vandenBerghal.2005;Sul"," This absence of small, old galaxies may also be due to the fact that these galaxies likely have a low SFR per unit mass and therefore do not produce many Type Ia events \citep{van90,man05,sul06}."547"livanet2006).. Figure 4 plots the ffit parameters, stretch and color, as a function of host galaxy mass-weighted average age."," Figure \ref{figSALTvAge} plots the fit parameters, stretch and color, as a function of host galaxy mass-weighted average age."548" By definition, higher values of stretch correspond to intrinsically brighterIa."," By definition, higher values of stretch correspond to intrinsically brighter."549. Our results indicate that intrinsically brighter ooccur preferentially in younger stellar populations., Our results indicate that intrinsically brighter occur preferentially in younger stellar populations.550" 'This is consistent with the known trend that brighter ooccur in late-type etal.1996a;Gallagher (Hamuy galaxies etal.2006),, and in bluerstar-forming environments (Sullivanetal.2000),, since these types of galaxies are generally(Hamuy also young."," This is consistent with the known trend that brighter occur in late-type \citep{ham96a,gal05}, star-forming galaxies \citep{sul06}, and in bluer environments \citep{ham00}, since these types of galaxies are generally also young."551" The trend we see of ccolor as a function of host age is not as clear; the distribution is essentially flat, although extreme values of color do seem to correlate with age."," The trend we see of color as a function of host age is not as clear; the distribution is essentially flat, although extreme values of color do seem to correlate with age."552" However, since the cparameterencapsulatesnotonlyintrinsicS ccolorbutalsopossibleextinctionduetodustinthehostgalaxy, N ade finit ccolorandhostage."," However, since the $c$ parameter encapsulates not only intrinsic color but also possible extinction due to dust in the host galaxy, a definitive statement cannot be made about the relation between color and host age."553Plotsof stretchandcolorversusthehostmassareno ," Plots of stretch and color versus the host mass are not shown here, though our results strongly resemble those found in \citet{how09}, \citet{nei09}, and \citet{sul10}."554Linear regression has a long history in where there are often measurement errors inastronomy both the “dependent” and “independent” variables.," Linear regression has a long history in astronomy where there are often measurement errors in both the “dependent"" and “independent"" variables."555" There is, however, no concensus on the best method to use when fitting a line."," There is, however, no concensus on the best method to use when fitting a line."556" Here, we fit for a linear dependence of HR with age and mass using the package LINMIX (Kelly 2007), as was used to determine the significance of trends with HR by Kellyetal.(2010)."," Here, we fit for a linear dependence of HR with age and mass using the package LINMIX \citep{kel07}, as was used to determine the significance of trends with HR by \citet{kel10}."557". LINMIX is a Bayesian approach to linear regression using a Markov chain Monte Carlo (MCMC) analysis, assuming that the measurement errors are Gaussian."," LINMIX is a Bayesian approach to linear regression using a Markov chain Monte Carlo (MCMC) analysis, assuming that the measurement errors are Gaussian."558 We make the assumption that our errors on the host properties are Gaussian and input into LINMIX the average of the upper and lower lo uncertainties as the error in the dependent variable., We make the assumption that our errors on the host properties are Gaussian and input into LINMIX the average of the upper and lower $1 \sigma$ uncertainties as the error in the dependent variable.559" When fitting, we do not add the intrinsic uncertainty (0.14 mag for SALT2)) in quadrature to the HR errors that is added by others when fitting for trends of host properties with HR (Kellyetal.2010;SullivanLampeitletal."," When fitting, we do not add the intrinsic uncertainty (0.14 mag for ) in quadrature to the HR errors that is added by others when fitting for trends of host properties with HR \citep{kel10,sul10,lam10}."560 This intrinsic uncertainty arises from the fit to the 2010)..Hubble diagram and is the amount of scatter that must be added to the distance modulus such that the reduced x? of the best-fit cosmology is close to unity., This intrinsic uncertainty arises from the fit to the Hubble diagram and is the amount of scatter that must be added to the distance modulus such that the reduced $\chi^2$ of the best-fit cosmology is close to unity.561 This is done in an attempt to account for unknown effects on, This is done in an attempt to account for unknown effects on562colour excess and metallicity agree with the SER. but the correlation is weaker than that between colour excess and metallicity.,"colour excess and metallicity agree with the SFR, but the correlation is weaker than that between colour excess and metallicity."563 Phe asymmetry in age does not match with the asvnunetry in any of the other parameters but the tightness in the relationship between age and metallicity (Figure 2 (£)) has potential in being exploited to make finer cuts in the morphological classification., The asymmetry in age does not match with the asymmetry in any of the other parameters but the tightness in the relationship between age and metallicity (Figure \ref{fig:asym} (f)) has potential in being exploited to make finer cuts in the morphological classification.564 Strong relationships between these properties allow for establishing criteria for. better ealaxy classification than if used on their own., Strong relationships between these properties allow for establishing criteria for better galaxy classification than if used on their own.565 The spread of galaxies at high asvnimetries in Figure 2 is highlv constrained., The spread of galaxies at high asymmetries in Figure \ref{fig:asym} is highly constrained.566 Liieh asvmunetries indicate that he distribution of the various physical properties will »f very “patchy., High asymmetries indicate that the distribution of the various physical properties will be very “patchy”.567 As a result. these properties will be ound in hiehly localised regions of each galaxy.," As a result, these properties will be found in highly localised regions of each galaxy."568 As hese properties have some relation to one another. it is ikely that they will all be found. in the same localisecl regions. resulting in hiehly asvnunetric galaxies having high asvmmetries for the measured attributes.," As these properties have some relation to one another, it is likely that they will all be found in the same localised regions, resulting in highly asymmetric galaxies having high asymmetries for the measured attributes."569" This also explains he large distributions of galaxies at low asvmametries as the distribution of physical properties within the galaxy will not oe ""patehy allowing for the bigger spread in the physical ooperties across the galaxy.", This also explains the large distributions of galaxies at low asymmetries as the distribution of physical properties within the galaxy will not be “patchy” allowing for the bigger spread in the physical properties across the galaxy.570 This spread will be largely independent of the other physical properties leading to lower correlations at low asvmimeltries., This spread will be largely independent of the other physical properties leading to lower correlations at low asymmetries.571 There is a limit of 2 for all the asvnimetry parameters in Figure 2.., There is a limit of 2 for all the asymmetry parameters in Figure \ref{fig:asym}.572 This is an artifact of the definition of asymmetry., This is an artifact of the definition of asymmetry.573 Asvmametry is defined as the absolute value of the difference in Lux between the original image and the same image rotated by 1807. divided by the Εαν of the original image.," Asymmetry is defined as the absolute value of the difference in flux between the original image and the same image rotated by $180\,^{\circ}$, divided by the flux of the original image."574 The maximum. possible value for asvmmetry that can be attained with this definition of asymmetry is two., The maximum possible value for asymmetry that can be attained with this definition of asymmetry is two.575 Performing the shapelet decomposition on the galaxy images using à shapelet order of 12 resulted in 91 coellicients per filter. making 455r coellicients per galaxy.," Performing the shapelet decomposition on the galaxy images using a shapelet order of 12 resulted in 91 coefficients per filter, making 455 coefficients per galaxy."576 A lower number of coefficients is insullicient to reproduce galaxy images reliably and even though a higher number of coelficients would have given a more accurate representation of the galaxy images it would have been too large to have been ellectively reduced bv the PCA., A lower number of coefficients is insufficient to reproduce galaxy images reliably and even though a higher number of coefficients would have given a more accurate representation of the galaxy images it would have been too large to have been effectively reduced by the PCA.577 A PCA was used to reduce the dimensionality of the results of the shapelet decomposition (Ixarhunen1947: 1978).," A PCA was used to reduce the dimensionality of the results of the shapelet decomposition \citep{Kar:47,Lov:78}."578. To carry out the PCA we first. used. the same procedure described in Welly&Melxay(2005) to caleulate the shapelet coetficients. with two notable dilferences.," To carry out the PCA we first used the same procedure described in \citet{KM:05} to calculate the shapelet coefficients, with two notable differences."579 As mentioned above. we do not artificially re-saniple the images to the same redshift.," As mentioned above, we do not artificially re-sample the images to the same redshift."580 Also. we use a Singular Value Decomposition (SVL) technique similar to the one described in Derryetal.(2004) to decompose the shapelet coellicients.," Also, we use a Singular Value Decomposition (SVD) technique similar to the one described in \citet{BHW:04} to decompose the shapelet coefficients."581 The SVD accounts for the loss of orthogonality in the shapelets that result. from the pixelization of the images., The SVD accounts for the loss of orthogonality in the shapelets that result from the pixelization of the images.582 llowever. unlike Berryctal.(2004).. the number of non-zero singular values is chosen in an objective manner.," However, unlike \citet{BHW:04}, the number of non-zero singular values is chosen in an objective manner."583 In our work. we chose the number of non-zero singular values to minimize the estimated. squared error between the true ealaxy image and the galaxy image reconstructed [roni the shapelet. coellicients.," In our work, we chose the number of non-zero singular values to minimize the estimated squared error between the true galaxy image and the galaxy image reconstructed from the shapelet coefficients."584. We use Steins Unbiased. IHisk Estimation to estimate this error (Stein1981)... which is easily calculated as a function of the number of non-zero singular values.," We use Stein's Unbiased Risk Estimation to estimate this error \citep{Stn:81}, which is easily calculated as a function of the number of non-zero singular values."585 The [first component contains the majority of the variance (27554)) in the cata set., The first component contains the majority of the variance $\approx$ ) in the data set.586 Even though the subsequent components contain a much lower fraction. of the variance they are nevertheless important., Even though the subsequent components contain a much lower fraction of the variance they are nevertheless important.587 The number of components was limited to 8. which contains of the total variance and is sullicient for our purposes.," The number of components was limited to 8, which contains of the total variance and is sufficient for our purposes."588 Discrimination between galaxy populations is not apparent in the first two panels of Figure 3. but becomes clear in the third. panel. plotting PCA 1 against PCA 4.," Discrimination between galaxy populations is not apparent in the first two panels of Figure 3, but becomes clear in the third panel, plotting PCA 1 against PCA 4."589 This bimodality in galaxy morphology has long been known to exist and it is related. to the two broad morphological classes of galaxies. cary ancl late twpes.," This bimodality in galaxy morphology has long been known to exist and it is related to the two broad morphological classes of galaxies, early and late types."590 Welly&/Melxay(2005) detected this same bimocality. between their 11 against 2.," \citet{KM:05} detected this same bimodality, between their 1 against 2."591 The fact that this bimodality is seen here in à higher order PCA component could be à result of many factors., The fact that this bimodality is seen here in a higher order PCA component could be a result of many factors.592 Welly&Melxay.(2005). carried out the principal component analysis using a sum-of-squares matrix while we used a covariance matrix.," \citet{KM:05}593 carried out the principal component analysis using a sum-of-squares matrix while we used a covariance matrix."594 Also. even though we used a sigma cut to limit any extreme outliers. there may still be fewer distant outliers that can significantly allect the results of PCA.," Also, even though we used a sigma cut to limit any extreme outliers, there may still be fewer distant outliers that can significantly affect the results of PCA."595 Thus the location of the bimodalitv in PCA space does not reveal any fundamental. property of galaxies as PCA is simply another way of representing the distribution of galaxies., Thus the location of the bimodality in PCA space does not reveal any fundamental property of galaxies as PCA is simply another way of representing the distribution of galaxies.596 The other separations in PCA space are very similar to the separations obtained by Welly&AlcIxay. (2005)., The other separations in PCA space are very similar to the separations obtained by \citet{KM:05}.597. Similarly. the galaxy. tvpes (or combination of them) that cach PCA component represents. will also. depend on the above factors.," Similarly, the galaxy types (or combination of them) that each PCA component represents will also depend on the above factors."598 To objectively identify particular classes contained within the PCAs. for à particular sample. one must apply a Alixture-ol-Gaussian methods. (Ixellv.&Ἀ]οίναν2004.2005). but this falls outside the aims of this experiment.," To objectively identify particular classes contained within the PCAs, for a particular sample, one must apply a Mixture-of-Gaussian methods \citep{KM:04,KM:05} but this falls outside the aims of this experiment."599 This analysis was reproduced for the sub-samples split into redshift bins., This analysis was reproduced for the sub-samples split into redshift bins.600 The distributions of galaxies in PCA space in each of the redshift bins are similar to the analysis with the full sample., The distributions of galaxies in PCA space in each of the redshift bins are similar to the analysis with the full sample.601 Furthermore. these distributions are consistent. with each other (Figure 4)). as well as those of Ixellv&Melxay(2005).," Furthermore, these distributions are consistent with each other (Figure \ref{fig:pca_bins}) ), as well as those of \citet{KM:05}."602.. These clistributions of galaxies in PCA space in each of the recdshift bins fall within very similar ranges., These distributions of galaxies in PCA space in each of the redshift bins fall within very similar ranges.603 DPhese similarities among the cilferent redshift bins allow us to conclude that. our. results. are not. strongly dependent on the treatment of the sample as a whole despite the range of redshift., These similarities among the different redshift bins allow us to conclude that our results are not strongly dependent on the treatment of the sample as a whole despite the range of redshift.604 Thus there is no need to simulate a common redshift. through artificially redshifting the galaxy images bv reducing their resolution. as implemented: by Iwelly&Melxay(2005).," Thus there is no need to simulate a common redshift, through artificially redshifting the galaxy images by reducing their resolution, as implemented by \citet{KM:05}."605. The principal components for the redshift bin subsamples are also correlated against the Dixel-z:CAS measurements below. to identify any potential statistical cüllerences.," The principal components for the redshift bin subsamples are also correlated against the Pixel-z:CAS measurements below, to identify any potential statistical differences."606 As with the Pixel-z::CCAS analysis. our objective is not to celine a classification svstem through the distribution of the QMM parameters of galaxies.," As with the CAS analysis, our objective is not to define a classification system through the distribution of the QMM parameters of galaxies."607 Rather we aim to identify relationships between the two methods to identify the connection between the multiwavelength morphology ancl the spatial distribution of the underlving. physical processes., Rather we aim to identify relationships between the two methods to identify the connection between the multiwavelength morphology and the spatial distribution of the underlying physical processes.608 The next step in our analysis is to quantify the relationships between the two methods., The next step in our analysis is to quantify the relationships between the two methods.609The reductions were carried out within IRAF (Image Reduction and Analysis Facility)'.,The reductions were carried out within IRAF (Image Reduction and Analysis Facility).610. All science frames were bias and flatfield corrected in a standard fashion., All science frames were bias and flatfield corrected in a standard fashion.611 The transformation to the Kron-Cousins system in RZ was based on standard stars selected from Landolt (1992)., The transformation to the Kron-Cousins system in $RI$ was based on standard stars selected from Landolt \cite*{landolt92}.612. Since the target objects are very red. care was taken to include the reddest dwarf stars from this list.," Since the target objects are very red, care was taken to include the reddest dwarf stars from this list."613 On a typical photometric night 10 different. standard fields were observed. each containing 3° stars on the average.," On a typical photometric night 10 different standard fields were observed, each containing 3 stars on the average."614 The colour range covered by the standard stars was 0<ΠΠ.fF«22. the red limit defined by G45-20 (ΜΟΝΟ. the reddest dwarf star in Landolt's list.," The colour range covered by the standard stars was $0 < R-I < 2.2$, the red limit defined by G45-20 (M6V), the reddest dwarf star in Landolt's list."615 83-33 (M5V) and G44-40 (M4V) were also used., G3-33 (M5V) and G44-40 (M4V) were also used.616 Transformation equations with linear colour terms were derived in a standard fashion. resulting in standard star residuals of less than 0.02 mag across the whole colour range.," Transformation equations with linear colour terms were derived in a standard fashion, resulting in standard star residuals of less than 0.02 mag across the whole colour range."617" The [J colours of our reddest targets indicate spectral types of -- MM9V, beyond the standard star range by ~ 0.3 mag in TJ."," The $I-J$ colours of our reddest targets indicate spectral types of $\sim$ M9V, beyond the standard star range by $\sim$ 0.3 mag in $R-I$."618 This is not a serious problem here. since even for a In N. standard stars provided by the ARNICA team were used (Huntetal.1995:Casali&Hawarden1992).," This is not a serious problem here, since even for a In $JK$, standard stars provided by the ARNICA team were used \cite{hunt95,casali92}."619. The Hunt transformation from ARNICA to the CIT system was adopted: JJT=JARXNKfX. VIJT=lanxwd0.12.," The Hunt transformation from ARNICA to the CIT system was adopted: $J_\mathrm{CIT} = J_\mathrm{ARNICA}$, $K_\mathrm{CIT} = K_\mathrm{ARNICA}+0.12$."620 The errors in these transformations are ~ 0.05 mag rms., The errors in these transformations are $\sim$ 0.05 mag rms.621 Night-to-night shifts in the zero point of up to 0.20 mag were noticed during the two ARNICA runs., Night-to-night shifts in the zero point of up to 0.20 mag were noticed during the two ARNICA runs.622 The errors in these shifts are ~0.05 mag rms., The errors in these shifts are $\sim0.05$ mag rms.623 Adding these two errors we end up with a final 1 calibration error in ο. A photometry of 0.07 mag.," Adding these two errors we end up with a final $1\,\sigma$ calibration error in the $JK$ photometry of 0.07 mag."624 The colour correction for 7 in the 7. fields was done by transforming [J (using a zero-point corrected 7) to RL via relations in Leggett (1992)., The colour correction for $I$ in the $IJ$ fields was done by transforming $I-J$ (using a zero-point corrected $I$ ) to $R-I$ via relations in Leggett \cite*{leggett92}.625. This procedure induced an extra error of 0.03 mag. and the final 10 transformation error in7 is 0.04 mag.," This procedure induced an extra error of 0.03 mag, and the final $1\,\sigma$ transformation error in$I$ is 0.04 mag."626 The extraction of instrumental magnitudes in the science fields was done with an empirical growth-curve technique outlined in Festin (1997).., The extraction of instrumental magnitudes in the science fields was done with an empirical growth-curve technique outlined in Festin \cite*{festin97a}.627 The completeness limit was defined as the magnitude at which (CNear.) vs 7 deviates from a straight line., The completeness limit was defined as the magnitude at which $N_\mathrm{stars}$ ) vs $I$ deviates from a straight line.628 This is justified by the model predictions in Fig. 3..," This is justified by the model predictions in Fig. \ref{Figcompleteness},"629 and by star counts in Santiago et al. (1996).," and by star counts in Santiago et al. \cite*{santiago96},"630. increasing to 7.=23.5. well beyond our limit.," increasing to $I=23.5$, well beyond our limit."631 The luminosity functions used in the model were taken from Gould et al., The luminosity functions used in the model were taken from Gould et al.632 (1997). (M Ss) and Scalo (1986) (WM <8)., \cite*{gould97} $M_\mathrm{V}>8$ ) and Scalo \cite*{scalo86} $M_\mathrm{V}<8$ ).633 The halo contribution was estimated from the model in Baheall Soneira (1980).. using an axis ratio of efa=0.6 and a local normalization of 1/500 of the local disk density.," The halo contribution was estimated from the model in Bahcall Soneira \cite*{bahcall80}, using an axis ratio of $c/a = 0.6$ and a local normalization of 1/500 of the local disk density."634 The disk model consisted for stars fainter than AA;=5 of two components. with scale heights and normalizations taken from Gould et al. (1997).," The disk model consisted for stars fainter than $M_\mathrm{V}=5$ of two components, with scale heights and normalizations taken from Gould et al. \cite*{gould97},"635. 700 pe (Gould upper limit). The completeness limit should be set as the magnitude at which the J counts start to decrease. which for our data occurs approximately at the same point as the deviation from a straight line.," 700 pc (Gould upper limit), The completeness limit should be set as the magnitude at which the $I$ counts start to decrease, which for our data occurs approximately at the same point as the deviation from a straight line."636 The completeness limits for the whole survey as defined by the worst cases are J= 21.1.7=15.5 in the 7 part. and J=51.1. R=22.3 (R=22.3—[~20.2 on the Pleiades sequence) in the #J part.," The completeness limits for the whole survey as defined by the worst cases are $I = 21.4$, $J = 18.8$ in the $IJ$ part, and $I = 21.4$, $R = 22.3$ $R = 22.3 \cor I\sim20.2$ on the Pleiades sequence) in the $RI$ part."637 For individual fields the internal magnitude error at the completeness limit is ~ 0.1 mag., For individual fields the internal magnitude error at the completeness limit is $\sim$ 0.1 mag.638 The best subframe of each combined 7 image was used to identify stars and binaries., The best subframe of each combined $I$ image was used to identify stars and binaries.639 Approximately 15000 sources were classified by eye as stars. binaries. galaxies or too faint for classification.," Approximately 15000 sources were classified by eye as stars, binaries, galaxies or too faint for classification."640 The final 7./ sample consists of 1513 stars brighter than the completeness limits in both filters., The final $IJ$ sample consists of 1513 stars brighter than the completeness limits in both filters.641 The corresponding number for RT is 693., The corresponding number for $RI$ is 693.642 Binaries and stars close to galaxies were checked by point- function fitting in addition to the routine procedure (Festin 1997).., Binaries and stars close to galaxies were checked by point-spread function fitting in addition to the routine procedure \cite{festin97a}. .643 Binaries that were resolved in 7 but remained, Binaries that were resolved in $I$ but remained644"this is the third brightest satellite in Aq-C-4, which has a V-band magnitude of —12.2 and a half-light radius of ~ 480pc.","this is the third brightest satellite in Aq-C-4, which has a V-band magnitude of $-12.2$ and a half-light radius of $\sim480$ pc."645" It has a very high mass fraction in stars and an unusual history, forming in series of violent major mergers at z~4 before being subjecteda to strong tidal disruption between z—2 and z—0."," It has a very high mass fraction in stars and an unusual history, forming in a series of violent major mergers at $z\sim4$ before being subjected to strong tidal disruption between $z=2$ and $z=0$."646 We discuss this satellite in detail in6., We discuss this satellite in detail in.647". In the highest resolution run, Aq-C-4, we expect the gravitational softening to be the main factor limiting the minimum sizes of star forming regions, since it is always larger than A;,gos."," In the highest resolution run, Aq-C-4, we expect the gravitational softening to be the main factor limiting the minimum sizes of star forming regions, since it is always larger than $\lambda_{J,EoS}$."648" In Aq-C-5 and Aq-C-6 (not shown here), which have lower threshold densities for star formation by factors of four and sixteen respectively, A;,gos at the threshold is comparable to the softening, so should also be important in setting the sizes of the stellar component."," In Aq-C-5 and Aq-C-6 (not shown here), which have lower threshold densities for star formation by factors of four and sixteen respectively, $\lambda_{J,EoS}$ at the threshold is comparable to the softening, so should also be important in setting the sizes of the stellar component."649" For both Aq-C-4 and Aq-C-5, the half-light radius of the most massive galaxy should not be limited by either effect and is consistent with the observations, given the large scatter."," For both Aq-C-4 and Aq-C-5, the half-light radius of the most massive galaxy should not be limited by either effect and is consistent with the observations, given the large scatter."650 The stellar kinematical properties of Local Group dwarf galaxies provide an important test of the cosmology., The stellar kinematical properties of Local Group dwarf galaxies provide an important test of the cosmology.651 Subhalos that form in N-body simulations of MW-mass systems appear to have potentials compatible with the stellar kinematics of the brightest MW satellites (?7)..," Subhalos that form in N-body simulations of MW-mass systems appear to have potentials compatible with the stellar kinematics of the brightest MW satellites \citep{Stoehr2002,StrigariFrenkWhite2010}."652" Nonetheless, the analytic calculations required to reach such conclusions necessarily include simplifying assumptions."," Nonetheless, the analytic calculations required to reach such conclusions necessarily include simplifying assumptions."653 Hydrodynamic simulations attempting to model star formation self consistently in a cosmological setting are inevitably some way behind the best N-body simulations in terms of resolution and must also model uncertain baryonic physics on sub-kiloparsec scales., Hydrodynamic simulations attempting to model star formation self consistently in a cosmological setting are inevitably some way behind the best N-body simulations in terms of resolution and must also model uncertain baryonic physics on sub-kiloparsec scales.654" As such, our simulations are not suitable for studying the detailed kinematics of the stars directly; instead, we resort to a somewhat cruder comparison and ask whether our satellites form in realistic potential wells, by comparing simulated and observationally determined masses."," As such, our simulations are not suitable for studying the detailed kinematics of the stars directly; instead, we resort to a somewhat cruder comparison and ask whether our satellites form in realistic potential wells, by comparing simulated and observationally determined masses."655 Historically there has been significant uncertainty associated with determining satellite masses from observations., Historically there has been significant uncertainty associated with determining satellite masses from observations.656" Typically, estimates are derived from the line-of-sight stellar velocity dispersion with three key assumptions: i) the system is spherically symmetric, ii) stellar orbits are isotropic and iii) the system is in equilibrium."," Typically, estimates are derived from the line-of-sight stellar velocity dispersion with three key assumptions: i) the system is spherically symmetric, ii) stellar orbits are isotropic and iii) the system is in equilibrium."657" Two recent studies have attempted a more general approach, with the aim of reducing the systematic uncertainties."," Two recent studies have attempted a more general approach, with the aim of reducing the systematic uncertainties."658" Using an approach based on the spherical Jeans equation, ? showed that for the brightest MW dSphs, the mass within the projected half-light radius is robust to changes in the anisotropy and underlying density profile."," Using an approach based on the spherical Jeans equation, \citet{Walker2009} showed that for the brightest MW dSphs, the mass within the projected half-light radius is robust to changes in the anisotropy and underlying density profile."659" This relation was explained analytically by ? who demonstrated that, if the stellar velocity dispersion profile remains relatively flat in the centre, as observations suggest (e.g.,?),, then the uncertainty introduced by assuming a particular anisotropy is minimised at the (3D) radius where the logarithmic slope of the stellar number density profile, —dlnn,/dlnr=3."," This relation was explained analytically by \citet{Wolf2010} who demonstrated that, if the stellar velocity dispersion profile remains relatively flat in the centre, as observations suggest \citep[e.g.,][]{Walker2007}, then the uncertainty introduced by assuming a particular anisotropy is minimised at the (3D) radius where the logarithmic slope of the stellar number density profile, ${\rm -dln}n_{*}/{\rm dln}r = 3$."660" They also showed that, for a range of realistic light profiles that have been used to model the MW dSphs, this minimum lies close to the (de-projected) half-light radius."," They also showed that, for a range of realistic light profiles that have been used to model the MW dSphs, this minimum lies close to the (de-projected) half-light radius."661" It is this radius, therefore, at which we choose to compare the enclosed masses of satellites in the simulations and observations."," It is this radius, therefore, at which we choose to compare the enclosed masses of satellites in the simulations and observations."662" In the previous subsection we described how aspects of our simulations, particularly the limitations of the subgrid treatment of the ISM and the gravitational softening scale, can set an artificial lower limit to the sizes of the stellar components of the satellites."," In the previous subsection we described how aspects of our simulations, particularly the limitations of the subgrid treatment of the ISM and the gravitational softening scale, can set an artificial lower limit to the sizes of the stellar components of the satellites."663" However, we also demonstrated that the luminosity function of the simulated satellites is close to that observed, the stellar mass in each satellite is relatively well converged and stellar mass is found to scale with subhalo mass similarly using an alternative modelling technique."," However, we also demonstrated that the luminosity function of the simulated satellites is close to that observed, the stellar mass in each satellite is relatively well converged and stellar mass is found to scale with subhalo mass similarly using an alternative modelling technique."664" With these checks in mind, we proceed with the assumption that the cooling, star formation and feedback prescriptions in our model result in a realistic stellar mass in each satellite, but that stars form in a configuration that is too diffuse."," With these checks in mind, we proceed with the assumption that the cooling, star formation and feedback prescriptions in our model result in a realistic stellar mass in each satellite, but that stars form in a configuration that is too diffuse."665" We then ask what the projected half-light radius of each simulated satellite at a fixed luminosity, based on the observed sizes of the brightest MW satellites."," We then ask what the projected half-light radius of each simulated satellite at a fixed luminosity, based on the observed sizes of the brightest MW satellites."666 We take a simple least-squares fit to the data points in (minimising the sum of the squared differences in the magnitude coordinate) and compute the scatter in the (log) radius coordinate about this line., We take a simple least-squares fit to the data points in (minimising the sum of the squared differences in the magnitude coordinate) and compute the scatter in the (log) radius coordinate about this line.667" For each simulated satellite, we assume a Gaussian distribution of possible sizes, with a mean equal to the fit evaluated at the satellite’s luminosity and dispersion defined by the observed scatter."," For each simulated satellite, we assume a Gaussian distribution of possible sizes, with a mean equal to the fit evaluated at the satellite's luminosity and dispersion defined by the observed scatter."668" Following this procedure we for magnitudes 12, findour that, fittotheobserveddataimpliessizesbelowthescaleatwhichsoftenedgr NewtonianintheAq−C Asimulation, whichleadstoanunderestimationo ftheenclosedmass."," Following this procedure we find that, for magnitudes $>-12$ , our fit to the observed data implies sizes below the scale at which softened gravitational forces become non-Newtonian in the Aq-C-4 simulation, which leads to an underestimation of the enclosed mass."669"W echoc 2,whichhasasmallersofteningscalebyafactorof~ 4, such that the fitted half-light radii of satellites down to My~—7.5 are larger than the force resolution."," We choose instead to measure the mass of each satellite in a much higher resolution dark matter only realisation of the simulation, Aquarius-C-2, which has a smaller softening scale by a factor of $\sim4$, such that the fitted half-light radii of satellites down to $\sim-7.5$ are larger than the force resolution."670 The central masses measured in the higher resolution simulation are typically forty to eighty percent higher for the ten brightest, The central masses measured in the higher resolution simulation are typically forty to eighty percent higher for the ten brightest671Because this is true for every i6—(elo...i)€RS. we deduce that la non-negative matvin.,"Because this is true for every $\bar{w}=(\bar{w}^1,\dots,\bar{w}^N)\in \R^N$, we deduce that $A$ a non-negative matrix."672 We refer the reader to El Hajj |?) and El Hajj.V-Forcadel |?| for a study in the specia case of a single slip direction. i.e. in (lie case =1.," $\hfill\Box$ We refer the reader to El Hajj \cite{EL} and El Hajj, Forcadel \cite{EF} for a study in the special case of a single slip direction, i.e. in the case $N=1$."673 Starting from the model (5.38))-(5.39)) where lor 7=1.....d. the function «ads L-periodic in ur. we now want to rescale (he unknowns to make the periodicity disappear.," Starting from the model \ref{EM:burger_loc}) \ref{EM:croissante}) ) where for $i=1,\dots,d$, the function $u^i(t,x)-l^i\cdot x$ is $1$ -periodic in $x$, we now want to rescale the unknowns to make the periodicity disappear."674 More precisely. we have the following Lemma: (5.43)) (1.1)) l.l ," More precisely, we have the following Lemma: \ref{EM:limit_p}) \ref{EM:burger}) \ref{EM:th1} "675"We derived the fundamental stellar parameters of HAT-P-14 using the following techniques, and the results are shown in Table 2..","We derived the fundamental stellar parameters of HAT-P-14 using the following techniques, and the results are shown in Table \ref{sparams}."676" First, we performed a spectral analysis using SME ?)., following the method of ?. and using the Kurucz model atmospheres (?).."," First, we performed a spectral analysis using SME \citep*[Spectroscopy Made Easy, see][]{VP96}, following the method of \citet{VF05} and using the Kurucz model atmospheres \citep{Kurucz84}."677 Individual NOT spectra were normalised and co-added to produce a single high signal-to-noise spectrum., Individual NOT spectra were normalised and co-added to produce a single high signal-to-noise spectrum.678" The4,,.. Na D and Mg b lines were fitted simultaneously to determine the spectral parameters."," The, Na D and Mg b lines were fitted simultaneously to determine the spectral parameters."679 This yielded the values == 6583 + 100 K and gc = 3.02 + 0.1. which indicatethat the star is of spectral type F5V (?)..," This yielded the values = 6583 $\pm$ 100 K and $_{\rm spec}$ = 4.02 $\pm$ 0.1, which indicatethat the star is of spectral type F5V \citep{Gray08}."680 Values for microturbulence --0.85kms )) and macroturbulence -- 528 L)are taken [rom the prescription of ?.., Values for microturbulence = 0.85 ) and macroturbulence = 5.28 ) are taken from the prescription of \citet{VF05}.681 The projected stellar rotation velocity /)) was determined to be ==84+1.0kms aand the metallically |M/H]| 2 0.08 + 0.10., The projected stellar rotation velocity ) was determined to be = 8.4 $\pm$ 1.0 and the metallically [M/H] = 0.08 $\pm$ 0.10.682" The mean stellar density (ρε). found from the light curve geometry, can be used as a luminosity indicator for stellar evolutionary models and often provides a stronger constraint than the value of {from spectral analysis (2).."," The mean stellar density $\rhostar$ ), found from the light curve geometry, can be used as a luminosity indicator for stellar evolutionary models and often provides a stronger constraint than the value of from spectral analysis \citep{Sozzetti07}."683" We used a Markov Chain MonteCarlo (MCMC) approach to globally model the photometric and radial velocity data (see Section ??)) and obtained a mean stellar density of 0.308,(i pos.", We used a Markov Chain MonteCarlo (MCMC) approach to globally model the photometric and radial velocity data (see Section \ref{Planet}) ) and obtained a mean stellar density of $^{+0.037}_{0.034}$ $\rho_{\astrosun}$.684" We then comparedτω |M/H] and wwith the theoreticalstellar evolutionary models of 2. to obtain the following stellar properties: == 136 + 0.04M... Age = 1.6 iri Gyr L, = (5i Le and gia, = 4.19 + 0.03."," We then compared, [M/H] and with the theoreticalstellar evolutionary models of \citet{Girardi00} to obtain the following stellar properties: = 1.36 $\pm$ 0.04, Age = 1.6 $^{+0.4}_{-0.3}$ Gyr, $_{*}$ = $_{-0.37}^{+0.54}$ $_{\astrosun}$ and $_{\rm iso}$ = 4.19 $\pm$ 0.03."685 The model isochrones are shown in Figure 5.., The model isochrones are shown in Figure \ref{iso}.686" The value of oobtained [rom the isochrone fit is somewhat larger than that found from spectral analysis, which was also noted by T10."," The value of obtained from the isochrone fit is somewhat larger than that found from spectral analysis, which was also noted by T10."687 We investigated the effect this higher wwould have on the fit to the spectral line shapes by fixing g;pc« to the isochrone value and reassessing the spectral analysis., We investigated the effect this higher would have on the fit to the spectral line shapes by fixing $_{\rm spec}$ to the isochrone value and reassessing the spectral analysis.688" We found that in orderto retain a good fit to the Mg b lines, the magnesium abundance IMg/H| must be reduced by 0.12 (in a similar fashion to WASP-1, see 2)) due to the inherent anti-correlation between |Mg/H] andg."," We found that in orderto retain a good fit to the Mg b lines, the magnesium abundance [Mg/H] must be reduced by 0.12 (in a similar fashion to WASP-1, see \citealt{Stempels07}) ) due to the inherent anti-correlation between [Mg/H] and."689. The degeneracies between the spectroscopic parameters do not rule out the higher vvalue as long as |Mg/H] is allowed to be under-abundant. and we take the uncertainty in (to include both values.," The degeneracies between the spectroscopic parameters do not rule out the higher value as long as [Mg/H] is allowed to be under-abundant, and we take the uncertainty in to include both values."690 Altering aand |Me/H] in this fashion had no significant effect on the derived effective temperature or metal abundance., Altering and [Mg/H] in this fashion had no significant effect on the derived effective temperature or metal abundance.691" To determine the properties of the planet HAT-P-14b, we simultaneously modelled the light curves and radial velocities with a global MCMC fit."," To determine the properties of the planet HAT-P-14b, we simultaneously modelled the light curves and radial velocities with a global MCMC fit."692 Details of this process are described in ?. and ?.., Details of this process are described in \citet{Cameron07} and \citet{Pollacco08}. .693 The free parameters in the fit are: orbital period P; transit epoch 75; transit duration Ty: squared ratio of planet, The free parameters in the fit are: orbital period $P$ ; transit epoch $T_{0}$ ; transit duration $T_{\rm dur}$ ; squared ratio of planet694with approximate hot blackbody colours (mainly single DB white dwarls). this is feasible.,"with approximate hot blackbody colours (mainly single DB white dwarfs), this is feasible."695 Further orbital period measurements would be needed to reduce the uncertainty in he colour evolution ancl orbital period distribution of the AM C¥n population., Further orbital period measurements would be needed to reduce the uncertainty in the colour evolution and orbital period distribution of the AM CVn population.696" The observed space density presented. here is. lower han expected from the population svnthesis mocels. which oediet 610"" ppe? for the pessimistic models to 3210 ppe for the optimistic models."," The observed space density presented here is lower than expected from the population synthesis models, which predict $6\times 10^{-6}$ $^{-3}$ for the pessimistic models to $3\times 10^{-5}$ $^{-3}$ for the optimistic models."697 At least one of he proposed dominant formation channels. the double-degenerate. WD channel. has to be suppressed. by at least an order of magnitude compared to the optimistic mocols. which assume that the mass transfer between white dwarfs can be stabilized in many cases due to a strong tidal coupling of spin and orbital angular momentum.," At least one of the proposed dominant formation channels, the double-degenerate WD channel, has to be suppressed by at least an order of magnitude compared to the optimistic models, which assume that the mass transfer between white dwarfs can be stabilized in many cases due to a strong tidal coupling of spin and orbital angular momentum."698 A significant effect of tidal coupling on the survival rate of AM. CVns fron the WD channel is possible only if the second. dominant formation channel. the single-degenerate Llo-star channel. is also severely. suppressed.," A significant effect of tidal coupling on the survival rate of AM CVns from the WD channel is possible only if the second dominant formation channel, the single-degenerate He-star channel, is also severely suppressed."699 We have presented. an inventory of ideas. based on current. theory. of how the formation channels may be suppressed relative το the models we have usec.," We have presented an inventory of ideas, based on current theory, of how the formation channels may be suppressed relative to the models we have used."700 Most of these (detachment of long-period AAL CVns. ignition of He|We WD aceretors) have only a limited effect. but inellicient common-envelope ejection in the Lle-star channel could potentially be effective in shutting down the Lle-star channel completely.," Most of these (detachment of long-period AM CVns, ignition of He+He WD accretors) have only a limited effect, but inefficient common-envelope ejection in the He-star channel could potentially be effective in shutting down the He-star channel completely."701 ]t is a pleasure to thank Jim Lichert and Chris Delove for stimulating cliscussions., It is a pleasure to thank Jim Liebert and Chris Deloye for stimulating discussions.702 GILAIU and Ελ were supported by NWO VIDI. grant. 639.042.201.VENI to DJ. Groot., GHAR and PJG were supported by NWO VIDI grant 639.042.201 to P.J. Groot.703 GN was supported by NWO gerant. 639.041.405. to Ci. Nelemans., GN was supported by NWO VENI grant 639.041.405 to G. Nelemans.704 Funding for the SDSS has been provided hy the Alfred PL Sloan Foundation. the Participating Institutions. the National Science. Foundation. the U.S. Department of Energy. the National Acronautics and Space Administration. the Japanese Monbukagakusho. the Alax Planck Society. and the Lieher Ecdueation Funding Council for. England.," Funding for the SDSS has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England."705 The SDSS is managed by the Astrophysical Research Consortium for the Participating lostitutions., The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions.706 The Participating lnstitutions are the American Museum of Natural History. Astrophysical Institute Potsdam. University of αρα. Cambridge University. Case Western Reserve University. University of Chicago. Drexel University. Fermilab. the. Institute for Advaneed Study. the Japan Participation Ciroup. Johns Lopkins University. the Joint Institute for Nuclear Astrophysics. the Ixavli Institute for Particle Astrophysics and. Cosmology. the Ixorcan Scientist Group. the Chinese Academy of Sciences (LAMOST). Los Alamos National Laboratory. the Alax-Planck-lostitute for Astronomy (AIPLA). the AMlax-Planck-Lostitute for Astrophysics (ALPA). New Mexico. State University. Ohio State University. University of Pittsburgh. University of Portsmouth. Princeton University. the United States Naval Observatory. and the University of Washington.," The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, Cambridge University, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington."707galaxies are unique; requiring all members of a subsample to be unique would skew the statistics 1981).,galaxies are unique; requiring all members of a subsample to be unique would skew the statistics .708". By matching our high- and low-density subsamples in stellar mass, redshift, as well as Sérrsic index, we are able to effectively study the correlation between galaxy size and environment at fixed stellar mass."," By matching our high- and low-density subsamples in stellar mass, redshift, as well as Sérrsic index, we are able to effectively study the correlation between galaxy size and environment at fixed stellar mass."709" To test whether our high-density subsample and the random low-density subsamples are consistent with being drawn from the same underlying stellar mass distribution, we apply two non-parametric (i.e., independent of Gaussian tests, the sided Kolmogorov-Smirnov assumptions)(KS) test and the one-sided Mann-Whitney (WMW) U test1947)."," To test whether our high-density subsample and the random low-density subsamples are consistent with being drawn from the same underlying stellar mass distribution, we apply two non-parametric (i.e., independent of Gaussian assumptions) tests, the two-sided Kolmogorov-Smirnov (KS) test and the one-sided Wilcoxon-Mann-Whitney (WMW) $U$ test."710" The result of each test (Mannis a P-value: the probability that a value of the KS or U statistic equal to the observed value or more extreme would be obtained, if the “null” hypothesis holds that the samples are drawn from the same parent distribution."," The result of each test is a $P$ -value: the probability that a value of the KS or $U$ statistic equal to the observed value or more extreme would be obtained, if the “null” hypothesis holds that the samples are drawn from the same parent distribution."711 The WMW U test is computed by ranking all elements of the two data sets together and then comparing the mean (or total) of the ranks from each data set., The WMW $U$ test is computed by ranking all elements of the two data sets together and then comparing the mean (or total) of the ranks from each data set.712" Because it relies on ranks rather than observed values, it is highly robust to non-Gaussianity."," Because it relies on ranks rather than observed values, it is highly robust to non-Gaussianity."713" The WMW test is particularly useful for small data sets comparedU to other related tests such as the chi-square (e.g.,two-sample test, 2003)), as we have when selecting galaxies from a narrow stellar mass range and in extreme environments, due to its insensitivity to outlying data points, its avoidance of binning, and its high efficiency."," The WMW $U$ test is particularly useful for small data sets (e.g., compared to other related tests such as the chi-square two-sample test, ), as we have when selecting galaxies from a narrow stellar mass range and in extreme environments, due to its insensitivity to outlying data points, its avoidance of binning, and its high efficiency."714" Note that since this test is one-sided, possible Pr; values rangefrom 0 to 0.5 (versus Pks which ranges from 0 to for a Py value below 0.025 closely to 1);2e for a we can reject the null (correspondinghypothesis (that the two samples Gaussian),have the same distribution) at greater than 9596 In Figure 3, we plot the cumulative distribution of stellar masses for the 93 sources in the high-density subsample alongside that for the 1000 random subsamples (each consisting of 93 galaxies) matched in redshift but residing in low-density environments."," Note that since this test is one-sided, possible $P_{U}$ values rangefrom $0$ to $0.5$ (versus $P_{\rm KS}$ which ranges from $0$ to $1$ ); for a $P_{U}$ value below $0.025$ (corresponding closely to $2\sigma$ for a Gaussian), we can reject the null hypothesis (that the two samples have the same distribution) at greater than $95\%$ In Figure \ref{fig_cdists}, we plot the cumulative distribution of stellar masses for the $93$ sources in the high-density subsample alongside that for the 1000 random subsamples (each consisting of $93$ galaxies) matched in redshift but residing in low-density environments."715" Performing a one-sided WMW test (and a two-sided KS test) on the size (Το) measurementsU for the low- and high-density populations, we find that the size distribution for the galaxies in high-density environments is skewed to larger sizes, with a probability of Pr;«0.01 (and Pks< 0.02)."," Performing a one-sided WMW $U$ test (and a two-sided KS test) on the size $r_{e}$ ) measurements for the low- and high-density populations, we find that the size distribution for the galaxies in high-density environments is skewed to larger sizes, with a probability of $P_{U} < 0.01$ (and $P_{\rm KS} < 0.02$ )."716" Meanwhile, the cumulative stellar mass, redshift, and Sérrsic index distributions for the low- and high-density subsamples, shown in the inset of Figure 3,, are well-matched with the WMW test yielding a Py>0.4."," Meanwhile, the cumulative stellar mass, redshift, and Sérrsic index distributions for the low- and high-density subsamples, shown in the inset of Figure \ref{fig_cdists}, are well-matched with the WMW $U$ test yielding a $P_{U} > 0.4$."717" This confirms that our sample-Uconstruction procedure has yielded sets of galaxies in low- and high-density environments whose redshift, mass, and Sérrsic index distributions match closely."," This confirms that our sample-construction procedure has yielded sets of galaxies in low- and high-density environments whose redshift, mass, and Sérrsic index distributions match closely."718" While not directly matched, the rest-frame color distributions for the two samples are also indistinguishable — not a surprising result given that the color-density relation shows no significant variation across the red sequence at a given luminosity"," While not directly matched, the rest-frame color distributions for the two samples are also indistinguishable — not a surprising result given that the color-density relation shows no significant variation across the red sequence at a given luminosity."719 See Table 1 for (Blantona complete summary of the probability2006).. values given by both the WMW U and KS tests., See Table \ref{res_tab1} for a complete summary of the probability values given by both the WMW $U$ and KS tests.720" The results of the WMW U test are confirmed by a comparison of the Hodges-Lehmann (H-L) estimator of the mean sizes for the low- and high-density subsamples, which differ by 0.54+0.22 h-! kpc."," The results of the WMW $U$ test are confirmed by a comparison of the Hodges-Lehmann (H-L) estimator of the mean sizes for the low- and high-density subsamples, which differ by $0.54 \pm 0.22$ $h^{-1}$ kpc."721 This reinforces the conclusion that there is a non-negligible size-environment relation on the red sequence at z~0.75., This reinforces the conclusion that there is a non-negligible size-environment relation on the red sequence at $z \sim 0.75$.722 The Hodges-Lehmann (H-L) estimator of the mean is given by the median value of the mean computed over all pairs of galaxies in the sample1963)., The Hodges-Lehmann (H-L) estimator of the mean is given by the median value of the mean computed over all pairs of galaxies in the sample.723". Like taking the median of a(Hodges distribution, the H-L estimator of the mean is robust to outliers, but, unlike the median, yields results with scatter (in the Gaussian case) comparable to the arithmetic mean."," Like taking the median of a distribution, the H-L estimator of the mean is robust to outliers, but, unlike the median, yields results with scatter (in the Gaussian case) comparable to the arithmetic mean."724" Thus, by using the H-L estimator of the mean, we gain robustness as in the case of the median, but unlike the median, our measurement errors are increased by only a few percent."," Thus, by using the H-L estimator of the mean, we gain robustness as in the case of the median, but unlike the median, our measurement errors are increased by only a few percent."725" In Figure 4,, we show the distribution of the differences between the Hodges-Lehmann estimator of the mean size, stellar mass, redshift, Sérrsic index, and color for the high-density subsample relative to that for each of the 1000 low-density subsamples, where the median difference in the H-L estimate of the mean size is Ar.=0.559 (as illustrated by the dashed vertical line) versus AMo)=—0.002, Az=—0.003, An=logy0.057,)(M,/h~? and A(U—B)=-—0.001 for stellar mass, redshift, Sérrsic index, and color, respectively (see Table 2))."," In Figure \ref{fig_hlmeans}, we show the distribution of the differences between the Hodges-Lehmann estimator of the mean size, stellar mass, redshift, Sérrsic index, and color for the high-density subsample relative to that for each of the $1000$ low-density subsamples, where the median difference in the H-L estimate of the mean size is $\Delta r_{e} = 0.559$ (as illustrated by the dashed vertical line) versus $\Delta \log_{10}({\rm M}_{\star} /726h^{-2}\ {\rm M}_{\sun}) = -0.002$, $\Delta z = -0.003$, $\Delta n =7270.057$, and $\Delta (U-B) = -0.001$ for stellar mass, redshift, Sérrsic index, and color, respectively (see Table \ref{res_tab2}) )."728" Within the stellar mass range of 10« 11, we find significant evidence for a correlation Mo)between galaxy size and environment at z~0.75, such that higher-density regions play host to larger galaxies at a given stellar mass on the red sequence."," Within the stellar mass range of $10 < \log_{10}({\rm729 M}_{\star} / h^{-2}\ {\rm M}_{\sun}) < 11$ , we find significant evidence for a correlation between galaxy size and environment at $z730\sim 0.75$, such that higher-density regions play host to larger galaxies at a given stellar mass on the red sequence."731 To test the robustness of our results to the, To test the robustness of our results to the732"Instead, a more subtle effect, also related to the narrow bandwidth oftheir observations might have been the culprit.","Instead, a more subtle effect, also related to the narrow bandwidth of their observations might have been the culprit."733 The velocity channels on the edge of the VLA bandpass are well known to be very noisy., The velocity channels on the edge of the VLA bandpass are well known to be very noisy.734" A continuum measurement based on these channels may have seriously underestimated the continuum flux density, and adversely affected the line to continuum ratio measurement."," A continuum measurement based on these channels may have seriously underestimated the continuum flux density, and adversely affected the line to continuum ratio measurement."735 Our results show that the excitation of the H66« line very nearly corresponds to LTE conditions., Our results show that the excitation of the $\alpha$ line very nearly corresponds to LTE conditions.736" In this situation, the line behaves as if it were approximately optically thin (see Rodrigguez 1982)."," In this situation, the line behaves as if it were approximately optically thin (see guez 1982)."737" Given its similar excitation and lower abundance. the He66a line will also behave as if it were approximately optically thin, so the integrated line intensity ratio provides a direct measure of the ionized helium over ionized hydrogen abundance ratio v.."," Given its similar excitation and lower abundance, the $\alpha$ line will also behave as if it were approximately optically thin, so the integrated line intensity ratio provides a direct measure of the ionized helium over ionized hydrogen abundance ratio $y^+$."738" From the unconstrained fit (Section 3), we obtain y—0.120.02, in good agreement with the value (0.10 + 0.01) found by Thum et ((1992) for the 41« lines."," From the unconstrained fit (Section 3), we obtain $y^+ = 0.12 \pm 0.02$, in good agreement with the value (0.10 $\pm$ 0.01) found by Thum et (1992) for the $\alpha$ lines."739" As à consequence of its relative abundance, the opacity of the helium lines 1s expected to be about 10 times less than that of the hydrogen lines, so the helium lines are not anticipated to be masing (even at mm wavelengths)."," As a consequence of its relative abundance, the opacity of the helium lines is expected to be about 10 times less than that of the hydrogen lines, so the helium lines are not anticipated to be masing (even at mm wavelengths)."740" This presumably explains why the helium lines associated with strongly masing hydrogen lines at mm, sub-mm, far-IR and mid-IR wavelengths have not been detected in existing observations."," This presumably explains why the helium lines associated with strongly masing hydrogen lines at mm, sub-mm, far-IR and mid-IR wavelengths have not been detected in existing observations."741" Since the hydrogen lines are tens of times stronger than thermal, the helium to hydrogen line intensity ratio will typically be less than at mm wavelengths."," Since the hydrogen lines are tens of times stronger than thermal, the helium to hydrogen line intensity ratio will typically be less than at mm wavelengths."742" The noise level of the mm observations was almost certainly adapted to detect the hydrogen lines, and was insufficient to reach the much weaker helium lines."," The noise level of the mm observations was almost certainly adapted to detect the hydrogen lines, and was insufficient to reach the much weaker helium lines."743" The high quality of the data presented here allows us to estimate the electron temperature of the ionized gas in MWC 3494. Following euez et (2009). and assuming LTE conditions. the electron temperature. 7;. of an ionized. partially optically-thick outflow is given by: where v; is the line frequency, Sc is the continuum flux density, 5; is the hydrogen peak line flux density, and Av ts the hydrogen FWHM line width."," The high quality of the data presented here allows us to estimate the electron temperature of the ionized gas in MWC 349A. Following guez et (2009), and assuming LTE conditions, the electron temperature, $T_e^*$, of an ionized, partially optically-thick outflow is given by: where $\nu_L$ is the line frequency, $S_C$ is the continuum flux density, $S_L$ is the hydrogen peak line flux density, and $\Delta v$ is the hydrogen FWHM line width."744 Using the helium abundance estimated above and the line and continuum parameters measured in Section 3. we obtain 77;=6.300600 K. This value is consistent with those determined from other radio observations (White Becker 1985:," Using the helium abundance estimated above and the line and continuum parameters measured in Section 3, we obtain $T_e^* = 6,300 \pm 600$ K. This value is consistent with those determined from other radio observations (White Becker 1985;"745In the standard A cold dark matter (LCDM) ποοἱ. small Gaussian perturbations in the dark matter density field. at carly times provide the seeds for the formation of structure in the Universe.,"In the standard $\Lambda$ cold dark matter (LCDM) model, small Gaussian perturbations in the dark matter density field at early times provide the seeds for the formation of structure in the Universe."746 The dark matter gravitationally collapses. and forms bound structures that eventually relax into a state of virial equilibrium.," The dark matter gravitationally collapses, and forms bound structures that eventually relax into a state of virial equilibrium."747 The number density of collapsed dark matter haloes at à given mass and epoch. the mass function. of these relaxed. haloes provides powerful constraints on the parameters of the LCDAM model (sece.g.llaimanctal.2001:Cunha&Ivrard 2010).," The number density of collapsed dark matter haloes at a given mass and epoch, the mass function, of these relaxed haloes provides powerful constraints on the parameters of the LCDM model \citep[see748e.g. ][]{Haiman01,Cunha10}."749.. Various analytical methocs (c.g.Press&Schechter1974:Bondetal.1991:ShethΓοι-men1999). also predict the halo mass function for collapsed. bound. and haloes in LCDM.," Various analytical methods \citep[e.g. ][]{PS, Bond91, ST} also predict the halo mass function for collapsed, bound, and haloes in LCDM."750 However. simulations ab high redshift. (2 1) have found that the majority. of collapsed. bound haloes are not in virial equilibrium (Jang- 2010).," However, simulations at high redshift $z > 1$ ) have found that the majority of collapsed, bound haloes are not in virial equilibrium \citep{JCH01,751Hetz06, Davis10}."752. Thus. there seems to be à mis- with simulations: they find. mass functions (which assume the haloes are virialized) that match the analytic predictions. anc vet the detailed structure of the haloes shows that they are not virialized.," Thus, there seems to be a mis-match with simulations; they find mass functions (which assume the haloes are virialized) that match the analytic predictions, and yet the detailed structure of the haloes shows that they are not virialized."753 In this paper. we explore in detail the virialization state of dark matter haloes at high redshift in order to understand this discrepancy.," In this paper, we explore in detail the virialization state of dark matter haloes at high redshift in order to understand this discrepancy."754 For an isolated: collapsed. bound dark matter halo in equilibrium. the scalar virial theorem. provides a simple relationship between the halo's total kinetic (A) and. potential (C) energies.," For an isolated collapsed, bound dark matter halo in equilibrium, the scalar virial theorem, provides a simple relationship between the halo's total kinetic $K$ ) and potential $U$ ) energies."755 In. LODAL. dark matter haloes are expected to reach virial equilibrium rapidlv upon collapse when they detach from the Llubble How.," In LCDM, dark matter haloes are expected to reach virial equilibrium rapidly upon collapse when they detach from the Hubble flow."756 The timescale for virialization is of the order of the dvnanücal time. which for a dark matter halo may be estimated as. f8]Pyes/ tone. Where {ιτ is the virial radius and Core the circular velocity. Poe=VOMHau.," The timescale for virialization is of the order of the dynamical time, which for a dark matter halo may be estimated as $t_r \approx \Rv/\Vc$ , where $\Rv$ is the virial radius and $\Vc$ the circular velocity, $\Vc = \sqrt{GM/\Rv}$."757 For a 10M. halo at z=6 this is roughly 1:105ves. or one percent of the Llubble time at that recdshift.," For a $10^7 \Msun$ halo at $z=6$ this is roughly $1 \times 10^8~ \mathrm{yrs}$, or one percent of the Hubble time at that redshift."758 Therefore. despite rapid. merging activity these haloes have had. sullicient time to reach virial equilibrium. but do not appear to do so in the simulations.," Therefore, despite rapid merging activity these haloes have had sufficient time to reach virial equilibrium, but do not appear to do so in the simulations."759 Llere we explore the energy. budget of these haloes. to determine why simulated. haloes at. high. redshift are apparently out of. virial equilibrium.," Here we explore the energy budget of these haloes, to determine why simulated haloes at high redshift are apparently out of virial equilibrium."760 Phere are. several possibilities which may explain this finding., There are several possibilities which may explain this finding.761 In this paper. we probe this issue by relaxing two assumptions tvpically mace when applving the virial theorem.," In this paper, we probe this issue by relaxing two assumptions typically made when applying the virial theorem."762 First. weinclude the non-negligible contributions of the environment to the halo's eravitational potential and. secondly. we do not truncate thedensity profile of the halo at the virial radius.," First, we include the non-negligible contributions of the environment to the halo's gravitational potential and secondly, we do not truncate thedensity profile of the halo at the virial radius."763 While, While764specifically made to extract BeppoSAX spectra.,specifically made to extract BeppoSAX spectra.765 It incorporates the current knowledge of the detectors. such as the point spread function. vignetting and absorption by the strong-backs.," It incorporates the current knowledge of the detectors, such as the point spread function, vignetting and absorption by the strong-backs."766 We used the response matrices of September 1997 and the standard background data (November 1998)., We used the response matrices of September 1997 and the standard background data (November 1998).767 However. there are still some uncertainties in the detector calibration. especially for off axis positions.," However, there are still some uncertainties in the detector calibration, especially for off axis positions."768 These uncertainties are larger for the LECS. which has a more complicated design than the MECS.," These uncertainties are larger for the LECS, which has a more complicated design than the MECS."769 For this reason we left the normalization of the LECS spectra and some off-axis MECS spectra free with respect to the on-axis MECS spectra., For this reason we left the normalization of the LECS spectra and some off-axis MECS spectra free with respect to the on-axis MECS spectra.770 The relative LECS normalizations turned out to be between 0.6 to 0.9. consistent with other BeppoSAX results (e.g. Favata et al. 1997)).," The relative LECS normalizations turned out to be between 0.6 to 0.9, consistent with other BeppoSAX results (e.g. Favata et al. \cite{Favata}) )."771 The spectra were binned to a bin size of roughly [/3rd the spectral resolution and some further rebinning was done for channels with low count rates., The spectra were binned to a bin size of roughly 1/3rd the spectral resolution and some further rebinning was done for channels with low count rates.772 In order to circumvent statistical problems with bins with very few counts we used a method proposed by Wheaton et al. (1995))., In order to circumvent statistical problems with bins with very few counts we used a method proposed by Wheaton et al. \cite{Wheaton}) ).773 This means that after obtaining a good fit. we used the best fit model to calculate the expected error per bin. instead of the observed counts.," This means that after obtaining a good fit, we used the best fit model to calculate the expected error per bin, instead of the observed counts."774 Using this method with two or three extra iterations gives in general a stable and in principle more reliable 47 value., Using this method with two or three extra iterations gives in general a stable and in principle more reliable $\chi^2$ value.775 Fitting six spectral regions simultaneously has the obvious disadvantage that the spectral model can become very complex., Fitting six spectral regions simultaneously has the obvious disadvantage that the spectral model can become very complex.776 So we took care to constrain the spectral model as far as possible without loosing too much of its heuristic qualities., So we took care to constrain the spectral model as far as possible without loosing too much of its heuristic qualities.777 For each sector we chose to have three to four spectral components., For each sector we chose to have three to four spectral components.778 A typical configuration consisted of the following components for each sky region: a power law component. one or two non-equilibrium ionization (NED thermal components and an absorption component (Morrison MeCammon 1983)).," A typical configuration consisted of the following components for each sky region: a power law component, one or two non-equilibrium ionization (NEI) thermal components and an absorption component (Morrison McCammon \cite{Morrison}) )."779 We only looked for spectral differences in the thermal emission between the Northern and Southern halves of the remnant., We only looked for spectral differences in the thermal emission between the Northern and Southern halves of the remnant.780 We assumed uniform abundances for SN 1006., We assumed uniform abundances for SN 1006.781 Based on their deprojection of the ROSAT PSPC image of SN 1006. Willingale et al. (1996))," Based on their deprojection of the ROSAT PSPC image of SN 1006, Willingale et al. \cite{Willingale}) )"782 reported that the synchrotron emission does not seem to originate from all around the remnant. but only from incomplete shells at the Northwest and Southeast of the remnant.," reported that the synchrotron emission does not seem to originate from all around the remnant, but only from incomplete shells at the Northwest and Southeast of the remnant."783 Consequently. in our simplest model we assume that no synchrotron emission is originating from the central region of the remnant.," Consequently, in our simplest model we assume that no synchrotron emission is originating from the central region of the remnant."784 This model produces a reasonable fit to the LECS spectra. but it does not fit the MECS spectra of the central regions above ~4 keV. where an excess i the observed spectra with respect to the model exists (Fig. 2)).," This model produces a reasonable fit to the LECS spectra, but it does not fit the MECS spectra of the central regions above $\sim$ 4 keV, where an excess in the observed spectra with respect to the model exists (Fig. \ref{hard_excess}) )."785 The temperature of the thermal components was {ιο1.5 keV. So clearly an additional emission component ts needed η order to fit the emission from the central regions., The temperature of the thermal components was $\sim 1.5$ keV. So clearly an additional emission component is needed in order to fit the emission from the central regions.786 This car be either a thermal component with an higher temperature. but it could also mean that the non-thermal emissior observed to come from the rims has in reality cylindrical symmetry. in which case the apparent structure of the remnant in rays may be due to an extreme case of limb brightening.," This can be either a thermal component with an higher temperature, but it could also mean that the non-thermal emission observed to come from the rims has in reality cylindrical symmetry, in which case the apparent structure of the remnant in X-rays may be due to an extreme case of limb brightening."787 The latter possibility would be in disagreement with the above mentioned ROSAT PSPC findings. but it is conceivable that the synchrotron emission is coming from such a thin layer that the deprojection scheme of Willingale et al. (1996))," The latter possibility would be in disagreement with the above mentioned ROSAT PSPC findings, but it is conceivable that the synchrotron emission is coming from such a thin layer that the deprojection scheme of Willingale et al. \cite{Willingale}) )"788 may not have worked adequately., may not have worked adequately.789 We investigated both possibilities., We investigated both possibilities.790 In. the case of an additional power law component we fixed the power law index of the central regions to a value of 2.8. similar to the the values found for the rims (see Table 2)).," In the case of an additional power law component we fixed the power law index of the central regions to a value of 2.8, similar to the the values found for the rims (see Table \ref{powerlaw}) )."791 We found. however. that an additional thermal component offers a better explanation.," We found, however, that an additional thermal component offers a better explanation."792 Only a hot thermal component fits adequately the Fe K emission seen, Only a hot thermal component fits adequately the Fe K emission seen793QSOs-25LAQ LRGs and. triangles. SDSS QSOs-28LACOQ LRGs.,QSOs-2SLAQ LRGs and triangles SDSS QSOs-2SLAQ LRGs.794 We see that the semi-projectec cross-correlation unction. confirms. our results in redshift-space. te. the measurements are in agreement regardless of the luminosity ofthe QSO sample.," We see that the semi-projected cross-correlation function confirms our results in redshift-space, i.e. the measurements are in agreement regardless of the luminosity of the QSO sample."795 This can also be confirmed by the fits to hese measurements shown in Table 5.., This can also be confirmed by the fits to these measurements shown in Table \ref{fig:table_wp}.796 Xs for the €(s) case. we also include the fits from the w(A) measurements of the whotometrie 2PSLAQ LRG sample. using Limber's formula.," As for the $\xi (s)$ case, we also include the fits from the $w(\theta )$ measurements of the photometric 2SLAQ LRG sample, using Limber's formula."797 The photometric fits are. again. in good agreement with he spectroscopic measurements. further supporting the idea hat the erosseclustering is independent of QSO luminosity.," The photometric fits are, again, in good agreement with the spectroscopic measurements, further supporting the idea that the cross-clustering is independent of QSO luminosity."798 Fig., Fig.799 11 shows the ii(om)/o results for the 2SLAQ (QSO-LRGs (filled. circles)., \ref {fig:projected2} shows the $w_p(\sigma)/\sigma$ results for the 2SLAQ QSO-LRGs (filled circles).800 As in the previous Section. we have also included the semi-projected correlation function results for the (2QZ|2PSLAQ) QSO (open circles) and the 25LAQ LRG-LRG (triangles) [rom da Angela et al. (," As in the previous Section, we have also included the semi-projected correlation function results for the (2QZ+2SLAQ) QSO (open circles) and the 2SLAQ LRG-LRG (triangles) from da $\hat{A}$ ngela et al. ("8012008) and Ross et al. (,2008) and Ross et al. (8022007). respectively.,"2007), respectively."803 We note that. at small scales 1 Mpe). although the results are noisier than for the £(s) measurements. QSO-LRG and QSO-OQSO measurements have a slightly smaller amplitude than the LRO-LRG one but to a much lesser degree than in the £68) measurements.," We note that, at small scales $\leq 3$ $^{-1}$ Mpc), although the results are noisier than for the $\xi (s)$ measurements, QSO-LRG and QSO-QSO measurements have a slightly smaller amplitude than the LRG-LRG one but to a much lesser degree than in the $\xi (s)$ measurements."804" This confirms our previous interpretation that the amplitude difference in the redshift-space measurements at small scales is due to the QSO redshift errors. an elfect which does not allect the w,fa)/o measurements."," This confirms our previous interpretation that the amplitude difference in the redshift-space measurements at small scales is due to the QSO redshift errors, an effect which does not affect the $w_p(\sigma)/\sigma$ measurements."805 On larger scales. wa)fr measurements confirm our previous observations for lower QSO-OSO amplitude comparing with the QSO-LI and the LRG-LRG amplitude.," On larger scales, $w_p(\sigma)/\sigma$ measurements confirm our previous observations for lower QSO-QSO amplitude comparing with the QSO-LRG and the LRG-LRG amplitude."806 Finally. the solid line shows our A7 fit to the QSO-LRG data from 525h ‘Alpe (for Consistency reasons with the €(s) fits). which gives ry=6.8noah IMpe and +=LT(3," Finally, the solid line shows our $\chi^2$ fit to the QSO-LRG data from $5-25$ $^{-1}$ Mpc (for consistency reasons with the $\xi (s)$ fits), which gives $r_0=6.8_{-0.3}^{+0.1}$ $^{-1}$ Mpc and $\gamma=1.7_{-0.3}^{+0.2}$."807 Chis is similar to the (28LAQ) LIG-LRG auto-correlation amplitude (ro=7.4530.35h. 1 Mpe) and both are higher than the (20Z|2S8LAQJ. QS&O-QSO amplitude (ro&5.0h. Alpe) at z—L4., This is similar to the (2SLAQ) LRG-LRG auto-correlation amplitude $r_0=7.45\pm0.35$ $^{-1}$ Mpc) and both are higher than the (2QZ+2SLAQ) QSO-QSO amplitude $r_0\simeq5.0$ $^{-1}$ Mpc) at $z=1.4$.808 Using the results. from the projected eross-correlation function. described in the previous Section. and following Saunders et al.," Using the results from the projected cross-correlation function, described in the previous Section, and following Saunders et al."809 1992. we can calculate the real-space correlation function. £(r). as follows: and assuming a step function for wi(m)=uw; we finally get forro.," 1992, we can calculate the real-space cross-correlation function, $\xi (r)$, as follows: and assuming a step function for $w_p(\sigma)=w_i$ we finally get, for $r=\sigma _i$."810 The QSO-25LAQ (spectroscopic) LRG real-space results are shown in bie. 12.., The QSO-2SLAQ (spectroscopic) LRG real-space results are shown in Fig. \ref{fig:xir}.811 In the same Figure we have also plotted the £67) fits from the QSO-photometric LRG w(A) measurements. described in Section 4.," In the same Figure we have also plotted the $\xi (r)$ fits from the QSO-photometric LRG $w(\theta )$ measurements, described in Section 4."812 ALL the samples seem to give consistent results although. as already mentioned. these €(r) measurements from the spectroscopic. samples are very noisy and no significant conclusions can be drawn.," All the samples seem to give consistent results although, as already mentioned, these $\xi (r)$ measurements from the spectroscopic samples are very noisy and no significant conclusions can be drawn."813 Finally. Table 6 shows the rj and > values from the fits to the spectroscopic samples. on scales of ὃςr<25h *Alpe.," Finally, Table \ref{fig:table_xir} shows the $r_0$ and $\gamma$ values from the fits to the spectroscopic samples, on scales of $\leq r\leq 25$ $^{-1}$ Mpc."814frequencies of the liishest peaks iu the 380 aud 175 plz regions vives vEMi /';0 with an accuracy better than ,frequencies of the highest peaks in the 380 and 475 $\mu$ Hz regions gives $\sqrt{3}$ /2 with an accuracy better than $\%$.815This nuuber was found iu other GW) Vir stars. as RNJ2211712112 and the central star of 11501 (Bond et al.," This number was found in other GW Vir stars, as 2117+3412 and the central star of 1501 (Bond et al."816 1996). aud is compatible with calculated trapping coefficieuts Usawaler Bradley 1991).," 1996), and is compatible with calculated trapping coefficients (Kawaler Bradley 1994)."817 When we discovered that the DET was unstable. we also tried to explain such apparent tine dependence of the DFT with a completely differeut quasi-periodic approach.," When we discovered that the DFT was unstable, we also tried to explain such apparent time dependence of the DFT with a completely different quasi-periodic approach."818 We considered the hvpothesis that the DFT temporal lustability was real aud due to a very short life time of the oscillations. which were continuously excited aud damped.," We considered the hypothesis that the DFT temporal instability was real and due to a very short life time of the oscillations, which were continuously excited and damped."819 We therefore applied to the 225321 data the Linear State Space model developed. by Michacl Iounie for the analysis of N-rav variability of AGN (xGnnie Tinuuer 1997. IKounie et al.," We therefore applied to the 2324 data the Linear State Space model developed by Michael Könnig for the analysis of X-ray variability of AGN (Könnig Timmer 1997, Könnig et al."820 1997)., 1997).821 The cient version of this program requires uniutermupted aud equally spaced datasets;, The current version of this program requires uninterrupted and equally spaced datasets.822 Moreover. iu order to provide reliable results. the Πο scales to be investigated must be sampled at least teu iues.," Moreover, in order to provide reliable results, the time scales to be investigated must be sampled at least ten times."823 The only part of our light curve which fulfills these criteria (JD 991.9. after rebinning with 20053) cau )e actually fitted with a period of bss and a damping inie of approximately 3.5 periods.," The only part of our light curve which fulfills these criteria (JD 94.9, after rebinning with s) can be actually fitted with a period of s and a damping time of approximately 3.5 periods."824 A further attempt has con done using a larger nearly wuiuterrupted part of the ight curve (JD 995.7). filliug the small ooOaps with white noise or with svuthetic data (both techniques give same results).," A further attempt has been done using a larger nearly uninterrupted part of the light curve (JD 95.7), filling the small gaps with white noise or with synthetic data (both techniques give same results)."825 The results are slirbitly different in this case: 215Iss and 3.1 periods., The results are slightly different in this case: s and 3.1 periods.826 Iu both cases from a I&-S test the residual is white noise with over 90% probabilitv., In both cases from a K-S test the residual is white noise with over $\%$ probability.827 If we trv to find a secondary period the results are unreliable (daanping time louecr than the dataset). but in auv case the inclusion of more frequencies does not iprove the fit.," If we try to find a secondary period the results are unreliable (damping time longer than the dataset), but in any case the inclusion of more frequencies does not improve the fit."828 Iu Figure 8 the fit from the Linear State Space model is compared with the iuultiàinusoidal fit: the quality is comparably ogood., In Figure 8 the fit from the Linear State Space model is compared with the multisinusoidal fit: the quality is comparably good.829 Despite this partial success; we cannot demoustrate that the damping nue found is really a fundamental quantity. constant over at least some davs.," Despite this partial success, we cannot demonstrate that the damping time found is really a fundamental quantity, constant over at least some days."830 We would need several datasets σαν. but uot necessarily colerent) of at least one dav leneth ) reject or corroborate this hwpothesis.," We would need several datasets (ideally, but not necessarily coherent) of at least one day length to reject or corroborate this hypothesis."831 Moreover. the excitation time-scale obtained from the Linear State Space model appears to be very short respect to the growth rates obtained frou CAV Vir non-adiabatie models.," Moreover, the excitation time-scale obtained from the Linear State Space model appears to be very short respect to the growth rates obtained from GW Vir non-adiabatic models."832 For these reasons the present results are uot convincing enough to abaudon the DFT results., For these reasons the present results are not convincing enough to abandon the DFT results.833 Qn the other haud. the inviting advantage of the quasi-periodic approach is the siiall umber of parameters required to describe the light curve.," On the other hand, the inviting advantage of the quasi-periodic approach is the small number of parameters required to describe the light curve."834 Unstable power spectra have been found also iu other luminous II159 stars (e.g. 22117123112) and [WC] CSPN (e.g. NGCT1501). variables., Unstable power spectra have been found also in other luminous 1159 stars (e.g. 2117+3412) and [WC] CSPN (e.g. 1501) variables.835 Changes were observed down to the time resolution of severa clays (Boud et al., Changes were observed down to the time resolution of several days (Bond et al.836 1996. 66).," 1996, 6)."837Low Surface Brightness (LSB) galaxies are the most unevolved class of galaxies in our nearby Universe (Impey Bothun 1997).,Low Surface Brightness (LSB) galaxies are the most unevolved class of galaxies in our nearby Universe (Impey Bothun \cite{ImpeyBothun1997}) ).838 They are optically dim with diffuse stellar. disks (Auld et al. 2006)).," They are optically dim with diffuse stellar disks (Auld et al. \cite{auld.etal.2006}) ),"839 massive HI gas disks (O'Neil et al. 2004:, massive HI gas disks (O'Neil et al. \cite{oneil.etal.2004};840 Matthews. van Driel. Monnier-Ragaigne 2001)) but have low star formation rates compared to regular. spiral galaxies (MeGaugh 1994)).," Matthews, van Driel, Monnier-Ragaigne \cite{matthews.etal.2001}) ) but have low star formation rates compared to regular spiral galaxies (McGaugh \cite{McGaugh.1994}) )."841 They are halo dominated galaxies (de Blok MeGaugh 1996:;: Kuzio de Naray. MeGaugh de Blok 2008:: Coceato et al. 2008)):," They are halo dominated galaxies (de Blok McGaugh \cite{deblok.etal.1996}; Kuzio de Naray, McGaugh de Blok \cite{KuziodeNaray.etal.2008}; Coccato et al. \cite{Coccato.etal.2008}) );"842 this may account for the weak spiral arms and small bar perturbations observed in these galaxies (Μήλος. de Blok MeGaugh 1997:; Mayer Wadsley 2004)).," this may account for the weak spiral arms and small bar perturbations observed in these galaxies (Mihos, de Blok McGaugh \cite{Mihos.etal.1997}; Mayer Wadsley \cite{Mayer.Wadsley.2004}) )."843 Although the most commonly observed LSB galaxies are the dwarf LSB galaxies (Sabatini et al. 2003)).," Although the most commonly observed LSB galaxies are the dwarf LSB galaxies (Sabatini et al. \cite{Sabatini.etal.2003}) ),"844 a significant fraction of LSB galaxies are large spirals having prominent bulges (Betjersbergen. de Blok van der Hulst 1999)).," a significant fraction of LSB galaxies are large spirals having prominent bulges (Beijersbergen, de Blok van der Hulst \cite{Beijersbergen.etal.1999}) )."845 These giant LSB (GLSB) galaxies have extended LSB disks that are poor in star formation and dust (Rahman et al. 2007::, These giant LSB (GLSB) galaxies have extended LSB disks that are poor in star formation and dust (Rahman et al. \cite{Rahman.etal.2007};846 Hinz et al. 2007))., Hinz et al. \cite{Hinz.etal.2007}) ).847 The bulge dominated GLSB galaxies often show AGN activity (Schombert 1998:: Das et al. 2009))., The bulge dominated GLSB galaxies often show AGN activity (Schombert \cite{Schombert.1998}; Das et al. \cite{Das.etal.2009}) ).848 Even though the optical properties of LSB galaxies have been investigated in great depth. not much is known about their molecular gas content.," Even though the optical properties of LSB galaxies have been investigated in great depth, not much is known about their molecular gas content."849 This is important as a knowledge of the cold gas distribution in LSB galaxies will help us understand star formation processes in these galaxies., This is important as a knowledge of the cold gas distribution in LSB galaxies will help us understand star formation processes in these galaxies.850 Surveys of LSB galaxies show that they have fairly massive HI disks that may be more than twice the size of the optical disk (de Blok et al. 1996::, Surveys of LSB galaxies show that they have fairly massive HI disks that may be more than twice the size of the optical disk (de Blok et al. \cite{deblok.etal.1996};851 Pickering et al. 1997::, Pickering et al. \cite{pickering.etal.1997};852 Das et al. 2007))., Das et al. \cite{Das.etal.2007}) ).853 In this paper we examine the molecular gas distribution in à GLSB galaxy and see how it relates to the overall star formation in its? disk., In this paper we examine the molecular gas distribution in a GLSB galaxy and see how it relates to the overall star formation in its' disk.854 Molecular gas has been detected in only a handful of LSB galaxies (ONeil. Hofner Schinnerer 2000:; Matthews Gao 2001 O'Neil. Schinnerer Hofner 2003:; Matthews et al. 2005:," Molecular gas has been detected in only a handful of LSB galaxies (O'Neil, Hofner Schinnerer \cite{oneil.etal.2000}; Matthews Gao \cite{matthews.gao.2001}; O'Neil, Schinnerer Hofner \cite{oneil.etal.2003}; Matthews et al. \cite{matthews.etal.2005};"855 Das et al. 2006))., Das et al. \cite{Das.etal.2006}) ).856 In most cases the galaxies were large spirals with extended optically dim disks., In most cases the galaxies were large spirals with extended optically dim disks.857 The low detection rate of molecular emission from LSB galaxies is probably due to several factors related to the poor star formation rate in these galaxies (e.g. de Blok van der Hulst 1998)); factors such as the lower dust content. lower metallicity and the lower surface denity of cold. neutral gas in these galaxies.," The low detection rate of molecular emission from LSB galaxies is probably due to several factors related to the poor star formation rate in these galaxies (e.g. de Blok van der Hulst \cite{deblok.vanderHulst.1998}) ); factors such as the lower dust content, lower metallicity and the lower surface denity of cold, neutral gas in these galaxies."858 All of these properties lead to a slower rate of gas cooling and molecule formation., All of these properties lead to a slower rate of gas cooling and molecule formation.859 For the few galaxies where molecular gas has been detected. not much is known about the gas extent and distribution.," For the few galaxies where molecular gas has been detected, not much is known about the gas extent and distribution."860 Such information is important if we want to understand star formation and disk evolution in LSB galaxies., Such information is important if we want to understand star formation and disk evolution in LSB galaxies.861 To investigate the molecular gas and star formation in GLSB galaxies we studied the CO distributior in a galaxy where molecular gas has been detected. F568-6 or Malin 2 as it is widely known (Das et al. 2006)).," To investigate the molecular gas and star formation in GLSB galaxies we studied the CO distribution in a galaxy where molecular gas has been detected, F568-6 or Malin 2 as it is widely known (Das et al. \cite{Das.etal.2006}) )."862 It is a nearly face-on GLSB galaxy at a distance of 201 Mpe., It is a nearly face-on GLSB galaxy at a distance of 201 Mpc.863 It has a prominent bulge and a very extended LSB disk., It has a prominent bulge and a very extended LSB disk.864 Its parameters are summarised in Table |., Its parameters are summarised in Table 1.865 There are several localized star forming regions distributed over its inner disk., There are several localized star forming regions distributed over its inner disk.866 Its metallicity is one third of the solar metallicity in value which is relatively high for an LSB galaxy (MeGaugh 1994))., Its metallicity is one third of the solar metallicity in value which is relatively high for an LSB galaxy (McGaugh \cite{McGaugh.1994}) ).867 The CO observations of Malin 2 were conducted using the HERA instrument mounted on the 30 m IRAM telescope., The CO observations of Malin 2 were conducted using the HERA instrument mounted on the 30 m IRAM telescope.868 Our main aim was to examine the molecular gas distribution: determine its extent. total gas mass and surface density.," Our main aim was to examine the molecular gas distribution; determine its extent, total gas mass and surface density."869 During March 2007 we observed the CO(2-1) line in Malin 2 with the HERA beam array (Schuster et al. 2004)), During March 2007 we observed the CO(2–1) line in Malin 2 with the HERA beam array (Schuster et al. \cite{Schuster.etal.2004}) )870 on the IRAM 30m telescope at a fequency of 220.372 GHz., on the IRAM 30m telescope at a fequency of 220.372 GHz.871 We specttically used this array as it has a wide field of view and good sensitivity., We specifically used this array as it has a wide field of view and good sensitivity.872 HERA is made of 9 receivers in a 3Χ array spaced by 24” on the sky., HERA is made of 9 receivers in a $3\times3$ array spaced by $24^{\prime\prime}$ on the sky.873 The backend used was the Wideband Line Multiple Autocorrelator (WILMA)., The backend used was the Wideband Line Multiple Autocorrelator (WILMA).874 The total bandwidth was 930 Hz: it was made up of 465 channels of 2MHz each., The total bandwidth was 930 Hz; it was made up of 465 channels of 2MHz each.875" The typical system temperatures 7,,, were in the range 200-250 K for 8 receivers: one receiver had a systematically higher T4, in the range 350-450K. The mean FWHM of each of the nine beams is 11.7"".", The typical system temperatures $T_{sys}$ were in the range 200-250 K for 8 receivers; one receiver had a systematically higher $T_{sys}$ in the range 350-450K. The mean FWHM of each of the nine beams is $11.7^{\prime\prime}$.876 As our main goal was to detect the CO emission line from the disk of Malin 2. we kept the array fixed on the sky in the standard pointed mode with the central beam pointed to the galactic nucleus: the field was tracked to get deep," As our main goal was to detect the CO emission line from the disk of Malin 2, we kept the array fixed on the sky in the standard pointed mode with the central beam pointed to the galactic nucleus; the field was tracked to get deep"877illustrated in Figure 3..,illustrated in Figure \ref{fig:hwp}.878 Alonochromatic linearly polarized light that passes through a HWI! rotating at a frequency. fy emerges linearly. polarized with its orientation rotating at 2fo., Monochromatic linearly polarized light that passes through a HWP rotating at a frequency $f_{0}$ emerges linearly polarized with its orientation rotating at $2f_{0}$.879 IHE this light then propagates through a fixed polarizer and its intensity is subsequentby nieasured. the resulting data stream will exhibit sinusoidal modulation at 4fo.," If this light then propagates through a fixed polarizer and its intensity is subsequently measured, the resulting data stream will exhibit sinusoidal modulation at $4f_{0}$."880 The amplitude of this modulation depends on the level of polarization of the incident radiation., The amplitude of this modulation depends on the level of polarization of the incident radiation.881 Perfectly polarized light will maximize the amplitude ancl perfectly unpolarized light will vield no moculation., Perfectly polarized light will maximize the amplitude and perfectly unpolarized light will yield no modulation.882 The advantage of HWDP polarimetry is that each detector in the array makes an independent measurement of the Stokes xuwameters of the incoming5 radiation., The advantage of HWP polarimetry is that each detector in the array makes an independent measurement of the Stokes parameters of the incoming radiation.883 In addition. this techniquei rejects svstematic errors.," In addition, this technique rejects systematic errors."884" Spatial polarization variations on the sky translate to temporal ampitude variations in the 4f, signal because the telescope is scanning.", Spatial polarization variations on the sky translate to temporal amplitude variations in the $4f_{0}$ signal because the telescope is scanning.885 Therefore. the polarization anisotropy. data will reside in the sidebands of the 4f signal in Fourier space.," Therefore, the polarization anisotropy data will reside in the sidebands of the $4f_{0}$ signal in Fourier space."886" Any spurious or systematic signals appearing in the data stream outside of this 4f, frequency band can be filtered. away with software during data analysis (sec Section 4)).", Any spurious or systematic signals appearing in the data stream outside of this $4f_{0}$ frequency band can be filtered away with software during data analysis (see Section \ref{sec:systematics}) ).887 The LWP is inherently a monochromatic device so the behavior described. above applies only to the frequencies v=mef2tAn where An is the dilference between the ordinary. ancl extraordinary. index of refraction in the birefringen crystal. £ is the propagation length through the ervstal. m is an odd integer and eis the speed of light.," The HWP is inherently a monochromatic device so the behavior described above applies only to the frequencies $\nu=mc/2t\Delta n$ where $\Delta n$ is the difference between the ordinary and extraordinary index of refraction in the birefringent crystal, $t$ is the propagation length through the crystal, $m$ is an odd integer and $c$ is the speed of light."888 Linearly polarized ligh at other frequencies emerges [rom the erystal ellipticallv polarized., Linearly polarized light at other frequencies emerges from the crystal elliptically polarized.889 We calculated the HP thickness that would minimize the fraction of clliptically polarizecL intensity and thereby optimize the overall polarimeter efficiency., We calculated the HWP thickness that would minimize the fraction of elliptically polarized intensity and thereby optimize the overall polarimeter efficiency.890 To do this. we found the maximum of the prodiict of the expected. ellieiencies for the 1H0 and 420 Cllz photomoeters as a function of ervsta thickness.," To do this, we found the maximum of the product of the expected efficiencies for the 140 and 420 GHz photometers as a function of crystal thickness."891 These expected ellieieney. curves incorporated the spectral breadth of the photometers and the convergence of ravs as they propagate through the LENP., These expected efficiency curves incorporated the spectral breadth of the photometers and the convergence of rays as they propagate through the HWP.892 The LENDP design that resulted from this caleulation is discussed in Section 2.3.., The HWP design that resulted from this calculation is discussed in Section \ref{sec:hwp}.893 ‘To ascertain the polarirneter elicieney. a polarized load was analvzed in the lab before Light.," To ascertain the polarimeter efficiency, a polarized load was analyzed in the lab before flight."894 For this measurement. a wire-grid. polarizer was mounted on the ervostat window with its transmission axis oriented parallel to that of the [οσα plane polarizer.," For this measurement, a wire-grid polarizer was mounted on the cryostat window with its transmission axis oriented parallel to that of the focal plane polarizer."895 Phermal radiation from a 273 Ix ice bath was chopped at ~6.5 Hz with a 300 Ix aluminum chopper blade Covered with 0.25 inch thick Eecosorlh LS-14 foam., Thermal radiation from a 273 K ice bath was chopped at $\sim$ 6.5 Hz with a 300 K aluminum chopper blade covered with 0.25 inch thick Eccosorb LS-14 foam.896 Phe LWP was then discretely stepped by hand in —5 intervals., The HWP was then discretely stepped by hand in $\sim$ $^{\circ}$ intervals.897 Twenty seconds of data were collected at cach LIP orientation., Twenty seconds of data were collected at each HWP orientation.898 The amplitude of the chopped signal in the bolometer time stream for one typical photometer was measured with a software lock-in analysis and then plotted in Figure 4.., The amplitude of the chopped signal in the bolometer time stream for one typical photometer was measured with a software lock-in analysis and then plotted in Figure \ref{fig:efficiency}.899 A nine parameter model consisting of sine waves for the first four harmonics of fy was then fit to the data (solid curve): fit. parameters included the amplitudes ancl phases of cach sine wave and an overall offset., A nine parameter model consisting of sine waves for the first four harmonics of $f_{0}$ was then fit to the data (solid curve); fit parameters included the amplitudes and phases of each sine wave and an overall offset.900 The level of polarization was then calculated from the fit parameters using the standard delinition P=Clineο|2lois) where Lis the amplitude of the 4f. signal.," The level of polarization was then calculated from the fit parameters using the standard definition $P = (A_{max} -901A_{min})/(A_{max} + A_{min})$ where $A$ is the amplitude of the $4f_{o}$ signal."902 This calibrated oad was measured to be polarized., This calibrated load was measured to be polarized.903 This corresponds to an overall polarimeter ellicieney of which is in agreement with predictions that take into account the LIN thie:kness. the known spectral response of the 140 11 photometers. the convergence of ravs at the aperature stop of the telescope and the wire-ericl polarizer elliciency.," This corresponds to an overall polarimeter efficiency of which is in agreement with predictions that take into account the HWP thickness, the known spectral response of the 140 GHz photometers, the convergence of rays at the aperature stop of the telescope and the wire-grid polarizer efficiency."904 Incident unpolarized ligit can become partially polarized inside the instrument if it reflects olf of the telescope mirrors at oblique angles., Incident unpolarized light can become partially polarized inside the instrument if it reflects off of the telescope mirrors at oblique angles.905 In additin. emission from the mirrors may also be partially polarized.," In addition, emission from the mirrors may also be partially polarized."906 To assess the level of instrumental polarization the procedure outlined above was repeated with unpolarized light., To assess the level of instrumental polarization the procedure outlined above was repeated with unpolarized light.907 We found the instrumental polarization to be for a typical 140 GLΖ channel., We found the instrumental polarization to be for a typical 140 GHz channel.908 The 3.4 mum thick A-cut sapphire LAVP was AR coated with a 0.013 inch thick wafer of Herasil to maximize transmission., The 3.4 mm thick A-cut sapphire HWP was AR coated with a 0.013 inch thick wafer of Herasil to maximize transmission.909 The Lerasil was bonded to the sapphire with Eccobond 24. an unfilled. low viscosity epoxy that was used to achieve eluc lavers as thin as 0.0005 inclres.," The Herasil was bonded to the sapphire with Eccobond 24, an unfilled, low viscosity epoxy that was used to achieve glue layers as thin as 0.0005 inches."910 For NLANIPOL-) we AR coated the LWP with a 0.010 inch thick laver of Stvcast 2850ET., For MAXIPOL-0 we AR coated the HWP with a 0.010 inch thick layer of Stycast 2850FT.911 The switch from Stveast to Herasil was made because Herasil thermally contracts in a way that is more compatible with sapphire., The switch from Stycast to Herasil was made because Herasil thermally contracts in a way that is more compatible with sapphire.912 Since the Alt coating was not birefringent. the two incident polarization orientations had. dillerent. coefficients. of rellection: this dillerential rellection. gave rise o à rotation svnchronous signal at a frequeney of 2fy.," Since the AR coating was not birefringent, the two incident polarization orientations had different coefficients of reflection; this differential reflection gave rise to a rotation synchronous signal at a frequency of $2f_{0}$."913 To minimize this elfect. we calculated the AR coating thickness that would minimize the dilference in reflection coefficients given the spectral breadth of the 140 011 pheXometers. the thickness of the eccobond 24 laver ancl the oblique incidence of rays.," To minimize this effect, we calculated the AR coating thickness that would minimize the difference in reflection coefficients given the spectral breadth of the 140 GHz photometers, the thickness of the eccobond 24 layer and the oblique incidence of rays."914 Because the 2fü signal resides out ofthe polarization signal xuicdiwith around 4fi it is not a source of svstematic error (see Section 4))., Because the $2f_{0}$ signal resides out of the polarization signal bandwith around $4f_0$ it is not a source of systematic error (see Section \ref{sec:systematics}) ).915 The focal plane wire-erid poarizer. mace by Buckbee-Moegrs. was constructed from electroformoed 0.0002 inch cianeter &old. wires bonded to 0.0)5 inch thick Mylar film at 250 lines per inch.," The focal plane wire-grid polarizer, made by Buckbee-Mears, was constructed from electroformed 0.0002 inch diameter gold wires bonded to 0.0015 inch thick Mylar film at 250 lines per inch."916" This Dexible material was mounted to a rigid ""roof-shaped frame that was positioned over the horn openings.", This flexible material was mounted to a rigid “roof-shaped” frame that was positioned over the horn openings.917" This ""roof-shaped"" polarizer reflected the unwanted polarization orientation ou tof the optical path ancl into blocks of millimeter-wave absorbing material O] mounted on either side of the focal plane.", This “roof-shaped” polarizer reflected the unwanted polarization orientation out of the optical path and into blocks of millimeter-wave absorbing material \cite{bockblack} mounted on either side of the focal plane.918 Tus design reduced spurious signals due to rellections., This design reduced spurious signals due to reflections.919 The UWP rotated at ~2 Hz during both ALANIPOL fights., The HWP rotated at $\sim$ 2 Hz during both MAXIPOL flights.920 Phis speed was selected because it provided eight measurements of the of Stokes parameters for one beam resolution clement per scan period while avoiding any significant Ευ signal attenuation from the 10 ms bolometer time constant., This speed was selected because it provided eight measurements of the of Stokes parameters for one beam resolution element per scan period while avoiding any significant $4f_{0}$ signal attenuation from the $\sim$ 10 ms bolometer time constant.921 During operation. this rotation speed. proved to be vibrationally gentle: it cid not excite any detectable mierophonic signals in the bolometer data.," During operation, this rotation speed proved to be vibrationally gentle; it did not excite any detectable microphonic signals in the bolometer data."922 The LWP was center turned near the Lyot stop of the telescope by a 0.078 inch ciameter driveshaft (see Figure 5))., The HWP was center turned near the Lyot stop of the telescope by a 0.078 inch diameter driveshaft (see Figure \ref{fig:polarimeter}) ).923 This driveshaft penetrated the tertiary mirror and the ervostat shell and was turned through a low-temperature ferrofluid, This driveshaft penetrated the tertiary mirror and the cryostat shell and was turned through a low-temperature ferrofluid924in the NLR.,in the NLR.925 We considered two key liue ratios: (1) The iuteusitv ratio gives a measure the Fe/Ne abundance ratio. (, We considered two key line ratios: (1) The intensity ratio gives a measure the Fe/Ne abundance ratio. (9262) The irafio eives a nicasure of the N/S abundance ratio. which js in turn a secondary nudicator of the overall iietallicitv of the eas.,"2) The ratio gives a measure of the N/S abundance ratio, which is in turn a secondary indicator of the overall metallicity of the gas."927 Our sample consists of 1571 quasars from SDSS Data Release 7 (DR)., 	Our sample consists of 1571 quasars from SDSS Data Release 7 (DR7).928" These objects were selected in the manner of the ""IIO"". sample of Salviaucderctal. (2007).. with the additional requirement of a signal-to- (S/N) ratio greater than 10 in the contiuuuna at ADLOO rest wavelength."," These objects were selected in the manner of the “HO3” sample of \citet{salviander07}, with the additional requirement of a signal-to-noise (S/N) ratio greater than 10 in the continuum at $\lambda5100$ rest wavelength."929 The flux and equivalent width (EW) of the broad line aud the optical bbleuds were measured with the aid of a spectrum fitting program described by Salviauderetal.(2007).. using a template fitting procedure to establish the flux iu rrelative to the local coutimmiun.," The flux and equivalent width (EW) of the broad line and the optical blends were measured with the aid of a spectrum fitting program described by \citet{salviander07}, using a template fitting procedure to establish the flux in relative to the local continuum."930 We characterized the comission streneth using the flux ratio of the 1570 bbleud to broadITJ.. following DG92.," We characterized the emission strength using the flux ratio of the 4570 blend to broad, following BG92."931. We used quasars at redshifts 0.2.<2<0.35 to eusure coverage of both A3125 and AGOST., We used quasars at redshifts $0.2 < z < 0.35$ to ensure coverage of both $\lambda3425$ and $\lambda6087$.932" Iu order to bring out the weak line. we binned the 1571 objects by streugth. and made five composite spectra of “very weak.” “weak.” Ποπ, cCstronss and “very strone” eenission."," In order to bring out the weak line, we binned the 1571 objects by strength, and made five composite spectra of “very weak,” “weak,” “medium,” “strong,” and “very strong” emission."933 These composites had 312 to 315 objects. within bius bounded by vvalues of 0. 0.215. (0.372. 0.521. 0.708. and 1.82. respectively.," These composites had 312 to 315 objects, within bins bounded by values of 0, 0.215, 0.372, 0.524, 0.708, and 1.82, respectively."934" Tudividual spectra were corrected for Calactic reddening using tle extinction values 4, given by the SDSS pipeline. and normalized to a mean fiux density oof unity using all wavelength poiuts in a particular spectrum."," Individual spectra were corrected for Galactic reddening using the extinction values $A_g$ given by the SDSS pipeline, and normalized to a mean flux density of unity using all wavelength points in a particular spectrum."935 The individual spectra in cach eroup were shifted iu wavelength to the rest frame aud re-biuned to a conmion waveleneth erid at a spacing of 1.11A., The individual spectra in each group were shifted in wavelength to the rest frame and re-binned to a common wavelength grid at a spacing of 1.41.936. The adopted composite spectrum was a mean of the τοπιο ffor all coutzxibutiug spectra at a given wavelength., The adopted composite spectrum was a mean of the rebinned for all contributing spectra at a given wavelength.937 The composite spectra are shown in Figures 6 and EL., The composite spectra are shown in Figures \ref{fig:comp} and \ref{fig:fene}.938 The region of the aaud line is shown iu Figure Ll., The region of the and line is shown in Figure \ref{fig:fene}.939 For a discussion of issues involving composite spectra of QSOs. see VandenBerketal (2001). and references therein.," For a discussion of issues involving composite spectra of QSOs, see \citet{vandenberk01}, and references therein."940" From these conrposites, we ieasured the eniüssion-liue fluxes of a nuniber of lines. including A5007. A3727. A3869. A3125. AAG716.6730. and AGOST. [Nov"," 	 From these composites, we measured the emission-line fluxes of a number of lines, including $\lambda5007$ , $\lambda3727$, $\lambda3869$, $\lambda3425$, $\lambda\lambda6716, 6730$, and $\lambda6087$."941]The results are|S givenup in Table 1 aud Figure 5.. where the vvalues are averages of the values for the individual spectra that compose cach composite.," The results are given in Table 1 and Figure \ref{fig:trend}, where the values are averages of the values for the individual spectra that compose each composite."942 Most lines were nieasured using a Caussian fit with the IRAF task SPLOT!., Most lines were measured using a Gaussian fit with the IRAF task SPLOT.943. The broad DBahliner cmissiou lines(Ia.. were measured using a Lorentzian profile.," The broad Balmer emission lines, ) were measured using a Lorentzian profile."944 Estimated uncertainties are 10:4 for the stronger lines. mcludiug σοι placement and faithfuluess of the fit.," Estimated uncertainties are $10\%$ for the stronger lines, including continuum placement and faithfulness of the fit."945 For aaud[Fevuv].. the uncertainty is as much as 20%. based on noise. contiuuunu uucertaimtyv. aud the presence of a stroug blue wing on both lines that we excluded frou the fit.," For and, the uncertainty is as much as $20\%$ , based on noise, continuum uncertainty, and the presence of a strong blue wing on both lines that we excluded from the fit."946 The A6583 and AGHI8 lines were fairly weak buups ouιν then] wines of the broad Hine and relatively difficult to measure., The $\lambda6583$ and $\lambda6548$ lines were fairly weak bumps on the wings of the broad line and relatively difficult to measure.947 Therefore we nüieasured the intensity by subtracting|[N11] from the bbleud a doublet with the theoretical 3.0-to-1 iutensitv ratio. cach line having a Gaussian profile with a central wavelength aud width based on the redshift and line width of A6716.," Therefore we measured the intensity by subtracting from the  – blend a doublet with the theoretical 3.0-to-1 intensity ratio, each line having a Gaussian profile with a central wavelength and width based on the redshift and line width of $\lambda6716$."948 The intensity of the doublet was adjusted so that the line had a smooth profile with no visible residual intensity or oyer-subtraction ofuj., The intensity of the doublet was adjusted so that the line had a smooth profile with no visible residual intensity or over-subtraction of.949. Exvor bars were estimated by determining Huteusities eiviug a slight under or over-subtraction as judged by eve., Error bars were estimated by determining intensities giving a slight under- or over-subtraction as judged by eye.950 This gave an uncertainty of about E124 for each composite., This gave an uncertainty of about $\pm12\%$ for each composite.951 Qur results will be diseussed ia terms of trends of observed line ratios., Our results will be discussed in terms of trends of observed line ratios.952 For actual ionic abunudauces. collision strengths from Berrington et al. (," For actual ionic abundances, collision strengths from Berrington et al. ("953"2000) and Osterbrock Ferland (2006) lead to the relation for an assumed T=15.000 IL based ou photoionizatiou models,","2000) and Osterbrock Ferland (2006) lead to the relation 	 for an assumed T=15,000 K based on photoionization models."954 Likewise. for the rratio we have for an assunied T=12.000 EK. These expressions eive the ionic abundance ratios. if collisional de-excitation isuuinuiportaut.," Likewise, for the ratio we have 	 for an assumed T=12,000 K. These expressions give the ionic abundance ratios, if collisional de-excitation isunimportant."955 NussbaunerἂνOsterbrock(1970) sugecsted that sshould be agood measure of the Fe/Ne ratio. based ou," \citet{nussbaumer70} suggested that should be agood measure of the Fe/Ne ratio, based on"956along with similar results for CON 339-I reported by Corbeletal.(2000. 2003).,"along with similar results for GX 339-4 reported by \citet{cor00,cor03}."957. The compact object iu CN 339-1 is also believed. to be a black hole (IIvnesetal.2003)., The compact object in GX 339-4 is also believed to be a black hole \citep{hyn03}.958. Corbeletal.(2000) find that for CUN 339-L. the radio Hux is stronglv correlated with both soft aud lard N-rax. covering the range 3-200 keV. in low-hard state. similar to he results obtained by us for (νο X-1.," \citet{cor00} find that for GX 339-4, the radio flux is strongly correlated with both soft and hard X-ray, covering the range 3-200 keV, in low-hard state, similar to the results obtained by us for Cyg X-1."959 Tf we cousider the results of the radio. soft N-rav aud ια Nav correlation analysis for these four sources. at first elance no consistent picture of the correlated variability pattern emerges.," If we consider the results of the radio, soft X-ray and hard X-ray correlation analysis for these four sources, at first glance no consistent picture of the correlated variability pattern emerges."960 However. it is maunuediatelv roticeable that Cve N-35 aud GRS 1915|105 have similar overall correlation pattern.," However, it is immediately noticeable that Cyg X-3 and GRS 1915+105 have similar overall correlation pattern."961 For both. the soft N-ray fux is correlated with the radio flux. aud the hard X-rav flux is anti-correlated with the both radio aud soft N-rav Hux.," For both, the soft X-ray flux is correlated with the radio flux, and the hard X-ray flux is anti-correlated with the both radio and soft X-ray flux."962 Additionally. the hardness ratio is also strongly auti-correlated with the radio flux.," Additionally, the hardness ratio is also strongly anti-correlated with the radio flux."963 Wide baud N-rav spectral analysis iu the hard state for both the sources at differeut radio Hux levels sugeests pivoting of the spectruu around 10 25 keV correlated with the radio emission., Wide band X-ray spectral analysis in the hard state for both the sources at different radio flux levels suggests pivoting of the spectrum around 10 – 25 keV correlated with the radio emission.964 Tt can also be noticed that correlation amoug the radio. soft aud hard X-ray fluxes for (νο N-1 and CX 339-1 is simular.," It can also be noticed that correlation among the radio, soft and hard X-ray fluxes for Cyg X-1 and GX 339-4 is similar."965 Both show a positive correlation among the racio. soft N-rav aud hard X-ray fluxes.," Both show a positive correlation among the radio, soft X-ray and hard X-ray fluxes."966 For Cyve N-1 the harducss ratio is not correlated with radio flux., For Cyg X-1 the hardness ratio is not correlated with radio flux.967 Further. Zdziarskietal.(2002) find a pivoting of the N-vay spectrum of Cre N-1 at higher energy of around 50-90 keV. Similarly. the wide baud N-rav to gamma-ray spectral analysis of CUN 339-1 AVardziushkietal.2002) has shown that there Is a pivoting in the spectra at energies ~300 keV in the low-hard state of the source.," Further, \citet{zdz02} find a pivoting of the X-ray spectrum of Cyg X-1 at higher energy of around 50-90 keV. Similarly, the wide band X-ray to gamma-ray spectral analysis of GX 339-4 \citep{war02} has shown that there is a pivoting in the spectrum at energies $\sim$ 300 keV in the low-hard state of the source."968 At this stage it will be worthwhile to note other simulavities iu the N-rav aud racio enission characteristics of Cre N-39 and GRS 1915|105 Cre N-1 aud CUN. 339-L., At this stage it will be worthwhile to note other similarities in the X-ray and radio emission characteristics of Cyg X-3 and GRS 1915+105 Cyg X-1 and GX 339-4.969 Most notable are that the first two sources are the strougest aud most variable radio sources amongst the Galactic N-vay binaries whereas both Cyve X-1 and OX 339-I1 are amonest the comparatively weak aud steacky radio sources., Most notable are that the first two sources are the strongest and most variable radio sources amongst the Galactic X-ray binaries whereas both Cyg X-1 and GX 339-4 are amongst the comparatively weak and steady radio sources.970 On the other hand. both (νο N-L and CX 339-Lb have a very hard A-rav spectruu compared to Cre N-3 and CRS 1915|105.," On the other hand, both Cyg X-1 and GX 339-4 have a very hard X-ray spectrum compared to Cyg X-3 and GRS 1915+105."971 Thus both X-rav sources with softer N-rav spectra ave a lower pivot euergv and (νο N-I with a much harder N-ray spectrum las à iimch higher pivot cherey. indicating hat the pivot energy is directly related to spectral shape.," Thus both X-ray sources with softer X-ray spectrum have a lower pivot energy and Cyg X-1 with a much harder X-ray spectrum has a much higher pivot energy, indicating that the pivot energy is directly related to spectral shape."972 The correlation between hard X-rav flux aud racio aud soft N-rav fluxes observed in (νο N-1 aud CX 339-L can hen be explained because hard X-ray flux (10 110 keV or (νο X-1. 20-200 keV for GX 2339-1) is arouud or below he pivot enerev in these two sources and will. therefore. ο correlated with the soft N-rav aud thereby the racio Huxes.," The correlation between hard X-ray flux and radio and soft X-ray fluxes observed in Cyg X-1 and GX 339-4 can then be explained because hard X-ray flux (40 – 140 keV for Cyg X-1, 20-200 keV for GX 339-4) is around or below the pivot energy in these two sources and will, therefore, be correlated with the soft X-ray and thereby the radio fluxes."973 Thus. it is quite evideut that N-rav fluxes below and above the pivot αιαον are auti-corrolated for these N-rayv sources aud the reported differences between radio. soft X-ray and hard X-ray correlation amongst these X-ray sources is an instrumental artifact where the RNTE-ASNI and CCRO-DATSE cuerev rauges are fixed aud the pivot energv varies fron source to source.," Thus, it is quite evident that X-ray fluxes below and above the pivot energy are anti-correlated for these X-ray sources and the reported differences between radio, soft X-ray and hard X-ray correlation amongst these X-ray sources is an instrumental artifact where the -ASM and -BATSE energy ranges are fixed and the pivot energy varies from source to source."974 This is supported by finding of Zdzirskictal.(2002) who report an anti-correlation between 1.5 90 keV and 100 300 keV fiux and find a very weak correlation between 1.5 3.0 keV and ο 100 keV flux for (νο N-1 in the low-hard state., This is supported by finding of \citet{zdz02} who report an anti-correlation between 1.5 – 3.0 keV and 100 – 300 keV flux and find a very weak correlation between 1.5 – 3.0 keV and 20 – 100 keV flux for Cyg X-1 in the low-hard state.975 Thus the N-ray radio behavior of these N-ray sources are cousisteut in terius of correlation between soft N-rav. παντα N-rav and radio ciissious reported here.," Thus the X-ray – radio behavior of these X-ray sources are consistent in terms of correlation between soft X-ray, hard X-ray and radio emissions reported here."976 Iu the previous sub-section we have shown that the X-rav radio eniüssion Characteristics in the hard states of the lughly variable sources (νο X-3 aud GRS 1915|105 are simular to those seen iu the low-hard states of the well studied black hole sources (νο XN-1 aud GNX 339-1. once we assune differeut pivot energy correlated to the radio enüssion.," In the previous sub-section we have shown that the X-ray radio emission characteristics in the hard states of the highly variable sources Cyg X-3 and GRS 1915+105 are similar to those seen in the low-hard states of the well studied black hole sources Cyg X-1 and GX 339-4, once we assume different pivot energy correlated to the radio emission."977 Here we explore whether the suppressed radio cnussion seen in the high-soft states of Cve δν (Drocksoppotal.1999) and CX 339-I (Corboletal.2000) are seen in these two sources., Here we explore whether the suppressed radio emission seen in the high-soft states of Cyg X-1 \citep{bro99} and GX 339-4 \citep{cor00} are seen in these two sources.978" We must caution that the identification of various spectral states using monitoriug data is frauelt with difficulties of flaring ciissious which could be quite delaved im the various emission αλά»,", We must caution that the identification of various spectral states using monitoring data is fraught with difficulties of flaring emissions which could be quite delayed in the various emission bands.979 Corbeletal.(2000). show that with the X-ray state transition from low-hard to high-soft the radio cutissiou evolves frou a jet like svuchrotron cussion to quenched. Cluission in CX 339-1., \citet{cor00} show that with the X-ray state transition from low-hard to high-soft the radio emission evolves from a jet like synchrotron emission to quenched emission in GX 339-4.980 This state is generallv preceded by a low-hard N-rav (with correlated radio enussion) aud followed by au X-ray off state (with radio off), This state is generally preceded by a low-hard X-ray (with correlated radio emission) and followed by an X-ray off state (with radio off).981 For a conpurative analysis we plot the radio (GBI. 2.2C€1IIz) and soft N-rav GCROXTE-ASML 2-12 keV) scatter diagram in Figure | for Cyg N-3 pancl). GRS 19151105 panel) (νο N-1 panel). for the nou Having states. which iuclude hard as well as soft states.," For a comparative analysis we plot the radio (GBI, 2.2GHz) and soft X-ray -ASM, 2-12 keV) scatter diagram in Figure \ref{fig4} for Cyg X-3 ), GRS 1915+105 ) Cyg X-1 ), for the non flaring states, which include hard as well as soft states."982 We have attempted to distinguish the hieh aud low states x the soft N-rav fux and denoted them by open aud filled sxaubols. respectively.," We have attempted to distinguish the high and low states by the soft X-ray flux and denoted them by open and filled symbols, respectively."983 For €vg ο the major flares are excluded. and iu the process we have excluded. the (very low) quenched radio emission inniediatelv preceding he major flares.," For Cyg X-3 the major flares are excluded, and in the process we have excluded the (very low) quenched radio emission immediately preceding the major flares."984 For GRS 1915|105. too. the data for he radio flares are excluded.," For GRS 1915+105, too, the data for the radio flares are excluded."985 It is evident that eveu or these two sources the radio enmüssiou i8 suppressed in the high state. analogous to the canonical high-soft state.," It is evident that even for these two sources the radio emission is suppressed in the high state, analogous to the canonical high-soft state."986 οσο N-3 shows a very systematic behaviour. with he radio positively correlated to the soft N-rav in the wad state. until if transits to the soft state. where the radio clussion is uceatively correlated to the soft Nav cluission.," Cyg X-3 shows a very systematic behaviour, with the radio positively correlated to the soft X-ray in the hard state, until it transits to the soft state, where the radio emission is negatively correlated to the soft X-ray emission."987 For GRS 1915|105 the transition iuto the sof state with suppressed radio emission is not that drastic bu definitely pronounced., For GRS 1915+105 the transition into the soft state with suppressed radio emission is not that drastic but definitely pronounced.988 (νο X-1 shows a iore scattere assoclatiou between the radio and ταν enusson. bu je suppression of the radio emission with higher ASA flux is evideut.," Cyg X-1 shows a more scattered association between the radio and X-ray emission, but the suppression of the radio emission with higher ASM flux is evident."989 Hence. it can be comfortably clauue lat the suppression of the radio enmüssiou with the X-rav state transition is a ecuerally consistent feature of je N-vav binary systems (BCs). mrespective of their oeidividual spectral characteristics.," Hence, it can be comfortably claimed that the suppression of the radio emission with the X-ray state transition is a generally consistent feature of the X-ray binary systems (BHCs), irrespective of their individual spectral characteristics."990 Therefore a cousisteu victure of the aceretion-ejection picture is enmiergiue from 1e observational analysis of sources with apparently very iverse behavioural patterus., Therefore a consistent picture of the accretion-ejection picture is emerging from the observational analysis of sources with apparently very diverse behavioural patterns.991 Tn the previous two sub-sections we have shown that the four sources. viz.," In the previous two sub-sections we have shown that the four sources, viz."992 Cre N- GRS 19151105. Cre X-l and CX 339-1. all show a consistent picture of accretion-ejection mechanisu. with the radio omission correlated to the ταν spectral pivoting iu the low state," Cyg X-3, GRS 1915+105, Cyg X-1 and GX 339-4, all show a consistent picture of accretion-ejection mechanism, with the radio emission correlated to the X-ray spectral pivoting in the low state"993In next section we explore (he consequences of the existence of an escape flix for the origin of Cosmic ravs in supernova remnants.,In next section we explore the consequences of the existence of an escape flux for the origin of cosmic rays in supernova remnants.994 The acceleration process in supernova remnants is expected to work in qualitatively dilferent wavs during the Ilree expansion and the Sedov-Tavlor phases., The acceleration process in supernova remnants is expected to work in qualitatively different ways during the free expansion and the Sedov-Taylor phases.995 Here we restrict our attention to the propagation in a spatially uniform interstellar medium., Here we restrict our attention to the propagation in a spatially uniform interstellar medium.996 During the free expansion phase the velocity of the shell remains constant aud (he maxinum momentum grows in lime in a wav that depends on the erowth of the turbulent magnetic field in the upstream region., During the free expansion phase the velocity of the shell remains constant and the maximum momentum grows in time in a way that depends on the growth of the turbulent magnetic field in the upstream region.997 During (his phase particles cannot escape., During this phase particles cannot escape.998 Nevertheless the standard approaches to the calculation of the shock modification would lead to predict an escape flux. a svanptonm of the need to carry out fully time dependent calculations to treat. this expansion regime.," Nevertheless the standard approaches to the calculation of the shock modification would lead to predict an escape flux, a symptom of the need to carry out fully time dependent calculations to treat this expansion regime."999 The lack of particles’ escape implies an increase in (he maximum momentum of the accelerated particles., The lack of particles' escape implies an increase in the maximum momentum of the accelerated particles.1000 This trend. ends at the beginning of the Sedov-Tavlor phase. when the inertia of the swept up material slows clown the expanding shell.," This trend ends at the beginning of the Sedov-Taylor phase, when the inertia of the swept up material slows down the expanding shell."1001 Physically. this is (he reason why we expect that the highest energies for particles accelerated in SNRs are reached at the beeinnimg of the Sedov-Tavlor phase.," Physically, this is the reason why we expect that the highest energies for particles accelerated in SNRs are reached at the beginning of the Sedov-Taylor phase."1002 During this phase. the shock velocity decreases and (he magnetic field. amplification upstream. as due to streaming instability. becomes less efficient.," During this phase, the shock velocity decreases and the magnetic field amplification upstream, as due to streaming instability, becomes less efficient."1003 The generation of magnetic turbulence via streaming instabiliies may proceed. through either resonant. (?22)) or (?)) coupling between particles and waves and the (wo channels are likely to dominate at different. times in (he historv of the supernova remnant (?7)). as discussed below.," The generation of magnetic turbulence via streaming instabilities may proceed through either resonant \cite{bell78a,bell78b}) ) or non-resonant \cite{bell04}) ) coupling between particles and waves and the two channels are likely to dominate at different times in the history of the supernova remnant \cite{pelletier06,ab08}) ), as discussed below."1004" This general picture leads to a maximum momentum (hat decreases with time and to particles. escape towards upstream infinity: particles of momentum p,,4,04) do not make it back to the shock at a time fs>/4.", This general picture leads to a maximum momentum that decreases with time and to particles' escape towards upstream infinity: particles of momentum $p_{max}(t_1)$ do not make it back to the shock at a time $t_2>t_1$.1005" In other words. during the time interval between /, and fo, particles with momentum between p,,,,C4) and p,,,,(/5) escape rom the svstem."," In other words, during the time interval between $t_1$ and $t_2$, particles with momentum between $p_{max}(t_1)$ and $p_{max}(t_2)$ escape from the system."1006 This happens al any time. and a net flix of particles (and enerev) lowards upstream infinity is realized.," This happens at any time, and a net flux of particles (and energy) towards upstream infinity is realized."1007 At anv given time / the spectrum of particles that escape is highly. peaked wound Dias(0) (see Fig., At any given time $t$ the spectrum of particles that escape is highly peaked around $p_{max}(t)$ (see Fig.1008 1. for the test-particle case)., \ref{fig:escapeflux} for the test-particle case).1009 The spectrum of accelerated. particles that is confined in the accelerator ancl advected towards downstream is eut. off at a gradually, The spectrum of accelerated particles that is confined in the accelerator and advected towards downstream is cut off at a gradually1010The adequate fit of the ? spectra by the scaled 1600 IX AMES-DUSTY model makes it lempting to choose this model as best describing 2\TASS 1207 b. However. we find that the 1000. IX. thick cloud atmosphere of ?.. with some modifications. mav be able to [it 2NLASS 1207 b's spectrum. without an unplivsical radius sealing.,"The adequate fit of the \citet{2010AA...517A..76P} spectra by the scaled 1600 K AMES-DUSTY model makes it tempting to choose this model as best describing 2MASS 1207 b. However, we find that the 1000 K thick cloud atmosphere of \citet{2011arXiv1102.5089M}, with some modifications, may be able to fit 2MASS 1207 b's spectrum, without an unphysical radius scaling."1011" Using the cooling eurve parameterizations of 7 and 2MASS 1207 b's assumed age of 5-12 Myr. a τω=10001Ix implies that 241ASS 1207 b's mass is between 5.,,, and τρ."," Using the cooling curve parameterizations of \citet{2001RvMP...73..719B} and 2MASS 1207 b's assumed age of 5-12 Myr, a $T_{\rm eff}=1000$ K implies that 2MASS 1207 b's mass is between $M_{jup}$ and $M_{jup}$."1012 We have investigated three hypothetical explanations for the observed under-Inmninosity ol 24M1ASS 1207 b: (1) the edge-on disk hypothesis proposed by ?.. (2) an isotropic dust-shell. motivated by the possible discovery of one around G 196-3 D (?).. and (3) thick cloud model atmospheres (7). (that might be able to fit simultaneously explain 2\IASS 1207 b's spectral shape and huminosity.," We have investigated three hypothetical explanations for the observed under-luminosity of 2MASS 1207 b: (1) the edge-on disk hypothesis proposed by \citet{2007ApJ...657.1064M}, (2) an isotropic dust-shell, motivated by the possible discovery of one around G 196-3 B \citep{2010ApJ...715.1408Z}, and (3) thick cloud model atmospheres \citep{2011arXiv1102.5089M} that might be able to fit simultaneously explain 2MASS 1207 b's spectral shape and luminosity."1013 We [ind the edge-on disk hypothesis unlikely for the following reasons: 1) Based on modeling and observations. voung stars of all masses are expected to exhibit variability. when occulted. by an edge-on disk. as a result of the disk's non-axisvmnmetric structure and hydrostatic fluetuations.," We find the edge-on disk hypothesis unlikely for the following reasons: 1) Based on modeling and observations, young stars of all masses are expected to exhibit variability when occulted by an edge-on disk, as a result of the disk's non-axisymmetric structure and hydrostatic fluctuations."1014 Using data from HST/NICMOS (?). and VLT/NACO (this work). we see no evidence for strong variability.," Using data from HST/NICMOS \citep{2006ApJ...652..724S} and VLT/NACO (this work), we see no evidence for strong variability."1015 ILowever. we caution that the magnitude and ubiquityv of variability in edge-on brown clwarl disks are not currently. well understood.," However, we caution that the magnitude and ubiquity of variability in edge-on brown dwarf disks are not currently well understood."1016 2) The inclination of 221ASS 1207 b has to be very tightly tuned to produce the observed under-huninositv elfect., 2) The inclination of 2MASS 1207 b has to be very tightly tuned to produce the observed under-luminosity effect.1017" At different inclinations. brown chwarls can beσος,erlineled.. or by their disks."," At different inclinations, brown dwarfs can be, or by their disks."1018 221ASS 1207 b falls into the regime of partially extineling disks. which our models predict only occur ~G.4% of the time in voung brown dwarls.," 2MASS 1207 b falls into the regime of partially extincting disks, which our models predict only occur $\sim$ of the time in young brown dwarfs."1019 Since 241ASS 1207 b is such a unique svstem. this low probability is not. in itself. enough to completely rule out the edge-on disk hypothesis.," Since 2MASS 1207 b is such a unique system, this low probability is not, in itself, enough to completely rule out the edge-on disk hypothesis."1020 3) Since the discoverv of 2MASS 1207 b and the ensuing discussion of its several more svstens have been found Chat appear to be under-Iuminous. including TID 203030 D. IIN Peg D and HR 8799 bede.," 3) Since the discovery of 2MASS 1207 b and the ensuing discussion of its under-luminosity, several more systems have been found that appear to be under-luminous, including HD 203030 B, HN Peg B and HR 8799 bcde."1021 Since these other svstems are likely all older than 241ASS 1207 b. their gas-rich disks will have cdissipated. precluding the geometrically (hick disk geometries necessary to extinct them.," Since these other systems are likely all older than 2MASS 1207 b, their gas-rich disks will have dissipated, precluding the geometrically thick disk geometries necessary to extinct them."1022" Thus at least one other phenomenon must be capable of producing the same under-Iuminosity οδοί, rendering the edge-on disk hypothesis linnecessarv."," Thus at least one other phenomenon must be capable of producing the same under-luminosity effect, rendering the edge-on disk hypothesis unnecessary."1023decreasing metallicity.,decreasing metallicity.1024 When taken this into account. the trend of bbecomes more flat and approaches |Mn/Fe]|~0 at all metallicities.," When taken this into account, the trend of becomes more flat and approaches $\mnfe \sim 0$ at all metallicities."1025 It was long thought that nickel closely follows iron (i.e. [Ni/Fe]=0) in both halo and disk stars., It was long thought that nickel closely follows iron (i.e. $\nife \simeq 0$ ) in both halo and disk stars.1026 Nissen Schuster (1997)) found. however. tto be slightly negative in eight halo stars having unusually low values of aand[Na/Fe].," Nissen Schuster \cite{nissen97}) ) found, however, to be slightly negative in eight halo stars having unusually low values of and."1027 Even more negative values of hhave been found in dSph galaxies (Venn et al. 2004))., Even more negative values of have been found in dSph galaxies (Venn et al. \cite{venn04}) ).1028 The underabundance of ffor low-« stars is confirmed in NSIO. and as seen from Fig. 5..," The underabundance of for $\alpha$ stars is confirmed in NS10, and as seen from Fig. \ref{fig:dX-dNa.limfe},"1029 there is a very tight correlation between A[Ni/Fe] and A[Na/Fe] for stars in the range —1.1<[Fe/H]«-0.7., there is a very tight correlation between $\Delta \nife$ and $\Delta \nafe$ for stars in the range $-1.1 \le \feh < -0.7$.1030 As discussed in Venn et al. (2004)).," As discussed in Venn et al. \cite{venn04}) ),"1031" the correlation between Na and Ni. can be explained if the production of ""Ni (the most abundant Ni isotope) in LL depends on the neutron excess in the same way as Na. i.e. the yields of both elements are metallicity dependent."," the correlation between Na and Ni, can be explained if the production of $^{58}$ Ni (the most abundant Ni isotope) in II depends on the neutron excess in the same way as $^{23}$ Na, i.e. the yields of both elements are metallicity dependent."1032 Ni is. however. also produced by IIa. Current models of Ia (e.g. Nomoto et al. 1997))," Ni is, however, also produced by Ia. Current models of Ia (e.g. Nomoto et al. \cite{nomoto97}) )"1033 predict an overproduction of Ni relative to Fe. and it is therefore puzzling that the low-a stars fall below the high-a group in the στ ddiagram.," predict an overproduction of Ni relative to Fe, and it is therefore puzzling that the $\alpha$ stars fall below the $\alpha$ group in the - diagram."1034 Evidently. there is something wrong with the yield calculations.," Evidently, there is something wrong with the yield calculations."1035 As noted by Kobayashi et al. (2006)).," As noted by Kobayashi et al. \cite{kobayashi06}) ),"1036" the Ni yield from Ila depends strongly on the electron excess. Y,. in the burning region. which is sensitive to uncertain parameters such as the propagation speed of the burning front and the central density of the white dwarf progenitor."," the Ni yield from Ia depends strongly on the electron excess, $Y_e$, in the burning region, which is sensitive to uncertain parameters such as the propagation speed of the burning front and the central density of the white dwarf progenitor."1037 Hence. there seems to be room for a downward revision of Ni yields for Ha. The increase in wwith ((Fig. 2))," Hence, there seems to be room for a downward revision of Ni yields for Ia. The increase in with (Fig. \ref{fig:mn.cu.zn-fe}) )"1038 for the high-alpha stars. can be explained 1f copper is mainly produced in massive stars by the weak s-process (e.g. Bisterzo et al. 2004)).," for the high-alpha stars, can be explained if copper is mainly produced in massive stars by the weak $s$ -process (e.g. Bisterzo et al. \cite{bisterzo04}) )."1039 The necessary neutrons come from the Νοία.π) Mg reaction. which also controls the production of Na.," The necessary neutrons come from the $^{22}$ $\alpha$ $^{25}$ Mg reaction, which also controls the production of Na."1040 Thus. the efficiency of Cu production by the weak s-process also increases with increasing original CNO abundance.," Thus, the efficiency of Cu production by the weak $s$ -process also increases with increasing original CNO abundance."1041 This is confirmed by detailed calculations of yields by Kobayashi et al. (2006)).," This is confirmed by detailed calculations of yields by Kobayashi et al. \cite{kobayashi06}) ),"1042 who find a steep increase in Cu/Fe as a function of heavy element abundance., who find a steep increase in Cu/Fe as a function of heavy element abundance.1043 Current [la models predict negligible Cu yields (e.g. Nomoto et al. 1997))., Current Ia models predict negligible Cu yields (e.g. Nomoto et al. \cite{nomoto97}) ).1044 The reduced Cu/Fe ratio in low-a stars therefore arises because they were formed from gas enriched with Fe from Ila and with Cu produced by CNO-poor massive stars., The reduced Cu/Fe ratio in $\alpha$ stars therefore arises because they were formed from gas enriched with Fe from Ia and with Cu produced by CNO-poor massive stars.1045 The same type of explanation was suggested in Sect., The same type of explanation was suggested in Sect.1046 3.2.1. for the underabundance of iin the low-e population., \ref{sect:alpha-na} for the underabundance of in the $\alpha$ population.1047 As seen from Fig. 5..," As seen from Fig. \ref{fig:dX-dNa.limfe},"1048 there is indeed a nice correlation between A[Cu/Fe] and A[Na/Fe] with a slope that is close to one., there is indeed a nice correlation between $\Delta \cufe$ and $\Delta \nafe$ with a slope that is close to one.1049 The distribution of stars 1n the στ ddiagram (Fig. 2)), The distribution of stars in the - diagram (Fig. \ref{fig:mn.cu.zn-fe}) )1050 suggests that zine behaves in much the same way as an v-element., suggests that zinc behaves in much the same way as an $\alpha$ -element.1051 lis near-constant at a level of ddex for the thick-disk and high-« halo stars. whereas the low-a stars show a declining trend in aas a function of increasing wwith an amplitude similar to that of ((Table 5)).," is near-constant at a level of dex for the thick-disk and $\alpha$ halo stars, whereas the $\alpha$ stars show a declining trend in as a function of increasing with an amplitude similar to that of (Table \ref{table:ratios}) )."1052" The heavy isotopes. 66—99 ""Zn. are probably made by the weak s-process in massive stars (Bisterzo et al. 2004))."," The heavy isotopes, $^{66-70}$ Zn, are probably made by the weak $s$ -process in massive stars (Bisterzo et al. \cite{bisterzo04}) )."1053 According to Kobayashi et al. (2006)).," According to Kobayashi et al. \cite{kobayashi06}) ),"1054 the most abundant isotope. Zn. is mainly formed by Si-burning in hypernovae.," the most abundant isotope, $^{64}$ Zn, is mainly formed by Si-burning in hypernovae."1055 Type la SNe produce relatively little Zn., Type Ia SNe produce relatively little Zn.1056 Hence. the decreasing trend of iin the Iow-r population may be explained by the production of iron in Ha. One may ask if the derived overabundance of Zn relative to Fe could be a spurious result because of the assumption of LTE.," Hence, the decreasing trend of in the $\alpha$ population may be explained by the production of iron in Ia. One may ask if the derived overabundance of Zn relative to Fe could be a spurious result because of the assumption of LTE."1057 According to the statistical equilibrium calculations for the energy level populations of the aatom by Takeda et al. (2005)).," According to the statistical equilibrium calculations for the energy level populations of the atom by Takeda et al. \cite{takeda05}) ),"1058" the non-LTE corrections of Zn abundances derived from the ,L01722.1.4810.5 lines increase with decreasing metallicity and reach about ddex relative to the Sun for à main-sequence star with 7,= 5800KK and |Fe/H]«-1."," the non-LTE corrections of Zn abundances derived from the $\lambda \lambda 4722.1, 4810.5$ lines increase with decreasing metallicity and reach about dex relative to the Sun for a main-sequence star with $\teff \simeq 5800$ K and $\feh \simeq -1$."1059 This is of the same order of size as the non-LTE correction for the Fe abundance derived from Ilines (as estimated from the difference in Fe abundances derived from aand llines: see Sect. 2.1))., This is of the same order of size as the non-LTE correction for the Fe abundance derived from lines (as estimated from the difference in Fe abundances derived from and lines; see Sect. \ref{sect:methods}) ).1060 There is some uncertainty in the statistical calculations due to a poor knowledge of the cross section for, There is some uncertainty in the statistical calculations due to a poor knowledge of the cross section for1061"metal-intermediate, and metal-rich groups.","metal-intermediate, and metal-rich groups."1062" Of course, there is a good overall agreement between [m/H] and [Fe/H], the linear correlation coefficient being r=0.58, which significance is extremely high given the size of the sample (797 stars)."," Of course, there is a good overall agreement between [m/H] and [Fe/H], the linear correlation coefficient being r=0.58, which significance is extremely high given the size of the sample (797 stars)."1063" An even better correlation is obtained with [a/H] (r=0.64; see Fig 5)), while the correlations are markedly poorer with e.g. [Na/H] or [O/H]."," An even better correlation is obtained with $\alpha$ /H] (r=0.64; see Fig \ref{f:fig4a}) ), while the correlations are markedly poorer with e.g. [Na/H] or [O/H]."1064" This confirms that [m/H] is a good proxy for a combination of [Fe/H] and [a/H] (these two quantities being extremely well correlated each other, with r=0.90)."," This confirms that [m/H] is a good proxy for a combination of [Fe/H] and $\alpha$ /H] (these two quantities being extremely well correlated each other, with r=0.90)."1065" We notice that when examining the results for the individual groups, while there is still a good correlation between [m/H] and [Fe/H] for the groups of intermediate metallicity, this correlation is much less obvious for the other groups."," We notice that when examining the results for the individual groups, while there is still a good correlation between [m/H] and [Fe/H] for the groups of intermediate metallicity, this correlation is much less obvious for the other groups."1066" In particular, for the metal-poor group the hint for a correlation is only given by a dozen points (less than of the total population of these groups) at rather high metallicity."," In particular, for the metal-poor group the hint for a correlation is only given by a dozen points (less than of the total population of these groups) at rather high metallicity."1067 The metallicity range appears very narrow for the remaining stars., The metallicity range appears very narrow for the remaining stars.1068" We then suspect that this group is essentially monometallic, the observed spreads in [Fe/H] and [m/H] being only due to observational errors, save for very few contaminants, probably assigned erroneously to this group because of a low measured value of [La/Fe]."," We then suspect that this group is essentially monometallic, the observed spreads in [Fe/H] and [m/H] being only due to observational errors, save for very few contaminants, probably assigned erroneously to this group because of a low measured value of [La/Fe]."1069" In addition, this plot suggests that for this group there is only a limited contamination by AGB stars (which should manifest as objects with low [m/H] for their [Fe/H], being bluer than RGB stars)."," In addition, this plot suggests that for this group there is only a limited contamination by AGB stars (which should manifest as objects with low [m/H] for their [Fe/H], being bluer than RGB stars)."1070" Indeed, some stars scatter in this region of the plot, but they are very few."," Indeed, some stars scatter in this region of the plot, but they are very few."1071" As mentioned above, there is an obvious correlation between [Fe/H] and [m/H] for the intermediate metallicity groups."," As mentioned above, there is an obvious correlation between [Fe/H] and [m/H] for the intermediate metallicity groups."1072 This suggests that there is a real spread in metallicity among these groups., This suggests that there is a real spread in metallicity among these groups.1073" However, a closer look reveals that the slope of the relation between [Fe/H] and [m/H] is significantly smaller than unity, that is [Fe/H] varies much more than [m/H]."," However, a closer look reveals that the slope of the relation between [Fe/H] and [m/H] is significantly smaller than unity, that is [Fe/H] varies much more than [m/H]."1074" In addition, average [m/H] values for the different metal intermediate groups (which differs in their [Na/O] value, that is their location along the Na/O anticorrelation) also differs much less than what is observed for [Fe/H]."," In addition, average [m/H] values for the different metal intermediate groups (which differs in their [Na/O] value, that is their location along the Na/O anticorrelation) also differs much less than what is observed for [Fe/H]."1075 We will come back later to this very interesting point., We will come back later to this very interesting point.1076 We also note that a few points scattered below the bulk of the points in this plot may be interpreted as AGB contaminants., We also note that a few points scattered below the bulk of the points in this plot may be interpreted as AGB contaminants.1077" Finally, there is some correlation between [Fe/H] and [m/H] also for the metal-rich group, suggesting that also in this case there is some real spread in metallicity."," Finally, there is some correlation between [Fe/H] and [m/H] also for the metal-rich group, suggesting that also in this case there is some real spread in metallicity."1078" Our data are not good enough to conclude if there is a continuous spread, or rather two or more discrete values (as suggested by Johnson and Pilachowski, 2010)."," Our data are not good enough to conclude if there is a continuous spread, or rather two or more discrete values (as suggested by Johnson and Pilachowski, 2010)."1079 More accurate analysis of these stars might establish this interesting point., More accurate analysis of these stars might establish this interesting point.1080 The results we obtain for the a—elements can be summarized as follows (see Table 2 for the abundances of the individual elements)., The results we obtain for the $\alpha-$ elements can be summarized as follows (see Table \ref{t:tab1b} for the abundances of the individual elements).1081" The two most metal-poor groups have the same value of [a/Fe]=0.20+0.01, within the small statistical error bars."," The two most metal-poor groups have the same value of $\alpha$ $0.20\pm 0.01$, within the small statistical error bars."1082 Systematic errors are likely much larger than this tiny statistical errors., Systematic errors are likely much larger than this tiny statistical errors.1083" The [Si/Fe] overabundances (on average, 0.25 dex for these two groups) are slightly larger than those obtained for Ca and Ti (0.24 and 0.12 dex), with almost negligible differences between groups #44 and #66."," The [Si/Fe] overabundances (on average, 0.25 dex for these two groups) are slightly larger than those obtained for Ca and Ti (0.24 and 0.12 dex), with almost negligible differences between groups 4 and 6."1084" On the whole, we cannot avoid to notice that the a—excess is quite modest, with respect to typical values found in halo stars, and more similar to those found in dwarf Spheroidals at this metallicity."," On the whole, we cannot avoid to notice that the $\alpha-$ excess is quite modest, with respect to typical values found in halo stars, and more similar to those found in dwarf Spheroidals at this metallicity."1085" On the other hand, the intermediate metallicity groups not only provide on average larger a—excess, but [a@/Fe] seems to"," On the other hand, the intermediate metallicity groups not only provide on average larger $\alpha-$ excess, but $\alpha$ /Fe] seems to"1086WDs.,WDs.1087 There are a few evolutionary scenarios that place a He or C/O WD in a tight enough orbit (following a common-envelope induced spiral-in) about a NS that gravity wave emission will place it in contact within 5-10 Gyr (Rasio. Pfahl Rappaport 2000: Yungelson. Nelemans van den Heuvel 2002).," There are a few evolutionary scenarios that place a He or C/O WD in a tight enough orbit (following a common-envelope induced spiral-in) about a NS that gravity wave emission will place it in contact within 5-10 Gyr (Rasio, Pfahl Rappaport 2000; Yungelson, Nelemans van den Heuvel 2002)."1088 In this case the WD has had some time to cool before initiating RL overflow., In this case the WD has had some time to cool before initiating RL overflow.1089 Nelemans et al. (, Nelemans et al. (10902001) discuss a similar scenario for the origin of AM CVn binartes.,2001) discuss a similar scenario for the origin of AM CVn binaries.1091 The rate at which they cool differentiates He and C/O WDs., The rate at which they cool differentiates He and C/O WDs.1092 The larger specific heat of a He WD slows its cooling (Althaus Benvenuto 1997; Hansen Phinney 1998)., The larger specific heat of a He WD slows its cooling (Althaus Benvenuto 1997; Hansen Phinney 1998).1093 For example. a 0.20M ..He WD would have 7.=10(3.3)«10°K at z1.0(4.0) Gyr (Althaus Benvenuto 1997) and be liquid when RL filling occurs.," For example, a $0.20 M_\odot$ He WD would have $T_c=10(3.3)\times 10^6 \ {\rm K} $ at $\approx 1.0(4.0)$ Gyr (Althaus Benvenuto 1997) and be liquid when RL filling occurs."1094 The smaller specific heat of a 0.6M ..C/O WD allows it to cool to 2.5«IO6K in 4 Gyr and begin crystallization (Salaris et al., The smaller specific heat of a $0.6M_\odot$ C/O WD allows it to cool to $2.5\times 10^6 {\rm K}$ in 4 Gyr and begin crystallization (Salaris et al.1095 2000)., 2000).1096 Hence. most C/O WDs would be solid prior to RL filling (this is needed for the enhancement of Ne by fractionation; Schulz et al.," Hence, most C/O WDs would be solid prior to RL filling (this is needed for the enhancement of $^{22}{\rm Ne}$ by fractionation; Schulz et al."1097 2001) and might only melt if heated during the GW inspiral (Iben. Tutukov Fedorova 1998).," 2001) and might only melt if heated during the GW inspiral (Iben, Tutukov Fedorova 1998)."1098 The other differentiation between such WDs comes from their mass. as Yungelson et al. (," The other differentiation between such WDs comes from their mass, as Yungelson et al. ("1099"2002) argue that the mass transfer at the onset of RL filling will be unstable if M,>0.44M... excluding traditional C/O WDs from ever reaching short orbital periods.","2002) argue that the mass transfer at the onset of RL filling will be unstable if $M_c>0.44M_\odot$, excluding traditional C/O WDs from ever reaching short orbital periods."1100 However. Yungelson et al. (," However, Yungelson et al. ("1101"2002) note that “hybrid” WDs with C/O cores can have M,<0.44M.. and thus evolve to lower mass systems filling the RL at 20-40 minutes.","2002) note that “hybrid” WDs with C/O cores can have $M_c<0.441102M_\odot$ and thus evolve to lower mass systems filling the RL at 20-40 minutes."1103 The inability for the donor WDs to cool on the ~ Gyr timescale of the mass transfer phase (Rappaport et al., The inability for the donor WDs to cool on the $\sim$ Gyr timescale of the mass transfer phase (Rappaport et al.1104 1987) makes it clear that the initial entropy is the minimum value attainable., 1987) makes it clear that the initial entropy is the minimum value attainable.1105 All of the entropy is in the liquid tons. which have an adiabatic scaling. T.x(07 (Hernanz et al.," All of the entropy is in the liquid ions, which have an adiabatic scaling, $T_c\propto \rho_c^{0.5-0.6}$ (Hernanz et al."1106 1988). less steep than for an ideal gas (T. (77).," 1988), less steep than for an ideal gas $T\propto1107\rho^{2/3}$ )."1108 Since p.x Mz. a c ..He WD made by the deep interior of a 0.20M ..WD would be a factor of z15 cooler. or T.z:6.6(2.2)«10? for the initial range of 7's discussed earlier.," Since $\rho_c\propto M_c^2$ , a $\approx 0.013M_\odot$ He WD made by the deep interior of a $0.201109M_\odot$ WD would be a factor of $\approx 15$ cooler, or $T_c\approx11106.6(2.2)\times 10^5 {\rm K}$ for the initial range of $T$ 's discussed earlier."1111 Of course. any tidalK heating will increase 7; (see $3).," Of course, any tidal heating will increase $T_c$ (see 3)."1112" So I have constructed M,<0.03M.. WDs of finite 7. that contains the Coulomb physics (from Chabrier Potekhin 1988) that causes the turnover to constant density ""rocks"" in the mass-radius relation at z10M seen in the ZS models in Figure 2.", So I have constructed $M_c<0.03M_\odot$ WDs of finite $T_c$ that contains the Coulomb physics (from Chabrier Potekhin 1988) that causes the turnover to constant density “rocks” in the mass-radius relation at $\approx 10^{-3} M_\odot$ seen in the ZS models in Figure 2.1113 [ have imposed an arbitrary.. (but convectively stable) temperature profile of T=T.(P/DP.)? while integrating hydrostatic balance and mass conservation., I have imposed an arbitrary (but convectively stable) temperature profile of $T=T_c(P/P_c)^{1/5}$ while integrating hydrostatic balance and mass conservation.1114 | used the electron equation of state of Paczynski (1983) and halt integrations at the point where the pressure has fallen to 107? of the central value. which avoids the need for an envelope model.," I used the electron equation of state of Paczynski (1983) and halt integrations at the point where the pressure has fallen to $10^{-5}$ of the central value, which avoids the need for an envelope model."1115 The results are shown in Figure 2 and make clear that the temperatures expected from ave adequate to provide the slight radius expansion needed to fill the RL for these accreting millisecond pulsars., The results are shown in Figure 2 and make clear that the temperatures expected from are adequate to provide the slight radius expansion needed to fill the RL for these accreting millisecond pulsars.1116 This is easter for He WDs because of the extra number of ions per electron compared to C/O WDs., This is easier for He WDs because of the extra number of ions per electron compared to C/O WDs.1117 White dwarfs made of C/O will need some tidal heating to fill these RLs., White dwarfs made of C/O will need some tidal heating to fill these RLs.1118 I also found that there is à minimum mass solution for à WD of fixed 7..., I also found that there is a minimum mass solution for a WD of fixed $T_c$.1119" This ts related to the electron Fermi energy of the nearly constant density solutions at low masses and is reflected in the radius divergence of the models in Figure 2 at low M,.", This is related to the electron Fermi energy of the nearly constant density solutions at low masses and is reflected in the radius divergence of the models in Figure 2 at low $M_c$.1120" My semr-analytic modeling finds that these finite 7. solutions eventually ""turnover"" to follow a track of R.xM... as expected for an ideal gas polytrope (where 7.x ΜΚΟ)."," My semi-analytic modeling finds that these finite $T_c$ solutions eventually “turnover” to follow a track of $R_c\propto M_c$, as expected for an ideal gas polytrope (where $T_c\propto1121M_c/R_c$ )."1122" Since there is no way to reach these solutions of higher M, while mass is being lost. these “evaporative” endpoints where dInR,./dM, diverges can only be reached if tidal heating is adequate to keep these models hot while the central density is dropping."," Since there is no way to reach these solutions of higher $M_c$ while mass is being lost, these “evaporative” endpoints where $d\ln R_c/d\ln M_c$ diverges can only be reached if tidal heating is adequate to keep these models hot while the central density is dropping."1123 More work remains to actually show that this will eliminate the companion and lead to an isolated millisecond radio pulsar., More work remains to actually show that this will eliminate the companion and lead to an isolated millisecond radio pulsar.1124 Barring tidal heating adequate to reach the “evaporative” edpoint alluded to in 32. I will now discuss a possible 1EIÉII2class transfer instability.," Barring tidal heating adequate to reach the “evaporative” endpoint alluded to in 2, I will now discuss a possible mass transfer instability."1125 Matter leaving the WD takes angular 1jomentum with it às it settles into the accretion disk., Matter leaving the WD takes angular momentum with it as it settles into the accretion disk.1126 This cgular momentum ts returned to the WD via tidal torques once σιt22here has been enough time for viscosity to move the material outwards from the splash point., This angular momentum is returned to the WD via tidal torques once there has been enough time for viscosity to move the material outwards from the splash point.1127" The timescale for this angular momentum loop to be closed has been considered to be long enough (or uncertain enough) that Ruderman Shaham (1983) raised the possibility that a mass transfer instability could oceur when the expansion of a low-mass donor (M,«M.) due to mass loss (measured by 244 of eq. [1]])", The timescale for this angular momentum loop to be closed has been considered to be long enough (or uncertain enough) that Ruderman Shaham (1983) raised the possibility that a mass transfer instability could occur when the expansion of a low-mass donor $M_c\ll M_x$ ) due to mass loss (measured by $n_{\rm Ad}$ of eq. \ref{eq:nad}] ])1128 exceeds that of the RL. measured by where « is the orbital separation.," exceeds that of the RL, measured by where $a$ is the orbital separation."1129" The value of i presuming the angular momentum ""sink"" of the disk (using the fitting formula of Verbunt Rappaport 1988) is shown in Figure 3 by the dotted lines for (from left to right) M.20.6.1.0.1.4. 1.8M..."," The value of $n_{\rm R}$ presuming the angular momentum “sink” of the disk (using the fitting formula of Verbunt Rappaport 1988) is shown in Figure 3 by the dotted lines for (from left to right) $M_x=0.6,1.0,1.4,$ $1.8 \ M_\odot$."1130 Ruderman Shaham (1983) presumed rag2—1/3. which was shown to be an overestimate by Hut Paezynski (1984) and Bonsema van den Heuvel (1985). who found 5 from the ZS relation (shown in Figure 3 by the solid{dashed] lines for He[C]).," Ruderman Shaham (1983) presumed $n_{\rm Ad}=-1/3$, which was shown to be an overestimate by Hut Paczynski (1984) and Bonsema van den Heuvel (1985), who found $n$ from the ZS relation (shown in Figure 3 by the solid[dashed] lines for He[C])."1131" These authors noted that a ZS model moved the crossing (ag— ng) to such low M, that the binary might not reach it 1n à Hubble time.", These authors noted that a ZS model moved the crossing $n_{\rm Ad}<n_{\rm R}$ ) to such low $M_c$ that the binary might not reach it in a Hubble time.1132 However. for finite 7 He WDs. I show that this conclusion is altered.," However, for finite $T$ He WDs, I show that this conclusion is altered."1133" The solid circles are my evaluation of nap for the 7.=10°K (set closest to the solid line) and 7.=10°K (bottom-most set) He WDs of Figure 2 and show that the finite entropy model sits between the 720 value and the ""naive"" 72—1/3 guess for a perfect gas.", The solid circles are my evaluation of $n_{\rm AD}$ for the $T_c=10^5 \ {\rm K}$ (set closest to the solid line) and $T_c=10^6 \ {\rm K}$ (bottom-most set) He WDs of Figure 2 and show that the finite entropy model sits between the $T=0$ value and the “naive” $n=-1/3$ guess for a perfect gas.1134" For a M,21.4M.. accretor. the instability question is first raised (since nay« ng) when a 10°K He WD has M,70.01M..."," For a $M_x=1.4 \ M_\odot$ accretor, the instability question is first raised (since $n_{\rm Ad}<n_{\rm R}$ ) when a $10^6 \ {\rm K}$ He WD has $M_c\approx 0.01\ M_\odot$."1135 This will occur about a Gyr after mass transfer has started presuming just gravity wave emission., This will occur about a Gyr after mass transfer has started presuming just gravity wave emission.1136 My evaluations of aq for C WDs at the 7..s of Figure 2 never found such a crossing., My evaluations of $n_{\rm Ad}$ for C WDs at the $T_c$ 's of Figure 2 never found such a crossing.1137 The instability question is thus raised for He WDs and requires some extra entropy from tidal heating., The instability question is thus raised for He WDs and requires some extra entropy from tidal heating.1138" The amount of heating is small. as for liquid He to reach 7.~10°K from about 1/2 that value (which it had initially) requires 3kg(0.5T)ΜΗ~31019ergg! (the specific heat in the liquid state is 23k,7 per ion)."," The amount of heating is small, as for liquid He to reach $T_c\approx 10^6 \ {\rm K}$ from about 1/2 that value (which it had initially) requires $3k_B(0.5T_c)/4m_p\approx 3\times 10^{13} \ {\rm1139erg \ g^{-1}}$ (the specific heat in the liquid state is $\approx11403k_BT$ per ion)."1141 This energy is comparable to the current rotational energy per gram for a tidally locked WD at the 40 minute orbital period., This energy is comparable to the current rotational energy per gram for a tidally locked WD at the 40 minute orbital period.1142 Hence. only a fraction of the higher rotational energy per gram from the tidally locked WD at a shorter orbital period needs to be deposited to yield 7.=10°K today.," Hence, only a fraction of the higher rotational energy per gram from the tidally locked WD at a shorter orbital period needs to be deposited to yield $T_c\approx 10^6 \ {\rm K}$ today."1143 The remaining eriticism against the mass transferinstability isone of relative timescales (Verbunt Rappaport 1988; Priedhorsky Verbunt 1988)., The remaining criticism against the mass transferinstability isone of relative timescales (Verbunt Rappaport 1988; Priedhorsky Verbunt 1988).1144" The mass-transfer instability most likely grows on a timescale τιzM.A/M.R, (Verbunt Rappaport 1988). where H is the scale height in the WD atmosphere. fixed by the X-ray heating in quiescence from the hot NS (Bildsten"," The mass-transfer instability most likely grows on a timescale $\tau_g\approx M_cH/\dot M_c R_c$ (Verbunt Rappaport 1988), where $H$ is the scale height in the WD atmosphere, fixed by the X-ray heating in quiescence from the hot NS (Bildsten"1145a line mask.,a line mask.1146" To compile such a mask, it is important to adopt correct stellar parameters since the intensities and the total number of spectral lines extracted from the Vienna Atomic Line Database (VALD,??) will depend on the effective temperature and chemical composition of a star."," To compile such a mask, it is important to adopt correct stellar parameters since the intensities and the total number of spectral lines extracted from the Vienna Atomic Line Database \citep[VALD,][]{VALD,Kupka:1999} will depend on the effective temperature and chemical composition of a star."1147" We estimated aand logg from the Strómmgren photometry (?) with the help of the TempLogG code (?),, using the calibration by ?.."," We estimated and $\log g$ from the Strömmgren photometry \citep{Hauck:1998} with the help of the TempLogG code \citep{Kaiser:2006}, using the calibration by \citet{Moon:1985}."1148" The resulting 2-110500 K and logg=3.8 agree with the parameters determined by ? (T.~=10700 K,logg = 3.8) and ? (Teg=10612 K,logg= 3.79)."," The resulting 10500 K and $\log g\,=\,3.8$ agree with the parameters determined by \citet{Smith:1993a} $\,=\,10700$ K, $\log g\,=\,3.8$ ) and \citet{Dolk:2003} $\,=\,10612$ K, $\log g\,=\,3.79$ )."1149" The scatter of the effective temperature determinations suggests uuncertainty around 200 K. According to ?,, the uncertainty of the effective temperature and surface gravity established using their calibration is +260 K and +0.1 dex, respectively."," The scatter of the effective temperature determinations suggests uncertainty around 200 K. According to \citet{Moon:1985}, the uncertainty of the effective temperature and surface gravity established using their calibration is $\pm$ 260 K and $\pm$ 0.1 dex, respectively."1150 The model atmosphere of wwas computed with the LLmodels code (?) for =10500 Kandlogg=3.8.," The model atmosphere of was computed with the LLmodels code \citep{LLmodels} for $\,=\,10500$ K and $\log g\,=\,3.8$."1151" The abundances of many chemical elements in aare unknown, although some other elements have been studied previously (see Sect. 1))"," The abundances of many chemical elements in are unknown, although some other elements have been studied previously (see Sect. \ref{intro}) )."1152" Using these individual abundance and adopting average values typical of HgMn stars for elements not analysed before, we compiled a preliminary line list and computed synthetic spectrum with the SYNTH3 code (?).."," Using these individual abundance and adopting average values typical of HgMn stars for elements not analysed before, we compiled a preliminary line list and computed synthetic spectrum with the SYNTH3 code \citep{SYNTH3}. ."1153" Chemical abundances were refined by comparing this calculation to the observed spectrum obtained at — 55210.03112, which has the highest S/N."," Chemical abundances were refined by comparing this calculation to the observed spectrum obtained at $\,=\,$ 55210.03112, which has the highest $S/N$."1154 Zero microturbulent velocity was assumed both for the VALD extraction and for the spectrum synthesis., Zero microturbulent velocity was assumed both for the VALD extraction and for the spectrum synthesis.1155 We found good agreement between our observations and the synthetic spectrum for the spectral lines of chemical elements studied previously., We found good agreement between our observations and the synthetic spectrum for the spectral lines of chemical elements studied previously.1156" However, since we adopted a somewhat cooler model atmosphere compared to ?,, we had to reduce the abundances of Fe, Cr, Mg, Mn, and Ga by up to «00.4 dex."," However, since we adopted a somewhat cooler model atmosphere compared to \citet{Smith:1993a}, we had to reduce the abundances of Fe, Cr, Mg, Mn, and Ga by up to $\approx$ 0.4 dex."1157" No changes were required for Si and Co. Relatively large corrections were introduced for Sc, Y, Pt, and Zr, because spectral lines of some of these chemical elements were excessively strong or too weak, mismatching the observations."," No changes were required for Si and Co. Relatively large corrections were introduced for Sc, Y, Pt, and Zr, because spectral lines of some of these chemical elements were excessively strong or too weak, mismatching the observations."1158" Since the precise quantitative abundance analysis is beyond the scope of our study, we adjusted abundances of individual chemical elements visually, without deriving formal error bars."," Since the precise quantitative abundance analysis is beyond the scope of our study, we adjusted abundances of individual chemical elements visually, without deriving formal error bars."1159 This is sufficient for compiling an LSD line mask., This is sufficient for compiling an LSD line mask.1160 The abundances are given in the Table 2 as follows: chemical element and the initial and final abundances., The abundances are given in the Table \ref{tab2} as follows: chemical element and the initial and final abundances.1161" The revised abundances were used to obtain a new line list from VALD, which provided 3827 spectral lines in the 3781-6915 rrange."," The revised abundances were used to obtain a new line list from VALD, which provided 3827 spectral lines in the 3781–6915 range."1162" To apply LSD, we constructed a line mask containing central wavelengths of spectral lines and a set of weights for Stokes J and V."," To apply LSD, we constructed a line mask containing central wavelengths of spectral lines and a set of weights for Stokes $I$ and $V$."1163 Central depths returned by VALD were used as weights for the intensity spectrum., Central depths returned by VALD were used as weights for the intensity spectrum.1164" For the circular polarisation spectrum, the weights were calculated as wy=dAg/4o, where d is the central depth of a spectral line, 4 the wavelength, and g the corresponding effective Landé factor."," For the circular polarisation spectrum, the weights were calculated as $w_V\,=\,d\lambda \overline{g}/\lambda_0$, where $d$ is the central depth of a spectral line, $\lambda$ the wavelength, and $\overline{g}$ the corresponding effective Landé factor."1165 The normalisation parameter Ap=4696 wwas chosen to be close to the averaged wavelength of all spectral lines in the mask., The normalisation parameter $\lambda_0=4696$ was chosen to be close to the averaged wavelength of all spectral lines in the mask.1166" To get optimal results from the LSD technique, it is essential not to include very weak spectral lines, because an extra noise might be added to the LSD profiles."," To get optimal results from the LSD technique, it is essential not to include very weak spectral lines, because an extra noise might be added to the LSD profiles."1167" To exclude weak lines, we apply a cutoff criterion, which sets athreshold for the line intensity."," To exclude weak lines, we apply a cutoff criterion, which sets athreshold for the line intensity."1168 All spectral lines weaker than the cutoff level are excluded from the LSD mask., All spectral lines weaker than the cutoff level are excluded from the LSD mask.1169" For wwe set the cutoff criterion to 0.05, which means that our LSD code (?) will use only those lines that are deeper than relative to the continuum level in the unbroadened spectrum."," For we set the cutoff criterion to 0.05, which means that our LSD code \citep{Kochukhov:2010a} will use only those lines that are deeper than relative to the continuum level in the unbroadened spectrum."1170 This yielded 962 spectral lines for computing LSD profiles., This yielded 962 spectral lines for computing LSD profiles.1171" Taking Vig=14 oof linto account, we reconstructed LSD profiles for the velocity range between —36 and 64kms™!,, which makes the profile extension symmetric with respect to the line centre."," Taking $V_\mathrm{rad}\,=\,14$ of into account, we reconstructed LSD profiles for the velocity range between $-36$ and 64, which makes the profile extension symmetric with respect to the line centre."1172 An average pixel of the HARPS CCDs has a resolution of 0.8kms!., An average pixel of the HARPS CCDs has a resolution of 0.8.1173. We adopted this value as a step for LSD profiles., We adopted this value as a step for LSD profiles.1174 The S/N reported for the final LSD profilescorrespond to this velocity bin., The $S/N$ reported for the final LSD profilescorrespond to this velocity bin.1175 The average S/N gain is nine., The average $S/N$ gain is nine.1176 The LSD Stokes J and V profiles for ten rotational phases are shown in Fig. 1.., The LSD Stokes $I$ and $V$ profiles for ten rotational phases are shown in Fig. \ref{LSDIV}. .1177 Based on, Based on11782,.1179002).. The XAZM- Newton and Chandra data thus reveal only one thermal component. while we have found (wo through the 44951 spectroscopy (Paper 1).," The ${\it XMM}$ ${\it Newton}$ and ${\it Chandra}$ data thus reveal only one thermal component, while we have found two through the ${\it ASCA}$ spectroscopy (Paper 1)."1180 Then. what causes (his difference?," Then, what causes this difference?"1181 At first glance. our method emploved in Paper 1 may appear much less reliable than the other one. in which all the bright point sources are removed through. high-resolution imagery.," At first glance, our method employed in Paper 1 may appear much less reliable than the other one, in which all the bright point sources are removed through high-resolution imagery."1182 Nevertheless. we ave concerned about the way emploved by SEAO01 to estimate the faint source contribution to the residual spectrum.," Nevertheless, we are concerned about the way employed by SEA01 to estimate the faint source contribution to the residual spectrum."1183 They estimated this contribution bv scaling down a template power-law model. which was determined bv fitting a summed spectrum of the removed. bright sources.," They estimated this contribution by scaling down a template power-law model, which was determined by fitting a summed spectrum of the removed bright sources."1184 In reality. this bright-source spectrum is likely to be contaminated by the diffuse component. because of the limited angular resolution of AXMBM- Neiwlon.," In reality, this bright-source spectrum is likely to be contaminated by the diffuse component, because of the limited angular resolution of ${\it XMM}$ ${\it Newton}$."1185 Furthermore. a power-law model is known to poorly reproduce the spectra of luminous LMXBDs. as pointed out by Makishimaetal.(19898). ancl Paper 1.," Furthermore, a power-law model is known to poorly reproduce the spectra of luminous LMXBs, as pointed out by \citet{LMXB_Makishima} and Paper 1."1186 For these reasons. we expect that the analvses of the ΑΛΑ -INeieton and Chandra data can be improved: this has motivated the present paper.," For these reasons, we expect that the analyses of the ${\it XMM}$ ${\it Newton}$ and ${\it Chandra}$ data can be improved; this has motivated the present paper."1187 In the present paper. we analvze archival data of the M 31 central region. obtained by XALAM-Neinton. and Chandra.," In the present paper, we analyze archival data of the M 31 central region obtained by ${\it XMM}$ ${\it Newton}$ and ${\it Chandra}$."1188 Although these datasets have already been analvzecl [or diffuse emission bv other authors (Garcia et 22000: Primini et 22000: SEAO01: Dosaj et 22002). there still remains room for improved analvses as described in § 1. especially in comparison wilh Paper 1 and employing more appropriate modeling of the point-source spectra.," Although these datasets have already been analyzed for diffuse emission by other authors (Garcia et 2000; Primini et 2000; SEA01; Dosaj et 2002), there still remains room for improved analyses as described in $\S$ 1, especially in comparison with Paper 1 and employing more appropriate modeling of the point-source spectra."1189 Here we describe the observation and data screening., Here we describe the observation and data screening.1190 Among the VALA-Newlon archival data. there are four observations of the central region of M 31 (observation ID — 0109270101. 0112570101. 0112570401 and 0112570601). all with the same pointing direction.," Among the ${\it XMM}$ ${\it Newton}$ archival data, there are four observations of the central region of M 31 (observation ID = 0109270101, 0112570101, 0112570401 and 0112570601), all with the same pointing direction."1191 While SEEAOI analvzed the 0112570401 dataset as the proprietors. we here analvze the 0112570101. dataset. which has the longest exposure of the four.," While SEA01 analyzed the 0112570401 dataset as the proprietors, we here analyze the 0112570101 dataset, which has the longest exposure of the four."1192 The 0112570101 dataset is characterized in Table 1.. and its field of view is shown over an optical image in Figure 1. together with that used for our previous .19C51 results (Paper 1).," The 0112570101 dataset is characterized in Table \ref{tab:obs}, and its field of view is shown over an optical image in Figure \ref{fig:M31_image} together with that used for our previous ${\it ASCA}$ results (Paper 1)."1193" The X-rav images obtained by the MOS1. MOS2 and PN detectors are superposed in Figure 2aa, As already reported (SEAO0L). the image clearly reveals the extended. apparently diffuse X-ray emission in (he central region."," The X-ray images obtained by the MOS1, MOS2 and PN detectors are superposed in Figure \ref{fig:M31_Ximage}a a. As already reported (SEA01), the image clearly reveals the extended, apparently diffuse X-ray emission in the central region."1194these particles calculated from (4)) using angular momenta J measured at /26: the points fall almost. precisely on the diagonal line. confirming that the eas particles are on nearly circular orbits and that the mass model is adequate.,"these particles calculated from \ref{eq:jcirc}) ) using angular momenta $J$ measured at $t = 6$; the points fall almost precisely on the diagonal line, confirming that the gas particles are on nearly circular orbits and that the mass model is adequate."1195 In the middle plot the same equations are used. but the angular momenta / are measured at /=4. which is just after the merger.," In the middle plot the same equations are used, but the angular momenta $J$ are measured at $t =11964$, which is just after the merger."1197 Lf individual gas particles conserved J precisely. this plot would be identical to the top one: the actual distribution is considerably broader. but still more or Less stracdcdles the diagonal line.," If individual gas particles conserved $J$ precisely, this plot would be identical to the top one; the actual distribution is considerably broader, but still more or less straddles the diagonal line."1198 Finally. in the bottom plot the horizontal axis shows the radii measured. just after the merger at /=4: this distribution is broader still and. clistinetly offset. from. the diagonal linc. showing that significant. infall has taken place between /—4 and /=6.," Finally, in the bottom plot the horizontal axis shows the radii measured just after the merger at $t =11994$; this distribution is broader still and distinctly offset from the diagonal line, showing that significant infall has taken place between $t = 4$ and $t = 6$."1200 1n sum. FigureS 12. represents a qualifiedi success for this simple mocel of disk formation by infall from tails.," In sum, Figure \ref{fig12} represents a qualified success for this simple model of disk formation by infall from tails."

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