ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 2002). but thev have very different. morpholoev-density relationships (Ferguson Bienelli 1994).," 2002), but they have very different morphology-density relationships (Ferguson Bignelli 1994)."3 Understanding the prevalance and distribution of LCBDGs in clusters should constrain (heir role as a progenitor population., Understanding the prevalance and distribution of LCBGs in clusters should constrain their role as a progenitor population.4 In this Letter we measure the densitv aud clustering properties of LCDGs in two rich clusters (Table 1): anclCIL604-2-4304., In this Letter we measure the density and clustering properties of LCBGs in two rich clusters (Table 1): and.5. MS0451 is an incredibly rich. X-ray bright cluster (Ellineson et al.," MS0451 is an incredibly rich, X-ray bright cluster (Ellingson et al."6 1998: Donahue et al., 1998; Donahue et al.7 2003)., 2003).8 CIHI6042-4304 is part of a super- complex. (Postman. Lubin. Oke 2001. Lubin. Mulchaey. Postman 2004. Gal Lubin 2005). but is not as x-ray luminous.," Cl1604+4304 is part of a super-cluster complex (Postman, Lubin, Oke 2001, Lubin, Mulchaey, Postman 2004, Gal Lubin 2005), but is not as x-ray luminous."9 The cluster redshifts span an epoch where the dvnamical mass of field LCDGs changes rapidly (P97). and ave sulliciently disparate to permil the derivation of complementary field samples using (he same cata.," The cluster redshifts span an epoch where the dynamical mass of field LCBGs changes rapidly (P97), and are sufficiently disparate to permit the derivation of complementary field samples using the same data."10" Observations were obtained with the WIYN 3.5m telescope’s Mini-Mosaic Camera. (0.14"" per pixel and 9.6’x9.6"" field of view) and augmented with archival IST WFPC2 and ACS images for both clusters. reduced via the standard IST reduction pipeline."," Observations were obtained with the WIYN 3.5m telescope's Mini-Mosaic Camera $0.14''$ per pixel and $9.6' \times 9.6'$ field of view) and augmented with archival HST WFPC2 and ACS images for both clusters, reduced via the standard HST reduction pipeline."11 \IS0451 is saniplecl by images in the F775W. Fsitw. and F550LP bandpasses: Cl1604 is imaged in F606W and ES14W. Llarris UBRI. Gunn z. and two narrow-band filters were obtained at WIYN between 1999 October and 2004 June.," MS0451 is sampled by images in the F775W, F814W, and F850LP bandpasses; Cl1604 is imaged in F606W and F814W. Harris UBRI, Gunn z, and two narrow-band filters were obtained at WIYN between 1999 October and 2004 June."12 We use data from nights with good (transparency and seeing (FWIIM ~0.85(022 arcsec).," We use data from nights with good transparency and seeing (FWHM $\sim130.85^{+0.45}_{-0.35}$ arcsec)."14 Reduced Mini-Mo images are flat to within 14 of their initial skv values., Reduced Mini-Mo images are flat to within $1\%$ of their initial sky values.15 We created deep mosaics by combining only high equality data weighted by the ratio of the flux from an average star lo (he square rool of the sky deviation and seeing for that image (Bershacly. Lowenthal. Koo 1998).," We created deep mosaics by combining only high quality data weighted by the ratio of the flux from an average star to the square root of the sky deviation and seeing for that image (Bershady, Lowenthal, Koo 1998)."16 Data were calibrated through: (1) spectro-photometrie standard, Data were calibrated through: (1) spectro-photometric standard17observations were not done. and this null result is essentially insignificant.,"observations were not done, and this null result is essentially insignificant."18 But this conclusion is not correct and in fact. our observations rule out the majority of transiting orbits for HAT-P-13c.," But this conclusion is not correct and in fact, our observations rule out the majority of transiting orbits for HAT-P-13c."19 We did à numerical experiment to determine the quantitative measure of the significance., We did a numerical experiment to determine the quantitative measure of the significance.20 A set of 10° exoplanets were simulated on a similar orbit to HAT-P-13 (428 days period around an 1.22 Rs. 1.56 R.. star).," A set of $10^5$ exoplanets were simulated on a similar orbit to HAT-P-13 (428 days period around an 1.22 $_\odot$, 1.56 $_\odot$ star)."21 What we are sure about is that ingress and egress phases were not detected within our time coverage., What we are sure about is that ingress and egress phases were not detected within our time coverage.22 Solely this information constrains the possible orbits seriously in the transit time-impact parameter space., Solely this information constrains the possible orbits seriously in the transit time–impact parameter space.23stars (gt39 mas/yr. O180 deg: u104. mas/yr. ©=183 deg). respectively.,"stars $\mu =24139$ mas/yr, $\Theta = 180$ deg; $\mu = 104$ mas/yr, $\Theta = 183$ deg), respectively."25 However. the 2MASS colours for the MS star indicate that this star should be a late K dwarf at a distance of at least 500 pe. which excludes them as physical binary.," However, the 2MASS colours for the MS star indicate that this star should be a late K dwarf at a distance of at least 500 pc, which excludes them as physical binary."26 Finally. the reason. for the discrepancy between the predicted and measured radial velocity (Silvestri for HZ 9 (7) seems to be a misinterpretation.," Finally, the reason for the discrepancy between the predicted and measured radial velocity \citep{2002AJ....124.1118S} for HZ 9 (7) seems to be a misinterpretation."27" Silvestrietal.(2002) regarded it as à epm pair with another star 13""away.", \citet{2002AJ....124.1118S} regarded it as a cpm pair with another star away.28 However. the proper motion of the latter is completely different (11.4 mas/y) from the proper motion of the white dwarf HZ 9 (115 mas/y).," However, the proper motion of the latter is completely different (11.4 mas/y) from the proper motion of the white dwarf HZ 9 (115 mas/y)."29 On the other hand. Stauffer(1987) analysed the radial-velocity curve of HZ 9. confirmed its binary nature. and determined an M. dwarf-white dwarf separation of less than ΙΓ AU and a radial velocity of 36.7 kms! for the system. which agrees well with the predicted radial velocity.," On the other hand, \citet{1987AJ.....94..996S} analysed the radial-velocity curve of HZ 9, confirmed its binary nature, and determined an M dwarf–white dwarf separation of less than 1 AU and a radial velocity of 36.7 $\rm{km\,s}^{-1}$ for the system, which agrees well with the predicted radial velocity."30 To summarise the above discussion: none of the 10 classical candidates and of the 17 new probable former Hyades white dwarfs can, To summarise the above discussion: none of the 10 classical candidates and of the 17 new probable former Hyades white dwarfs can31"Perturbation of the momentum equation vields Now. the perturbation of the Doltzmann equation vields which implies df=0 because. [or entropy perturbations. w=ul, and koe=0. as deduced above.","Perturbation of the momentum equation yields Now, the perturbation of the Boltzmann equation yields which implies $\delta\! f = 0$ because, for entropy perturbations, $\omega = uk_x$ and $\vec{k}\cdot\delta\!\vec{v}=0$, as deduced above."32 Furthermore. since df=0. necessarily 917.QO. and (hus dP?=0.," Furthermore, since $\delta\!f =0$, necessarily $\delta\!P_c33=0$, and thus $\delta\!P =0$."34 It follows that entropy perturbations and particle perturbations are completely decoupled: in fact. entropy. perturbations are just advected by the zero-th order flow.," It follows that entropy perturbations and particle perturbations are completely decoupled: in fact, entropy perturbations are just advected by the zero-th order flow."35 In summary. entropy perturbations have the following characteristics. where we celine. for future convenience. =1/p: where (he last equation applies to ideal fluids: i is the average particle mass and fy3 Doltzmann's constant.," In summary, entropy perturbations have the following characteristics, where we define, for future convenience, $V\equiv361/\rho$: where the last equation applies to ideal fluids: $m$ is the average particle mass and $k_B$ Boltzmann's constant."37 We (urn now to isentropic perturbations. which antomatically satisly eq. 3..," We turn now to isentropic perturbations, which automatically satisfy eq. \ref{entropycons}."38 Mass conservation implies while momentum conservation implies Let us begin bv assuming that the left-hand-sile of eq.l1 vanishes: the same is then true for xy«óc.," Mass conservation implies while momentum conservation implies Let us begin by assuming that the left-hand-side of \ref{mass1}39 vanishes; the same is then true for $\bigtriangledown\cdot\delta\!\vec{v}$."40 Mulüiplàing eq., Multiplying eq.41 12 by AA. we see that XyAor=0. unless w=uh.," \ref{momentum1} by $\vec{k}\wedge$ , we see that $\bigtriangledown\wedge\delta\!\vec{v} = 0$, unless $\omega = uk_x$."42 If the cur] vanishes. then so does à. because anv vector with vanishing divergence and curl is a constant. which can alwavs be set to zero by a suitable choice of referencesvstem.," If the curl vanishes, then so does $\delta\!\vec{v}$, because any vector with vanishing divergence and curl is a constant, which can always be set to zero by a suitable choice of referencesystem."43 So we, So we44ages <10 kyr.,ages $\la10$ kyr.45 As argued by Gaensler ((1999)). this implies a lower limit on the Galactic birth-rate for AXPs of one per 1700 yr.," As argued by Gaensler \nocite{ggv99}) ), this implies a lower limit on the Galactic birth-rate for AXPs of one per 1700 yr."46 The young ages inferred for AXPs can place constraints on both magnetar and aceretion models for these sources., The young ages inferred for AXPs can place constraints on both magnetar and accretion models for these sources.47 In the context of the magnetar model. our upper limit on AXP ages. combined with their narrow range of spin periods. can be explained only if these sources undergo rapid magnetic field decay. as can result from a Hall cascade in the neutron star crust ()).," In the context of the magnetar model, our upper limit on AXP ages, combined with their narrow range of spin periods, can be explained only if these sources undergo rapid magnetic field decay, as can result from a Hall cascade in the neutron star crust \cite{cgp00}) )."48 Such a model specifically predicts that an AXP of true age ~10* will have a characteristic age τςP/2P~10°. which indeed is the case for AXP IE 22594586 (7~225 kyr: )) in the SNR CTB 109 (age ~ 10 kyr: )).," Such a model specifically predicts that an AXP of true age $\sim10^4$ will have a characteristic age $\tau = P/2\dot{P} \sim 10^5$, which indeed is the case for AXP 1E 2259+586 $\tau \sim 225$ kyr; \cite{kcs99}) ) in the SNR CTB 109 (age $\sim$ 10 kyr; \cite{rp97}) )."49 Any viable accretion model must produce sufficient torque to spin down an AXP from its presumed rapid birth period (<1 s) to its current spin-period (~10 s) in less than 107 yr., Any viable accretion model must produce sufficient torque to spin down an AXP from its presumed rapid birth period $\ll1$ s) to its current spin-period $\sim10$ s) in less than $10^4$ yr.50 While this rapid braking rules out many standard accretion scenarios ()). Chatterjee ((2000)) propose a model in which an AXP is a ~10? G neutron star which accretes from a fall-back disk of supernova debris.," While this rapid braking rules out many standard accretion scenarios \cite{vg97}) ), Chatterjee \nocite{chn00}) ) propose a model in which an AXP is a $\sim10^{13}$ G neutron star which accretes from a fall-back disk of supernova debris."51 In. this model. the neutron star is initially in a propellor phase in which its X-ray luminosity 1s too low to be detected.," In this model, the neutron star is initially in a propellor phase in which its X-ray luminosity is too low to be detected."52 After a few thousand years. the AXP will slow down sufficiently that it can begin to accrete and will become X-ray bright.," After a few thousand years, the AXP will slow down sufficiently that it can begin to accrete and will become X-ray bright."53 However. the mass aceretion rate will steadily decline as the disk is depleted. and after ~10 kyr the AXP will again become too faint to be detected.," However, the mass accretion rate will steadily decline as the disk is depleted, and after $\sim10$ kyr the AXP will again become too faint to be detected."54" This model thus predicts that AXPs will only be observed with ages ~101 yr and with a narrow range of spin periods, as is observed."," This model thus predicts that AXPs will only be observed with ages $\sim10^4$ yr and with a narrow range of spin periods, as is observed."55 Marsden ((2001)) have also recently considered associations of AXPs with SNRs., Marsden \nocite{mlrh01}) ) have also recently considered associations of AXPs with SNRs.56 In discussing such systems. they include the pairings // G346.6-0.2 and IE 1048.1-5937 / G287.8-0.5. both of which we have argued in Section 4.3. above to be spurious associations.," In discussing such systems, they include the pairings / G346.6–0.2 and 1E 1048.1–5937 / G287.8–0.5, both of which we have argued in Section \ref{sec_axp_other}57 above to be spurious associations."58 For the remaining three associations (listed in Table ??)). Marsden ((2001) assume each SNR to be in the Sedov phase of evolution and to have resulted from a supernova of kinetic energy Ep=10?! ere.," For the remaining three associations (listed in Table \ref{tab_snrs}) ), Marsden (2001) assume each SNR to be in the Sedov phase of evolution and to have resulted from a supernova of kinetic energy $E_0 = 10^{51}$ erg."59 They then use the SNR's estimated age. fgn and radius. Rsvp. to infer an ambient density. Πρ.," They then use the SNR's estimated age, $t_{\rm SNR}$ and radius, $R_{\rm SNR}$, to infer an ambient density, $n_0$."60 They conclude that the supernovae which form AXPs (and SGRs) oceur m regions of significantly higher density regions than those which make radio pulsars., They conclude that the supernovae which form AXPs (and SGRs) occur in regions of significantly higher density regions than those which make radio pulsars.61 Marsden ((2001)) argue that this result favors accreting models for AXPs. and specifically propose that the neutron star either aceretes gas as It overtakes the slowly-expanding SNR shell. or forms an aceretion disk from material pushed back by the encounter of the SNR with dense material.," Marsden \nocite{mlrh01}) ) argue that this result favors accreting models for AXPs, and specifically propose that the neutron star either accretes gas as it overtakes the slowly-expanding SNR shell, or forms an accretion disk from material pushed back by the encounter of the SNR with dense material."62 In either case. a high ambient density for AXPs suggests that their properties are due to their environment rather than are intrinsic to the source. a conclusion which would argue against the magnetar hypothesis.," In either case, a high ambient density for AXPs suggests that their properties are due to their environment rather than are intrinsic to the source, a conclusion which would argue against the magnetar hypothesis."63 However. there are a number of deficiencies with this argument.," However, there are a number of deficiencies with this argument."64 First. Kes 73 and possibly 6G29.64-0.1] are very young SNRs. which may not yet be in the Sedov phase.," First, Kes 73 and possibly G29.6+0.1 are very young SNRs, which may not yet be in the Sedov phase."65 In this case. the calculation used to infer an ambient density is not valid.," In this case, the calculation used to infer an ambient density is not valid."66 Second. for SNRs in the Sedov phase the ambient density depends on other parameters as foXEvtennare ," Second, for SNRs in the Sedov phase the ambient density depends on other parameters as $n_0 \propto E_0\, t_{\rm SNR}^2\, R_{\rm SNR}^{-5}$."67Uncertainties 1n fsyj and Ep of a factor of two. along with a uncertainty in the distance (all quite reasonable for Galactic SNRs). result in an uncertainty of two orders of magnitude in any estimate of o.," Uncertainties in $t_{\rm SNR}$ and $E_0$ of a factor of two, along with a uncertainty in the distance (all quite reasonable for Galactic SNRs), result in an uncertainty of two orders of magnitude in any estimate of $n_0$."68 Regardless of the uncertainties in these calculations. the conclusion that AXPs occur predominantly in denser regions (tg>0.1 em™) than do radio pulsars Gig~0.001 em) ean be entirely attributed to selection effects.," Regardless of the uncertainties in these calculations, the conclusion that AXPs occur predominantly in denser regions $n_0 > 0.1$ $^{-3}$ ) than do radio pulsars $n_0 \sim 0.001$ $^{-3}$ ) can be entirely attributed to selection effects."69 AXPs have generally been discovered serendipitously in X-ray observations of bright SNRs. the latter which are generally only detectable in high density regions (:: )).," AXPs have generally been discovered serendipitously in X-ray observations of bright SNRs, the latter which are generally only detectable in high density regions \cite{ksbg80}; \cite{gj95c}) )."70 On the other hand. young radio pulsars have mostly been detected in all-sky surveys. and their inferred values of no reflect the fact that most of the interstellar medium by volume is of low density.," On the other hand, young radio pulsars have mostly been detected in all-sky surveys, and their inferred values of $n_0$ reflect the fact that most of the interstellar medium by volume is of low density."71 When only radio pulsars associated with SNRs are considered. ambientdensities no~0.2 cm are inferred. ()). indicating that there is no obvious difference in ambient density between SNRs associated with radio pulsars and those containing AXPs.," When only radio pulsars associated with SNRs are considered, ambient densities $n_0 \sim 0.2$ $^{-3}$ are inferred \cite{fgw94}) ), indicating that there is no obvious difference in ambient density between SNRs associated with radio pulsars and those containing AXPs."72 A detection of radio pulsations from an AXP would make a strong case that these sources are isolated neutron stars rather than accreting systems., A detection of radio pulsations from an AXP would make a strong case that these sources are isolated neutron stars rather than accreting systems.73 Furthermore. this would make these sources amenable to radio timing observations and would provide distance estimates from their dispersion measures.," Furthermore, this would make these sources amenable to radio timing observations and would provide distance estimates from their dispersion measures."74 We have shown that there is no radio emission from oor 10ddown to limits of 3 mJy and 0.3 my respectively (5o. limits at 1.4 GHz)., We have shown that there is no radio emission from or down to limits of 3 mJy and 0.3 mJy respectively $\sigma$ limits at 1.4 GHz).75 Because these limits are determined from continuum images. they are more constraining than comparable non-detections from pulsed searches. which can have reduced sensitivity at long periods.," Because these limits are determined from continuum images, they are more constraining than comparable non-detections from pulsed searches, which can have reduced sensitivity at long periods."76 Similar non-detections of radio emission from the AXPs IE 2259+586 (0.08 mJy: ). and IE 1841-045 (0.6 mJy: )) have led Baring Harding (1998)) to argue that AXPs are “radio-quiet™.," Similar non-detections of radio emission from the AXPs 1E 2259+586 (0.08 mJy; \cite{cjl94}) ), and 1E 1841–045 (0.6 mJy; \cite{kbhc85}) ) have led Baring Harding \nocite{bh98b}) ) to argue that AXPs are “radio-quiet”."77 If AXPs are magnetars. this could result from photon-splitting in their magnetospheres. which prevents pair-production and thus suppresses the radio pulse mechanism.," If AXPs are magnetars, this could result from photon-splitting in their magnetospheres, which prevents pair-production and thus suppresses the radio pulse mechanism."78 The distances to these AXPs imply upper limits on their GHz radio luminosities of 1.2. 2.0. 29 and 320 mJy kpc? for O142+61u. TE 22594586. IE 1841-045 and Lyne ((1998)) derive a 400-MHz luminosity function for potentially observable radio pulsars aall pulsars in. the Galaxy beaming towards us. whether detected by current searches or as yet undiscovered).," The distances to these AXPs imply upper limits on their 1.4-GHz radio luminosities of 1.2, 2.0, 29 and 320 mJy $^2$ for u, 1E 2259+586, 1E 1841–045 and Lyne \nocite{lml+98}) ) derive a 400-MHz luminosity function for potentially observable radio pulsars all pulsars in the Galaxy beaming towards us, whether detected by current searches or as yet undiscovered)."79 Scaling this luminosity distribution to an observing frequency of 1.4 GHz by assuming a typical pulsar spectral index of ©=—2. we find that >60% of potentially observable radio pulsars have pulsed luminosities below | mJy kpe-. fainter than the deepest limits obtained towards the AXPs.," Scaling this luminosity distribution to an observing frequency of 1.4 GHz by assuming a typical pulsar spectral index of $\alpha = -2$, we find that $>$ of potentially observable radio pulsars have pulsed luminosities below 1 mJy $^2$, fainter than the deepest limits obtained towards the AXPs."80 The faet that that this small set of X-ray selected sources has not been detected at radio wavelengths therefore does not place any strong constraints on their intrinsic radio properties., The fact that that this small set of X-ray selected sources has not been detected at radio wavelengths therefore does not place any strong constraints on their intrinsic radio properties.81 Furthermore. models for pulsar beaming generally. predict that slower-spinning pulsars have narrower radio beams.," Furthermore, models for pulsar beaming generally predict that slower-spinning pulsars have narrower radio beams."82 Indeed the slowest radio pulsar. PSR J2144-3933 (for which P28.5 s. comparable to that of the AXPs). has the narrowest known pulse. of width less than 1* of the pulse phase ()).," Indeed the slowest radio pulsar, PSR J2144–3933 (for which $P=8.5$ s, comparable to that of the AXPs), has the narrowest known pulse, of width less than $1^\circ$ of the pulse phase \cite{ymj99}) )."83 If we assume a population of radio pulsars in which the magnetic axis is randomly oriented with respect both to the pulsar spin axis and, If we assume a population of radio pulsars in which the magnetic axis is randomly oriented with respect both to the pulsar spin axis and84"Finally. given the recent studies (e.g. see Zaldagarriaga aud Loeb. 2002) on the possible detection. wihiu the microwave background anisotropies. of the earlier imprint from the recombination history of lithium. the present results strongly suggest that such aulsotropies could be amenable to observation due to the changed optical depth induced by the changes on lithium abuucdauces We thank the CINECA aud CASPUR consortia for providing us with the necessary computational facilities aud the University of Roma ""Sapienza"" for partial financial support.","Finally, given the recent studies (e.g. see Zaldagarriaga and Loeb, 2002) on the possible detection, wihin the microwave background anisotropies, of the earlier imprint from the recombination history of lithium, the present results strongly suggest that such anisotropies could be amenable to observation due to the changed optical depth induced by the changes on lithium abundances We thank the CINECA and CASPUR consortia for providing us with the necessary computational facilities and the University of Roma “Sapienza” for partial financial support."85 Bennett QO.J.. 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C., 1996, ApJ, 458,"97Survevs (ACS) (Sarajeclinietal.2007)..,Surveys (ACS) \citep{2007AJ....133.1658S}.98 The data were taken as part of an treasury program to obtain high signal-to-noise ratio photometry down the to (he lower main sequence for a large number of Galactic globular clusters., The data were taken as part of an treasury program to obtain high signal-to-noise ratio photometry down the to the lower main sequence for a large number of Galactic globular clusters.99" We use Ἑρουμ and Lypoung (hereafter ""V and ""E) photometry. which were transformed from the original5 FGOGI and FSI4IV photometry."," We use $V_{ground}$ and $I_{ground}$ (hereafter $V$ ” and $I$ ”) photometry, which were transformed from the original $F606W$ and $F814W$ photometry."100 Artificial star tests demonstrate that the photometry is expected to be very. precise an| complete at the brightness of the RGDD (Andersonοἱal.2003).., Artificial star tests demonstrate that the photometry is expected to be very precise and complete at the brightness of the RGBB \citep{2008AJ....135.2055A}. .101 We also use U. B. V. and / observations that come from a database of original an| archival observations (Stetson2000).. which are calibrated oi the Landolt(1992) photometric svstem.," We also use $U$, $B$, $V$, and $I$ observations that come from a database of original and archival observations \citep{2000PASP..112..925S}, which are calibrated on the \citet{1992AJ....104..340L} photometric system."102 These observations and the general properties of the 47 Tue coloramagnitude diagram (CAID) are described in Bergbusch&Stetson(2009).., These observations and the general properties of the 47 Tuc color-magnitude diagram (CMD) are described in \citet{2009AJ....138.1455B}.103 We make use of stars in (hese observations that are outside of the coordinate range observed by the ACS dataset., We make use of stars in these observations that are outside of the coordinate range observed by the ACS dataset.104" The 135 point sources that are located within 30"" of (a.0) =(00:21:30.3 — 71:56:03). corresponding to the location of Bologna A (Bellazzinietal.2005).. ave not included in our analvsis."," The 135 point sources that are located within $\arcsec$ of $(\alpha,\delta)=$ (00:21:30.3 $-$ 71:56:03), corresponding to the location of Bologna A \citep{2005A&A...435..871B}, are not included in our analysis."105 This does not affect our analvsis as (he background population is way outside the cluster center and its spatial extent is only GO”., This does not affect our analysis as the background population is way outside the cluster center and its spatial extent is only $\arcsec$.106 We show the respective fields of view in Figure 1.., We show the respective fields of view in Figure \ref{Fig:FieldOfView}. .107 CMDs for the space-based and ground-based are respectively shown in Figures 2. and 3.., CMDs for the space-based and ground-based are respectively shown in Figures \ref{Fig:CMDHubble} and \ref{Fig:CMDGroundBased}.108 We use (he Yale Rotating Evolution Code (Delahaveetal.2010) to compare our output parameters to theory for the RG and RGBB populations., We use the Yale Rotating Evolution Code \citep{2010arXiv1005.0423D} to compare our output parameters to theory for the RG and RGBB populations.109 Theoretical considerations for the IIB population are taken [rom the literature (Renzini1994:VenturaSalaris2001:Ventura&D'Antona2009:diCriscienzoetal. 2010)..," Theoretical considerations for the HB population are taken from the literature \citep{1994A&A...285L...5R,1998A&A...334..953V,2001MNRAS.323..109G,2009A&A...499..835V,2010MNRAS.408..999D}."110 At the expected metallicity ([M/I]o —0.50) and age (512 Gyr) of 47 Tuc (MeWilliam 2010).. we find that every increase in the initial helium abundance by total stellar mass vields a 7104 decrease in the lifetime of the RGBB. corresponding to a decrease of «0.02 mag in the EW.," At the expected metallicity $\sim -0.50$ ) and age $\sim$ 12 Gyr) of 47 Tuc \citep{2008ApJ...684..326M,2010A&A...516A..55C}, we find that every increase in the initial helium abundance by total stellar mass yields a $\sim$ decrease in the lifetime of the RGBB, corresponding to a decrease of $\sim$ 0.02 mag in the EW."111 Two representative models are shown in Figure 4.., Two representative models are shown in Figure \ref{Fig:StellarTracks}.112 Within the models. we compute the EW of the RGDD by multiplving the lifetime of the RGBB by the average of the two slopes of magnitude versus time belore and after the RGBB.," Within the models, we compute the EW of the RGBB by multiplying the lifetime of the RGBB by the average of the two slopes of magnitude versus time before and after the RGBB."113 The predicted stellar properties of the RGDD as a function of initial composition are summarized in Table 1., The predicted stellar properties of the RGBB as a function of initial composition are summarized in Table 1.114 We note the helium-rich track has a higher initial [M/II] only because it has a lower initial hydrogen abundance the initial metallicity content by mass are the same., We note the helium-rich track has a higher initial [M/H] only because it has a lower initial hydrogen abundance – the initial metallicity content by mass are the same.115 We also introduce thenotation 9Vge;psg to refer to the dillerence in magnitudes between the brightest ancl faintest parts of the RGDD phase aspredicted by stellar mocels., We also introduce thenotation ${\delta}V_{RGBB}$ to refer to the difference in magnitudes between the brightest and faintest parts of the RGBB phase aspredicted by stellar models.116Very sensitive test the sample is also consistent with an assumed scale height of 120 pe (in this case. the probability that the model and. observed distributions are drawn from the same population is 0.14).,"very sensitive test — the sample is also consistent with an assumed scale height of 120 pc (in this case, the probability that the model and observed distributions are drawn from the same population is 0.14)."117" In Pretoriusctal.(2007b).. we found. po=1.1""e10""pe? from the NEP sample of only 4 CVs."," In \cite{NEPrho}, we found $\rho_0 = 1.1^{+2.3}_{-0.7} \times 10^{-5}\,\mathrm{pc^{-3}}$ from the NEP sample of only 4 CVs."118 Given the large errors in both this previous measurement and the one based on the combined survey presented: here. they are not too dillerent.," Given the large errors in both this previous measurement and the one based on the combined survey presented here, they are not too different."119 However. if we calculate po based on the RBS alone. the result is almost an order of magnitude less than a measurement based only on the NEP survey.," However, if we calculate $\rho_0$ based on the RBS alone, the result is almost an order of magnitude less than a measurement based only on the NEP survey."120 The logtpo/pc) probability distribution functions for the two separate samples are shown in Fig., The $\log(\rho_0/\mathrm{pc})$ probability distribution functions for the two separate samples are shown in Fig.121 G and are at first sight inconsistent., \ref{fig:comparepdf} and are at first sight inconsistent.122 This would be easy. to understand if the NEP survey were simply more powerful than the RBS. ie. if it reached a fainter population (represented by the faint system LEX Dra) than the RBS was capable of finding.," This would be easy to understand if the NEP survey were simply more powerful than the RBS, i.e. if it reached a fainter population (represented by the faint system EX Dra) than the RBS was capable of finding."123" However. this is not the case.the RBS is in fact more powerful than the NEP survey,"," However, this is not the case—the RBS is in fact more powerful than the NEP survey."124 Despite the much brighter Hux limit of the RBS. it reached a larger volume (at all Ly) than the NEP survey. because of its wider angle (see Fig. 7)).," Despite the much brighter flux limit of the RBS, it reached a larger volume (at all $L_X$ ) than the NEP survey, because of its wider angle (see Fig. \ref{fig:survey_vol}) )."125 lt is then a Luke that the faintest CV in our combined sample was detected in the NEP survey. rather than in the RBS.," It is then a fluke that the faintest CV in our combined sample was detected in the NEP survey, rather than in the RBS."126 Based on the detection of EX Dra in the NEP survey. we would expect to detect around 2 such svstems in the RBS (since the volume of the RBS for CVs as bright as EX Dra is roughly twice that of the NEP survey): the non-detection of any CY at that Ly in the RBS is therefore unlucky. but has less than 2-0 significance.," Based on the detection of EX Dra in the NEP survey, we would expect to detect around 2 such systems in the RBS (since the volume of the RBS for CVs as bright as EX Dra is roughly twice that of the NEP survey); the non-detection of any CV at that $L_X$ in the RBS is therefore unlucky, but has less than $\sigma$ significance."127 )evond. this one dominant system. to determine whether the results of the two surveys can be reconciled. we need to consider the luminosities of all the observed systems.," Beyond this one dominant system, to determine whether the results of the two surveys can be reconciled, we need to consider the luminosities of all the observed systems."128 Fig., Fig.129 S shows the observed luminosity functions (constructed in the same wav as for the combined survey in Section 4.2)) of the RBS and NIZP separately., \ref{fig:rbsnepconsistent} shows the observed luminosity functions (constructed in the same way as for the combined survey in Section \ref{sec:obsphi}) ) of the RBS and NEP separately.130 Over-plotted are the output distributions. found as is Section 5.2.1.. but again treating the (wo surveys separately.," Over-plotted are the output distributions, found as is Section \ref{sec:simphicalc}, but again treating the two surveys separately."131 Both simulations use as input the best-estimate power law d found in the previous section., Both simulations use as input the best-estimate power law $\Phi$ found in the previous section.132 Least-squares fits of the output from the models to the observed Luminosity functions give reduced x7 o£ 0.8 and 0.9 for the RBS and. NEP survey. respectively: both acceptable values.," Least-squares fits of the output from the models to the observed luminosity functions give reduced $\chi^2$ of 0.8 and 0.9 for the RBS and NEP survey, respectively; both acceptable values."133" Therefore. despite the large difference in py when the two surveys are considered separately, they are consistent to within their uncertainties."," Therefore, despite the large difference in $\rho_0$ when the two surveys are considered separately, they are consistent to within their uncertainties."134" A basic assumption of the 1/1,,,; method is that the detected. objects. are. representative of the luminosity function of the true underlying CV population.", A basic assumption of the $1/V_{max}$ method is that the detected objects are representative of the luminosity function of the true underlying CV population.135 Note that ‘representative’ here does not imply that faint svstems are as common in the observed sample as intrinsically. but only that some (or even one) are detected (see Section 3.2.3)).," Note that `representative' here does not imply that faint systems are as common in the observed sample as intrinsically, but only that some (or even one) are detected (see Section \ref{sec:test}) )."136 For an indication of whether our sample is likely to be representative of the underlying CW population. ancl thus gives reliable p and & estimates. it is important to know how faint CVs can be in X-rays.," For an indication of whether our sample is likely to be representative of the underlying CV population, and thus gives reliable $\rho$ and $\Phi$ estimates, it is important to know how faint CVs can be in X-rays."137 Theory predicts that the vast majority of CVs should, Theory predicts that the vast majority of CVs should138of the spectra and give an insight into the presence of basic components of the spectra and the extent to which a possibly relativistically broadened component is required to model the FeKK line region.,of the spectra and give an insight into the presence of basic components of the spectra and the extent to which a possibly relativistically broadened component is required to model the K line region.139" None of the spectra required any significant warm absorber (see Section 2.1), thereby simplifying any present broadening in the region."," None of the spectra required any significant warm absorber (see Section 2.1), thereby simplifying any present broadening in the region."140" Additionally the model representing Comptonization of soft photons in a hot plasma above the disc (Titarchuk 1994) with a soft photon input temperature of kkeV, is employed to account for the soft excess if present in the spectra (see Figure 1))."," Additionally, the model representing Comptonization of soft photons in a hot plasma above the disc (Titarchuk 1994) with a soft photon input temperature of keV, is employed to account for the soft excess if present in the spectra (see Figure \ref{fig:soft}) )."141 Porquet et al. (, Porquet et al. (142"2004) also found that in a sample of PG quasars the soft excess was better modelled in this way, rather than by thermal emission from the accretion disc.","2004) also found that in a sample of PG quasars the soft excess was better modelled in this way, rather than by thermal emission from the accretion disc."143 A second soft component instead of also gives a similar parametrization of the soft excess., A second soft component instead of also gives a similar parametrization of the soft excess.144 The narrow 6.4kkeV core due to reflection from distant material is present in all six objects and has been modelled with a narrow Gaussian with width σκα free to vary., The narrow keV core due to reflection from distant material is present in all six objects and has been modelled with a narrow Gaussian with width $\sigma_{\rm K{\alpha}}$ free to vary.145" The narrow component is not resolved in any of the spectra and as such the width is fixed at oka=0.01 kkeV. Emission resulting from KK is also accounted for with the line energy fixed at kkeV, width fixed to that of the narrow Ka and flux tied to of the Ko component."," The narrow component is not resolved in any of the spectra and as such the width is fixed at $\sigma_{\rm K{\alpha}}=0.01$ keV. Emission resulting from $\beta$ is also accounted for with the line energy fixed at keV, width fixed to that of the narrow $\alpha$ and flux tied to of the $\alpha$ component."146" Consistent with this, neutral distant reflection is accounted for using the model (Magdziarz Zdziarski 1995) applied to the broad-band εν spectra."," Consistent with this, neutral distant reflection is accounted for using the model (Magdziarz Zdziarski 1995) applied to the broad–band keV spectra."147" This model requires the input of a photon index I which is tied to the continuum powerlaw, the normalization of the component is also tied to that of the powerlaw, abundances are assumed to be Solar (Anders Grevesse 1989) and the disc inclination to the observer is fixed at cosi—0.87 throughout."," This model requires the input of a photon index $\Gamma$ which is tied to the continuum powerlaw, the normalization of the component is also tied to that of the powerlaw, abundances are assumed to be Solar (Anders Grevesse 1989) and the disc inclination to the observer is fixed at $cos\,i=0.87$ throughout."148 The reflection fraction RΩ/2π is left as a free parameter (where R=1 denotes reflection from material subtending 27 ssr)., The reflection fraction $R=\Omega/2\pi$ is left as a free parameter (where $R=1$ denotes reflection from material subtending $2\pi$ sr).149" The cut- energy for the component is fixed at kkeV,"," The cut-off energy for the component is fixed at keV,"150lligh resolution simulations by Abel.Bryan.&Norman(2000.2002) of the formation of the first star suggest that fragmentation during the collapse of metal-Iree pregalactic halos is rather inefficient. resulting in the formation of single. massive stars rather than clusters of lower-imass objects.,"High resolution simulations by \citet{abn00, abn02} of the formation of the first star suggest that fragmentation during the collapse of metal-free pregalactic halos is rather inefficient, resulting in the formation of single, massive stars rather than clusters of lower-mass objects."151 In the absence of metals. inefficient cooling max result in hieh 5. perhaps helping to explain these results.," In the absence of metals, inefficient cooling may result in high $\gamma$, perhaps helping to explain these results."152" We do note. however. (hat simulations by DBromam.Coppi.&Larson(1999.2002). show ereater multiplicity,"," We do note, however, that simulations by \citet{bcl99, bcl02} show greater multiplicity."153 Thev use similar chemistvy. but. examine more massive. more isolated halos. with substantially larger limiting mass resolution.," They use similar chemistry, but examine more massive, more isolated halos, with substantially larger limiting mass resolution."154 The EOS will have less effect on these larger scales. which are more dominated by gravity.," The EOS will have less effect on these larger scales, which are more dominated by gravity."155 If the metal-free gas indeed shows a high effective 5. our models would suggest that their collapsing regions will show little further fragmentation if followed clown to stellar mass scales.," If the metal-free gas indeed shows a high effective $\gamma$, our models would suggest that their collapsing regions will show little further fragmentation if followed down to stellar mass scales."156 We thank M. Fall. IL. Lamers. IL. Zinnecker. for valuable discussions. ancl D. Janies and W. Wheeler for their work on the AMNIL Parallel Computing Facility. which we used for the computations presented here.," We thank M. Fall, H. Lamers, H. Zinnecker, for valuable discussions, and D. Janies and W. Wheeler for their work on the AMNH Parallel Computing Facility, which we used for the computations presented here."157corrections.. YL thanks the AIP for its warm hospitality. and the Ixade Foundation for support of her visits there.," YL thanks the AIP for its warm hospitality, and the Kade Foundation for support of her visits there."158 M-MML acknowledges partial support bv NASA ATP erant NÀG5-10103. and by NSF CAREER grant. AST99-85392.," M-MML acknowledges partial support by NASA ATP grant NAG5-10103, and by NSF CAREER grant AST99-85392."159 RSI acknowledges support bv the Emmy Noether Program of the Deutsche Forsehungsgemeinschalt (DEG. KL1358/1).," RSK acknowledges support by the Emmy Noether Program of the Deutsche Forschungsgemeinschaft (DFG, KL1358/1)."160low binary fractious for lowe-inass stars. which ds not observed.,"low binary fractions for low-mass stars, which is not observed."161 Nonetheless. since the ejection model predicts the disruption of potential brown cawarf binarics at very carly ages. while also imposing a limit to the dimoenusious of such svsteuis (Reipurth&Clarke2001).. it slows some pronuse in explaining the origius of substellar svstenis in eoncral.," Nonetheless, since the ejection model predicts the disruption of potential brown dwarf binaries at very early ages, while also imposing a limit to the dimensions of such systems \citep{rpt01}, it shows some promise in explaining the origins of substellar systems in general."162 The preference for brown dwarts to form close binaries may not uccessarily require a disruptive process. however.," The preference for brown dwarfs to form close binaries may not necessarily require a disruptive process, however."163 Studies of voung binary stars favor fragnieutatiou (Boss198S) as the doniunuaut mode of binary formation. due to coevality of components. the presence of circinibinarvyv structures. aud the prefereuce for equalauass components in closely-sceparated svstenis (White&Chez9001).," Studies of young binary stars favor fragmentation \citep{bos88} as the dominant mode of binary formation, due to coevality of components, the presence of circumbinary structures, and the preference for equal-mass components in closely-separated systems \citep{whi01}."164" These conditious do not require dynamical disruption frou, neighboring protostellu systems.", These conditions do not require dynamical disruption from neighboring protostellar systems.165 In general. a low-mass eas and dust core must collapse to smaller dimensions before 3t achieves sufficient densities to continue fragmentation. producing multiple svstemis which are initially closely separated.," In general, a low-mass gas and dust core must collapse to smaller dimensions before it achieves sufficient densities to continue fragmentation, producing multiple systems which are initially closely separated."166 This suggests a miaxinmuu separation dependence on nass as hinted at in Figure S. although: no theoretical prediction as such has beeu made.," This suggests a maximum separation dependence on mass, as hinted at in Figure 8, although no theoretical prediction as such has been made."167 The ceficicney of low-ass pairs may arise frou the inability for very small cloud clamps to both form and also continue fragmenting. although the influence of magnetic fields. turbulence. and external perturbations would also have substantial influence.," The deficiency of low-mass pairs may arise from the inability for very small cloud clumps to both form and also continue fragmenting, although the influence of magnetic fields, turbulence, and external perturbations would also have substantial influence."168" Current models (o.@.. Boss 2001) are capable of producing core fragimoeuts in the range of LOs of Jupiter masses ii the mass range of Geld L aud T brown dwarfs. but (ΛΕΡ).masses down 1l Mj, require dynamical ejection to prevent further accretion."," Current models (e.g., Boss 2001) are capable of producing core fragments in the range of 10s of Jupiter masses $_{Jup}$ ), in the mass range of field L and T brown dwarfs, but masses down to 1 $_{Jup}$ require dynamical ejection to prevent further accretion."169 The sinulavity in the binary fractions and separation distributions for cluster aud field low-inass svstenis. and the low probabilitysom of dwuamic disruption m allbut the densest stellar cuviromueuts. makes it highly probable that the fieldbrown dwarfbinary distribution is quite simular to the natal distribution.," The similarity in the binary fractions and separation distributions for young cluster and field low-mass systems, and the low probability of dynamic disruption in all but the densest stellar environments, makes it highly probable that the field brown dwarf binary distribution is quite similar to the natal distribution."170 This is important. as the distances aud dust opacity of protostcllar euviromuenuts. and the relative füutuess of protosubstellar objects. males investigation of brown dwarf formation at very carly ages quite difficult.," This is important, as the distances and dust opacity of protostellar environments, and the relative faintness of protosubstellar objects, makes investigation of brown dwarf formation at very early ages quite difficult."171 Bhuproviug the statistics for field ποπ dwarf systems. and cxamining closer separation roges through radial velocity techniques. should provide considerable insight iuto the formation of these very ow-lnass objects.," Improving the statistics for field brown dwarf systems, and examining closer separation regimes through radial velocity techniques, should provide considerable insight into the formation of these very low-mass objects."172 We find that both fracmentation and ejection inodels produce some of the qualitative characteristics of Ilate-M. L. aud T cuf binaries. aud it is xossible that substellar svsteiis form by some combination of these processes.," We find that both fragmentation and ejection models produce some of the qualitative characteristics of late-M, L, and T dwarf binaries, and it is possible that substellar systems form by some combination of these processes."173 However. more detailed quantitative xedietious niust be matched with large. unbiased sample statistics before conclusive statements can be mace ou the onuation of brown dwarfs.," However, more detailed quantitative predictions must be matched with large, unbiased sample statistics before conclusive statements can be made on the formation of brown dwarfs."174 We thiuk our referee. CClose. for in-depth criticisius iid helpful sugeestions for our manuscript. and useful discussions on wide stellar biuaries.," We thank our referee, Close, for in-depth criticisms and helpful suggestions for our manuscript, and useful discussions on wide stellar binaries."175" We also thank GChez. Whocrner, LLiebert for discussions on disks aud binary star formation: aud Whoerner ivl DDolphin for useful discussions ou PSF fittine."," We also thank Ghez, Koerner, Liebert for discussions on disks and binary star formation; and Koerner and Dolphin for useful discussions on PSF fitting."176" AJB acknowledges support by NASA through IHubble Fellowship eraut IIST-IIE-O011237.01. awarded by the Space Telescope Science Institute. which is operated bv the Association of Universities. for Research iu Astronomy. Πιο, for NASA. uuder contract NASPropulsion 5-26555,"," AJB acknowledges support by NASA through Hubble Fellowship grant HST-HF-01137.01 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS 5-26555."177 1Ο] acknowledges the support of the Jet Laboratory. California Tustitute of Technology. which is operated under contract with the Natioual Acronautics and Space Adininistration.," JDK acknowledges the support of the Jet Propulsion Laboratory, California Institute of Technology, which is operated under contract with the National Aeronautics and Space Administration."178" Based im part on observations made with the NASA/ESA IDIubble Space Telescope. obtained at the Space Telescope Science Tustitute. which is operated by the Association of Universities for Research in Astronomy. Inc.. under NASA contract NAS 5-26555,"," Based in part on observations made with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555."179 These observations are associated with proposal ID. 8563, These observations are associated with proposal ID 8563.180 This publication makes use of data from the Two Micron All Sky Survey. which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Ceuter. fundedby theNational Aeronauties aud Space Achuinistration aud theNational Science Foundation.," This publication makes use of data from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center, funded by the National Aeronautics and Space Administration and the National Science Foundation."181 When binary fractions (or other equivalent frequency statistics) are quoted in the literature. they are frequently assigned Poisson uucertaiuties.," When binary fractions (or other equivalent frequency statistics) are quoted in the literature, they are frequently assigned Poisson uncertainties."182 However. the Poisson limit applies ouly in the case of a large sample. whereas the brown dwarf salples discussed here are less than 30 qn nuuber.," However, the Poisson limit applies only in the case of a large sample, whereas the brown dwarf samples discussed here are less than 30 in number."183 Hence. we derived statistical uncertaintiesby coustructing a probability distribution for e; u the total sample size. NV. and the ummber of binaries in the sample. ον ," Hence, we derived statistical uncertaintiesby constructing a probability distribution for ${\epsilon}_b$ given the total sample size, $N$, and the number of binaries in the sample, $n$ ."184"The binomial distribution determines the probabilityge of finding v binaries elven the sample size and binary fraction. as: ILowever. this equation may also be used the probability distribution of ej; given the observed. quantities N aud i. To do this we compute B'(eyi.IN)x""na€,) for 0xej 1l. normalizing which vields B/=(N|LB."," The binomial distribution determines the probability of finding $n$ binaries given the sample size and binary fraction, as: However, this equation may also be used to derive the probability distribution of ${\epsilon}_b$ given the observed quantities N and n. To do this, we compute $B^{\prime}({\epsilon}_b;n,N) \propto B(n;N,{\epsilon}_b)$ for $0185\leq {\epsilon}_b \leq 1$ , normalizing which yields $B^{\prime} = (N+1)B$."186 Figure 9 plots B’ for our T dwarf sample. NV=10 aud 5= 2.," Figure 9 plots $B^{\prime}$ for our T dwarf sample, $N = 10$ and $n = 2$ ."187" To derive upper aud lower uucertaiutv limits. 6 and c. we computed thevalues forBH whichB [οCüBide, = mBide,= ONL. equivaleut to lolimits for a Gaussian distribution."," To derive upper and lower uncertainty limits, ${\epsilon}^U_b$ and ${\epsilon}^L_b$ , we computed thevalues for which $\int_0^{{\epsilon}^U_b}{B^{\prime}{\rm d}{\epsilon}_b}$ = $\int_{{\epsilon}^L_b}^{1}{B^{\prime}{\rm d}{\epsilon}_b}$= 0.84, equivalent to $\sigma$limits for a Gaussian distribution."188are most useful.,are most useful.189 For clistaut stars. arouud which only relativly high planets can be detected. the H and As bands are much better.," For distant stars, around which only relativly high planets can be detected, the $H$ and $K_S$ bands are much better."190 We will now quantitatively describe the advantage of L’ and AL band observatious over shorter waveleneths [or plauet-searcl observatious of nearby stars., We will now quantitatively describe the advantage of $L'$ and $M$ band observations over shorter wavelengths for planet-search observations of nearby stars.191 Alost AO planet searches to date have used the Η and vy bands. or specialized filters in the same wavelenetl regune.," Most AO planet searches to date have used the $H$ and $K_S$ bands, or specialized filters in the same wavelength regime."192 While the Avg baud lias been used exteusively to search lor planets around voung stars (Masceiadrietal.2005:Chauvin 2010).. our comparison here will focus on the H baud regine.," While the $K_S$ band has been used extensively to search for planets around young stars \citep{masciadri,chauvin}, , our comparison here will focus on the $H$ band regime."193fae) Models indicate it offers better sensitivity than the As baud except for planets younger than 100 Myr (Burrowsetal.2003:Baralle2003).. ancl most of the stars we will suggestMOD the L’ and the AZ bands are useful for will be older than this.," Models indicate it offers better sensitivity than the $K_S$ band except for planets younger than 100 Myr \citep{bur,bar}, and most of the stars we will suggest the $L'$ and the $M$ bands are useful for will be older than this."194 The most sensitive H-reeime planet search observations made to date are those of Lafreniereetal.(2007).. in part because oL their optimized narrow-baud filter.," The most sensitive $H$ -regime planet search observations made to date are those of \citet{GDPS}, in part because of their optimized narrow-band filter."195 They attaiued au effective background-limited poiut-source sensitivity of about -23.0., They attained an effective background-limited point-source sensitivity of about $H=23.0$.196 Based on the models of Burrowsetal.(2003).. would Lave set better planetarymj mass limits than our observatious around all of our own survey targets except the very uearest objects. such as € Eri and 61 Cyg.," Based on the models of \citet{bur}, \citet{GDPS} would have set better planetary mass limits than our observations around all of our own survey targets except the very nearest objects, such as $\epsilon$ Eri and 61 Cyg."197 Thus. : present. the A-rveeime delivers far better planet detection prospects than the £/ aud AZ bands for most stars.," Thus, at present, the $H$ -regime delivers far better planet detection prospects than the $L'$ and $M$ bands for most stars."198 However. as detector technology improves. larger telescopes are built. aud louger planet detection exposures are attempted. the seusitivity at all waveleugths will increase.," However, as detector technology improves, larger telescopes are built, and longer planet detection exposures are attempted, the sensitivity at all wavelengths will increase."199 This means that planets. with their red IR colors. will be detectable at larger clistauces. aud the utility of the £/ and especially the AZ bands will increase.," This means that low-temperature planets, with their red IR colors, will be detectable at larger distances, and the utility of the $L'$ and especially the $M$ bands will increase."200 In Figure 2. we show the minimum detectable planet mass for hypotlietical stars at LO aud 25 pe distauce as a function of the increase over current sensitivity in the A. ή. and M bands. and in Figure G we present the same comparison for a star at 2 pc.," In Figure \ref{fig:HLM1} we show the minimum detectable planet mass for hypothetical stars at 10 and 25 pc distance as a function of the increase over current sensitivity in the $H$ , $L'$, and $M$ bands, and in Figure \ref{fig:HLM2} we present the same comparison for a star at 5 pc."201 We have taken current sensitivity to be H=23.0 (i.e.. Lalreniereetal. (2007))). L/=16.5. aud AZ=13.5 (Le.. the present work. scaled to au Sim telescope such as used).," We have taken current sensitivity to be $H = 23.0$ (i.e., \citet{GDPS}) ), $L' = 16.5$, and $M = 13.5$ (i.e., the present work, scaled to an 8m telescope such as \citet{GDPS}202 used)."203 These are background limits. uot applicable close to bright stars.," These are background limits, not applicable close to bright stars."204 Based ou. (2008).. we believe the £/ and A bands will do even better relative to A closer to the star where observations are no longer background limited.," Based on \citet{newvega}, we believe the $L'$ and $M$ bands will do even better relative to $H$ closer to the star where observations are no longer background limited."205 Of course A band observatious witli next-geueratiou extremeAO systems such as GPI aud SPHERE will offer improved performance close to the star. but advances in A/-baud AO coronography (e.g. Wenworthyetal. (2007))). will also improve the longer-waveleneth results.," Of course $H$ band observations with next-generation extremeAO systems such as GPI and SPHERE will offer improved performance close to the star, but advances in $M$ -band AO coronography (e.g. \citet{phaseplate}) ), will also improve the longer-wavelength results."206 Iu any. case. Figures 5 and 6 Compare backerounucd-limitecdl performance ouly.," In any case, Figures \ref{fig:HLM1}207 and \ref{fig:HLM2} compare background-limited performance only."208 The supression of [lux in the AZ baud due to elevated levels of CO does uot apply to planets at the low temperatures relevant lor Figures 5 anc 6..," The supression of flux in the $M$ band due to elevated levels of CO \citep{L07,reid} does not apply to planets at the low temperatures relevant for Figures \ref{fig:HLM1} and \ref{fig:HLM2}."209 Based ou Burrowsetal.(2003).. the entire mass range covered by both Figures corresponds to plauets with below 500k. except for planets with masses above 6.5 in the left panel of Figure 5 (25 pe distauce. 300 Myr age).This upper section of the 25 pe. 300 Myr panel is irrelevant to the important implications ofthe ligure.," Based on \citet{bur}, the entire mass range covered by both Figures corresponds to planets with below 500K, except for planets with masses above 6.5 in the left panel of Figure \ref{fig:HLM1} (25 pc distance, 300 Myr age).This upper section of the 25 pc, 300 Myr panel is irrelevant to the important implications ofthe figure."210 According to Hubeuy&Burrows (2007).. there is no supression of the AZ baud [or effective temperatures below 2001. We have deliberately chosen the characteristies of the bypothetical stars in Figures 2. aud 6 ," According to \citet{NCE}, , there is no supression of the $M$ band for effective temperatures below 500K. We have deliberately chosen the characteristics of the hypothetical stars in Figures \ref{fig:HLM1} and \ref{fig:HLM2} "211due to the collision of the mainly. vertical flow in the bulk of the box with the impenetrable boundaries.,due to the collision of the mainly vertical flow in the bulk of the box with the impenetrable boundaries.212 This large horizontal flow is non physical and as such we do not include the regions near (he boundaries in our caleulations., This large horizontal flow is non physical and as such we do not include the regions near the boundaries in our calculations.213 Ignoring this external energy source is not important for the fitting of the spatial dependence of the deposited energy since it will be ignored from both e and Wu., Ignoring this external energy source is not important for the fitting of the spatial dependence of the deposited energy since it will be ignored from both $W_{xy}^{turb}$ and $W_{xy}^{visc}$.214" llowever. if some amount of this energv makes it (o the region of the box used to caleulate Ww belore the turbulent cascade has dissipated it. i will act to artificially increase Wow, and consequently decrease the effective viscosity we calculate."," However, if some amount of this energy makes it to the region of the box used to calculate $\widetilde{W}_{xy}^{visc}$ before the turbulent cascade has dissipated it, it will act to artificially increase $\widetilde{W}_{xy}^{visc}$, and consequently decrease the effective viscosity we calculate."215" The (11ος dependences in each of the plots of figures 11. and 19 correspond to three different forcing strengths: strong forcing with ej,/Crone722.7. weak forcing with τος)Cooney82OF and the pertubative caleulation with epo0,«l. where eg, is the peak velocity due to the external forcing and ¢,,,,. is the root mean square velocity for the central plane of the box in the absence of forcing."," The three dependences in each of the plots of figures \ref{fig:216xz_visc_comparison} and \ref{fig: xy_visc_comparison} correspond to three different forcing strengths: strong forcing with $v_{forc}/v_{conv}\approx2.7$, weak forcing with $v_{forc}/v_{conv}\approx0.4$ and the pertubative calculation with $v_{forc}/v_{conv}\ll1$, where $v_{forc}$ is the peak velocity due to the external forcing and $v_{conv}$ is the root mean square velocity for the central plane of the box in the absence of forcing."217 The svstematic difference between the three viscosities suggests a possibly important amplitude dependence of the dissipation efficiency., The systematic difference between the three viscosities suggests a possibly important amplitude dependence of the dissipation efficiency.218" Ir order to get some idea for the importance of the magnitude of the external shear in determining the values of AT, we performed four additional simulations with : dependent external forcing with period T—7/2 with strengths intermediate between the strong and weak Iorcing cases considered above (see table 72? [or the details of each run and figures 7 and LO [or the energy rate curves)."," In order to get some idea for the importance of the magnitude of the external shear in determining the values of $K_{1313}^0$ we performed four additional simulations with $z$ dependent external forcing with period $T=\tau_c/2$ with strengths intermediate between the strong and weak forcing cases considered above (see table \ref{tbl:amp runs}219 for the details of each run and figures \ref{fig: Amp_W_fit} and \ref{fig:220Amp_W_visc} for the energy rate curves)."221 Using the same (wo methods discussed above. we estimate the effective viscosity for Chose cases. which we plot in figure 13.. where we have also added (he value of the fitted straight lines for the strong and weak forcing from figure 11. at half the convective turnover (ime.," Using the same two methods discussed above, we estimate the effective viscosity for those cases, which we plot in figure \ref{fig: A dependence}, where we have also added the value of the fitted straight lines for the strong and weak forcing from figure \ref{fig:222xz_visc_comparison} at half the convective turnover time."223" A. 100 LOAL, 10/9 cre&Ἐν in the Milkv Wav and other Local Cwoup galaxies2006).", $\Msun$ $100$ $10^5 \Msun$ $10^{40}$ $\rm erg \; s^{-1}$ in the Milky Way and other Local Group galaxies.224.. These SOTDον call casily be explained by the theory of stellar evolution aud collapse., These sources can easily be explained by the theory of stellar evolution and collapse.225 Cool thermal components found in the spectra of some ULX sources provide additional support for the IMDBII interpretation., Cool thermal components found in the spectra of some ULX sources provide additional support for the IMBH interpretation.226 Due to the scaling of the characteristic eravitational radius aud Iumiuositv with mass. accretion disks radiating at a fixed fraction of the Eddinegtou uniunositv will tend to have lower maxiunun effective cluperatures for huger masses if the tuner radius of he accretion. flow scales with the eravitational radius of the BIT1973).," Due to the scaling of the characteristic gravitational radius and luminosity with mass, accretion disks radiating at a fixed fraction of the Eddington luminosity will tend to have lower maximum effective temperatures for larger masses if the inner radius of the accretion flow scales with the gravitational radius of the BH."227. In many luminous ULNs. fits with multicolor cist dlackbody models favor relatively cool disksla.," In many luminous ULXs, fits with multicolor disk blackbody models favor relatively cool disks."228b).. Towever. the disk component im uauv of these spectral fits only accounts for a small or niodest fraction of the bolometric power2009).. which is instead dominated by a power law component. eenerallv hought to be inverse Compton scattering of disk xiotous by hot electrous.," However, the disk component in many of these spectral fits only accounts for a small or modest fraction of the bolometric power, which is instead dominated by a power law component, generally thought to be inverse Compton scattering of disk photons by hot electrons."229 If the majority of the enission originates in the hard compoucut. it is no longer clear hat the thermal component is associated with euission roni near the inner edee of the disk (as opposed to arecr radi). aud the areuneut that a larger emüttiug area follows from a larger eravitational racius (1.0. a large nass) is weakened.," If the majority of the emission originates in the hard component, it is no longer clear that the thermal component is associated with emission from near the inner edge of the disk (as opposed to larger radii), and the argument that a larger emitting area follows from a larger gravitational radius (i.e. a large mass) is weakened."230 Making a couvineing arguineut for au IMDITI on the vasis of spectral fits requires observations in which a hermal component dominates the bolometric cussion., Making a convincing argument for an IMBH on the basis of spectral fits requires observations in which a thermal component dominates the bolometric emission.231 However. such observations appear to be rare forULXS with luminosities >109 eres| ," However, such observations appear to be rare forULXs with luminosities $\gtrsim 10^{40}$ $\rm erg \; s^{-1}$ "232rate to the IEddington limit and consequently the recycling is weaker.,rate to the Eddington limit and consequently the recycling is weaker.233 Soon after this mass transfer the second. pulsar is born. and for the following 23 Alwrs the binary contains two radio loud. pulsars.," Soon after this mass transfer the second pulsar is born, and for the following 23 Myrs the binary contains two radio loud pulsars."234 At around t=50.74 Alves the second born pulsar falls below the death line., At around t=50.74 Myrs the second born pulsar falls below the death line.235 At this stage the system contains the reevelecd pulsar which slowly evolves to the death line., At this stage the system contains the recycled pulsar which slowly evolves to the death line.236 lt does not reach it throughout the whole simulation. which ends after 10 Gyrs have passed.," It does not reach it throughout the whole simulation, which ends after 10 Gyrs have passed."237 Some of the pulsars in our simulations manage to pass the death line before coalescence., Some of the pulsars in our simulations manage to pass the death line before coalescence.238 This binary is relatively wide. so it docs not coalesce within that time.," This binary is relatively wide, so it does not coalesce within that time."239 In order to analyse the properties of the population of binary pulsars we have to take into account the selection effects., In order to analyse the properties of the population of binary pulsars we have to take into account the selection effects.240 We define two types of selection elfects that [eads to dillerences between the intrinsic aid the observed population., We define two types of selection effects that leads to differences between the intrinsic and the observed population.241 The first is the simple ellects connected with the fact that any racio survey has limiting flux., The first is the simple effects connected with the fact that any radio survey has limiting flux.242 We select the radio population as all pulsars with the observed. [flux on Earth £2 Indy., We select the radio population as all pulsars with the observed flux on Earth $F> 1$ mJy.243 Additionally. it has been noted that binaries with the orbital period between 0.3 and 4h are difficult to detect (Faulkner. 2004) so we also remove these systems from the observed population unless otherwise noted.," Additionally, it has been noted that binaries with the orbital period between $0.3$ and $4$ h are difficult to detect (Faulkner, 2004) so we also remove these systems from the observed population unless otherwise noted."244 We start with the analvsis of the population of binary πλ on the PP diagram., We start with the analysis of the population of binary pulsars on the $P-\dot P$ diagram.245 To obtain the present observable. population of binary neutron stars we assume hat star formation rate in the galaxy is constant., To obtain the present observable population of binary neutron stars we assume that star formation rate in the galaxy is constant.246 We place hem in the Galaxy according to the mocdel described. in section 2.3.11.. and we propagate them in the Calactic »otential taking into account the additional kick velocities hat the binary receives at birth of the two pulsars.," We place them in the Galaxy according to the model described in section \ref{motion}, and we propagate them in the Galactic potential taking into account the additional kick velocities that the binary receives at birth of the two pulsars."247 We then ook for the observable population taking into account the selection elfects described above., We then look for the observable population taking into account the selection effects described above.248" The density of the objects inthe 2P plane is found by summing the times that cach »ulsar spends in a given cell on the log2?2 plane. i.c. he density in the ina given cellon P?PP is: where AlogP?20.08 and MogP=0.18 denote bin width of spin period and its derivative respectively, &=7£5 and where Nj; is acount of simulated. pulsars with £ contained in the ibi and 2 in j-th bin and U is a time p-th pulsar spends in these bins."," The density of the objects in the $P-\dot P$ plane is found by summing the times that each pulsar spends in a given cell on the $\log P- \log\dot P$ plane, i.e. the density in the in a given cell on $P-\dot{P}$ is: where $\Delta\log P=0.08$ and $\Delta\log\dot{P}=0.18$ denote bin width of spin period and its derivative respectively, $F=\sum\limits_{i,j=1}^{50}F_{ij}$ and where $N_{ij}$ is a count of simulated pulsars with $P$ contained in the i-th and $\dot{P}$ in j-th bin and $t^p_{ij}$ is a time p-th pulsar spends in these bins."249" Range of log),2 from 3 to 1 as well as logy, Prange from 21to 12 were divided into 50 bins.", Range of $\log_{10}P$ from $-3$ to $1$ as well as $\log_{10}\dot{P}$ range from $-21$ to $-12$ were divided into 50 bins.250 The density of the population in the P plane (shown on Fig., The density of the population in the $P-\dot P$ plane (shown on Fig.251 and 4)) is determined by the properties of the two component3. of the population: the first. born. possibly recycled: pulsar ancl in a much smaller degree by the second born pulsar.," \ref{pop2Ar} and \ref{pop2Br}) ) is determined by the properties of the two component of the population: the first born, possibly recycled pulsar and in a much smaller degree by the second born pulsar."252 Phe details of the binary evolution and recycling are influencing strongly the region where we expect the reevelecl pulsars., The details of the binary evolution and recycling are influencing strongly the region where we expect the recycled pulsars.253 For the models where we allow for the full spin-up (Ας APE) the population of millisecond pulsars extends to period below 20ms.," For the models where we allow for the full spin-up (AF, APF) the population of millisecond pulsars extends to period below 20ms."254 Another model where there are Many pusags in this region is model LIP. where we allow for very strong accretion and therefore reeveling is always full.," Another model where there are many pulsars in this region is model HP, where we allow for very strong accretion and therefore recycling is always full."255 In inodel LP most. pulsars end. up in the small region. with he pulsar period. of approx 1-2ms. and »riod derivative of z10.77.," In model HP most pulsars end up in the small region with the pulsar period of approx 1-2ms, and period derivative of $\approx 10^{-21}$."256 In the remaining models the mass transfer leads to decrease of the field in the CE phase. out at the same time the period is not changed by much.," In the remaining models the mass transfer leads to decrease of the field in the CE phase, but at the same time the period is not changed by much."257 Inclusion of the propeller οσοι (models denoted by P) limits he amount of accreted matter anc thus may. limits the iclcl decay., Inclusion of the propeller effect (models denoted by P) limits the amount of accreted matter and thus may limits the field decay.258 This. decreases slightly the density. of pulsars with the lowest values of D. sce cg. model A ys model AP.," This decreases slightly the density of pulsars with the lowest values of $\dot P$, see e.g. model A vs model AP."259 Phe time scale of the spontaneous decay. of magnetic ield does not influence the overall shape of the distribution inthe PoP« iagram see model AP ancl ADP'T20., The time scale of the spontaneous decay of magnetic field does not influence the overall shape of the distribution in the $P-\dot P$ diagram see model AP and APT20.260" Finally. he magnetic field mass decay. scale inlluences the values of he magnetic fields of the reevelecd pulsars ancl hence the distribution of their period derivatives Z. see model APDOS with the AZ,=0.05A. and AP with AAJ,=0.025M..."," Finally, the magnetic field mass decay scale influences the values of the magnetic fields of the recycled pulsars and hence the distribution of their period derivatives $\dot P$, see model APD05 with the $\Delta M_d =0.05\,M_\odot$ and AP with $\Delta M_d =0.025\,M_\odot$."261" If the value of 2M, is large than the magnetic field. of pulsar does not decay fast and they end. up as millisecond reevelec pulsars with a little stronger magnetic field in the region. between 10; and LO1.T whileqoe for the small value of AAI, the final magnetic field of pulsars are lower and they populate the region below LO15 - see model AD."," If the value of $\Delta M_d$ is large than the magnetic field of pulsar does not decay fast and they end up as millisecond recycled pulsars with a little stronger magnetic field in the region between $10^{-19}$ and $10^{-17}$, while for the small value of $\Delta M_d$ the final magnetic field of pulsars are lower and they populate the region below $10^{-18}$ - see model AP."262 In order to quantify which model of the distribution in the PP best describes the data we calculate the likelihood of cach mocle| eiven the data [from Table 1., In order to quantify which model of the distribution in the $P-\dot P$ best describes the data we calculate the likelihood of each model given the data from Table 1.263" We define the likelihood as: where £ is the likelihood. £9; and D, are period and its derivative values for à k-th observed pulsar (see Tab. 12) "," We define the likelihood as: where ${\cal L}$ is the likelihood, $P_k$ and $\dot{P}_k$ are period and its derivative values for a k-th observed pulsar (see Tab. \ref{pulsobswlas}) )"264and fis the probability density defined by equation 5. in section 3.2.1.., and $f$ is the probability density defined by equation \ref{fij} in section \ref{popnappdot}.265 We use two sets of data to caleulate the likelihood: (Comparison 1) the standard. model. where we take into account the flux selection elfect as well as rejection of pulsars with the orbital periods between 0.3 and 4h is compared with the data set with 0737-3039 A and D excluded: as its orbital period. lies in this range: (Comparison 2) the extended: model where we do not reject the pulsars with the orbital periods between 0.3 and 4h is compared to the full data set of Table 1.. and (Comparison 3) with the data set where we exclude 0737-3039D. We present the results in ‘Table 4..," We use two sets of data to calculate the likelihood: (Comparison 1) the standard model, where we take into account the flux selection effect as well as rejection of pulsars with the orbital periods between $0.3$ and $4$ h is compared with the data set with J0737-3039 A and B excluded as its orbital period lies in this range; (Comparison 2) the extended model where we do not reject the pulsars with the orbital periods between $0.3$ and $4$ h is compared to the full data set of Table \ref{pulsobswlas}, and (Comparison 3) with the data set where we exclude J0737-3039B. We present the results in Table \ref{like}."266 In all three comparisons in Table 3.3. the model APDOS best fits the data., In all three comparisons in Table \ref{porow} the model APD05 best fits the data.267 This is à model with the propeller effect taken into account and with increased: mass scale for the magnetic field. decay., This is a model with the propeller effect taken into account and with increased mass scale for the magnetic field decay.268 Phe models with the standard. value leac to too small magnetic field of the svnthetic sample., The models with the standard value lead to too small magnetic field of the synthetic sample.269 Increasing the magnetic field mass decay scale AAL; τοις to smaller decay of the field., Increasing the magnetic field mass decay scale $\Delta M_d$ leads to smaller decay of the field.270 and therefore better agreement with the data., and therefore better agreement with the data.271 Also the models with full recycling are very, Also the models with full recycling are very272The past several vears have seen a surge in interest related to the electromagnetic signatures of merging black holes.,The past several years have seen a surge in interest related to the electromagnetic signatures of merging black holes.273 Such a signature would have to come not from the black holes themselves. but from the gas that surrounds them.," Such a signature would have to come not from the black holes themselves, but from the gas that surrounds them."274 Heating of this gas ancl consequent emission. of. electromagnetic radiation has been discussed. both in the context. of the inspiral phase (Chaneetal.2010).. the coalescence (Ixocsis&Loch 2008).. and in the post-mereer phase as the mass loss and. kick of the final black hole modify the orbits of the gas particles (Bode&Phinney2007:ShieldsBonning2008: 2010)..," Heating of this gas and consequent emission of electromagnetic radiation has been discussed both in the context of the inspiral phase \citep{2009arXiv0906.0825C}, the coalescence \citep{2008PhRvL.101d1101K}, and in the post-merger phase as the mass loss and kick of the final black hole modify the orbits of the gas particles \citep{2007APS..APR.S1010B, 2008ApJ...682..758S, 2008ApJ...684..835S, 2010PhRvD..81d4004A, 2010MNRAS.401.2021R}."275 Lt is often suggested that torques arising from Lindblad play a Κον role in redistributing gas in the inspiral phase (Armitage&Natarajan2002:MilosavIjevicetal.2010). and controlling the surface density. profile and heating rate of the gas disc.," It is often suggested that torques arising from Lindblad play a key role in redistributing gas in the inspiral phase \citep{2002ApJ...567L...9A, 2005ApJ...622L..93M, 2008ApJ...672...83M, 2009arXiv0906.0825C} and controlling the surface density profile and heating rate of the gas disc."276 These torques act by. exciting density. perturbations at the location of either inner or outer Lindblad. resonances (LLRs or OLRs). at which the svnodie period (i.e. the time between successive passages of the secondary black hole and a dise particle) is an integer multiple of the period. of radial epievelie oscillations in the disc.," These torques act by exciting density perturbations at the location of either inner or outer Lindblad resonances (ILRs or OLRs), at which the synodic period (i.e. the time between successive passages of the secondary black hole and a disc particle) is an integer multiple of the period of radial epicyclic oscillations in the disc."277 In some scenarios. the resonant torques. operate in the nonrelativistic Newtonian regime. which has a long ustory of study in the context of galactic disces. planetary rings. and circumstellar clises (e.g.Lynelen-Bell&Ixalnajsxioizou 1979). L," In some scenarios, the resonant torques operate in the nonrelativistic Newtonian regime, which has a long history of study in the context of galactic discs, planetary rings, and circumstellar discs \citep[e.g.][]{1972MNRAS.157....1L, 1978ApJ...222..850G, 1979ApJ...233..857G, 1980ApJ...241..425G, 1979MNRAS.186..799L}."278lowever. in others particularly the cases of inner disces (Changctal.2010) Lindblad: resonant orques are used all the way in to radii of a 1037.," However, in others – particularly the cases of inner discs \citep{2009arXiv0906.0825C} – Lindblad resonant torques are used all the way in to radii of a $\times 10M$."279 In hese cases. it is cesirable to revisit the Lindblad resonances in a fully. relativistic context.," In these cases, it is desirable to revisit the Lindblad resonances in a fully relativistic context."280 This is especially true since »ericentre. precession introduces. an additional ILIt (the m— lor 0:1 ILI) that has no analogue in the Newtonian-Ixeplerian. problem., This is especially true since pericentre precession introduces an additional ILR (the $m=1$ or 0:1 ILR) that has no analogue in the Newtonian-Keplerian problem.281 Vhe principal purpose of this paper and its companion is to provide a relativistic treatment of the Lindblad. torques. including computation of the torque formula in black hole spacetimes (Schwarzschild or Ixerr). in the extreme mass ratio limit.," The principal purpose of this paper and its companion is to provide a relativistic treatment of the Lindblad torques, including computation of the torque formula in black hole spacetimes (Schwarzschild or Kerr), in the extreme mass ratio limit."282 This paper and its companion are not concerned with a full analysis of any one scenario for the generation. of an electromagnetic counterpart to a. black hole merger. although they are most relevant to the proposal of Changetal. (2010)...," This paper and its companion are not concerned with a full analysis of any one scenario for the generation of an electromagnetic counterpart to a black hole merger, although they are most relevant to the proposal of \citet{2009arXiv0906.0825C}."283 Rather. our motivation is to establish the relativistic Lindblad. torque formula so that it can be used to establish the role (or lack thereof) of Lindblad: torques in future work.," Rather, our motivation is to establish the relativistic Lindblad torque formula so that it can be used to establish the role (or lack thereof) of Lindblad torques in future work."284 In this paper (“Paper P). we develop the general formalism. for. Lindblad: torques in. thin. disces orbiting in the equatorial planes of axisvmumetric. time-independent spacetimes with a plane of svmametry.. ancl with weak perturbations of general form respecting the equatorial rellection symmetry.," In this paper (“Paper I”), we develop the general formalism for Lindblad torques in thin discs orbiting in the equatorial planes of axisymmetric, time-independent spacetimes with a plane of symmetry, and with weak perturbations of general form respecting the equatorial reflection symmetry."285" This covers the case of a binary Schwarzschilel black hole with an extreme mass ratio (q=Al/fAl, 1) and a gas disc orbiting in the same plane.", This covers the case of a binary Schwarzschild black hole with an extreme mass ratio $q=M_2/M_1\ll 1$ ) and a gas disc orbiting in the same plane.286 Le also covers the Kerr case i£ the primary hole's spin is aligned with the orbital angular momentum of the binary and dise (whieh may or may not be the physical case: here it, It also covers the Kerr case if the primary hole's spin is aligned with the orbital angular momentum of the binary and disc (which may or may not be the physical case; here it287"(Navarro. Frenk. White 1997. hereafter NEW). nicely tracing the dispersion of the halo of NGC 5128 and theinner galaxies of (he Centaurus group as well. for a scale radius. r,=14 kpe.","(Navarro, Frenk, White 1997, hereafter NFW), nicely tracing the dispersion of the halo of NGC 5128 and the galaxies of the Centaurus group as well, for a scale radius, $r_s = 14$ kpc."288 However. the entire Centaurus group over all radii and halo of NGC 5128 cannot be lit by a single NEW curve.," However, the entire Centaurus group over all radii and halo of NGC 5128 cannot be fit by a single NFW curve."289 That is. the group as a whole likely has a density profile (hat is shallower than 2*ni at large radius.," That is, the group as a whole likely has a density profile that is shallower than $R^{-3}$ at large radius."290 The only other direct. kinematic comparison between the GCS of a dominant. galaxy with its surrounding satellite galaxies is for M37 in the Virgo cluster by Cotéetal.(2001)., The only other direct kinematic comparison between the GCS of a dominant galaxy with its surrounding satellite galaxies is for M87 in the Virgo cluster by \cite{cote01}.291. Cotéοἱal.(2001). showed the velocity dispersions of the halo GC's in M87 aud (he satellite ealaxies clearly matched their constructed 2-component mass model for the Virgo cluster., \cite{cote01} showed the velocity dispersions of the halo GCs in M87 and the satellite galaxies clearly matched their constructed 2-component mass model for the Virgo cluster.292 Bul. unlike our results lor NGC 5128 and the Centaurus group. (the Virgo galaxies have a dispersion that is much hieher than the GCs in the M87 halo.," But, unlike our results for NGC 5128 and the Centaurus group, the Virgo galaxies have a dispersion that is much higher than the GCs in the M87 halo."293 These results are not surprising because MIST ancl the Virgo cluster contain a large X-ray halo. tracing the large dark matter component in the Virgo cluster that dominates the potential well bevond the halo itself.," These results are not surprising because M87 and the Virgo cluster contain a large X-ray halo, tracing the large dark matter component in the Virgo cluster that dominates the potential well beyond the halo itself."294 In the Centaurus group. we clearly do not see this same effect of a very massive. extended outer component to the same degree.," In the Centaurus group, we clearly do not see this same effect of a very massive, extended outer component to the same degree."295" The total mass. M, of NGC 5128 and the Centaurus group can be determined by the addition of the mass components supported bv rotation. A. ancl random internal motion (pressure""). MM, The mass supported by pressure was determined here by the Tracer Mass Estimator. developed by Evansοἱal.(2003) as a generalized projected mass estimator that determines (he mass enclosed within the outermost object in the sample."," The total mass, $M_t$ of NGC 5128 and the Centaurus group can be determined by the addition of the mass components supported by rotation, $M_r$ , and random internal motion (”pressure”), $M_p$, The mass supported by pressure was determined here by the Tracer Mass Estimator, developed by \cite{evans03} as a generalized projected mass estimator that determines the mass enclosed within the outermost object in the sample."296 The (spherically svimnmnetric) tracer population. in (he Tracer Mass estimator. does not necessarily lollow (he same mass profile as the svstem.," The (spherically symmetric) tracer population, in the Tracer Mass estimator, does not necessarily follow the same mass profile as the system."297 Although the Tracer Mass Estimator is not the typically selected mass estimator to determine galaxy eroup mass. il allows a direct comparison with the masses determined from the eglobular clusters.," Although the Tracer Mass Estimator is not the typically selected mass estimator to determine galaxy group mass, it allows a direct comparison with the masses determined from the globular clusters."298 The pressure supported mass in the Tracer Mass Estimator formulation is where Vis the number of objects in the sample and ορ is the radial velocity of the tracer object with the rotation calculated in Section2. removed., The pressure supported mass in the Tracer Mass Estimator formulation is where $N$ is the number of objects in the sample and $v_{f_i}$ is the radial velocity of the tracer object with the rotation calculated in Section\ref{kin} removed.299 For an isotropic population, For an isotropic population300(he corresponclinge magnitudes.e and ZP is the photometric zero point (total flux of 1 count per second).,"the corresponding magnitudes, and $ZP$ is the photometric zero point (total flux of 1 count per second)."301" We use an analyGcal function to describe the elliciency in detecting objects of a given difference magnitude: where 7' is the maximum elliciency. Am, represents a cutoff magnitude where z(2) drops below of T. and 5 controls the shape of the roll-off."," We use an analytical function to describe the efficiency in detecting objects of a given difference magnitude: where $T$ is the maximum efficiency, $\Delta m_{c}$ represents a cutoff magnitude where $\varepsilon(\Delta m)$ drops below of $T$, and $S$ controls the shape of the roll-off."302" We find that 7=0.98. m,=25.60. and 5=0.20 well describes the efficiency histograun for the. FILOW passband. and 0.97. m.= 24.20. and ο=0.21 parameterizes (he efliiency in the £160) passband (see Figure 1))."," We find that $T=0.98$, $m_c=25.60$, and $S=0.20$ well describes the efficiency histogram for the $F110W$ passband, and $T=0.97$ , $m_c=24.20$ , and $S=0.21$ parameterizes the efficiency in the $F160W$ passband (see Figure \ref{fig:fig1}) )."303 In the F850LP passband of the UDF and UDFP survevs. false star tests show nearly identical efficiency. function parameters asthose used in 504. with Z'=1 and 5=0.35. however with adjusted 50% efficiency eutoff magnitudes (01) corresponding to the 5o sensitivity limits for the difference of a given pair of stacks (also shown in Tables 1. and 2)).," In the $F850LP$ passband of the UDF and UDFP surveys, false star tests show nearly identical efficiency function parameters asthose used in S04, with $T=1$ and $S=0.38$, however with adjusted $50\%$ efficiency cutoff magnitudes $m_c$ ) corresponding to the $5\sigma$ sensitivity limits for the difference of a given pair of stacks (also shown in Tables \ref{tab:tab3} and \ref{tab:tab4}) )."304 These limits are in good agreement with those expected [rom the exposure times of the search and (emplate images using the ACS Exposure Time Calculators., These limits are in good agreement with those expected from the exposure times of the search and template images using the ACS Exposure Time Calculators.305 The typical brightness threshold of detection for the F350LP template-search pairs was 27 mag., The typical brightness threshold of detection for the $F850LP$ template-search pairs was $27$ mag.306 An illustration of the sensitivity threshold can be seen in Figure 2. where we have added six lake SNe (PSFs) al F850LP= 24. 25. 26. 27. 27.5. and 28 mag in a region of the 12241230 image stack.," An illustration of the sensitivity threshold can be seen in Figure \ref{fig:fig2} where we have added six fake SNe (PSFs) at $F850LP=$ 24, 25, 26, 27, 27.5, and 28 mag in a region of the 1224-1230 image stack."307 By differencing it with the 1212-1213 image stack. we can clearly detect the sources to a flux level of 27 mag. but Tainter than 27 mag was difficult to identilv without prior knowledge of where the fake SNe were.," By differencing it with the 1212-1218 image stack, we can clearly detect the sources to a flux level of 27 mag, but fainter than 27 mag was difficult to identify without prior knowledge of where the fake SNe were."308 This is in good agreement with the estimated detection threshold (from the exposure times) of 21.1 mag for this template-search pair., This is in good agreement with the estimated detection threshold (from the exposure times) of 27.1 mag for this template-search pair.309 The detection thresholds are bright enough to detect SNe Ia al peak at zx2.2 in each passband., The detection thresholds are bright enough to detect SNe Ia at peak at $z\le2.2$ in each passband.310 Despite the intrapixel sensitüivitv limitations of the IRDUF survey. interestinglyv. no candidate SNe were discovered in the deep IRUDE imaging.," Despite the intrapixel sensitivity limitations of the IRDUF survey, interestingly, no candidate SNe were discovered in the deep IRUDF imaging."311 However. [our 9Ne were discovered in (he UDF and UDEP images.," However, four SNe were discovered in the UDF and UDFP images."312 For each. vega based aperture magnitudes were measured from difference images in the F'6061V.. ΕΤ and F850LP bandpasses. using aperture corrections and photometric error estimations described in $04.," For each, vega based aperture magnitudes were measured from difference images in the $F606W$, $F775W$, and $F850LP$ bandpasses, using aperture corrections and photometric error estimations described in S04."313 In all cases. we used photometric redshifts (phot-:) determined from the mulli-waveleneth GOODS data to estimate the redshifts of the host galaxies (Alobasheretal.2004)..," In all cases, we used photometric redshifts $z$ ) determined from the multi-wavelength GOODS data to estimate the redshifts of the host galaxies \citep{Mobasher:2003bm}."314 Spectroscopic conlivmation has nol been obtained [or these SNe., Spectroscopic confirmation has not been obtained for these SNe.315 We also generally lack (he photometric data anc age constraints necessary (o assuredly identify the SN types using the identification conlidence scheme detailecl in SO4 and color selectionmethods described in Riessetal. (2004a).., We also generally lack the photometric data and age constraints necessary to assuredly identify the SN types using the identification confidence scheme detailed in S04 and color selectionmethods described in \citet{Riess:2003gz}. .316 Llowever. we can slill use these techiiques to reject combinations of SN type ancl redshift space.," However, we can still use these techniques to reject combinations of SN type and redshift space,"317two points are quantified as lt is shown in this example that the cubic spline interpolation leads to a more accurate location of the skeleton knots. and the distribution. of skeleton length herein.,"two points are quantified as It is shown in this example that the cubic spline interpolation leads to a more accurate location of the skeleton knots, and the distribution of skeleton length therein."318 Note that there are two suspicious skeleton knots within ory and orp in this case but they would. not. be involved. in analysis since wry and wy are not canceling pixels., Note that there are two suspicious skeleton knots within $x_3$ and $x_4$ in this case but they would not be involved in analysis since $x_3$ and $x_4$ are not canceling pixels.319 Lt ds also noteworthy that the point £2) belongs o a piece of the first-tvpe secondary. skeleton according o the classification in Pogosvanetal.(2000)., It is also noteworthy that the point $P$ belongs to a piece of the first-type secondary skeleton according to the classification in \citet{Pogosyan_etal_2009}.320. The robust equivalence between kc and the eigenvalue indicates accurate and unbiased: classification. in. particular around he underlving demarcation point between two types of skeleton where the two eigenvalues are quite close to each other.," The robust equivalence between $r$ and the eigenvalue indicates accurate and unbiased classification, in particular around the underlying demarcation point between two types of skeleton where the two eigenvalues are quite close to each other."321 Phe cases for PWLAL=60 are listed below For the dillerence between the five-vear ancl one-vear skeleton processing. we must investigate the impact of method selection on the results.," The cases for $\rm FWHM=60\arcmin$ are listed below For the difference between the five-year and one-year skeleton processing, we must investigate the impact of method selection on the results."322 Given the IKQ75D processed data and Gaussian simulations. we carry out the skeleton analvsis following the steps described in Section 3.2. but utilising linear interpolation to locate the skeleton knots.," Given the KQ75B processed data and Gaussian simulations, we carry out the skeleton analysis following the steps described in Section \ref{subsec_analysis} but utilising linear interpolation to locate the skeleton knots."323 The resulting length departure of the data is then obtained and the dilferences between the cubie spline and linear results are. plotted. in. Figure B2 for FWNIIM=0753. Y/64. 0785 and 1728.," The resulting length departure of the data is then obtained and the differences between the cubic spline and linear results are plotted in Figure \ref{fig_diff_lincub} for $\rm FWHM=0\fdg53$, $0\fdg64$, $0\fdg85$ and $1\fdg28$."324 Ht is noteworthy that the magnituce of such a cillerence contributes less than to. the cliscrepaney between the WALAPSS and. WALAPIL skeleton ength distribution profile., It is noteworthy that the magnitude of such a difference contributes less than to the discrepancy between the 5 and 1 skeleton length distribution profile.325" However. the structure shown in Figure B2 suggests that the linearmethod would lead to an over-enhanced peak ancl over-depressed trough. which for he sstructure of AL, suggested by the data may bias the itting value offy."," However, the structure shown in Figure \ref{fig_diff_lincub} suggests that the linearmethod would lead to an over-enhanced peak and over-depressed trough, which for the structure of $\Delta \mathcal{L}_{a}$ suggested by the data may bias the best-fitting value of."326.. In this section we test for the presence of bias in. our combined estimator., In this section we test for the presence of bias in our combined estimator.327" Given simulated noisy realisations from the KQT5B processing and. the predetermined. expectation LM(yp,fixie}. we randomly pick up No=250 sets of -samples. CIC(y.fey) GF-—1.2....250) with Nia=4 and 9. to form the conditional v7 functions and the ellective likelihood function for each sample. We plot σοκfx) as histograms for two given fx""arie values (0 and. 200) in Figure ο for /Npwuwu4 and 9. noticing that the sampling width: εδνι is 2.5."," Given simulated noisy realisations from the KQ75B processing and the predetermined expectation $\langle\mathcal{L}^{\rm328NG}_{\rm C}(\nu,f_{\rm NL})\rangle$, we randomly pick up $N=250$ sets of -samples, $\mathcal{L}^{\rm NG}_{\rm C}(\nu,f_{\rm329NL}^{j})$ $j=1,2,...,250$ ) with $N_{\rm FWHM} = 4$ and $9$, to form the conditional $\chi^2$ functions and the effective likelihood function for each sample, We plot $\mathscr{L}_{\rm C}(f_{\rm NL}|f_{\rm NL}^{\rm true})$ as histograms for two given $f_{\rm NL}^{\rm true}$ values (0 and 200) in Figure \ref{fig_likeli_comb} for $N_{\rm FWHM}=4$ and $9$, noticing that the sampling width $\Delta f_{\rm NL}$ is 2.5."330 Again. the likelihoods are perfectly fitted by Craussian functions with the parameters listed in Table €C2..," Again, the likelihoods are perfectly fitted by Gaussian functions with the parameters listed in Table \ref{tab_cmbntest}. ."331 Despite the noise contribution and skv-cut. it is cemonstrated that the inverse-variance-combination still leads to an unbiased skeleton estimator for κι...," Despite the noise contribution and sky-cut, it is demonstrated that the inverse-variance-combination still leads to an unbiased skeleton estimator for ."332because the S/N ratio and the resolution of the spectrum are not sufficiently good.,because the S/N ratio and the resolution of the spectrum are not sufficiently good.333 For the continuum level. the blue part of Lyo. which is more prone to extinction. is extrapolated from the red portion of the spectrum given by Kulkarni et al. (," For the continuum level, the blue part of $\alpha$, which is more prone to extinction, is extrapolated from the red portion of the spectrum given by Kulkarni et al. ("3341998).,1998).335" They quote F,,=174(/v4)"" nJy with à=—0.7+0.2. where F,, is the spectral density at frequency 7 and vp24.7103 Hz. the central frequency of the R band."," They quote $F_{\nu}=174(\nu/\nu_R)^{\alpha}$ nJy with $\alpha=-0.7\pm0.2$, where $F_{\nu}$ is the spectral density at frequency $\nu$ and $\nu_R = 4.7\times10^{14}$ Hz, the central frequency of the R band."336 We show the result in Fig., We show the result in Fig.337 |. where the dotted line represents the best fit profile. the solid line the observed profile. and the horizontal solid line the continuum level.," 1, where the dotted line represents the best fit profile, the solid line the observed profile, and the horizontal solid line the continuum level."338" The best fit expansion velocity of the supershell relative to the H II region is determined to be v,=1500kms!, and the best fit line center optical depth z;26« 10°. which corresponds to em."," The best fit expansion velocity of the supershell relative to the H II region is determined to be $v_{exp} = 1500\kms$, and the best fit line center optical depth $\tau_0=6\times10^6$ , which corresponds to $N_{HI}=10^{20}\cm^{-2}$ ."339 The best fit Lye profile has the width of σ-5 and the line center flux /(À25280.8)0.675 jv. which gives the unobscured flux to be 9.1«1070?ereem™s! and the systemic redshift z23.425.," The best fit $\alpha$ profile has the width of $\sigma=5\ {\rm \AA}$ and the line center flux $f(\lambda=5280.8\ {\rm \AA})=0.675\ \mu$ Jy, which gives the unobscured flux to be $9.1\times10^{-18}\erg\cm^{-2}\s^{-1}$ and the systemic redshift $z=3.425$."340 This is slightly larger than the redshift proposed by Kulkarni et al. (, This is slightly larger than the redshift proposed by Kulkarni et al. (3411998). who may have overestimated the absorption in the blue part of the Ένα.,"1998), who may have overestimated the absorption in the blue part of the $\alpha$."342 However. the absorption trough is sufficiently remote from the line center in the velocity space only to erode the extreme blue part of the Lyo emission.," However, the absorption trough is sufficiently remote from the line center in the velocity space only to erode the extreme blue part of the $\alpha$ emission."343 Hence. we prefer the redshift ofz23.425 of GRB971214 to the redshift of z23.418. and subsequently other physical parameters need to be revised.," Hence, we prefer the redshift of $z=3.425$ of GRB971214 to the redshift of $z=3.418$, and subsequently other physical parameters need to be revised."344 Assuming a standard Friedman cosmology with Πο=66kms!Mpe! and Ὁρ=0.3. the luminosity distance dj;=9.7«10%em.," Assuming a standard Friedman cosmology with $H_0=65\kms\Mpc^{-1}$ and $\Omega_0=0.3$, the luminosity distance $d_L = 9.7\times10^{28}\cm$."345" Considering the Galactic extinction. the unobscured Ένα flux is corrected to be Fy,=(1.540.7)«107""ergem? s7!. where the observational error given by Kulkarni et al. ("," Considering the Galactic extinction, the unobscured $\alpha$ flux is corrected to be $F_{Ly\alpha} = (1.5\pm0.7)\times10^{-17}\erg\cm^{-2}\s^{-1}$ , where the observational error given by Kulkarni et al. ("3461998) is introduced.,1998) is introduced.347" Therefore. for the assumed cosmology. the Lya line luminosity Lj,(18+0.8)«107erg κ."," Therefore, for the assumed cosmology, the $\alpha$ line luminosity $L_{Ly\alpha} = (1.8\pm0.8)\times 10^{42} \erg \s^{-1}$ ."348 If there is nointernal. extinction in the interior. of the Ένα source. this corresponds. to ne=04+0GSPRYIkpecm? or os=40+10x—DTTETS em. of which the ionization can be maintained by ~10 OS stars as the ionizing source.," If there is nointernal extinction in the interior of the $\alpha$ source, this corresponds to $n_e = (1.4\pm0.4) ({ L \over L_{Ly\alpha}})^{0.5}349({R \over {1 \kpc}})^{-1.5}\ \cm^{-3}$ or $n_e = (40\pm10) ({ L \over L_{Ly\alpha}})^{0.5}350({R \over {100 \pc}})^{-1.5}\ \cm^{-3}$ , of which the ionization can be maintained by $\sim 10^4$ O5 stars as the ionizing source."351 From the Lya luminosity. we can estimate the star-formation rate (Thompson. Djorgovski. Trauger 1995) to be Rs;(33)M.. yr. with both the internal and the Galactic extinction being corrected.," From the $\alpha$ luminosity, we can estimate the star-formation rate (Thompson, Djorgovski, Trauger 1995) to be $R_{SF} = (7\pm3){\rm M}_\odot\yr^{-1}$ , with both the internal and the Galactic extinction being corrected."352 This is consistent with the star forming rate given by Kulkarni et al. (, This is consistent with the star forming rate given by Kulkarni et al. (3531998) as a lower limit. Rog=5.2M.yr! which was obtained from the rest-frame continuum luminosity at 1.500.,"1998) as a lower limit, $R_{SF}=5.2\ {\rm M}_\odot\yr^{-1}$ which was obtained from the rest-frame continuum luminosity at $1,500\ {\rm \AA}$."354 Using the revised redshift of the GRB host galaxy. we refine other absorption lines in the observed spectrum.," Using the revised redshift of the GRB host galaxy, we refine other absorption lines in the observed spectrum."355 In Fig., In Fig.356 2. we show the spectrum of the GRB host in the UV regime.," 2, we show the spectrum of the GRB host in the UV regime."357 It is seen that the revised wavelengths are in good agreement with the absorption features., It is seen that the revised wavelengths are in good agreement with the absorption features.358 We consider the dynamical evolutionary model of the supernova remnant to derive the physical quantities of the shell., We consider the dynamical evolutionary model of the supernova remnant to derive the physical quantities of the shell.359 According to Woltjer (1972). the supernova remnant has four evolutionary phases. that is. the free expansion phase. the Sedov-Taylor or adiabatic phase. the snowplow or radiative phase. and finally the merging or dissipation phase (see also Reynolds 1988).," According to Woltjer (1972), the supernova remnant has four evolutionary phases, that is, the free expansion phase, the Sedov-Taylor or adiabatic phase, the snowplow or radiative phase, and finally the merging or dissipation phase (see also Reynolds 1988)."360" According to. Woltjer(1972). the radiative phase begins roughly when the expansion velocity of the shell becomes where 7, is the number density of the ambient medium and E is the initial explosion energy."," According to Woltjer(1972), the radiative phase begins roughly when the expansion velocity of the shell becomes where $n_1$ is the number density of the ambient medium and $E$ is the initial explosion energy."361 Since the expansion velocity v=Ve=1500kms! of the supershell exceeds the velocity in the radiative phase by a large margin. we propose that the supershell is in the adiabatic phase. which is described by the Sedov solution.," Since the expansion velocity $v=v_{exp}=1500\kms$ of the supershell exceeds the velocity in the radiative phase by a large margin, we propose that the supershell is in the adiabatic phase, which is described by the Sedov solution."362" According to the Sedov solutionin a uniform medium of number density 2, in which we have the relation jj,23N/R. where v is the expansion velocity of the supershell. R the size of the supershell. E the initial explosion energy. N the column"," According to the Sedov solutionin a uniform medium of number density $n_1$ in which we have the relation $n_1 = 3N/R$ , where $v$ is the expansion velocity of the supershell, $R$ the size of the supershell, $E$ the initial explosion energy, $N$ the column"363with which large-scale. magnetic structures have been inferred. and the great. heights at which they form above he stellar surface indicates circumstances are ideal for the generation of substantial torques opposing stellar rotation.,with which large-scale magnetic structures have been inferred and the great heights at which they form above the stellar surface indicates circumstances are ideal for the generation of substantial torques opposing stellar rotation.364 Large-scale magnetic reconnection. in addition to shedcing mass ancl angular momentum. also bombards circumstellar material with high energv photons ancl particles.," Large-scale magnetic reconnection, in addition to shedding mass and angular momentum, also bombards circumstellar material with high energy photons and particles."365 “Phis could. potentially play a pivotal role in. planet. formation by stimulating grain growth ?)., This could potentially play a pivotal role in planet formation by stimulating grain growth .366. Lligh energy. radiation and particle Ηχος can influence disc chemistry and structure: showed that hard stellar N-ravs could. potentially ionise the cise sullicienthy for accretion ο occur via magnetohyvdrodyvnamic instabilitv., High energy radiation and particle fluxes can influence disc chemistry and structure: showed that hard stellar X-rays could potentially ionise the disc sufficiently for accretion to occur via magnetohydrodynamic instability.367 Phe large wights inferred. Lor these loops would put. X-ray emitting Alasma closer to the disc. reducing the column depth hrough which the hard. X-rays would have to travel before ionising disc material.," The large heights inferred for these loops would put X-ray emitting plasma closer to the disc, reducing the column depth through which the hard X-rays would have to travel before ionising disc material."368 Given these potential impacts of large scale magnetic oops (and their destabilization) on carly star and disc evolution. we aim to ascertain whether the existence of hot. arge. magnetic loops. as inferred from the analvsis of the wiehtest. most. energetic events in X-ray surveys of T'TS. is physically plausible.," Given these potential impacts of large scale magnetic loops (and their destabilization) on early star and disc evolution, we aim to ascertain whether the existence of hot, large, magnetic loops, as inferred from the analysis of the brightest, most energetic events in X-ray surveys of TTS, is physically plausible."369 To do this. we address an evident buovaney defecit in the previous models by including a stellar wind in the model physics.," To do this, we address an evident buoyancy defecit in the previous models by including a stellar wind in the model physics."370 We do not. distinguish between the single loop UCL model or the possibility. of multiple loop events: we only seek to demonstrate that it is possible to find hot loops beyond the typical 7quiescent X-ray emitting corona. and in some cases. bevone corotation.," We do not distinguish between the single loop UCL model or the possibility of multiple loop events; we only seek to demonstrate that it is possible to find hot loops beyond the typical “quiescent” X-ray emitting corona, and in some cases, beyond corotation."371 Cool. extended promincnces have been observed in abundance on the= voung rapid rotator AB Dor. ranging in height [rom 2-5 I. well above the corotation radius of 1.7 Ry(2).. and slingshot prominences much like those seen on the Sun have been observed on LTS?2?).," Cool, extended prominences have been observed in abundance on the young rapid rotator AB Dor, ranging in height from 2-5 $_{*}$, well above the corotation radius of 1.7 $_{*}$, and slingshot prominences much like those seen on the Sun have been observed on TTS."372. From a theoretical. perspective. other groups have assessed the stability of cool loops. determining where in parameter space mechanical equilibria can be found.," From a theoretical perspective, other groups have assessed the stability of cool loops, determining where in parameter space mechanical equilibria can be found."373 Loops found. beyond. the closed coronal field ancl possibly even bevond corotation are likely embedded: in the stellar wind (these loops could. form. via reconnection of open field. lines in the wind: see Jv05. ligure 2).," Loops found beyond the closed coronal field and possibly even beyond corotation are likely embedded in the stellar wind (these loops could form via reconnection of open field lines in the wind; see JvB05, Figure 2)."374 This work builds upon the prescription of JCCOL and Jv05. save our addition of a stellar wind (Section ??)).," This work builds upon the prescription of JCC91 and JvB05, save our addition of a stellar wind (Section \ref{S-wind}) )."375 We list below the four major forces our model accounts for (aud the parameters upon which each depends) that dictate the height and shape of a magnetic loop: A magnetic loop is in equilibrium when the pressure eradients internal ancl external to. the loop. magnetic tension. and gravity are evenly balanced: the loop is stable. neither expanding nor contracting.," We list below the four major forces our model accounts for (and the parameters upon which each depends) that dictate the height and shape of a magnetic loop: A magnetic loop is in equilibrium when the pressure gradients internal and external to the loop, magnetic tension, and gravity are evenly balanced: the loop is stable, neither expanding nor contracting."376 We describe the general mechanical equilibrium model. and the addition of a stellar wind term.," We describe the general mechanical equilibrium model, and the addition of a stellar wind term."377 In Section. ??.. the case of a simple PLS is demonstrated.," In Section \ref{S-toymodel}, the case of a simple TTS is demonstrated."378 We incorporate a number of fairly standard. simplifving assumptions in our 2D model.," We incorporate a number of fairly standard, simplifying assumptions in our 2D model."379 First. the arcade in which the loop is embedded is not twistedseparation).," First, the arcade in which the loop is embedded is not twisted."380 Secondly. the external field. is potential (e. current. free) ancl closed up to a height y;: beyond this point. the source surface. the external field is open.," Secondly, the external field is potential (i.e. current free) and closed up to a height $_s$; beyond this point, the source surface, the external field is open."381 The source surface sets. then. the maximum height quiescent coronal loops can reach.," The source surface sets, then, the maximum height quiescent coronal loops can reach."382 The magnetic loop itself is assumed to be narrow. its width less than the length. scale of the external field. ancl dt is isothermal.," The magnetic loop itself is assumed to be narrow, its width less than the length scale of the external field, and it is isothermal."383 Finally. the loop is treated. as non-clisruptive of its surroundings.," Finally, the loop is treated as non-disruptive of its surroundings."384 “Phe equation of motion for plasma in the COLON Ls:, The equation of motion for plasma in the corona is:385"and the corresponding rate 1s """,and the corresponding rate is .386"2MUST Values of the polarizability arepy,=0.667 A. pu.=0:804 A. and pij,=0.207 (Osterbrock 1961)."," Values of the polarizability are$p_{\rm H}=0.667$ $^3$, $p_{{\rm H}_2}=0.804$ $^3$ , and $p_{\rm He}=0.207$ (Osterbrock 1961)."387luterstellar (IENCO) was first detected towards Ser D2 (777)..,"Interstellar (HNCO) was first detected towards Sgr B2 \citep{Snyder72, Churchwell86, Kuan96}."388 Since the first detection in this source. the molecule has been observed in other hot. cores around massive (27) and low mass protostars (2?)..," Since the first detection in this source, the molecule has been observed in other hot cores around massive \citep{Blake87, MacDonald96} and low mass protostars \citep{vanDishoeck95, Bisschop08}."389 It has also been detected in translucent clouds (2). and in the dense regions of Galactic uolecular clouds (??).. including those in the Calactic ceuter (??7??7).. ITNC'O.," It has also been detected in translucent clouds \citep{Turner99} and in the dense regions of Galactic molecular clouds \citep{Jackson84, Zinchenko00}, including those in the Galactic center \citep{Huttemeister93, Lindqvist95, Dahmen97, Rizzo00, Minh05, Martin08}."390 has also been detected iu some extragalactic sources (277?)..," HNCO has also been detected in some extragalactic sources \citep{Nguyen91, Meier05, Martin09}."391 The isotopoloene ΠοΝΟ (fulinic acid) has recently been detected by ?.., The isotopologue HCNO (fulminic acid) has recently been detected by\cite{Marcelino09}. .392" The cimission in IINCO lines with A=0+ Jigκι. Wo,1=O A (2). (??).. 7=—1.657 (?7).. (2)..."," The emission in HNCO lines with $K_{-1} = 0$ $J_{K_{-1}K_1}$ $K_{-1} = 0$ $K$ $K_{-1} > 0$ \citep{Meier05} \citep{Lindqvist95, Dahmen97}."393 (77).. ?. ΟΡ the laddersCA.>0)areprobablyexcitedbyFURradiation(?).," $l=1.65^\circ$ \citep{Dahmen97}. \citep{Rodriguez08}. \citep{Huttemeister98, Rodriguez06}."394.thereiu).. ο suggested that IINCO. as ΠΟΠ. could trace large scale shocks.," \cite{Minh06} $_3$ , \cite{Meier05} suggested that HNCO, as $_3$ OH, could trace large scale shocks."395 Nevertheless. the hvpothesis that TNCO is a οοος shock tracer at the scale of galaxies still needs to be probe since the IENCOÓ emission has never been studied in wellknown Galactic templates of interstellar shocks.," Nevertheless, the hypothesis that HNCO is a good shock tracer at the scale of galaxies still needs to be probed since the HNCO emission has never been studied in well-known Galactic templates of interstellar shocks."396 In order to better uudoerstaud the excitation and the chemistry of this promising molecule. we have observed the protostar L1157 aud its associated molecular outflow.," In order to better understand the excitation and the chemistry of this promising molecule, we have observed the protostar L1157 and its associated molecular outflow."397 This outflow preseuts the morphological signature of shocks (77). iux it is frequently used to beuchimark nunmierical models of shocks (?7)..," This outflow presents the morphological signature of shocks \citep[][]{Gueth98, Codella09} and it is frequently used to benchmark numerical models of shocks \citep{Gusdorf08a, Gusdorf08b}."398" LILS7 is the best example of ""chemically active outflow (2) and a template of shock chemistry. since inany species exhibit large abundance increments with respect to the protostar (?).."," L1157 is the best example of “chemically active outflow"" \citep[][]{Bachiller01}399 and a template of shock chemistry, since many species exhibit large abundance increments with respect to the protostar \citep[][]{Bachiller97}."400 Therefore. it is a source of choice to characterize the emission of a given molecule in a shocked euviromuent (seeforinstauce7??77)..," Therefore, it is a source of choice to characterize the emission of a given molecule in a shocked environment \cite[see for instance][]{Bachiller97, Bachiller01, Benedettini07, 401Arce08, Codella09}."402" We have observed three lines of the A,=0 ladder of IENCO towards the two main shocks iu the southern lobe of the L1157 molecular outflow: the Bl and B2 positions of ?..", We have observed three lines of the $K_{-1} = 0$ ladder of HNCO towards the two main shocks in the southern lobe of the L1157 molecular outflow: the B1 and B2 positions of \cite{Bachiller97}.403 Tn addition. we have observed as refercuce the continu source LI157-uuu (the protostar).," In addition, we have observed as reference the continuum source L1157-mm (the protostar)."404" The equatorial coordinates of L1157-uuu are RA=20'39706.19% Dec-68702/15.9"".. (J2000)."," The equatorial coordinates of L1157-mm are $20^h39^m06.19^s$ $68^\circ02'15.9''$, (J2000)."405 The offsets of Bl and B2 with respect to Ll1157-uuu are (20°. 607) and (357. O57). respectively.," The offsets of B1 and B2 with respect to L1157-mm are $20"", -60""$ ) and $35"", -95""$ ), respectively."406 The observations were done with the IRAM 301m elescope in Pico Veleta in July 2007., The observations were done with the IRAM 30m telescope in Pico Veleta in July 2007.407 The line quantum Muubers. frequencies aud the telescope parameters are Istoc πι Table 1..," The line quantum numbers, frequencies and the telescope parameters are listed in Table \ref{tab:obs}."408 As backends we used the 100 Kz flterbaulk and the VESPA autocorrelator with a channel resolution of 20-10. MITIz. which allows to study in detail he line wines.," As backends we used the 100 KHz filterbank and the VESPA autocorrelator with a channel resolution of 20-40 MHz, which allows to study in detail the line wings."409 The observations were carried out in yosition switching mode with the position located2UNE from L1157-uuun., The observations were carried out in position switching mode with the position located24'NE from L1157-mm.410Typicalsvstem temperatures aud rns noise of the spectra are are given in Table 1..,Typicalsystem temperatures and rms noise of the spectra are are given in Table \ref{tab:obs}. .411" Table 2. givestheiutegrated fluxoftheciffereutlines colputed from spectra in Jj, units (forward audbeam", Table \ref{tab:lines} givestheintegrated fluxofthedifferentlines computed from spectra in $T_{mb}$ units (forward andbeam412temperature lies in the desired range and assigning a zero value elsewhere.,temperature lies in the desired range and assigning a zero value elsewhere.413 We are aware that this procedure can introduce high frequency noise in the spectrum but this effect should affect in a comparable way all the spectra in a given temperature range., We are aware that this procedure can introduce high frequency noise in the spectrum but this effect should affect in a comparable way all the spectra in a given temperature range.414" Also we recall that the slopes are measured for relatively small values of k (see 83.2), which is hardly affected by the high frequency noise."," Also we recall that the slopes are measured for relatively small values of $k$ (see 3.2), which is hardly affected by the high frequency noise."415" The density power spectrum for the warm gas Pwp, the unstable gas P,, and the cold gas Pcp follows the same behavior as P,, namely it becomes flatter as M increases (see Table 4))."," The density power spectrum for the warm gas $P_{w\rho}$, the unstable gas $P_{u\rho}$ and the cold gas $P_{c\rho}$ follows the same behavior as $P_{\rho}$, namely it becomes flatter as $M$ increases (see Table \ref{tab:indices}) )."416" When comparing the slopes obtained for spectra at different temperature regimes for the same value of M, the sole consistent behavior is that at large M (transonic or supersonic with respect to the gas at 10*K) the spectrum flattens as the temperature decreases, and for M=4.0 and 4.5 the slope even changes its sign."," When comparing the slopes obtained for spectra at different temperature regimes for the same value of $M$, the sole consistent behavior is that at large $M$ (transonic or supersonic with respect to the gas at $10^4$K) the spectrum flattens as the temperature decreases, and for $M=4.0$ and $4.5$ the slope even changes its sign."417" As the averaged turbulent velocity is approximately the same in all the three temperature ranges implying that colder gas has considerably larger Mach numbers, this behavior is not surprising because is the same as the one reported by Kim Ryu (2005)."," As the averaged turbulent velocity is approximately the same in all the three temperature ranges implying that colder gas has considerably larger Mach numbers, this behavior is not surprising because is the same as the one reported by Kim Ryu (2005)."418 The slopes are however much shallower than the ones they obtain., The slopes are however much shallower than the ones they obtain.419" For instance, in our simulation with M=1.3 the slope of the power spectrum for cold gas is —0.12, whereas the slope of the power spectrum they get for an isothermalsimulation with M=7.3 is —0.75 (note that the Mach number for gas at 313K corresponding to M—1.3 is 7.35)."," For instance, in our simulation with $M=1.3$ the slope of the power spectrum for cold gas is $-0.12$, whereas the slope of the power spectrum they get for an isothermalsimulation with $M=7.3$ is $-0.75$ (note that the Mach number for gas at $313$ K corresponding to $M=1.3$ is 7.35)."420" In order to confirm that turbulence statistics is significantly affected by the presence of TI, in this section we compare a thermally unstable simulation with an isothermal one."," In order to confirm that turbulence statistics is significantly affected by the presence of TI, in this section we compare a thermally unstable simulation with an isothermal one."421 We use our lower M simulation because in this case the velocity power spectrum for the isothermal regime is expected to have a slope close to that predicted by Kolmogorov (i.e. -5/3)., We use our lower $M$ simulation because in this case the velocity power spectrum for the isothermal regime is expected to have a slope close to that predicted by Kolmogorov (i.e. -5/3).422 For completeness sake we do also include a comparison between density power spectra., For completeness sake we do also include a comparison between density power spectra.423 In Figure 9 we show density (left) and velocity spectra (right) for the thermally unstable line) and the isothermal line) simulations., In Figure \ref{fig:compiso} we show density ) and velocity spectra ) for the thermally unstable ) and the isothermal ) simulations.424" For the former case the fitted slopes are the same as those reported in Table 4,, while for the isothermal case slopes are -1.89 and -1.60 for the density and the velocity spectrum, respectively."," For the former case the fitted slopes are the same as those reported in Table \ref{tab:indices}, while for the isothermal case slopes are -1.89 and -1.60 for the density and the velocity spectrum, respectively."425 The first value is consistent with the trend found by Kim Ryu (2005) and the second one is close to the expected value., The first value is consistent with the trend found by Kim Ryu (2005) and the second one is close to the expected value.426 These slopes indicate that the effects presented in previous sections concerning the flattening of the density and the velocity power spectra in thermally unstable flows are not due to the time interval we use to compute averaged values and that the presence of TI has in fact important effects on turbulence statistics., These slopes indicate that the effects presented in previous sections concerning the flattening of the density and the velocity power spectra in thermally unstable flows are not due to the time interval we use to compute averaged values and that the presence of TI has in fact important effects on turbulence statistics.427 Note that all the spectra in Figure 9 have been computed by averaging values in the same time interval (see Table 3)) and that the isothermal simulation has been done with an isothermal version of the same code as the one described in §??.., Note that all the spectra in Figure \ref{fig:compiso} have been computed by averaging values in the same time interval (see Table \ref{tab:tiempos}) ) and that the isothermal simulation has been done with an isothermal version of the same code as the one described in \ref{sec:model}.428 Observational results on the HI power spectrum show a power law behavior with an extended range of slope values., Observational results on the HI power spectrum show a power law behavior with an extended range of slope values.429 This is true for the spectrum resulting from intensity fluctuations as well as for the spectrum deduced for the underlying 3D density distribution., This is true for the spectrum resulting from intensity fluctuations as well as for the spectrum deduced for the underlying 3D density distribution.430 The latter spectrum describes the statistics of a density distribution strongly influenced by the presence of TI and turbulence., The latter spectrum describes the statistics of a density distribution strongly influenced by the presence of TI and turbulence.431" On the other hand, it is well known that TI can be triggered in the warm stable gas by turbulent motions characterized by large enough sonic Mach numbers (Hennebelle Pérrault 1999) and that the density PDF is strongly influenced by the characteristics of turbulence (Klessen 2000; Federrath et al."," On the other hand, it is well known that TI can be triggered in the warm stable gas by turbulent motions characterized by large enough sonic Mach numbers (Hennebelle Pérrault 1999) and that the density PDF is strongly influenced by the characteristics of turbulence (Klessen 2000; Federrath et al."432" 2008) as well as by the equation of state (e.g. Passot Vázzquez-Semadeni 1998, Nordlund Padoan 1999, Li et al."," 2008) as well as by the equation of state (e.g. Passot Vázzquez-Semadeni 1998, Nordlund Padoan 1999, Li et al."433" 2003, Gazol et al."," 2003, Gazol et al."434" 2005, Kowal et al."," 2005, Kowal et al."435 2007)., 2007).436" In particular Passot Vázzquez-Semadeni (1998) showed that the density PDF is lognormal for isothermal flows (y=1, with y being the effective polytropic index), but develops a power-law tail at high densities for y« 1, and at low densities for y> 1."," In particular Passot Vázzquez-Semadeni (1998) showed that the density PDF is lognormal for isothermal flows $\gamma=1$, with $\gamma$ being the effective polytropic index), but develops a power-law tail at high densities for $\gamma < 1$ , and at low densities for $\gamma >1$ ."437 For a polytropic self-gravitating gas Li et al. (, For a polytropic self-gravitating gas Li et al. (4382003) found imperfect lognormal distributions,2003) found imperfect lognormal distributions439Determining how and when the Universe was reionized is one of the major outstanding questions of modern. cosmology.,Determining how and when the Universe was reionized is one of the major outstanding questions of modern cosmology.440 Observations of the cosmic microwave background. confirm that hyelrogen gas first became neutral at zz1100 around 400.000 vears alter the Big Bang.," Observations of the cosmic microwave background confirm that hydrogen gas first became neutral at $z\approx1100$ around 400,000 years after the Big Bang."441 Observations of absorption spectra of quasars at redshifts 2<6 indicate that. the intergalactic medium (GAL) is largely ionized., Observations of absorption spectra of quasars at redshifts $z<6$ indicate that the intergalactic medium (IGM) is largely ionized.442 Therefore a cosmic phase transition occurred. whereby. the LGAL went from being fully neutral to being almost fully ionized2001)., Therefore a cosmic phase transition occurred whereby the IGM went from being fully neutral to being almost fully ionized.443. Our picture of when exactly this phase transition occurred. and what was the nature of the sources that drove it remains cloudy., Our picture of when exactly this phase transition occurred and what was the nature of the sources that drove it remains cloudy.444 In recent vears. improved observational data has begun to probe the reionization era.," In recent years, improved observational data has begun to probe the reionization era."445 By pursuing observations of the forest in QSO spectra at ever higher redshifts. Cunn-Peterson troughs have been seen along several quasar sight lines at 2= 2001).. providing an indication of an increase in the IGM neutral fraction at these redshifts.," By pursuing observations of the forest in QSO spectra at ever higher redshifts, Gunn-Peterson troughs have been seen along several quasar sight lines at $z\gtrsim6$ , providing an indication of an increase in the IGM neutral fraction at these redshifts."446 Interpretation of these observations is subtle. since the LGAL ionization state depends upon its thermal history. the spectrum of the ionizing sources. and the history of the production of ionizing radiation in those sources.," Interpretation of these observations is subtle, since the IGM ionization state depends upon its thermal history, the spectrum of the ionizing sources, and the history of the production of ionizing radiation in those sources."447 Complementing forest observations. ds. the detection of the imprint. of reionization in the polarization of the cosmic microwave background (CAIB).," Complementing forest observations, is the detection of the imprint of reionization in the polarization of the cosmic microwave background (CMB)."448" Iescattering of CAIB photons by the ionized ICM. produces a distinctive ""bump"" in the CMD power spectrum on Large angular scales that has been detected by WALAP2009)."," Rescattering of CMB photons by the ionized IGM produces a distinctive “bump"" in the CMB power spectrum on large angular scales that has been detected by WMAP."449. This places a constraint on the integrated optical depth to the surface of last scattering. and suggests that a significant. fraction of the LGAL was ionizecll wo 2xm10.," This places a constraint on the integrated optical depth to the surface of last scattering, and suggests that a significant fraction of the IGM was ionized by $z\approx10$."450 In a few vears time. results from the Planck are expected to tighten these constraints considerably.," In a few years time, results from the Planck are expected to tighten these constraints considerably."451 1n addition to these relatively robust observations. a host of other observations contribute to our understanding of the state of the IGM. at high. redshift.," In addition to these relatively robust observations, a host of other observations contribute to our understanding of the state of the IGM at high redshift."452 These. include constraints on the temperature of the LGAL in the range 2-21(Schave , These include constraints on the temperature of the IGM in the range $z=2-4$ 453significantly greater racial extent(1835 for the NE disk extension: 1450au for the SW) than has been previously measured.,significantly greater radial extent$1835$ for the NE disk extension; $1450$ for the SW) than has been previously measured.454 Smith Verrile (1987) reported the maximum extent of 2 Pie's disc at LB00au (ιο aaresec) for the NE midplane at optical wavelengths., Smith Terrile (1987) reported the maximum extent of $\beta$ Pic's disc at $1300$ (i.e arcsec) for the NE midplane at optical wavelengths.455 However. this was known as a sensitivity-limitecl value rather than the true physical extent of the disc.," However, this was known as a sensitivity-limited value rather than the true physical extent of the disc."456 Here too we are unable to define the outer disc extents above the level of the background noise., Here too we are unable to define the outer disc extents above the level of the background noise.457 The existence of a dise miplane out to 210 radius. as well as the 7107 vertical thickness of the SW extension (see Fig.," The existence of a disc miplane out to $\sim$ $^3$ radius, as well as the $\sim$ $^2$ vertical thickness of the SW extension (see Fig."458 4 in Kalas Jewitt 1995). is unexpected given our current understanding of planetesimal formation as applied to the Solar System (reviewed by. Weidenschilling Cuzzi 1993).," $4$ in Kalas Jewitt 1995), is unexpected given our current understanding of planetesimal formation as applied to the Solar System (reviewed by Weidenschilling Cuzzi 1993)."459 Thus we must conclude that. planetesimals were created at much smaller radii than they are presently inferred to exist. ino Pie. ancl subsequently sullered redistribution.," Thus we must conclude that planetesimals were created at much smaller radii than they are presently inferred to exist in $\beta$ Pic, and subsequently suffered redistribution."460 Moreover this redistribution must allow [or the existence of a lopsided and vertically Uared disc., Moreover this redistribution must allow for the existence of a lopsided and vertically flared disc.461 Global redistribution of this kind is a general outcome of a close stellar. Ilv-by. encounter. (INLSS)., Global redistribution of this kind is a general outcome of a close stellar fly-by encounter (KLSS).462 Below we shall. present numerical investigations of the cvnamics involved., Below we shall present numerical investigations of the dynamics involved.463 In the Dv-by. model presented in INLSS a transient. system of circumstellar eccentric rings was found to form in the perturbecl cise of particles. as shown in Fig.," In the fly-by model presented in KLSS a transient system of circumstellar eccentric rings was found to form in the perturbed disc of particles, as shown in Fig."464 3., $3$ .465 ElLv-by parameters. anc viewing angle and epoch. were chosen to," Fly-by parameters, and viewing angle and epoch, were chosen to"466the training set by a factor of ten.,the training set by a factor of ten.467 The single component plane of the SOM seen at different stages of the learning process is shown in 11., The single component plane of the SOM seen at different stages of the learning process is shown in 1.468" The component plane is coloured by the ‘value’ of the (in this case single element) weight of each node, each of which has competed to represent the values of the training set."," The component plane is coloured by the `value' of the (in this case single element) weight of each node, each of which has competed to represent the values of the training set."469 It is clear that the map has arranged itself into two distinct regions — this is because the training sample is itself distributed around two distinct values (the means of the distributions)., It is clear that the map has arranged itself into two distinct regions – this is because the training sample is itself distributed around two distinct values (the means of the distributions).470" Nodes that are close together (in terms of map distance) have similar values, and there is a clear interface region on the map where the distributions overlap."," Nodes that are close together (in terms of map distance) have similar values, and there is a clear interface region on the map where the distributions overlap."471" To reinforce this point, next to the component plane we also show the so-called Unified Distance Matrix (UDM, or U-Matrix), which visualises the average distance between the weights of neighbouring nodes."," To reinforce this point, next to the component plane we also show the so-called Unified Distance Matrix (UDM, or U-Matrix), which visualises the average distance between the weights of neighbouring nodes."472 The U-Matrix is a means of identifying boundaries of ‘clusters’ within the map., The U-Matrix is a means of identifying boundaries of `clusters' within the map.473 Small UDM values indicate that neighbouring nodes have very similar weights and larger values indicate transition regions between clusters., Small UDM values indicate that neighbouring nodes have very similar weights and larger values indicate transition regions between clusters.474" The segregation of the different parts of the map allows us to label certain nodes in the map as ‘Blue’ and some as ‘Red’ — in other words, it will allow us to classify new inputs nnew samples that the SOM has never seen) based on their BMU (it will either be in the Red or Blue class)."," The segregation of the different parts of the map allows us to label certain nodes in the map as `Blue' and some as `Red' – in other words, it will allow us to classify new inputs new samples that the SOM has never seen) based on their BMU (it will either be in the Red or Blue class)."475" To further demonstrate this, in 11 we show two versions of the SOM but this time scale the size of nodes based on the probability that their weight value was drawn from the Red or Blue distributions."," To further demonstrate this, in 1 we show two versions of the SOM but this time scale the size of nodes based on the probability that their weight value was drawn from the Red or Blue distributions."476 This clearly highlights how the different parts of the map defined by the UDM correspond to the two clusters in the input parameter space., This clearly highlights how the different parts of the map defined by the UDM correspond to the two clusters in the input parameter space.477" In 22 we show the actual input distribution of Red and Blue objects, and the distribution of the values of the weights of nodes in the trained map."," In 2 we show the actual input distribution of Red and Blue objects, and the distribution of the values of the weights of nodes in the trained map."478 Note that the SOM has identified several nodes which define an ambiguous classification where the two abundance of the two populations is equal at values near zero., Note that the SOM has identified several nodes which define an ambiguous classification where the two abundance of the two populations is equal at values near zero.479 We have labelled 101/400 nodes as ‘Red’ and 135/400 nodes as ‘Blue’ classifications based on the map division made apparent by the UDM., We have labelled 101/400 nodes as `Red' and 135/400 nodes as `Blue' classifications based on the map division made apparent by the UDM.480" To test the SOM, we use these nodes to classify 1000 inputs from each of the Red and Blue populations to find the identification rate, defined by the fraction of new Blue or Red objects that correctly classified based on their Best Matching Unit in the trained SOM."," To test the SOM, we use these nodes to classify 1000 inputs from each of the Red and Blue populations to find the identification rate, defined by the fraction of new Blue or Red objects that correctly classified based on their Best Matching Unit in the trained SOM."481 The results are shown in 22., The results are shown in 2.482" Not only does this simple classification procedure successfully identify new test data, it correctly recovers the main properties of the underlying distribution: the mean and standard deviations of the values of objects classified as Red and Blue are URea= 1.03, HBlue=—1.01, ORea=0.49 and σΒιις=0.51, compared to the input distribution of WRea=1 and µβιιο=—1 and σ=0.5."," Not only does this simple classification procedure successfully identify new test data, it correctly recovers the main properties of the underlying distribution: the mean and standard deviations of the values of objects classified as Red and Blue are $\mu_{\rm Red}=1.03$ , $\mu_{\rm483Blue}=-1.01$ , $\sigma_{\rm Red}=0.49$ and $\sigma_{\rm Blue}=0.51$, compared to the input distribution of $\mu_{\rm Red}=1$ and $\mu_{\rm Blue}=-1$ and $\sigma=0.5$."484" Exactly the same principle can be applied to astronomical data sets, and so building on this trivial example we now demonstrate two real world applications of a SOM trained on galaxy data from the COSMOS survey, where we now include many more parameters in the training."," Exactly the same principle can be applied to astronomical data sets, and so building on this trivial example we now demonstrate two real world applications of a SOM trained on galaxy data from the COSMOS survey, where we now include many more parameters in the training."485" Colour-colour plots are a traditional method of isolating objects of interest, since populations with similar spectral properties will have similar broadband colours and therefore cluster together, or follow loci in appropriate colour-magnitude or colour-colour planes."," Colour-colour plots are a traditional method of isolating objects of interest, since populations with similar spectral properties will have similar broadband colours and therefore cluster together, or follow loci in appropriate colour-magnitude or colour-colour planes."486" Perhaps the most successful example in extragalactic studies is the selection of distant galaxies by virtue of the Lyman break drop out, where UV—optical broadband filters that straddle the redshifted Lyman break can efficiently sift z~3 galaxies from a field (Steidel 11993; 11995; Steidel et 11996)."," Perhaps the most successful example in extragalactic studies is the selection of distant galaxies by virtue of the Lyman break drop out, where UV–optical broadband filters that straddle the redshifted Lyman break can efficiently sift $z\sim3$ galaxies from a field (Steidel 1993; 1995; Steidel et 1996)."487" There are many similar examples of highly effective selection of objects using simple colour criteria, and more recently this has been applied with great success for very high-z (z~ 6-9) galaxies that drop-out of optical bands altogether BBouwens et 22010; McLure et 22010)."," There are many similar examples of highly effective selection of objects using simple colour criteria, and more recently this has been applied with great success for very $z$ $z\sim6$ $9$ ) galaxies that drop-out of optical bands altogether Bouwens et 2010; McLure et 2010)."488" More complicated selections can be constructed not only to pick-out galaxies at specific redshifts, but also isolate those with certain properties tthe star-forming / passive z1.4 galaxy selection of Daddi et 22004)."," More complicated selections can be constructed not only to pick-out galaxies at specific redshifts, but also isolate those with certain properties the star-forming / passive $z>1.4$ galaxy selection of Daddi et 2004)."489" Here we demonstrate how the SOM can be used like an N-dimensional colour-magnitude diagram, and when trained using a large catalogue, exploited to identify those ‘clusters’ of interesting objects."," Here we demonstrate how the SOM can be used like an }-dimensional colour-magnitude diagram, and when trained using a large catalogue, exploited to identify those `clusters' of interesting objects."490 The trained SOM can then be applied as a classification and filtering tool to extract objects of interest from a new input catalogue., The trained SOM can then be applied as a classification and filtering tool to extract objects of interest from a new input catalogue.491"Spitzer IRAC (2.6-δμπι) colours have been shown to be very effective at selecting AGN, including those whose optical emission is obscured by dust, since theseobjects havea characteristic red power-law continuum in the near/mid-infared that starts to"," IRAC $\mu$ m) colours have been shown to be very effective at selecting AGN, including those whose optical emission is obscured by dust, since theseobjects havea characteristic red power-law continuum in the near/mid-infared that starts to"492been argued for (Drake&Testa2005;DrakeErcolano2007).,"been argued for \citep{drake05,drake07}."493". However, the bulk of evidence in the Sun appears to favor a lower ratio (Schmelzetal.2005;Young2005):; see AGSSO9 for a detailed discussion."," However, the bulk of evidence in the Sun appears to favor a lower ratio \citep{Schmelz05, Young05}; see AGSS09 for a detailed discussion."494" In DP06 we used only the scalar constraints (Rey and Y,,.,) as diagnostic features to infer abundances.", In DP06 we used only the scalar constraints $R_{CZ} $ and $Y_{surf}$ ) as diagnostic features to infer abundances.495" However, Ne retains electrons to higher temperatures than O does, and as a result different Ne+O mixtures with the same opacity at the base of the surface convection zone will have different opacity in deeper layers."," However, Ne retains electrons to higher temperatures than O does, and as a result different Ne+O mixtures with the same opacity at the base of the surface convection zone will have different opacity in deeper layers."496 This leads to a distinct signature in the sound speed profile., This leads to a distinct signature in the sound speed profile.497" In this letter we update the mixture constraints based on the same method, but with improved stellar interiors model physics."," In this letter we update the mixture constraints based on the same method, but with improved stellar interiors model physics."498" By adding the sound speed profile as an additional constraint we can set interesting bounds on the solar Ne/O ratio, and these are reinforced by considering the seismic metallicity bounds based on ionization and mean molecular weight."," By adding the sound speed profile as an additional constraint we can set interesting bounds on the solar $Ne/O$ ratio, and these are reinforced by considering the seismic metallicity bounds based on ionization and mean molecular weight."499" In section 2 we recall the method used in DP06, to determine the appropriate composition in order to reproduce the two observable scalars Rey and νε, and the extension of this method including the additional constraint C,,,,,; to determine the ratio Ne/O."," In section 2 we recall the method used in DP06, to determine the appropriate composition in order to reproduce the two observable scalars $R_{CZ}$ and $Y_{surf}$ and the extension of this method including the additional constraint $C_{sound}$ to determine the ratio $Ne/O$."500 In Section 3 we discuss our results., In Section 3 we discuss our results.501" In DP06 we presented our method to infer the solar heavy and light metal abundances required for theoretical models that reproduce the observed solar Y;,,; and Rey.", In DP06 we presented our method to infer the solar heavy and light metal abundances required for theoretical models that reproduce the observed solar $Y_{surf} $ and $R_{CZ} $.502 There are three essential steps involved in determining a seismic solar composition and its associated error., There are three essential steps involved in determining a seismic solar composition and its associated error.503 First. the observed solar properties and their errors must be obtained.," First, the observed solar properties and their errors must be obtained."504" Second, errors in the input solar model physics introduce uncertainties in the theoretically predicted Ἐν and Rey."," Second, errors in the input solar model physics introduce uncertainties in the theoretically predicted $Y_{surf} $ and $R_{CZ} $."505" These uncertainties can be correlated: for example. increasing the degree of gravitational settling both deepens the model Rey and decreases the Y,,,."," These uncertainties can be correlated; for example, increasing the degree of gravitational settling both deepens the model $R_{CZ} $ and decreases the $Y_{surf} $."506 Both the difference between theory and observation and the associated error are now defined for a given solar composition., Both the difference between theory and observation and the associated error are now defined for a given solar composition.507nuderestimation of the errors.,underestimation of the errors.508 It this were the case. the range of allowed c. values would be larger aud the exponential|NEW. πο prediction would still be viable.," It this were the case, the range of allowed $v_c$ values would be larger and the exponential+NFW model prediction would still be viable."509 We have also explored other effects that cau affect our modeling., We have also explored other effects that can affect our modeling.510 Our system is likely to be influenced bv some external shear which will coutribute to the nuage separation but not to the rotational velocity of the leus galaxy., Our system is likely to be influenced by some external shear which will contribute to the image separation but not to the rotational velocity of the lens galaxy.511 In fact. CY2201-3201 lies 77 away from the Hickson compact eroup ICC 90.," In fact, CY2201-3201 lies 7' away from the Hickson compact group HCG 90."512 We have computed what would be the external shear produced by the group assuninue it is modeled with a SIE with the same velocity dispersion as measured frou the galaxy imoemiboers., We have computed what would be the external shear produced by the group assuming it is modeled with a SIE with the same velocity dispersion as measured from the galaxy members.513 ICC 90 as relatively small aud the external shear induced iu the CY fro2201-3201 system is neeligible for our purposes., HCG 90 is relatively small and the external shear induced in the CY 2201-3201 system is negligible for our purposes.514 Apart u HCG 90. CY 2201-3201 appears to be isolated and not iu auy eroup. cluster. or obvious larec-scale structure.," Apart from HCG 90, CY 2201-3201 appears to be isolated and not in any group, cluster, or obvious large-scale structure."515 Iun fact. as part of the CYDER survey we have obtained spectra of several sources iu the field aud. with the limited spectroscopic data we have. not fouud any sie of a massive structure.," In fact, as part of the CYDER survey we have obtained spectra of several sources in the field and, with the limited spectroscopic data we have, not found any sign of a massive structure."516 Another possible flaw in our modeling could be that the ealaxy center is miscalculated., Another possible flaw in our modeling could be that the galaxy center is miscalculated.517 If the ealaxy ceuter is much. closer to the QSO images than the position we have measured then most of the discussed configurations would no longer apply aud the svsteni would displav other image coufigurations. which can iu fact place tiehter constraiuts on the relative contribution of the halo and disk to the total mass budect in the ceutral regions of the lens galaxy.," If the galaxy center is much closer to the QSO images than the position we have measured then most of the discussed configurations would no longer apply and the system would display other image configurations, which can in fact place tighter constraints on the relative contribution of the halo and disk to the total mass budget in the central regions of the lens galaxy."518 However. the seciug aud pixel size of our images and the consistency of the galaxy. center m our different filter inasges make us believe that the true center if different from the one measured should uot be very far off.," However, the seeing and pixel size of our images and the consistency of the galaxy center in our different filter images make us believe that the true center if different from the one measured should not be very far off."519 We lave preseuted the discovery aud subsequent follow up observations of the CY2201-32OL system composed of an edec-on spiral at 2=0.323 splitting a backeroux >=3.903 QSO into two observed images each at opposite sides of the disk., We have presented the discovery and subsequent follow up observations of the CY2201-3201 system composed of an edge-on spiral at $z=0.323$ splitting a background $z=3.903$ QSO into two observed images each at opposite sides of the disk.520 We have modeled the system with one (disk) aux two (disk|halo} nass components., We have modeled the system with one (disk) and two (disk+halo) mass components.521" The most likely configuration is the ""disk with three images of the QSO one at each side of configurationthe disk ax the fainter one approximately behind the disk.", The most likely configuration is the “disk”configuration with three images of the QSO one at each side of the disk and the fainter one approximately behind the disk.522 There are also possible configurations that produce four or even five(this one uulikelv) observableimages., There are also possible configurations that produce four or even five (this one unlikely) observable images.523 However we only observe two nuages., However we only observe two images.524 We have discussed the possibility that the third (aud fourth. if existent) iniage is extincted by the disk.," We have discussed the possibility that the third (and fourth, if existent) image is extincted by the disk."525 We estimate that an ely>LT at th epredicted position of the third nuage at the ealaxy Ileus redshift is required to be cousisteut with our observations., We estimate that an $A_V>4.7$ at th epredicted position of the third image at the galaxy lens redshift is required to be consistent with our observations.526 We have measured the rotational velocity of the leus ealaxy to be Vo=130420 kn Lat a radius 2.7 times the scale radius of the galaxy exponential light distribution., We have measured the rotational velocity of the lens galaxy to be $V_c=130\pm20$ km $^{-1}$ at a radius 2.7 times the scale radius of the galaxy exponential light distribution.527 If we use an SIE|SIS inodel to fit the QSO inage positions aud fuxes aud this value of the rotational velocity. we find that the contribution by the SIE (disk)- to the e. at this radius is required. to be the same or lavecr than the contribution of the SIS (halo).," If we use an SIE+SIS model to fit the QSO image positions and fluxes and this value of the rotational velocity, we find that the contribution by the SIE (disk) to the $v_c$ at this radius is required to be the same or larger than the contribution of the SIS (halo)."528 If we use au exponential|NEW 1uodel then we are unable to reproduce this value of the rotational velocity if we fit the positions and fluxes of the QSO nuages., If we use an exponential+NFW model then we are unable to reproduce this value of the rotational velocity if we fit the positions and fluxes of the QSO images.529 We have speculated whether we have underestimated the error in our deternunation of the ce. which would male the exponential|NEW imodel viable., We have speculated whether we have underestimated the error in our determination of the $v_c$ which would make the exponential+NFW model viable.530 CY 2201-3201 is the best lensing spiral galaxy known to date that can be used to ciscutanele the contributions of its different nass coupoucuts., CY 2201-3201 is the best lensing spiral galaxy known to date that can be used to disentangle the contributions of its different mass components.531 Unfortunatelv our current follow up observations are not constrainiug enough to elucidate between different possible models., Unfortunately our current follow up observations are not constraining enough to elucidate between different possible models.532 Alore accurate image source positions. the discovery or uot of the predicted third image and the measurement of its properties aud a precise rotational velocity would make this svstei fulfill its potential.," More accurate image source positions, the discovery or not of the predicted third image and the measurement of its properties and a precise rotational velocity would make this system fulfill its potential."533 CY 2201-3201. has heen awardedTelescope (IST) ACS time in evele 13., CY 2201-3201 has been awarded (HST) ACS time in cycle 13.534 We have also been awarded more spectroscopic time at Magellan., We have also been awarded more spectroscopic time at Magellan.535 We expect that the ligher quality iages aud extra spectra will help us Huprove our modcling and place strong constraints ou the relative contribution of the disk aud halo mass coniponcents., We expect that the higher quality images and extra spectra will help us improve our modeling and place strong constraints on the relative contribution of the disk and halo mass components.536 We thauk C. Keeton for making public his CRAVLENS code and replying to our questions., We thank C. Keeton for making public his GRAVLENS code and replying to our questions.537 We thank Paul Schechter for his cucouragcment aud helpful discussions., We thank Paul Schechter for his encouragement and helpful discussions.538 We thank all observatory staff for their help duriug observations., We thank all observatory staff for their help during observations.539 We thank the anouvinous referee for us/her conunents that have helped us inprove the paper., We thank the anonymous referee for his/her comments that have helped us improve the paper.540 F.J.C. acknowledges support frou the Spanish Ministerio de Educacióun ν΄ Ciencia (ATEC). project AYA2005-9113-C02-01 with EC-FEDER fuudiug aud from the research project 2OO5SCGR00728 from the Generalitat de Catalunya.," F.J.C. acknowledges support from the Spanish Ministerio de Educaciónn y Ciencia (MEC), project AYA2005-09413-C02-01 with EC-FEDER funding and from the research project 2005SGR00728 from the Generalitat de Catalunya."541 J.M. eratefully ackuoledges support from he Chilean Centro de Astrofífsica FONDAP 15010003., J.M. gratefully acknowledges support from the Chilean Centro de sica FONDAP 15010003.542" F.J.C. aud JAL acknowledge support frou à. ""convenio àlateral CSIC-Uuiversidad de Chile”.", F.J.C. and J.M. acknowledge support from a “convenio bilateral CSIC-Universidad de Chile”.543 E.G. is supported N NENational Science Foundation under erant AST 2-0166, E.G. is supported by the National Science Foundation under grant AST 02-01667.544sseems to be a1 obscured BeXB located far away in the Galaxy.,seems to be an obscured BeXB located far away in the Galaxy.545"(the axis perpendicular to the orbital plane of the galaxy center of niass). aud we adopt ey,=0.2 rad.","(the axis perpendicular to the orbital plane of the galaxy center of mass), and we adopt $\psiM546=0.2$ rad."547 We note here that the set-up of the initial conditions is considerably more time-expensive that iu the case of the ealaxv at the cluster center., We note here that the set-up of the initial conditions is considerably more time-expensive that in the case of the galaxy at the cluster center.548" Iu fact. iu the preseut case. ""galaxw at rest micaus that the galaxw ceuter of niass is actually (uniforiulv)rofating arouud the cluster center. and this induces a centrifugal acceleration ou the galaxy stars. as apparent by setting 42=0=o =0in cq. ("," In fact, in the present case, “galaxy at rest” means that the galaxy center of mass is actually (uniformly) around the cluster center, and this induces a centrifugal acceleration on the galaxy stars, as apparent by setting $\varphi=\vartheta=\dot\psi=0$ in eq. ("54931).,31).550 Thus. if one erroneously adopt as stellar orbit initial conditions the same conditions adopted im the previous Section. the result is a vigorous stellar escape. just due to the centrifugal acceleration.," Thus, if one erroneously adopt as stellar orbit initial conditions the same conditions adopted in the previous Section, the result is a vigorous stellar escape, just due to the centrifugal acceleration."551 Accordingly. test umuerical saunulatious (uot shown rere} were characterized by a sjenificaut number of stars escaped up to μιαςcLOO.," Accordingly, test numerical simulations (not shown here) were characterized by a significant number of stars escaped up to $\mmax\simeq 100$."552 Of course this is not a phvsical process; but only the result of the non-equilibriuni mitial couditious: in order to avoid this problem we proceeded as follows.," Of course this is not a physical process, but only the result of the non-equilibrium initial conditions: in order to avoid this problem we proceeded as follows."553 For each ealaxv model. we first performed the orbital calculation for a lareeoO nuniber (sav 107) initial coucditions arrangedc» as in Sect.," For each galaxy model, we first performed the orbital calculation for a large number (say $10^5$ ) initial conditions arranged as in Sect."554 5.1. iiüutainius the galaxy in uniform rotatio- around the cluster ceuter and without oscillations.," 5.1, maintaining the galaxy in uniform rotation around the cluster center and without oscillations."555 We then discarded all the initial conditions correspouding to orbits for which. over an Hubble time. μαςmzl.2. in order to nünüc the result shown in the bottom panel of Fig.," We then discarded all the initial conditions corresponding to orbits for which, over an Hubble time, $\mmax/\mi\gsim 1.2$, in order to mimic the result shown in the bottom panel of Fig."556 2., 2.557 We finally used the remaining initial conditions to study the orbital evolution iu he correspouding ealaxy., We finally used the remaining initial conditions to study the orbital evolution in the corresponding galaxy.558 The results are sunuuiarize in Fie., The results are summarized in Fig.559 3., 3.560 Several interesting coments can be made from inspection of Fig., Several interesting comments can be made from inspection of Fig.561 3., 3.562 The first. aud more obvious. is that also in the rotatingo osalaxies. oscillations are expected to produce stellar evaporation.," The first, and more obvious, is that also in the rotating galaxies, oscillations are expected to produce stellar evaporation."563 However. in the rotating cases we invariably found that the largest nmngjas/1) are lavecr that the correspondiug quautity relative to the ealaxies at the cluster ceuter (cfr.," However, in the rotating cases we invariably found that the largest $\mmax/\mi$ are larger that the corresponding quantity relative to the galaxies at the cluster center (cfr."564 Fig., Fig.565 2). and this is due to the additional effect of the centrifugal terii on escaping stars.," 2), and this is due to the additional effect of the centrifugal term on escaping stars."566 Strictly related to this poiut is also the systematic behavior of yas1 shown in Fie., Strictly related to this point is also the systematic behavior of $\mmax/\mi$ shown in Fig.567 3. where it is apparent how the largest ratios for galaxy models placed at r=ay. 01/2 and 2«4. respectively.," 3, where it is apparent how the largest ratios for galaxy models placed at $r=\acu$, $\acu/2$ and $2\acu$, respectively."568 This non-monotonic trend si just a reflection of the same behavior of P. shown in Fie.," This non-monotonic trend si just a reflection of the same behavior of $\Ppsi$, shown in Fig."569 Ll: shorter the ealaxy oscillation times. larger are the nnn that can be reached by escaping stars.," 1: shorter the galaxy oscillation times, larger are the $\mmax/\mi$ that can be reached by escaping stars."570 In this respect. the peculiar dynamical situation of galaxies orbiting near the cluster core radius it is well known: not only there is a chauge in the topological nature of the CTF there (see. e.$.. CD91). but also oscillation periods are the shortest (for a given galaxv model)," In this respect, the peculiar dynamical situation of galaxies orbiting near the cluster core radius it is well known: not only there is a change in the topological nature of the CTF there (see, e.g., CD94), but also oscillation periods are the shortest (for a given galaxy model)."571 The third comment about , The third comment about Fig.5723 is the conunon pattern of the radial behavior of the upper euvelope of Miyax/iy. hes a quite well defined. sharp increase followed by a somewhat smoother decline at increasing mm.," 3 is the common pattern of the radial behavior of the upper envelope of $\mmax/\mi$, i.e., a quite well defined, sharp increase followed by a somewhat smoother decline at increasing $\mi$."573 Lluis behavior basically correspouds to the place in the galaxy where orbital times (sce eq. [, This behavior basically corresponds to the place in the galaxy where orbital times (see eq. [57418]) become comparable with the oscillation times.,18]) become comparable with the oscillation times.575 Inside this radius stellar orbits react adiabatically to the forcing due to ealaxy oscillations (see CD91). while outside ealaxy oscillations become effective in chaugiug siguificantly the stellar orbits.," Inside this radius stellar orbits react adiabatically to the forcing due to galaxy oscillations (see CD94), while outside galaxy oscillations become effective in changing significantly the stellar orbits."576 As expected. the effect. becomes however «παλ. and smaller for stellar orbits with increasing orbital times.," As expected, the effect becomes however smaller and smaller for stellar orbits with increasing orbital times."577 Finallv. note how there are not significant differences between the results iu the large (Ca) aud simall (Cb) clusters: wo interpret this as another niuüfestatiou of the comparable oscillatory periods iu the two cases (see Fie.," Finally, note how there are not significant differences between the results in the large (Ca) and small (Cb) clusters: we interpret this as another manifestation of the comparable oscillatory periods in the two cases (see Fig."578 1)., 1).579 Iu this paper we presented a representativo selectiou of nunerical models aiued at the study of collisiouless evaporation of stars from cluster elliptical galaxies., In this paper we presented a representative selection of numerical models aimed at the study of collisionless evaporation of stars from cluster elliptical galaxies.580 Frou. a theoretical poiut of view this possibility was pointed out in CCGÓ98. who showed that characteristic oscillation times of elliptical galaxies in near equilibria configurations in the tidal field of the parent cluster are curiously comparable to the stellar orbital times in the outskirts of the galaxies themselves.," From a theoretical point of view this possibility was pointed out in CG98, who showed that characteristic oscillation times of elliptical galaxies in near equilibrium configurations in the tidal field of the parent cluster are curiously comparable to the stellar orbital times in the outskirts of the galaxies themselves."581 Frou a numerical point of view the present work represents the natural follow-up of two recent preparatory works ou the same subject (AICO3ab). where we explored the simplest equilibrium configuration (ec. a galaxy with the center of mass at rest at the center of a triaxial cluster). but we left unaddressed the more colplicate (although more astroplvsically represeutative) case of galaxies with their ceuter of mass in rotation around the (spherica cluster center.," From a numerical point of view the present work represents the natural follow-up of two recent preparatory works on the same subject (MC03ab), where we explored the simplest equilibrium configuration (i.e., a galaxy with the center of mass at rest at the center of a triaxial cluster), but we left unaddressed the more complicate (although more astrophysically representative) case of galaxies with their center of mass in rotation around the (spherical) cluster center."582 We recall tha oe1 all the presented simulations the effect of he cluster eravitational feld ou stellar orbits was included. in order to study the effects of galaxy. oscillations onlv: we also recall that its effec is inside the cluster core radius. whilecrpanding outside (sec. e... καὶ 1993. CD91).," We recall that in all the presented simulations the effect of the cluster gravitational field on stellar orbits was included, in order to study the effects of galaxy oscillations only; we also recall that its effect is inside the cluster core radius, while outside (see, e.g., Valluri 1993, CD94)."583 The main resultscan be sununarized as follows:, The main resultscan be summarized as follows:584step is determined by the Courant condition with a Courant nuuber of 0.5.,step is determined by the Courant condition with a Courant number of 0.5.585 The Ll stellar wind sources are modeled by forcing the velocity in Ll subregions of 125 zones cach to be constant with time while the densities in these subvolumes are set so that the total mass flow into the volue of solution. M. Is given by Table 1..," The 14 stellar wind sources are modeled by forcing the velocity in 14 subregions of 125 zones each to be constant with time while the densities in these subvolumes are set so that the total mass flow into the volume of solution, $\dot M_w$, is given by Table \ref{srcs}."586 Also. the maguetic field of the winds is assumed to always be at equipartition.," Also, the magnetic field of the winds is assumed to always be at equipartition."587" The aneular momentum and mass accretion rates reported iu the next section are calculated by stingτσ the relevant quantity in zones located within 0.12, of the origin.", The angular momentum and mass accretion rates reported in the next section are calculated by summing the relevant quantity in zones located within $0.1 R_A$ of the origin.588 Although we are modcling the wind sources more realistically than in previous work. we here ignore the effects of the maguetic field ou the large scale kinematics.," Although we are modeling the wind sources more realistically than in previous work, we here ignore the effects of the magnetic field on the large scale kinematics."589 We take the medium to be an adiabatie polvtropic gas. with +=5/3.," We take the medium to be an adiabatic polytropic gas, with $\gamma = 5/3$."590 Building on previous work (Melia1901 auc Coker&Melia1997)). we have included a first order approximation to magnetic dissipative heating as well as au accurate expression for the cooling due to magnetic bremsstralline. thermal bremisstraliluug. line emission. radiative recombination. and 2 photon coutimmiun cussion for a gas with cosmic abundance.," Building on previous work \cite{Me94} and \cite{CM97}) ), we have included a first order approximation to magnetic dissipative heating as well as an accurate expression for the cooling due to magnetic bremsstrahlung, thermal bremsstrahlung, line emission, radiative recombination, and 2 photon continuum emission for a gas with cosmic abundance."591 For magnetic heating. we assume that the magnetic feld never rises above equipartition.," For magnetic heating, we assume that the magnetic field never rises above equipartition."592 If compression aud flux conservation would otherwise dictate a maeuctic field larger than the equipartition value. the field lines are asstmed to reconnect rapidly. converting the magnetic field cuerev iuto thermal energy. thereby re-establishing equipartition couditious.," If compression and flux conservation would otherwise dictate a magnetic field larger than the equipartition value, the field lines are assumed to reconnect rapidly, converting the magnetic field energy into thermal energy, thereby re-establishing equipartition conditions."593 Iu the future. we will use a more detailed treatment of this dissipation process based ou the sclicme described in Wowalenko Melia (1997).," In the future, we will use a more detailed treatment of this dissipation process based on the scheme described in Kowalenko Melia (1997)."594 The cooling functiou iucludes a uultiple-Caussian fit to the relevant cooling emissivities provided by N. Gelrels (see Celrels&Willams1993 and references cited therein). though with the thermal bremsstrahlung portion supplanted with more accurate expressions that are valid over a broader range of physical conditions aud with the inclusion of magnetic bremsstrallune.," The cooling function includes a multiple-Gaussian fit to the relevant cooling emissivities provided by N. Gehrels (see \cite{GW93} and references cited therein), though with the thermal bremsstrahlung portion supplanted with more accurate expressions that are valid over a broader range of physical conditions and with the inclusion of magnetic bremsstrahlung."595" For the former. we use 1979)) with a Gaunt factor of 1.2 aud à Z of 1.3 (Rvbicki&Lightman 1979)). while for the latter 13) where o, is the electron προς density. Tis the temperature, B is the magnetic field. aud. CD) is"," For the former, we use \cite{RL79}) ) with a Gaunt factor of 1.2 and a Z of 1.3 \cite{RL79}) ), while for the latter \cite{Me94}) ) where $n_e$ is the electron number density, $T$ is the temperature, $B$ is the magnetic field, and $G(T)$ is"596overwhelining backeround of the umnucerous stars which are ouly moderately iagnuified.,overwhelming background of the numerous stars which are only moderately magnified.597 Conversely. if the huuinositv function consists of onlv very uniuous stars then onlv a small ummber are required to account for the Iuninosity iu a pixel.," Conversely, if the luminosity function consists of only very luminous stars then only a small number are required to account for the luminosity in a pixel."598 It is very uulikelv that auy individual star is strongly uaegui&ed., It is very unlikely that any individual star is strongly magnified.599 When this rare event docs occur. rowever. the contribution from the magnified star can dominate the fiux received ina pixel. resulting in a substantial fluctuation in the observed surface rightness.," When this rare event does occur, however, the contribution from the magnified star can dominate the flux received in a pixel, resulting in a substantial fluctuation in the observed surface brightness."600 The real situation. however. is a conibination of the above and we expect that a stellar population sampled iu a pixel consists of a large proportion of faint stars which are insensitive to the effects of microleusime. resulting in a backeround flux. and a relatively sinall uuniber of very hDunuinous stars which dominate the hunuinosity.," The real situation, however, is a combination of the above and we expect that a stellar population sampled in a pixel consists of a large proportion of faint stars which are insensitive to the effects of microlensing, resulting in a background flux, and a relatively small number of very luminous stars which dominate the luminosity."601 The huuinosity function model we choose is the stellar LF front aud Wiclen (1997). derived from Hipparclios data within 20pe of the Sun.," The luminosity function model we choose is the stellar LF from and Wielen (1997), derived from Hipparchos data within $20\pc$ of the Sun."602 The characteristics of his Inniuositv function are presented in Figure L: representing a population with a total luuinesity of 109L... the solid line shows the wuuber of stars possessing a luminosity greater than some value. while the dot-dashed line is their coutribution to he total huuinositv of the pixel," The characteristics of this luminosity function are presented in Figure 4; representing a population with a total luminosity of $10^6\lsun$, the solid line shows the number of stars possessing a luminosity greater than some value, while the dot-dashed line is their contribution to the total luminosity of the pixel."603 It is obvious roni this picture that while stars with L>LOL. represent less than of the population o» umuuber. they account for of the total uninositv.," It is obvious from this picture that while stars with $L>10\lsun$ represent less than of the population by number, they account for of the total luminosity."604 Given a population of nmücroleusing niasses. the magnification of a single star cau be choscu by selecting from the maeuification probability distribution eiven by Equation 5.," Given a population of microlensing masses, the magnification of a single star can be chosen by selecting from the magnification probability distribution given by Equation \ref{probability}."605 For a sample of stars. maguificatious cau be drawn from this distribution multiple times to deteruiue the total maguifcation of the population.," For a sample of stars, magnifications can be drawn from this distribution multiple times to determine the total magnification of the population."606 While this is straight forward. it becomes computationally expensive when the population consists of a very large imuuber stars.," While this is straight forward, it becomes computationally expensive when the population consists of a very large number stars."607 The procedure employed in this study is to determine the magnification statistics for various nunibers of source stars. conibinius the results to reproduce the effect of mucrolensing the eutire source stellar population.," The procedure employed in this study is to determine the magnification statistics for various numbers of source stars, combining the results to reproduce the effect of microlensing the entire source stellar population."608" Analvtically this cau be caleulated by convolving the iaeuification probability distribution for a single star (Equation 5)) with itself 6044, times. Where Asamnp is the nunbor of stars being mucroleused."," Analytically this can be calculated by convolving the magnification probability distribution for a single star (Equation \ref{probability}) ) with itself $n_{samp}$ times, where $n_{samp}$ is the number of stars being microlensed."609 Again. while this is simple for a small population of source stars. the calculation becomes muuerically uuwieldy for a large nuuber of stars.," Again, while this is simple for a small population of source stars, the calculation becomes numerically unwieldy for a large number of stars."610 For tle purpose of this paper. these statistics were generated a Moute Carlo approach. drawing 1semp observations frou Equation ο and combining thei to determine the mean maguification of the sample.," For the purpose of this paper, these statistics were generated a Monte Carlo approach, drawing $n_{samp}$ observations from Equation \ref{probability} and combining them to determine the mean magnification of the sample."611 Repeating this procedure 105 times for each Γκ Ut is then possible to determine the distribution of neanmaeuificatious., Repeating this procedure $10^6$ times for each $n_{samp}$ it is then possible to determine the distribution of mean magnifications.612 The results of this sampling for several source redshifts between 2=0.05 aud i=0.5 are presented iu Figure 5.. with sample sizes ranging from 1 to LO! source stars.," The results of this sampling for several source redshifts between $z=0.05$ and $z=0.5$ are presented in Figure \ref{fig4}, with sample sizes ranging from 1 to $10^4$ source stars."613 At all τουςτς tle same trend is seen with the distribution of the means evolving from the single realization for (Equation 5)) to a more Ganssian forni as the sample size is increased: this is a consequence of the eeutral lait theorem., At all redshifts the same trend is seen with the distribution of the means evolving from the single realization for (Equation \ref{probability}) ) to a more Gaussian form as the sample size is increased; this is a consequence of the central limit theorem.614 These distributions can then be combined to determine the distributions of incus for any saunple size., These distributions can then be combined to determine the distributions of means for any sample size.615 Aried with this information it is now possible to tackle the question of the overall brigltucss fluctuations expected for a population of stars drawn from a luminosity function. aud hence the expected surface Dbrightuess fluctuation within a pixel.," Armed with this information it is now possible to tackle the question of the overall brightness fluctuations expected for a population of stars drawn from a luminosity function, and hence the expected surface brightness fluctuation within a pixel."616 For this. the above maenification distributions are convolved with the stellar luminosity function described in Section ??.. ΠΕ a total huninosity. and hence ΠΡΟ of stars in the population.," For this, the above magnification distributions are convolved with the stellar luminosity function described in Section \ref{lumfun}, assuming a total luminosity, and hence number of stars in the population."617 Again. a AMoute Carlo approach is taken and he Iuninositv function is biuned logarithmically.," Again, a Monte Carlo approach is taken and the luminosity function is binned logarithmically."618 While the bius at lower luminosity contain niv stars they contribute a neglieible fraction of the otal huunositv and are uniformly maenitied wo Gay., While the bins at lower luminosity contain many stars they contribute a negligible fraction of the total luminosity and are uniformly magnified by $\left<\mu\right>$.619 At the high huninosity cud. where the uniünositv coutnbutious of the bins become a nore appreciable fraction ofthe total Iuniuosity. uaguification probability distribution for cach uu is caleulated by combining the appropriate »opulationu maenuification probability distributions oxeseuted in Figure 5..," At the high luminosity end, where the luminosity contributions of the bins become a more appreciable fraction of the total luminosity, magnification probability distribution for each bin is calculated by combining the appropriate population magnification probability distributions presented in Figure \ref{fig4}."620 The distribution for cach iu is then combined. weighted by the huuinosityv raction of the bin. to determine the maeuification xobabilitv distribution for the eutire population of stars.," The distribution for each bin is then combined, weighted by the luminosity fraction of the bin, to determine the magnification probability distribution for the entire population of stars."621 Two constraints. that the mean value of," Two constraints, that the mean value of"622"simple populations, i.e. globular clusters, and the results were highly encouraging, indicating that theoreticallj SSPs might be confidently used in the analysis of more complex systems.","simple populations, i.e. globular clusters, and the results were highly encouraging, indicating that theoretical SSPs might be confidently used in the analysis of more complex systems."623" There were two additional results that wil be important in future analyses: we quantitatively showed that the presence of hot stars (e.g., blue stragglers and blue horizontal branch (B-HB) objects, which, by the way, are among the main contributors to the far-UV rising branch) can significantly dilute the mid-UV absorption indices, and that the enhancement of a-elements considerably modifies the overall SED of evolved populations."," There were two additional results that will be important in future analyses: we quantitatively showed that the presence of hot stars (e.g., blue stragglers and blue horizontal branch (B-HB) objects, which, by the way, are among the main contributors to the far-UV rising branch) can significantly dilute the mid-UV absorption indices, and that the enhancement of $\alpha$ -elements considerably modifies the overall SED of evolved populations."624" Based on the results obtained so far, the project at its current stage is now focusing on the detailed analysis of local (mostly based on IUE observations) and distant evolved systems."," Based on the results obtained so far, the project at its current stage is now focusing on the detailed analysis of local (mostly based on IUE observations) and distant evolved systems."625" This study will include, in a similar way as Cimattietal.(2008), two steps: we are first conducting a UV analysis that will be later followed by a panchromatic study using, for instance, the modelling machinery developed by Panuzzoetal.(2005)."," This study will include, in a similar way as \citet{cimatti08}, two steps: we are first conducting a UV analysis that will be later followed by a panchromatic study using, for instance, the modelling machinery developed by \citet{panuzzo05}."626. We are also carrying out a detailed study of the far-UV indices and its validation process (as we did in the mid-UV) with the main goal of determining the metallicity of the objects responsible of the far-UV up turn., We are also carrying out a detailed study of the far-UV indices and its validation process (as we did in the mid-UV) with the main goal of determining the metallicity of the objects responsible of the far-UV up turn.627" In Bertone&Chavez(2009),, we presented a preliminarylj study of the mid-UV spectra of the Sun and M32 and determined, through a x2 analysis, their age and chemical composition."," In \citet{bertone09}, we presented a preliminary study of the mid-UV spectra of the Sun and M32 and determined, through a $\chi_\nu^2$ analysis, their age and chemical composition."628" Briefly, this analysis consisted in comparing the observed SEDs of the Sun, extracted from the UARS/SUSIMarchive?,, and that of M32, taken with the Faint Object Spectrograph onboard the Hubble Space Telescope (program 1D=6636; PI: M. Gregg), to a set of theoretical integrated spectra calculated with the synthesis code developed by Buzzoniff (1989)."," Briefly, this analysis consisted in comparing the observed SEDs of the Sun, extracted from the UARS/SUSIM, and that of M32, taken with the Faint Object Spectrograph onboard the Hubble Space Telescope (program 1D=6636; PI: M. Gregg), to a set of theoretical integrated spectra calculated with the synthesis code developed by \citet{buz89}."629". In the synthesis code, we have incorporated the stellar library and considered a red HB morphology with a Salpeter initial mass function (s=2.35)."," In the synthesis code, we have incorporated the stellar library and considered a red HB morphology with a Salpeter initial mass function $s$ =2.35)."630" The results are listed in Table 5.2 (seeBertone&Chavez2009,formore details).."," The results are listed in Table \ref{tab:sunm32} \citep[see][for more631details]{bertone09}."632" Interestingly, we obtained that for the Sun (or, equivalently, for a population whose mid-UV spectrum is dominated by stars like the Sun), the absolute chi-square minimum is found for the solar metallicity and an age of 10.1"," Interestingly, we obtained that for the Sun (or, equivalently, for a population whose mid-UV spectrum is dominated by stars like the Sun), the absolute chi-square minimum is found for the solar metallicity and an age of 10.1"633For the initial models presented here we have assumed that the ionization structure produced at any point is given by LIE: an assumption we justify in Appendix A..,For the initial models presented here we have assumed that the ionization structure produced at any point is given by LTE; an assumption we justify in Appendix \ref{sec:ltevalidity}.634 In reality. of course. once the LPL bouncary is crossed. the ionization will drop as the net recombination rate gradually ekes away at the ions and we make a transition towards coronal equilibrium.," In reality, of course, once the LTE boundary is crossed, the ionization will drop as the net recombination rate gradually ekes away at the ions and we make a transition towards coronal equilibrium."635 However. since we know the time-evolution of density and temperature for any region outside of the LEE limiting raclius. we can derive the time and conditions when it crossed. this LTI boundary.," However, since we know the time-evolution of density and temperature for any region outside of the LTE limiting radius, we can derive the time and conditions when it crossed this LTE boundary."636 In. principle then. we can follow the non-LTI evolution of the gas through this outer region and bevond the ion-electron equilibrium radius to the non-equilibrium ionization states present in the outer fringe.," In principle then, we can follow the non-LTE evolution of the gas through this outer region and beyond the ion-electron equilibrium radius to the non-equilibrium ionization states present in the outer fringe."637 In a purely ΓΙ fireball we expect high ionization states to occur in the outer regions as a result of the lower density., In a purely LTE fireball we expect high ionization states to occur in the outer regions as a result of the lower density.638 With. the more detailed. prescription above. the higher ionization would result from the higher temperature of the fireball when the region in question Crosse the LTE boundary.," With the more detailed prescription above, the higher ionization would result from the higher temperature of the fireball when the region in question crossed the LTE boundary."639 In. practice. we expect that this correction may have little ellect on the optical spectra because the emission is dominated by the higher density inner regions of the fireball.," In practice, we expect that this correction may have little effect on the optical spectra because the emission is dominated by the higher density inner regions of the fireball."640 his elfect may. well become important. however. when we come to consider the ultraviolet spectra where high ionization lines are present: and which we hope to consider in a future paper.," This effect may well become important, however, when we come to consider the ultraviolet spectra where high ionization lines are present; and which we hope to consider in a future paper."641 An alternative explanation for the ultraviolet behaviour may be that there is a hot. low density outer fringe to the fireballs.," An alternative explanation for the ultraviolet behaviour may be that there is a hot, low density outer fringe to the fireballs."642 These conditions may occur in regions that have always been optically thin and inellicient. at. cooling racdiativelv., These conditions may occur in regions that have always been optically thin and inefficient at cooling radiatively.643 These lines may then arise from a transition region similar to that between the solar chromosphere and COLONEA., These lines may then arise from a transition region similar to that between the solar chromosphere and corona.644 The radiative transfer equation has a formal solution where / is the intensity of the emerging radiation. 59 is the source function. and 7 is the optical depth measure along the line of sight from the observer.," The radiative transfer equation has a formal solution where $I$ is the intensity of the emerging radiation, $S$ is the source function, and $\tau$ is the optical depth measured along the line of sight from the observer."645 This integral sums contributions Sdr to the radiation intensity. attenuating each by the factor ο7 because it has to pass through optica depth 7 to reach the observer.," This integral sums contributions $S d\tau$ to the radiation intensity, attenuating each by the factor $e^{-\tau}$ because it has to pass through optical depth $\tau$ to reach the observer."646 Since we have assumed. LEE. the source function. is the Planck function. ancl opacities both for lines aux continuum are also known once the velocity. temperature. and density profiles and element abundances are specified.," Since we have assumed LTE, the source function is the Planck function, and opacities both for lines and continuum are also known once the velocity, temperature, and density profiles and element abundances are specified."647 ‘The integral can therefore be evaluated numerically. either in this form or more quickly by using Sobolev resonant surface approximations.," The integral can therefore be evaluated numerically, either in this form or more quickly by using Sobolev resonant surface approximations."648 The above line integral gives the intensity. f(y) [or lines of sight with different impact parameters j.., The above line integral gives the intensity $I(y)$ for lines of sight with different impact parameters $y$.649 We Let x measure distance from the lireball centre toward the observer. and y the distance perpendicular to the line of sight.," We let $x$ measure distance from the fireball centre toward the observer, and $y$ the distance perpendicular to the line of sight."650 The fireball Εικ. obtained. by summing intensities weighted by the solid angles of annuli on the sky. is then where d is the source cistance.," The fireball flux, obtained by summing intensities weighted by the solid angles of annuli on the sky, is then where $d$ is the source distance."651 In a forthcoming paper (Pearson. Lorne Skidmore. in prep.)," In a forthcoming paper (Pearson, Horne Skidmore, in prep.)"652 we will consider generic analytic models for fireball behaviour applicable to a variety of systems., we will consider generic analytic models for fireball behaviour applicable to a variety of systems.653 We use the general opacity given in equation CX4))., We use the general opacity given in equation \ref{eqn:genopac}) ).654 We quote here an approximation to the lightcurve behaviour being the sum of optically thick and optically thin contributions: where Llere oy ds the time that the fireball first. becomes optically thin through its centre and 75 is the current optical depth through the fireball centre., We quote here an approximation to the lightcurve behaviour being the sum of optically thick and optically thin contributions: where Here $\beta_{0}$ is the time that the fireball first becomes optically thin through its centre and $\tau_{0}$ is the current optical depth through the fireball centre.655 The peak Dux occurs when which occurs at a time We note that equations (37)) anc (43)) predict that the peak ας will occur at dillerent times for clillcrent wavelengths., The peak flux occurs when which occurs at a time We note that equations \ref{eqn:beta0}) ) and \ref{eqn:betapk}) ) predict that the peak flux will occur at different times for different wavelengths.656 La principle we could use this as a test for the cllective E., In principle we could use this as a test for the effective $\Gamma$.657 However. in practice. both the assumptions in our treatment. and the necessary accuracy of observations. müght make it clillicult to detect. the dillerence. between AgA® for an isothermal fireball and. ~AT dor acliabatic cooling.," However, in practice, both the assumptions in our treatment and the necessary accuracy of observations, might make it difficult to detect the difference between $\beta_{\rm pk}\sim\lambda^{\frac{3}{5}}$ for an isothermal fireball and $\beta_{\rm pk}\sim\lambda^{\frac{3}{4}}$ for adiabatic cooling."658 ln contrast. the late time behaviour is predicted to have a more significant dependance on E Coverage of a full Dare may well make the 93~27 or >? dilference cliscernable.," In contrast, the late time behaviour is predicted to have a more significant dependance on $\Gamma$ Coverage of a full flare may well make the $\beta\sim\beta^{-2}$ or $\beta^{-3}$ difference discernable."659 The total Dux at several wavelengths and the optically thick contribution at S000 are plotted in Figs., The total flux at several wavelengths and the optically thick contribution at $8~000$ are plotted in Figs.660 9 and 10 for 2 sets of physical conditions. using Population 1," \ref{fig:adithecur} and \ref{fig:isothecur} for 2 sets of physical conditions, using Population I"661as homogeneously distributed over the FOV.,as homogeneously distributed over the FOV.662" We highlight the importance of understanding the effects of photospheric vortical motions on the configuration of magnetic fields in their way up to higher solar atmospheric layers, that are yet to be found."," We highlight the importance of understanding the effects of photospheric vortical motions on the configuration of magnetic fields in their way up to higher solar atmospheric layers, that are yet to be found."663" The data were acquired during a particular observing run on 29 September 2007 with the Swedish 1-m Solar Telescope (SST,Scharmeretal.2003) in La Palma, Canary Islands, as part of a long international campaign with joint observations making use of other solar facilities at the Canary Islands Observatories."," The data were acquired during a particular observing run on 29 September 2007 with the Swedish 1-m Solar Telescope \citep[SST,][]{scharmer2003} in La Palma, Canary Islands, as part of a long international campaign with joint observations making use of other solar facilities at the Canary Islands Observatories."664 The region of interest corresponds to a quiet Sun area close to the solar disc centre (u=0.99)., The region of interest corresponds to a quiet Sun area close to the solar disc centre $\mu$ =0.99).665" Images in G-band (4430.56 nm) were recorded at a fast cadence and the (MFBD,Lófdahl2002) restoration technique was applied to correct the images from the aberrations induced by the turbulent atmospheric medium that affect their quality."," Images in G-band $\lambda 430.56$ nm) were recorded at a fast cadence and the \citep[MFBD,][]{lofdahl2002} restoration technique was applied to correct the images from the aberrations induced by the turbulent atmospheric medium that affect their quality."666" The restored images with an effective FOV of 69x square arcsec and spatial sampling of 0034/pix were corrected with the standard procedures of flat-fielding, dark current substraction, elimination of spurious pixels and borders, and were grouped in two continuous time series of images,s/:: 08:47 to 09:07 UT, ands2:: 09:14 to 09:46 UT, with 15s cadence."," The restored images with an effective FOV of $69 \times 69$ square arcsec and spatial sampling of $0\farcs034$ /pix were corrected with the standard procedures of flat-fielding, dark current substraction, elimination of spurious pixels and borders, and were grouped in two continuous time series of images,: 08:47 to 09:07 UT, and: 09:14 to 09:46 UT, with 15s cadence."667 The ~7-min gap between and corresponds to poor quality images that had to be discarded due to bad observing conditions., The $\sim$ 7-min gap between and corresponds to poor quality images that had to be discarded due to bad observing conditions.668" The final steps included the compensation for diurnal field rotation, destretching and subsonic filtering to eliminate residual jittering."," The final steps included the compensation for diurnal field rotation, destretching and subsonic filtering to eliminate residual jittering."669 More details on the data preparation can be found in Balmacedaetal.(2010)., More details on the data preparation can be found in \cite{balmaceda2010}.670". Our analysis is based on the widely used local correlation tracking techniques (LCT,November&Simon1988), implemented by Molowny-Horas&Yi(1994)."," Our analysis is based on the widely used local correlation tracking techniques \citep[LCT,][]{november1988}, implemented by \cite{molowny1994}."671". We compute the horizontal proper motions of structures using a Gaussian tracking window with a Full-Width at Half-Maximum (FWHM) of 1’’0, to generate maps of horizontal velocity (flow maps)."," We compute the horizontal proper motions of structures using a Gaussian tracking window with a Full-Width at Half-Maximum (FWHM) of $\farcs$ 0, to generate maps of horizontal velocity (flow maps)."672" The same procedure was used by Balmacedaetal.(2010) on the same data for the analysis of a fraction of the whole FOV (10"" x 10"") displaying a region of strong negative divergence.", The same procedure was used by \cite{balmaceda2010} on the same data for the analysis of a fraction of the whole FOV $\arcsec$ $\times$ $\arcsec$ ) displaying a region of strong negative divergence.673" These authors found converging horizontal flows, i.e the velocity arrows pointing to a common destination being the location of the sink."," These authors found converging horizontal flows, i.e the velocity arrows pointing to a common destination being the location of the sink."674 In this work we present the results obtained from the LCT analysis for series and over the complete FOV for 20- intervals., In this work we present the results obtained from the LCT analysis for series and over the complete FOV for 20-min intervals.675" From the horizontal velocity maps we compute the divergence field defined as: V¥=9h3.4Oya where v, and v, are the corresponding x and y components of the horizontal velocity vector."," From the horizontal velocity maps we compute the divergence field defined as: $\nabla \vec v=\frac{\partial \vec v_{x}}{\partial x}+\frac{\partial \vec v_{y}}{\partial y}$, where $ v_{x}$ and $ v_{y}$ are the corresponding $x$ and $y$ components of the horizontal velocity vector."676" Vertical velocities are inferred after multiplying the horizontal flow divergence by the so-called scale height of the flux mass (4m=150 km), following November(1989)."," Vertical velocities are inferred after multiplying the horizontal flow divergence by the so-called scale height of the flux mass $h_m=150$ km), following \cite{november1989}."677. Note that the term divergence refers to the divergence of the horizontal velocities., Note that the term divergence refers to the divergence of the horizontal velocities.678" For a detailed derivation, physical explanation and validity of this relation, we refer the reader to Márquez,SánchezAlmeida&Bonet(2006).."," For a detailed derivation, physical explanation and validity of this relation, we refer the reader to \cite{marquez2006}."679 Resulting vertical velocities are manifestly conditioned by the LCT average and therefore can not be directly compared to Doppler velocities., Resulting vertical velocities are manifestly conditioned by the LCT average and therefore can not be directly compared to Doppler velocities.680 An upcoming work attempts to establish margins for the comparison of the two., An upcoming work attempts to establish margins for the comparison of the two.681 In our data the velocity values as corresponding to a 20-min average range between 1.8 (upflows) and -1.2 km s! (downflows)., In our data the velocity values as corresponding to a 20-min average range between 1.8 (upflows) and -1.2 km $^{-1}$ (downflows).682 The overall distribution of horizontal velocities of one of these events is shown in Fig. 1.., The overall distribution of horizontal velocities of one of these events is shown in Fig. \ref{vortexsample}.683" There is a clear trend in the direction of the velocity vectors, pointing towards the centre of the image point)) and forming a swirl motion with a counterclockwise sense of rotation."," There is a clear trend in the direction of the velocity vectors, pointing towards the centre of the image ) and forming a swirl motion with a counterclockwise sense of rotation."684 The background image is the G-band intensity average over the 20-min interval., The background image is the G-band intensity average over the 20-min interval.685 The centre coincides with a dark structure formed by the junction of various intergranular lanes., The centre coincides with a dark structure formed by the junction of various intergranular lanes.686" Figure 2. displays the vertical velocity maps for panel)) and panel)) respectively, using a common time coverage of 20 min for both time series (i.e. the total duration of and the first 20 min of s2)) in order for the results to be comparable."," Figure \ref{verticalvel} displays the vertical velocity maps for ) and ) respectively, using a common time coverage of 20 min for both time series (i.e. the total duration of and the first 20 min of ) in order for the results to be comparable."687" Regions showing intense upflows denoted in different shades of red color correspond to intensive and recurrent activity from exploding granules with velocities of 1 km s!, whereas strong sinks with negative, i.e. entering the plane of the figure, vertical velocities ofmagnitude ~0.9 km s'! are observed as dark features."," Regions showing intense upflows denoted in different shades of red color correspond to intensive and recurrent activity from exploding granules with velocities of $\sim$ 1 km $^{-1}$, whereas strong sinks with negative, i.e. entering the plane of the figure, vertical velocities ofmagnitude $\sim$ 0.9 km $^{-1}$ are observed as dark features."688 The intergranular lanes are generally traced by the elongated structures in blue with downflows (-0.2 km s~!)., The intergranular lanes are generally traced by the elongated structures in blue with downflows (-0.2 km $^{-1}$ ).689 The black box in the upper panel represents the FOV studied by Balmacedaetal.(2010)., The black box in the upper panel represents the FOV studied by \cite{balmaceda2010}.690. Encircled in black are the locations of the detected vortical motions (also referred to as events) from the horizontal flow pattern., Encircled in black are the locations of the detected vortical motions (also referred to as events) from the horizontal flow pattern.691" The selection was performed by visual inspection, considering a vortex where velocity vectors in the flow map was converging and changing direction defining a swirl."," The selection was performed by visual inspection, considering a vortex where velocity vectors in the flow map was converging and changing direction defining a swirl."692 The area coverage of the swirl events are assumed to be circular and drawn as circles in the maps following the mentioned visual criteria., The area coverage of the swirl events are assumed to be circular and drawn as circles in the maps following the mentioned visual criteria.693 In all detected cases the events are located in regions with strong downflows (v;  -0.8 km 5-1)., In all detected cases the events are located in regions with strong downflows $v_z$ $\sim$ -0.8 km $^{-1}$ ).694" Note that v, represents the averaged γιος over the time elapsed.", Note that $v_z$ represents the averaged $v_{LOS}$ over the time elapsed.695 The presence of all the events in at least two of the consecutive flow maps over 5-min intervals suggest that they remain coherent in a range between 10 and 20 min., The presence of all the events in at least two of the consecutive flow maps over 5-min intervals suggest that they remain coherent in a range between 10 and 20 min.696 The positions of the events change from the first to the second time series after the 7-min gap in the observing run in the in Fig., The positions of the events change from the first to the second time series after the 7-min gap in the observing run in the in Fig.697 2 show the location of the events in the upper panel in the same figure for comparison.), \ref{verticalvel} show the location of the events in the upper panel in the same figure for comparison.)698 These events do not seem to be homogeneously distributed over the FOV but rather grouped in certain locations resembling the mesogranular and supergranular patterns., These events do not seem to be homogeneously distributed over the FOV but rather grouped in certain locations resembling the mesogranular and supergranular patterns.699" Figure 3 shows the final destination of passive tracers or in the figure) driven by the computed mean field of horizontal velocities, as commonly used to trace the evolution of plasma motions (seeforinstanceYi1992;Márquez, 2006)."," Figure \ref{corchos} shows the final destination of passive tracers or in the figure) driven by the computed mean field of horizontal velocities, as commonly used to trace the evolution of plasma motions \citep[see for instance][]{yi1992,marquez2006}. ."700 The background represents the averaged image in every case., The background represents the averaged image in every case.701 The position of the events, The position of the events702assuming the distance to the Galactic center of 8.54 kpc given in Section 4..,assuming the distance to the Galactic center of $R_0=8.54$ kpc given in Section \ref{sec:distance}.703 'The distribution of RR. Lyr stars in the central part (r«0.2 kpc) remains unknown., The distribution of RR Lyr stars in the central part $r<0.2$ kpc) remains unknown.704 We may speculate that it probably gets more flat toward the center., We may speculate that it probably gets more flat toward the center.705" The answer may come from K,-band observations currently collected by the VVV survey (Minnitietal. 2010)).", The answer may come from $K_s$ -band observations currently collected by the VVV survey \citealt{2010NewA...15..433M}) ).706" Using the OGLE-III data, we are able to assess the number of RR. Lyr stars which should be detected within the VVV bulge area in Figure "," Using the OGLE-III data, we are able to assess the number of RR Lyr stars which should be detected within the VVV bulge area (marked in Figure \ref{fig:mapRRlb}) )."707"If we extrapolate the inner distribution (markedtoward the center,7)). we find that VVV should detect (60+7)x10? RRab stars."," If we extrapolate the inner distribution toward the center, we find that VVV should detect $(60\pm7)\times10^3$ RRab stars."708 With a flat distribution in the central part we obtain (49+7)x10? stars., With a flat distribution in the central part we obtain $(49\pm7)\times10^3$ stars.709 For RR Lyr variables of all types the numbers are the following: (82+9)x10? and (71+9)x10%., For RR Lyr variables of all types the numbers are the following: $(82\pm9)\times10^3$ and $(71\pm9)\times10^3$.710" In summary, if we assume that the OGLE-III catalog of RRab variables is complete, we can estimate the VVV survey should detect (4-7)x10* RR Lyr stars of this type."," In summary, if we assume that the OGLE-III catalog of RRab variables is complete, we can estimate the VVV survey should detect $(4$ $7)\times10^4$ RR Lyr stars of this type."711" In Figure 20 we draw density distributions of bulge RRab variables in longitudinal and latitudinal slices, each with width of 6?, to verify if there are any significant differences between metal-poor ([Fe/H]5,< —1.0) and metal-rich ([Fe/H];og;> --1.θ) stars."," In Figure \ref{fig:densityRRab} we draw density distributions of bulge RRab variables in longitudinal and latitudinal slices, each with width of $6\degr$, to verify if there are any significant differences between metal-poor $\feh_{\rm J95}<-1.0$ ) and metal-rich $\feh_{\rm J95}>-1.0$ ) stars."712" No differences are found in the linear fits, leading us to the earlier conclusion that the RR Lyr bulge population is metal uniform."," No differences are found in the linear fits, leading us to the earlier conclusion that the RR Lyr bulge population is metal uniform."713" The observed slope of the latitudinal distributions is always shallower than the longitudinal one, confirming earlier suggestions of Minnitietal. that the whole population is slightly flattened along (1998)Galactic longitude."," The observed slope of the latitudinal distributions is always shallower than the longitudinal one, confirming earlier suggestions of \cite{1998IAUS..184..123M} that the whole population is slightly flattened along Galactic longitude."714" Based on the longitudinal and latitudinal fits obtained we find a mean density of at distances diong=4°9 = 0.69) and diat=6°4 (logdjaz= 0.81), respectively."," Based on the longitudinal and latitudinal fits obtained we find a mean density of at distances $d_{\rm long}=4\fdg9$ ${\rm log}d_{\rm long}=0.69$ ) and $d_{\rm lat}=6\fdg4$ ${\rm log}d_{\rm lat}=0.81$ ), respectively."715"(logdiong From this we can derive that the RR Lyr surface distribution is flattened in the observed outer part, with =~0.75."," From this we can derive that the RR Lyr surface distribution is flattened in the observed outer part, with $b/a=d_{\rm long}/d_{\rm lat}\sim0.75$."716 Complete data from the near-IR b/aVVV diong/diatsurvey will allow to study the distribution in the very central part of the bulge and to determine final parameters for the bulge RR Lyr population., Complete data from the near-IR VVV survey will allow to study the distribution in the very central part of the bulge and to determine final parameters for the bulge RR Lyr population.717" We have analyzed the data on 16,836 RR Lyr stars observed toward the Galactic bulge during the third phase of the OGLE project (years 2001-2009)."," We have analyzed the data on 16,836 RR Lyr stars observed toward the Galactic bulge during the third phase of the OGLE project (years 2001–2009)."718" After eliminating low-amplitude stars, objects likely foreground and background sources, and GC members the sample includes 10,472 RRab, 4608 RRc, and 78 RRd bulge variables with derived mean V- and J-band brightness."," After eliminating low-amplitude stars, objects likely foreground and background sources, and GC members the sample includes 10,472 RRab, 4608 RRc, and 78 RRd bulge variables with derived mean $V$ - and $I$ -band brightness."719" For an additional 627 RRab, 151 RRc, and 2 RRd stars, all located close to the Galactic plane, we possess mean magnitudes in the J filter alone."," For an additional 627 RRab, 151 RRc, and 2 RRd stars, all located close to the Galactic plane, we possess mean magnitudes in the $I$ filter alone."720" Using color information for this type of standard candles, we find that the ratio of total to selective extinction E;=A;/E(V—I) is independent of color and equals 1.08040.007."," Using color information for this type of standard candles, we find that the ratio of total to selective extinction $R_I=A_I/E(V-I)$ is independent of color and equals $1.080\pm0.007$."721 This result confirms the anomalous nature of the extinction toward the bulge., This result confirms the anomalous nature of the extinction toward the bulge.722" Our analysis clearly demonstrates that the bulge RR Lyr stars constitute a very uniform population, different to the majority of the stars in the central regions of the Milky Way."," Our analysis clearly demonstrates that the bulge RR Lyr stars constitute a very uniform population, different to the majority of the stars in the central regions of the Milky Way."723 The photometrically derived metallicity distribution is sharply peaked at, The photometrically derived metallicity distribution is sharply peaked at724"We split the 1602 primary galaxies by color at M,— 0.9.",We split the 1602 primary galaxies by color at $M_g-M_r =0.9$ .725 The 591 red primary galaxies have 358 objects in their satellite sample. while the 1011 blue primary galaxies have 332 candidate satellites.," The 591 red primary galaxies have 358 objects in their satellite sample, while the 1011 blue primary galaxies have 332 candidate satellites."726 The interloper percentages for the red and blue primary sample are and28%.. respectively.," The interloper percentages for the red and blue primary sample are and, respectively."727" Red primaries of M,—>0.9 have a larger fraction of red objects in their satellite sample than than blue primaries to 30%)) and. subsequently. more true satellites (see Fig. 5))."," Red primaries of $M_g-M_r > 0.9$ have a larger fraction of red objects in their satellite sample than than blue primaries to ) and, subsequently, more true satellites (see Fig. \ref{fig:color_hist_pri}) )."728 This can also be seen in Fig. 6..," This can also be seen in Fig. \ref{fig:int_sub_pri},"729 where the amplitude of the satellite profile of red primaries is greater than that of the blue primary profile., where the amplitude of the satellite profile of red primaries is greater than that of the blue primary profile.730 After interloper subtraction. the slopes of the density profiles of satellites for blue and red primaries are consistent.," After interloper subtraction, the slopes of the density profiles of satellites for blue and red primaries are consistent."731 Figure + additionally shows that red primaries are in general brighter than blue primaries., Figure \ref{fig:test6} additionally shows that red primaries are in general brighter than blue primaries.732" Splitting the color- primaries into faint and bright samples at M,=—20.8. Table 2. shows significant differences for the distribution of satellites of faint and bright primaries. depending on the color of the primary."," Splitting the color-selected primaries into faint and bright samples at $M_{r} = -20.8$, Table \ref{tab:slope_all} shows significant differences for the distribution of satellites of faint and bright primaries, depending on the color of the primary."733 Red. brighter primaries have an interloper-subtracted satellite profile that is shallower than the distribution of satellites in red. fainter primaries. e=-1.34+0.11 toa=-pL827.," Red, brighter primaries have an interloper-subtracted satellite profile that is shallower than the distribution of satellites in red, fainter primaries, $\alpha = -1.34\pm 0.11$ to $\alpha = -1.82^{+0.15}_{-0.14}$."734 This i$ not unexpected; from numerical simulations we expect the satellite distribution to scale with the mass distribution of the primary. and larger primaries have smaller concentrations leading to shallower slopes at the radii at which we measure.," This is not unexpected; from numerical simulations we expect the satellite distribution to scale with the mass distribution of the primary, and larger primaries have smaller concentrations leading to shallower slopes at the radii at which we measure."735 Interestingly. blue primaries show the opposite dependence: the distribution of satellites around brighter primaries seems to have a steeper slope than around fainter primaries.," Interestingly, blue primaries show the opposite dependence: the distribution of satellites around brighter primaries seems to have a steeper slope than around fainter primaries."736 This trend is accompanied by a change in the fraction of red satellites: of the satellite sample for bright. blue primaries are red. while of the corresponding sample for faint. blue primaries are red.," This trend is accompanied by a change in the fraction of red satellites: of the satellite sample for bright, blue primaries are red, while of the corresponding sample for faint, blue primaries are red."737 The errors. however. are nearly as large as the discrepancy between the samples. and larger samples will be required to confirm this result.," The errors, however, are nearly as large as the discrepancy between the samples, and larger samples will be required to confirm this result."738 In addition. the slope for satellites of bright. blue primaries Is steeper than that for bright. red primaries. which may reflect color dependence in using luminosity as a proxy for mass.," In addition, the slope for satellites of bright, blue primaries is steeper than that for bright, red primaries, which may reflect color dependence in using luminosity as a proxy for mass."739Stellar dynamics. a well established discipline. coutiuues to be au active field of research due to its couples dvnainics.,"Stellar dynamics, a well established discipline, continues to be an active field of research due to its complex dynamics."740 Newly developed sophisticated tools on uonlinear dynamics or ever mereasiug nunerical capacities are readilv applied to N-body eravitating svstenis., Newly developed sophisticated tools on nonlinear dynamics or ever increasing numerical capacities are readily applied to N-body gravitating systems.741 The problem of relaxation of gravitating svstenüs is αλλος the kev ones iu stellar dynamics since it cau be directly coustrained by observations. especially. of relaxed elobular clusters aud elliptical ealaxies.," The problem of relaxation of gravitating systems is among the key ones in stellar dynamics since it can be directly constrained by observations, especially, of well-relaxed globular clusters and elliptical galaxies."742 Ilstoricallv. plasima methods were amoung the first to © applied to eravitating svstenis (Chandrascklar19 12)). reelecting. however. a drastic difference between plasma aud loue-ranee eravity.," Historically, plasma methods were among the first to be applied to gravitating systems \cite{Chandra}) ), neglecting, however, a drastic difference between plasma and long-range gravity."743 In retrospect. it cau seen strauge row easily were ignored the challenges im theory aud observations. aud later also iu nuinerical simmlations: (a) he Coulomb logarithmic cut-off aud hence the canceling the N-body effects was applied at the absence of Debye screeniue: (b) the result contradicted observations. 1.0. the asma two-body relaxation timescale exceeds the age of liptical galaxies by several orders of magnitude: (0) the wo-bodv timescale could never be ideutified iu uuncerical studies.," In retrospect, it can seem strange how easily were ignored the challenges in theory and observations, and later also in numerical simulations: (a) the Coulomb logarithmic cut-off and hence the canceling of the N-body effects was applied at the absence of Debye screening; (b) the result contradicted observations, i.e. the plasma two-body relaxation timescale exceeds the age of elliptical galaxies by several orders of magnitude; (c) the two-body timescale could never be identified in numerical studies."744 Then comes the epoch of realization of miportance of chaos. occasionally in unexpected forms. for uonlinear svstenis.," Then comes the epoch of realization of importance of chaos, occasionally in unexpected forms, for nonlinear systems."745 Chaos caused by small perturbations appears crucial even to nearly inteerable problems. such as the dynamics of planetary system. (που Laskar&Robutel1993.9Morbidelli2002 and τοῖς therein): for non-inteerable N-body svstcis the situation is far more complex.," Chaos caused by small perturbations appears crucial even to nearly integrable problems, such as the dynamics of planetary system, (see \cite{Laskar,Morb} and refs therein); for non-integrable N-body systems the situation is far more complex."746 The Fermi-Pasta-Ulam problem is another example of apparently simple. but still not well uuderstood system (Fermietal. 1955)).," The Fermi-Pasta-Ulam problem is another example of apparently simple, but still not well understood system \cite{FPU}) )."747 Do chaos. chance aud randomness have significaut role also in the evolution of stellar svstems. or the two-body plasina approach is the whole storv?," Do chaos, chance and randomness have significant role also in the evolution of stellar systems, or the two-body plasma approach is the whole story?"748" Although it has been eenerallv agreed that chaos must affect N-body dynamics (see Carzacdvan&οσα1991,Contopoulos2002.Regey 20051). proper treatments require well-fotudedapproachest."," Although it has been generally agreed that chaos must affect N-body dynamics (see \cite{GP,Cont,Reg}) ), proper treatments require well-founded."749. Application of ergodic theory methods enabled us to prove a notable result: the spherical svsteuis are expoucutially unstable and that chaoticity drives their dlvnainics (Couzacvan&Savvidy1981.1986)., Application of ergodic theory methods enabled us to prove a notable result: the spherical systems are exponentially unstable and that chaoticity drives their dynamics \cite{GS}) ).750 An exponential law defines an intrinsic timescale. the collective relaxation time. which for real stellar svstenis has a value intermediate )otween the dynamical (crossing) and the two-body timescales.," An exponential law defines an intrinsic timescale, the collective relaxation time, which for real stellar systems has a value intermediate between the dynamical (crossing) and the two-body timescales."751 This was obtained by estimating the divergence of he trajectories of the svsteii in a Riemannian space defined bv the potential of he interaction (Maupoertuis principle). i.c. bv a method kuown iu theory of ανασα. svstems (Arnold 1989)).," This was obtained by estimating the divergence of the trajectories of the system in a Riemannian space defined by the potential of the interaction (Maupertuis principle), i.e. by a method known in theory of dynamical systems \cite{Arnold}) )."752 huportautlv. the derived collective (N-body) relaxation timescale fits the observational data (Vesperiui 1992)).," Importantly, the derived collective (N-body) relaxation timescale fits the observational data \cite{Vesp}) )."753" The three timescales. i.e. the dynamical 7/5,. collective τς. and wo-body 7, timescales. correspond to the 3 distance scales of the svsteni. specifically. its size D. ean iuter-particle distance d. and radius of gravitational influcuce of particles rj. iu particular (Camzadvan&Savvidy1981. 1986)). (κος also Lang 1999). When the role of complex N-body dviziauics was finally recognized. another confusion did appear. uaimely. iu οπα of the dynamical time as the relaxation timescale. 1.6.. for reaching finc-erained equilibrimui."," The three timescales, i.e., the dynamical $\tau_{dyn}$, collective $\tau_{cr}$, and two-body $\tau_{b}$ timescales, correspond to the 3 distance scales of the system, specifically, its size $D$, mean inter-particle distance $d$, and radius of gravitational influence of particles $r_h$, in particular \cite{GS}) ) (see also \cite{Lang}) ), When the role of complex N-body dynamics was finally recognized, another confusion did appear, namely, in assigning of the dynamical time as the relaxation timescale, i.e., for reaching fine-grained equilibrium."754 Uowever. this again contradicts observations: globular clusters would then have already disappeared because of the evaporation of stars (Ambartstmian 1938)) within 100 crossing fines. be. within around 100 mlu," However, this again contradicts observations: globular clusters would then have already disappeared because of the evaporation of stars \cite{Amb}) ) within 100 crossing times, i.e., within around 100 mln"755The idea of exploiting cosmic anutiprotous measurements to probe unconventional particle plivsics aud astroplivsics scenarios is certainly not new.,The idea of exploiting cosmic antiprotons measurements to probe unconventional particle physics and astrophysics scenarios is certainly not new.756 The investigation ou exotic antiproton sources was stimmiated by early reports (Coldeu ct al., The investigation on exotic antiproton sources was stimulated by early reports (Golden et al.757 L979: Buthnetou ct al., 1979; Buffington et al.758 1981) of unexpectedlv larec values for the :itiproton. to proton ratio mi cosniüc ravs., 1981) of unexpectedly large values for the antiproton to proton ratio in cosmic rays.7593. A possibility which has been discussed iu some details is that a significant contribution to the autiprotou flux nay be eiven by pair aunililation of relic neutralinos., A possibility which has been discussed in some details is that a significant contribution to the antiproton flux may be given by pair annihilation of relic neutralinos.760 The lightest neutralino. plausible the lightest supersyiuuetric ouwticle iu the Mininial Supersvnuuctric extension to the Standard Model (AISSAI). Ix one of the leading dark natter candidates.," The lightest neutralino, plausible the lightest supersymmetric particle in the Minimal Supersymmetric extension to the Standard Model (MSSM), is one of the leading dark matter candidates."761 Its coupling with ordinary articles jas the streneth of weak interaction., Its coupling with ordinary particles has the strength of weak interaction.762 This is exactly what it is needed to provide a relic density of the right order or a flat Universe., This is exactly what it is needed to provide a relic density of the right order for a flat Universe.763 It implies as well that. if oue iuvokes a population of relic neutralinos iu the halo of galaxies o solve the dark matter problem. these neutralinos can annihilate in pairs iuto standard model particles. which nieht eventually be detected.," It implies as well that, if one invokes a population of relic neutralinos in the halo of galaxies to solve the dark matter problem, these neutralinos can annihilate in pairs into standard model particles, which might eventually be detected."764 In particular it has been shown that the neutralino-iuduced autiproton flux can be at the level of the backerouncl fiux from cosmic rays (sec ce. Silk Srednuicki (198D: Stecker et al. (, In particular it has been shown that the neutralino-induced antiproton flux can be at the level of the background flux from cosmic rays (see e.g. Silk Srednicki (1984); Stecker et al. (7651985): Bottino ct al. (,1985); Bottino et al. (7661998): Berestrouun et al. (,1998); Bergströmm et al. (7671999h)).,1999b)).768 The question to address is of course if there are distinctive features in this exotic component so that it can be singled out unanbieuouslv., The question to address is of course if there are distinctive features in this exotic component so that it can be singled out unambiguously.769 The ordinary cosmic rav induced antiprotous are eenerated in collisions of primary particles with the oeiterstellar imediunn., The ordinary cosmic ray induced antiprotons are generated in collisions of primary particles with the interstellar medium.770 The main source are pp collisious which. for kinematical reasous. produce a characteristic 4.etra peaked at a kinetic οπσον of about 2 GeV and rapidly decreasing at low energies.," The main source are $pp$ collisions which, for kinematical reasons, produce a characteristic spectrum peaked at a kinetic energy of about 2 GeV and rapidly decreasing at low energies."771 The component roni neutralino annihilatiouns niv uot fall as fast: in sonie cases its miaximuuni is actually iu the low energv region., The component from neutralino annihilations may not fall as fast; in some cases its maximum is actually in the low energy region.772 This is the signature which was proposed more iu a decade ago in connection with carly autiproton neasurements (Silk Sredaicki 198E: Stecker et al., This is the signature which was proposed more than a decade ago in connection with early antiproton measurements (Silk Srednicki 1984; Stecker et al.773 1985)., 1985).774 The more recent (and probably more accurate] data frou 16 experiment (Matsunaea et 11998: Orito L998) oeidicate unfortunately that the ow chorey fiux may nof ο so high as previously thought., The more recent (and probably more accurate) data from the experiment (Matsunaga et 1998; Orito 1998) indicate unfortunately that the low energy flux may not be so high as previously thought.775 It actually secs to ) at a level hat is in very good agreement with a PAandard prediction for the secondary fux if oue takes into account plfe collisions aud energy losses during autiprotou xopagation (see Berestromun et al., It actually seems to be at a level that is in very good agreement with a standard prediction for the secondary flux if one takes into account $pHe$ collisions and energy losses during antiproton propagation (see Bergströmm et al.776 1999b. hereafter Paper D.," 1999b, hereafter Paper I)."777 If future measurements will confirii data. this will ead inevitably to an iupasse in this neutralino detection echuique: if the measured flux is consistent withn some estimate of the background. there is no way 1n inproviues he signal to background ratio.," If future measurements will confirm data, this will lead inevitably to an impasse in this neutralino detection technique: if the measured flux is consistent with some estimate of the background, there is no way in improving the signal to background ratio."778 There are however signatures of a neutralinoduduced Hux which are alternative to the one we have just discussed., There are however signatures of a neutralino-induced flux which are alternative to the one we have just discussed.779 The strategy we propose here is to search for an exotic componcut in the high euergv autiproton spectrum. above the expectec maxim of the background.," The strategy we propose here is to search for an exotic component in the high energy antiproton spectrum, above the expected maximum of the background."780 This kind of investigation is motivated w the fact that the secondarv antiproton flux at hieh energies is predicted with ereat confidence., This kind of investigation is motivated by the fact that the secondary antiproton flux at high energies is predicted with great confidence.781 It is remarkable that in this energy reeion nearlv all estimates in the literature are consistent, It is remarkable that in this energy region nearly all estimates in the literature are consistent782for the Alexander&Ferguson(1994) low temperature and Iglesias&Rogers(1996) high temperature opacities used in the reference calculations.,for the \citet{ale94} low temperature and \citet{igl96} high temperature opacities used in the reference calculations.783 A linear ramp between log(T)<4.1 provides a smooth transition between the (wo opacity tables., A linear ramp between $\la \log$ $\la$ 4.1 provides a smooth transition between the two opacity tables.784 For the reference model. we supplement the Alexander&Ferguson.(1994) low temperature opacity toward higher densities with the molecular opacity table of Alexauder.Johnson.&Rypma.(1933).," For the reference model, we supplement the \citet{ale94} low temperature opacity toward higher densities with the molecular opacity table of \citet{ale83}."785. In Figure 1.. the dotted line starting at log(D)—4.0 with an uneven upper-density boundary toward lower temperatures outlines the Alexander.Johnson.&Rapma(1983) molecular opacity table.," In Figure \ref{runrho}, the dotted line starting at $\log$ (T)=4.0 with an uneven upper-density boundary toward lower temperatures outlines the \citet{ale83} molecular opacity table."786 A linear ramp toward higher densities over 1 dex starting at the R=1 boundary is used to transition smoothly between the Alexander&Ferguson.(1994). and Alexander.Johnson.&Rypma(1983). opacities.," A linear ramp toward higher densities over 1 dex starting at the R=1 boundary is used to transition smoothly between the \citet{ale94} and \citet{ale83}787 opacities."788 A linear extrapolation in density provides the opacity for densities higher than the table boundaries., A linear extrapolation in density provides the opacity for densities higher than the table boundaries.789 The OPAL opacity table (Iglesias&Rogers1996) and OPAL equation of state Swenson.&Iglesias1996) share the same R=1 boundary shown in Figure 1.., The OPAL opacity table \citep{igl96} and OPAL equation of state \citep{rog96} share the same R=1 boundary shown in Figure \ref{runrho}.790 For densities hieher than the R=1 boundary. we apply a linear ramp constant in densitwv to transition to the Sammon.Chabrier.&VanHorn.(1995) equation of state.," For densities higher than the R=1 boundary, we apply a linear ramp constant in density to transition to the \citet{sau95} equation of state."791 The ramp has a width of the final two density values of the OPAL table., The ramp has a width of the final two density values of the OPAL table.792 The OPAL equation of state also has a low-temperature boundary at log(D)23.75 Ix. For temperatures below the R=1 boundary. we (transition to the Saumon.Chabrier.&VanHorn.(1995) equation of state with a linear ramp starting at log(D)—3.80 kx. We update the conductive opacities with (the extensive calculations from. Potekhin.Chabrier.&Yakovlev(1997) and Potekhinetal.|(1999).," The OPAL equation of state also has a low-temperature boundary at $\log$ (T)=3.75 K. For temperatures below the R=1 boundary, we transition to the \citet{sau95} equation of state with a linear ramp starting at $\log$ (T)=3.80 K. We update the conductive opacities with the extensive calculations from \citet{pot97} and \citet{pot99}."793. Their conductive opacity caleulations are for a fully ionized sinele-ion species., Their conductive opacity calculations are for a fully ionized single-ion species.794 We lollow (he procedure given in Potekhinetal.(1999). to caleulate an arbitrary mixture for the conductive opacity by expressing the electron-ion collision lrequency. as a summation over the coulomb logarithm [actors [or the ion species present., We follow the procedure given in \citet{pot99} to calculate an arbitrary mixture for the conductive opacity by expressing the electron-ion collision frequency as a summation over the coulomb logarithm factors for the ion species present.795 We assume singlv ionized O [or the entire stellar metal content., We assume singly ionized $^{16}$ for the entire stellar metal content.796 IL and He are assumed fully ionized. valid since in the unionized regime. log(p)350.0 and log(T)<4.0. conduction is inellicient and the radiative opacity dominates.," H and He are assumed fully ionized, valid since in the unionized regime, $\log(\rho)\la 0.0$ and $\log$ $\la 4.0$, conduction is inefficient and the radiative opacity dominates."797 The initial stellar models start at the deuterium-burning birthline (Staliler.1988)., The initial stellar models start at the deuterium-burning birthline \citep{sta88}.798. We obtain our deuterium birthline by starting a stellar model high up on the Hyashi track and designate the birthline when the core temperature reaches (he same core temperature when deuterium decreases by a factor of 100 in the caleulations of D'Antona (see (their Table 7)., We obtain our deuterium birthline by starting a stellar model high up on the Hyashi track and designate the birthline when the core temperature reaches the same core temperature when deuterium decreases by a factor of 100 in the calculations of \citet{dan94} (see their Table 7).799 Since deuterium burning completes in <3%3t of the time for lithium depletion. our results are insensitive to the adopted initial conditions.," Since deuterium burning completes in $\lesssim 3\%$ of the time for lithium depletion, our results are insensitive to the adopted initial conditions."800 Using the above mentioned input physics. we calculate a reference relation [or the huninositv aud age when lithium is depleted bv a [factor of 100 from its initial value.," Using the above mentioned input physics, we calculate a reference relation for the luminosity and age when lithium is depleted by a factor of 100 from its initial value."801 The lithium depletion ages are svstematically and vounger at fixed. huninosity, The lithium depletion ages are systematically and younger at fixed luminosity802Other relevant data exist in the archive. which we plan to explore.,"Other relevant data exist in the archive, which we plan to explore."803 Those observations provide better coverage of the CNO lines at the longer wavelengths. ancl they include several stars not observed byChandra.," Those observations provide better coverage of the CNO lines at the longer wavelengths, and they include several stars not observed by."804 The 535 AA-rav spectra of 14 normal OD stars (or binary svstenis) are shown in order of advancing optical spectral (vpes in Figures 1 and 2. which contain primarily main-sequence stars and supergiants. respectively. albeit with a few giants included (ο augment the coverage in each case.," The 5–25 X-ray spectra of 14 normal OB stars (or binary systems) are shown in order of advancing optical spectral types in Figures 1 and 2, which contain primarily main-sequence stars and supergiants, respectively, albeit with a few giants included to augment the coverage in each case."805 In (hese plots. each X-ray. spectrogram has been scaled (ο 1.0 at the peak enussion feature.," In these plots, each X-ray spectrogram has been scaled to 1.0 at the peak emission feature."806 Thus. absolute intensities cannot be directly. compared between clilferent objects. although line ratios can be.," Thus, absolute intensities cannot be directly compared between different objects, although line ratios can be."807 Because of the large range of line intensiües in the calibrated. data. a complementary presentation of the same data. but with three clilferent scalings al wavelengths below 11A.. from I1 to 15À.. and above I8 A is given in Figures 3 and 4.," Because of the large range of line intensities in the calibrated data, a complementary presentation of the same data, but with three different scalings at wavelengths below 11, from 11 to 18, and above 18 A is given in Figures 3 and 4."808 The three normalization [actors lor each object are listed in Table 1: their units are photons Fem ? +., The three normalization factors for each object are listed in Table 1; their units are photons $^{-1}$ $^{-2}$ $^{-1}$.809 The largest of the three values (usually the third. except [or three ol the earliest types where it is the second) applies to Figures 1 ancl 2.," The largest of the three values (usually the third, except for three of the earliest types where it is the second) applies to Figures 1 and 2."810 As indicated by the spectral (vpes. several objects are known close binaries.," As indicated by the spectral types, several objects are known close binaries."811 Parameters of the strong spectral lines are listed in Table 2., Parameters of the strong spectral lines are listed in Table 2.812 several correlations between (he X-ray line ionization and the optical spectral (vpes are immediately apparent in these figures., Several correlations between the X-ray line ionization and the optical spectral types are immediately apparent in these figures.813 First. in Figures 1 and 2. (he higher ionization. shorter wavelength lines weaken markedly relative to the lower ionization. longer wavelength lines in a given spectrum along the sequences. although the oxvgen lines are usually the strongest.," First, in Figures 1 and 2, the higher ionization, shorter wavelength lines weaken markedly relative to the lower ionization, longer wavelength lines in a given spectrum along the sequences, although the oxygen lines are usually the strongest."814 second. in Figures 3 and 4. the behaviors of individual lines and line ratios. particularly those of the close pairs of lines from the II-like and Ile-like a ions. display strong; trends along (he sequences.," Second, in Figures 3 and 4, the behaviors of individual lines and line ratios, particularly those of the close pairs of lines from the H-like and He-like $\alpha$ ions, display strong trends along the sequences."815 Specifically. essentially disappears alter O3.5 on (he main sequence. aud after O4 in (he supergiants.," Specifically, essentially disappears after O3.5 on the main sequence, and after O4 in the supergiants."816 The and ratios diminish drastically between 03.5 and O4 in both sequences., The and ratios diminish drastically between O3.5 and O4 in both sequences.817 The ratio is the best diagnostic. because it is (he most sensitive throughout this range.," The ratio is the best diagnostic, because it is the most sensitive throughout this spectral-type range."818 Unfortunately. the," Unfortunately, the"819on the DSS-II with the latest version (1998) of FOCAS (Faint Object Classification and Analysis System: JarvisandTyson (1981))). and was limited to galaxy. companions that could be unambiguously distinguished from stars by the FOCAS algorithm.,"on the DSS-II with the latest version (1998) of FOCAS (Faint Object Classification and Analysis System; \citet{jarvis81}) ), and was limited to galaxy companions that could be unambiguously distinguished from stars by the FOCAS algorithm."820 Each set of pixels with a flix value larger than the sky threshold is considered an object bv FOCAS. and can be classified as galaxy or star only if its diameter is lareer (han 4 pixels.," Each set of pixels with a flux value larger than the sky threshold is considered an object by FOCAS, and can be classified as galaxy or star only if its diameter is larger than 4 pixels."821 Since the scale ol the DSS-II plates is zz 1.0 arcsee per pixel. the minimum angular size to which FOCAS is able (to classify objects on the DSS-II is 22 4 arcsec (which corresponds (o 2 1.4 Ixpe of projected linear distance).," Since the scale of the DSS-II plates is $\approx$ 1.0 arcsec per pixel, the minimum angular size to which FOCAS is able to classify objects on the DSS-II is $\approx$ 4 arcsec (which corresponds to $\approx$ 1.4 Kpc of projected linear distance)."822 However. we further restrict our search (ο companion galaxies of diameters De>5 Ixpe.," However, we further restrict our search to companion galaxies of diameters $D_C \geq 5$ Kpc."823 With our methodology we cannot study. smaller objects because the distribution of companions is domünated by optical pairs (not physically. associated: as pointed out in 84.1. optical pairs ave (hie wide majority also in the case of companion diameter between 5 and 10 προ).," With our methodology we cannot study smaller objects because the distribution of companions is dominated by optical pairs (not physically associated; as pointed out in 4.1, optical pairs are the wide majority also in the case of companion diameter between 5 and 10 Kpc)."824 A third limitation is that FOCAS classifies bright stars as ealaxies. since (μον appear as extended objects due to scintillation effects.," A third limitation is that FOCAS classifies bright stars as galaxies, since they appear as extended objects due to scintillation effects."825 To avoid gross we ehecked by eve on (he computer screen each object classified by FOCAS as a galaxy.," To avoid gross mis-classifications, we checked by eye on the computer screen each object classified by FOCAS as a galaxy."826 Furthermore. border-Iime objects of marginally resolved appearance were nol taken into account to avoil also second order nmüs-classifications.," Furthermore, border-line objects of marginally resolved appearance were not taken into account to avoid also second order mis-classifications."827 Elfect of plate quality. point spread function. skv background. and of automatic identification and measurement of companion and background galaxies have been discussed in INrongokl.Marziani (2001).," Effect of plate quality, point spread function, sky background, and of automatic identification and measurement of companion and background galaxies have been discussed in \citet{k01}."828. They will not be discussed again here: tlie same effects are still influencing the analvsis of the DSS-II., They will not be discussed again here; the same effects are still influencing the analysis of the DSS-II.829 As is customary in many previous works (e.g. Diltzin-Hacvanetal.(1999b):: IXrongold.Jultzin-Lacvan.n.&AMarzianiMarziani (2001))). the fraction of objectsobject withith “physical“physical”companionsDnipanioli Ponys Us taken as the fraction with one or more observed companions fj. reduced by the fraction of galaxies wilh one or more optical companions (derived Irom Poisson distribution). namely fj.=fou—flop. Ehe number of background galaxies expected to follow a Poisson statistics has been obtained as described by IXrongold.Dultzin-IHIacyan.&Marziani(2001).," As is customary in many previous works (e.g. \citet{dd99b}; \citet{k01}) ), the fraction of objects with “physical""companions $f_{phys}$ is taken as the fraction with one or more observed companions $f_{obs}$, reduced by the fraction of galaxies with one or more optical companions (derived from Poisson distribution), namely $f_{phys} = f_{obs} - f_{opt}.$ The number of background galaxies expected to follow a Poisson statistics has been obtained as described by \citet{k01}."830. We looked for companions in a circular area with radius equal to 3 times the diameterol the central object (324)., We looked for companions in a circular area with radius equal to 3 times the diameterof the central object $3D_S$ ).831 Our results are summarized in Table 1., Our results are summarized in Table 1.832 OL 87 DIRGs galaxies. 2 has at least one companion within 342g. vs. 43 of the 90 objects of the CS.," Of 87 BIRGs galaxies, $\approx$ has at least one companion within $D_S$ , vs. 43 of the 90 objects of the CS."833 The expected number, The expected number834To acldress these issues. we determine various regimes for ο and //; before the onset of gravitational instabilitv.,"To address these issues, we determine various regimes for $v_c$ and $H_d$ before the onset of gravitational instability."835" These regimes depend on the quantities ry. c. the turbulent viscosilv. parameter a and the mean [ree path of the gas /,,5,."," These regimes depend on the quantities $r_d$, $c_s$, the turbulent viscosity parameter $\alpha$ and the mean free path of the gas $l_{mfp}$."836" We then use (3)) and the values for the ratio of e, and. fy, lo calculate the peak collisional velocities aud the total growth time before the onset of gravitational instability.", We then use \ref{main}) ) and the values for the ratio of $v_c$ and $H_d$ to calculate the peak collisional velocities and the total growth time before the onset of gravitational instability.837" We assume the disc has an essentially isotropic turbulent viscosity where ea; and Ag, are the maximum turbulent velocity and length seales in our assumed ]xolmogorov spectrum and α is (he Shakura-Sunvaev viscosity. parameter vaev 1973).", We assume the disc has an essentially isotropic turbulent viscosity where $v_M$ and $\lambda_M$ are the maximum turbulent velocity and length scales in our assumed Kolmogorov spectrum and $\alpha$ is the Shakura-Sunyaev viscosity parameter \citep{SS73}.838". Using Ag/rayc1/0. HW,Q=0; and (4)) it follows that Ifa is extremely. low. the GW process will proceed as in (he absence of turbulence."," Using $\lambda_M/v_M \sim 1/\Omega$, $H_g\Omega=c_s$, and \ref{4a}) ) it follows that If $\alpha$ is extremely low, the GW process will proceed as in the absence of turbulence."839 It is likely that. at least. dust-gas shear (e.g. Ishitsu&Sekiva (2003))) prevents a from dropping to values where it could otherwise be ignored., It is likely that at least dust-gas shear (e.g. \cite{Ishitsu03}) ) prevents $\alpha$ from dropping to values where it could otherwise be ignored.840 Our model will involve a progression of dust growth regimes whose order requires approximately a>2xLO5., Our model will involve a progression of dust growth regimes whose order requires approximately $\alpha > 2 \times 10^{-6}$.841 Our model needs mocification lor values of a below that lower bound and if the turbulence is adequately weaker vet (hat the dust settling Gime becomes significant (hen our approach fails completely., Our model needs modification for values of $\alpha$ below that lower bound and if the turbulence is adequately weaker yet that the dust settling time becomes significant then our approach fails completely.842 Thus alihough we are conceptually extending the a=0 model of GW. our present techniques cdo not apply in the turbulence-free limit.," Thus although we are conceptually extending the $\alpha=0$ model of GW, our present techniques do not apply in the turbulence-free limit."843 We (ake a minimum mass solar nebula (MMSN) model with the following scalings from Sanoetal. (2000)::, We take a minimum mass solar nebula (MMSN) model with the following scalings from \citet{Sano00}: :844This difference in Facing timescales arises because (he slowest particles to escape Irom a bodxy leave the target with a speed comparable to the gravitational escape speed.,This difference in fading timescales arises because the slowest particles to escape from a body leave the target with a speed comparable to the gravitational escape speed.845 For P/2010 A2 is is 0.1 om +. allowing large. slow grains to persist for 21 vr after impact while. for scheila. particles ejected at less Chan the GO or 70 m 1 escape speed simply [ell back on je sur[ace (Jewitt et al.," For P/2010 A2 this is $\sim$ 0.1 m $^{-1}$, allowing large, slow grains to persist for $>$ 1 yr after impact while, for Scheila, particles ejected at less than the 60 or 70 m $^{-1}$ escape speed simply fell back on the surface (Jewitt et al."846 2011. Ishiguro et al.," 2011, Ishiguro et al."847 2011)., 2011).848 Furthermore. most grains traveling [ast enough to be ejected. were also small enough to be deflected by solar radiation pressure. providing another mechanism to quickly clear (he coma.," Furthermore, most grains traveling fast enough to be ejected were also small enough to be deflected by solar radiation pressure, providing another mechanism to quickly clear the coma."849 There are no direct measurements IF the total. earlv-time brightening. only a limit Am.< 19 (Jewitt et al.," There are no direct measurements of the total, early-time brightening, only a limit $\Delta m <$ 19 (Jewitt et al."850 2011)., 2011).851 However. the model suggests that if the D/2010 A2 were hit by a two meter-sized projectile. (he brightening would be Am~ 15 (Figure 6)). which is consistent with the empirical constraint.," However, the model suggests that if the P/2010 A2 were hit by a two meter-sized projectile, the brightening would be $\Delta m \sim$ 15 (Figure \ref{dmag}) ), which is consistent with the empirical constraint."852" Extreme brightening caused by impact has been suggested as an explanation of ""guest stars” recorded in ancient Chinese records (Reach 1992).", Extreme brightening caused by impact has been suggested as an explanation of “guest stars” recorded in ancient Chinese records (Reach 1992).853 Rotational instability. offers another explanation for mass loss from P/2010 A2 (Jewitt et al., Rotational instability offers another explanation for mass loss from P/2010 A2 (Jewitt et al.854 2010)., 2010).855 The small diameter of the primary body (120 mi) corresponds to a short spin-up timescale under the action of YORD., The small diameter of the primary body (120 m) corresponds to a short spin-up timescale under the action of YORP.856 In fact. for sub-kilometer main-belt objects the YORDP spin-up timescale is less (han (he timescale for collisional disruption (Alarzari et al.," In fact, for sub-kilometer main-belt objects the YORP spin-up timescale is less than the timescale for collisional disruption (Marzari et al."857 2011. Jacobson and Scheeres 2011).," 2011, Jacobson and Scheeres 2011)."858" While the rotation period of the primary body in P/2010 A? is unknown. it would not be surprising to find that it had exceeded the centripetal limit,"," While the rotation period of the primary body in P/2010 A2 is unknown, it would not be surprising to find that it had exceeded the centripetal limit."859 Unfortunately. there are few published predictions for the detailed appearance of a rotationallv. disrupted body (Richardson et al.," Unfortunately, there are few published predictions for the detailed appearance of a rotationally disrupted body (Richardson et al."860 2005)., 2005).861 Object. (3200) Phaethon is distinguished from the other active asteroids by its small perihelion. ¢q = 0.14 AU. allowing it to reach extreme sub-solar temperatures (~ L000 Ix).," Object (3200) Phaethon is distinguished from the other active asteroids by its small perihelion, $q$ = 0.14 AU, allowing it to reach extreme sub-solar temperatures $\sim$ 1000 K)."862 These are sufficient to trigger thermal fracture and to delvelrate water-bearing minerals. if they are present (Jewitt and Li 2010).," These are sufficient to trigger thermal fracture and to dehydrate water-bearing minerals, if they are present (Jewitt and Li 2010)."863 It has been suggested that Phaethon was recently scaltered. inwards [rom a Pallas-like orbit (@ = 2.771 AU. e = 0.281. 7 = 33°: de Leon et al.," It has been suggested that Phaethon was recently scattered inwards from a Pallas-like orbit $a$ = 2.771 AU, $e$ = 0.281, $i$ = $\degr$; de Leon et al."864 2010) where a laree proportion of (he asteroids are volatile-rich. B- and C-tvpes., 2010) where a large proportion of the asteroids are volatile-rich B- and C-types.865 If Phaethon originated in the vicinity (or as part) of Pallas then finding hydrated minerals would not be surprising. since Pallas itself contains hydrated minerals.," If Phaethon originated in the vicinity (or as part) of Pallas then finding hydrated minerals would not be surprising, since Pallas itself contains hydrated minerals."866 The small asteroids associated dynamically with Phaethon (1999 YC and 2005 UD) should have similar compositions. but have not been observed close to perihelion aud have shown no evidence for mass loss.," The small asteroids associated dynamically with Phaethon (1999 YC and 2005 UD) should have similar compositions, but have not been observed close to perihelion and have shown no evidence for mass loss."867 In addition to the creation of dust and fragments by thermal fracture and dehydration shrinkage. we conjecture that the escape of particles produced by these thermal mechanisis is [acilitated by radiation pressure sweeping.," In addition to the creation of dust and fragments by thermal fracture and dehydration shrinkage, we conjecture that the escape of particles produced by these thermal mechanisms is facilitated by radiation pressure sweeping."868 This is especially important in (3200) Phaethon, This is especially important in (3200) Phaethon869"the power is (iy=22/L!.. then the multiple numbers are sampled with the interval down to the smallest scale decided by the size of the pixel p: Gua,=x/p.","the power is $\l_{\min}= 2 \pi/L$, then the multiple numbers are sampled with the interval $\Delta \l= 2 \pi/L$ down to the smallest scale decided by the size of the pixel $p$: $\l_{\rm max}= \pi/p$."870 So the disadvantage of estimation of power spectrum from patches is that sampling interval AC is much larger (han 1. which can be viewed as intrinsic binning.," So the disadvantage of estimation of power spectrum from patches is that sampling interval $\Delta \l$ is much larger than 1, which can be viewed as intrinsic binning."871 In Figure 1 we test the scaling relation of Eq.(2))., In Figure \ref{scaling} we test the scaling relation of \ref{relat}) ).872 We simulate a full skv CMD map with WMAP best-fit ACIDM model and take 50 patches. each 24°x24 with pixel size 3 arcmin.," We simulate a full sky CMB map with WMAP best-fit $\Lambda$ CDM model and take 50 patches, each $24^\circ \times 24^\circ$ with pixel size 3 arcmin."873 One can see that (he mean power spectrum from the 50 patches fits nicely with (he input power spectrum and the error from the discontinuous boundary condition usually present in data analvsis of square patches is negligible., One can see that the mean power spectrum from the 50 patches fits nicely with the input power spectrum and the error from the discontinuous boundary condition usually present in data analysis of square patches is negligible.874" The signal 7;, in the sky at [requencey v is a combination of the CMD signal 7; and diffuse Ioregrouncds (svuchrotron. Iree-Iree ancl dust emission) plus extragalactic point sources. altogether denoted as total foreground. Εν."," The signal $T_\nu$ in the sky at frequency $\nu$ is a combination of the CMB signal $T_\cmb$ and diffuse foregrounds (synchrotron, free-free and dust emission) plus extragalactic point sources, altogether denoted as total foreground $F_\nu$."875" They are measured with an antenna beam D: where ©: denotes convolution ancl :N, is the instrument noise.", They are measured with an antenna beam $B_\nu$: where $\otimes$ denotes convolution and $N_\nu$ is the instrument noise.876 In order to reach the CMD power spectrum. we discuss below the 3parts in Eq.(3)): foreground contamination. noise and the window function.," In order to reach the CMB power spectrum, we discuss below the 3parts in \ref{general}) ): foreground contamination, noise and the window function."877 NASA Cosmic Backeround Explorer has measured with 10* FWIIM the CMD temperature [Inctuation al a level 10.5 (Smootοἱal.1992).., NASA Cosmic Background Explorer has measured with $10^\circ$ FWHM the CMB temperature fluctuation at a level $10^{-5}$ \citep{coberms}.878" From Eq.(3)) the variance of the measured T, includes foreground component: o7=02+07.Cov[F7. N,]. where σε. σε, and ση are the variance of the beam-convolved CMB. foreground. and noise at lrequencey. p. respectively. and Che last 3 terms denote their covariances."," From \ref{general}) ) the variance of the measured $T_\nu$ includes foreground component: $\sigma^2_\nu= \sigma^2_\cmb + \sigma^2_{F_\nu}+ \sigma^2_n+{\rm Cov}[T^{\rm sm}_\cmb,F^{\rm sm}_\nu]+{\rm Cov}[T^{\rm sm}_\cmb,N_\nu]+{\rm Cov}[F^{\rm sm}_\nu,N_\nu]$ , where $\sigma_\cmb^2$, $\sigma_{F_\nu}^2$ and $\sigma_n^2$ are the variance of the beam-convolved CMB, beam-convolved foreground and noise at frequency $\nu$ , respectively, and the last 3 terms denote their covariances."879 For an ensemble of small patches. the average," For an ensemble of small patches, the average"880"Finally. the units of the flux f(x.2) are “ionizing photons ="".","Finally, the units of the flux $\flux$ are 'ionizing photons $^{-1}$ $^{-2}$ '."881 On the other hand. the ionizing background is commonly quantified in terms of its mean intensity (7) which has the units .erg 1 2 IO UU.," On the other hand, the ionizing background is commonly quantified in terms of its mean intensity $J(\nu)$ which has the units 'erg $^{-1}$ $^{-2}$ $^{-1}$ $^{-1}$ '."882" If the spectrum of the ionizing background radiation fieldis assumed to be of the form ο)=ονfig)""10? emsAY + Hz+ 2 orto then the fo, value in the cell located at(x.z) is trivially obtained from f(x.2) through the equation To explicitly show the dependence of our calculated JJ»,(x.z) on the fiducial efficiency choice cia. some of our results below will be presented in terms of Joi/eiq."," If the spectrum of the ionizing background radiation fieldis assumed to be of the form $J(\nu)=J_{\rm 21}(\nu/\nu_H)^{-\alpha}\times 10^{-21}$ erg $^{-1}$ $^{-1}$ $^{-2}$ $^{-1}$, then the $J_{21}$ value in the cell located at$({\bf x}, z)$ is trivially obtained from $\flux$ through the equation To explicitly show the dependence of our calculated $ J_{\rm 21}({\bf x}, z)$ on the fiducial efficiency choice $\toteff$, some of our results below will be presented in terms of $J_{21}/\toteff$."883 This allows the reader to substitute his/her preferred value. of cj. and obtain. the corresponding physical Jo.(x.2).," This allows the reader to substitute his/her preferred value of $\toteff$ and obtain the corresponding physical $J_{\rm 21}({\bf x}, z)$."884 In this study. all calculations assume that only halos with masses AL7171O°AZ. contribute to the generation of the ionization. and flux fields.," In this study, all calculations assume that only halos with masses $M\gsim1.7 \times 10^8 \Msun$ contribute to the generation of the ionization and flux fields."885 This mass at 2.=7 roughly corresponds to the minimum temperature facilitating efficient atomic cooling. 7=104 K. However. since this mapping is redshift-dependent. this same virial temperature corresponds to somewhat lower halo masses at higher redshifts: AJ— IQ. 8.60510'. and 6.0.10 AZ. ats= 7. 10. and 13. respectively.," This mass at $z=7$ roughly corresponds to the minimum temperature facilitating efficient atomic cooling, $\Tvir=10^4$ K. However, since this mapping is redshift-dependent, this same virial temperature corresponds to somewhat lower halo masses at higher redshifts: $M=1.4 \times 10^8$ , $8.6 \times 10^7$, and $6.0 \times 10^7$ $\Msun$ at $z=$ 7, 10, and 13, respectively."886 Because of this. and since this atomic cooling cut-off is approximate. we assume a couple of different minimum masses when studying the impact of feedback on reionization.," Because of this, and since this atomic cooling cut-off is approximate, we assume a couple of different minimum masses when studying the impact of feedback on reionization."887 ote that our fiducial. parametrized UVB distributions can be (fairly accurately) adjusted to accommodate different contributing minimum masses by adjusting qi accordingly (i.e. by the factor of the ratio of the fraction of collapsed matter contained in halos of mass o>Adin and our fiducial choice of M21.7TOTAL. ).," Note that our fiducial, parametrized UVB distributions can be (fairly accurately) adjusted to accommodate different contributing minimum masses by adjusting $\toteff$ accordingly (i.e. by the factor of the ratio of the fraction of collapsed matter contained in halos of mass $M \gsim M_{\rm min}$ and our fiducial choice of $M \gsim 1.7 \times 10^8 \Msun$ )."888 We stress again that the main goal of this paper is not to precisely model UV flux distributions at high redshifts (such a thing being impossible given our current modest knowledge/inferences of 2 sources): instead we explore a wide parameter space to attempt to approximately answer how likely is it for radiative feedback to delay the advanced stages of reionization when Jvir2101 K sources dominate the ionizing photon budget., We stress again that the main goal of this paper is not to precisely model UV flux distributions at high redshifts (such a thing being impossible given our current modest knowledge/inferences of $z$ sources); instead we explore a wide parameter space to attempt to approximately answer how likely is it for radiative feedback to delay the advanced stages of reionization when $\Tvir \gsim 10^4$ K sources dominate the ionizing photon budget.889 Uncertainties of order unity will thus not deter us from this noble task., Uncertainties of order unity will thus not deter us from this noble task.890 In Figure |.. we present slices through several of our UV flux boxes. generated with the above procedure.," In Figure \ref{fig:pics}, we present slices through several of our UV flux boxes, generated with the above procedure."891 The slices are shown on a linear scale. scaled to the same maximum value.," The slices are shown on a linear scale, scaled to the same maximum value."892 The impac of the evolution of structure from >= 13 to 7. and the truncation of the flux fields in neutral patches of gas. are qualitatively eviden in these panels.," The impact of the evolution of structure from $z=$ 13 to 7, and the truncation of the flux fields in neutral patches of gas, are qualitatively evident in these panels."893 It is important to note that we treat the global neutra Traction yy. redshift 2. and the source ionizing efficiency rate Yer MASS ενα. all as separate free parameters.," It is important to note that we treat the global neutral fraction $\avenf$, redshift $z$, and the source ionizing efficiency rate per mass $\epsilon_{\rm ion}$ , all as separate free parameters."894 We can afforc his luxury because of the speed and versatility of our semi-numerical approach. as well as the confidence that our resulting ionization field topologies provide a good match to those generatec by cosmological radiative transfer simulations (2)..," We can afford this luxury because of the speed and versatility of our semi-numerical approach, as well as the confidence that our resulting ionization field topologies provide a good match to those generated by cosmological radiative transfer simulations \citep{MF07}."895 In numerica simulations of reionization. the source efficiencies are coupled © the neutral fraction at redshift z.," In numerical simulations of reionization, the source efficiencies are coupled to the neutral fraction at redshift $z$."896" Since we are not modeling he progress of reionization. in this work (such a task being impossible at present). we keep ci, and cgi separate. the former quantifying the ""instantaneous"" ionizing background at 2. and the later depending on a complicated of star formation and feedback."," Since we are not modeling the progress of reionization in this work (such a task being impossible at present), we keep $\epsilon_{\rm ion}$ and $\avenf$ separate, the former quantifying the ” ionizing background at $z$, and the later depending on a complicated of star formation and feedback."897 Again. we do this in order to be as general as possible and explore a very wide swath of parameter space.," Again, we do this in order to be as general as possible and explore a very wide swath of parameter space."898 In Figure 2.. we present some results from the spherically symmetric collapse simulations.," In Figure \ref{fig:fcoll}, we present some results from the spherically symmetric collapse simulations."899 The fraction of the σας (normalized to the case with no which collapses into halos of mass A/ at 2= 7. 10. 13 panels) is shown as a function of the halo mass.," The fraction of the gas (normalized to the case with no which collapses into halos of mass $M$ at $z=$ 7, 10, 13 ) is shown as a function of the halo mass."900" Curves correspond to Jo,= 0.001. 0.01. 0.1. 1.0."," Curves correspond to $J_{21}=$ 0.001, 0.01, 0.1, 1.0."901" The figures show that the amount of suppression is a strong function of the time elapsed since the halo started being exposed to the UVB (2).. with even 10A7. halos at 2=13 being too evolved at z,,4=14 to lose more 20% of their gas to negative feedback even for fluxes as high as JJ»,=100 (not shown in the Fig.)."," The figures show that the amount of suppression is a strong function of the time elapsed since the halo started being exposed to the UVB \citep{Dijkstra04}, , with even $10^8 \Msun$ halos at $z=13$ being too evolved at $\zon=14$ to lose more $\sim20\%$ of their gas to negative feedback even for fluxes as high as $J_{21}=100$ (not shown in the Fig.)."902 Since our primary interest in this work is how reionization is effected by radiative feedback. we will be especially interested in the critical specific flux values. JS]CA.z). required to suppress the collapse of gas onto halos of mass AJ at z.," Since our primary interest in this work is how reionization is effected by radiative feedback, we will be especially interested in the critical specific flux values, $\Jcrit$, required to suppress the collapse of gas onto halos of mass $M$ at $z$."903 We consider this to be more relevant to the issue of reionization than the fractional suppression of gas seen in Fig. 2.., We consider this to be more relevant to the issue of reionization than the fractional suppression of gas seen in Fig. \ref{fig:fcoll}.904" This is because star formation likely occurs on a longer time-scale than the time remaining for reionization to be completed once a large fraction of the universe is ionized and the 7i,=,107 halos begin dominating the photon (see also for example. Fig."," This is because star formation likely occurs on a longer time-scale than the time remaining for reionization to be completed once a large fraction of the universe is ionized and the $\Tvir \gsim10^4$ halos begin dominating the photon (see also for example, Fig."905 9 in 2.. Fig.," 9 in \citealt{MJH06}, Fig."906 2 in?) and Fig., 2 in \citealt{HB06} and Fig.907 | in 23)., 1 in \citealt{Lidz07}) ).908 The gas which was prevented from collapsing in Fig., The gas which was prevented from collapsing in Fig.909 2 was in the outer regions of the halo. and would likely have formed stars later. probably after reionization was completed.," \ref{fig:fcoll} was in the outer regions of the halo, and would likely have formed stars later, probably after reionization was completed."910 Halos which retain even a little of their gas reservoir can form stars fairly quickly. as this gas is close to the high density core where cooling is efficient.," Halos which retain even a little of their gas reservoir can form stars fairly quickly, as this gas is close to the high density core where cooling is efficient."911" Thus the contribution of halos to the ""relative immediacy” of completing reionization is better judgec with JST""(AL.+).", Thus the contribution of halos to the “relative immediacy” of completing reionization is better judged with $\Jcrit$.912 However. since these assumptions are by no means certain. we present total feedback estimates in $3.3. based on two models: 6) partial gas suppression. in which we use the collapsed fraction. f... that is plotted in Fig. 2.. ," However, since these assumptions are by no means certain, we present total feedback estimates in \ref{sec:feedback} based on two models: ) partial gas suppression, in which we use the collapsed fraction, $f_{\rm gas}$ , that is plotted in Fig. \ref{fig:fcoll}, ,"913and ο) and tota gus suppression. in which halos that see a UVB that is greater (less) than 44; retain none Call) of their gas.," and ) and total gas suppression, in which halos that see a UVB that is greater (less) than $J_{\rm crit}$ retain none (all) of their gas."914 In Figure 3. we show the critical JST'(M.z)values required to entirely suppress the collapse of gas onto halos of mass A üt 2=Y curve) and 2=10 curve).We obtain JST(M.z) at each AZ by extrapolating the results from. our, In Figure \ref{fig:MvsJcrit} we show the critical $\Jcrit$values required to entirely suppress the collapse of gas onto halos of mass $M$ at $z=7$ ) and $z=10$ ).We obtain $\Jcrit$ at each $M$ by extrapolating the results from our915"We present a model of spiral arm fragmentation in gravitationally unstable discs, based on the observation from the simulations of the previous section that reduced cooling times lead to thinner arms, which are more likely to fragment.","We present a model of spiral arm fragmentation in gravitationally unstable discs, based on the observation from the simulations of the previous section that reduced cooling times lead to thinner arms, which are more likely to fragment."916 This model can be broken into two components: the first is a model for the (roughly) steady-state spiral structure in an unstable disc; while the second is a criterion for the fragmentation of these spirals., This model can be broken into two components: the first is a model for the (roughly) steady-state spiral structure in an unstable disc; while the second is a criterion for the fragmentation of these spirals.917" Many of the details of our model are empirical in nature: we have used results from the simulations of ?,, as well as our own set of simulations in determining some of the important parameters."," Many of the details of our model are empirical in nature: we have used results from the simulations of \citet{Cossins2009}, as well as our own set of simulations in determining some of the important parameters."918 We begin with a model for the spiral structure that results in a gravitationally unstable disc., We begin with a model for the spiral structure that results in a gravitationally unstable disc.919" We consider a patch of an initially axisymmetric disc that will develop spiral structure, such as our initial condition for the simulations of the preceding section."," We consider a patch of an initially axisymmetric disc that will develop spiral structure, such as our initial condition for the simulations of the preceding section."920" This patch is located at some distance, R, away from the central star and is of a radial extent lo, with a characteristic surface density Xo."," This patch is located at some distance, $R$, away from the central star and is of a radial extent $l_0$, with a characteristic surface density $\Sigma_0$."921" GI acts on the scale of lo to collapse massradially!,, resulting in the formation of a spiral arm of thickness |; and characteristic surface density Σα."," GI acts on the scale of $l_0$ to collapse mass, resulting in the formation of a spiral arm of thickness $l_1$ and characteristic surface density $\Sigma_1$ ."922 This process is demonstrated in Figure 4.., This process is demonstrated in Figure \ref{figArmCollapse}.923 What is the appropriate scale for lo? ?, What is the appropriate scale for $l_0$ ?924" performed a number of simulations of marginally stable (Q~ 1) discs and found that, from a radial Fourier transform of these discs, the dominant radial wavenumber was typically 'Therefore, we expect the scale of spiral arm formation to be lo=27H."," \citet{Cossins2009} performed a number of simulations of marginally stable $Q\sim 1$ ) discs and found that, from a radial Fourier transform of these discs, the dominant radial wavenumber was typically Therefore, we expect the scale of spiral arm formation to be $l_0 = 2\pi H$."925 We have tested that this is consistent with our own simulations., We have tested that this is consistent with our own simulations.926 Figure 5 shows the results of a radial Fourier transform of Simulation B ata timeof 2.5 ORPs., Figure \ref{figRadialFourier} shows the results of a radial Fourier transform of Simulation B ata timeof 2.5 ORPs.927to a resolution of 7.4 kHz (0.09 ')) while (3.3) and (4.4) spectra were smoothed to a resolution of 50.2 KHz (due to the expected lower signal to noise ratio).,"to a resolution of 7.4 kHz $\sim$ 0.09 ) while (3,3) and (4,4) spectra were smoothed to a resolution of 50.2 kHz (due to the expected lower signal to noise ratio)."928 A polynomial baseline was subtracted from all spectra for normalisation., A polynomial baseline was subtracted from all spectra for normalisation.929 Several sources were detected in the (3.3) and (4.4) transitions.," Several sources were detected in the (3,3) and (4,4) transitions."930 However. analyses of these data contribute little to the scope of this paper and so the spectra and related parameters are presented in appendix A..," However, analyses of these data contribute little to the scope of this paper and so the spectra and related parameters are presented in appendix \ref{ap}."931 The corrected antenna temperature71.. hypertine linewidth Av. and central velocity vvalues for each source in the (1.1) and (2.2) inversion transitions were determined by fitting with the NH3¢1.1) METHOD process in the CLASS data analysispackage?.," The corrected antenna temperature, hyperfine linewidth $\Delta v$, and central velocity values for each source in the (1,1) and (2,2) inversion transitions were determined by fitting with the NH3(1,1) METHOD process in the CLASS data analysis."932. In some cases (SFO 09. LIE. 17. 26. 35 and 42) the main quadrupole of ammonia was detected but the hypertines were not seen at a level required for CLASS to fit them.," In some cases (SFO 09, 11E, 17, 26, 35 and 42) the main quadrupole of ammonia was detected but the hyperfines were not seen at a level required for CLASS to fit them."933 For these sources. and the (3.3) and (44) transitions presented in Appendix A.. the main quadrupoles were fitted by a single Gaussian using the ‘fitgauss” procedure in GBTIDL.," For these sources, and the (3,3) and (4,4) transitions presented in Appendix \ref{ap}, the main quadrupoles were fitted by a single Gaussian using the `fitgauss' procedure in GBTIDL."934 The optical depth (7) associated with ammonia emission in our sources may be determined through the ratio of main to satellite antenna temperatures of the CI.1) inversion transition (2):: where m and s subscripts indicate quantities associated with the main and satellite quadrupole lines. respectively. and a is the ratio of intensities of satellite to main lines (0.278 and 0.221 for inner and outer satellites. respectively).," The optical depth $\tau$ ) associated with ammonia emission in our sources may be determined through the ratio of main to satellite antenna temperatures of the (1,1) inversion transition \citep{Ho1983}: where m and s subscripts indicate quantities associated with the main and satellite quadrupole lines, respectively, and a is the ratio of intensities of satellite to main lines (0.278 and 0.221 for inner and outer satellites, respectively)."935 Optical depth values were determined through use of the NH3CI.1) METHOD process in the CLASS data analysis package.," Optical depth values were determined through use of the NH3(1,1) METHOD process in the CLASS data analysis package."936" Given the optical depth associated with the (1.1) transition. corrected antenna temperatures can be used to calculate the rotational temperature (7,9) associated with the (2.2) and (1.1) transitions (2): where 75;=LiuΜιLug 4.9. For iTo. a relationship between rotational and kinetic temperature may be calculated by consideration of (1.1). (2.2). and (2.1) states only Qe although Kinetic temperatures calculated by this method associated with =fy may be overestimated."," Given the optical depth associated with the (1,1) transition, corrected antenna temperatures can be used to calculate the rotational temperature ) associated with the (2,2) and (1,1) transitions \citep{Ho1983}: where $T_0 = \frac{E_{(2,2)} - E_{(1,1)}}{\mathrm{k_B}} \approx 41.5$ K. For $< T_0$, a relationship between rotational and kinetic temperature may be calculated by consideration of (1,1), (2,2), and (2,1) states only \citep{Walmsley1983,Swift2005}: : although kinetic temperatures calculated by this method associated with $ \approx T_0$ may be overestimated."937 Calculated values range from 11.9. to 27.3K.. suggesting that. this approximation is reasonable for these source objects.," Calculated values range from 11.9 to 27.3K, suggesting that this approximation is reasonable for these source objects."938 In order to calculate the column density of our sources. it is necessary to calculate the excitation temperature of each source.," In order to calculate the column density of our sources, it is necessary to calculate the excitation temperature of each source."939 This may be found via where the quantity is defined as rr. Has is the main beam etficiency of the GBT (0.897)) and jj; is the filling factor of the source in the relevant observation.," This may be found via where the quantity is defined as , $\eta_{\mathrm{mb}}$ is the main beam efficiency of the GBT ) and $\eta_{\mathrm{f}}$ is the filling factor of the source in the relevant observation."940 The filling factor of each source is somewhat hard to determine: values of dderived assuming a value of yp equal to unity are presented in Table 2? along with values of jj; determined by assuming LTE in our sources and letting 7..=7i., The filling factor of each source is somewhat hard to determine; values of derived assuming a value of $\eta_{\mathrm{f}}$ equal to unity are presented in Table \ref{tbl:Detections} along with values of $\eta_{\mathrm{f}}$ determined by assuming LTE in our sources and letting =.941". This assumption is supported by the rough equivalence of7,.. aand the values of Z4 determined by ?.."," This assumption is supported by the rough equivalence of, and the values of $T_{\mathrm{dust}}$ determined by \citet{Morgan2008}."942 A typical value of a filling factor in a similar study was determined by ? in their study of dense cores in Perseus to be «0.3., A typical value of a filling factor in a similar study was determined by \citet{Rosolowsky2008} in their study of dense cores in Perseus to be $\sim$ 0.3.943 Given the relatively large distances of our sources compared to Perseus. our values of jj appear reasonable. ranging from 0.03 to 0.35 with a mean of 0.12.," Given the relatively large distances of our sources compared to Perseus, our values of $\eta_{\mathrm{f}}$ appear reasonable, ranging from 0.03 to 0.35 with a mean of 0.12."944 If excitation conditions are homogeneous along the beam andall hypertine lines have the same excitation temperature. then the column densities at à given (JI.K=J) transition can be written as (?) where A is the Einstein spontaneous emission coethcient.," If excitation conditions are homogeneous along the beam andall hyperfine lines have the same excitation temperature, then the column densities at a given (J,K=J) transition can be written as \citep{Rosolowsky2008}945 where A is the Einstein spontaneous emission coefficient."946 Our determination of the filling factors associated with each source indicate that the oof our sources may be significantly underestimated., Our determination of the filling factors associated with each source indicate that the of our sources may be significantly underestimated.947 This is likely due to beam dilution or clumping within the beam of our observations. in order to account for this effect we have assumed LTE in our sources and set 7..= iin our determinations of column density.," This is likely due to beam dilution or clumping within the beam of our observations, in order to account for this effect we have assumed LTE in our sources and set = in our determinations of column density."948 Overall column density is obtained from ΝΤ.) and/or Νο) and the partition function: where the partition function. The values of the rotational constants B and C are 298117 and 186726 MHz respectively and the function SCIT) is 2 for J=3.6.9.... and | for all otherJ. Valuesfor optical depth. aand column density are listed for each source in Table ??..," Overall column density is obtained from N(1,1) and/or N(2,2) and the partition function: where the partition function, The values of the rotational constants B and C are 298117 and 186726 MHz respectively and the function S(J) is 2 for J=3,6,9,... and 1 for all otherJ. Valuesfor optical depth, and column density are listed for each source in Table \ref{tbl:Detections}. ."949The (ransport of accelerated. particles consists of both advection and diffusion.,The transport of accelerated particles consists of both advection and diffusion.950 The correct treatment of these processes in Che limit of small perturbation amplitudes (0«&By). also including the presence of bot wave trains. are well known and can be found e.g. in the work by Skilling(1975a.b)..," The correct treatment of these processes in the limit of small perturbation amplitudes $\delta B\ll B_0$ ), also including the presence of both wave trains, are well known and can be found e.g. in the work by \cite{skillinga,skillingc}."951 Unfortunately. in the case of strong magnetic field amplification a full theory of cosmic ray. transport is süll missing. ancl even (he definition of an effective wave velocity. v4. is troublesome.," Unfortunately, in the case of strong magnetic field amplification a full theory of cosmic ray transport is still missing, and even the definition of an effective wave velocity, $v_A$, is troublesome."952 A semi-analvtieal treatment. which is what we are interested in. is only possible within the framework of quasi-linear theory.," A semi-analytical treatment, which is what we are interested in, is only possible within the framework of quasi-linear theory."953 We adopt an Allvénn velocity defined as where p(.c) is the gas censity in the precursor al the position xc and. {4 is the strength of the unperturbed magnetic field., We adopt an Alfvénn velocity defined as where $\rho(x)$ is the gas density in the precursor at the position $x$ and $B_0$ is the strength of the unperturbed magnetic field.954 In the unlikely case that the waves could keep (heir Alfvénnic nature even in the strong turbulence regime. this wave velocity would in [aet be well defined.," In the unlikely case that the waves could keep their Alfvénnic nature even in the strong turbulence regime, this wave velocity would in fact be well defined."955 As to the interactions between streaming particles and Alfvénn waves. we do not neglect the velocity of the scattering centers e4 wilh respect to the fluid velocity u(r).," As to the interactions between streaming particles and Alfvénn waves, we do not neglect the velocity of the scattering centers $v_A$ with respect to the fluid velocity $u(x)$."956 This means (hat. in principle. (he compression ratios of (he background fluid ave different from (le ones experienced by the scattering centers. which turn out to be In the recipes above we have implicitly assumed (hat upstream waves are produced preferentially with //.=—1.," This means that, in principle, the compression ratios of the background fluid are different from the ones experienced by the scattering centers, which turn out to be In the recipes above we have implicitly assumed that upstream waves are produced preferentially with $H_c=-1$."957 Behind the subshock. instead. (he net velocity of the two opposile-propagating wave trains. when caleulated in the downstream gas reference frame (042). turns out to be in the same direction as the {nid one (seealsoBell1973).," Behind the subshock, instead, the net velocity of the two opposite-propagating wave trains, when calculated in the downstream gas reference frame $v_{A2}$ ), turns out to be in the same direction as the fluid one \cite[see also][]{bell78}."958. In a tvpicalSNR the condition ey«uw usually holds. hence the dillerence between (Sup Sor) and (Iu. Rigs) is expected not to be very relevant.," In a typicalSNR the condition $v_A\ll u$ usually holds, hence the difference between $\Ss,\St$ ) and $\Rs,\Rt$ ) is expected not to be very relevant."959" Bul if for some reason AL, is small enough. the compression ratios felt bv the accelerated particles may be sienificantlv different. with respect to the fluid ones. leading to a mocdilied spectral slope. as already showed bv Bell(1973)."," But if for some reason $M_A$ is small enough, the compression ratios felt by the accelerated particles may be significantly different with respect to the fluid ones, leading to a modified spectral slope, as already showed by \cite{bell78}."960. This is why we retain c4 in the calculations and checkposteriori that in (he cases considered this correction is not important., This is why we retain $v_A$ in the calculations and check that in the cases considered this correction is not important.961 In Sec., In Sec.962 5.1. we investigate the consequences of adopting a dillerent prescription for the velocity of the scattering centers., \ref{sec:modif} we investigate the consequences of adopting a different prescription for the velocity of the scattering centers.963 From the kinetic point of view. cosnic ravs are described by their distribution function in phase space 1. p).," From the kinetic point of view, cosmic rays are described by their distribution function in phase space $f(\vec{x},\vec{p})$ ."964 Keeping onlv the isotropic. part (since /(p)=[(p)+Olu? /e)), Keeping only the isotropic part (since $f(\vec{p})=f(p)+O(u^2/c^2)$ )965" Keeping onlv the isotropic. part (since /(p)=[(p)+Olu? /e))""", Keeping only the isotropic part (since $f(\vec{p})=f(p)+O(u^2/c^2)$ )966»oints) as a function of RA using a 17 window (upper panels). as a function of Dec using a 07001 window (middle panels). and as a 'unction of mean r PSF magnitude using a 0.1 mag window (lower yanels).,"points) as a function of RA using a $^{\circ}$ window (upper panels), as a function of Dec using a 01 window (middle panels), and as a function of mean $r$ PSF magnitude using a 0.1 mag window (lower panels)."967 The mean difference is only calculated if there are at least 100 stars in the sliding window., The mean difference is only calculated if there are at least 100 stars in the sliding window.968 The left hand panels correspond to oroper motion in RA and the right hand panels correspond to proper motion in Dec. We also plot the mean difference plus or minus the running 3c-clipped standard deviation as the upper and lower sets of smaller points. respectivelv. in each panel.," The left hand panels correspond to proper motion in RA and the right hand panels correspond to proper motion in Dec. We also plot the mean difference plus or minus the running $\sigma$ -clipped standard deviation as the upper and lower sets of smaller points, respectively, in each panel."969 Figure 9. illustrates that the systematic differences between the HLC proper motions and those of GKOX are at a very small level. generally 2 mas yr+," Figure \ref{fig:comp_usno} illustrates that the systematic differences between the HLC proper motions and those of GK04 are at a very small level, generally $\la$ 2 mas $^{-1}$."970 We note one clear systematic trend that the GKO4 Dee— proper motions are offset from the HLC Dec proper motions by = 2 mas 1 which is especially visible in the bottom right hand panel of Figure 9..," We note one clear systematic trend that the GK04 Dec proper motions are offset from the HLC Dec proper motions by $\la$ 2 mas $^{-1}$, which is especially visible in the bottom right hand panel of Figure \ref{fig:comp_usno}."971 We are currently unable to identify unambiguously the origin of the small systematic offset., We are currently unable to identify unambiguously the origin of the small systematic offset.972 The scatter in the proper motion differences (represented by the upper and lower sets of smaller points in each panel) is consistent with the stated proper motion uncertainties of ~3.9 mas yr. in GKO4. and. = 5 mas * for these particular stars in the HLC.," The scatter in the proper motion differences (represented by the upper and lower sets of smaller points in each panel) is consistent with the stated proper motion uncertainties of $\sim$ 3.9 mas $^{-1}$ in GK04, and $\la$ 5 mas $^{-1}$ for these particular stars in the HLC."973 Each light-motion curve in the LMCC has a different temporal coverage and number of epochs. a situation which is highlighted in Figure 2..," Each light-motion curve in the LMCC has a different temporal coverage and number of epochs, a situation which is highlighted in Figure \ref{fig:tcov}."974 Consequently the uncertainties on the HLC proper motions exhibit a very inhomogeneous spatial distribution. and selecting proper motion objects using cuts on proper motion uncertainty results in à very inhomogeneous sample of objects.," Consequently the uncertainties on the HLC proper motions exhibit a very inhomogeneous spatial distribution, and selecting proper motion objects using cuts on proper motion uncertainty results in a very inhomogeneous sample of objects."975 In Figure 10.. we present the mean proper motion uncertainty in the HLC as a function of mean x PSF magnitude. number of epochs and time span of a light-motion curve for PSF-like objects ©).," In Figure \ref{fig:pmerr}, we present the mean proper motion uncertainty in the HLC as a function of mean $r$ PSF magnitude, number of epochs and time span of a light-motion curve for PSF-like objects )."976 The three panels from left to right correspond to different light-motion curve time spans of 3. 5 and 7 yeurs. respectively. while in each panel three curves are plotted. dotted. dashed and continuous. corresponding to 10. 20 and 2230 epochs. respectively.," The three panels from left to right correspond to different light-motion curve time spans of 3, 5 and 7 years, respectively, while in each panel three curves are plotted, dotted, dashed and continuous, corresponding to $\le$ 10, $\approx$ 20 and $\ge$ 30 epochs, respectively."977 The curves in each panel show the mean proper motion uncertainty in the HLC as a function of mean + PSF magnitude., The curves in each panel show the mean proper motion uncertainty in the HLC as a function of mean $r$ PSF magnitude.978 It is worth noting that ~76% of objects in the LMCC have at least 20 epochs. and that ~37% have at least 20 epochs with atime span of greater than + years.," It is worth noting that $\sim$ of objects in the LMCC have at least 20 epochs, and that $\sim$ have at least 20 epochs with a time span of greater than 4 years."979" We find that 312819 objects in the LMCC tor ~8%)}) have proper motions jr with fra,>5.", We find that 312819 objects in the LMCC (or $\sim$ ) have proper motions $\mu$ with $\mu / \sigma_{\mu} > 5$.980 The Light-Motion Curve Catalogue (LMCC) contains almost million light-motion curves for stars and galaxies covering ~249 deg? in the SDSS Stripe 82., The Light-Motion Curve Catalogue (LMCC) contains almost 4 million light-motion curves for stars and galaxies covering $\sim$ 249 $^{2}$ in the SDSS Stripe 82.981 A light-motion curve provides wave band and time dependent photometric and astrometric quantities. where ~76 per cent of light-motion curves in the LMCC have at least 20 epochs of measurements.," A light-motion curve provides wave band and time dependent photometric and astrometric quantities, where $\sim$ 76 per cent of light-motion curves in the LMCC have at least 20 epochs of measurements."982 The LMCC is complete to magnitude 21.5 in i. g. r and 7. and to magnitude 20.5 in z. making it the deepest large-area catalogue of its kind.," The LMCC is complete to magnitude 21.5 in $u$ , $g$, $r$ and $i$, and to magnitude 20.5 in $z$, making it the deepest large-area catalogue of its kind."983 The photometric RMS accuracy for stars is ~20 mmag at kp. —18 mag and for galaxies it is ~30 mmag at ~18 mag., The photometric RMS accuracy for stars is $\sim$ 20 mmag at $r\sim$ 18 mag and for galaxies it is $\sim$ 30 mmag at $r\sim$ 18 mag.984" In both the RA and Dee coordinates. an RMS accuracy of ~32 mas and ~35 mas at r ~18 mag is achieved for pre-2005 data for stars and galaxies. respectively. and an RMS accuracy of ~35 mas and ~46 mas at r—I8 mag is achieved for 2005 data for stars and galaxies. respectively,"," In both the RA and Dec coordinates, an RMS accuracy of $\sim$ 32 mas and $\sim$ 35 mas at $r\sim$ 18 mag is achieved for pre-2005 data for stars and galaxies, respectively, and an RMS accuracy of $\sim$ 35 mas and $\sim$ 46 mas at $r\sim$18 mag is achieved for 2005 data for stars and galaxies, respectively."985with numerous approaches such as. 1D. Hydro simulations. 2.5D MIID simulations and full 3D MIID simulations (Gonzalez-Esparzaetal.2003:Cargill1996;&Sclinidi2002:Odstréil&Pizzo1999:Ocdstrciletal.2004:Smith2009:Falkenberg 2010)..,"with numerous approaches such as, 1D Hydro simulations, 2.5D MHD simulations and full 3D MHD simulations \citep{GonzalezEsparza:2003p8164,Cargill:1996p1291,Cargill:2002p1268,Odstrcil:1999p7707,Odstrcil:2004p8047,Smith:2009p8212,Falkenberg:2010p8153}."986 Slalistical studies comparing with white light observations indicate a trend of CME velocity converging towards the SW velocity as they propagate to AAU 2007).., Statistical studies comparing with white light observations indicate a trend of CME velocity converging towards the SW velocity as they propagate to AU \citep{Gopalswamy:2007p18}.987 Other studies. based on white light observations have indicated that aerodynamic drag of some form may explain this trend (Vrsnak2001:Shanmugarajuetal.2009)..," Other studies, based on white light observations have indicated that aerodynamic drag of some form may explain this trend \citep{Vrsnak:2001p3953,Shanmugaraju:2009p5226}."988 Raclio observations suggest (hat a linear form of aerodynamic drag is most appropriate for Last CAIEs (Reinerοἱal.2003).., Radio observations suggest that a linear form of aerodynamic drag is most appropriate for fast CMEs \citep{Reiner:2003p5332}.989 Tappin(2006) showed (hat acceleration can continue far oul AAU) into the Heliosphere., \cite{Tappin:2006p47} showed that acceleration can continue far out AU) into the Heliosphere.990 LIowever. these studies are subject to the dilliculties associated with the observations they are based on.," However, these studies are subject to the difficulties associated with the observations they are based on."991 For example white light observations were limited {ο single. narrow. fixed. view-points meaning only observation of the inner Heliosphere could be made and even these were subject to projection effects (Ilowardetal.2008b)..," For example white light observations were limited to single, narrow, fixed, view-points meaning only observation of the inner Heliosphere could be made and even these were subject to projection effects \citep{Howard:2008p15}."992 Also. linking features in imaging andin-siu observations is complex and can be ambiguous. a problem exacerbated during periods of high activitv.," Also, linking features in imaging and observations is complex and can be ambiguous, a problem exacerbated during periods of high activity."993 In (hie case of numerical simulations (heir complexity can make it hard (o extract which effects are (he most important. possibly obscuring the important underlying phlivsies.," In the case of numerical simulations their complexity can make it hard to extract which effects are the most important, possibly obscuring the important underlying physics."994" The unique STEREO mission consists of two nearlv-identical spacecraft in heliocentric orbits. STEREO-D(ehind) and STEREO-A(head) which separate from the Sun-Earth line at 22.5"" per vear."," The unique STEREO mission consists of two nearly-identical spacecraft in heliocentric orbits, STEREO-B(ehind) and STEREO-A(head) which separate from the Sun-Earth line at $^{\circ}$ per year."995 Each spacecralt carries (he Sun Earth Connection Coronal ancl Heliospheric Investigation (SECCII: Howardetal. 2008a)) suite. which images the inner Ileliosphere [rom the Sun's surlace to bevond 1. AU.," Each spacecraft carries the Sun Earth Connection Coronal and Heliospheric Investigation (SECCHI: \citealt{Howard:2008p4742}) ) suite, which images the inner Heliosphere from the Sun's surface to beyond 1 AU."996 Using STEREO observations. a munber of papers have been published which extract 3D information and study CMESs at extended heliocentric cistaces. over-coming some ol the difficulties outlined above.," Using STEREO observations, a number of papers have been published which extract 3D information and study CMEs at extended heliocentric distances, over-coming some of the difficulties outlined above."997 Davisetal.(2009). identified a CME in HIT and Το. using a constant velocity. assumption (Sheelevetal.2008) ον derived the speed ancl trajectory of (he CME.," \citet{Davis:2009p6240} identified a CME in HI1 and HI2, using a constant velocity assumption \citep{Sheeley:2008p6253} they derived the speed and trajectory of the CME."998 The preclicated arrival time. based on the speed derived. agreed with then-5szi observations.," The predicated arrival time, based on the speed derived, agreed with the observations."999" Woodetal.(2009) used the Point-P and ""Fixed-ó methods to derive the height. speed. and direction [rom elongation measurements out to distances of —120 RR..."," \citet{Wood:2009p4888} used the “Point-P” and $\phi$ ” methods to derive the height, speed, and direction from elongation measurements out to distances of $\sim$ $_{\odot}$."1000 A recent paper by Liuetal.(2010). tracked a CME to e-150 RIAL. in 3D using J-maps from both spacecraft to triangulate the CMESs position in 3D. On the other hand Maloney.οἱal.(2009) (Cracked the trajectory of CME apexes in 3D using (riangulation. some as [ar as 240 Ht...," A recent paper by \citet{Liu:2010p7366} tracked a CME to $\sim$ $_{\odot}$ in 3D using J-maps from both spacecraft to triangulate the CMEs position in 3D. On the other hand \citet{Maloney:2009p6617} tracked the trajectory of CME apexes in 3D using triangulation, some as far as 240 $_{\odot}$."1001 Byrneetal.(2010). developed a new reconstruction method with allowed the entire CME front to be reconstructed., \citet{Byrne:2010} developed a new reconstruction method with allowed the entire CME front to be reconstructed.1002 They. found. evidence [ου CME deflection. expansion and acceleration low down (< RR.) followed by a solar wind drag interaction.," They found evidence for CME deflection, expansion and acceleration low down $<$ $_{\odot}$ ) followed by a solar wind drag interaction."1003 For a review of some of the different 3D reconstruction methods which have been applied to STEREO CME observations see Mierlaοἱal. (2010).., For a review of some of the different 3D reconstruction methods which have been applied to STEREO CME observations see \citet{Mierla:2010p7463}. .1004 :~1 ~1 2 5+ , $z \sim 1$ $\sim \! 1$ $2$ $h^{-1}$ 1005spectral index reaches its limit of 2.2 and we apply this value in further simulations.,spectral index reaches its limit of 2.2 and we apply this value in further simulations.1006 The relation between 7. 5 and c can be roughly fitted with the equation 7=03255.to in the considered range of shock parameters.," The relation between $\tau^{U}$ ,$\gamma$ and $\psi$ can be roughly fitted with the equation $\tau^{U} = 0.25\, \gamma^{-1.2}\, \psi$ in the considered range of shock parameters."1007 We repeated simulations for a number of cases with dilferent ~ and c and TDxz0., We repeated simulations for a number of cases with different $\gamma$ and $\psi$ and $\tau^{D}\not = 0$.1008 ENDhe obtained. results are in. good agreement with. the ones derived. from the above equation: up to 7?)=0.11., The obtained results are in good agreement with the ones derived from the above equation up to $\tau^{D} = 0.11$.1009 Values of the acceleration time fice for three amplitudes of magnetic field Huetuations downstream of the shock are presented in Fie., Values of the acceleration time $t_{acc}$ for three amplitudes of magnetic field fluctuations downstream of the shock are presented in Fig.1010 3., 3.1011" In the figure one can see the lack of change of /, with c. but it slowly decreases to the asymptotic value with 5."," In the figure one can see the lack of change of $t_{acc}$ with $\psi$, but it slowly decreases to the asymptotic value with $\gamma$ ."1012 In the simulations we have observed. tendency of face to grow when o increases up to 2.3-2.4 and. no further change if magnetic field Ductuations upstream of the shock grow., In the simulations we have observed tendency of $t_{acc}$ to grow when $\sigma$ increases up to 2.3-2.4 and no further change if magnetic field fluctuations upstream of the shock grow.1013 ForBJ 7?><0.11 the asvmptotieH value of the acceleration time is close to rjfe., For $\tau^{D}\leq0.11$ the asymptotic value of the acceleration time is close to $r_{g}/c$.1014 H occurs that ryé¢isa good unit provided that the homogeneous magnetic field. dominates the randomly. component., It occurs that $r_{g}/c$ is a good unit provided that the homogeneous magnetic field dominates the randomly component.1015" Unfortunately. when this condition fails the meaning of /,; becomes unclear in the simulations then."," Unfortunately, when this condition fails the meaning of $t_{acc}$ becomes unclear in the simulations then."1016 For this reason we will not cliscuss further the case of 7P=0.69 anv more., For this reason we will not discuss further the case of $\tau^{D} = 0.69$ any more.1017 Approximate calculations. of Gallant Achterberg (1999) showed that ἐνc1. where ff. is the particle mean residence time upstream of the shock (upper index) as measured in the upstream plasma rest [rame (lower index). and D in /£ stands for the downstream: residence time.," Approximate calculations of Gallant Achterberg (1999) showed that $t^{U}_{U}/t^{D}_{U}\simeq 1$, where $t^{U}_{U}$ is the particle mean residence time upstream of the shock (upper index) as measured in the upstream plasma rest frame (lower index), and D in $t^{D}_{U}$ stands for the downstream residence time."1018 Llowever. they were not able to consider the anisotropic particle momentum clistribution and ou results in Fig.," However, they were not able to consider the anisotropic particle momentum distribution and our results in Fig."1019 4 with (i/1P within the range 0.010.1 are more adequate for rea situations., 4 with $t^{U}_{U}/t^{D}_{U}$ within the range $0.01-0.1$ are more adequate for real situations.1020 Aclditionally. the above authors applied an extremely irregular magnetic field. upstream. of the shock represented by randomly. oriented magnetic cells with fick amplitude £ and they measured time in the upstream uni of ry(B)feo," Additionally, the above authors applied an extremely irregular magnetic field upstream of the shock represented by randomly oriented magnetic cells with field amplitude $B$ and they measured time in the upstream unit of $r_{g}(B)/c$."1021 As a result they obtained. that nIP could be much larger than 1 in the case., As a result they obtained that $t^{U}_{U}/t^{D}_{U}$ could be much larger than 1 in the case.1022 Just before the spectral index reaches its minimal value (cf., Just before the spectral index reaches its minimal value (cf.1023 Fie., Fig.1024 2) Qs stabilizes near the limit which value does not further depend on the magnetic field. inclination as is seen in Fig., 2) $\Delta \Omega_{S}$ stabilizes near the limit which value does not further depend on the magnetic field inclination as is seen in Fig.1025 5., 5.1026 Momentum vectors of particles. crossing downstream of the shock have similar distributions as measured in the downstream. plasma rest. [rame if λος approaches the maximum value., Momentum vectors of particles crossing downstream of the shock have similar distributions as measured in the downstream plasma rest frame if $\Delta \Omega_{S}$ approaches the maximum value.1027 Then. it follows. that parameters we consider; below depend only on D77.," Then, it follows that parameters we consider below depend only on $\tau^{D}$."1028 For growing zr? (τη20.L0-10%L1:102. 0.11) the acceleration time is constant and accompanied by a slow increase of the mean energy. gain in one evele downstream νοο=0.89.0.94.1.0.1.1. and a slight decrease. of the fraction. of particles that reach the shock again after crossing it downstream (Anη)=0.51.0.50.0.48. O44.," For growing $\tau^{D}$ $\tau^{D} = 0,\, 1.0\cdot 10^{-3},\, 1.1\cdot 10^{-2},\, 0.11$ ) the acceleration time is constant and accompanied by a slow increase of the mean energy gain in one cycle downstream-upstream-downstream $\langle\Delta E/E\rangle_{D} = 0.89,\, 0.94,\, 1.0,\, 1.1$, and a slight decrease of the fraction of particles that reach the shock again after crossing it downstream $\langle\Delta n/n\rangle = 0.51,\, 0.50,\, 0.48,\, 0.44$ ."1029 Simultaneously the mean time a particle. spends. downstream: of the shock grows as /5D=0.96.1.0.1.2. 1.35.," Simultaneously the mean time a particle spends downstream of the shock grows as $t^{D}_{D} = 0.96,\, 1.0,\, 1.2,\, 1.35$ ."1030 Time that a particle spends upstream of the shock can be neglected in this rest frame as is visible in Fig., Time that a particle spends upstream of the shock can be neglected in this rest frame as is visible in Fig.1031 4., 4.1032 Ht implies. approximately. fac=(ALSey if one neglects correlations between these quantities (ef," It implies, approximately, $t_{acc} = t_{D}^{D}/\langle\Delta E/E\rangle_{D}$ if one neglects correlations between these quantities (cf."1033 Bednarz Ostrowski 1996)., Bednarz Ostrowski 1996).1034 Similarly we can roughly estimate the value of the energy spectral index of accelerated. particles as σοιμηο)αλE5p|1), Similarly we can roughly estimate the value of the energy spectral index of accelerated particles as $\sigma\simeq 1- \ln(\langle\Delta n/n\rangle)/\ln(\langle\Delta E/E\rangle_{D}+1)$.1035 The simulated. maximum cistance in downstream medium the particle is able to depart from the shock and reach it. again Mis. respectively.. d;M=O.S4.1.5.2.5.4.0 (the values were derived from ~LO” events).," The simulated maximum distance in downstream medium the particle is able to depart from the shock and reach it again is, respectively, $d^{M}_{D}\, =\, 0.84,\, 1.5,\, 2.5,\, 4.0$ (the values were derived from $\sim 10^{5}$ events)."1036 We calculated the average values of sin?6 for returning particles wandering downstream of the shock and found. respectively. (in6;= 0.651.," We calculated the average values of $\sin^{2}\theta$ for returning particles wandering downstream of the shock and found, respectively, $\langle\sin^{2}\theta\rangle = 0.676,\, 0.658,\, 0.650,\, 0.651$ ."1037 Because of newly founcl acceleration mechanism in ultrarelativistic shock waves wepropose that some part of GRBs radiation could arise due to svachrotron racdation of electrons or electron pairs accelerated across the mechanism., Because of newly found acceleration mechanism in ultrarelativistic shock waves wepropose that some part of GRBs radiation could arise due to synchrotron radiation of electrons or electron pairs accelerated across the mechanism.1038 We follow the internal shocks mocel of GRBs (e£., We follow the internal shocks model of GRBs (cf.1039 Ixobavashi, Kobayashi1040rotating cases. (,rotating cases. (1041a) Iu the expancing case. the isovelocity vine is circular in projection. but for rotation the ring is viewed edge-on aud therefore appears to the observer as a strip of leugth 24. (,"a) In the expanding case, the isovelocity ring is circular in projection, but for rotation the ring is viewed edge-on and therefore appears to the observer as a strip of length $2q$. ("1042b) For expansion the shell is frout-back. sviunietrie. so that for every ring of velocity shift ez on he front side of the shell. an exact replica exists ou the yack. side. only with oof opposite sign.,"b) For expansion the shell is front-back symmetric, so that for every ring of velocity shift $\vz$ on the front side of the shell, an exact replica exists on the back side, only with of opposite sign."1043 Iowever. for rotation the svinnetry is ecftaieht. so that all the poiuts on the left hemisphere Im oof the same sien. aud all the points on the the right remisphere also have the same sigu but opposite to that ou the left.," However, for rotation the symmetry is left-right, so that all the points on the left hemisphere have of the same sign, and all the points on the the right hemisphere also have the same sign but opposite to that on the left."1044 These differences in the ring projection aud the distribution of projected Doppler shifts between the two cases will have significant cousequences for the evolution of the line profile shape during a uicroleusiug eveut., These differences in the ring projection and the distribution of projected Doppler shifts between the two cases will have significant consequences for the evolution of the line profile shape during a microlensing event.1045 As discussed iu the introduction. the effect of nüicroleusiug is to introduce the amplification factor A(d) from Eq. (3))," As discussed in the introduction, the effect of microlensing is to introduce the amplification factor $A(d)$ from Eq. \ref{eq:amp}) )"1046 iuto the flux iuteeraL which now becomes where d ds the projected impact parameter from the lens to anv differential clement of material iu je. envelope.," into the flux integral, which now becomes where $d$ is the projected impact parameter from the lens to any differential element of material in the envelope."1047 Iu Figs., In Figs.1048 1 and 2.. we further define dp as the impact paralcter from the eus to the shell ceuter.," \ref{fig:f1} and \ref{fig:f2}, we further define $d_{\rm L}$ as the impact parameter from the lens to the shell center."1049 The ΕΠΗ of value of di is denoted by dy siguifviug Le niünimuuni nupact paraiuter of the leus trajectory., The minimum of value of $d_{\rm L}$ is denoted by $d_0$ signifying the minimum impact paramter of the lens trajectory.1050 Note hat Eq. (3)), Note that Eq. \ref{eq:amp}) )1051 is the expression derived for the amplification of a point source lens (c.f.," is the expression derived for the amplification of a point source lens (c.f.,"1052 Paczwüsshki 1986)). thus the flux reduces to a convolution of the uuleused iutensitv and the amplification by the points lens. integrated across the source plane.," Paczyńsski \cite{paczynski1986}) ), thus the flux reduces to a convolution of the unlensed intensity and the amplification by the points lens, integrated across the source plane."1053 Note tvat as d29T. (d) tends towarcl unity. and the uuleused case is recovered.," Note that as $d\gg 1$, $A(d)$ tends toward unity, and the unlensed case is recovered."1054 Using Eq. (9)).," Using Eq. \ref{eq:lensed}) ),"1055 we have computed enüssion line profiles for shells in either uniform expausion or rotation., we have computed emission line profiles for shells in either uniform expansion or rotation.1056 Table 1 sunnurises the simulations that are shown in Fies. 3- $2," Table \ref{tab:t1}1057 summarises the simulations that are shown in Figs. \ref{fig:f3}- \ref{fig:f7}."1058 In Tab. 1.," In Tab. \ref{tab:t1},"1059 the paraimcter 5 defines the orientation of the leus tra.jectory (c.f.," the parameter $\gamma$ defines the orientation of the lens trajectory (c.f.,"1060 Sect. 2.2.33).," Sect. \ref{subsub:posang}) ),"1061 uas is the ανα amplfication at any frequency in t1ο profile during the nücroleusimg event. and fu. d fie maxi eulhaucenmenut o the line eiissiou duniie the nuücroleusiug event relative to that in the absence of lensing.," $A_{\rm max}$ is the maximum amplification at any frequency in the profile during the microlensing event, and $f_{\rm line}$ is the maximum enhancement of the line emission during the microlensing event relative to that in the absence of lensing."1062 The following sections describe the consequence of the uvicrolensing as it relaes to (a) the flow velocity field. (b) the Einstein radius of he leus. aud (ο) the orientation of the lens trajectory with respect to the axis of rotation.," The following sections describe the consequence of the microlensing as it relates to (a) the flow velocity field, (b) the Einstein radius of the lens, and (c) the orientation of the lens trajectory with respect to the axis of rotation."1063 Figure 3 coutrasts the mucrolensed line profiles frou au expanding shell (left) to one that is rotating (right). where the observed velocity shift is eon.=cz and the maxima velocity shift Όμως ik egial either to cy for expausion or C98lij for rotation.," Figure \ref{fig:f3} contrasts the microlensed line profiles from an expanding shell (left) to one that is rotating (right), where the observed velocity shift is $v_{\rm obs}=\vz$ and the maximum velocity shift $v_{\rm max}$ is equal either to $v_0$ for expansion or $v_0\,\sin i$ for rotation."1064 In lis simulation we lave chosen rafteo=LO., In this simulation we have chosen $\rsh/\rein=1.0$.1065" The lens is taseu to transit the shell across the inc-ofsight to the shell ceuter with uniuinmu nuract paraucter dyfra,=O.", The lens is taken to transit the shell across the line-of-sight to the shell center with minimum impact parameter $d_0/\rsh = 0$.1066 Ii the case of rotation. we lave furtrer asstuued that the leis trajectory is orthogonal to the xojection of the rotatio1 axis in the plane of the sky.," In the case of rotation, we have further assumed that the lens trajectory is orthogonal to the projection of the rotation axis in the plane of the sky."1067 The wo panels srow a sequence of Ime profiles. begiuinue with the leis at a projected «istance of rg from the centre oft je sheL which then decreases to zero aud increases back to 3vg on the opposie side of the sιο.," The two panels show a sequence of line profiles, beginning with the lens at a projected distance of $3 \rein$ from the centre of the shell, which then decreases to zero and increases back to $3 \rein$ on the opposite side of the shell."1068" Results are plotted as the ratio of the ensed flux. E,. to he nuleused flux. Fy (t1e latter being just he fla-top profile). plus a coustaut offset imroduced betweereach tiuestep to better display the time evolution oft 1C profile sape."," Results are plotted as the ratio of the lensed flux, $\Fnu$, to the unlensed flux, $F_0$ (the latter being just the flat-top profile), plus a constant offset introduced between each timestep to better display the time evolution of the profile shape."1069 iFrom Fig. 3..," >From Fig. \ref{fig:f3},"1070 it is evident tha he microlensed profiles for an expanding shell are distinctlv different from those of a rotating shell., it is evident that the microlensed profiles for an expanding shell are distinctly different from those of a rotating shell.1071 For expausio1 he profile shape is sviunietrie both iu velocity abou ine center aud in time with respect to the leus positiou a iupact parameter dofrg., For expansion the profile shape is symmetric both in velocity about line center and in time with respect to the lens position at impact parameter $d_0/\rein$.1072 Iu contrast. the profile shaaC in the rotating case is nof sviunietric in velocity. aud although it is svuiuetric in time for the leus trajectory assmnued in Fig. 3..," In contrast, the profile shape in the rotating case is not symmetric in velocity, and although it is symmetric in time for the lens trajectory assumed in Fig. \ref{fig:f3},"1073 the profile evolution is not time «ος in general. as will be shown in Sect. 2.2.5..," the profile evolution is not time symmetric in general, as will be shown in Sect. \ref{subsub:posang}."1074 The difference between the expansion aud rotation cases for the microlensed line profile evolution can be tnclerstoor from considerations of the bulk flow properties of the two cases., The difference between the expansion and rotation cases for the microlensed line profile evolution can be understood from considerations of the bulk flow properties of the two cases.1075 À siehtline from the observer to t ens will iiersect the shell at two poiuts one iu t yout heiisphere aud oue in the back., A sightline from the observer to the lens will intersect the shell at two points: one in the front hemisphere and one in the back.1076 Ax note oevious he observed Doppler shift at these two poius ds equ n maeunitide but opposite in sign for expecine shells. hereby resuting in an amplification at preOlaitly wo points in the profile. with the two poiuts Del equidistautlv located from line center.," As note previously, the observed Doppler shift at these two points is equal in magnitude but opposite in sign for expanding shells, thereby resulting in an amplification at predominantly two points in the profile, with the two points being equidistantly located from line center."1077 Ilowever. for a rotating shel. the Doppler shifts at the two 1itersection )olnts are ecual both in magnitude and direction. hence he amplificaion of line enission occurs predonminautlv at ouly one point in the line resulting iu the asviunetric xofile shapes.," However, for a rotating shell, the Doppler shifts at the two intersection points are equal both in magnitude and direction, hence the amplification of line emission occurs predominantly at only one point in the line – resulting in the asymmetric profile shapes."1078 Figures {- 6 clemonstrate how the variation of the ratio αμΈτ affects the response of the line profile o inicrolensing., Figures \ref{fig:f4}- \ref{fig:f6} demonstrate how the variation of the ratio $\rsh/\rein$ affects the response of the line profile to microlensing.1079 The three figures are respectively for rar= 0.3. 1.0. and 3.0.," The three figures are respectively for $\rsh/\rein =$ 0.3, 1.0, and 3.0."1080 Each plot slOWS SIX panels. with μοιpper set for an expanding shell αιid the lower one for a rotati1ο shell.," Each plot shows six panels, with the upper set for an expanding shell and the lower one for a rotating shell."1081 As laelled. the differeit panels correspond o different impact xuanmeters of the lens. with values of dyFE= 0.0. 0.3. and 1.0.," As labelled, the different panels correspond to different impact parameters of the lens, with values of $d_0/\rein=$ 0.0, 0.3, and 1.0."1082 Note tlia as in the previous section. we assunie hat the Ίος trajectory iuercepts the xojected axis of roation at a right anele.," Note that as in the previous section, we assume that the lens trajectory intercepts the projected axis of rotation at a right angle."1083 Tucreasing ra/rg leads to three primary effects for the eused Ine profiles:, Increasing $\rsh/\rein$ leads to three primary effects for the lensed line profiles:1084? in model44) and the pairs ἆ vy and feo Ze in 22 and 3 respectively. the parameters are well determined.,"$\beta$ in 4) and the pairs $T$ $\nu_0$ and $F_{\rm wc}$ $T_{\rm w}$ in 2 and 3 respectively, the parameters are well determined."1085 The well-determined. pairs of parameters 7 a and a 3 ave illustrated in 33. with almost circular probability contours.," The well-determined pairs of parameters $T$ $\alpha$ and $\alpha$ $\beta$ are illustrated in 3, with almost circular probability contours."1086 The probabilities for the relatively ill-constrained »airs discussed above are illustrated in 4 and 5., The probabilities for the relatively ill-constrained pairs discussed above are illustrated in 4 and 5.1087 There are two points to note from these oobabilitw figures., There are two points to note from these probability figures.1088 First. along the track of maximum oobability in these figures. the value of the associated xometric [u-Hi luminosity of the galaxv changes hy only lOpper cent.," First, along the track of maximum probability in these figures, the value of the associated bolometric far-IR luminosity of the galaxy changes by only per cent."1089 This is much less variation than the actor of 2 variation across the wider range of the T: »wameter space shown in 22., This is much less variation than the factor of 2 variation across the wider range of the $T$ $\beta$ parameter space shown in 2.1090 Secondly. bye is not defined accurately even by the excellent data lor 9058. as shown in 55.," Secondly, $F_{\rm wc}$ is not defined accurately even by the excellent data for 958, as shown in 5."1091 Llence. this is likely to provide the cast informative presentation of SED data amonest the four nmiodels used.," Hence, this is likely to provide the least informative presentation of SED data amongst the four models used."1092 For APALOOS279|5255. the extra. population of 20-IX. dust in this model can be seen generating a weak in the low-frequency slope of the SED in 1.," For 08279+5255, the extra population of 20-K dust in this model can be seen generating a break in the low-frequency slope of the SED in 1."1093 The mass of cold dust. present in far-H. luminous galaxies may dominate the total mass of dust at all temperatures. ane provide information concerning the history of metal enrichment within. but it is far from enerectically dominant. and dillieult to measure to better than a factor of a few.," The mass of cold dust present in far-IR luminous galaxies may dominate the total mass of dust at all temperatures, and provide information concerning the history of metal enrichment within, but it is far from energetically dominant, and difficult to measure to better than a factor of a few."1094 For consistency with our earlier treatments (Blain et 119992. 2002: Barnard Blain 2003) we will adopt the 7 a 7 model 11) in the following discussions.," For consistency with our earlier treatments (Blain et 1999a, 2002; Barnard Blain 2003) we will adopt the $T$ $\alpha$ $\beta$ model 1) in the following discussions."1095 Subject to the effective dust temperature 7 being slightly different from that in the other SED parametrizations. this model provides a good cdeseription of observations for galaxies ranging from Iow-Iuminosity spirals to the most. luminous high-redshift systems 11).," Subject to the effective dust temperature $T$ being slightly different from that in the other SED parametrizations, this model provides a good description of observations for galaxies ranging from low-luminosity spirals to the most luminous high-redshift systems 1)."1096 Phe results that follow are not only valid or this description of the SED. but are generic results that apply to all 4 cleseriptions discussed above.," The results that follow are not only valid for this description of the SED, but are generic results that apply to all 4 descriptions discussed above."1097 The well-defined. pseuco-thermal SED of dusty galaxies 11) offers a prospect. of recognizing the redshifts of galaxies with the same intrinsic SEDs bv comparing far-LR and submm colours., The well-defined pseudo-thermal SED of dusty galaxies 1) offers a prospect of recognizing the redshifts of galaxies with the same intrinsic SEDs by comparing far-IR and submm colours.1098 This was discussed in the context. of identifving high-redshift galaxies amongst more nunmcrous ow-redshilt ealaxies in a shallow submim-wave survey by Blain (1998) and for observations of the first. generation of harel-to-iclentily submam galaxies. with Uusx-density limits romLRAS observations by Hughes ct ((1998) and Eales et ((1999).," This was discussed in the context of identifying high-redshift galaxies amongst more numerous low-redshift galaxies in a shallow submm-wave survey by Blain (1998) and for observations of the first generation of hard-to-identify submm galaxies, with flux-density limits from observations by Hughes et (1998) and Eales et (1999)."1099 Eales et nnoted that it is not. possible. à oiori. to be certain of whether a clusty galaxy. is hot anc ap away. or cool and close by. and that there could be significant consequences for the cosmological implications of the population of submm-Iuminous galaxies if the clus emperature/redshift is not estimated. correctly.," Eales et noted that it is not possible, a priori, to be certain of whether a dusty galaxy is hot and far away, or cool and close by, and that there could be significant consequences for the cosmological implications of the population of submm-luminous galaxies if the dust temperature/redshift is not estimated correctly."1100 LE the clus emperature defining. the SED is too hot. and/or the redshift of the population is too great. then the cosmologica importance of submum galaxies can be overstated.," If the dust temperature defining the SED is too hot, and/or the redshift of the population is too great, then the cosmological importance of submm galaxies can be overstated."1101 The reason for the similar effects of increasing both redshift anc temperature is that the peak of the SED is determined. by the value of £/T in the exponential term of the Planck function., The reason for the similar effects of increasing both redshift and temperature is that the peak of the SED is determined by the value of $\nu/T$ in the exponential term of the Planck function.1102 Itedshifting the spectrum by a factor of (1|z) in frequeney £z thus has a directIy equivalent effect to mocifving the temperature 7 by the same fraction., Redshifting the spectrum by a factor of $(1+z)$ in frequency $\nu$ thus has a directly equivalent effect to modifying the temperature $T$ by the same fraction.1103The correction described above significantly reduces the fluctuations due to seeing variations.,The correction described above significantly reduces the fluctuations due to seeing variations.1104 Figure 20 displays the relative dispersion computed after this correction., Figure \ref{fig:stabi2} displays the relative dispersion computed after this correction.1105" With respect to the histograms presented in Fig. 11,,"," With respect to the histograms presented in Fig. \ref{fig:stabi1},"1106" this dispersion is reduced by in blue and in red, achieving a stability of in blue and in red, respectively 1.6 times the photon noise in blue and 1.9 in red."," this dispersion is reduced by in blue and in red, achieving a stability of in blue and in red, respectively 1.6 times the photon noise in blue and 1.9 in red."1107" The improvement on the overall relative stability remains modest, because most light curvesnot show a correlation with the seeing andnot need a correction."," The improvement on the overall relative stability remains modest, because most light curves show a correlation with the seeing and need a correction."1108 The importance of the seeing correction as a function of the correlation coefficient p can be more precisely quantified., The importance of the seeing correction as a function of the correlation coefficient $\rho$ can be more precisely quantified.1109" Figure 21 displays for both colours the ratio o[cP, where a is the dispersion measured along the super-pixel light curvesafter the seeing correction, and cP the one measuredbefore the correction, as a function of the initial correlation coefficient p."," Figure \ref{fig:parabolla} displays for both colours the ratio $\sigma^A /1110\sigma^B$, where $\sigma^A$ is the dispersion measured along the super-pixel light curves the seeing correction, and $\sigma^B$ the one measured the correction, as a function of the initial correlation coefficient $\rho$."1111" It can be shown that, if the slope o defined in Eq."," It can be shown that, if the slope $\alpha$ defined in Eq."1112" 8 is measured with an error Aa, then the following correlation is expected: where og is the dispersion of the seeing."," \ref{eq:see} is measured with an error $\Delta \alpha$, then the following correlation is expected: where ${\sigma_S}$ is the dispersion of the seeing."1113" This correlation shows that the stronger the correlation with seeing, the more important the seeing correction is."," This correlation shows that the stronger the correlation with seeing, the more important the seeing correction is."1114 The dispersion of the measurements can be reduced up to for very correlated light curves., The dispersion of the measurements can be reduced up to for very correlated light curves.1115 The limitation of this correction comes from the errors Aa which explain why most points are slightly above this envelope., The limitation of this correction comes from the errors $\Delta a$ which explain why most points are slightly above this envelope.1116" When [οἱ<0.15, most points in fact lie above 1, in which case the ""correction"" worthens things."," When $\vert \rho \vert < 0.15$, most points in fact lie above 1, in which case the ""correction"" worthens things."1117 Therefore we do not apply the correction to light curves with |p|<0.15.," Therefore we do not apply the correction to light curves with $\vert \rho \vert <11180.15$."1119" As the seeing is randomly distributed in time, the above correction will not induce artificial variations that could be mistaken for a microlensing event or a variable star."," As the seeing is randomly distributed in time, the above correction will not induce artificial variations that could be mistaken for a microlensing event or a variable star."1120 One can wonder however what happens to the super-pixel flux when the flux of the contributing star varies., One can wonder however what happens to the super-pixel flux when the flux of the contributing star varies.1121" In this case, the slope a of the correlation between the flux and the seeing does change, thus resulting in a lower correlation coefficient."," In this case, the slope $a$ of the correlation between the flux and the seeing does change, thus resulting in a lower correlation coefficient."1122" In extreme cases, when the correction coefficient is small (|p|< 0.15), the correction is thus not appropriate and not applied."," In extreme cases, when the correction coefficient is small $\vert \rho \vert < 0.15$ ), the correction is thus not appropriate and not applied."1123a [actor of ten or so.,a factor of ten or so.1124 We therefore feel that the massive stars near are the first observational evidence for a star formation in an accretion disk., We therefore feel that the massive stars near are the first observational evidence for a star formation in an accretion disk.1125 Similar but quantitatively less constraining conclusions were reached by Navakshin et al. (, Similar but quantitatively less constraining conclusions were reached by Nayakshin et al. (11262005. to be submitted) on a completely: independent basis of stellar orbits for the voung stars in the GC.,"2005, to be submitted) on a completely independent basis of stellar orbits for the young stars in the GC."1127 Several authors have previously suggested. (e.g...Mor- that duc to the extreme environment near the SMDLIL in our Galactic Centre. formation of [ow mass stars may be much less ellicient than elsewhere in the Galaxy.," Several authors have previously suggested \citep[e.g.,][]{Morris93,Krabbe95,Levin03} that due to the extreme environment near the SMBH in our Galactic Centre, formation of low mass stars may be much less efficient than elsewhere in the Galaxy."1128 Convincing quantitative arguments were never made. however. as any stellar mass estimates. such as à Jeans mass estimate. depend on a range of poorly known parameters (initial eas density. temperature. or the quantities determining these).," Convincing quantitative arguments were never made, however, as any stellar mass estimates, such as a Jeans mass estimate, depend on a range of poorly known parameters (initial gas density, temperature, or the quantities determining these)."1129 A detailed theoretical analysis of the implications of the observational constraints found here will be given elsewhere., A detailed theoretical analysis of the implications of the observational constraints found here will be given elsewhere.1130 The Galactic Centre region “spans the central few hundred parsecs of the Galaxy and represents about of the volume in the Galactic disk.," The Galactic Centre region ""spans the central few hundred parsecs of the Galaxy and represents about of the volume in the Galactic disk."1131" Although small in size. the region contains of the molecular material and. voung stars inthe Galaxy..."" (Figer.2001)."," Although small in size, the region contains of the molecular material and young stars inthe Galaxy..."" \citep{Figer01}."1132. In particular. the inner 50 parsec of the Galaxy contain three massive voung star clusters. the Arches. the Quintuplet anc the Central (the sstar cluster).," In particular, the inner $\sim 50$ parsec of the Galaxy contain three massive young star clusters, the Arches, the Quintuplet and the Central (the star cluster)."1133 Their heavy mass content (AZ220 M.) is very similar. with each containing about LOO stars. but the Archesis 2.3 million vears old versus 3.6 million vears for the other two clusters (Figer.2004).," Their heavy mass content $M \simgt 20 \msun$ ) is very similar, with each containing about 100 stars, but the Arches is $2-3$ million years old versus $3-6$ million years for the other two clusters \citep{Figer04}."1134. In view of our results. it is interesting to compare the vvoung star cluster to the other two star clusters.," In view of our results, it is interesting to compare the young star cluster to the other two star clusters."1135 The best studied of the two is the Arches star cluster., The best studied of the two is the Arches star cluster.1136 The estimated mass of the cluster is 1.210?M. (c.g.Stolte 2002).. and its stellar density is cerived to be of same order or larger than that of the voung sstar cluster (Vable1:in.Figer.2004).," The estimated mass of the cluster is $\sim 1.2 \times 10^4 \msun$ \citep[e.g.][]{Stolte02}, and its stellar density is derived to be of same order or larger than that of the young star cluster \citep[Table 1 in ][]{Figer04}."1137. The IME. is much Hatter than the classical Salpeter(1955).— IME in. the innermost few areseconds of the cluster. but it steepens to an IME steeper than the classical one at the outer regions of the cluster (Stoltectal..2002).," The IMF is much flatter than the classical \cite{Salpeter55} IMF in the innermost few arcseconds of the cluster, but it steepens to an IMF steeper than the classical one at the outer regions of the cluster \citep{Stolte02}."1138. This is interpreted. as evidence for a dynamical mass segregation in which massive stars sink close to the center of the cluster (PortegiesZwartetal.200: 2).. rather than evidence for the IME to be top- originally.," This is interpreted as evidence for a dynamical mass segregation in which massive stars sink close to the center of the cluster \citep{Portegies-Zwart02}, rather than evidence for the IMF to be top-heavy originally."1139 As à sel[-consistency check. it is also interesting to estimate the X-ray. emission from voung low mass stars in 16 Arches cluster and compare it to the observed spectrum in a way similar to what we did forA.," As a self-consistency check, it is also interesting to estimate the X-ray emission from young low mass stars in the Arches cluster and compare it to the observed spectrum in a way similar to what we did for."1140.. Repeating 1e arguments similar to those presented in ??.. we would estimate the expected YSOs hard N-ray emission. at. ~(12).10% cre/see.," Repeating the arguments similar to those presented in \ref{sec:insitu}, we would estimate the expected YSOs hard X-ray emission at $\sim (1-2) \times 10^{34}$ erg/sec."1141" Yusct-Zadehetal.(2002) find that vw hard. N-rav. luminosity of the Arches cluster is about L~10"" crefsce. (probablydominatedbycollidingfast 2005)."," \cite{Yusef-Zadeh02} find that the hard X-ray luminosity of the Arches cluster is about $L \sim 10^{35}$ erg/sec, \citep[probably dominated by colliding fast stellar winds, e.g.][]{Yusef-Zadeh02,Rockefeller05}."1142. Without a detailed analysis it is hard to sav with a complete certainty that the expected YSO's X-ray emission can be hidden in the observed spectrum. but it does appear quite plausible to us.," Without a detailed analysis it is hard to say with a complete certainty that the expected YSO's X-ray emission can be hidden in the observed spectrum, but it does appear quite plausible to us."1143 For completeness of the discussion. we note that the dvnanücal mass segregation would not have worked in iin contrast to the other two voung star clusters.," For completeness of the discussion, we note that the dynamical mass segregation would not have worked in in contrast to the other two young star clusters."1144 Phe Ie I stars. the most massive in the sstellar svstem. belong to the two well defined stellar rings (Levin&DBeloborodov.2003:Genzeletal;PaumareletaL.2005).. that is two not. relaxed. systems.," The He I stars, the most massive in the stellar system, belong to the two well defined stellar rings \citep{Levin03,Genzel03a,Paumard05}, that is two not relaxed systems."1145 On the theoretical side. while the stars near aare a factor of ~2 older than stars in the Arches cluster. the former have a much higher velocity dispersion than the latter because of the SALBLTE presence.," On the theoretical side, while the stars near are a factor of $\sim 2$ older than stars in the Arches cluster, the former have a much higher velocity dispersion than the latter because of the SMBH presence."1146 The sstar cluster relaxation time is thus much longer than the age of the voung stars there. whereas this is not true for the Arches cluster (PortegiesZwartetal.2002).," The star cluster relaxation time is thus much longer than the age of the young stars there, whereas this is not true for the Arches cluster \citep{Portegies-Zwart02}."1147. Therefore. iis distinct from the other two GC voung star clusters in its lack of low mass YSOs. and it seems obvious that it owes its uniqeness to the SMDIL in the centre of the Galaxy.," Therefore, is distinct from the other two GC young star clusters in its lack of low mass YSOs, and it seems obvious that it owes its uniqeness to the SMBH in the centre of the Galaxy."1148 If top-heavy LAL is a general feature of star formation in AGN disks. then several immediate consequences result.," If top-heavy IMF is a general feature of star formation in AGN disks, then several immediate consequences result."1149 First of all. stellar feedback. is then more important for accretion and the whole AGN phenomenon than thought based on a standard EME.," First of all, stellar feedback is then more important for accretion and the whole AGN phenomenon than thought based on a standard IMF."1150 For example. το]&Beeclnan(1988) showed that with the usual LME. star formation inside the (putative) molecular torus (e.gAntonucci.1993) around AGN would fal to account. for the large random speeds observed. there. as the low mass voung stars give out too little. feedback. ancl the high. mass stars are too rare.," For example, \cite{Krolik88} showed that with the usual IMF, star formation inside the (putative) molecular torus \citep[e.g][]{Antonucci93} around AGN would fail to account for the large random speeds observed there, as the low mass young stars give out too little feedback and the high mass stars are too rare."1151 An IME dominated by massive stars could reverse tha conclusion (seealso.Wada&Norman.2002)., An IMF dominated by massive stars could reverse that conclusion \citep[see also ][]{Wada02}.1152. Next. the metal enrichment of ACN/quasar disks a the surrounding inner galaxy (Collin&Zahn.1999). hy the in situ star formation is then more clicient.," Next, the metal enrichment of AGN/quasar disks and the surrounding inner galaxy \citep{Collin99} by the in situ star formation is then more efficient."1153 Indeed. massive stars live short lives and return metal-rich materia into their surroundines much quicker than low mass stars.," Indeed, massive stars live short lives and return metal-rich material into their surroundings much quicker than low mass stars."1154 This would. be especially important for a rapid enrichmen of young quasar accretion disks., This would be especially important for a rapid enrichment of young quasar accretion disks.1155 In addition. massive stellar remnants. inclucing stellar mass black holes. will be the en result of stellar evolution of the most massive stars (Leger&Woosley. 2002).," In addition, massive stellar remnants, including stellar mass black holes, will be the end result of stellar evolution of the most massive stars \citep{Heger02}."1156. These black holes may migrate through the accretion disk (e.g.Sveretal.1991). and become interesting sources of gravitational radiation if they travel close enough to the SAIBLT (Levin.2003).., These black holes may migrate through the accretion disk \citep[e.g.][]{Clarke91} and become interesting sources of gravitational radiation if they travel close enough to the SMBH \citep{Levin03b}.1157 The EME is a crucial test for any theory of star formation., The IMF is a crucial test for any theory of star formation.1158 Vhe IMF found in nearby sites of active or recent star formation. such as Orton Nebula Cluster. appears to. be broadly consistent with that of the EME of the Ποια stars in the solar neighborhood (Llillenbrand.1997:Meveretal. 2000).," The IMF found in nearby sites of active or recent star formation, such as Orion Nebula Cluster, appears to be broadly consistent with that of the IMF of the field stars in the solar neighborhood \citep{Hillenbrand97,Meyer00}. ."1159. Large pe-collapse gas densities or very high rates of star formation in immediate vicinity of galactic centres or in starburst galaxies lead to theoretical suggestions (e.g. or observational claims of a low-mass cutoll," Large pe-collapse gas densities or very high rates of star formation in immediate vicinity of galactic centres or in starburst galaxies lead to theoretical suggestions \citep[e.g.,][]{Morris93} or observational claims of a low-mass cutoff"1160belt. filling the eap between the Kuiper belt and the outer Oort cloud.,"belt, filling the gap between the Kuiper belt and the outer Oort cloud."1161 Semi-major axes in the inner Oort cloud. are typically between 15000 AU (2)., Semi-major axes in the inner Oort cloud are typically between $-$ 15000 AU \citep{Leto2008}.1162 Ehe steady state Dux from the inner Oort cloud cannot be uniformly. clistributect in perihelion distance. since the planetary. perturbations move comets cllicicnth from gq values less than qi515 AU to either hyperbolic orbits or into orbits that are more tightly bound to the solar svstem (?)..," The steady state flux from the inner Oort cloud cannot be uniformly distributed in perihelion distance, since the planetary perturbations move comets efficiently from $q$ values less than $q_{lc} \simeq 15$ AU to either hyperbolic orbits or into orbits that are more tightly bound to the solar system \citep{Hills81}."1163 In the steady state situation. the new comets come uniformly to. perihelion distances qxqui when a30000 AU. while the d2qr. comets also come from the inner region.," In the steady state situation, the new comets come uniformly to perihelion distances $q \leq q_{lc}$ when $a>30000$ AU, while the $q>q_{lc}$ comets also come from the inner region."1164 Due to this complicated picture. we study. different semi-major axes in separate simulations. ancl evaluate the cllicicney of tidal injection in each simulation.," Due to this complicated picture, we study different semi-major axes in separate simulations, and evaluate the efficiency of tidal injection in each simulation."1165 We chose initial sample conditions for the Oort cloud comets. setting the semi-major axis to be 10000. 20000. 30000. 40000. 50000. ancl GOOOO AU.," We chose initial sample conditions for the Oort cloud comets, setting the semi-major axis to be 10000, 20000, 30000, 40000, 50000, and 60000 AU."1166 We choose the comet's eccentricity (c) randomly. so that the resulting values of g would. be uniformly. distributed. from 35 to the value of the semi-major axis (e).," We choose the comet's eccentricity $e$ ) randomly, so that the resulting values of $q$ would be uniformly distributed from 35 to the value of the semi-major axis $a$ )."1167 All the other parameters. cos(7). Q. d. and the initial eccentric anomaly were all chosen randomly in appropriate intervals.," All the other parameters, $\cos(i)$, $\Omega$, $\omega$, and the initial eccentric anomaly were all chosen randomly in appropriate intervals."1168" The number of comets in. cach simulation is 10"" at cach of the sampled. semi-major axes.", The number of comets in each simulation is $10^6$ at each of the sampled semi-major axes.1169 For the computation of the numbers of comets reaching the inner Solar System. the results from cach semi-major axis are normalised to the adopted number density law.," For the computation of the numbers of comets reaching the inner Solar System, the results from each semi-major axis are normalised to the adopted number density law."1170" ‘To study the elfect of the Galactic potential on cometary motion. we chose two hypothetical solar systems: a ""constant! background. density. where the Sun would be on a pure circular orbit with no vertical motion. and a realistic ‘dynamic Solar orbit."," To study the effect of the Galactic potential on cometary motion, we chose two hypothetical solar systems: a `constant' background density, where the Sun would be on a pure circular orbit with no vertical motion, and a realistic 'dynamic' Solar orbit."1171 In all svsems. we analyse the [ux of Oort cloud comets into the Solar System.," In all systems, we analyse the flux of Oort cloud comets into the Solar System."1172 This means that we consider a comet to have been detected in the inner Solar System when its qd is within 30 AU. and it has a heliocentric radius of less than 1000 AU.," This means that we consider a comet to have been detected in the inner Solar System when its $q$ is within 30 AU, and it has a heliocentric radius of less than 1000 AU."1173 The last criterion 1s important. as the osculating elements of comets can evolve to have qx: 30 AU. far away from the Sun. and evolve to more than 30 AU. without ever entering the inner Solar System.," The last criterion is important, as the osculating elements of comets can evolve to have $q$ $\leq$ 30 AU, far away from the Sun, and evolve to more than 30 AU, without ever entering the inner Solar System."1174 Since the minimum of the osculating q is at the aphelion. the criterion ας 30 AU is approximate.," Since the minimum of the osculating $q$ is at the aphelion, the criterion $q \leq$ 30 AU is approximate."1175 For this reason. we also check if the comet is actually approaching the aphelion. by choosing r«1000 AU.," For this reason, we also check if the comet is actually approaching the aphelion, by choosing $r < 1000$ AU."1176 This requires use of the mean anomaly. which is approximately calculated from the derived time co-ordinate.," This requires use of the mean anomaly, which is approximately calculated from the derived time co-ordinate."1177 Comets which have been detected, Comets which have been detected1178array.,array.1179 All the experiments used the same phase-referencing source (PMN J1755—2232) and the same duty-cycle., All the experiments used the same phase-referencing source (PMN $-$ 2232) and the same duty-cycle.1180" The VLBI calibration procedure was identical as well, and it is described in Paper I. We note that the new EVN observations show a weak extended jet in the calibrator source, but since the radio core accounts for ~90% of the emission, this extension did not have a significant effect on the phase calibration in the first four epochs."," The VLBI calibration procedure was identical as well, and it is described in Paper I. We note that the new EVN observations show a weak extended jet in the calibrator source, but since the radio core accounts for $\sim$ of the emission, this extension did not have a significant effect on the phase calibration in the first four epochs."1181" In the WSRT data, we did self-calibration on PMN J1755—2232 and applied the solutions to the target."," In the WSRT data, we did self-calibration on PMN $-$ 2232 and applied the solutions to the target."1182 The VLBI total intensity images of XTE J1752—223 are shown in Figure 1.., The VLBI total intensity images of XTE $-$ 223 are shown in Figure \ref{fig1}.1183 The associated image parameters and Gaussian model-fitting results are listed in Table 1 and 2.., The associated image parameters and Gaussian model-fitting results are listed in Table \ref{tab1} and \ref{tab2}.1184" There are totally four jet features detected along the position angle of around —51° and marked as A, B, C and D. Components A and B have been reported in Paper I. The EVN image in Figure lee has achieved a sensitivity of lo= bbeam™"", a factor of two better than other images, and revealed another weak ejecta component C with the peak brightness of 0.14 bbeam~'."," There are totally four jet features detected along the position angle of around $-51\degr$ and marked as A, B, C and D. Components A and B have been reported in Paper I. The EVN image in Figure \ref{fig1}e e has achieved a sensitivity of $1\sigma=0.03$ $^{-1}$, a factor of two better than other images, and revealed another weak ejecta component C with the peak brightness of 0.14 $^{-1}$."1185" Another jet feature, component D, is clearly seen on 2010 April 25 in Figure 1ff, but it was initially not detected on 2010 April 29."," Another jet feature, component D, is clearly seen on 2010 April 25 in Figure \ref{fig1}f f, but it was initially not detected on 2010 April 29."1186" However, it is present clearly during part of the last observations, at exactly the same position as four days earlier."," However, it is present clearly during part of the last observations, at exactly the same position as four days earlier."1187" This indicates that the component has no detectable proper motion, and it is likely variable."," This indicates that the component has no detectable proper motion, and it is likely variable."1188 The variation of the image peak brightness during the last two VLBI experiments is shown in Figure 2.., The variation of the image peak brightness during the last two VLBI experiments is shown in Figure \ref{fig2}.1189" To pinpoint the peak time, a variable bin length was used."," To pinpoint the peak time, a variable bin length was used."1190" On 2010 April 25, the image peak brightness of XTE J1752—223 boosted by a factor of five from the non-detection in the first 1-hour bin (8:00 — 9:00 UT) to 4c detection in a bin (10:00 — 10:15 UT)."," On 2010 April 25, the image peak brightness of XTE $-$ 223 boosted by a factor of five from the non-detection in the first 1-hour bin (8:00 – 9:00 UT) to $\sigma$ detection in a bin (10:00 – 10:15 UT)."1191" After that, there was no significant decaying."," After that, there was no significant decaying."1192 A hint on variability was seen again on 2010 April 29., A hint on variability was seen again on 2010 April 29.1193 The source was not detected in the first 2.5 hours., The source was not detected in the first 2.5 hours.1194" While, it was detected at 5o during 11:10 — 12:48 UT as shown in Figure 1gg. The position difference from the previous detections is within the 3c error circle."," While, it was detected at $\sigma$ during 11:10 – 12:48 UT as shown in Figure \ref{fig1}g g. The position difference from the previous detections is within the $\sigma$ error circle."1195 Note that the variation of the uv-coverage does not affect the peak brightness in the case of a compact source., Note that the variation of the $uv$ -coverage does not affect the peak brightness in the case of a compact source.1196 The WSRT image is shown in Figure 3.., The WSRT image is shown in Figure \ref{fig3}.1197" To show possible extended emission, a circular restoring beam with a size 30""was used."," To show possible extended emission, a circular restoring beam with a size was used."1198 The transient XTE J1752—223 is a point source with a total flux density 2.8+0.2 mJy., The transient XTE $-$ 223 is a point source with a total flux density $2.8\pm0.2$ mJy.1199 We also, We also1200Our robust detection rates of the four main lines(NUI.TING...WCO!.. aud )) were high (>90%) for the TOPS. ATLASCAL aud IRAS catalogs. and lower εςGO%) for sources chosen based on the morphology of omission (seo Figure 1)),"Our robust detection rates of the four main lines, and ) were high $>90\%$ ) for the HOPS, ATLASGAL and IRAS catalogs, and lower $<60\%$ ) for sources chosen based on the morphology of emission (see Figure \ref{detections}) )."

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